FRM Exam questions you must master to pass the Part I FRM ExamPreparing for the Part I exam is tough, but you can make life easier with an effective studyplan. If you have yet to get a plan, Wiley’s adaptive Digital Exam Planner in our Silver andSelf-Study FRM review courses will help you create a personalized plan down to the day,provide a dashboard to keep on track and track your progress every step of the way.But first, here are some questions to test your knowledge of typical, fundamental topics thatare likely to appear on the actual exam.1. The minimum variance frontier most likely consists of:A. 9.20%A. Individual assets only.B. 8.34%B. Portfolios only.C. 10.40%C. Individual assets and portfolios.D. 12.20%D. Only risk-free assets.Answer: DExpected return Rf R (Rm – Rf)Answer: BAssets with low correlations can be combined intoportfolios that have a lower risk than any of the individualassets in the portfolio. The minimum variance frontierconsists of portfolios that minimize the level of risk for eachlevel of expected return.2. Compute her portfolio’s standard deviation, if thecorrelation between the two assets equals 0.7.A. 8.05%II. Manager A’s Sharpe ratio is closest to:A. 0.51B. 0.40C. 0.20D. 0.68Answer: AB. 9.86%Sharpe ratio (RA – Rf) / RA (0.19 – 0.05) / 0.27 0.5185C. 7.06%III. Manager C’s Treynor ratio is closest to:D. 12.68%A. 0.20Answer: D2Expected return 0.05 1.2 (0.11 – 0.05) 12.20%222[(0.3 0.12 ) (0.7 0.0 ) 2 (0.3) (0.7) (0.12) (0.1414)0.5(0.7)] 12.68%3. Use the following information to answer the next fourquestions:The following information is available regarding theportfolio performance of three investment managers:ManagerReturnStandardDeviationB. 0.25C. 0.57D. 0.12Answer: DTreynor ratio (RC – Rf) / RC (0.16 – 0.05) / 0.9 0.1222IV. Manager C’s Jensen’s alpha is closest to:BetaA. 5.60%A19%27%0.7B. 10.40%B14%22%1.2C. 8.5%C16%19%0.9Market (M)11%24%D. 9.0%Risk-free rate5%I. Manager B’s expected return is closest to:Answer: AManager C’s expected return Rf R (Rm – Rf) 0.05 0.9(0.11 – 0.05) 10.4%Jensen’s alpha 16% 10.4% 5.6%Wiley 2016

FRM Exam Review4. Darren Peters, FRM, has gathered information on allthe monthly returns of actively managed portfolios andpassive indices. He is using multifactor models, of whichhe has examined many. Darren determines the optimalnumber of factors using the R-squares for differentmodels.He selects a model that has a reasonable but smallnumber of factors. He uses the difference in monthlyreturns between the managed portfolios and the marketindex represented by the S&P 500, represented as RTN, asthe dependent variable. The independent variables arethe S&P 500 return less the 90-day T-bill rate representedas MKT, the monthly returns to a passive portfolio of highEPS stocks less the returns of a passive portfolio of lowEPS stocks represented by EPSS, and the monthly returnsto a passive portfolio of small cap stocks less the returnsof a passive portfolio of large cap stocks, represented systematic risk.The Sharpe ratio is standardized bysigma, not beta, so the Treynor ratio is the correct ratio touse in this case. The Treynor formula is Tρ [E(Rρ) – Rf] / βρ,which describes the difference between excess return oversystematic risk—the beta—which is what the question asks.6. Ashley selected a sample of 20 stocks and calculated theirmean return over a three-year period to be 4.25%. Giventhat the sample standard deviation is 0.3% and assumingthat the population is normally distributed, the 90% confidence interval is closest to:A. 4.13% to 4.37%B. 4.22% to 4.44%C. 4.14% to 4.36%Answer: AThe following results were derived for the historical data:Since the population variance is not known, but thepopulation is assumed to be normally distributed, and thesample size is small we must use the t-distribution.RTN –.0025 .15MKT – .08EPSS – .07LCSCStandard error 0.3 / (20) 0.06708Which of the following is not a reason to support the casefor active portfolio management?Degrees of freedom 20 1 19A. Failure of the CAPM beta to explain returnsB. Excess volatility in market pricesC. The existence of market anomaliesD. Efficient frontier theoryAnswer: DAll are valid reasons to support the case for active portfoliomanagement except for the efficient frontier theory. Theefficient frontier theory is the theory that all investorsallocate their money between the risk-free asset and thetangency efficient portfolio.5. Assume that you are concerned only with systematic risk.Which of the following would be the best measure to useto rank order funds with different betas based on theirrisk-return relationship with the market portfolio?A. Treynor ratioB. Sharpe ratioC. Jensen’s alphaD. Sortino ratioAnswer: ASystematic risk is the risk that can’t be diversified awayand the beta of our portfolio is:βP (ρPM * σP * σM) / σ2 where ρPM is the correlation coefficient between the portfolio and the market, σp is the risk ofthe portfolio, and σM is the risk of the market.In either case, beta explains the volatility of the portfoliocompared to the volatility of the market, which captures0.5For a 90% confi dence interval, we need 5% in either tail.The relevant t-score with 19 degrees of freedom is 1.7291.Confidence interval 4.25% (1.7291 0.067%) 4.13% to 4.37%7. Alexis is conducting research on the stock market of anemerging economy. She believes that the mean dailyreturn on the market’s all-share index is statisticallysignifi cantly different from zero. She randomly selects 50stocks that are traded on the country’s stock exchangeand calculates their average daily return to be 0.3%. Theindex that comprises all the shares in the country has adaily standard deviation of 0.2%. At the 5% level of significance, Alexis would most likely:A. Reject the null hypothesis, and conclude that themean daily return is not statistically significantlydifferent from zero.B. Fail to reject the null hypothesis, and conclude thatthe mean daily return is not statistically significantlydifferent from zero.C. Reject the null hypothesis, and conclude that themean daily return is statistically significantly differentfrom zero.Answer: CH0: μ 0; Ha: μ 0Since the population (index comprising of all shares tradedin the country) standard deviation is known, use the z-test.This is a two-tailed test. At the 5% level of significance, thecritical z-values for a two-tailed test are stat {(0.003 0) / [(0.002) / (50) ]} 10.607Wiley 2016

FRM Exam the test stat (10.607) is greater than the uppercritical value ( 1.96), the null hypothesis is rejected. Alexiswould conclude that the mean daily return is statisticallysignificantly different from zero.8. Use the following information to answer the next fivequestions:SSRegression18.395Residual47.428A. 0.3879B. 736.14C. 0.0014An analyst regresses the bid/ask spread (dependentvariable) for a sample of 1,900 stocks against the naturallog of trading volume (independent variable). The resultsof the regression are provided below:ANOVAIV. The F-stat is closest to:Answer: BF-stat MSR / MSE (RSS / 1) / [SSE / (n – k – 1)]F-stat (18.395 / 1) / [47.428 / (1900 – 1 – 1)] 736.14139. Consider the following statements:Statement 1: The lower the risk aversion coefficient, thelower the negative impact of risk on portfolio pt0.629410.02663523.63094Slope coefficient 0.052480.002941 17.84427I. The coefficient of determination is closest to:Statement 2: The fact that indifference curves are upwardsloping suggests that investors experience diminishingmarginal utility of wealth.Which of the following is most likely?A. Only Statement 1 is correct.B. Only Statement 2 is correct.C. Both statements are incorrect.A. 0.2795D. Neither is correct.B. 0.3879Answer: AC. 0.7205Answer: ACoefficient of determination Explained variation / Totalvariation Coefficient of determination 18.395 / (18.395 47.428) 0.2795II. The correlation coefficient (r) is closest to:A. 0.6228B. 0.5286C. 0.5286Answer: BCorrelation coefficient (Coefficient of determination)0.50.5Correlation coefficient 0.2795 0.5286As the slope coefficient provided in the regression is anegative figure, so the correlation coefficient (r) is 0.5286.III. The standard error is closest to:Statement 1 is correct. A lower risk aversion coefficientmeans that the effect of risk on portfolio utility will belower.The fact that indifference curves are curved suggests thatinvestors exhibit diminishing marginal utility of wealth. Asmore risk is added to the portfolio, the increase in returnrequired increases at an increasing rate. The upward slopeof indifference curve tells us that investors are risk averse—in order to be indifferent between two portfolios withdifferent levels of risk, the high risk portfolio must offer ahigher return as well.10. The chief risk officer of your firm has asked you to decidebetween buying a futures contract on an exchange andbuying a forward contract directly in the OTC Space withthe firm’s best client. Both have the identical terms. Youfind that the forward price is higher than the futuresprice. What single factor acting alone would be a realisticexplanation for this price difference?A. 0.0984A. The asset is strongly negatively correlated withinterest rates.B. 0.1581B. The futures contract is more liquid and easier to clear.C. 0.0250C. The forward contract counterparty has a higherdefault probability.Answer: B0.5Standard error [SSE / (n – 2)]0.5Standard error [47.428 / (1900 – 2)] 0.1581D. The convenience yield on the forward contract is lessthan on the futures contract.Wiley 2016

FRM Exam ReviewAnswer: CForward contracts do not have a daily settlement featureand is the reason for the convexity impact on eurodollarfutures. The futures contract has a “free” option on thepotential to earn the risk-free rate of return on the markto mark movement of the futures price. This free optionimpact—also called the convexity impact—is closely relatedto both volatility of the futures and how closely negativelycorrelated with interest rates the underlying asset is. If thefutures contract moves higher in price, and you are longthe future (hence have an overnight gain), that gain will beinvested at lower rates.11. Sarah Carter is a trader in the arbitrage unit of a largebank. She finds that an asset is trading at USD 2,000, theprice of a 1-year futures contract on that asset is USD2,025, and the price of a 2-year futures contract is USD2,055. Assume that there are no cash flows from the assetfor two years. If the term structure of interest rates is flatat 1% per year, which of the following is an appropriatearbitrage strategy?A. Short 2-year futures and long 1-year futuresB. Short 1-year futures and long 2-year futuresC. Short 2-year futures and long the underlying assetfunded by borrowing for 2 yearsThe forward rate, FT , is given by the interest rate parityequation:Ft So e(r r )TfwhereSo is the spot exchange rate,r is the domestic (USD) risk-free rate, andrf is the foreign (EUR) risk-free rate.T is the time to delivery.Substituting the values in the equation:(0.01 0.02)Ft 1.35 e13. Jacquie Chan is an analyst with Donahue ManagementInc. She is studying value at risk as a means to measureand manage risk. Jacquie believes that using a riskbudgeting program based on VaR could significantlyenhance SIM’s risk management processes. Whenpresenting her idea to senior members of the firm,Jacquie receives the following responses: Amanda Peters, Chief Market Strategist: We havea solid process in place to determine the optimalasset allocation for various market conditions. Riskbudgeting is basically another way to conduct assetallocation. Kathy Hu, Chief Compliance Officer: We haveguidelines in place that include principal limits,sensitivity limits, and leverage limits. The thresholdsset under a risk budget program accomplish the samething. Thomas Archer, Director of Portfolio Management: Wealready use tools such as beta, standard deviation,and duration to determine risk. These tools arewidely used in the market and provide all the riskmeasurement we need.D. Short 1-year futures and long the underlying assetfunded by borrowing for 1 yearAnswer: C.01The 1-year futures price should be 2000 e 2020.10. The.01*22-year futures price should be 2000 e 2040.40.The current 2-year futures price in the market is overvaluedcompared to the theoretical price. To lock in a profit, youwould short the 2 year futures, borrow USD 2000 at 1%,and buy the underlying asset. At the end of 2 years, you willsell the asset at USD 2,055 and return the borrowed money.01*2with interest, which would be 2,000 e USD2040.40,resulting in a USD 14.60 gain.12. You are examining the exchange rate between theU.S. dollar and the euro and are given the followinginformation regarding the USD/EUR exchange rate andthe respective domestic risk-free rates:Current USD/EUR exchange rate is 1.35Current USD-denominated 1-year risk-free interest rateis 1% per year. Current EUR-denominated 1-year risk-freeinterest rate is 2% per yearAccording to the interest rate parity theorem, what is the1-year forward USD/EUR exchange rate?A. 1.24B. 0.95C. 1.34D. 1.37 1.336Which of the following is the least effective response forChan to use in countering Archer’s argument?A. When computed for fixed income portfolios, VaR usesinterrelationships between different yield curves.B. VaR accounts for illiquidity, which may be present inlarger positions.C. VaR is based on the current portfolio and does notrequire a large amount of historical datafor its computation.D. VaR is based on tracking error and does not require aspecific index for its computation.Answer: BVaR accounts for illiquidity, which may be present in largerpositions. Accounting for liquidity is actually a weaknessWiley 2016

FRM Exam Reviewof VaR. On its own, VaR fails to distinguish the higher riskof a position that is too large for market liquidity versus aposition that could easily be liquidated. The other answersall distinguish VaR from traditional risk measures: standarddeviation is based on historical data and may not reflectthe risk characteristics of a current portfolio, VaR does notrequire a specific index for its calculation, unlike beta, andVaR accounts for interrelationships between different yieldcurves.14. Ben Johnson, FRM, serves as a consultant to numerousrisk management firms. He is currently advisingRST Corporation on the implementation of a riskmanagement program. RST is a newly formed companywith little expertise in risk management, and has hiredJohnson to train its staff.A. Scenario analysis is useful for allowing risk managersto assess secondary consequences of changes in riskfactors.B. Scenario analysis is useful for assessing exposure tochanges in the correlation between the componentsecurities.C. Scenario analysis is useful for discovering flaws in therisk measurement model and/or its assumptions.D. Scenario analysis is useful for assessing exposure tochanges in the volatility of the component securities.Answer: AScenario analysis is useful for allowing risk managers toassess secondary consequences of changes in risk factors.The incorrect statement is that scenario analysis isuseful for allowing risk managers to assess secondaryconsequences of changes in risk factors. Scenario analysisallows the managers to assess the impact of changes tovarious inputs into the risk measurement model. However,scenario analysis does not do a good job of assessingsecondary effects of changes in the risk factors.15. You are discussing dynamic hedging with the chief riskofficer who oversees all nonlinear risk at the enterpriselevel.The debate is the incremental value of how often to hedgenonlinear option greeks under conditions of large marketmoves when the Federal Reserve continues to raise ratesin 2016.Before you can consider the transactional cost ofhedging, you want to consider the incremental impact ofthe addition of an option hedge to the initial gamma anddelta of the portfolio.You have recently rebalanced the portfolio and added anew hedge consisting of 3,000 standard, exchange-tradedequity option contracts to enforce a gamma-neutralposition after a large market the addition of the gamma hedge, the original deltaneutral position also changes, so what trade must you doto restore delta neutrality after gamma hedging?Assume a delta of 0.75 for the options.A. Sell 225,000 shares of the underlying asset.B. Buy 2,250 shares of the underlying asset.C. Sell 500,000 shares of the underlying asset.D. Buy 5,000 shares of the underlying asset.Answer: AThe addition of the 3,000 long options to bring aboutgamma neutrality disturbed the original delta neutralposition of the portfolio.Since 3,000 options have been added, (3,000)(0.75) 2,250contracts of the underlying must be sold to restore deltaneutrality to the portfolio or 225,000 shares because theproblem states these are standard (100 shares per contact).Quick note: In the real world, the delta-gamma balancechanges by the second. All GARP wants you to know is that“hedging” always has secondary impacts that need to beconsidered. The argument could be, after this delta hedge,what does the gamma hedge look like, and go back andforth to infinity. Just understand that nothing happens in avacuum but more important why this changes.16. Albert Morrison is preparing a seminar on the termstructure of interest rates.In preparation for the seminar, Albert has taken thefollowing sample data on daily yield changes for 10year Treasuries. (Note: given yields are intentionally /20165.299Albert calculates the sum of the squared deviations fromthe mean to be 0.6405.Calculate the daily standard deviation of the data in thetable.A. 0.3812B. 0.3579C. 0.4002D. 0.4210Wiley 2016

FRM Exam CDaily standard deviationNote: This is at the upper limit if a tricky question andI almost hesitate to include it. Referring to the “sum ofsquared deviations from the mean” requires you to knowthe formula for variance and standard deviation. It alsorequires that you know you are calculating the change inrates, not just the average level of rates. The first data pointisn’t January of 2016 but rather a 1.3 basis point change inrates at the end of February of 2016. This also means wehave 5 sample points of rate changes. Since you are toldthis is a sample, we have N – 1 in the denominator. (sum of the squared deviations from mean / (N 1)) (0.6405 / (5 1)) (0.6405 / 4) (0.1601) 0.4002Good luck and stay on track.Remember, good preparation is essential to 2016

Top questions you must master to pass the Part I FRM Exam Preparing for the Part I exam is tough, but you can make life easier with an effective study plan. If you have yet to get a plan, Wiley’s adaptive Digital Exam Planner in our Silver and . But first, here are some questions to test your knowledge of typical, fundamental topics that .File Size: 608KBPage Count: 7EXPLORE FURTHER40 FRM Sample Questions You Must See FRMQuestionBank.comfrmquestionbank.comFRM Sample Questions 2022test-questions.comFRM Question Bank for Part 1 & 2 Exam - EduPristineedupristine.comFRM Part I Mock Exams GARP Approved Full . - AnalystPrepanalystprep.comFRM Part 1 Practice Questions GARP Approved Exam Prep .analystprep.comFRM Question Papers - Free PDF Download -