{"v":1,"topics":[[10,"Ethical and Professional Standards"],[1,"Quantitative Methods"],[2,"Economics"],[3,"Corporate Issuers"],[4,"Financial Statement Analysis"],[5,"Equity Investments"],[6,"Fixed Income"],[7,"Derivatives"],[8,"Alternative Investments"],[9,"Portfolio Management"]],"q":[[10,"How many components does the CFA Institute Code of Ethics have?",["Six","Ten","Seven"],0,"The Code has six components; the Standards of Professional Conduct are grouped into seven parts (I to VII).",0],[10,"Which is a component of the Code of Ethics?",["Disclose all personal holdings publicly","Place the integrity of the investment profession and the interests of clients above their own personal interests","Always outperform the client's benchmark"],1,"Members must put clients and the profession above themselves.",0],[10,"The Standards of Professional Conduct are organised into how many main sections?",["Five","Seven","Six"],1,"I Professionalism, II Integrity of Capital Markets, III Duties to Clients, IV Duties to Employers, V Investment Analysis, Recommendations and Actions, VI Conflicts of Interest, VII Responsibilities as a CFA Member or Candidate.",0],[10,"When local law and the CFA Institute Code and Standards differ, a member should follow:",["Local law in every case","The stricter of the two","The Code and Standards in every case, even if they break the law"],1,"Standard I(A) Knowledge of the Law requires following the more strict of applicable law or the Code and Standards.",0],[10,"A member learns that a colleague is breaking the law in client accounts. Under Standard I(A), the member should first:",["Dissociate from the activity, which may mean reporting to compliance or supervisors","Ignore it if it is not the member's own client","Report it directly to the press"],0,"Dissociation is required; the Standards encourage but do not require reporting to authorities.",0],[10,"Does Standard I(A) require a member to report a legal violation to government authorities?",["No, it is encouraged in some cases but not required","Yes, in every case","Only if the member gains from it"],0,"Members must dissociate; reporting to regulators may be advisable or required by law but not by the Standards.",0],[10,"An analyst accepts business-class flights paid by a company she covers to visit its plant. This mostly raises concerns under:",["Standard I(B) Independence and Objectivity","Standard V(C) Record Retention","Standard III(C) Suitability"],0,"Accepting gifts that could compromise objectivity is the issue; she should pay for her own travel where possible.",0],[10,"Under Standard I(B), modest gifts from clients are generally:",["Allowed only in cash","Acceptable if disclosed to the employer, since clients are rewarding past work","Never allowed"],1,"Client gifts are less likely to compromise objectivity than gifts from third parties, but should be disclosed to the employer.",0],[10,"A portfolio manager presents a competitor's research as his own without credit. This violates:",["Standard VI(B) Priority of Transactions","Standard I(C) Misrepresentation","Standard IV(C) Responsibilities of Supervisors"],1,"Plagiarism is misrepresentation.",0],[10,"Guaranteeing a specific return on an investment that is inherently risky violates:",["Standard VII(B)","Standard II(A) Material Nonpublic Information","Standard I(C) Misrepresentation"],2,"Members must not guarantee returns on investments that carry risk; insured or guaranteed products can be described accurately.",0],[10,"Standard I(D) Misconduct covers:",["Dishonesty, fraud, deceit or any act that reflects badly on professional reputation, integrity or competence","Only illegal acts done at work","Personal political opinions"],0,"Personal behaviour counts if it involves dishonesty or reflects poorly on the profession.",0],[10,"A member is arrested once for peaceful protest unrelated to his job. Under Standard I(D) this is:",["Not a violation, as it does not involve dishonesty or reflect on professional integrity","A violation only if he is a CFA charterholder","Always a violation"],0,"Standard I(D) is not meant to police personal matters that do not reflect on honesty or competence.",0],[10,"Under Standard I(D) Misconduct, which act is most clearly a violation?",["Taking a long holiday","Holding unpopular political views","Repeatedly coming to work drunk and making errors in client accounts"],2,"Behaviour that affects professional competence is misconduct.",0],[10,"Material nonpublic information under Standard II(A) is information that:",["Would likely affect price if disclosed and has not been made public","Is known to more than one person","Comes from a newspaper"],0,"Both conditions, material and nonpublic, must hold.",0],[10,"The mosaic theory allows an analyst to:",["Combine public information and non-material nonpublic information into a conclusion and act on it","Act on any inside information if combined with public data","Trade on information from a company's CFO before results"],0,"Conclusions drawn from public and non-material pieces do not violate Standard II(A).",0],[10,"An analyst overhears a CEO in an elevator say the firm will miss earnings badly next week. She should:",["Sell her shares quickly","Not trade or cause others to trade on it, and encourage public disclosure","Tell her clients first"],1,"The information is material and nonpublic.",0],[10,"A firm-wide control that separates research from investment banking to protect information is called:",["A mosaic","A sinking fund","A firewall (information barrier)"],2,"Firewalls help prevent misuse of material nonpublic information.",0],[10,"Spreading false rumours to push up a stock price violates:",["Standard V(B) Communication","Standard III(B) Fair Dealing","Standard II(B) Market Manipulation"],2,"Information-based manipulation is covered by II(B).",0],[10,"Executing trades to create a false impression of volume in a security violates:",["Standard VI(C) Referral Fees","Standard I(B) Independence","Standard II(B) Market Manipulation"],2,"Transaction-based manipulation distorts prices or volume.",0],[10,"Legitimate tax-loss selling or trading strategies that exploit known market inefficiencies are:",["Not market manipulation if not intended to mislead","Allowed only for institutions","Always manipulation"],0,"Intent to mislead is the key to II(B).",0],[10,"Under Standard III(A) Loyalty, Prudence and Care, in managing a pension plan the client is:",["The fund manager's employer","The plan sponsor's management","The plan participants and beneficiaries"],2,"Duty is owed to the ultimate beneficiaries.",0],[10,"Directing client brokerage to a broker in exchange for research that benefits the client is called:",["Front running","Soft dollars, acceptable if it benefits the client","Churning"],1,"Brokerage is the client's asset and must be used for the client's benefit.",0],[10,"Proxy voting under Standard III(A) means:",["Voting the way the company's management prefers","Voting proxies in the best interests of clients, with a cost-benefit view of when to vote","Never voting proxies"],1,"Proxies have value and are part of loyalty to clients.",0],[10,"Standard III(B) Fair Dealing requires members to:",["Treat all clients exactly the same in every respect","Deal fairly and objectively with all clients when giving recommendations or taking investment action","Give every client the same returns"],1,"Different service levels are fine if disclosed and available to all; no client can be disadvantaged.",0],[10,"A hot IPO is oversubscribed. Under Standard III(B), the manager should:",["Give all shares to the largest client","Keep some for the manager's own account first","Allocate shares pro rata to eligible clients and not favour personal or family accounts"],2,"Fair allocation is required; family accounts that are fee-paying clients are treated like others.",0],[10,"Before taking investment action for a client, Standard III(C) Suitability requires a member to:",["Make a reasonable inquiry into the client's experience, objectives and constraints","Only consider the client's age","Guarantee returns"],0,"An IPS is the usual tool, updated at least annually.",0],[10,"An investment policy statement (IPS) should be reviewed:",["Regularly, at least annually, and when circumstances change","Once, at account opening","Only when the client complains"],0,"Suitability is an ongoing duty.",0],[10,"Standard III(D) Performance Presentation requires:",["Showing only the best-performing accounts","Using GIPS in every case","Fair, accurate and complete performance information"],2,"GIPS compliance is one way to meet it but is not required.",0],[10,"Showing only the performance of a manager's best accounts as representative is:",["Required by GIPS","A violation of Standard III(D)","Allowed if past results are positive"],1,"Cherry-picking misleads clients.",0],[10,"Standard III(E) Preservation of Confidentiality allows disclosure of client information when:",["It concerns illegal activity, disclosure is required by law, or the client permits it","It helps sell other products","A friend asks"],0,"Cooperating with a CFA Institute Professional Conduct Program inquiry is also allowed.",0],[10,"Confidentiality under Standard III(E) applies to:",["Only current clients","Only institutional clients","Current, former and prospective clients"],2,"The duty continues after the relationship ends.",0],[10,"Standard IV(A) Loyalty to employers means a member planning to leave:",["May prepare to compete but must not take client lists or confidential records","Must not speak to clients ever again","Can take client files"],0,"Simple knowledge of client names and memory is allowed; taking records is not.",0],[10,"Whistleblowing that breaks loyalty to the employer can be justified when:",["The member dislikes the manager","The member wants a promotion","It protects clients or the integrity of the market, not for personal gain"],2,"Loyalty does not require following illegal or unethical orders.",0],[10,"Standard IV(B) Additional Compensation Arrangements requires:",["Verbal approval from a colleague","No disclosure","Written consent from the employer before accepting outside compensation that may conflict"],2,"Written consent from all parties involved is required.",0],[10,"Standard IV(C) Responsibilities of Supervisors requires supervisors to:",["Make reasonable efforts to ensure those they supervise comply with laws and the Standards","Ignore violations by top performers","Personally approve every trade"],0,"Adequate compliance procedures are needed; if absent, supervisors should not accept responsibility until fixed.",0],[10,"Standard V(A) Diligence and Reasonable Basis requires:",["Only quantitative models","Diligence, independence and thoroughness, with a reasonable and adequate basis supported by research","A guarantee that the recommendation will work"],1,"Members may rely on third-party research after checking its soundness.",0],[10,"When a group research decision differs from an analyst's own opinion, the analyst:",["Must publicly dissent","Must always remove her name","May let her name stay on the report if she believes the process was reasonable"],2,"She may also ask to remove her name; it is not mandatory.",0],[10,"Standard V(B) Communication with Clients requires members to:",["Use complex language","Communicate only gains","Disclose the investment process, distinguish fact from opinion and explain significant limitations and risks"],2,"Clients must be told about material changes in process.",0],[10,"A report stating that a company's earnings 'will rise 20% next year' violates Standard V(B) because:",["It uses numbers","It is too optimistic","It presents an opinion as a fact"],2,"Forecasts must be clearly labelled as opinions.",0],[10,"Standard V(C) Record Retention: if no regulation sets a period, CFA Institute recommends keeping records for at least:",["One year","Seven years","Three years"],1,"Records belong to the firm, not the individual.",0],[10,"Under Standard V(C), research records that support a recommendation belong to:",["The analyst personally","The client","The employer"],2,"An analyst who changes jobs must recreate supporting records from public sources.",0],[10,"Standard VI(A) Avoid or Disclose Conflicts requires:",["Full and fair disclosure of matters that could impair independence and objectivity","Disclosure only when asked","Avoiding all business relationships"],0,"Disclosures must be prominent, in plain language and effective.",0],[10,"Owning shares of a company you recommend is:",["Always prohibited","A conflict that must be disclosed","Irrelevant"],1,"Disclosure lets clients judge the recommendation.",0],[10,"Standard VI(B) Priority of Transactions sets the order of priority as:",["Member, clients, employer","Employer, clients, member","Clients, then employer, then the member's own account"],2,"Clients always come first.",0],[10,"Front running a client's large order with a personal trade violates:",["Standard VII(A)","Standard VI(B) Priority of Transactions","Standard I(C) Misrepresentation"],1,"Personal trades must not disadvantage clients.",0],[10,"Family accounts that pay normal fees should be treated:",["As lower priority than all others","Like any other client account","As the member's own account always"],1,"Fee-paying family accounts are clients; members with beneficial ownership need extra care.",0],[10,"Standard VI(C) Referral Fees requires disclosure of referral compensation to:",["Only the employer","The employer, clients and prospective clients","No one"],1,"Disclosure should be made before the client enters the arrangement.",0],[10,"Standard VII(A) Conduct as Participants in CFA Institute Programs is violated by:",["Discussing the curriculum in general terms","Disclosing specific exam questions or topics tested after the exam","Saying the exam was difficult"],1,"Exam confidentiality must be protected.",0],[10,"Which statement about the CFA designation is acceptable under Standard VII(B)?",["I am a CFA","Passing three exams in a row on the first attempt (if true)","As a Level II CFA, I outperform the market"],1,"CFA is an adjective, never a noun; no partial designation such as CFA Level II exists.",0],[10,"A candidate who passed Level I may describe herself as:",["A CFA Level I holder","A Level II candidate in the CFA Program (if registered for Level II)","Partially CFA certified"],1,"Candidate status requires being registered for the next exam.",0],[10,"Using the CFA designation to imply superior investment results violates:",["Standard II(A)","Standard III(D)","Standard VII(B)"],2,"The designation shows completion of the program, not superior performance.",0],[10,"A charterholder who has not paid annual dues and filed the Professional Conduct Statement:",["Becomes a Level III candidate","Cannot use the CFA designation until reinstated","May keep using it"],1,"Membership must be current to use the marks.",0],[10,"The Professional Conduct Program (PCP) of CFA Institute investigates:",["Possible violations of the Code and Standards by members and candidates","Exam grading errors only","Market manipulation by any investor"],0,"Sanctions can include public censure, suspension or revocation.",0],[10,"Which sanction is NOT one that CFA Institute can impose?",["Imprisonment","Suspension of the right to use the designation","Revocation of membership"],0,"CFA Institute is not a court; legal penalties come from regulators.",0],[10,"GIPS stands for:",["General Investment Policy Statement","Global Investment Performance Standards","Global Index Pricing System"],1,"GIPS are voluntary standards for presenting investment performance.",0],[10,"Who can claim compliance with GIPS?",["Any mutual fund","Investment firms (and asset owners), not individuals or single products","Individual portfolio managers"],1,"Compliance is firm-wide.",0],[10,"Under GIPS, a composite is:",["An index","A single client portfolio","An aggregation of portfolios managed to a similar investment mandate or strategy"],2,"Composites stop firms from showing only their best accounts.",0],[10,"Verification under GIPS is:",["Done by the firm's own staff","Mandatory for all firms","Optional but recommended, done by an independent third party"],2,"Verification tests firm-wide policies, not a specific composite's returns.",0],[10,"Can a firm claim partial compliance with GIPS?",["Yes, for some composites","No, compliance must be with all applicable requirements","Yes, if it complies with most rules"],1,"There is no partial compliance.",0],[10,"A member who uses a third party's research without checking its basis risks violating:",["Standard VII(A)","Standard V(A) Diligence and Reasonable Basis","Standard II(B)"],1,"Reasonable checks of the third party's methods are required.",0],[10,"A manager trades in client accounts excessively to generate commissions. This is called:",["Soft dollars","Mosaic theory","Churning, a violation of loyalty to clients"],2,"It puts the manager's interests above the client's.",0],[10,"A member forgets to update a client's IPS after the client retires and keeps an aggressive allocation. This mainly violates:",["Standard VII(B)","Standard IV(B)","Standard III(C) Suitability"],2,"Changes in circumstances require updating the IPS.",0],[10,"An analyst changes a rating after a company threatens to stop giving her access. This violates:",["Standard III(E)","Standard V(C)","Standard I(B) Independence and Objectivity"],2,"Pressure from issuers must not influence research.",0],[10,"A member sends a rating change by email to a few large clients before posting it to all clients. This violates:",["Standard I(D)","Standard III(B) Fair Dealing","Standard VI(C)"],1,"Material changes must reach all clients fairly.",0],[10,"When a member cannot meet a duty because of a conflict between the Code and the employer's policy, the member should:",["Resign immediately in every case","Follow the employer always","Follow the stricter requirement and, if needed, dissociate"],2,"The Code is the minimum standard for members.",0],[10,"Applying mosaic theory, an analyst who finds a factory is busy by counting trucks outside it:",["Has used inside information","Has done legitimate research and may act on the conclusion","Must report the company"],1,"Public observation is not nonpublic information.",0],[10,"Under Standard III(A), when managing a trust, the duty is owed to:",["The firm's shareholders","The trustee personally","The beneficiaries of the trust"],2,"Identify who the actual client is.",0],[10,"Which practice best meets Standard III(B) Fair Dealing when a new recommendation is issued?",["Disseminate it to all clients at the same time where practicable","Delay it for small clients","Phone favourite clients first"],0,"Firms should have procedures for fair dissemination.",0],[10,"A member who learns of a client's past fraud from their files must keep it confidential unless:",["It helps win new business","A colleague is curious","The information concerns illegal activity that the law requires to be reported"],2,"Confidentiality is not a shield for ongoing illegal activity.",0],[10,"Under Standard I(A), a member who knowingly assists someone else's violation of the law is:",["Not responsible if acting on instructions","In violation of the Standards","Excused if not paid"],1,"Knowing participation or assistance is prohibited.",0],[10,"Disclosing to clients that a recommended stock is also held in the firm's proprietary account relates to:",["Standard VI(A) Disclosure of Conflicts","Standard II(B)","Standard V(C)"],0,"The firm's holdings may bias recommendations.",0],[10,"A member doing independent consulting in the evening for a client of his employer, without employer consent, violates:",["Standard IV(A) Loyalty, since it competes with the employer without consent","Standard III(D)","Standard VII(A)"],0,"Written consent is needed before competing work.",0],[10,"A research report that omits the main risks of a recommended product violates:",["Standard I(D)","Standard V(B) Communication with Clients","Standard VI(C)"],1,"Significant risks and limitations must be disclosed.",0],[10,"Which use of the designation is correct?",["Priya Shah, a CFA","Priya Shah, CFA (expected)","Priya Shah, CFA"],2,"CFA follows the name as an adjective; there is no expected or partial designation.",0],[10,"A supervisor who discovers a violation should:",["Respond promptly, investigate and take steps to prevent recurrence","Wait until year-end review","Ignore minor issues"],0,"Simply reporting up the chain is not always enough.",0],[10,"Under GIPS, returns for a composite must include:",["All actual, fee-paying, discretionary portfolios managed to that strategy","Only portfolios over a minimum size chosen after the fact","Only the best portfolio"],0,"Non-discretionary portfolios are excluded.",0],[10,"A member gives a prospective client a performance history that includes simulated results without saying so. This violates:",["Standard III(E)","Standard III(D) Performance Presentation","Standard IV(C)"],1,"Simulated or hypothetical results must be clearly labelled.",0],[10,"A member has a material conflict that cannot be avoided. Under Standard VI(A) she should:",["Disclose it fully and fairly","Mention it only if asked","Hide it"],0,"Disclosure is the minimum requirement.",0],[10,"Which is consistent with Standard VII(A)?",["Expressing an opinion on the CFA Program in general terms","Sharing a list of exam formula questions with friends","Bringing notes into the exam room"],0,"Opinions are fine; breaching exam integrity is not.",0],[10,"If a client asks a member to hide a trade from the client's spouse who is co-owner of the account, the member should:",["Hide it as asked","Delete the trade record","Not mislead the co-owner and follow legal account terms"],2,"Duties are owed to all account owners.",0],[10,"Personal trading policies such as blackout periods help firms comply with:",["Standard VI(B) Priority of Transactions","Standard I(C)","Standard V(C)"],0,"They ensure clients trade before employees.",0],[10,"An analyst publishes a 'buy' while privately selling the stock. Most relevant standards are:",["Only VII(B)","Only III(D)","Misconduct and conflicts of interest (I(D) and VI(A)/VI(B))"],2,"Acting against one's own published view without disclosure is dishonest.",0],[10,"Standard III(A) requires a member to exercise:",["Personal preference","Reasonable care and prudent judgement, acting for the benefit of clients","Employer's interest first"],1,"The prudent person standard applies.",0],[10,"Relying on a credit rating without understanding its basis may violate:",["Standard V(A) Diligence and Reasonable Basis","Standard II(B)","Standard III(E)"],0,"Members should understand third-party inputs they rely on.",0],[10,"A firm's code of ethics is most effective when:",["Supported by senior management, training and enforcement","Kept confidential from staff","Written only by lawyers"],0,"Tone at the top matters.",0],[10,"Under Standard II(A), material information is information that:",["A reasonable investor would want to know before making an investment decision","Only the CEO knows","Has already moved the price"],0,"Materiality depends on likely price effect and reliability of the source.",0],[10,"An analyst receives an unsolicited tip of uncertain reliability from an unknown source. Generally:",["Its materiality is lower because reliability is doubtful, but care is still needed","It can be traded on immediately","It is always material"],0,"Reliability of the source affects materiality.",0],[10,"A firm restricts trading in a company when its bankers work on a deal for it. This list is called:",["A restricted (or watch) list","A soft dollar list","A composite list"],0,"It supports firewalls under Standard II(A).",0],[10,"Which is a requirement of Standard III(D)?",["Present results for only one year","Present only gross returns","Make reasonable efforts to ensure performance is fair, accurate and complete"],2,"Members can comply by presenting accurate, complete data with disclosures.",0],[10,"Ethics is the largest topic area of the Level I exam. Its 2026 weight is:",["15% to 20%","30% to 35%","5% to 8%"],0,"Weights are given as ranges by CFA Institute.",0],[1,"The time-weighted rate of return is preferred for evaluating a portfolio manager because it:",["Removes the effect of the timing and size of client cash flows","Includes the effect of client deposits","Is always higher than the money-weighted return"],0,"Managers do not control external cash flows, so TWR isolates their skill.",0],[1,"The money-weighted rate of return is equivalent to:",["The internal rate of return of the portfolio's cash flows","The geometric mean of sub-period returns","The arithmetic mean return"],0,"It is affected by the timing and size of cash flows.",0],[1,"Compared with the arithmetic mean of the same returns, the geometric mean is:",["Always greater","Less than or equal to it","Always equal"],1,"They are equal only when all returns are identical.",0],[1,"The harmonic mean is most appropriate for:",["Averaging the cost per share when investing equal amounts periodically (cost averaging)","Averaging returns over many years","Measuring dispersion"],0,"Harmonic mean ≤ geometric mean ≤ arithmetic mean.",0],[1,"A distribution with a long tail to the right is:",["Symmetrical","Negatively skewed","Positively skewed, with mean greater than median"],2,"In positive skew the mean is pulled to the right of the median and mode.",0],[1,"A distribution with excess kurtosis greater than zero is called:",["Platykurtic","Leptokurtic, with fatter tails than the normal distribution","Mesokurtic"],1,"Financial returns often show fat tails.",0],[1,"The coefficient of variation measures:",["Risk per unit of mean return","The correlation between two assets","Return per unit of risk"],0,"CV = standard deviation divided by the mean.",0],[1,"If two events are independent, the probability that both occur is:",["Always zero","The sum of their probabilities","The product of their individual probabilities"],2,"P(A and B) = P(A) × P(B) for independent events.",0],[1,"Bayes' formula is used to:",["Calculate a portfolio's standard deviation","Find the median","Update the probability of an event given new information"],2,"It revises prior probabilities into posterior probabilities.",0],[1,"Two mutually exclusive events:",["Are always independent","Always occur together","Cannot occur together"],2,"If one occurs, the other cannot, so their joint probability is zero.",0],[1,"Covariance between two assets that tend to move together is:",["Always zero","Negative","Positive"],2,"Correlation standardises covariance to between −1 and +1.",0],[1,"Adding an asset with a correlation below +1 to a portfolio:",["Can reduce portfolio standard deviation through diversification","Has no effect on risk","Always increases risk"],0,"Diversification benefits exist whenever correlation is less than perfect.",0],[1,"Monte Carlo simulation is mainly used to:",["Generate many random scenarios to model the distribution of outcomes","Test historical data only","Find exact closed-form prices"],0,"It is useful when analytic solutions are hard.",0],[1,"Historical simulation differs from Monte Carlo simulation because it:",["Assumes a normal distribution for all inputs","Uses no data","Draws scenarios from actual past data"],2,"It cannot generate events that did not happen in the sample.",0],[1,"Bootstrapping in resampling means:",["Repeatedly drawing samples with replacement from the observed sample","Assuming a normal distribution","Drawing without replacement from a population once"],0,"It estimates sampling distributions without strong assumptions.",0],[1,"The central limit theorem states that, for a large sample, the distribution of the sample mean is:",["Approximately normal, regardless of the population distribution","Always skewed","Exactly the same as the population"],0,"Sample size of 30 or more is the common rule of thumb.",0],[1,"The standard error of the sample mean:",["Rises as sample size increases","Falls as sample size increases","Is unaffected by sample size"],1,"It equals the standard deviation divided by the square root of n.",0],[1,"Which is a property of a good estimator?",["Always being larger than the true value","Using the smallest possible sample","Unbiasedness, efficiency and consistency"],2,"These three properties describe desirable estimators.",0],[1,"A Type I error is:",["Using the wrong sample size","Failing to reject a false null hypothesis","Rejecting a true null hypothesis"],2,"The significance level is the probability of a Type I error.",0],[1,"A Type II error is:",["Rejecting a true null hypothesis","Choosing a two-tailed test","Failing to reject a false null hypothesis"],2,"Power of a test = 1 − probability of a Type II error.",0],[1,"If a test's p-value is less than the significance level, the analyst should:",["Reject the null hypothesis","Fail to reject the null hypothesis","Increase the significance level"],0,"The p-value is the smallest level at which the null can be rejected.",0],[1,"To test whether the variances of two normal populations are equal, the appropriate test is:",["A paired t-test","The z-test for means","The F-test"],2,"The F-statistic is the ratio of two sample variances.",0],[1,"To test the variance of a single normal population, the appropriate test uses the:",["F-distribution","Standard normal distribution","Chi-square distribution"],2,"The chi-square test compares a sample variance with a hypothesised value.",0],[1,"Nonparametric tests are most appropriate when:",["Sample sizes are very large and normal","Data are ranks or the distribution assumptions of parametric tests do not hold","The population is known to be normal"],1,"The Spearman rank correlation is an example.",0],[1,"In simple linear regression, the coefficient of determination (R²) measures:",["The slope of the line","The share of the variation in the dependent variable explained by the independent variable","The standard error of the intercept"],1,"R² ranges from 0 to 1.",0],[1,"Which is an assumption of simple linear regression?",["The independent variable is random noise","The residuals are homoskedastic (constant variance)","Residuals are perfectly correlated"],1,"Other assumptions include linearity, independence and normality of residuals.",0],[1,"Heteroskedasticity in a regression means:",["The variance of residuals is not constant across observations","The sample is too small","The relationship is non-linear"],0,"It makes standard errors unreliable.",0],[1,"In a regression ANOVA table, the F-statistic tests whether:",["The residuals are normal","The intercept is zero","The slope coefficient is significantly different from zero"],2,"In simple regression, the F-test equals the square of the slope's t-test.",0],[1,"The standard error of estimate in regression measures:",["The number of observations","The typical distance of actual values from the regression line","The slope of the line"],1,"Lower values mean a better fit.",0],[1,"A log-lin regression model is useful when:",["There is no time element","The relationship is perfectly linear","The dependent variable grows at a constant rate over time"],2,"Taking logs turns exponential growth into a straight line.",0],[1,"Supervised machine learning differs from unsupervised learning because it:",["Uses labelled data with known outcomes","Has no target variable","Cannot make predictions"],0,"Clustering is a typical unsupervised task.",0],[1,"Overfitting in machine learning means the model:",["Uses too little data","Fits the training data too closely and performs poorly on new data","Is too simple"],1,"Cross-validation helps detect it.",0],[1,"The 'volume, velocity and variety' characteristics describe:",["Normal distributions","Big data","Annuities"],1,"Veracity is often added as a fourth V.",0],[1,"An annuity due differs from an ordinary annuity because its payments occur:",["At the end of each period","At the beginning of each period","Only once"],1,"An annuity due is worth more, all else equal.",0],[1,"A perpetuity is:",["A single lump sum","A series of equal payments that continues forever","An annuity of 10 years"],1,"Its present value is payment divided by the discount rate.",0],[1,"The effective annual rate rises when:",["Compounding frequency decreases","The stated rate falls","Compounding frequency increases, for the same stated annual rate"],2,"Continuous compounding gives the highest EAR.",0],[1,"Lognormal distributions are used for asset prices because:",["They allow negative prices","They are always symmetrical","They are bounded below by zero and right-skewed"],2,"If returns are normal, prices are lognormal.",0],[1,"Continuously compounded returns are additive:",["Over time","Never","Across assets in a portfolio"],0,"Multi-period log returns sum, which simplifies analysis.",0],[1,"The Sharpe ratio uses which measure of risk?",["Beta","Downside deviation only","Standard deviation of portfolio returns"],2,"It is excess return divided by standard deviation.",0],[1,"Shortfall risk is the probability that:",["A portfolio's return falls below a minimum acceptable level","A bond defaults","Returns are positive"],0,"Roy's safety-first ratio helps choose the portfolio that minimises it.",0],[1,"Roy's safety-first criterion selects the portfolio with:",["The highest standard deviation","The lowest return","The highest ratio of (mean return minus threshold) to standard deviation"],2,"A higher ratio means lower shortfall probability.",0],[1,"A confidence interval becomes wider when:",["The standard deviation falls","The confidence level increases","Sample size increases"],1,"More confidence requires a wider range.",0],[1,"The t-distribution, compared with the standard normal, has:",["No variance","Fatter tails, approaching normal as degrees of freedom rise","Thinner tails"],1,"It is used when the population variance is unknown and samples are small.",0],[1,"A paired comparisons test is used when:",["Samples are dependent, such as before and after on the same subjects","Samples are independent","Testing a variance"],0,"The test is on the mean of the differences.",0],[1,"Correlation does not imply causation because:",["Causation is always negative","Correlation is always zero","A third variable or chance can create a relationship"],2,"Spurious correlation is a common trap.",0],[1,"Outliers can distort which measure most?",["The mode","The median","The arithmetic mean"],2,"Trimmed or winsorised means reduce their effect.",0],[1,"A target downside deviation measures:",["Upside surprises only","Variability of returns below a chosen target","All variability"],1,"It is used in the Sortino ratio.",0],[1,"Which data type is a time series?",["A single price quote","Returns of 100 stocks in one month","Monthly returns of one stock over five years"],2,"Cross-sectional data are many units at one point in time.",0],[1,"In a binomial model, the number of up moves follows:",["A binomial distribution","A normal distribution exactly","A uniform distribution"],0,"Each trial has two outcomes with constant probability.",0],[1,"Topic weight of Quantitative Methods in the 2026 Level I exam is:",["11% to 14%","15% to 20%","6% to 9%"],2,"CFA Institute publishes weights as ranges.",0],[2,"In perfect competition, a firm in the long run earns:",["Large economic profits","Zero economic profit","Losses forever"],1,"Free entry and exit push economic profit to zero.",0],[2,"A firm under perfect competition is a:",["Monopolist","Price maker","Price taker"],2,"It faces a horizontal demand curve at the market price.",0],[2,"A monopolist maximises profit where:",["Average revenue equals average cost","Price equals marginal cost","Marginal revenue equals marginal cost"],2,"This is true for all market structures.",0],[2,"Monopolistic competition is characterised by:",["Many firms with differentiated products and low barriers to entry","A few firms with high interdependence","One firm"],0,"Advertising and branding are important.",0],[2,"Oligopoly is characterised by:",["A few firms whose decisions are interdependent","Many small firms","Identical products and no barriers"],0,"Models include kinked demand, Cournot and Stackelberg.",0],[2,"The Herfindahl-Hirschman Index measures:",["Price elasticity","Inflation","Market concentration, as the sum of squared market shares"],2,"A higher HHI means a more concentrated market.",0],[2,"A shutdown point in the short run is where price falls below:",["Average variable cost","Marginal revenue","Average total cost"],0,"Below AVC, the firm loses less by stopping production.",0],[2,"Economies of scale occur when:",["Average cost rises with output","Long-run average cost falls as output rises","Fixed costs disappear"],1,"Diseconomies of scale are the opposite.",0],[2,"Elastic demand means that a price rise causes:",["Revenue to rise","No change in quantity","A proportionately larger fall in quantity demanded, lowering total revenue"],2,"Elasticity greater than 1 in absolute value.",0],[2,"Which is a leading economic indicator?",["Unemployment rate","Average duration of unemployment","Average weekly hours in manufacturing"],2,"Leading indicators turn before the economy does.",0],[2,"The phase of the business cycle with rising output, falling unemployment and firms adding capacity is:",["Trough","Contraction","Expansion"],2,"Inflation pressure often builds late in expansion.",0],[2,"Cost-push inflation comes from:",["Falling money supply","Excess aggregate demand","Rising input costs such as wages or commodities"],2,"Demand-pull inflation is the other main type.",0],[2,"Stagflation is a combination of:",["High inflation and weak or falling growth","Low inflation and strong growth","Deflation and boom"],0,"Supply shocks can cause it.",0],[2,"Expansionary fiscal policy includes:",["Higher policy interest rates","Higher government spending or lower taxes","Selling government bonds by the central bank"],1,"Fiscal policy is run by the government; monetary policy by the central bank.",0],[2,"Automatic stabilisers are:",["Tariffs","Taxes and transfers that change with the economy without new legislation","Central bank rate cuts"],1,"Progressive taxes and unemployment benefits are examples.",0],[2,"Crowding out refers to:",["Too many firms in a market","Imports replacing exports","Government borrowing raising interest rates and reducing private investment"],2,"It weakens the effect of fiscal stimulus.",0],[2,"A central bank's open market purchase of government bonds:",["Reduces money supply","Raises tax revenue","Increases bank reserves and tends to lower interest rates"],2,"It is an expansionary monetary tool.",0],[2,"The neutral policy rate is the rate that:",["Is always zero","Neither stimulates nor slows the economy","Equals the inflation rate"],1,"It is roughly the real trend growth rate plus inflation target.",0],[2,"A liquidity trap occurs when:",["Monetary policy loses effect because people hold cash even at very low rates","Banks run out of cash","Inflation is very high"],0,"Quantitative easing has been used in such conditions.",0],[2,"Inflation targeting by a central bank requires:",["Fixed exchange rates","Independence, credibility and transparency","Government control of the bank"],1,"Credible targets anchor expectations.",0],[2,"Comparative advantage means a country should produce goods where it has:",["The lowest opportunity cost","The most workers","The lowest absolute cost"],0,"Trade based on comparative advantage benefits both sides.",0],[2,"A tariff on imports typically:",["Increases consumer surplus","Raises domestic prices and reduces imports, with a deadweight loss","Lowers domestic prices"],1,"Domestic producers and the government gain; consumers lose more.",0],[2,"A free trade area differs from a customs union because it:",["Has no common external tariff","Uses a common currency","Allows free movement of labour"],0,"A customs union adds a common external tariff.",0],[2,"The current account of the balance of payments records:",["Trade in goods and services, primary income and transfers","Purchases of foreign assets","Central bank reserves only"],0,"The capital and financial accounts record asset flows.",0],[2,"A current account deficit must be financed by:",["A financial account surplus (net capital inflows)","A current account surplus","Higher exports"],0,"The accounts balance overall.",0],[2,"In an exchange rate quote USD/INR = 83, the base currency is:",["USD","Neither","INR"],0,"The quote shows how many rupees one dollar buys.",0],[2,"If a currency appreciates, a country's exports tend to become:",["More expensive for foreign buyers","Unaffected","Cheaper for foreign buyers"],0,"Appreciation hurts export competitiveness.",0],[2,"Covered interest rate parity implies that a currency with a higher interest rate trades at:",["The same forward rate as spot","A forward premium","A forward discount"],2,"Forward rates offset interest differentials to remove arbitrage.",0],[2,"The Marshall-Lerner condition says a depreciation improves the trade balance if:",["The sum of export and import demand elasticities exceeds 1","Elasticities are zero","Imports are perfectly inelastic"],0,"Otherwise the trade balance can worsen.",0],[2,"The J-curve effect describes:",["A fall in GDP","A trade balance that first worsens after depreciation, then improves","A smooth rise in exports"],1,"Contracts set at old prices delay the volume response.",0],[2,"A currency board arrangement means:",["Domestic currency is fully backed by foreign reserves at a fixed rate","A free float","No central bank exists"],0,"It limits independent monetary policy.",0],[2,"Geopolitical risk can affect investments through:",["Nothing measurable","Changes in trade, sanctions, conflict and policy uncertainty","Only interest rates"],1,"Analysts assess likelihood, speed and size of impact.",0],[2,"Globalization in geopolitical frameworks refers to:",["Tariff wars only","Isolationism","Greater cross-border cooperation in trade, capital and information"],2,"Its opposite is nationalism or autarky.",0],[2,"A cartel is most likely to break down because:",["Each member has an incentive to cheat by producing more","Members always agree","Prices are too low"],0,"This is a classic prisoner's dilemma.",0],[2,"In the kinked demand curve model of oligopoly, prices tend to be:",["Sticky","Set by the government","Very volatile"],0,"Rivals match price cuts but not price rises.",0],[2,"In a Stackelberg model, the firm that moves first:",["Usually gains a larger market share","Has no advantage","Always loses"],0,"First-mover advantage shapes output.",0],[2,"A Nash equilibrium is reached when:",["All players cooperate","Prices equal zero","No player can improve its outcome by changing strategy alone"],2,"It is a key idea in game theory.",0],[2,"Quantitative easing refers to:",["Raising reserve requirements","Large-scale central bank purchases of securities to lower long-term rates","Fiscal tax cuts"],1,"It is used when policy rates are near zero.",0],[2,"Fiscal policy implementation is slowed by:",["Instant data","Independent central banks","Recognition, action and impact lags"],2,"Political processes can delay budgets.",0],[2,"Real GDP differs from nominal GDP because it:",["Excludes government spending","Includes imports twice","Is adjusted for changes in prices"],2,"It measures output volume.",0],[2,"The GDP deflator measures:",["The price level of all goods and services in GDP","Only wages","Only consumer prices"],0,"Nominal GDP divided by real GDP times 100.",0],[2,"A decline in a country's policy rate relative to others tends to:",["Weaken its currency, other things equal","Have no effect","Strengthen its currency"],0,"Lower returns reduce demand for the currency.",0],[2,"Capital restrictions such as controls on inflows are used to:",["Increase imports","Raise tariffs","Limit volatile short-term flows and protect stability"],2,"They can reduce efficiency of capital allocation.",0],[2,"Which is a tool of monetary policy?",["Government spending","Income tax rates","Reserve requirements"],2,"Open market operations and the policy rate are others.",0],[2,"In the short run, an increase in aggregate demand tends to:",["Lower both","Raise output and the price level","Change only the price level"],1,"In the long run, output returns to potential.",0],[2,"Economic profit differs from accounting profit because it:",["Ignores revenue","Subtracts opportunity costs, including a normal return on capital","Adds depreciation back"],1,"Zero economic profit still covers a normal return.",0],[2,"Price discrimination by a firm requires:",["Identical buyers","Perfect competition","Market power, separable customer groups and no resale"],2,"It can increase output compared with a single monopoly price.",0],[2,"Natural monopolies often face regulation because:",["They have no fixed costs","They are too small","Their large economies of scale make one producer efficient, but pricing needs control"],2,"Utilities are common examples.",0],[2,"Which is a lagging indicator?",["New orders for capital goods","Stock prices","Average prime rate charged by banks"],2,"Lagging indicators turn after the economy.",0],[2,"Credit cycles tend to:",["Move opposite to asset prices","Have no link with the economy","Amplify business cycles as lending loosens in booms and tightens in busts"],2,"Credit conditions affect investment and housing.",0],[2,"A cross rate is:",["An exchange rate between two currencies derived through a third currency","An interest rate","A forward rate"],0,"For example, EUR/INR from EUR/USD and USD/INR.",0],[2,"Forward points are added to the spot rate when the base currency:",["Has higher interest rates","Trades at a forward discount","Trades at a forward premium"],2,"Points are subtracted for a discount.",0],[2,"A fixed exchange rate regime requires the central bank to:",["Intervene in currency markets to hold the rate","Never hold reserves","Let the rate float"],0,"Defending a peg can drain reserves.",0],[2,"Supply-side shocks such as an oil price spike shift:",["Short-run aggregate supply to the left","Aggregate demand right","Long-run supply right"],0,"They raise prices and cut output.",0],[2,"Topic weight of Economics in the 2026 Level I exam is:",["15% to 20%","6% to 9%","11% to 14%"],1,"Same range as Quantitative Methods.",0],[3,"A key feature of a corporation compared with a sole proprietorship is:",["Unlimited personal liability","No taxes","Limited liability for owners and separate legal identity"],2,"Owners risk only their investment.",0],[3,"In a general partnership, partners have:",["Unlimited liability for the firm's debts","Limited liability always","No liability"],0,"Limited partnerships give limited partners limited liability.",0],[3,"Debtholders and equity holders differ because debtholders:",["Vote on all decisions","Have a fixed claim and prefer lower risk","Benefit fully from upside"],1,"Equity holders have residual claims and benefit more from risk.",0],[3,"A principal-agent conflict arises when:",["Managers act in their own interest rather than shareholders'","Suppliers are unpaid","Shareholders own debt"],0,"Incentive design and monitoring reduce it.",0],[3,"An independent board director is one who:",["Has no material relationship with the company beyond board service","Is the largest supplier","Is the CEO"],0,"Independence supports objective oversight.",0],[3,"An audit committee mainly oversees:",["Product design","Financial reporting, internal controls and the external audit","Marketing plans"],1,"It should consist of independent directors.",0],[3,"A staggered (classified) board:",["Increases shareholder power","Makes hostile takeovers harder by electing only part of the board each year","Requires annual election of all directors"],1,"It is an anti-takeover device.",0],[3,"Cumulative voting helps:",["Minority shareholders elect at least some directors","Management keep control","Bondholders vote"],0,"Votes can be concentrated on one candidate.",0],[3,"ESG integration in investment analysis means:",["Ignoring risk","Considering environmental, social and governance factors alongside financial analysis","Excluding all oil companies"],1,"It aims to improve risk-adjusted returns.",0],[3,"Dual-class share structures can:",["Remove all governance risk","Give all shareholders equal votes","Give founders control beyond their economic ownership"],2,"Investors may face weaker influence.",0],[3,"Working capital management aims to:",["Balance liquidity and profitability in current assets and liabilities","Delay all payments forever","Maximise inventory"],0,"Too much working capital ties up cash.",0],[3,"The cash conversion cycle equals:",["Revenue divided by assets","Days of payables plus days of receivables","Days of inventory plus days of receivables minus days of payables"],2,"A shorter cycle means faster cash recovery.",0],[3,"A primary source of liquidity for a company is:",["Filing for bankruptcy","Selling a major division","Cash balances and short-term funds such as bank lines"],2,"Secondary sources involve changes in operations.",0],[3,"Factoring receivables means:",["Issuing shares","Selling receivables to a third party for immediate cash","Paying suppliers early"],1,"It speeds cash collection at a cost.",0],[3,"Taking a trade discount by paying suppliers early is attractive when:",["The implied annual cost of forgoing it exceeds the company's borrowing cost","The company has no cash","Interest rates are very high"],0,"Forgoing early-payment discounts is often expensive.",0],[3,"The NPV rule says to accept a project if:",["IRR is below the cost of capital","NPV is greater than zero","Payback exceeds five years"],1,"Positive NPV adds value.",0],[3,"When NPV and IRR give conflicting rankings for mutually exclusive projects, prefer:",["Payback period","NPV","IRR"],1,"NPV assumes reinvestment at the cost of capital, which is more realistic.",0],[3,"A limitation of the IRR method is that:",["Projects with non-conventional cash flows can have multiple IRRs","It cannot be computed","It ignores the time value of money"],0,"Sign changes in cash flows create this problem.",0],[3,"Sunk costs in capital budgeting should be:",["Ignored, because they cannot be recovered","Treated as revenue","Added to project costs"],0,"Only incremental cash flows matter.",0],[3,"Cannibalisation in capital budgeting refers to:",["Selling assets","A new project reducing sales of existing products","Buying competitors"],1,"It is a negative externality to include.",0],[3,"Opportunity costs should be:",["Ignored","Included in project analysis","Treated as sunk costs"],1,"Using an existing asset has a value forgone.",0],[3,"Return on invested capital (ROIC) compared with the cost of capital shows:",["The share price","The dividend yield","Whether a company is creating value"],2,"ROIC above cost of capital creates value.",0],[3,"A real option in capital investment is:",["A bond covenant","A traded stock option","The right to change a project later, such as expand, delay or abandon"],2,"Real options add value to projects.",0],[3,"Under Modigliani-Miller with no taxes, firm value is:",["Maximised with all debt","Independent of capital structure","Maximised with all equity"],1,"Proposition I without taxes.",0],[3,"Under MM with no taxes, the cost of equity:",["Falls with leverage","Stays constant","Rises linearly with leverage"],2,"Proposition II: higher debt raises equity risk.",0],[3,"With corporate taxes and no other costs, MM implies firm value:",["Rises with debt because of the interest tax shield","Falls with debt","Is unaffected"],0,"Taxes make debt valuable.",0],[3,"The static trade-off theory says optimal capital structure balances:",["Dividends against buybacks","Revenue against costs","The tax benefit of debt against costs of financial distress"],2,"Beyond a point, distress costs outweigh tax benefits.",0],[3,"The pecking order theory suggests firms prefer financing in which order?",["New equity, then debt, then internal funds","Internal funds, then debt, then new equity","Debt, then equity, then internal funds"],1,"It is based on information asymmetry.",0],[3,"Issuing new equity is often read by investors as a signal that:",["Debt is too cheap","Managers think shares are overvalued","The firm is undervalued"],1,"This is the signalling argument in pecking order theory.",0],[3,"Agency costs of equity are reduced by:",["Paying no dividends","Removing the board","Using more debt, which disciplines managers"],2,"Debt limits free cash flow that managers could waste.",0],[3,"A company's target capital structure is usually stated in terms of:",["Number of shares","Market value weights of debt and equity","Book value of assets"],1,"WACC uses target weights.",0],[3,"Credit rating agencies and lenders focus on leverage because:",["Higher leverage increases default risk","It raises liquidity","It lowers interest costs"],0,"Coverage and leverage ratios drive ratings.",0],[3,"A business model describes:",["The organisation chart","Only the product price","How a company creates value, delivers it and earns money"],2,"It covers customers, offering, channels and pricing.",0],[3,"A subscription pricing model generates:",["One-time sales only","Recurring revenue over time","No revenue"],1,"It improves revenue visibility.",0],[3,"Network effects mean a product becomes:",["Less valuable with more users","More valuable as more users join","Cheaper to produce"],1,"Platforms such as marketplaces benefit from them.",0],[3,"Shareholder activism involves:",["Shareholders selling quietly","Creditors enforcing covenants","Shareholders pushing management for changes, such as through proxy fights"],2,"Activists seek to unlock value.",0],[3,"Proxy voting allows shareholders to:",["Sell shares","Receive dividends","Vote without attending the meeting in person"],2,"It is how most institutional votes are cast.",0],[3,"Debt covenants protect lenders by:",["Restricting borrower actions, such as additional borrowing or dividend payouts","Raising interest rates","Lowering credit ratings"],0,"Breaches can trigger default.",0],[3,"The weighted average cost of capital (WACC) is:",["The firm's overall required return, weighting costs of debt, preferred and equity by target weights","The risk-free rate","The cost of equity only"],0,"After-tax cost of debt is used.",0],[3,"Why is the cost of debt taken after tax in WACC?",["Debt has no risk","Interest is tax-deductible","Equity is taxed"],1,"The tax shield lowers the effective cost.",0],[3,"Free cash flow to the firm represents cash available to:",["Only shareholders","All providers of capital after operating expenses, taxes and investment","Only lenders"],1,"FCFE is cash to equity holders after debt flows.",0],[3,"Operating leverage is higher when:",["A larger share of costs is fixed","Most costs are variable","Sales are falling"],0,"High operating leverage magnifies changes in operating income.",0],[3,"Financial leverage increases:",["Revenue","Gross margin","The variability of net income and return on equity"],2,"Fixed interest costs magnify earnings swings.",0],[3,"Stakeholder theory of governance holds that a company should consider:",["The interests of all stakeholders, not only shareholders","Only shareholders","Only creditors"],0,"Shareholder theory focuses on shareholders.",0],[3,"Topic weight of Corporate Issuers in the 2026 Level I exam is:",["15% to 20%","6% to 9%","11% to 14%"],1,"It was earlier called Corporate Finance.",0],[4,"Which body sets IFRS?",["The SEC","The International Accounting Standards Board (IASB)","The FASB"],1,"US GAAP is set by the FASB.",0],[4,"The auditor's opinion that financial statements are fairly presented is called:",["An unqualified (unmodified) opinion","An adverse opinion","A qualified opinion"],0,"Adverse means they are not fairly presented.",0],[4,"Under IFRS 15 and ASC 606, the first step of revenue recognition is to:",["Recognise revenue when cash is received","Identify the contract with a customer","Allocate the price"],1,"Five steps: contract, performance obligations, price, allocation, recognition.",0],[4,"Revenue is recognised when:",["Cash is collected","The entity satisfies a performance obligation by transferring control","The contract is signed"],1,"Cash timing is separate from recognition.",0],[4,"Basic EPS is calculated as:",["Dividends divided by shares","Net income divided by total assets","Net income minus preferred dividends, divided by weighted average common shares"],2,"Diluted EPS includes potential shares.",0],[4,"A convertible security is antidilutive if converting it would:",["Increase diluted EPS","Decrease diluted EPS","Not change revenue"],0,"Antidilutive securities are excluded from diluted EPS.",0],[4,"The treasury stock method is used to account for the dilution from:",["Preferred dividends","Convertible bonds","Options and warrants"],2,"It assumes proceeds are used to buy back shares.",0],[4,"Other comprehensive income includes items such as:",["Cost of goods sold","Sales revenue","Foreign currency translation adjustments"],2,"OCI bypasses the income statement.",0],[4,"Under IFRS, interest paid can be classified in the cash flow statement as:",["Only investing","Operating or financing","Only operating"],1,"US GAAP requires operating.",0],[4,"Under US GAAP, dividends paid are classified as:",["Financing cash flows","Operating cash flows","Investing cash flows"],0,"IFRS allows operating or financing.",0],[4,"In the indirect method, depreciation is:",["Shown as investing outflow","Added back to net income to get cash flow from operations","Subtracted from net income"],1,"It is a non-cash expense.",0],[4,"An increase in accounts receivable, in the indirect method, is:",["Added to net income","Subtracted from net income","Ignored"],1,"Sales were booked but cash not yet received.",0],[4,"Purchase of equipment appears in:",["Operating cash flows","Financing cash flows","Investing cash flows"],2,"Capital expenditure is investing.",0],[4,"Free cash flow to the firm can be derived from:",["Revenue minus taxes","CFO plus after-tax interest minus fixed capital investment","Net income only"],1,"FCFF is cash available to all capital providers.",0],[4,"The DuPont analysis breaks ROE into:",["Dividend yield and growth","Gross margin and tax rate only","Net profit margin, asset turnover and financial leverage"],2,"The extended version adds tax and interest burdens.",0],[4,"A higher current ratio generally indicates:",["Higher profitability","Lower liquidity","Greater short-term liquidity"],2,"Too high can mean idle assets.",0],[4,"The quick ratio excludes which assets from the current ratio?",["Receivables","Inventory and prepaid expenses","Cash"],1,"It focuses on the most liquid assets.",0],[4,"Inventory turnover measures:",["Total inventory value","How many times inventory is sold and replaced in a period","Gross profit"],1,"Higher turnover can mean efficiency or low stock.",0],[4,"The interest coverage ratio indicates:",["How easily operating earnings cover interest expense","Debt as a share of equity","Liquidity"],0,"It is a solvency measure.",0],[4,"In a period of rising prices and stable inventory, LIFO compared with FIFO gives:",["Lower COGS","Higher ending inventory","Higher cost of goods sold and lower reported profit"],2,"LIFO matches the latest higher costs with revenue.",0],[4,"LIFO is permitted under:",["US GAAP but not IFRS","IFRS but not US GAAP","Both"],0,"IFRS prohibits LIFO.",0],[4,"Under IFRS, inventory is measured at:",["The lower of cost and net realisable value","Historical cost always","Market value always"],0,"Write-downs can be reversed under IFRS.",0],[4,"Reversal of inventory write-downs is:",["Allowed under both","Allowed under neither","Allowed under IFRS, not under US GAAP for most inventory"],2,"US GAAP prohibits reversal for most cases.",0],[4,"In rising prices, FIFO ending inventory compared with LIFO is:",["The same","Higher and closer to current cost","Lower"],1,"FIFO leaves the newest costs in inventory.",0],[4,"A LIFO liquidation occurs when:",["Units sold exceed units purchased, so older low costs flow into COGS","Inventory rises","The firm switches to FIFO"],0,"It can temporarily inflate profits.",0],[4,"Capitalising a cost rather than expensing it results in the first year in:",["Lower net income","Higher net income and higher assets","Lower assets"],1,"The cost is spread through depreciation.",0],[4,"Capitalising costs moves the related cash outflow into:",["Operating activities","Financing activities","Investing activities, raising CFO"],2,"Expensed costs reduce CFO instead.",0],[4,"Under IFRS, research costs are:",["Never disclosed","Expensed, while development costs may be capitalised if criteria are met","Always capitalised"],1,"US GAAP expenses both in most cases.",0],[4,"The revaluation model for property, plant and equipment is allowed under:",["IFRS, not US GAAP","US GAAP, not IFRS","Both"],0,"Upward revaluations generally go to equity through OCI.",0],[4,"Accelerated depreciation compared with straight-line gives in early years:",["Higher depreciation expense and lower net income","Lower expense","Higher net income"],0,"Total depreciation over the life is the same.",0],[4,"Impairment of a long-lived asset under IFRS is recognised when:",["Fair value rises","The asset is fully depreciated","Carrying amount exceeds the recoverable amount"],2,"Recoverable amount is the higher of fair value less costs to sell and value in use.",0],[4,"Reversal of impairment losses on long-lived assets held for use is:",["Allowed under neither","Allowed under IFRS, not US GAAP","Allowed under both"],1,"Goodwill impairment cannot be reversed under either.",0],[4,"Goodwill is:",["Expensed immediately","Amortised over 40 years under IFRS","Not amortised but tested for impairment"],2,"It arises from acquisitions.",0],[4,"A deferred tax liability arises when:",["Tax rates fall","A company has losses","Taxable income is lower than pre-tax accounting income due to a temporary difference"],2,"Accelerated tax depreciation is a typical cause.",0],[4,"A deferred tax asset arises when:",["Equity rises","Tax payable is lower","Taxes payable exceed tax expense because of a temporary difference"],2,"Warranty expenses deductible later are an example.",0],[4,"Permanent differences between tax and book income:",["Do not create deferred taxes; they change the effective tax rate","Reverse over time","Always create deferred tax liabilities"],0,"Examples include tax-exempt income.",0],[4,"A valuation allowance against a deferred tax asset is used under US GAAP when:",["Tax rates rise","It is more likely than not that part of the asset will not be realised","Profits are certain"],1,"It reduces the asset's carrying value.",0],[4,"A bond issued at a discount has interest expense that is:",["Equal to the coupon","Lower than the coupon","Higher than the coupon payment"],2,"The discount is amortised into interest expense.",0],[4,"Under the effective interest method, interest expense equals:",["Face value times the coupon","Zero","Carrying amount times the market rate at issue"],2,"IFRS requires this method.",0],[4,"Under IFRS 16, a lessee recognises for most leases:",["A right-of-use asset and a lease liability","Only rent expense","Nothing on the balance sheet"],0,"Short-term and low-value leases are exceptions.",0],[4,"Under US GAAP, lessees classify leases as:",["Off-balance sheet only","Finance or operating, both recognised on the balance sheet","Only operating"],1,"The expense pattern differs between the two.",0],[4,"A defined benefit pension plan's net liability equals:",["Contributions paid","Plan assets only","The present value of the obligation minus the fair value of plan assets"],2,"Funded status shows over- or under-funding.",0],[4,"Under a defined contribution plan, the employer's obligation is:",["To cover investment losses","Limited to agreed contributions","To guarantee a pension level"],1,"Employees bear investment risk.",0],[4,"Aggressive accounting choices that boost current earnings include:",["Shortening asset lives","Extending useful lives of assets to lower depreciation","Taking larger provisions"],1,"These choices lower earnings quality.",0],[4,"High-quality earnings are:",["Sustainable and backed by cash flow","Always growing fast","Volatile and one-off"],0,"Accruals far above cash flow can be a warning sign.",0],[4,"A warning sign of poor earnings quality is:",["Net income consistently exceeding operating cash flow","Stable margins","Low accruals"],0,"Large accruals can indicate aggressive accounting.",0],[4,"Channel stuffing refers to:",["Shipping excess goods to distributors to inflate current revenue","Reducing inventory","Paying suppliers early"],0,"It often reverses as returns later.",0],[4,"Non-GAAP measures such as adjusted EBITDA require analysts to:",["Accept them without question","Ignore them always","Check the reconciliation to the nearest GAAP measure and question exclusions"],2,"Recurring costs labelled one-off are a red flag.",0],[4,"Common-size income statement analysis expresses each line as:",["A percentage of total assets","Absolute rupees","A percentage of revenue"],2,"It makes companies of different sizes comparable.",0],[4,"Days sales outstanding rising sharply may signal:",["Faster collections","Weaker collections or aggressive revenue recognition","Lower sales"],1,"Compare with sales growth and peers.",0],[4,"The statement of changes in equity shows:",["Movements in each equity component, such as net income, dividends and share issues","Cash flows","Revenue by segment"],0,"It reconciles opening and closing equity.",0],[4,"Financial statement notes are important because they:",["Are optional","Repeat the income statement","Explain accounting policies, estimates and details not shown on the face of statements"],2,"Analysts often find key risks in notes.",0],[4,"MD&A (management commentary) provides:",["Tax returns","Management's discussion of results, trends and risks","Audited numbers only"],1,"It is not audited in the same way as statements.",0],[4,"A company that changes its accounting policy must usually:",["Apply it only to future periods always","Apply it retrospectively and restate prior periods","Not disclose it"],1,"Changes in estimates are applied prospectively.",0],[4,"A change in an accounting estimate, such as useful life, is applied:",["Never","Retrospectively","Prospectively"],2,"Prior periods are not restated.",0],[4,"Intangible assets with indefinite lives are:",["Amortised over 5 years","Expensed immediately","Not amortised but tested for impairment"],2,"Goodwill is the main example.",0],[4,"Financial assets measured at amortised cost under IFRS 9 are those held to:",["Collect contractual cash flows of principal and interest","Trade actively","Speculate on prices"],0,"Business model and cash flow tests decide classification.",0],[4,"Treasury shares (buybacks) are shown as:",["An expense","A reduction of equity","An asset"],1,"They are not assets of the company.",0],[4,"Minority (non-controlling) interest appears in consolidated statements because:",["It is a liability to lenders","The parent consolidates 100% of a subsidiary it controls but does not fully own","It is a type of debt"],1,"The non-owned share is shown separately in equity.",0],[4,"Off-balance-sheet financing can make a company look:",["Less leveraged than it really is","More leveraged","Less profitable"],0,"Analysts adjust for such items.",0],[4,"Return on assets measures:",["Debt relative to assets","Net income relative to total assets","Revenue relative to equity"],1,"It shows how efficiently assets earn profit.",0],[4,"A high debt-to-equity ratio indicates:",["High liquidity","Low leverage","More reliance on borrowed funds and higher financial risk"],2,"Compare with industry norms.",0],[4,"Activity ratios measure:",["Market valuation","Profit margins","How efficiently a company uses its assets"],2,"Turnover ratios are activity ratios.",0],[4,"Under IFRS, an investment property may be measured using:",["The cost model or the fair value model","Only market value through OCI","Only the cost model"],0,"Fair value changes go through profit or loss.",0],[4,"Capitalised interest during construction of an asset:",["Is recorded in equity","Is added to the asset's cost and later depreciated","Is expensed immediately"],1,"It lowers current interest expense.",0],[4,"The direct method of presenting operating cash flows shows:",["Net income adjusted for non-cash items","Only investing flows","Major classes of cash receipts and payments"],2,"Standards encourage it; most firms use the indirect method.",0],[4,"Sale-and-leaseback transactions should be examined because they can:",["Reduce revenue","Remove all leases","Generate cash and gains while keeping use of the asset"],2,"Analysts check the economic substance.",0],[4,"Segment reporting helps analysts by:",["Showing revenue and profit by business or geography","Hiding weak divisions","Replacing consolidated accounts"],0,"It reveals where growth and risk come from.",0],[4,"Which ratio is a measure of solvency?",["Inventory turnover","Debt-to-assets","Current ratio"],1,"Solvency is long-term ability to meet obligations.",0],[4,"Topic weight of Financial Statement Analysis in the 2026 Level I exam is:",["11% to 14%","6% to 9%","15% to 20%"],0,"It is one of the larger topics.",0],[5,"A long position in an asset benefits when:",["The asset's price rises","The price falls","Volatility falls"],0,"A short position benefits when the price falls.",0],[5,"Buying shares on margin means:",["Selling borrowed shares","Borrowing part of the purchase price from a broker","Paying in full"],1,"Leverage magnifies gains and losses.",0],[5,"A margin call occurs when:",["The stock rises","Dividends are paid","Equity in the margin account falls below the maintenance margin"],2,"The investor must add funds or have positions closed.",0],[5,"A limit order to buy is executed:",["Only at the limit price or lower","At any price","Only at the closing price"],0,"It controls price but may not be filled.",0],[5,"A stop-loss sell order becomes a market order when:",["The market closes","The price rises to the stop","The price falls to the stop price"],2,"Execution price may be worse than the stop in fast markets.",0],[5,"A quote-driven market is one where:",["Dealers post bid and ask prices and trade from inventory","Prices are set by brokers privately","Orders are matched by rules without dealers"],0,"Order-driven markets match buyers and sellers by rules.",0],[5,"A well-functioning financial system has:",["No liquidity","Operational, informational and allocational efficiency","No regulation"],1,"Prices reflect information and capital goes to its best uses.",0],[5,"A price-weighted index gives more weight to:",["Larger companies by market cap","All stocks equally","Higher-priced stocks"],2,"The Dow Jones Industrial Average is an example.",0],[5,"A market-capitalisation-weighted index tends to be dominated by:",["The smallest companies","Equal weights","The largest companies"],2,"Nifty 50 uses free-float market cap.",0],[5,"An equal-weighted index requires:",["Price-based weights","No rebalancing","Frequent rebalancing to keep weights equal"],2,"It tilts toward smaller stocks relative to cap weighting.",0],[5,"Index rebalancing differs from reconstitution because rebalancing:",["Changes the constituents","Changes the base date","Adjusts weights, while reconstitution changes the constituents"],2,"Both affect index funds' trading.",0],[5,"A total return index includes:",["Only dividends","Price changes and reinvested dividends","Only price changes"],1,"Price return indices exclude income.",0],[5,"In a weak-form efficient market:",["No information is priced","Inside information is priced","Past prices and volume cannot be used to earn abnormal returns"],2,"Technical analysis would not work.",0],[5,"In a semi-strong form efficient market:",["Only past prices are reflected","Private information is reflected","Prices reflect all public information"],2,"Fundamental analysis of public data would not earn abnormal returns.",0],[5,"Strong-form efficiency means prices reflect:",["Only historical data","Only earnings","All public and private information"],2,"Evidence generally does not support strong-form efficiency.",0],[5,"A market anomaly is:",["A normal return","A stock split","A pattern of returns that appears to contradict efficiency"],2,"Examples include the January effect and momentum.",0],[5,"Behavioural finance explains some anomalies through:",["Perfectly rational investors","Investor biases such as overconfidence and loss aversion","Government rules"],1,"Biases can cause mispricing.",0],[5,"Preference shares typically:",["Have more voting rights than common shares","Never pay dividends","Have priority over common shares for dividends and in liquidation"],2,"Cumulative preference shares accrue unpaid dividends.",0],[5,"Cumulative preferred shares require that:",["Dividends grow with profits","Unpaid dividends be paid before common dividends","Dividends are optional forever"],1,"Arrears must be cleared first.",0],[5,"Depository receipts allow investors to:",["Avoid all currency risk","Hold foreign shares through securities traded locally","Own bonds"],1,"ADRs are an example.",0],[5,"Private equity securities differ from public equity because they:",["Are not traded on exchanges and are less liquid","Have no risk","Are more liquid"],0,"Valuation is less transparent.",0],[5,"Return on equity is a key equity metric because it shows:",["The share price","The dividend amount","How efficiently the company earns profit on shareholders' capital"],2,"ROE drives sustainable growth.",0],[5,"The book value of equity differs from market value because:",["Book value is always higher","They are always equal","Market value reflects investors' expectations of future cash flows"],2,"Price-to-book compares the two.",0],[5,"Porter's five forces include:",["GDP growth","Interest rates and inflation","Threat of new entrants and bargaining power of buyers"],2,"The others are suppliers, substitutes and rivalry.",0],[5,"High barriers to entry in an industry usually mean:",["More competition","Lower margins","Greater pricing power for existing firms"],2,"Capital needs and regulation can create barriers.",0],[5,"In the industry life cycle, the shakeout phase features:",["Slowing growth, intense competition and weaker firms exiting","Stable mature profits","Rapid early growth"],0,"It follows the growth phase.",0],[5,"A cyclical company's earnings are:",["Highly sensitive to the business cycle","Unaffected by GDP","Stable in all conditions"],0,"Autos and capital goods are examples.",0],[5,"A defensive company typically:",["Has very volatile earnings","Benefits mainly in booms","Has stable earnings across the cycle"],2,"Utilities and consumer staples are examples.",0],[5,"Company analysis usually starts with:",["Dividends alone","Only the share price chart","Understanding the business model, competitive position and industry"],2,"Forecasts build on this understanding.",0],[5,"Forecasting revenue using market share times market size is a:",["Bottom-up approach","Top-down approach","Technical approach"],1,"Bottom-up builds from units or segments.",0],[5,"The Gordon growth model is suitable for companies that:",["Pay dividends growing at a stable rate below the required return","Grow faster than the required return forever","Have no dividends"],0,"Value = next dividend ÷ (required return − growth).",0],[5,"In the Gordon growth model, if the growth rate rises (all else equal), the value:",["Is unchanged","Rises","Falls"],1,"Higher growth increases future dividends.",0],[5,"A multistage dividend discount model is used when:",["Dividends are constant forever","The firm never pays dividends","A company has a high-growth period followed by stable growth"],2,"Value is the sum of discounted stages.",0],[5,"Free cash flow to equity valuation is preferred when:",["Dividends equal FCFE exactly","The firm has no cash flow","Dividends do not reflect the company's capacity to pay"],2,"FCFE is cash available to shareholders.",0],[5,"The justified P/E from the Gordon model rises when:",["The required return rises","Growth falls","The payout ratio or growth rises, or the required return falls"],2,"Justified forward P/E = payout ÷ (r − g).",0],[5,"Enterprise value is:",["Book value of assets","Market value of equity plus debt minus cash","Equity value only"],1,"EV/EBITDA compares firms with different capital structures.",0],[5,"Price multiples based on comparables assume:",["Similar companies should trade at similar multiples","All companies are unique","Prices are irrelevant"],0,"The law of one price underlies it.",0],[5,"Asset-based valuation is most suitable for:",["Companies with mostly tangible, marketable assets, such as holding companies or firms in liquidation","Service firms with few assets","Fast-growing technology firms"],0,"Intangibles make asset values harder to measure.",0],[5,"If a stock's estimated intrinsic value is above its market price, the stock is:",["Overvalued","Fairly valued","Undervalued"],2,"Analysts would consider buying.",0],[5,"Preferred stock with a fixed dividend and no maturity is valued as:",["A perpetuity: dividend divided by required return","A growing annuity","Zero"],0,"Same formula as a perpetuity.",0],[5,"Short selling involves:",["Borrowing shares, selling them and buying back later","Buying shares on margin","Holding shares for the long term"],0,"The short seller pays any dividends to the lender.",0],[5,"Which order type guarantees execution but not price?",["Stop-limit order","Market order","Limit order"],1,"It executes at the best available price.",0],[5,"Primary market transactions include:",["Dividend payments","Trades on the stock exchange between investors","IPOs and seasoned offerings"],2,"The secondary market trades existing securities.",0],[5,"A rights offering gives existing shareholders:",["Free shares","The right to buy new shares, usually at a discount","Bonds"],1,"It avoids dilution for those who take up rights.",0],[5,"Market value of equity can be below book value when:",["The company has no debt","The company is very profitable","Investors expect returns below the cost of equity"],2,"P/B below 1 signals weak expected returns or asset concerns.",0],[5,"Investment value of equity depends on:",["The company's accounting policies only","The investor's own required return and expected cash flows","Only the market price"],1,"Different investors can value the same share differently.",0],[5,"A sector rotation strategy shifts investments:",["Randomly","Only between bonds","Between sectors based on the expected business cycle phase"],2,"Cyclicals tend to do well early in recoveries.",0],[5,"Economic moat refers to:",["A legal barrier against bondholders","A tax rule","A durable competitive advantage that protects profits"],2,"Brands, network effects and cost advantages create moats.",0],[5,"The momentum anomaly refers to:",["Small stocks outperforming in January","Stocks that performed well recently continuing to do well in the short term","Low P/E stocks always outperforming"],1,"It challenges weak-form efficiency.",0],[5,"The value effect suggests that:",["Growth stocks always outperform","Prices never change","Stocks with low price multiples have historically outperformed"],2,"Some see it as compensation for risk.",0],[5,"Index-based investing is popular because:",["It beats every active fund","It guarantees returns","It offers broad diversification at low cost"],2,"It is a passive strategy.",0],[5,"Float-adjusted market cap weighting excludes:",["Shares not available for trading, such as promoter or government holdings","All foreign holdings","Shares held by retail investors"],0,"It better reflects investable shares.",0],[5,"A fundamental-weighted index weights stocks by:",["Measures such as earnings, dividends or sales","Price only","Market cap only"],0,"It reduces overweighting of expensive stocks.",0],[5,"The pre-money and post-money valuation concept is most associated with:",["Index funds","Venture capital investments","Government bonds"],1,"Post-money = pre-money plus new investment.",0],[5,"An industry with many substitutes faces:",["No competition","Limited pricing power","Strong pricing power"],1,"Substitutes cap prices.",0],[5,"Return on equity can be boosted by higher leverage because:",["Revenue rises automatically","Less equity supports the same assets","Debt has no cost"],1,"DuPont shows the leverage component.",0],[5,"Book value per share is calculated as:",["Market price times shares","Dividends divided by shares","Common shareholders' equity divided by shares outstanding"],2,"It is an accounting measure.",0],[5,"Investors require a higher return on common equity than on the same firm's debt because:",["Equity is riskier, with a residual claim","Equity is safer","Debt has no claim"],0,"Debt is paid first.",0],[5,"A company's sustainable growth rate equals:",["Dividend yield plus ROE","Retention ratio times ROE","Payout ratio times ROA"],1,"It assumes constant capital structure.",0],[5,"Topic weight of Equity Investments in the 2026 Level I exam is:",["11% to 14%","5% to 8%","15% to 20%"],0,"Same range as Fixed Income and FSA.",0],[6,"The legal contract that sets out a bond's terms is the:",["Term sheet only","Prospectus summary","Indenture (trust deed)"],2,"It includes covenants and the rights of bondholders.",0],[6,"An affirmative covenant requires the issuer to:",["Not sell assets","Do something, such as maintain insurance or file reports","Not take on more debt"],1,"Negative covenants restrict actions.",0],[6,"A negative covenant is a promise to:",["Pay coupons on time","Maintain books","Not do certain things, such as pledge assets already pledged"],2,"It protects bondholders from actions that raise risk.",0],[6,"A sinking fund provision requires the issuer to:",["Extend maturity","Retire a portion of the bond issue periodically","Pay no coupons"],1,"It reduces credit risk but adds reinvestment risk for investors.",0],[6,"A fully amortising bond:",["Pays no interest","Repays principal over its life, with nothing left at maturity","Repays all principal at maturity"],1,"Mortgages are typical examples.",0],[6,"A bullet bond:",["Repays all principal at maturity","Repays principal in instalments","Has no maturity"],0,"Most government bonds are bullets.",0],[6,"A callable bond is worth less than an otherwise identical straight bond because:",["It has a higher coupon always","The issuer holds a valuable option to redeem early","It cannot be traded"],1,"Callable bond = straight bond − call option.",0],[6,"A putable bond is worth more than an identical straight bond because:",["The issuer can redeem early","It has no credit risk","The investor holds an option to sell it back"],2,"Putable bond = straight bond + put option.",0],[6,"A convertible bond allows the holder to:",["Exchange the bond for a set number of the issuer's shares","Extend maturity","Sell it back at par"],0,"Investors accept a lower coupon for the option.",0],[6,"Bond prices and yields are:",["Positively related","Inversely related","Unrelated"],1,"When yields rise, prices fall.",0],[6,"A bond trades at a premium when its coupon rate is:",["Equal to its yield","Above its yield to maturity","Below its yield"],1,"Par bonds have coupon equal to yield.",0],[6,"As a premium bond approaches maturity, its price:",["Stays constant","Moves away from par","Moves down towards par"],2,"This is the pull to par.",0],[6,"Spot rates are:",["Coupon rates","Forward rates only","Yields on zero-coupon bonds for each maturity"],2,"Each cash flow can be discounted at its own spot rate.",0],[6,"Forward rates are:",["Interest rates for a future period implied by today's spot rates","Rates on callable bonds","Current coupon rates"],0,"They link the spot curve across maturities.",0],[6,"The par curve shows:",["Zero-coupon yields only","Credit spreads","Coupon rates at which bonds of each maturity would trade at par"],2,"It is derived from spot rates.",0],[6,"The flat (clean) price of a bond excludes:",["Accrued interest","Principal","Coupons"],0,"Full price = flat price + accrued interest.",0],[6,"Matrix pricing is used for bonds that:",["Have no coupons","Trade rarely, by using yields of comparable bonds","Trade every second"],1,"It estimates prices for illiquid bonds.",0],[6,"Current yield measures:",["Annual coupon divided by the bond's price","Price change","Total return to maturity"],0,"It ignores capital gains and reinvestment.",0],[6,"Yield to maturity assumes that:",["Coupons are spent","The bond is sold next year","The bond is held to maturity, no default occurs and coupons are reinvested at the YTM"],2,"Realised returns differ if these do not hold.",0],[6,"Yield to worst for a callable bond is:",["The lowest of yield to maturity and yields to each call date","The highest yield","The coupon rate"],0,"It is conservative for investors.",0],[6,"The G-spread is the yield spread over:",["The swap rate","An actual or interpolated government bond yield","Zero"],1,"The I-spread uses swap rates.",0],[6,"The Z-spread is:",["A constant spread added to each spot rate so that discounted cash flows equal the price","A spread over the swap rate only","The coupon minus the yield"],0,"It uses the full spot curve.",0],[6,"Option-adjusted spread (OAS) for a callable bond equals:",["Z-spread plus the option cost","Z-spread minus the option cost","The coupon"],1,"OAS removes the effect of embedded options.",0],[6,"Macaulay duration is:",["The coupon rate","The weighted average time to receive a bond's cash flows","The bond's maturity"],1,"Weights are present values of cash flows.",0],[6,"Modified duration measures:",["The approximate percentage price change for a 1% change in yield","Time to maturity","Credit quality"],0,"Modified = Macaulay ÷ (1 + yield per period).",0],[6,"Effective duration is used for bonds with embedded options because:",["They have no cash flows","Their cash flows change when yields change","Modified duration is always zero"],1,"It uses prices from shifts in the benchmark curve.",0],[6,"Holding other features constant, a bond has higher duration when it has:",["A shorter maturity","A longer maturity and a lower coupon","A higher coupon"],1,"Lower yields also raise duration.",0],[6,"A zero-coupon bond's Macaulay duration equals:",["Its time to maturity","Half its maturity","Zero"],0,"There is only one cash flow.",0],[6,"Convexity improves on duration by:",["Ignoring large yield changes","Accounting for the curvature of the price-yield relationship","Removing credit risk"],1,"Positive convexity benefits the bondholder.",0],[6,"Callable bonds can show negative convexity when:",["The bond is putable","Yields rise","Yields fall and the call price caps price gains"],2,"Price gains are limited near the call price.",0],[6,"Money duration (or PVBP) measures:",["The bond's coupon","The currency change in a bond's value for a change in yield","Days to maturity"],1,"PVBP is for a one basis point change.",0],[6,"If an investor's horizon equals the bond's Macaulay duration:",["There is no interest rate risk at all in any case","Reinvestment risk dominates","Price risk and reinvestment risk roughly offset"],2,"This is the basis of immunisation.",0],[6,"Expected loss from credit risk equals:",["Probability of default times loss given default","Coupon times maturity","Duration times convexity"],0,"LGD = exposure × (1 − recovery rate).",0],[6,"The '4 Cs' of credit analysis include:",["Coupon, cash, call and convexity","Currency, country, capital and cost","Capacity, collateral, covenants and character"],2,"They organise credit assessment.",0],[6,"Investment-grade ratings start at:",["A+","BB","BBB- (S&P/Fitch) or Baa3 (Moody's)"],2,"Lower ratings are high yield.",0],[6,"Notching refers to:",["Splitting a bond","Rating a specific issue above or below the issuer rating based on seniority","Changing coupons"],1,"Subordinated debt is usually notched down.",0],[6,"In the priority of claims, senior secured debt ranks:",["Ahead of senior unsecured and subordinated debt","Behind equity","Behind subordinated debt"],0,"Recovery rates are higher for senior secured debt.",0],[6,"Sovereign credit analysis considers:",["Only population size","Only the stock market","Institutional, economic, external, fiscal and monetary factors"],2,"Ability and willingness to pay both matter.",0],[6,"Securitisation benefits issuers by:",["Removing all risk","Increasing their liabilities","Converting illiquid assets into tradable securities and freeing capital"],2,"A special purpose entity holds the assets.",0],[6,"A special purpose entity (SPE) in securitisation is used to:",["Isolate the assets from the originator's bankruptcy risk","Avoid paying investors","Increase the originator's leverage"],0,"Bankruptcy remoteness is key.",0],[6,"In a tranched securitisation, the senior tranche:",["Pays the highest yield","Is paid first and has the lowest credit risk","Absorbs the first losses"],1,"Subordinated tranches absorb losses first.",0],[6,"Prepayment risk in mortgage-backed securities includes:",["Contraction risk when rates fall and extension risk when rates rise","Default risk only","Currency risk"],0,"Borrowers refinance when rates fall.",0],[6,"A collateralised mortgage obligation (CMO) redistributes:",["Prepayment risk among different tranches","Credit risk to the government","Interest to equity"],0,"Sequential-pay and PAC tranches are examples.",0],[6,"Covered bonds differ from ABS because:",["The issuer's balance sheet remains liable and the cover pool is dynamic","They have no collateral","They are always unsecured"],0,"Investors have dual recourse.",0],[6,"Credit enhancement through overcollateralisation means:",["There is no collateral","Coupons are higher","Collateral value exceeds the securities issued"],2,"It provides a cushion for losses.",0],[6,"Repurchase agreements (repos) are:",["Short-term collateralised borrowing","Long-term unsecured bonds","Equity derivatives"],0,"The repo rate is lower with higher-quality collateral.",0],[6,"Eurobonds are:",["Domestic bonds","Bonds issued only in euros","Bonds issued outside the jurisdiction of the currency they are denominated in"],2,"They are often bearer bonds.",0],[6,"A floating-rate note's price is relatively stable because:",["It has no coupon","Its coupon resets with market rates","It is always callable"],1,"Duration is roughly the time to the next reset.",0],[6,"Inflation-linked bonds protect investors from:",["Default","Loss of purchasing power","Liquidity risk"],1,"Principal or coupons are indexed to inflation.",0],[6,"Commercial paper is:",["Short-term unsecured debt issued by companies","Equity","Long-term secured debt"],0,"Issuers usually keep backup lines of credit.",0],[6,"The liquidity preference theory explains an upward-sloping yield curve by:",["Supply only","Investors requiring a premium to hold longer maturities","Expected rate cuts"],1,"It adds a term premium to expectations.",0],[6,"Pure expectations theory states that forward rates equal:",["Coupon rates","Current spot rates","Expected future spot rates"],2,"It ignores risk premiums.",0],[6,"Higher yield volatility generally:",["Removes credit risk","Lowers duration of all bonds","Increases the value of convexity"],2,"Convexity is more valuable when yields move a lot.",0],[6,"Credit spreads typically widen when:",["The economy is booming","Inflation falls","The economy weakens and default fears rise"],2,"Lower-rated bonds widen more.",0],[6,"Liquidity risk in bonds is reflected in:",["Lower coupons","Wider bid-ask spreads","Higher ratings"],1,"Less liquid bonds require higher yields.",0],[6,"Bond equivalent yield (semi-annual basis) is used to:",["Value equities","Compare yields on bonds with different payment frequencies","Measure credit risk"],1,"Periodicity must match for comparison.",0],[6,"An increase in market yields reduces bond prices more for:",["Short-duration bonds","Long-duration bonds","Floating-rate notes"],1,"Duration measures sensitivity.",0],[6,"A bond's full price is the:",["Flat price plus accrued interest","Face value only","Coupon times years"],0,"The buyer pays the full price.",0],[6,"Key rate durations measure sensitivity to:",["Credit ratings","Changes in yields at specific maturities on the curve","Parallel shifts only"],1,"They capture non-parallel curve changes.",0],[6,"Topic weight of Fixed Income in the 2026 Level I exam is:",["5% to 8%","11% to 14%","6% to 9%"],1,"Same range as Equity and FSA.",0],[7,"A derivative is a contract whose value:",["Equals its face value","Is fixed at issue","Depends on an underlying asset, rate or index"],2,"Options, forwards, futures and swaps are derivatives.",0],[7,"A forward commitment differs from a contingent claim because it:",["Obliges both parties to perform","Has no underlying","Gives one party a choice"],0,"Options are contingent claims.",0],[7,"Futures differ from forwards because futures are:",["Standardised, exchange-traded and marked to market daily","Free of margin","Customised and private"],0,"Clearing houses guarantee futures.",0],[7,"A swap can be viewed as:",["A bond with no coupons","A series of forward contracts","A single option"],1,"Each exchange of payments is like a forward.",0],[7,"In a plain vanilla interest rate swap, one party:",["Pays both legs","Pays fixed and receives floating","Exchanges principal every period"],1,"Notional principal is usually not exchanged.",0],[7,"A call option buyer has:",["The obligation to buy","The right to sell","The right, not the obligation, to buy at the exercise price"],2,"The seller has the obligation.",0],[7,"A put option is in the money when:",["The price equals the strike","The underlying is above the exercise price","The underlying price is below the exercise price"],2,"Put intrinsic value = strike − underlying.",0],[7,"European options can be exercised:",["Only at expiration","At any time before expiry","Never"],0,"American options allow early exercise.",0],[7,"An American option is worth at least as much as a European option because:",["It is always cheaper","It has a lower strike","It gives the extra right of early exercise"],2,"Extra rights cannot have negative value.",0],[7,"The value of an option has two components:",["Intrinsic value and time value","Coupon and principal","Margin and premium"],0,"Time value falls as expiry approaches.",0],[7,"An increase in the underlying's volatility generally:",["Has no effect","Decreases call values","Increases the value of both calls and puts"],2,"More chance of large favourable moves.",0],[7,"Higher interest rates (all else equal) generally:",["Decrease call values","Increase put values","Increase call values and decrease put values"],2,"The present value of the strike falls.",0],[7,"Benefits of the cost of carry for the underlying, such as dividends, cause a forward price to be:",["Higher","Lower","Unchanged"],1,"Forward price = spot compounded at the risk-free rate minus benefits plus costs.",0],[7,"Storage costs of a commodity cause its forward price to be:",["Lower","Higher","Unchanged"],1,"Costs of carry increase the forward price.",0],[7,"Convenience yield refers to:",["The non-cash benefit of holding a physical commodity","The option premium","Interest on margin"],0,"It lowers the forward price.",0],[7,"At initiation, the value of a forward contract is typically:",["Zero","Equal to the forward price","Equal to the spot price"],0,"The forward price is set so no money changes hands.",0],[7,"Arbitrage in derivative pricing relies on:",["Insider information","Predicting market direction","Replication: two portfolios with identical payoffs must have the same price"],2,"No-arbitrage pricing does not need risk preferences.",0],[7,"Put-call parity relates:",["A European call, a European put, the underlying and a risk-free bond with the same strike and expiry","Two different strikes","American options only"],0,"Call + PV(strike) = put + underlying.",0],[7,"A fiduciary call consists of:",["Two calls","A call option plus a risk-free bond paying the strike at expiry","A put plus the underlying"],1,"It equals a protective put by parity.",0],[7,"A protective put consists of:",["Two puts","A short call and a bond","The underlying plus a put option"],2,"It limits downside while keeping upside.",0],[7,"Put-call-forward parity replaces the underlying with:",["A swap","A futures option","A forward contract on the underlying"],2,"It links options and forwards.",0],[7,"In a one-period binomial model, option value is found using:",["Real-world probabilities","Risk-neutral probabilities and discounting at the risk-free rate","The investor's own return"],1,"It replicates the option with the underlying and borrowing.",0],[7,"Risk-neutral pricing implies the expected return on the underlying is:",["Zero","The risk-free rate","The market return"],1,"This is a pricing device, not a forecast.",0],[7,"Derivatives can benefit markets by:",["Guaranteeing returns","Removing all risk","Improving price discovery and allowing efficient risk transfer"],2,"They also lower transaction costs.",0],[7,"A risk of derivatives is that:",["High implicit leverage can magnify losses","They have no counterparty","They cannot be traded"],0,"Leverage and complexity create systemic concerns.",0],[7,"Central clearing of derivatives reduces:",["Market risk","Volatility of the underlying","Counterparty credit risk"],2,"The clearing house stands between parties.",0],[7,"Initial margin in futures is:",["A deposit required to open a position","The futures price","A fee paid to the exchange only"],0,"Maintenance margin triggers margin calls.",0],[7,"Variation margin in futures is:",["A one-time deposit","The daily gain or loss settled after marking to market","A dividend"],1,"It restores the account to initial margin after a call.",0],[7,"When interest rates are positively correlated with futures prices, futures prices are likely to be:",["Equal always","Slightly higher than forward prices","Lower than forward prices"],1,"Gains are reinvested at higher rates.",0],[7,"An interest rate swap's value at inception is:",["Zero, with the fixed rate set to make it so","Equal to the notional","Always positive for the fixed payer"],0,"Value changes as rates move.",0],[7,"A credit default swap transfers:",["Interest rate risk only","Credit risk from the protection buyer to the protection seller","Currency risk"],1,"The buyer pays periodic premiums.",0],[7,"A long call's maximum loss is:",["The premium paid","Unlimited","The strike price"],0,"Potential gain is unlimited.",0],[7,"A short put's maximum loss is:",["Unlimited","The strike price minus the premium received","The premium"],1,"The underlying cannot fall below zero.",0],[7,"A covered call strategy:",["Buys a put on the underlying","Sells the underlying short","Holds the underlying and sells a call"],2,"It earns premium but caps upside.",0],[7,"Exchange-traded derivatives differ from OTC derivatives because they:",["Have higher counterparty risk","Are customised","Are standardised and have a clearing house"],2,"OTC contracts are privately negotiated.",0],[7,"A forward rate agreement (FRA) is a forward contract on:",["A commodity","An interest rate","A share price"],1,"It locks in a rate for a future period.",0],[7,"The lower bound of a European call on a non-dividend-paying stock is:",["Zero only","The larger of zero and the underlying minus PV of the strike","The strike price"],1,"Option values have no-arbitrage bounds.",0],[7,"Time value of an option is greatest when the option is:",["Deep out of the money","At the money","Deep in the money"],1,"Uncertainty about finishing in the money is highest.",0],[7,"Hedgers use derivatives mainly to:",["Increase leverage","Avoid all costs","Reduce exposure to price movements"],2,"Speculators take on risk.",0],[7,"Replicating a forward with spot and borrowing shows that the forward price:",["Equals the expected future spot","Is random","Equals the spot price compounded at the risk-free rate (adjusted for carry)"],2,"This is the cost-of-carry model.",0],[7,"A long futures position gains when:",["The futures price rises","The futures price falls","Volatility rises"],0,"Short futures gain when prices fall.",0],[7,"Settlement of futures at expiry can be:",["Physical delivery or cash settlement","Only physical delivery","Only by rolling over"],0,"Index futures are cash settled.",0],[7,"Exchange-traded options on indices are usually:",["Physically settled in shares","Cash settled","Settled in bonds"],1,"Delivery of an index is impractical.",0],[7,"Which statement on options is correct?",["Buying a call is bearish","Selling a call is bullish","Buying a put is bearish; selling a put is bullish"],2,"Directional views follow from payoffs.",0],[7,"Topic weight of Derivatives in the 2026 Level I exam is:",["11% to 14%","15% to 20%","5% to 8%"],2,"Derivatives is among the smaller topics.",0],[8,"Alternative investments typically have:",["Lower liquidity, less transparency and higher fees than traditional assets","No diversification benefits","Daily liquidity and low fees"],0,"They may offer diversification and return benefits.",0],[8,"Investing through a fund (such as a limited partnership) means:",["A general partner manages and limited partners provide capital","No fees are paid","The investor manages directly"],0,"LPs have limited liability.",0],[8,"Co-investment allows an investor to:",["Avoid all risk","Invest directly in a deal alongside a fund, often with lower fees","Manage the fund"],1,"It requires due diligence capability.",0],[8,"A '2 and 20' fee structure means:",["A 2% management fee and 20% incentive fee on profits","20% management fee and 2% incentive","2% of profits only"],0,"Common in hedge funds and private equity.",0],[8,"A hurdle rate in an incentive fee structure is:",["A minimum return that must be earned before incentive fees are paid","A management fee","A cap on returns"],0,"Hard and soft hurdles differ in how fees are calculated.",0],[8,"A high-water mark ensures:",["Losses are shared","Incentive fees are paid only on gains above the previous highest fund value","Fees are paid every year"],1,"Investors do not pay twice for the same gains.",0],[8,"A catch-up clause lets the general partner:",["Receive a larger share of profits after the hurdle until reaching its agreed share","Avoid the hurdle","Return capital first"],0,"It is common in private equity waterfalls.",0],[8,"A clawback provision requires the general partner to:",["Pay management fees twice","Return incentive fees if later losses mean it was overpaid","Invest more capital"],1,"It protects limited partners.",0],[8,"A European (whole-of-fund) distribution waterfall pays carried interest:",["Only after LPs receive all contributed capital and the preferred return","Deal by deal","Before any capital is returned"],0,"American waterfalls pay carry deal by deal.",0],[8,"Private equity performance is commonly measured using:",["Dividend yield","Daily returns","IRR and multiples such as MOIC or TVPI"],2,"Cash flow timing matters.",0],[8,"A leveraged buyout (LBO) uses:",["Only equity","Large amounts of debt to acquire a company","Government grants"],1,"Returns depend on improvement and debt paydown.",0],[8,"Venture capital invests in:",["Early-stage companies with high growth potential and high risk","Government bonds","Mature, stable firms"],0,"Stages include seed, early and later.",0],[8,"Exit routes for private equity include:",["Paying coupons","IPO, trade sale, secondary sale and recapitalisation","Daily redemption"],1,"Exit timing affects returns.",0],[8,"Private debt includes:",["Listed shares","Direct lending, mezzanine debt and distressed debt","Only government bonds"],1,"It offers higher yields with less liquidity.",0],[8,"Mezzanine debt is:",["Senior secured debt","Subordinated debt, often with equity features like warrants","Common equity"],1,"It sits between senior debt and equity.",0],[8,"Real estate investment trusts (REITs) are:",["Commodity futures","Publicly traded vehicles that own income-producing real estate","Private loans"],1,"They provide liquid access to real estate.",0],[8,"The income approach to valuing real estate:",["Capitalises or discounts expected net operating income","Uses recent sales only","Uses replacement cost only"],0,"The cap rate links NOI and value.",0],[8,"The cost approach to real estate valuation estimates value as:",["Replacement cost of the building plus land value, less depreciation","Average of sales prices","NOI divided by cap rate"],0,"It is useful for unique properties.",0],[8,"Appraisal-based real estate indices tend to:",["Be perfectly accurate","Understate volatility and correlation because of smoothing","Overstate volatility"],1,"Appraisals lag market prices.",0],[8,"Infrastructure investments are typically characterised by:",["No capital requirement","Long-lived assets with stable, often regulated cash flows","Very short lives"],1,"Examples include toll roads and utilities.",0],[8,"Brownfield infrastructure investments refer to:",["Undeveloped land only","Existing assets with operating history","New construction projects"],1,"Greenfield means new assets.",0],[8,"Commodity futures returns include:",["Coupon income","Price return, roll return and collateral return","Dividends"],1,"Roll return depends on the curve shape.",0],[8,"In backwardation, futures prices are:",["Above spot prices","Equal to spot","Below spot prices, giving positive roll return to long positions"],2,"Contango gives negative roll return.",0],[8,"Contango in commodity markets means:",["No futures exist","Futures are below spot","Futures prices are above spot prices"],2,"Long positions face negative roll return.",0],[8,"Farmland and timberland returns come from:",["Crop or timber sales, and changes in land value","Coupons","Only rental income"],0,"Timber can be stored on the stump if prices are low.",0],[8,"A long/short equity hedge fund strategy:",["Only holds cash","Only buys bonds","Buys undervalued and shorts overvalued stocks"],2,"Net exposure varies by manager.",0],[8,"An event-driven hedge fund strategy focuses on:",["Corporate events such as mergers, restructurings and bankruptcies","Long-only bonds","Index tracking"],0,"Merger arbitrage is an example.",0],[8,"A relative value hedge fund strategy seeks:",["Profit from pricing discrepancies between related securities","Pure directional bets","Index replication"],0,"Convertible arbitrage is an example.",0],[8,"Global macro hedge funds:",["Only buy small caps","Take views on broad economic trends across asset classes","Avoid derivatives"],1,"They may use currencies, rates and commodities.",0],[8,"Hedge fund return indices can suffer from survivorship bias because:",["Failed funds stop reporting and drop out","All funds report forever","Fees are excluded"],0,"Backfill bias adds to the problem.",0],[8,"Backfill bias occurs when:",["Funds report losses","Indices are equal weighted","Funds add their good past returns to a database when they start reporting"],2,"It inflates historical performance.",0],[8,"Lock-up periods in hedge funds:",["Lower fees","Guarantee returns","Restrict investors from redeeming for a set time"],2,"Notice periods also limit liquidity.",0],[8,"Digital assets such as cryptocurrencies are characterised by:",["Guaranteed value","Central bank backing in all cases","High volatility and use of distributed ledger technology"],2,"Regulation varies widely across countries.",0],[8,"A distributed ledger is:",["A paper record","A bank's internal ledger","A shared database maintained across many participants"],2,"Blockchain is a type of distributed ledger.",0],[8,"Permissionless blockchains allow:",["Only approved members","Anyone to participate and validate transactions","Only banks"],1,"Bitcoin is permissionless.",0],[8,"Smart contracts are:",["Paper contracts","Legal advice","Programs on a blockchain that execute automatically when conditions are met"],2,"They can automate settlement.",0],[8,"Diversification benefits of alternatives come from:",["Low or imperfect correlation with stocks and bonds","Guaranteed returns","High liquidity"],0,"Smoothed data can overstate them.",0],[8,"Due diligence for alternative managers should cover:",["Only fees","Only past returns","Strategy, risk management, operations, fees and legal terms"],2,"Operational risk is significant in alternatives.",0],[8,"Net asset value in a private fund is:",["Market price on an exchange","Total assets minus liabilities, often based on estimates","Committed capital"],1,"Valuations can be stale.",0],[8,"Committed capital in private equity is:",["Capital already invested","The total amount investors have agreed to provide when called","Profits"],1,"Capital calls draw it over time.",0],[8,"The J-curve in private equity describes:",["Negative early returns from fees and costs, followed by gains as investments mature","Stable returns","Returns falling forever"],0,"Early valuations are often conservative.",0],[8,"Commodity index returns may differ from spot price changes mainly because of:",["Dividends","Coupons","Roll return and collateral return"],2,"Investors usually hold futures, not physical goods.",0],[8,"Real estate debt investments include:",["Mortgages and mortgage-backed securities","Land ownership","REIT shares"],0,"Equity investments own property directly or via REITs.",0],[8,"Fund of funds structures offer:",["Daily liquidity always","Lower fees than direct funds","Diversification across managers but add another layer of fees"],2,"They can help smaller investors access managers.",0],[8,"Topic weight of Alternative Investments in the 2026 Level I exam is:",["15% to 20%","7% to 10%","11% to 14%"],1,"Most published guides give 7% to 10%.",0],[9,"The portfolio management process has three main steps:",["Research, trade and report only","Buy, hold and sell","Planning, execution and feedback"],2,"Planning includes the IPS.",0],[9,"An investment policy statement (IPS) includes:",["The manager's personal holdings","Only asset prices","Return objectives, risk tolerance and constraints"],2,"Constraints include liquidity, time horizon, taxes, legal and unique needs.",0],[9,"Willingness to take risk differs from ability to take risk because willingness is:",["A psychological attitude, while ability depends on financial circumstances","Always higher","Fixed by law"],0,"When they conflict, the lower usually governs.",0],[9,"A defined benefit pension plan's investment horizon is generally:",["Very short","Long, depending on the age of participants","One year"],1,"Liabilities stretch over decades.",0],[9,"Endowments typically have:",["Long time horizons and relatively high risk tolerance","Very short horizons","No spending needs"],0,"They support institutions in perpetuity.",0],[9,"Banks typically invest securities portfolios with:",["Low risk tolerance and high liquidity needs","No liquidity needs","Very high risk"],0,"They match liabilities like deposits.",0],[9,"Insurance companies' investment portfolios are shaped by:",["The nature of their policy liabilities","No regulation","Only equity returns"],0,"Life insurers have longer liabilities than property insurers.",0],[9,"Diversification reduces:",["All risk","Systematic risk","Unsystematic (company-specific) risk"],2,"Systematic risk remains.",0],[9,"The efficient frontier shows portfolios that:",["Have the lowest returns","Hold only one asset","Offer the highest expected return for each level of risk"],2,"Portfolios below it are inefficient.",0],[9,"An investor's optimal portfolio is where:",["Return is highest regardless of risk","The investor's highest indifference curve touches the efficient frontier (or CAL)","Risk is zero"],1,"Utility is maximised there.",0],[9,"A more risk-averse investor has indifference curves that are:",["Flatter","Steeper","Horizontal"],1,"They need more return for each unit of risk.",0],[9,"The capital allocation line combines:",["A risk-free asset with a risky portfolio","Only bonds","Two risky assets only"],0,"Its slope is the Sharpe ratio of the risky portfolio.",0],[9,"The capital market line is the CAL where the risky portfolio is:",["The market portfolio","The minimum variance portfolio","A single stock"],0,"It applies to efficient portfolios.",0],[9,"Investors who lend at the risk-free rate along the CML hold:",["A combination of the risk-free asset and the market portfolio","Only stocks","Only the market portfolio on margin"],0,"Borrowing portfolios lie beyond the market portfolio.",0],[9,"Beta measures:",["Systematic risk relative to the market","Unsystematic risk","Total risk"],0,"Market beta is 1.",0],[9,"The CAPM states that expected return equals:",["Risk-free rate plus beta times the market risk premium","Market return plus alpha","Risk-free rate only"],0,"Only systematic risk is priced.",0],[9,"The security market line plots:",["Price against time","Return against total risk","Expected return against beta"],2,"Securities above the SML are undervalued.",0],[9,"A stock plotting above the SML is:",["Undervalued, offering more return than its beta requires","Overvalued","Fairly priced"],0,"Its alpha is positive.",0],[9,"Jensen's alpha measures:",["Standard deviation","Return above that predicted by the CAPM","Total return"],1,"Positive alpha suggests skill.",0],[9,"The Treynor ratio uses which risk measure?",["Beta","Downside deviation","Standard deviation"],0,"It suits well-diversified portfolios.",0],[9,"M-squared (M²) adjusts a portfolio's return to:",["Double leverage","The same total risk as the market, for direct comparison","Zero risk"],1,"It is expressed in percentage terms.",0],[9,"Which assumption is part of the CAPM?",["Markets have high taxes","Investors have different expectations","Investors can lend and borrow at the risk-free rate"],2,"Homogeneous expectations and no frictions are others.",0],[9,"Behavioral biases are grouped as:",["Legal and illegal","Cognitive errors and emotional biases","Short and long"],1,"Cognitive errors are easier to correct.",0],[9,"Confirmation bias is:",["Fear of losses","Overtrading","Seeking information that supports existing beliefs"],2,"It is a cognitive error.",0],[9,"Loss aversion is:",["Taking excessive risk always","Feeling losses more strongly than equal gains","Ignoring losses"],1,"It is an emotional bias.",0],[9,"Anchoring bias means:",["Following the crowd","Avoiding losses","Relying too much on an initial reference point"],2,"Forecasts stick to old numbers.",0],[9,"Overconfidence bias leads investors to:",["Diversify widely","Overestimate their knowledge and trade too much","Avoid trading"],1,"It is an emotional bias in the curriculum.",0],[9,"Status quo bias leads investors to:",["Trade constantly","Leave portfolios unchanged even when change is needed","Sell winners early"],1,"Defaults strongly influence choices.",0],[9,"The disposition effect describes:",["Rebalancing regularly","Selling winners too early and holding losers too long","Buying index funds"],1,"It relates to loss aversion.",0],[9,"Risk governance in an organisation refers to:",["Daily trading","Top-level oversight that sets risk appetite and policies","Marketing"],1,"It is led by the board.",0],[9,"Risk tolerance is:",["The amount of risk an organisation is willing to accept","A trading limit only","The maximum possible loss"],0,"Risk budgeting allocates it.",0],[9,"Risk budgeting means:",["Allocating total risk across activities or assets","Setting a profit target","Cutting all risk"],0,"It links risk to expected return.",0],[9,"Financial risks include:",["Reputational risk only","Operational risk only","Market, credit and liquidity risk"],2,"Non-financial risks include operational, legal and model risk.",0],[9,"Technical analysis assumes that:",["Prices reflect supply and demand and trends tend to persist","Markets are strong-form efficient","Prices follow fundamentals only"],0,"It studies price and volume patterns.",0],[9,"A head-and-shoulders pattern is generally seen as:",["A continuation pattern","A volume indicator","A reversal pattern"],2,"An inverse version signals a bottom.",0],[9,"Relative strength index (RSI) is a:",["Momentum oscillator","Volume measure only","Trend line"],0,"Readings above 70 are often called overbought.",0],[9,"Fintech applications in investment management include:",["Robo-advisers, algorithmic trading and big data analysis","Only paper reports","Manual order books"],0,"They change how advice and trading are delivered.",0],[9,"Robo-advisers mainly provide:",["Hedge fund access","Personal phone advice only","Automated, low-cost portfolio management based on client inputs"],2,"They rely on algorithms and passive products.",0],[9,"Mutual funds offer investors:",["Diversification and professional management with pooled money","No fees","Guaranteed returns"],0,"Open-end funds redeem at NAV.",0],[9,"Exchange-traded funds differ from open-end mutual funds because ETFs:",["Never trade","Have no NAV","Trade on an exchange at market prices throughout the day"],2,"Creation and redemption keep prices near NAV.",0],[9,"A closed-end fund:",["Has no manager","Redeems shares daily at NAV","Has a fixed number of shares that trade on an exchange, possibly at a discount to NAV"],2,"Supply of shares does not change with demand.",0],[9,"Defined contribution plans shift investment risk to:",["The government","Employees","Employers"],1,"Benefits depend on contributions and returns.",0],[9,"Strategic asset allocation is:",["The long-term target mix of asset classes in the IPS","Picking single stocks","Short-term market timing"],0,"Tactical allocation makes short-term deviations.",0],[9,"Rebalancing a portfolio means:",["Returning asset weights to targets after market moves","Selling everything","Changing the IPS each day"],0,"It controls drift in risk.",0],[9,"Systematic risk is also called:",["Idiosyncratic risk","Market risk or non-diversifiable risk","Specific risk"],1,"Only it is compensated in CAPM.",0],[9,"A minimum-variance portfolio is:",["The portfolio with the lowest risk for its level of expected return","The highest-return portfolio","A single asset always"],0,"The global minimum-variance portfolio is the lowest risk overall.",0],[9,"Two-fund separation means all investors hold:",["The risk-free asset and the same market portfolio, in different proportions","Different risky portfolios","Only one asset"],0,"It follows from CAPM assumptions.",0],[9,"Correlation of −1 between two assets means:",["They always rise together","Diversification has no benefit","A risk-free combination can be formed"],2,"Perfect negative correlation removes risk at the right weights.",0],[9,"Asset allocation decisions often explain:",["A large part of the variation in portfolio returns over time","Only taxes","None of the returns"],0,"Security selection adds or subtracts around it.",0],[9,"Topic weight of Portfolio Management in the 2026 Level I exam is:",["8% to 12%","15% to 20%","5% to 8%"],0,"It covers planning, risk, behaviour and fintech.",0],[1,"An investor deposits $17,500 at 7% a year, compounded annually. What is it worth after 4 years?",["$21,438.25","$22,938.93","$22,400.00"],1,"FV = PV × (1 + r)^n = $17,500 × 1.07^4 = $22,938.93.",1],[1,"What is the present value of $31,000 received in 3 years if the discount rate is 6%?",["$26,028.20","$26,271.19","$27,589.89"],0,"PV = FV ÷ (1 + r)^n = $31,000 ÷ 1.06^3 = $26,028.20.",1],[1,"What is the present value of an ordinary annuity of $4,900 a year for 9 years at 7%?",["$31,924.64","$44,100.00","$34,159.36"],0,"PV = A × [1 − (1 + r)^−n] ÷ r = $31,924.64. An annuity due would be worth $34,159.36.",1],[1,"An investor saves $3,700 at the end of each year for 9 years at 8%. What is the future value?",["$33,300.00","$46,203.96","$49,900.28"],1,"FV = A × [(1 + r)^n − 1] ÷ r = $46,203.96.",1],[1,"A preferred share pays a fixed $8.50 a year forever. At a required return of 8.0%, what is it worth?",["$106.25","$114.75","$94.44"],0,"Perpetuity value = payment ÷ r = $8.50 ÷ 8.0% = $106.25.",1],[1,"A stated annual rate of 13% is compounded daily. What is the effective annual rate?",["13.000%","13.880%","14.083%"],1,"EAR = (1 + 13% ÷ 365)^365 − 1 = 13.880%.",1],[1,"A share bought at $87.00 is sold a year later at $108.00 after paying a dividend of $0.50. What is the holding period return?",["19.91%","24.14%","24.71%"],2,"HPR = (P1 − P0 + D) ÷ P0 = (108.00 − 87.00 + 0.50) ÷ 87.00 = 24.71%.",1],[1,"Annual returns over three years are 19%, −7%, 0%. What is the geometric mean return?",["3.44%","4.00%","9.50%"],0,"Geometric mean = [(1 + r1)(1 + r2)(1 + r3)]^(1/3) − 1 = 3.44%. The arithmetic mean is 4.00%.",1],[1,"Returns of −4%, 5%, 15% have probabilities of 0.20, 0.30, 0.50. What is the expected return?",["8.20%","5.00%","5.33%"],0,"E(R) = Σ p × R = 8.20%.",1],[1,"A portfolio holds 80% in asset A (σ = 10%) and 20% in asset B (σ = 20%). Their correlation is 0.00. What is the portfolio standard deviation?",["9.44%","12.00%","8.94%"],2,"σp = √(w²σA² + (1 − w)²σB² + 2w(1 − w)ρσAσB) = 8.94%.",1],[1,"A sample of 36 observations has a standard deviation of 33. What is the standard error of the sample mean?",["5.878","5.500","0.917"],1,"Standard error = s ÷ √n = 33 ÷ 6 = 5.500.",1],[1,"A portfolio has expected return 10% and standard deviation 8%. The minimum acceptable return is 5%. What is Roy's safety-first ratio?",["1.250","0.781","0.625"],2,"SFRatio = (E(R) − threshold) ÷ σ = 0.625. A higher ratio means lower shortfall risk.",1],[1,"Two independent events have probabilities 0.40 and 0.70. What is the probability that both occur?",["0.5500","0.2800","0.8200"],1,"For independent events, P(A and B) = P(A) × P(B) = 0.2800.",1],[2,"A 5% rise in price leads to a 4% fall in quantity demanded. What is the own-price elasticity of demand?",["−0.80","1.25","−0.04"],0,"Elasticity = %ΔQ ÷ %ΔP = −4% ÷ 5% = −0.80. Demand is inelastic.",1],[2,"EUR/USD is 1.0700 and USD/INR is 85.00. What is the EUR/INR cross rate?",["79.44","90.95","86.07"],1,"EUR/INR = EUR/USD × USD/INR = 1.0700 × 85.00 = 90.95 rupees per euro.",1],[2,"Spot USD/INR is 86.75. One-year rates are 7.3% in India and 3.9% in the US. By covered interest parity, the one-year forward USD/INR is:",["86.75","89.59","84.00"],1,"Forward = spot × (1 + i INR) ÷ (1 + i USD) = 89.59. The higher-rate currency (INR) trades at a forward discount.",1],[2,"Four firms in a market have shares of 11%, 31%, 9%, 18% (the rest are tiny). What is the Herfindahl-Hirschman Index (as a decimal)?",["0.1725","0.6900","0.1487"],2,"HHI = sum of squared shares = 0.11² + 0.31² + 0.09² + 0.18² = 0.1487.",1],[3,"A project costs $1,100 today and returns $440, $440, $500 over the next three years. At a 9% cost of capital, what is its NPV?",["$280.00","$60.10","$65.51"],1,"NPV = −$1,100 + Σ CFt ÷ (1 + 9%)^t = $60.10. Accept.",1],[3,"A firm's target weights are 40% debt and 60% equity. Pre-tax cost of debt is 6%, the tax rate is 27% and the cost of equity is 11%. What is the WACC?",["9.00%","8.35%","8.50%"],1,"WACC = wd × rd × (1 − t) + we × re = 8.35%.",1],[3,"The risk-free rate is 6%, the equity risk premium is 7% and the stock's beta is 1.40. What is the cost of equity under CAPM?",["9.80%","15.80%","13.00%"],1,"re = Rf + β × ERP = 6% + 1.40 × 7% = 15.80%.",1],[3,"Days of inventory on hand are 87, days sales outstanding 58 and days payables 49. What is the cash conversion cycle?",["96 days","78 days","194 days"],0,"CCC = DIO + DSO − DPO = 87 + 58 − 49 = 96 days.",1],[3,"A supplier offers terms of 2/10, net 30. What is the effective annual cost of not taking the discount?",["2.0%","36.5%","44.6%"],2,"Cost = (1 + 2/98)^(365/20) − 1 = 44.6%. Usually far above bank borrowing costs.",1],[3,"When sales rise 15%, operating income rises 21.0%. What is the degree of operating leverage?",["0.71","6.00","1.40"],2,"DOL = %Δ EBIT ÷ %Δ sales = 1.40.",1],[4,"Current assets are $900m, of which inventory is $110m (no prepaid expenses). Current liabilities are $190m. What is the quick ratio?",["0.58","4.74","4.16"],2,"Quick ratio = (current assets − inventory) ÷ current liabilities = 4.16. Current ratio = 4.74.",1],[4,"A company has a net profit margin of 7%, asset turnover of 1.00 and financial leverage (assets ÷ equity) of 2.40. What is its ROE?",["17.80%","7.00%","16.80%"],2,"DuPont: ROE = margin × turnover × leverage = 16.80%. ROA = 7.00%.",1],[4,"Cost of goods sold is $1,620m and average inventory is $210m. How many days of inventory on hand does the firm hold?",["47.3 days","28.2 days","7.7 days"],0,"Inventory turnover = 7.71; days of inventory = 365 ÷ 7.71 = 47.3 days.",1],[4,"Equipment costs $170,000, has a salvage value of $17,000 and a useful life of 6 years. What is annual straight-line depreciation?",["$31,167","$25,500","$28,333"],1,"(Cost − salvage) ÷ life = ($170,000 − $17,000) ÷ 6 = $25,500.",1],[4,"Equipment costs $170,000 with a 8-year life. What is first-year depreciation under the double-declining balance method?",["$31,875","$21,250","$42,500"],2,"DDB rate = 2 ÷ 8 = 25.0%; year 1 = $170,000 × 25.0% = $42,500. Salvage is ignored until the end.",1],[4,"A firm buys 160 units at $15 and later 210 units at $16, then sells 220 units. What is cost of goods sold under FIFO?",["$3,425","$3,510","$3,360"],2,"FIFO uses the oldest costs first: 160 × $15 + 60 × $16 = $3,360. LIFO would give $3,510.",1],[4,"Net income is $230m, preferred dividends are $10m and the weighted average number of common shares is 110m. What is basic EPS?",["$2.09","$2.00","$2.18"],1,"Basic EPS = (NI − preferred dividends) ÷ weighted shares = $2.00.",1],[4,"EBIT is $540m and interest expense is $125m. What is the interest coverage ratio?",["3.32×","0.23×","4.32×"],2,"Interest coverage = EBIT ÷ interest = 4.32 times.",1],[4,"Tax depreciation exceeds book depreciation, creating a cumulative temporary difference of $170m. At a 22% tax rate, what is the deferred tax liability?",["$170.00m","$37.40m","$132.60m"],1,"DTL = temporary difference × tax rate = $170m × 22% = $37.40m.",1],[5,"A stock just paid a dividend of $2.00. Dividends grow at 3% forever and the required return is 10%. What is its value?",["$29.43","$20.60","$28.57"],0,"Gordon model: V0 = D0(1 + g) ÷ (r − g) = $2.06 ÷ 7% = $29.43.",1],[5,"A company retains 30% of earnings and has an ROE of 14%. What is its sustainable growth rate?",["9.80%","14.00%","4.20%"],2,"g = retention ratio × ROE = 30% × 14% = 4.20%.",1],[5,"A firm pays out 60% of earnings, grows at 5% and has a required return of 9%. What is its justified forward P/E?",["10.00×","15.00×","6.67×"],1,"Justified forward P/E = payout ÷ (r − g) = 0.60 ÷ 4% = 15.00.",1],[5,"An investor buys a share at $113.00 with 50% initial margin. The maintenance margin is 25%. Below what price will a margin call occur?",["$56.50","$84.75","$75.33"],2,"Trigger price = P0 × (1 − initial margin) ÷ (1 − maintenance margin) = $75.33.",1],[5,"A share is bought at $55.00 with 40% margin and sold at $59.40 (ignore interest and dividends). What is the return on the investor's equity?",["20.00%","3.20%","8.00%"],0,"Return = price change ÷ equity invested = (59.40 − 55.00) ÷ $22.00 = 20.00%. Leverage is 1 ÷ 0.40.",1],[5,"A price-weighted index has three stocks priced at $68, $52, $74, with a divisor of 3. What is the index value?",["64.67","194.00","74.00"],0,"Price-weighted index = sum of prices ÷ divisor = 64.67. The highest-priced stock has the most weight.",1],[5,"A firm has equity market value of $4,400m, debt of $1,950m and cash of $610m. What is its enterprise value?",["$6,960m","$3,790m","$5,740m"],2,"EV = equity + debt − cash = $5,740m.",1],[5,"A non-callable, non-convertible preferred share pays $3.50 a year. The required return is 6.0%. What is its value?",["$43.75","$58.33","$21.00"],1,"Value = dividend ÷ required return = $58.33.",1],[6,"A 3-year bond pays an annual coupon of 7% on a par of 100. If the yield to maturity is 8%, what is its price?",["103.00","87.50","97.42"],2,"Price = Σ coupon ÷ (1 + y)^t + 100 ÷ (1 + y)^3 = 97.42. Coupon below yield, so a discount.",1],[6,"A bond with a 8% annual coupon on par 100 trades at 94.50. What is its current yield?",["8.00%","7.56%","8.47%"],2,"Current yield = annual coupon ÷ price = 8.00 ÷ 94.50 = 8.47%.",1],[6,"A bond has modified duration of 7.00. If its yield falls by 25 basis points, the approximate percentage change in price is:",["3.50%","−1.75%","1.75%"],2,"%ΔP ≈ −ModDur × Δy = −7.00 × −0.25% = 1.75%.",1],[6,"A bond has modified duration 7.10 and convexity 41. For a fall in yield of 100 bp, the estimated price change including convexity is:",["7.100%","6.895%","7.305%"],2,"%ΔP ≈ −ModDur × Δy + ½ × convexity × (Δy)² = 7.305%.",1],[6,"A bond's Macaulay duration is 5.30 years and its yield is 6% (annual periodicity). What is its modified duration?",["5.300","5.000","5.618"],1,"ModDur = MacDur ÷ (1 + y/k) = 5.30 ÷ 1.0600 = 5.000.",1],[6,"The 1-year spot rate is 3.1% and the 2-year spot rate is 3.9%. What is the 1-year forward rate one year from now?",["4.706%","3.500%","4.900%"],0,"(1 + S2)² = (1 + S1)(1 + f) gives f = 4.706%.",1],[6,"A bond exposure of $400m has a probability of default of 3.9% and an expected recovery rate of 28%. What is the expected loss?",["$11.23m","$4.37m","$15.60m"],0,"Expected loss = PD × exposure × (1 − recovery) = $11.23m.",1],[6,"A bond pays a 8% coupon semi-annually on par 100 (30/360 basis). It has been 28 days since the last coupon. What is the accrued interest?",["0.622","4.000","1.244"],0,"AI = (coupon per period) × days ÷ 180 = 4.00 × 28 ÷ 180 = 0.622.",1],[7,"A non-dividend-paying share trades at $191.00. The risk-free rate is 6% (annual compounding). What is the no-arbitrage forward price for one year?",["$202.46","$191.00","$202.96"],0,"F0 = S0 × (1 + r)^T = $191.00 × 1.06^1 = $202.46.",1],[7,"A European call with strike $128 and one year to expiry costs $5.00. The stock is at $128.00 and the risk-free rate is 3%. By put-call parity, the put with the same terms is worth:",["$1.27","$8.73","$5.00"],0,"p = c + X ÷ (1 + r) − S = 5.00 + 124.27 − 128.00 = $1.27.",1],[7,"An investor buys a call with strike $75 for $4.00. At expiry the stock is $94.00. What is the profit per share?",["$16.00","$19.00","$15.00"],2,"Profit = max(ST − X, 0) − premium = $19.00 − $4.00 = $15.00.",1],[7,"An investor buys a put with strike $120 for $7.00. At expiry the stock is $103.00. What is the profit per share?",["$10.00","$11.00","$17.00"],0,"Profit = max(X − ST, 0) − premium = $10.00.",1],[7,"In a one-period binomial model, the up factor is 1.12, the down factor is 0.88 and the risk-free rate is 2%. What is the risk-neutral probability of an up move?",["0.5833","0.4167","0.5000"],0,"π = (1 + r − d) ÷ (u − d) = 0.5833.",1],[7,"A stock at $104.00 can move to $130.00 or $93.60 in one period. The risk-free rate is 6%. What is a one-period European call with strike $104 worth?",["$11.89","$12.26","$11.21"],2,"π = 0.4571; c = [π × 26.00 + (1 − π) × 0.00] ÷ 1.06 = $11.21.",1],[8,"A hedge fund starts the year at $250m and ends at $292.50m before fees. It charges 2% of year-end assets and 20% of gains net of the management fee (no hurdle, above the high-water mark). Total fees are:",["$13.18m","$14.35m","$5.85m"],0,"Management fee = $5.85m; incentive fee = 20% × (292.50 − 5.85 − 250.00) = $7.33m; total $13.18m.",1],[8,"A property produces net operating income of $1,200k a year. Comparable properties sell at a cap rate of 8.50%. What is its estimated value?",["$10,200k","$12,632k","$14,118k"],2,"Value = NOI ÷ cap rate = $1,200k ÷ 8.50% = $14,118k.",1],[8,"A commodity futures position earned a price return of −7%, a roll return of 2% and a collateral return of 5%. What is its total return?",["−2.00%","−7.00%","0.00%"],2,"Total return = price + roll + collateral = 0.00%.",1],[8,"A private equity fund called $135m from investors and has returned $216.00m in total. What is its multiple on invested capital (MOIC)?",["0.63×","1.60×","0.60×"],1,"MOIC = total value returned ÷ invested capital = 1.60.",1],[9,"The risk-free rate is 2%, the expected market return is 10% and a stock's beta is 0.50. What is its CAPM expected return?",["6.00%","5.00%","7.00%"],0,"E(R) = Rf + β(Rm − Rf) = 2% + 0.50 × 8% = 6.00%.",1],[9,"A portfolio returned 14% with a beta of 1.00. The risk-free rate is 2%. What is its Treynor ratio?",["0.1300","0.1400","0.1200"],2,"Treynor = (Rp − Rf) ÷ β = 0.1200.",1],[9,"A portfolio returned 11% with beta 0.70. The market returned 8% and the risk-free rate was 4%. What is Jensen's alpha?",["4.20%","7.00%","3.00%"],0,"α = Rp − [Rf + β(Rm − Rf)] = 11% − 6.80% = 4.20%.",1],[9,"A portfolio holds 80% in a stock with beta 0.80 and the rest in a stock with beta 0.90. What is the portfolio beta?",["0.880","0.850","0.820"],2,"Portfolio beta = Σ weight × beta = 0.820.",1],[9,"An investor with risk aversion A = 6 considers a portfolio with expected return 10% and standard deviation 15%. What is its utility?",["−3.50%","−35.00%","3.25%"],2,"U = E(R) − ½ × A × σ² = 10% − 0.5 × 6 × 0.0225 = 3.25%.",1],[9,"A portfolio returned 15% with σ 22%; the market returned 8% with σ 17%; Rf is 5%. What is M² (relative to the market)?",["7.00%","4.73%","27.81%"],1,"M² = (Rp − Rf) × σm ÷ σp + Rf − Rm = 4.73%.",1],[1,"An investor deposits $5,000 at 7% a year, compounded annually. What is it worth after 9 years?",["$8,590.93","$8,150.00","$9,192.30"],2,"FV = PV × (1 + r)^n = $5,000 × 1.07^9 = $9,192.30.",1],[1,"What is the present value of $9,000 received in 8 years if the discount rate is 8%?",["$4,862.42","$5,487.80","$5,251.41"],0,"PV = FV ÷ (1 + r)^n = $9,000 ÷ 1.08^8 = $4,862.42.",1],[1,"What is the present value of an ordinary annuity of $3,300 a year for 12 years at 10%?",["$39,600.00","$22,485.18","$24,733.70"],1,"PV = A × [1 − (1 + r)^−n] ÷ r = $22,485.18. An annuity due would be worth $24,733.70.",1],[1,"An investor saves $4,400 at the end of each year for 19 years at 6%. What is the future value?",["$157,456.60","$83,600.00","$148,543.96"],2,"FV = A × [(1 + r)^n − 1] ÷ r = $148,543.96.",1],[1,"A preferred share pays a fixed $3.00 a year forever. At a required return of 10.0%, what is it worth?",["$33.00","$30.00","$27.27"],1,"Perpetuity value = payment ÷ r = $3.00 ÷ 10.0% = $30.00.",1],[1,"A stated annual rate of 6% is compounded quarterly. What is the effective annual rate?",["6.000%","6.384%","6.136%"],2,"EAR = (1 + 6% ÷ 4)^4 − 1 = 6.136%.",1],[1,"A share bought at $62.00 is sold a year later at $63.00 after paying a dividend of $0.50. What is the holding period return?",["1.61%","2.42%","2.38%"],1,"HPR = (P1 − P0 + D) ÷ P0 = (63.00 − 62.00 + 0.50) ÷ 62.00 = 2.42%.",1],[1,"Annual returns over three years are −3%, −2%, 13%. What is the geometric mean return?",["2.67%","5.00%","2.41%"],2,"Geometric mean = [(1 + r1)(1 + r2)(1 + r3)]^(1/3) − 1 = 2.41%. The arithmetic mean is 2.67%.",1],[1,"Returns of −1%, 3%, 14% have probabilities of 0.40, 0.40, 0.20. What is the expected return?",["3.00%","5.33%","3.60%"],2,"E(R) = Σ p × R = 3.60%.",1],[1,"A portfolio holds 60% in asset A (σ = 20%) and 40% in asset B (σ = 23%). Their correlation is 0.50. What is the portfolio standard deviation?",["21.20%","18.41%","15.12%"],1,"σp = √(w²σA² + (1 − w)²σB² + 2w(1 − w)ρσAσB) = 18.41%.",1],[1,"An asset has a mean return of 9% and a standard deviation of 17%. What is its coefficient of variation?",["1.89","0.53","0.08"],0,"CV = σ ÷ mean = 17% ÷ 9% = 1.89.",1],[1,"A portfolio returned 7% with a standard deviation of 9%. The risk-free rate is 4%. What is its Sharpe ratio?",["3.704","0.778","0.333"],2,"Sharpe = (Rp − Rf) ÷ σp = (7% − 4%) ÷ 9% = 0.333.",1],[1,"A sample of 144 observations has a standard deviation of 10. What is the standard error of the sample mean?",["0.069","1.136","0.833"],2,"Standard error = s ÷ √n = 10 ÷ 12 = 0.833.",1],[1,"A portfolio has expected return 8% and standard deviation 17%. The minimum acceptable return is 2%. What is Roy's safety-first ratio?",["0.208","0.471","0.353"],2,"SFRatio = (E(R) − threshold) ÷ σ = 0.353. A higher ratio means lower shortfall risk.",1],[1,"Two independent events have probabilities 0.20 and 0.50. What is the probability that both occur?",["0.3500","0.6000","0.1000"],2,"For independent events, P(A and B) = P(A) × P(B) = 0.1000.",1],[2,"A 12% rise in price leads to a 18% fall in quantity demanded. What is the own-price elasticity of demand?",["0.67","−0.18","−1.50"],2,"Elasticity = %ΔQ ÷ %ΔP = −18% ÷ 12% = −1.50. Demand is elastic.",1],[2,"EUR/USD is 1.1800 and USD/INR is 86.25. What is the EUR/INR cross rate?",["87.43","73.09","101.77"],2,"EUR/INR = EUR/USD × USD/INR = 1.1800 × 86.25 = 101.77 rupees per euro.",1],[2,"Spot USD/INR is 87.25. One-year rates are 6.7% in India and 3.8% in the US. By covered interest parity, the one-year forward USD/INR is:",["89.69","84.88","87.25"],0,"Forward = spot × (1 + i INR) ÷ (1 + i USD) = 89.69. The higher-rate currency (INR) trades at a forward discount.",1],[2,"Four firms in a market have shares of 22%, 11%, 31%, 13% (the rest are tiny). What is the Herfindahl-Hirschman Index (as a decimal)?",["0.1735","0.7700","0.1925"],0,"HHI = sum of squared shares = 0.22² + 0.11² + 0.31² + 0.13² = 0.1735.",1],[3,"A project costs $1,250 today and returns $370, $630, $340 over the next three years. At a 8% cost of capital, what is its NPV?",["$90.00","−$97.38","−$105.17"],1,"NPV = −$1,250 + Σ CFt ÷ (1 + 8%)^t = −$97.38. Reject.",1],[3,"A firm's target weights are 40% debt and 60% equity. Pre-tax cost of debt is 10%, the tax rate is 34% and the cost of equity is 12%. What is the WACC?",["11.20%","9.84%","11.00%"],1,"WACC = wd × rd × (1 − t) + we × re = 9.84%.",1],[3,"The risk-free rate is 5%, the equity risk premium is 4% and the stock's beta is 1.50. What is the cost of equity under CAPM?",["11.00%","9.00%","6.00%"],0,"re = Rf + β × ERP = 5% + 1.50 × 4% = 11.00%.",1],[3,"Days of inventory on hand are 40, days sales outstanding 62 and days payables 29. What is the cash conversion cycle?",["131 days","7 days","73 days"],2,"CCC = DIO + DSO − DPO = 40 + 62 − 29 = 73 days.",1],[3,"A supplier offers terms of 1/10, net 30. What is the effective annual cost of not taking the discount?",["18.3%","1.0%","20.1%"],2,"Cost = (1 + 1/99)^(365/20) − 1 = 20.1%. Usually far above bank borrowing costs.",1],[3,"When sales rise 11%, operating income rises 31.9%. What is the degree of operating leverage?",["0.34","2.90","20.90"],1,"DOL = %Δ EBIT ÷ %Δ sales = 2.90.",1],[4,"Current assets are $350m, of which inventory is $70m (no prepaid expenses). Current liabilities are $460m. What is the quick ratio?",["0.15","0.61","0.76"],1,"Quick ratio = (current assets − inventory) ÷ current liabilities = 0.61. Current ratio = 0.76.",1],[4,"A company has a net profit margin of 13%, asset turnover of 1.60 and financial leverage (assets ÷ equity) of 1.80. What is its ROE?",["23.40%","37.44%","20.80%"],1,"DuPont: ROE = margin × turnover × leverage = 37.44%. ROA = 20.80%.",1],[4,"Cost of goods sold is $1,680m and average inventory is $280m. How many days of inventory on hand does the firm hold?",["21.9 days","60.8 days","6.0 days"],1,"Inventory turnover = 6.00; days of inventory = 365 ÷ 6.00 = 60.8 days.",1],[4,"Equipment costs $90,000, has a salvage value of $6,000 and a useful life of 6 years. What is annual straight-line depreciation?",["$16,000","$15,000","$14,000"],2,"(Cost − salvage) ÷ life = ($90,000 − $6,000) ÷ 6 = $14,000.",1],[4,"Equipment costs $130,000 with a 4-year life. What is first-year depreciation under the double-declining balance method?",["$32,500","$65,000","$65,500"],1,"DDB rate = 2 ÷ 4 = 50.0%; year 1 = $130,000 × 50.0% = $65,000. Salvage is ignored until the end.",1],[4,"A firm buys 290 units at $15 and later 240 units at $20, then sells 310 units. What is cost of goods sold under FIFO?",["$5,352","$4,750","$5,850"],1,"FIFO uses the oldest costs first: 290 × $15 + 20 × $20 = $4,750. LIFO would give $5,850.",1],[4,"Net income is $290m, preferred dividends are $10m and the weighted average number of common shares is 130m. What is basic EPS?",["$2.23","$2.31","$2.15"],2,"Basic EPS = (NI − preferred dividends) ÷ weighted shares = $2.15.",1],[4,"EBIT is $360m and interest expense is $90m. What is the interest coverage ratio?",["0.25×","3.00×","4.00×"],2,"Interest coverage = EBIT ÷ interest = 4.00 times.",1],[4,"Tax depreciation exceeds book depreciation, creating a cumulative temporary difference of $180m. At a 28% tax rate, what is the deferred tax liability?",["$129.60m","$50.40m","$180.00m"],1,"DTL = temporary difference × tax rate = $180m × 28% = $50.40m.",1],[5,"A stock just paid a dividend of $3.25. Dividends grow at 3% forever and the required return is 7%. What is its value?",["$47.82","$83.69","$81.25"],1,"Gordon model: V0 = D0(1 + g) ÷ (r − g) = $3.35 ÷ 4% = $83.69.",1],[5,"A company retains 40% of earnings and has an ROE of 22%. What is its sustainable growth rate?",["22.00%","13.20%","8.80%"],2,"g = retention ratio × ROE = 40% × 22% = 8.80%.",1],[5,"A firm pays out 40% of earnings, grows at 2% and has a required return of 7%. What is its justified forward P/E?",["8.00×","5.71×","12.00×"],0,"Justified forward P/E = payout ÷ (r − g) = 0.40 ÷ 5% = 8.00.",1],[5,"An investor buys a share at $98.00 with 50% initial margin. The maintenance margin is 25%. Below what price will a margin call occur?",["$65.33","$73.50","$49.00"],0,"Trigger price = P0 × (1 − initial margin) ÷ (1 − maintenance margin) = $65.33.",1],[5,"A share is bought at $78.00 with 50% margin and sold at $67.86 (ignore interest and dividends). What is the return on the investor's equity?",["−26.00%","−13.00%","−6.50%"],0,"Return = price change ÷ equity invested = (67.86 − 78.00) ÷ $39.00 = −26.00%. Leverage is 1 ÷ 0.50.",1],[5,"A price-weighted index has three stocks priced at $44, $82, $105, with a divisor of 3. What is the index value?",["231.00","105.00","77.00"],2,"Price-weighted index = sum of prices ÷ divisor = 77.00. The highest-priced stock has the most weight.",1],[5,"A firm has equity market value of $5,000m, debt of $1,650m and cash of $700m. What is its enterprise value?",["$7,350m","$5,950m","$4,300m"],1,"EV = equity + debt − cash = $5,950m.",1],[5,"A non-callable, non-convertible preferred share pays $6.00 a year. The required return is 7.0%. What is its value?",["$42.00","$85.71","$66.67"],1,"Value = dividend ÷ required return = $85.71.",1],[6,"A 3-year bond pays an annual coupon of 4% on a par of 100. If the yield to maturity is 5%, what is its price?",["80.00","97.28","103.00"],1,"Price = Σ coupon ÷ (1 + y)^t + 100 ÷ (1 + y)^3 = 97.28. Coupon below yield, so a discount.",1],[6,"A bond with a 6% annual coupon on par 100 trades at 101.50. What is its current yield?",["5.91%","6.00%","6.09%"],0,"Current yield = annual coupon ÷ price = 6.00 ÷ 101.50 = 5.91%.",1],[6,"A bond has modified duration of 7.60. If its yield falls by 50 basis points, the approximate percentage change in price is:",["7.60%","−3.80%","3.80%"],2,"%ΔP ≈ −ModDur × Δy = −7.60 × −0.50% = 3.80%.",1],[6,"A bond has modified duration 12.00 and convexity 93. For a fall in yield of 100 bp, the estimated price change including convexity is:",["12.000%","12.465%","11.535%"],1,"%ΔP ≈ −ModDur × Δy + ½ × convexity × (Δy)² = 12.465%.",1],[6,"A bond's Macaulay duration is 4.40 years and its yield is 2% (annual periodicity). What is its modified duration?",["4.314","4.400","4.488"],0,"ModDur = MacDur ÷ (1 + y/k) = 4.40 ÷ 1.0200 = 4.314.",1],[6,"The 1-year spot rate is 4.2% and the 2-year spot rate is 5.5%. What is the 1-year forward rate one year from now?",["4.850%","7.000%","6.816%"],2,"(1 + S2)² = (1 + S1)(1 + f) gives f = 6.816%.",1],[6,"A bond exposure of $500m has a probability of default of 4.2% and an expected recovery rate of 49%. What is the expected loss?",["$10.29m","$10.71m","$21.00m"],1,"Expected loss = PD × exposure × (1 − recovery) = $10.71m.",1],[6,"A bond pays a 8% coupon semi-annually on par 100 (30/360 basis). It has been 108 days since the last coupon. What is the accrued interest?",["2.400","4.800","4.000"],0,"AI = (coupon per period) × days ÷ 180 = 4.00 × 108 ÷ 180 = 2.400.",1],[7,"A non-dividend-paying share trades at $191.00. The risk-free rate is 5% (annual compounding). What is the no-arbitrage forward price for 6 months?",["$195.72","$200.55","$191.00"],0,"F0 = S0 × (1 + r)^T = $191.00 × 1.05^0.5 = $195.72.",1],[7,"An investor buys a call with strike $90 for $2.00. At expiry the stock is $95.00. What is the profit per share?",["$5.00","$3.00","$4.00"],1,"Profit = max(ST − X, 0) − premium = $5.00 − $2.00 = $3.00.",1],[7,"An investor buys a put with strike $55 for $3.00. At expiry the stock is $37.00. What is the profit per share?",["$18.00","$15.00","$16.00"],1,"Profit = max(X − ST, 0) − premium = $15.00.",1],[7,"In a one-period binomial model, the up factor is 1.24, the down factor is 0.80 and the risk-free rate is 5%. What is the risk-neutral probability of an up move?",["0.4318","0.5000","0.5682"],2,"π = (1 + r − d) ÷ (u − d) = 0.5682.",1],[7,"A stock at $54.00 can move to $70.20 or $44.82 in one period. The risk-free rate is 3%. What is a one-period European call with strike $54 worth?",["$7.86","$6.89","$6.69"],2,"π = 0.4255; c = [π × 16.20 + (1 − π) × 0.00] ÷ 1.03 = $6.69.",1],[8,"A hedge fund starts the year at $190m and ends at $229.90m before fees. It charges 2% of year-end assets and 20% of gains net of the management fee (no hurdle, above the high-water mark). Total fees are:",["$12.58m","$4.60m","$11.66m"],2,"Management fee = $4.60m; incentive fee = 20% × (229.90 − 4.60 − 190.00) = $7.06m; total $11.66m.",1],[8,"A property produces net operating income of $950k a year. Comparable properties sell at a cap rate of 7.75%. What is its estimated value?",["$7,363k","$12,258k","$10,857k"],1,"Value = NOI ÷ cap rate = $950k ÷ 7.75% = $12,258k.",1],[8,"A commodity futures position earned a price return of 4%, a roll return of −1% and a collateral return of 4%. What is its total return?",["7.00%","8.00%","4.00%"],0,"Total return = price + roll + collateral = 7.00%.",1],[8,"A private equity fund called $190m from investors and has returned $551.00m in total. What is its multiple on invested capital (MOIC)?",["0.34×","2.90×","1.90×"],1,"MOIC = total value returned ÷ invested capital = 2.90.",1],[9,"The risk-free rate is 3%, the expected market return is 8% and a stock's beta is 1.50. What is its CAPM expected return?",["12.00%","15.00%","10.50%"],2,"E(R) = Rf + β(Rm − Rf) = 3% + 1.50 × 5% = 10.50%.",1],[9,"A portfolio returned 15% with a beta of 1.50. The risk-free rate is 3%. What is its Treynor ratio?",["0.1800","0.0800","0.1000"],1,"Treynor = (Rp − Rf) ÷ β = 0.0800.",1],[9,"A portfolio returned 15% with beta 1.20. The market returned 8% and the risk-free rate was 3%. What is Jensen's alpha?",["12.00%","6.00%","7.00%"],1,"α = Rp − [Rf + β(Rm − Rf)] = 15% − 9.00% = 6.00%.",1],[9,"A portfolio holds 70% in a stock with beta 0.50 and the rest in a stock with beta 0.90. What is the portfolio beta?",["0.780","0.620","0.700"],1,"Portfolio beta = Σ weight × beta = 0.620.",1],[9,"An investor with risk aversion A = 6 considers a portfolio with expected return 12% and standard deviation 22%. What is its utility?",["−54.00%","−2.52%","−17.04%"],1,"U = E(R) − ½ × A × σ² = 12% − 0.5 × 6 × 0.0484 = −2.52%.",1],[9,"A portfolio returned 15% with σ 21%; the market returned 11% with σ 15%; Rf is 4%. What is M² (relative to the market)?",["0.86%","5.71%","4.00%"],0,"M² = (Rp − Rf) × σm ÷ σp + Rf − Rm = 0.86%.",1],[1,"An investor deposits $5,500 at 7% a year, compounded annually. What is it worth after 10 years?",["$10,111.53","$9,350.00","$10,819.33"],2,"FV = PV × (1 + r)^n = $5,500 × 1.07^10 = $10,819.33.",1],[1,"What is the present value of $23,000 received in 12 years if the discount rate is 8%?",["$9,133.62","$11,734.69","$9,864.31"],0,"PV = FV ÷ (1 + r)^n = $23,000 ÷ 1.08^12 = $9,133.62.",1],[1,"What is the present value of an ordinary annuity of $2,100 a year for 12 years at 8%?",["$25,200.00","$15,825.76","$17,091.82"],1,"PV = A × [1 − (1 + r)^−n] ÷ r = $15,825.76. An annuity due would be worth $17,091.82.",1],[1,"An investor saves $4,800 at the end of each year for 18 years at 6%. What is the future value?",["$148,347.13","$86,400.00","$157,247.96"],0,"FV = A × [(1 + r)^n − 1] ÷ r = $148,347.13.",1],[1,"A preferred share pays a fixed $4.00 a year forever. At a required return of 5.0%, what is it worth?",["$80.00","$84.00","$66.67"],0,"Perpetuity value = payment ÷ r = $4.00 ÷ 5.0% = $80.00.",1],[1,"A stated annual rate of 6% is compounded daily. What is the effective annual rate?",["6.000%","6.183%","6.384%"],1,"EAR = (1 + 6% ÷ 365)^365 − 1 = 6.183%.",1],[1,"A share bought at $117.00 is sold a year later at $138.00 after paying a dividend of $0.50. What is the holding period return?",["15.58%","18.38%","17.95%"],1,"HPR = (P1 − P0 + D) ÷ P0 = (138.00 − 117.00 + 0.50) ÷ 117.00 = 18.38%.",1],[1,"Annual returns over three years are 20%, 0%, 14%. What is the geometric mean return?",["17.00%","11.01%","11.33%"],1,"Geometric mean = [(1 + r1)(1 + r2)(1 + r3)]^(1/3) − 1 = 11.01%. The arithmetic mean is 11.33%.",1],[1,"Returns of −8%, 8%, 17% have probabilities of 0.20, 0.60, 0.20. What is the expected return?",["6.60%","8.00%","5.67%"],0,"E(R) = Σ p × R = 6.60%.",1],[1,"A portfolio holds 20% in asset A (σ = 20%) and 80% in asset B (σ = 19%). Their correlation is −0.30. What is the portfolio standard deviation?",["14.51%","19.20%","15.72%"],0,"σp = √(w²σA² + (1 − w)²σB² + 2w(1 − w)ρσAσB) = 14.51%.",1],[1,"An asset has a mean return of 11% and a standard deviation of 23%. What is its coefficient of variation?",["2.09","0.48","0.12"],0,"CV = σ ÷ mean = 23% ÷ 11% = 2.09.",1],[1,"A portfolio returned 16% with a standard deviation of 17%. The risk-free rate is 2%. What is its Sharpe ratio?",["4.844","0.824","0.941"],1,"Sharpe = (Rp − Rf) ÷ σp = (16% − 2%) ÷ 17% = 0.824.",1],[1,"A sample of 100 observations has a standard deviation of 32. What is the standard error of the sample mean?",["3.516","3.200","0.320"],1,"Standard error = s ÷ √n = 32 ÷ 10 = 3.200.",1],[1,"A portfolio has expected return 8% and standard deviation 10%. The minimum acceptable return is 5%. What is Roy's safety-first ratio?",["0.350","0.300","0.800"],1,"SFRatio = (E(R) − threshold) ÷ σ = 0.300. A higher ratio means lower shortfall risk.",1],[1,"Two independent events have probabilities 0.20 and 0.80. What is the probability that both occur?",["0.8400","0.5000","0.1600"],2,"For independent events, P(A and B) = P(A) × P(B) = 0.1600.",1],[2,"A 10% rise in price leads to a 5% fall in quantity demanded. What is the own-price elasticity of demand?",["2.00","−0.50","−0.05"],1,"Elasticity = %ΔQ ÷ %ΔP = −5% ÷ 10% = −0.50. Demand is inelastic.",1],[2,"EUR/USD is 1.1600 and USD/INR is 80.00. What is the EUR/INR cross rate?",["81.16","68.97","92.80"],2,"EUR/INR = EUR/USD × USD/INR = 1.1600 × 80.00 = 92.80 rupees per euro.",1],[2,"Spot USD/INR is 85.25. One-year rates are 6.6% in India and 3.8% in the US. By covered interest parity, the one-year forward USD/INR is:",["87.55","85.25","83.01"],0,"Forward = spot × (1 + i INR) ÷ (1 + i USD) = 87.55. The higher-rate currency (INR) trades at a forward discount.",1],[2,"Four firms in a market have shares of 7%, 20%, 32%, 5% (the rest are tiny). What is the Herfindahl-Hirschman Index (as a decimal)?",["0.1498","0.1600","0.6400"],0,"HHI = sum of squared shares = 0.07² + 0.20² + 0.32² + 0.05² = 0.1498.",1],[3,"A project costs $1,250 today and returns $240, $190, $660 over the next three years. At a 13% cost of capital, what is its NPV?",["−$160.00","−$431.40","−$487.48"],1,"NPV = −$1,250 + Σ CFt ÷ (1 + 13%)^t = −$431.40. Reject.",1],[3,"A firm's target weights are 50% debt and 50% equity. Pre-tax cost of debt is 5%, the tax rate is 32% and the cost of equity is 14%. What is the WACC?",["8.70%","9.50%","9.00%"],0,"WACC = wd × rd × (1 − t) + we × re = 8.70%.",1],[3,"The risk-free rate is 3%, the equity risk premium is 6% and the stock's beta is 1.60. What is the cost of equity under CAPM?",["12.60%","9.00%","9.60%"],0,"re = Rf + β × ERP = 3% + 1.60 × 6% = 12.60%.",1],[3,"Days of inventory on hand are 90, days sales outstanding 39 and days payables 58. What is the cash conversion cycle?",["109 days","71 days","187 days"],1,"CCC = DIO + DSO − DPO = 90 + 39 − 58 = 71 days.",1],[3,"A supplier offers terms of 2/15, net 60. What is the effective annual cost of not taking the discount?",["2.0%","17.8%","16.2%"],1,"Cost = (1 + 2/98)^(365/45) − 1 = 17.8%. Usually far above bank borrowing costs.",1],[3,"When sales rise 17%, operating income rises 25.5%. What is the degree of operating leverage?",["1.50","8.50","0.67"],0,"DOL = %Δ EBIT ÷ %Δ sales = 1.50.",1],[4,"Current assets are $250m, of which inventory is $110m (no prepaid expenses). Current liabilities are $570m. What is the quick ratio?",["0.44","0.19","0.25"],2,"Quick ratio = (current assets − inventory) ÷ current liabilities = 0.25. Current ratio = 0.44.",1],[4,"A company has a net profit margin of 10%, asset turnover of 1.70 and financial leverage (assets ÷ equity) of 1.80. What is its ROE?",["18.00%","17.00%","30.60%"],2,"DuPont: ROE = margin × turnover × leverage = 30.60%. ROA = 17.00%.",1],[4,"Cost of goods sold is $860m and average inventory is $340m. How many days of inventory on hand does the firm hold?",["144.3 days","2.5 days","9.2 days"],0,"Inventory turnover = 2.53; days of inventory = 365 ÷ 2.53 = 144.3 days.",1],[4,"Equipment costs $30,000, has a salvage value of $0 and a useful life of 5 years. What is annual straight-line depreciation?",["$6,000","$5,500","$6,500"],0,"(Cost − salvage) ÷ life = ($30,000 − $0) ÷ 5 = $6,000.",1],[4,"Equipment costs $190,000 with a 8-year life. What is first-year depreciation under the double-declining balance method?",["$35,625","$47,500","$23,750"],1,"DDB rate = 2 ÷ 8 = 25.0%; year 1 = $190,000 × 25.0% = $47,500. Salvage is ignored until the end.",1],[4,"A firm buys 130 units at $20 and later 300 units at $25, then sells 370 units. What is cost of goods sold under FIFO?",["$8,900","$8,600","$8,691"],1,"FIFO uses the oldest costs first: 130 × $20 + 240 × $25 = $8,600. LIFO would give $8,900.",1],[4,"Net income is $200m, preferred dividends are $10m and the weighted average number of common shares is 25m. What is basic EPS?",["$8.40","$7.60","$8.00"],1,"Basic EPS = (NI − preferred dividends) ÷ weighted shares = $7.60.",1],[4,"EBIT is $590m and interest expense is $90m. What is the interest coverage ratio?",["0.15×","5.56×","6.56×"],2,"Interest coverage = EBIT ÷ interest = 6.56 times.",1],[4,"Tax depreciation exceeds book depreciation, creating a cumulative temporary difference of $130m. At a 25% tax rate, what is the deferred tax liability?",["$32.50m","$97.50m","$130.00m"],0,"DTL = temporary difference × tax rate = $130m × 25% = $32.50m.",1],[5,"A stock just paid a dividend of $4.75. Dividends grow at 4% forever and the required return is 9%. What is its value?",["$98.80","$95.00","$54.89"],0,"Gordon model: V0 = D0(1 + g) ÷ (r − g) = $4.94 ÷ 5% = $98.80.",1],[5,"A company retains 50% of earnings and has an ROE of 13%. What is its sustainable growth rate?",["13.00%","6.50%","7.00%"],1,"g = retention ratio × ROE = 50% × 13% = 6.50%.",1],[5,"A firm pays out 70% of earnings, grows at 5% and has a required return of 12%. What is its justified forward P/E?",["4.29×","10.00×","5.83×"],1,"Justified forward P/E = payout ÷ (r − g) = 0.70 ÷ 7% = 10.00.",1],[5,"An investor buys a share at $64.00 with 40% initial margin. The maintenance margin is 30%. Below what price will a margin call occur?",["$44.80","$54.86","$25.60"],1,"Trigger price = P0 × (1 − initial margin) ÷ (1 − maintenance margin) = $54.86.",1],[5,"A share is bought at $39.00 with 50% margin and sold at $46.41 (ignore interest and dividends). What is the return on the investor's equity?",["9.50%","38.00%","19.00%"],1,"Return = price change ÷ equity invested = (46.41 − 39.00) ÷ $19.50 = 38.00%. Leverage is 1 ÷ 0.50.",1],[5,"A price-weighted index has three stocks priced at $32, $95, $20, with a divisor of 3. What is the index value?",["49.00","95.00","147.00"],0,"Price-weighted index = sum of prices ÷ divisor = 49.00. The highest-priced stock has the most weight.",1],[5,"A firm has equity market value of $1,550m, debt of $150m and cash of $750m. What is its enterprise value?",["$950m","$2,450m","$800m"],0,"EV = equity + debt − cash = $950m.",1],[5,"A non-callable, non-convertible preferred share pays $6.00 a year. The required return is 5.5%. What is its value?",["$80.00","$33.00","$109.09"],2,"Value = dividend ÷ required return = $109.09.",1],[6,"A 4-year bond pays an annual coupon of 9% on a par of 100. If the yield to maturity is 7%, what is its price?",["128.57","97.00","106.77"],2,"Price = Σ coupon ÷ (1 + y)^t + 100 ÷ (1 + y)^4 = 106.77. Coupon above yield, so a premium.",1],[6,"A bond with a 3% annual coupon on par 100 trades at 97.00. What is its current yield?",["3.09%","2.91%","3.00%"],0,"Current yield = annual coupon ÷ price = 3.00 ÷ 97.00 = 3.09%.",1],[6,"A bond has modified duration of 10.60. If its yield falls by 100 basis points, the approximate percentage change in price is:",["10.60%","−10.60%","21.20%"],0,"%ΔP ≈ −ModDur × Δy = −10.60 × −1.00% = 10.60%.",1],[6,"A bond has modified duration 7.50 and convexity 42. For a fall in yield of 100 bp, the estimated price change including convexity is:",["7.500%","7.290%","7.710%"],2,"%ΔP ≈ −ModDur × Δy + ½ × convexity × (Δy)² = 7.710%.",1],[6,"A bond's Macaulay duration is 7.10 years and its yield is 7% (annual periodicity). What is its modified duration?",["7.100","7.597","6.636"],2,"ModDur = MacDur ÷ (1 + y/k) = 7.10 ÷ 1.0700 = 6.636.",1],[6,"The 1-year spot rate is 2.4% and the 2-year spot rate is 3.4%. What is the 1-year forward rate one year from now?",["4.600%","2.900%","4.410%"],2,"(1 + S2)² = (1 + S1)(1 + f) gives f = 4.410%.",1],[6,"A bond exposure of $500m has a probability of default of 0.7% and an expected recovery rate of 30%. What is the expected loss?",["$1.05m","$3.50m","$2.45m"],2,"Expected loss = PD × exposure × (1 − recovery) = $2.45m.",1],[6,"A bond pays a 7% coupon semi-annually on par 100 (30/360 basis). It has been 50 days since the last coupon. What is the accrued interest?",["3.500","1.944","0.972"],2,"AI = (coupon per period) × days ÷ 180 = 3.50 × 50 ÷ 180 = 0.972.",1],[7,"A non-dividend-paying share trades at $196.00. The risk-free rate is 2% (annual compounding). What is the no-arbitrage forward price for 3 months?",["$196.00","$196.97","$199.92"],1,"F0 = S0 × (1 + r)^T = $196.00 × 1.02^0.25 = $196.97.",1],[7,"An investor buys a call with strike $85 for $2.00. At expiry the stock is $75.00. What is the profit per share?",["−$10.00","−$2.00","$0.00"],1,"Profit = max(ST − X, 0) − premium = $0.00 − $2.00 = −$2.00.",1],[7,"An investor buys a put with strike $55 for $4.00. At expiry the stock is $32.00. What is the profit per share?",["$19.00","$23.00","$20.00"],0,"Profit = max(X − ST, 0) − premium = $19.00.",1],[7,"In a one-period binomial model, the up factor is 1.17, the down factor is 0.91 and the risk-free rate is 3%. What is the risk-neutral probability of an up move?",["0.5000","0.4615","0.5385"],1,"π = (1 + r − d) ÷ (u − d) = 0.4615.",1],[7,"A stock at $80.00 can move to $96.00 or $68.80 in one period. The risk-free rate is 6%. What is a one-period European call with strike $80 worth?",["$8.88","$7.55","$9.41"],0,"π = 0.5882; c = [π × 16.00 + (1 − π) × 0.00] ÷ 1.06 = $8.88.",1],[8,"A hedge fund starts the year at $180m and ends at $234.00m before fees. It charges 2% of year-end assets and 20% of gains net of the management fee (no hurdle, above the high-water mark). Total fees are:",["$14.54m","$15.48m","$4.68m"],0,"Management fee = $4.68m; incentive fee = 20% × (234.00 − 4.68 − 180.00) = $9.86m; total $14.54m.",1],[8,"A property produces net operating income of $1,400k a year. Comparable properties sell at a cap rate of 7.00%. What is its estimated value?",["$17,500k","$9,800k","$20,000k"],2,"Value = NOI ÷ cap rate = $1,400k ÷ 7.00% = $20,000k.",1],[8,"A commodity futures position earned a price return of −8%, a roll return of −3% and a collateral return of 5%. What is its total return?",["−8.00%","−3.00%","−6.00%"],2,"Total return = price + roll + collateral = −6.00%.",1],[8,"A private equity fund called $180m from investors and has returned $450.00m in total. What is its multiple on invested capital (MOIC)?",["0.40×","2.50×","1.50×"],1,"MOIC = total value returned ÷ invested capital = 2.50.",1],[9,"The risk-free rate is 4%, the expected market return is 9% and a stock's beta is 1.60. What is its CAPM expected return?",["12.00%","18.40%","14.40%"],0,"E(R) = Rf + β(Rm − Rf) = 4% + 1.60 × 5% = 12.00%.",1],[9,"A portfolio returned 16% with a beta of 1.10. The risk-free rate is 3%. What is its Treynor ratio?",["0.1182","0.1430","0.1455"],0,"Treynor = (Rp − Rf) ÷ β = 0.1182.",1],[9,"A portfolio returned 7% with beta 0.60. The market returned 13% and the risk-free rate was 3%. What is Jensen's alpha?",["−6.00%","4.00%","−2.00%"],2,"α = Rp − [Rf + β(Rm − Rf)] = 7% − 9.00% = −2.00%.",1],[9,"A portfolio holds 50% in a stock with beta 0.60 and the rest in a stock with beta 1.30. What is the portfolio beta?",["0.950","0.900","1.000"],0,"Portfolio beta = Σ weight × beta = 0.950.",1],[9,"An investor with risk aversion A = 2 considers a portfolio with expected return 13% and standard deviation 16%. What is its utility?",["7.88%","10.44%","−3.00%"],1,"U = E(R) − ½ × A × σ² = 13% − 0.5 × 2 × 0.0256 = 10.44%.",1],[9,"A portfolio returned 15% with σ 15%; the market returned 12% with σ 17%; Rf is 5%. What is M² (relative to the market)?",["3.00%","25.49%","4.33%"],2,"M² = (Rp − Rf) × σm ÷ σp + Rf − Rm = 4.33%.",1],[1,"An investor deposits $16,000 at 4% a year, compounded annually. What is it worth after 2 years?",["$17,305.60","$17,280.00","$16,640.00"],0,"FV = PV × (1 + r)^n = $16,000 × 1.04^2 = $17,305.60.",1],[1,"What is the present value of $24,000 received in 12 years if the discount rate is 5%?",["$14,032.30","$15,000.00","$13,364.10"],2,"PV = FV ÷ (1 + r)^n = $24,000 ÷ 1.05^12 = $13,364.10.",1],[1,"What is the present value of an ordinary annuity of $700 a year for 8 years at 4%?",["$5,600.00","$4,901.44","$4,712.92"],2,"PV = A × [1 − (1 + r)^−n] ÷ r = $4,712.92. An annuity due would be worth $4,901.44.",1],[1,"An investor saves $1,400 at the end of each year for 19 years at 4%. What is the future value?",["$26,600.00","$38,739.72","$40,289.31"],1,"FV = A × [(1 + r)^n − 1] ÷ r = $38,739.72.",1],[1,"A preferred share pays a fixed $6.50 a year forever. At a required return of 9.5%, what is it worth?",["$68.42","$74.92","$61.90"],0,"Perpetuity value = payment ÷ r = $6.50 ÷ 9.5% = $68.42.",1],[1,"A share bought at $104.00 is sold a year later at $121.00 after paying a dividend of $1.50. What is the holding period return?",["17.79%","16.35%","15.29%"],0,"HPR = (P1 − P0 + D) ÷ P0 = (121.00 − 104.00 + 1.50) ÷ 104.00 = 17.79%.",1],[1,"Annual returns over three years are 14%, 18%, 7%. What is the geometric mean return?",["13.00%","12.91%","10.50%"],1,"Geometric mean = [(1 + r1)(1 + r2)(1 + r3)]^(1/3) − 1 = 12.91%. The arithmetic mean is 13.00%.",1],[1,"Returns of −2%, 4%, 11% have probabilities of 0.20, 0.20, 0.60. What is the expected return?",["4.00%","7.00%","4.33%"],1,"E(R) = Σ p × R = 7.00%.",1],[1,"A portfolio holds 80% in asset A (σ = 15%) and 20% in asset B (σ = 16%). Their correlation is 0.30. What is the portfolio standard deviation?",["15.20%","12.42%","13.31%"],2,"σp = √(w²σA² + (1 − w)²σB² + 2w(1 − w)ρσAσB) = 13.31%.",1],[1,"An asset has a mean return of 12% and a standard deviation of 20%. What is its coefficient of variation?",["0.08","1.67","0.60"],1,"CV = σ ÷ mean = 20% ÷ 12% = 1.67.",1],[1,"A portfolio returned 11% with a standard deviation of 14%. The risk-free rate is 5%. What is its Sharpe ratio?",["3.061","0.429","0.786"],1,"Sharpe = (Rp − Rf) ÷ σp = (11% − 5%) ÷ 14% = 0.429.",1],[1,"A sample of 36 observations has a standard deviation of 24. What is the standard error of the sample mean?",["4.357","4.000","0.667"],1,"Standard error = s ÷ √n = 24 ÷ 6 = 4.000.",1],[1,"A portfolio has expected return 14% and standard deviation 15%. The minimum acceptable return is 2%. What is Roy's safety-first ratio?",["0.933","0.800","0.533"],1,"SFRatio = (E(R) − threshold) ÷ σ = 0.800. A higher ratio means lower shortfall risk.",1],[1,"Two independent events have probabilities 0.50 and 0.50. What is the probability that both occur?",["0.5000","0.7500","0.2500"],2,"For independent events, P(A and B) = P(A) × P(B) = 0.2500.",1],[2,"A 7% rise in price leads to a 16% fall in quantity demanded. What is the own-price elasticity of demand?",["−2.29","0.44","−0.16"],0,"Elasticity = %ΔQ ÷ %ΔP = −16% ÷ 7% = −2.29. Demand is elastic.",1],[2,"EUR/USD is 1.2000 and USD/INR is 87.75. What is the EUR/INR cross rate?",["88.95","73.13","105.30"],2,"EUR/INR = EUR/USD × USD/INR = 1.2000 × 87.75 = 105.30 rupees per euro.",1],[2,"Spot USD/INR is 84.75. One-year rates are 5.7% in India and 4.3% in the US. By covered interest parity, the one-year forward USD/INR is:",["84.75","85.89","83.63"],1,"Forward = spot × (1 + i INR) ÷ (1 + i USD) = 85.89. The higher-rate currency (INR) trades at a forward discount.",1],[2,"Four firms in a market have shares of 26%, 14%, 6%, 28% (the rest are tiny). What is the Herfindahl-Hirschman Index (as a decimal)?",["0.1692","0.7400","0.1850"],0,"HHI = sum of squared shares = 0.26² + 0.14² + 0.06² + 0.28² = 0.1692.",1],[3,"A project costs $900 today and returns $420, $660, $790 over the next three years. At a 11% cost of capital, what is its NPV?",["$591.69","$656.78","$970.00"],0,"NPV = −$900 + Σ CFt ÷ (1 + 11%)^t = $591.69. Accept.",1],[3,"A firm's target weights are 50% debt and 50% equity. Pre-tax cost of debt is 7%, the tax rate is 34% and the cost of equity is 12%. What is the WACC?",["8.31%","9.50%","8.61%"],0,"WACC = wd × rd × (1 − t) + we × re = 8.31%.",1],[3,"The risk-free rate is 3%, the equity risk premium is 7% and the stock's beta is 1.00. What is the cost of equity under CAPM?",["10.00%","7.00%","10.50%"],0,"re = Rf + β × ERP = 3% + 1.00 × 7% = 10.00%.",1],[3,"Days of inventory on hand are 86, days sales outstanding 38 and days payables 60. What is the cash conversion cycle?",["184 days","108 days","64 days"],2,"CCC = DIO + DSO − DPO = 86 + 38 − 60 = 64 days.",1],[3,"When sales rise 12%, operating income rises 27.6%. What is the degree of operating leverage?",["2.30","0.43","15.60"],0,"DOL = %Δ EBIT ÷ %Δ sales = 2.30.",1],[4,"Current assets are $510m, of which inventory is $150m (no prepaid expenses). Current liabilities are $390m. What is the quick ratio?",["1.31","0.38","0.92"],2,"Quick ratio = (current assets − inventory) ÷ current liabilities = 0.92. Current ratio = 1.31.",1],[4,"A company has a net profit margin of 4%, asset turnover of 1.90 and financial leverage (assets ÷ equity) of 2.30. What is its ROE?",["9.20%","7.60%","17.48%"],2,"DuPont: ROE = margin × turnover × leverage = 17.48%. ROA = 7.60%.",1],[4,"Cost of goods sold is $560m and average inventory is $170m. How many days of inventory on hand does the firm hold?",["12.0 days","3.3 days","110.8 days"],2,"Inventory turnover = 3.29; days of inventory = 365 ÷ 3.29 = 110.8 days.",1],[4,"Equipment costs $130,000, has a salvage value of $11,000 and a useful life of 5 years. What is annual straight-line depreciation?",["$28,200","$23,800","$26,000"],1,"(Cost − salvage) ÷ life = ($130,000 − $11,000) ÷ 5 = $23,800.",1],[4,"Equipment costs $135,000 with a 9-year life. What is first-year depreciation under the double-declining balance method?",["$23,333","$15,000","$30,000"],2,"DDB rate = 2 ÷ 9 = 22.2%; year 1 = $135,000 × 22.2% = $30,000. Salvage is ignored until the end.",1],[4,"A firm buys 210 units at $19 and later 210 units at $24, then sells 360 units. What is cost of goods sold under FIFO?",["$7,590","$7,740","$7,890"],0,"FIFO uses the oldest costs first: 210 × $19 + 150 × $24 = $7,590. LIFO would give $7,890.",1],[4,"Net income is $205m, preferred dividends are $25m and the weighted average number of common shares is 115m. What is basic EPS?",["$1.78","$1.57","$2.00"],1,"Basic EPS = (NI − preferred dividends) ÷ weighted shares = $1.57.",1],[4,"EBIT is $690m and interest expense is $140m. What is the interest coverage ratio?",["3.93×","4.93×","0.20×"],1,"Interest coverage = EBIT ÷ interest = 4.93 times.",1],[4,"Tax depreciation exceeds book depreciation, creating a cumulative temporary difference of $65m. At a 29% tax rate, what is the deferred tax liability?",["$18.85m","$65.00m","$46.15m"],0,"DTL = temporary difference × tax rate = $65m × 29% = $18.85m.",1],[5,"A stock just paid a dividend of $5.50. Dividends grow at 3% forever and the required return is 8%. What is its value?",["$70.81","$110.00","$113.30"],2,"Gordon model: V0 = D0(1 + g) ÷ (r − g) = $5.67 ÷ 5% = $113.30.",1],[5,"A company retains 60% of earnings and has an ROE of 21%. What is its sustainable growth rate?",["8.40%","12.60%","21.00%"],1,"g = retention ratio × ROE = 60% × 21% = 12.60%.",1],[5,"A firm pays out 60% of earnings, grows at 5% and has a required return of 11%. What is its justified forward P/E?",["6.67×","10.00×","5.45×"],1,"Justified forward P/E = payout ÷ (r − g) = 0.60 ÷ 6% = 10.00.",1],[5,"An investor buys a share at $99.00 with 40% initial margin. The maintenance margin is 30%. Below what price will a margin call occur?",["$69.30","$39.60","$84.86"],2,"Trigger price = P0 × (1 − initial margin) ÷ (1 − maintenance margin) = $84.86.",1],[5,"A share is bought at $65.00 with 40% margin and sold at $54.60 (ignore interest and dividends). What is the return on the investor's equity?",["−16.00%","−6.40%","−40.00%"],2,"Return = price change ÷ equity invested = (54.60 − 65.00) ÷ $26.00 = −40.00%. Leverage is 1 ÷ 0.40.",1],[5,"A price-weighted index has three stocks priced at $90, $46, $67, with a divisor of 3. What is the index value?",["90.00","67.67","203.00"],1,"Price-weighted index = sum of prices ÷ divisor = 67.67. The highest-priced stock has the most weight.",1],[5,"A firm has equity market value of $4,000m, debt of $1,250m and cash of $590m. What is its enterprise value?",["$3,410m","$4,660m","$5,840m"],1,"EV = equity + debt − cash = $4,660m.",1],[5,"A non-callable, non-convertible preferred share pays $4.00 a year. The required return is 8.5%. What is its value?",["$38.10","$47.06","$34.00"],1,"Value = dividend ÷ required return = $47.06.",1],[6,"A 6-year bond pays an annual coupon of 9% on a par of 100. If the yield to maturity is 7%, what is its price?",["128.57","97.00","109.53"],2,"Price = Σ coupon ÷ (1 + y)^t + 100 ÷ (1 + y)^6 = 109.53. Coupon above yield, so a premium.",1],[6,"A bond with a 8% annual coupon on par 100 trades at 88.00. What is its current yield?",["7.04%","8.00%","9.09%"],2,"Current yield = annual coupon ÷ price = 8.00 ÷ 88.00 = 9.09%.",1],[6,"A bond has modified duration of 7.90. If its yield falls by 25 basis points, the approximate percentage change in price is:",["1.98%","3.95%","−1.98%"],0,"%ΔP ≈ −ModDur × Δy = −7.90 × −0.25% = 1.98%.",1],[6,"A bond has modified duration 9.30 and convexity 46. For a rise in yield of 100 bp, the estimated price change including convexity is:",["−9.070%","−9.300%","−9.530%"],0,"%ΔP ≈ −ModDur × Δy + ½ × convexity × (Δy)² = −9.070%.",1],[6,"A bond's Macaulay duration is 9.70 years and its yield is 2% (semi-annual periodicity). What is its modified duration?",["9.797","9.604","9.700"],1,"ModDur = MacDur ÷ (1 + y/k) = 9.70 ÷ 1.0100 = 9.604.",1],[6,"The 1-year spot rate is 4.7% and the 2-year spot rate is 4.3%. What is the 1-year forward rate one year from now?",["3.902%","4.500%","4.100%"],0,"(1 + S2)² = (1 + S1)(1 + f) gives f = 3.902%.",1],[6,"A bond exposure of $600m has a probability of default of 1.3% and an expected recovery rate of 27%. What is the expected loss?",["$2.11m","$5.69m","$7.80m"],1,"Expected loss = PD × exposure × (1 − recovery) = $5.69m.",1],[6,"A bond pays a 4% coupon semi-annually on par 100 (30/360 basis). It has been 157 days since the last coupon. What is the accrued interest?",["3.489","2.000","1.744"],2,"AI = (coupon per period) × days ÷ 180 = 2.00 × 157 ÷ 180 = 1.744.",1],[7,"A non-dividend-paying share trades at $73.00. The risk-free rate is 6% (annual compounding). What is the no-arbitrage forward price for 3 months?",["$74.07","$73.00","$77.38"],0,"F0 = S0 × (1 + r)^T = $73.00 × 1.06^0.25 = $74.07.",1],[7,"A European call with strike $71 and one year to expiry costs $14.00. The stock is at $76.00 and the risk-free rate is 2%. By put-call parity, the put with the same terms is worth:",["$7.61","$9.00","$20.39"],0,"p = c + X ÷ (1 + r) − S = 14.00 + 69.61 − 76.00 = $7.61.",1],[7,"An investor buys a call with strike $65 for $4.00. At expiry the stock is $65.00. What is the profit per share?",["−$3.00","$0.00","−$4.00"],2,"Profit = max(ST − X, 0) − premium = $0.00 − $4.00 = −$4.00.",1],[7,"An investor buys a put with strike $60 for $6.00. At expiry the stock is $35.00. What is the profit per share?",["$25.00","$20.00","$19.00"],2,"Profit = max(X − ST, 0) − premium = $19.00.",1],[7,"In a one-period binomial model, the up factor is 1.17, the down factor is 0.89 and the risk-free rate is 6%. What is the risk-neutral probability of an up move?",["0.5000","0.6071","0.3929"],1,"π = (1 + r − d) ÷ (u − d) = 0.6071.",1],[7,"A stock at $131.00 can move to $163.75 or $113.97 in one period. The risk-free rate is 2%. What is a one-period European call with strike $131 worth?",["$12.67","$16.05","$12.93"],0,"π = 0.3947; c = [π × 32.75 + (1 − π) × 0.00] ÷ 1.02 = $12.67.",1],[8,"A hedge fund starts the year at $230m and ends at $269.10m before fees. It charges 2% of year-end assets and 20% of gains net of the management fee (no hurdle, above the high-water mark). Total fees are:",["$13.20m","$12.13m","$5.38m"],1,"Management fee = $5.38m; incentive fee = 20% × (269.10 − 5.38 − 230.00) = $6.74m; total $12.13m.",1],[8,"A property produces net operating income of $2,800k a year. Comparable properties sell at a cap rate of 8.00%. What is its estimated value?",["$22,400k","$35,000k","$31,111k"],1,"Value = NOI ÷ cap rate = $2,800k ÷ 8.00% = $35,000k.",1],[8,"A commodity futures position earned a price return of 15%, a roll return of 2% and a collateral return of 5%. What is its total return?",["20.00%","22.00%","15.00%"],1,"Total return = price + roll + collateral = 22.00%.",1],[8,"A private equity fund called $100m from investors and has returned $210.00m in total. What is its multiple on invested capital (MOIC)?",["2.10×","0.48×","1.10×"],0,"MOIC = total value returned ÷ invested capital = 2.10.",1],[9,"The risk-free rate is 6%, the expected market return is 9% and a stock's beta is 1.80. What is its CAPM expected return?",["22.20%","11.40%","16.20%"],1,"E(R) = Rf + β(Rm − Rf) = 6% + 1.80 × 3% = 11.40%.",1],[9,"A portfolio returned 16% with a beta of 1.50. The risk-free rate is 3%. What is its Treynor ratio?",["0.0867","0.1067","0.1950"],0,"Treynor = (Rp − Rf) ÷ β = 0.0867.",1],[9,"A portfolio returned 7% with beta 1.30. The market returned 10% and the risk-free rate was 3%. What is Jensen's alpha?",["−5.10%","−3.00%","4.00%"],0,"α = Rp − [Rf + β(Rm − Rf)] = 7% − 12.10% = −5.10%.",1],[9,"A portfolio holds 40% in a stock with beta 0.50 and the rest in a stock with beta 1.20. What is the portfolio beta?",["0.850","0.920","0.780"],1,"Portfolio beta = Σ weight × beta = 0.920.",1],[9,"An investor with risk aversion A = 5 considers a portfolio with expected return 15% and standard deviation 26%. What is its utility?",["−1.90%","−18.80%","−50.00%"],0,"U = E(R) − ½ × A × σ² = 15% − 0.5 × 5 × 0.0676 = −1.90%.",1],[9,"A portfolio returned 12% with σ 22%; the market returned 10% with σ 15%; Rf is 2%. What is M² (relative to the market)?",["−7.88%","−1.18%","2.00%"],1,"M² = (Rp − Rf) × σm ÷ σp + Rf − Rm = −1.18%.",1],[1,"An investor deposits $18,000 at 11% a year, compounded annually. What is it worth after 4 years?",["$24,617.36","$25,920.00","$27,325.27"],2,"FV = PV × (1 + r)^n = $18,000 × 1.11^4 = $27,325.27.",1],[1,"What is the present value of $33,000 received in 8 years if the discount rate is 7%?",["$20,550.74","$21,153.85","$19,206.30"],2,"PV = FV ÷ (1 + r)^n = $33,000 ÷ 1.07^8 = $19,206.30.",1],[1,"What is the present value of an ordinary annuity of $4,900 a year for 6 years at 5%?",["$24,870.89","$26,114.44","$29,400.00"],0,"PV = A × [1 − (1 + r)^−n] ÷ r = $24,870.89. An annuity due would be worth $26,114.44.",1],[1,"An investor saves $4,400 at the end of each year for 9 years at 7%. What is the future value?",["$39,600.00","$56,392.37","$52,703.15"],2,"FV = A × [(1 + r)^n − 1] ÷ r = $52,703.15.",1],[1,"A preferred share pays a fixed $11.50 a year forever. At a required return of 7.5%, what is it worth?",["$135.29","$164.83","$153.33"],2,"Perpetuity value = payment ÷ r = $11.50 ÷ 7.5% = $153.33.",1],[1,"A stated annual rate of 11% is compounded semi-annually. What is the effective annual rate?",["11.828%","11.302%","11.000%"],1,"EAR = (1 + 11% ÷ 2)^2 − 1 = 11.302%.",1],[1,"A share bought at $58.00 is sold a year later at $57.00 after paying a dividend of $0.00. What is the holding period return?",["−0.72%","−1.75%","−1.72%"],2,"HPR = (P1 − P0 + D) ÷ P0 = (57.00 − 58.00 + 0.00) ÷ 58.00 = −1.72%.",1],[1,"Annual returns over three years are 14%, 0%, 6%. What is the geometric mean return?",["10.00%","6.51%","6.67%"],1,"Geometric mean = [(1 + r1)(1 + r2)(1 + r3)]^(1/3) − 1 = 6.51%. The arithmetic mean is 6.67%.",1],[1,"Returns of −1%, 6%, 18% have probabilities of 0.10, 0.10, 0.80. What is the expected return?",["6.00%","14.90%","7.67%"],1,"E(R) = Σ p × R = 14.90%.",1],[1,"A portfolio holds 50% in asset A (σ = 13%) and 50% in asset B (σ = 27%). Their correlation is 0.80. What is the portfolio standard deviation?",["14.98%","19.10%","20.00%"],1,"σp = √(w²σA² + (1 − w)²σB² + 2w(1 − w)ρσAσB) = 19.10%.",1],[1,"An asset has a mean return of 10% and a standard deviation of 24%. What is its coefficient of variation?",["2.40","0.42","0.14"],0,"CV = σ ÷ mean = 24% ÷ 10% = 2.40.",1],[1,"A portfolio returned 12% with a standard deviation of 14%. The risk-free rate is 3%. What is its Sharpe ratio?",["4.592","0.643","0.857"],1,"Sharpe = (Rp − Rf) ÷ σp = (12% − 3%) ÷ 14% = 0.643.",1],[1,"A sample of 64 observations has a standard deviation of 29. What is the standard error of the sample mean?",["0.453","3.954","3.625"],2,"Standard error = s ÷ √n = 29 ÷ 8 = 3.625.",1],[1,"A portfolio has expected return 7% and standard deviation 20%. The minimum acceptable return is 3%. What is Roy's safety-first ratio?",["0.100","0.200","0.350"],1,"SFRatio = (E(R) − threshold) ÷ σ = 0.200. A higher ratio means lower shortfall risk.",1],[2,"A 8% rise in price leads to a 30% fall in quantity demanded. What is the own-price elasticity of demand?",["−0.30","0.27","−3.75"],2,"Elasticity = %ΔQ ÷ %ΔP = −30% ÷ 8% = −3.75. Demand is elastic.",1],[2,"EUR/USD is 1.2000 and USD/INR is 85.00. What is the EUR/INR cross rate?",["70.83","102.00","86.20"],1,"EUR/INR = EUR/USD × USD/INR = 1.2000 × 85.00 = 102.00 rupees per euro.",1],[2,"Spot USD/INR is 82.00. One-year rates are 6.7% in India and 3.2% in the US. By covered interest parity, the one-year forward USD/INR is:",["79.31","82.00","84.78"],2,"Forward = spot × (1 + i INR) ÷ (1 + i USD) = 84.78. The higher-rate currency (INR) trades at a forward discount.",1],[2,"Four firms in a market have shares of 38%, 15%, 20%, 24% (the rest are tiny). What is the Herfindahl-Hirschman Index (as a decimal)?",["0.2425","0.9700","0.2645"],2,"HHI = sum of squared shares = 0.38² + 0.15² + 0.20² + 0.24² = 0.2645.",1],[3,"A project costs $700 today and returns $220, $240, $170 over the next three years. At a 11% cost of capital, what is its NPV?",["−$70.00","−$182.71","−$202.81"],1,"NPV = −$700 + Σ CFt ÷ (1 + 11%)^t = −$182.71. Reject.",1],[3,"A firm's target weights are 20% debt and 80% equity. Pre-tax cost of debt is 10%, the tax rate is 30% and the cost of equity is 14%. What is the WACC?",["13.20%","12.00%","12.60%"],2,"WACC = wd × rd × (1 − t) + we × re = 12.60%.",1],[3,"The risk-free rate is 3%, the equity risk premium is 4% and the stock's beta is 0.70. What is the cost of equity under CAPM?",["5.80%","2.80%","7.00%"],0,"re = Rf + β × ERP = 3% + 0.70 × 4% = 5.80%.",1],[3,"Days of inventory on hand are 69, days sales outstanding 45 and days payables 26. What is the cash conversion cycle?",["88 days","50 days","140 days"],0,"CCC = DIO + DSO − DPO = 69 + 45 − 26 = 88 days.",1],[3,"A supplier offers terms of 2/15, net 30. What is the effective annual cost of not taking the discount?",["63.5%","2.0%","48.7%"],0,"Cost = (1 + 2/98)^(365/15) − 1 = 63.5%. Usually far above bank borrowing costs.",1],[3,"When sales rise 6%, operating income rises 14.4%. What is the degree of operating leverage?",["2.40","0.42","8.40"],0,"DOL = %Δ EBIT ÷ %Δ sales = 2.40.",1],[4,"Current assets are $380m, of which inventory is $90m (no prepaid expenses). Current liabilities are $590m. What is the quick ratio?",["0.15","0.49","0.64"],1,"Quick ratio = (current assets − inventory) ÷ current liabilities = 0.49. Current ratio = 0.64.",1],[4,"A company has a net profit margin of 11%, asset turnover of 1.80 and financial leverage (assets ÷ equity) of 3.00. What is its ROE?",["19.80%","59.40%","33.00%"],1,"DuPont: ROE = margin × turnover × leverage = 59.40%. ROA = 19.80%.",1],[4,"Cost of goods sold is $1,420m and average inventory is $220m. How many days of inventory on hand does the firm hold?",["56.5 days","23.6 days","6.5 days"],0,"Inventory turnover = 6.45; days of inventory = 365 ÷ 6.45 = 56.5 days.",1],[4,"Equipment costs $50,000, has a salvage value of $7,000 and a useful life of 8 years. What is annual straight-line depreciation?",["$5,375","$6,250","$7,125"],0,"(Cost − salvage) ÷ life = ($50,000 − $7,000) ÷ 8 = $5,375.",1],[4,"Equipment costs $200,000 with a 9-year life. What is first-year depreciation under the double-declining balance method?",["$34,568","$22,222","$44,444"],2,"DDB rate = 2 ÷ 9 = 22.2%; year 1 = $200,000 × 22.2% = $44,444. Salvage is ignored until the end.",1],[4,"A firm buys 140 units at $17 and later 170 units at $21, then sells 230 units. What is cost of goods sold under FIFO?",["$4,415","$4,270","$4,590"],1,"FIFO uses the oldest costs first: 140 × $17 + 90 × $21 = $4,270. LIFO would give $4,590.",1],[4,"Net income is $445m, preferred dividends are $15m and the weighted average number of common shares is 190m. What is basic EPS?",["$2.26","$2.42","$2.34"],0,"Basic EPS = (NI − preferred dividends) ÷ weighted shares = $2.26.",1],[4,"EBIT is $300m and interest expense is $115m. What is the interest coverage ratio?",["1.61×","2.61×","0.38×"],1,"Interest coverage = EBIT ÷ interest = 2.61 times.",1],[4,"Tax depreciation exceeds book depreciation, creating a cumulative temporary difference of $50m. At a 21% tax rate, what is the deferred tax liability?",["$10.50m","$39.50m","$50.00m"],0,"DTL = temporary difference × tax rate = $50m × 21% = $10.50m.",1],[5,"A stock just paid a dividend of $1.25. Dividends grow at 3% forever and the required return is 6%. What is its value?",["$42.92","$21.46","$41.67"],0,"Gordon model: V0 = D0(1 + g) ÷ (r − g) = $1.29 ÷ 3% = $42.92.",1],[5,"A company retains 40% of earnings and has an ROE of 8%. What is its sustainable growth rate?",["4.80%","8.00%","3.20%"],2,"g = retention ratio × ROE = 40% × 8% = 3.20%.",1],[5,"A firm pays out 40% of earnings, grows at 4% and has a required return of 7%. What is its justified forward P/E?",["13.33×","5.71×","20.00×"],0,"Justified forward P/E = payout ÷ (r − g) = 0.40 ÷ 3% = 13.33.",1],[5,"An investor buys a share at $106.00 with 40% initial margin. The maintenance margin is 25%. Below what price will a margin call occur?",["$79.50","$84.80","$42.40"],1,"Trigger price = P0 × (1 − initial margin) ÷ (1 − maintenance margin) = $84.80.",1],[5,"A share is bought at $120.00 with 50% margin and sold at $127.20 (ignore interest and dividends). What is the return on the investor's equity?",["3.00%","6.00%","12.00%"],2,"Return = price change ÷ equity invested = (127.20 − 120.00) ÷ $60.00 = 12.00%. Leverage is 1 ÷ 0.50.",1],[5,"A price-weighted index has three stocks priced at $29, $112, $54, with a divisor of 3. What is the index value?",["195.00","112.00","65.00"],2,"Price-weighted index = sum of prices ÷ divisor = 65.00. The highest-priced stock has the most weight.",1],[5,"A firm has equity market value of $4,050m, debt of $1,000m and cash of $680m. What is its enterprise value?",["$5,730m","$3,370m","$4,370m"],2,"EV = equity + debt − cash = $4,370m.",1],[5,"A non-callable, non-convertible preferred share pays $7.50 a year. The required return is 5.0%. What is its value?",["$107.14","$37.50","$150.00"],2,"Value = dividend ÷ required return = $150.00.",1],[6,"A bond with a 4% annual coupon on par 100 trades at 103.50. What is its current yield?",["3.86%","4.14%","4.00%"],0,"Current yield = annual coupon ÷ price = 4.00 ÷ 103.50 = 3.86%.",1],[6,"A bond has modified duration of 9.70. If its yield falls by 25 basis points, the approximate percentage change in price is:",["2.43%","−2.43%","4.85%"],0,"%ΔP ≈ −ModDur × Δy = −9.70 × −0.25% = 2.43%.",1],[6,"A bond has modified duration 9.30 and convexity 61. For a fall in yield of 50 bp, the estimated price change including convexity is:",["4.574%","4.726%","4.650%"],1,"%ΔP ≈ −ModDur × Δy + ½ × convexity × (Δy)² = 4.726%.",1],[6,"A bond's Macaulay duration is 10.00 years and its yield is 4% (semi-annual periodicity). What is its modified duration?",["10.200","9.804","10.000"],1,"ModDur = MacDur ÷ (1 + y/k) = 10.00 ÷ 1.0200 = 9.804.",1],[6,"The 1-year spot rate is 2.6% and the 2-year spot rate is 3.1%. What is the 1-year forward rate one year from now?",["2.850%","3.602%","3.800%"],1,"(1 + S2)² = (1 + S1)(1 + f) gives f = 3.602%.",1],[6,"A bond exposure of $700m has a probability of default of 3.5% and an expected recovery rate of 60%. What is the expected loss?",["$24.50m","$9.80m","$14.70m"],1,"Expected loss = PD × exposure × (1 − recovery) = $9.80m.",1],[6,"A bond pays a 7% coupon semi-annually on par 100 (30/360 basis). It has been 94 days since the last coupon. What is the accrued interest?",["3.500","1.828","3.656"],1,"AI = (coupon per period) × days ÷ 180 = 3.50 × 94 ÷ 180 = 1.828.",1],[7,"A non-dividend-paying share trades at $177.00. The risk-free rate is 5% (annual compounding). What is the no-arbitrage forward price for 3 months?",["$177.00","$179.17","$185.85"],1,"F0 = S0 × (1 + r)^T = $177.00 × 1.05^0.25 = $179.17.",1],[7,"A European call with strike $113 and one year to expiry costs $7.00. The stock is at $103.00 and the risk-free rate is 3%. By put-call parity, the put with the same terms is worth:",["$13.71","$17.00","$0.29"],0,"p = c + X ÷ (1 + r) − S = 7.00 + 109.71 − 103.00 = $13.71.",1],[7,"An investor buys a call with strike $85 for $8.00. At expiry the stock is $71.00. What is the profit per share?",["$0.00","−$14.00","−$8.00"],2,"Profit = max(ST − X, 0) − premium = $0.00 − $8.00 = −$8.00.",1],[7,"An investor buys a put with strike $45 for $7.00. At expiry the stock is $32.00. What is the profit per share?",["$7.00","$13.00","$6.00"],2,"Profit = max(X − ST, 0) − premium = $6.00.",1],[7,"In a one-period binomial model, the up factor is 1.10, the down factor is 0.92 and the risk-free rate is 2%. What is the risk-neutral probability of an up move?",["0.4444","0.5000","0.5556"],2,"π = (1 + r − d) ÷ (u − d) = 0.5556.",1],[7,"A stock at $126.00 can move to $153.72 or $110.88 in one period. The risk-free rate is 3%. What is a one-period European call with strike $126 worth?",["$11.87","$12.23","$13.46"],0,"π = 0.4412; c = [π × 27.72 + (1 − π) × 0.00] ÷ 1.03 = $11.87.",1],[8,"A hedge fund starts the year at $270m and ends at $342.90m before fees. It charges 2% of year-end assets and 20% of gains net of the management fee (no hurdle, above the high-water mark). Total fees are:",["$6.86m","$20.07m","$21.44m"],1,"Management fee = $6.86m; incentive fee = 20% × (342.90 − 6.86 − 270.00) = $13.21m; total $20.07m.",1],[8,"A property produces net operating income of $1,350k a year. Comparable properties sell at a cap rate of 6.25%. What is its estimated value?",["$8,438k","$18,621k","$21,600k"],2,"Value = NOI ÷ cap rate = $1,350k ÷ 6.25% = $21,600k.",1],[8,"A commodity futures position earned a price return of 5%, a roll return of 0% and a collateral return of 5%. What is its total return?",["10.00%","11.00%","5.00%"],0,"Total return = price + roll + collateral = 10.00%.",1],[8,"A private equity fund called $180m from investors and has returned $252.00m in total. What is its multiple on invested capital (MOIC)?",["1.40×","0.40×","0.71×"],0,"MOIC = total value returned ÷ invested capital = 1.40.",1],[9,"The risk-free rate is 4%, the expected market return is 13% and a stock's beta is 1.70. What is its CAPM expected return?",["22.10%","19.30%","26.10%"],1,"E(R) = Rf + β(Rm − Rf) = 4% + 1.70 × 9% = 19.30%.",1],[9,"A portfolio returned 10% with a beta of 0.70. The risk-free rate is 5%. What is its Treynor ratio?",["0.0714","0.1429","0.0350"],0,"Treynor = (Rp − Rf) ÷ β = 0.0714.",1],[9,"A portfolio returned 13% with beta 1.40. The market returned 13% and the risk-free rate was 4%. What is Jensen's alpha?",["0.00%","−3.60%","9.00%"],1,"α = Rp − [Rf + β(Rm − Rf)] = 13% − 16.60% = −3.60%.",1],[9,"A portfolio holds 30% in a stock with beta 0.50 and the rest in a stock with beta 0.80. What is the portfolio beta?",["0.650","0.590","0.710"],2,"Portfolio beta = Σ weight × beta = 0.710.",1],[9,"An investor with risk aversion A = 2 considers a portfolio with expected return 15% and standard deviation 12%. What is its utility?",["12.12%","3.00%","13.56%"],2,"U = E(R) − ½ × A × σ² = 15% − 0.5 × 2 × 0.0144 = 13.56%.",1],[9,"A portfolio returned 14% with σ 17%; the market returned 8% with σ 14%; Rf is 5%. What is M² (relative to the market)?",["31.51%","4.41%","6.00%"],1,"M² = (Rp − Rf) × σm ÷ σp + Rf − Rm = 4.41%.",1],[1,"An investor deposits $9,500 at 12% a year, compounded annually. What is it worth after 15 years?",["$46,427.57","$51,998.87","$26,600.00"],1,"FV = PV × (1 + r)^n = $9,500 × 1.12^15 = $51,998.87.",1],[1,"What is the present value of $50,000 received in 5 years if the discount rate is 8%?",["$34,029.16","$36,751.49","$35,714.29"],0,"PV = FV ÷ (1 + r)^n = $50,000 ÷ 1.08^5 = $34,029.16.",1],[1,"What is the present value of an ordinary annuity of $3,400 a year for 6 years at 6%?",["$17,722.04","$20,400.00","$16,718.90"],2,"PV = A × [1 − (1 + r)^−n] ÷ r = $16,718.90. An annuity due would be worth $17,722.04.",1],[1,"An investor saves $4,300 at the end of each year for 14 years at 4%. What is the future value?",["$81,801.43","$78,655.22","$60,200.00"],1,"FV = A × [(1 + r)^n − 1] ÷ r = $78,655.22.",1],[1,"A preferred share pays a fixed $9.50 a year forever. At a required return of 6.5%, what is it worth?",["$146.15","$155.65","$126.67"],0,"Perpetuity value = payment ÷ r = $9.50 ÷ 6.5% = $146.15.",1],[1,"A stated annual rate of 14% is compounded quarterly. What is the effective annual rate?",["14.000%","14.752%","15.227%"],1,"EAR = (1 + 14% ÷ 4)^4 − 1 = 14.752%.",1],[1,"A share bought at $25.00 is sold a year later at $10.00 after paying a dividend of $1.50. What is the holding period return?",["−54.00%","−60.00%","−135.00%"],0,"HPR = (P1 − P0 + D) ÷ P0 = (10.00 − 25.00 + 1.50) ÷ 25.00 = −54.00%.",1],[1,"Annual returns over three years are 3%, 20%, 4%. What is the geometric mean return?",["8.73%","3.50%","9.00%"],0,"Geometric mean = [(1 + r1)(1 + r2)(1 + r3)]^(1/3) − 1 = 8.73%. The arithmetic mean is 9.00%.",1],[1,"Returns of −9%, 6%, 17% have probabilities of 0.40, 0.40, 0.20. What is the expected return?",["4.67%","2.20%","6.00%"],1,"E(R) = Σ p × R = 2.20%.",1],[1,"A portfolio holds 80% in asset A (σ = 11%) and 20% in asset B (σ = 23%). Their correlation is 0.70. What is the portfolio standard deviation?",["12.46%","9.93%","13.40%"],0,"σp = √(w²σA² + (1 − w)²σB² + 2w(1 − w)ρσAσB) = 12.46%.",1],[1,"An asset has a mean return of 7% and a standard deviation of 24%. What is its coefficient of variation?",["3.43","0.29","0.17"],0,"CV = σ ÷ mean = 24% ÷ 7% = 3.43.",1],[1,"A portfolio returned 6% with a standard deviation of 24%. The risk-free rate is 2%. What is its Sharpe ratio?",["0.250","0.167","0.694"],1,"Sharpe = (Rp − Rf) ÷ σp = (6% − 2%) ÷ 24% = 0.167.",1],[1,"A sample of 36 observations has a standard deviation of 25. What is the standard error of the sample mean?",["4.167","0.694","4.526"],0,"Standard error = s ÷ √n = 25 ÷ 6 = 4.167.",1],[1,"A portfolio has expected return 8% and standard deviation 16%. The minimum acceptable return is 2%. What is Roy's safety-first ratio?",["0.234","0.500","0.375"],2,"SFRatio = (E(R) − threshold) ÷ σ = 0.375. A higher ratio means lower shortfall risk.",1],[1,"Two independent events have probabilities 0.40 and 0.40. What is the probability that both occur?",["0.1600","0.4000","0.6400"],0,"For independent events, P(A and B) = P(A) × P(B) = 0.1600.",1],[2,"A 11% rise in price leads to a 25% fall in quantity demanded. What is the own-price elasticity of demand?",["0.44","−2.27","−0.25"],1,"Elasticity = %ΔQ ÷ %ΔP = −25% ÷ 11% = −2.27. Demand is elastic.",1],[2,"EUR/USD is 1.1700 and USD/INR is 83.50. What is the EUR/INR cross rate?",["97.70","84.67","71.37"],0,"EUR/INR = EUR/USD × USD/INR = 1.1700 × 83.50 = 97.70 rupees per euro.",1],[2,"Spot USD/INR is 87.00. One-year rates are 7.4% in India and 3.4% in the US. By covered interest parity, the one-year forward USD/INR is:",["87.00","90.37","83.76"],1,"Forward = spot × (1 + i INR) ÷ (1 + i USD) = 90.37. The higher-rate currency (INR) trades at a forward discount.",1],[2,"Four firms in a market have shares of 38%, 9%, 14%, 12% (the rest are tiny). What is the Herfindahl-Hirschman Index (as a decimal)?",["0.7300","0.1825","0.1865"],2,"HHI = sum of squared shares = 0.38² + 0.09² + 0.14² + 0.12² = 0.1865.",1],[3,"A project costs $950 today and returns $350, $470, $450 over the next three years. At a 6% cost of capital, what is its NPV?",["$320.00","$186.89","$176.32"],2,"NPV = −$950 + Σ CFt ÷ (1 + 6%)^t = $176.32. Accept.",1],[3,"A firm's target weights are 40% debt and 60% equity. Pre-tax cost of debt is 8%, the tax rate is 22% and the cost of equity is 10%. What is the WACC?",["9.00%","9.20%","8.50%"],2,"WACC = wd × rd × (1 − t) + we × re = 8.50%.",1],[3,"The risk-free rate is 5%, the equity risk premium is 8% and the stock's beta is 1.60. What is the cost of equity under CAPM?",["17.80%","12.80%","13.00%"],0,"re = Rf + β × ERP = 5% + 1.60 × 8% = 17.80%.",1],[3,"Days of inventory on hand are 33, days sales outstanding 49 and days payables 55. What is the cash conversion cycle?",["27 days","137 days","39 days"],0,"CCC = DIO + DSO − DPO = 33 + 49 − 55 = 27 days.",1],[3,"When sales rise 15%, operating income rises 18.0%. What is the degree of operating leverage?",["0.83","3.00","1.20"],2,"DOL = %Δ EBIT ÷ %Δ sales = 1.20.",1],[4,"Current assets are $780m, of which inventory is $240m (no prepaid expenses). Current liabilities are $410m. What is the quick ratio?",["1.32","1.90","0.59"],0,"Quick ratio = (current assets − inventory) ÷ current liabilities = 1.32. Current ratio = 1.90.",1],[4,"A company has a net profit margin of 15%, asset turnover of 1.40 and financial leverage (assets ÷ equity) of 2.20. What is its ROE?",["46.20%","21.00%","33.00%"],0,"DuPont: ROE = margin × turnover × leverage = 46.20%. ROA = 21.00%.",1],[4,"Cost of goods sold is $1,480m and average inventory is $230m. How many days of inventory on hand does the firm hold?",["56.7 days","6.4 days","23.5 days"],0,"Inventory turnover = 6.43; days of inventory = 365 ÷ 6.43 = 56.7 days.",1],[4,"Equipment costs $150,000, has a salvage value of $19,000 and a useful life of 6 years. What is annual straight-line depreciation?",["$25,000","$28,167","$21,833"],2,"(Cost − salvage) ÷ life = ($150,000 − $19,000) ÷ 6 = $21,833.",1],[4,"Equipment costs $175,000 with a 5-year life. What is first-year depreciation under the double-declining balance method?",["$35,000","$70,000","$42,000"],1,"DDB rate = 2 ÷ 5 = 40.0%; year 1 = $175,000 × 40.0% = $70,000. Salvage is ignored until the end.",1],[4,"A firm buys 300 units at $12 and later 200 units at $14, then sells 340 units. What is cost of goods sold under FIFO?",["$4,160","$4,352","$4,480"],0,"FIFO uses the oldest costs first: 300 × $12 + 40 × $14 = $4,160. LIFO would give $4,480.",1],[4,"Net income is $135m, preferred dividends are $5m and the weighted average number of common shares is 20m. What is basic EPS?",["$6.75","$6.50","$7.00"],1,"Basic EPS = (NI − preferred dividends) ÷ weighted shares = $6.50.",1],[4,"EBIT is $450m and interest expense is $30m. What is the interest coverage ratio?",["15.00×","0.07×","14.00×"],0,"Interest coverage = EBIT ÷ interest = 15.00 times.",1],[4,"Tax depreciation exceeds book depreciation, creating a cumulative temporary difference of $155m. At a 26% tax rate, what is the deferred tax liability?",["$40.30m","$114.70m","$155.00m"],0,"DTL = temporary difference × tax rate = $155m × 26% = $40.30m.",1],[5,"A stock just paid a dividend of $4.00. Dividends grow at 6% forever and the required return is 11%. What is its value?",["$84.80","$80.00","$38.55"],0,"Gordon model: V0 = D0(1 + g) ÷ (r − g) = $4.24 ÷ 5% = $84.80.",1],[5,"A company retains 70% of earnings and has an ROE of 20%. What is its sustainable growth rate?",["14.00%","6.00%","20.00%"],0,"g = retention ratio × ROE = 70% × 20% = 14.00%.",1],[5,"A firm pays out 30% of earnings, grows at 3% and has a required return of 7%. What is its justified forward P/E?",["17.50×","4.29×","7.50×"],2,"Justified forward P/E = payout ÷ (r − g) = 0.30 ÷ 4% = 7.50.",1],[5,"An investor buys a share at $68.00 with 40% initial margin. The maintenance margin is 30%. Below what price will a margin call occur?",["$47.60","$58.29","$27.20"],1,"Trigger price = P0 × (1 − initial margin) ÷ (1 − maintenance margin) = $58.29.",1],[5,"A share is bought at $74.00 with 50% margin and sold at $79.18 (ignore interest and dividends). What is the return on the investor's equity?",["7.00%","14.00%","3.50%"],1,"Return = price change ÷ equity invested = (79.18 − 74.00) ÷ $37.00 = 14.00%. Leverage is 1 ÷ 0.50.",1],[5,"A price-weighted index has three stocks priced at $27, $35, $60, with a divisor of 3. What is the index value?",["60.00","122.00","40.67"],2,"Price-weighted index = sum of prices ÷ divisor = 40.67. The highest-priced stock has the most weight.",1],[5,"A firm has equity market value of $2,200m, debt of $450m and cash of $480m. What is its enterprise value?",["$1,720m","$3,130m","$2,170m"],2,"EV = equity + debt − cash = $2,170m.",1],[5,"A non-callable, non-convertible preferred share pays $8.00 a year. The required return is 8.0%. What is its value?",["$80.00","$64.00","$100.00"],2,"Value = dividend ÷ required return = $100.00.",1],[6,"A 3-year bond pays an annual coupon of 8% on a par of 100. If the yield to maturity is 6%, what is its price?",["133.33","97.00","105.35"],2,"Price = Σ coupon ÷ (1 + y)^t + 100 ÷ (1 + y)^3 = 105.35. Coupon above yield, so a premium.",1],[6,"A bond with a 3% annual coupon on par 100 trades at 107.00. What is its current yield?",["2.80%","3.00%","3.21%"],0,"Current yield = annual coupon ÷ price = 3.00 ÷ 107.00 = 2.80%.",1],[6,"A bond has modified duration of 5.60. If its yield rises by 100 basis points, the approximate percentage change in price is:",["−11.20%","−5.60%","5.60%"],1,"%ΔP ≈ −ModDur × Δy = −5.60 × 1.00% = −5.60%.",1],[6,"A bond has modified duration 4.20 and convexity 126. For a rise in yield of 100 bp, the estimated price change including convexity is:",["−4.830%","−4.200%","−3.570%"],2,"%ΔP ≈ −ModDur × Δy + ½ × convexity × (Δy)² = −3.570%.",1],[6,"A bond's Macaulay duration is 5.70 years and its yield is 7% (annual periodicity). What is its modified duration?",["5.327","6.099","5.700"],0,"ModDur = MacDur ÷ (1 + y/k) = 5.70 ÷ 1.0700 = 5.327.",1],[6,"The 1-year spot rate is 5.9% and the 2-year spot rate is 6.9%. What is the 1-year forward rate one year from now?",["6.400%","7.909%","8.100%"],1,"(1 + S2)² = (1 + S1)(1 + f) gives f = 7.909%.",1],[6,"A bond exposure of $650m has a probability of default of 2.9% and an expected recovery rate of 23%. What is the expected loss?",["$18.85m","$4.34m","$14.51m"],2,"Expected loss = PD × exposure × (1 − recovery) = $14.51m.",1],[6,"A bond pays a 4% coupon semi-annually on par 100 (30/360 basis). It has been 144 days since the last coupon. What is the accrued interest?",["2.000","3.200","1.600"],2,"AI = (coupon per period) × days ÷ 180 = 2.00 × 144 ÷ 180 = 1.600.",1],[7,"A non-dividend-paying share trades at $183.00. The risk-free rate is 6% (annual compounding). What is the no-arbitrage forward price for 3 months?",["$193.98","$183.00","$185.69"],2,"F0 = S0 × (1 + r)^T = $183.00 × 1.06^0.25 = $185.69.",1],[7,"An investor buys a call with strike $105 for $6.00. At expiry the stock is $109.00. What is the profit per share?",["−$2.00","$4.00","−$1.00"],0,"Profit = max(ST − X, 0) − premium = $4.00 − $6.00 = −$2.00.",1],[7,"An investor buys a put with strike $100 for $8.00. At expiry the stock is $89.00. What is the profit per share?",["$4.00","$11.00","$3.00"],2,"Profit = max(X − ST, 0) − premium = $3.00.",1],[7,"In a one-period binomial model, the up factor is 1.18, the down factor is 0.82 and the risk-free rate is 3%. What is the risk-neutral probability of an up move?",["0.5833","0.5000","0.4167"],0,"π = (1 + r − d) ÷ (u − d) = 0.5833.",1],[7,"A stock at $126.00 can move to $149.94 or $110.88 in one period. The risk-free rate is 2%. What is a one-period European call with strike $126 worth?",["$10.60","$11.74","$10.81"],0,"π = 0.4516; c = [π × 23.94 + (1 − π) × 0.00] ÷ 1.02 = $10.60.",1],[8,"A hedge fund starts the year at $230m and ends at $280.60m before fees. It charges 2% of year-end assets and 20% of gains net of the management fee (no hurdle, above the high-water mark). Total fees are:",["$14.61m","$5.61m","$15.73m"],0,"Management fee = $5.61m; incentive fee = 20% × (280.60 − 5.61 − 230.00) = $9.00m; total $14.61m.",1],[8,"A property produces net operating income of $1,400k a year. Comparable properties sell at a cap rate of 8.00%. What is its estimated value?",["$15,556k","$11,200k","$17,500k"],2,"Value = NOI ÷ cap rate = $1,400k ÷ 8.00% = $17,500k.",1],[8,"A commodity futures position earned a price return of 4%, a roll return of −4% and a collateral return of 4%. What is its total return?",["4.00%","8.00%","5.00%"],0,"Total return = price + roll + collateral = 4.00%.",1],[8,"A private equity fund called $70m from investors and has returned $140.00m in total. What is its multiple on invested capital (MOIC)?",["1.00×","2.00×","0.50×"],1,"MOIC = total value returned ÷ invested capital = 2.00.",1],[9,"The risk-free rate is 3%, the expected market return is 10% and a stock's beta is 1.60. What is its CAPM expected return?",["19.00%","14.20%","16.00%"],1,"E(R) = Rf + β(Rm − Rf) = 3% + 1.60 × 7% = 14.20%.",1],[9,"A portfolio returned 10% with a beta of 0.80. The risk-free rate is 4%. What is its Treynor ratio?",["0.1250","0.0480","0.0750"],2,"Treynor = (Rp − Rf) ÷ β = 0.0750.",1],[9,"A portfolio returned 16% with beta 1.30. The market returned 10% and the risk-free rate was 2%. What is Jensen's alpha?",["3.60%","6.00%","14.00%"],0,"α = Rp − [Rf + β(Rm − Rf)] = 16% − 12.40% = 3.60%.",1],[9,"A portfolio holds 70% in a stock with beta 1.00 and the rest in a stock with beta 1.30. What is the portfolio beta?",["1.090","1.210","1.150"],0,"Portfolio beta = Σ weight × beta = 1.090.",1],[9,"An investor with risk aversion A = 4 considers a portfolio with expected return 10% and standard deviation 15%. What is its utility?",["1.00%","−20.00%","5.50%"],2,"U = E(R) − ½ × A × σ² = 10% − 0.5 × 4 × 0.0225 = 5.50%.",1],[9,"A portfolio returned 9% with σ 20%; the market returned 9% with σ 17%; Rf is 4%. What is M² (relative to the market)?",["0.00%","−0.75%","−4.41%"],1,"M² = (Rp − Rf) × σm ÷ σp + Rf − Rm = −0.75%.",1],[1,"An investor deposits $20,000 at 10% a year, compounded annually. What is it worth after 5 years?",["$32,210.20","$29,282.00","$30,000.00"],0,"FV = PV × (1 + r)^n = $20,000 × 1.10^5 = $32,210.20.",1],[1,"What is the present value of $32,000 received in 3 years if the discount rate is 6%?",["$26,867.82","$27,118.64","$28,479.89"],0,"PV = FV ÷ (1 + r)^n = $32,000 ÷ 1.06^3 = $26,867.82.",1],[1,"What is the present value of an ordinary annuity of $4,100 a year for 10 years at 7%?",["$28,796.68","$41,000.00","$30,812.45"],0,"PV = A × [1 − (1 + r)^−n] ÷ r = $28,796.68. An annuity due would be worth $30,812.45.",1],[1,"An investor saves $4,600 at the end of each year for 16 years at 6%. What is the future value?",["$125,179.25","$118,093.63","$73,600.00"],1,"FV = A × [(1 + r)^n − 1] ÷ r = $118,093.63.",1],[1,"A preferred share pays a fixed $5.00 a year forever. At a required return of 4.5%, what is it worth?",["$116.11","$111.11","$90.91"],1,"Perpetuity value = payment ÷ r = $5.00 ÷ 4.5% = $111.11.",1],[1,"A stated annual rate of 4% is compounded monthly. What is the effective annual rate?",["4.281%","4.000%","4.074%"],2,"EAR = (1 + 4% ÷ 12)^12 − 1 = 4.074%.",1],[1,"A share bought at $114.00 is sold a year later at $116.00 after paying a dividend of $0.00. What is the holding period return?",["1.75%","2.75%","1.72%"],0,"HPR = (P1 − P0 + D) ÷ P0 = (116.00 − 114.00 + 0.00) ÷ 114.00 = 1.75%.",1],[1,"Returns of −4%, 6%, 10% have probabilities of 0.30, 0.40, 0.30. What is the expected return?",["4.20%","4.00%","6.00%"],0,"E(R) = Σ p × R = 4.20%.",1],[1,"A portfolio holds 30% in asset A (σ = 17%) and 70% in asset B (σ = 31%). Their correlation is −0.50. What is the portfolio standard deviation?",["19.65%","22.29%","26.80%"],0,"σp = √(w²σA² + (1 − w)²σB² + 2w(1 − w)ρσAσB) = 19.65%.",1],[1,"An asset has a mean return of 12% and a standard deviation of 8%. What is its coefficient of variation?",["−0.04","0.67","1.50"],1,"CV = σ ÷ mean = 8% ÷ 12% = 0.67.",1],[1,"A portfolio returned 12% with a standard deviation of 11%. The risk-free rate is 5%. What is its Sharpe ratio?",["1.091","0.636","5.785"],1,"Sharpe = (Rp − Rf) ÷ σp = (12% − 5%) ÷ 11% = 0.636.",1],[1,"A sample of 36 observations has a standard deviation of 40. What is the standard error of the sample mean?",["6.667","1.111","7.061"],0,"Standard error = s ÷ √n = 40 ÷ 6 = 6.667.",1],[1,"A portfolio has expected return 7% and standard deviation 19%. The minimum acceptable return is 3%. What is Roy's safety-first ratio?",["0.111","0.211","0.368"],1,"SFRatio = (E(R) − threshold) ÷ σ = 0.211. A higher ratio means lower shortfall risk.",1],[2,"EUR/USD is 1.1900 and USD/INR is 87.25. What is the EUR/INR cross rate?",["73.32","103.83","88.44"],1,"EUR/INR = EUR/USD × USD/INR = 1.1900 × 87.25 = 103.83 rupees per euro.",1],[2,"Spot USD/INR is 84.75. One-year rates are 6.4% in India and 4.9% in the US. By covered interest parity, the one-year forward USD/INR is:",["84.75","83.56","85.96"],2,"Forward = spot × (1 + i INR) ÷ (1 + i USD) = 85.96. The higher-rate currency (INR) trades at a forward discount.",1],[2,"Four firms in a market have shares of 22%, 18%, 9%, 7% (the rest are tiny). What is the Herfindahl-Hirschman Index (as a decimal)?",["0.5600","0.1400","0.0938"],2,"HHI = sum of squared shares = 0.22² + 0.18² + 0.09² + 0.07² = 0.0938.",1],[3,"A project costs $1,550 today and returns $430, $250, $670 over the next three years. At a 12% cost of capital, what is its NPV?",["−$200.00","−$489.88","−$548.67"],1,"NPV = −$1,550 + Σ CFt ÷ (1 + 12%)^t = −$489.88. Reject.",1],[3,"A firm's target weights are 40% debt and 60% equity. Pre-tax cost of debt is 5%, the tax rate is 21% and the cost of equity is 15%. What is the WACC?",["10.58%","11.00%","10.00%"],0,"WACC = wd × rd × (1 − t) + we × re = 10.58%.",1],[3,"The risk-free rate is 5%, the equity risk premium is 4% and the stock's beta is 1.60. What is the cost of equity under CAPM?",["6.40%","11.40%","9.00%"],1,"re = Rf + β × ERP = 5% + 1.60 × 4% = 11.40%.",1],[3,"Days of inventory on hand are 35, days sales outstanding 24 and days payables 35. What is the cash conversion cycle?",["24 days","94 days","46 days"],0,"CCC = DIO + DSO − DPO = 35 + 24 − 35 = 24 days.",1],[3,"A supplier offers terms of 1/10, net 45. What is the effective annual cost of not taking the discount?",["10.4%","11.1%","1.0%"],1,"Cost = (1 + 1/99)^(365/35) − 1 = 11.1%. Usually far above bank borrowing costs.",1],[3,"When sales rise 10%, operating income rises 29.0%. What is the degree of operating leverage?",["0.34","2.90","19.00"],1,"DOL = %Δ EBIT ÷ %Δ sales = 2.90.",1],[4,"Current assets are $340m, of which inventory is $100m (no prepaid expenses). Current liabilities are $600m. What is the quick ratio?",["0.57","0.17","0.40"],2,"Quick ratio = (current assets − inventory) ÷ current liabilities = 0.40. Current ratio = 0.57.",1],[4,"A company has a net profit margin of 9%, asset turnover of 0.80 and financial leverage (assets ÷ equity) of 2.80. What is its ROE?",["20.16%","7.20%","25.20%"],0,"DuPont: ROE = margin × turnover × leverage = 20.16%. ROA = 7.20%.",1],[4,"Cost of goods sold is $640m and average inventory is $150m. How many days of inventory on hand does the firm hold?",["15.6 days","85.5 days","4.3 days"],1,"Inventory turnover = 4.27; days of inventory = 365 ÷ 4.27 = 85.5 days.",1],[4,"Equipment costs $30,000, has a salvage value of $2,000 and a useful life of 8 years. What is annual straight-line depreciation?",["$3,750","$4,000","$3,500"],2,"(Cost − salvage) ÷ life = ($30,000 − $2,000) ÷ 8 = $3,500.",1],[4,"Equipment costs $20,000 with a 7-year life. What is first-year depreciation under the double-declining balance method?",["$4,082","$5,714","$2,857"],1,"DDB rate = 2 ÷ 7 = 28.6%; year 1 = $20,000 × 28.6% = $5,714. Salvage is ignored until the end.",1],[4,"A firm buys 110 units at $17 and later 180 units at $19, then sells 240 units. What is cost of goods sold under FIFO?",["$4,440","$4,378","$4,340"],2,"FIFO uses the oldest costs first: 110 × $17 + 130 × $19 = $4,340. LIFO would give $4,440.",1],[4,"Net income is $245m, preferred dividends are $10m and the weighted average number of common shares is 115m. What is basic EPS?",["$2.04","$2.22","$2.13"],0,"Basic EPS = (NI − preferred dividends) ÷ weighted shares = $2.04.",1],[4,"EBIT is $270m and interest expense is $105m. What is the interest coverage ratio?",["2.57×","1.57×","0.39×"],0,"Interest coverage = EBIT ÷ interest = 2.57 times.",1],[4,"Tax depreciation exceeds book depreciation, creating a cumulative temporary difference of $120m. At a 21% tax rate, what is the deferred tax liability?",["$94.80m","$120.00m","$25.20m"],2,"DTL = temporary difference × tax rate = $120m × 21% = $25.20m.",1],[5,"A stock just paid a dividend of $3.75. Dividends grow at 4% forever and the required return is 10%. What is its value?",["$39.00","$62.50","$65.00"],2,"Gordon model: V0 = D0(1 + g) ÷ (r − g) = $3.90 ÷ 6% = $65.00.",1],[5,"A company retains 40% of earnings and has an ROE of 19%. What is its sustainable growth rate?",["11.40%","19.00%","7.60%"],2,"g = retention ratio × ROE = 40% × 19% = 7.60%.",1],[5,"A firm pays out 30% of earnings, grows at 2% and has a required return of 6%. What is its justified forward P/E?",["5.00×","7.50×","17.50×"],1,"Justified forward P/E = payout ÷ (r − g) = 0.30 ÷ 4% = 7.50.",1],[5,"An investor buys a share at $105.00 with 60% initial margin. The maintenance margin is 25%. Below what price will a margin call occur?",["$63.00","$78.75","$56.00"],2,"Trigger price = P0 × (1 − initial margin) ÷ (1 − maintenance margin) = $56.00.",1],[5,"A share is bought at $72.00 with 40% margin and sold at $65.52 (ignore interest and dividends). What is the return on the investor's equity?",["−22.50%","−3.60%","−9.00%"],0,"Return = price change ÷ equity invested = (65.52 − 72.00) ÷ $28.80 = −22.50%. Leverage is 1 ÷ 0.40.",1],[5,"A price-weighted index has three stocks priced at $36, $99, $114, with a divisor of 3. What is the index value?",["114.00","83.00","249.00"],1,"Price-weighted index = sum of prices ÷ divisor = 83.00. The highest-priced stock has the most weight.",1],[5,"A firm has equity market value of $1,500m, debt of $500m and cash of $80m. What is its enterprise value?",["$2,080m","$1,920m","$1,420m"],1,"EV = equity + debt − cash = $1,920m.",1],[5,"A non-callable, non-convertible preferred share pays $5.50 a year. The required return is 8.5%. What is its value?",["$52.38","$46.75","$64.71"],2,"Value = dividend ÷ required return = $64.71.",1],[6,"A 4-year bond pays an annual coupon of 3% on a par of 100. If the yield to maturity is 4%, what is its price?",["75.00","103.00","96.37"],2,"Price = Σ coupon ÷ (1 + y)^t + 100 ÷ (1 + y)^4 = 96.37. Coupon below yield, so a discount.",1],[6,"A bond with a 5% annual coupon on par 100 trades at 95.50. What is its current yield?",["5.00%","5.24%","4.78%"],1,"Current yield = annual coupon ÷ price = 5.00 ÷ 95.50 = 5.24%.",1],[6,"A bond has modified duration of 5.90. If its yield rises by 100 basis points, the approximate percentage change in price is:",["−5.90%","−11.80%","5.90%"],0,"%ΔP ≈ −ModDur × Δy = −5.90 × 1.00% = −5.90%.",1],[6,"A bond has modified duration 7.40 and convexity 140. For a fall in yield of 50 bp, the estimated price change including convexity is:",["3.525%","3.700%","3.875%"],2,"%ΔP ≈ −ModDur × Δy + ½ × convexity × (Δy)² = 3.875%.",1],[6,"A bond's Macaulay duration is 4.00 years and its yield is 5% (annual periodicity). What is its modified duration?",["4.200","4.000","3.810"],2,"ModDur = MacDur ÷ (1 + y/k) = 4.00 ÷ 1.0500 = 3.810.",1]]}