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2015FRMPracticeExam

2015 Financial Risk Manager (FRM ) Practice ExamTABLE OF CONTENTSIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1Reference Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2Special instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32015 FRM Part I Practice Exam Candidate Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . .52015 FRM Part I Practice Exam Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72015 FRM Part I Practice Exam Answer Sheet/Answers . . . . . . . . . . . . . . . . . . . . . . . . .192015 FRM Part I Practice Exam Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .212015 FRM Part II Practice Exam Candidate Answer Sheet . . . . . . . . . . . . . . . . . . . . . . .452015 FRM Part II Practice Exam Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .472015 FRM Part II Practice Exam Answer Sheet/Answers . . . . . . . . . . . . . . . . . . . . . . . .572015 FRM Part II Practice Exam Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59 2015 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this materialin any format without prior written approval of GARP, Global Association of Risk Professionals, Inc.i

2015 Financial Risk Manager (FRM ) Practice ExamINTRODUCTIONCore readings were selected by the FRM Committeeto assist candidates in their review of the subjects coveredThe FRM Exam is a practice-oriented examination. Its questionsby the Exam. Questions for the FRM Exam are derivedare derived from a combination of theory, as set forth in thefrom the “core” readings. It is strongly suggested thatcore readings, and “real-world” work experience. Candidatescandidates review these readings in depth prior to sittingare expected to understand risk management concepts andfor the Exam.approaches and how they would apply to a risk manager’sday-to-day activities.The FRM Exam is also a comprehensive examination,testing a risk professional on a number of risk managementSuggested Use of Practice ExamsTo maximize the effectiveness of the Practice Exams, candidates are encouraged to follow these recommendations:concepts and approaches. It is very rare that a risk managerwill be faced with an issue that can immediately be slotted1. Plan a date and time to take each Practice Exam.into one category. In the real world, a risk manager must beSet dates appropriately to give sufficient study/able to identify any number of risk-related issues and bereview time for the Practice Exam prior to theable to deal with them effectively.actual Exam.The 2015 FRM Practice Exams I and II have been developedto aid candidates in their preparation for the FRM Exam in2. Simulate the test environment as closely as possible.May and November 2015. These Practice Exams are based Take each Practice Exam in a quiet place.on a sample of questions from the 2011 through 2014 FRM Have only the practice exam, candidate answersheet, calculator, and writing instruments (pencils,Exams and are suggestive of the questions that will be inerasers) available.the 2015 FRM Examination.The 2015 FRM Practice Exam for Part I contains 25 cell phones and study material.multiple-choice questions and the 2015 FRM Practice Examfor Part II contains 20 multiple-choice questions. Note thatMinimize possible distractions from other people, Allocate 60 minutes for the Practice Exam andthe 2015 FRM Exam Part I will contain 100 multiple-choiceset an alarm to alert you when 60 minutes havequestions and the 2015 FRM Exam Part II will containpassed. Complete the exam but note the questions80 multiple-choice questions. The Practice Exams wereanswered after the 60 minute mark.designed to be shorter to allow candidates to calibrate Follow the FRM calculator policy. You may only usea Texas Instruments BA II Plus (including the BA IItheir preparedness without being overwhelming.Plus Professional), Hewlett Packard 12C (includingThe 2015 FRM Practice Exams do not necessarily coverall topics to be tested in the 2015 FRM Exam as the materialthe HP 12C Platinum and the Anniversary Edition),covered in the 2015 Study Guide may be different fromHewlett Packard 10B II, Hewlett Packard 10B II orthat covered by the 2011 through 2014 Study Guides. TheHewlett Packard 20B calculator.questions selected for inclusion in the Practice Exams werechosen to be broadly reflective of the material assigned for2015 as well as to represent the style of question that the3. After completing the Practice Exam, Calculate your score by comparing your answerFRM Committee considers appropriate based on assignedsheet with the Practice Exam answer key. Onlymaterial.include questions completed in the first 60 minutes. Use the Practice Exam Answers and ExplanationsFor a complete list of current topics, core readings, and key learningto better understand correct and incorrectobjectives candidates should refer to the 2015 FRM Exam Study Guideanswers and to identify topics that require addi-and Program Manual.tional review. Consult referenced core readings toprepare for Exam. 2015 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this materialin any format without prior written approval of GARP, Global Association of Risk Professionals, Inc.1

2015 Financial Risk Manager (FRM ) Practice ExamReference Table: Let Z be a standard normal random variable.2 2015 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this materialin any format without prior written approval of GARP, Global Association of Risk Professionals, Inc.

2015 Financial Risk Manager (FRM ) Practice ExamSpecial Instructions and Definitions1.Unless otherwise indicated, interest rates are assumed to be continuously compounded.2.Unless otherwise indicated, option contracts are assumed to be on one unit of the underlying asset.3.VaR value-at-risk4.ES expected shortfall5.GARCH generalized auto-regressive conditional heteroskedasticity6.CAPM capital asset pricing model7.LIBOR London interbank offer rate8.EWMA exponentially weighted moving average9.CDS credit default swap (s)10. MBS mortgage-backed security (securities)11. CEO/CFO/CRO Senior management positions: Chief Executive Officer, Chief Financial Officer,and Chief Risk Officer, respectively12. The following acronyms are used for selected currencies:AcronymCurrencyARSArgentine pesoAUDAustralian dollarBRLBrazilian realCADCanadian dollarCHFSwiss francEUReuroGBPBritish pound sterlingHKDHong Kong dollarINRIndian rupeeJPYJapanese yenMXNMexican pesoSGDSingapore dollarUSDUS dollar 2015 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this materialin any format without prior written approval of GARP, Global Association of Risk Professionals, Inc.3

2015 FRMPractice ExamPart IAnswer Sheet

2015 Financial Risk Manager (FRM ) Practice .23.9.24.10.25.b.c.d. 11.12.Correct way to complete13.1.14.Wrong way to complete15.1. 2015 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this materialin any format without prior written approval of GARP, Global Association of Risk Professionals, Inc. 5

2015 FRMPractice ExamPart IQuestions

2015 Financial Risk Manager (FRM ) Practice Exam1.A risk manager performs an ordinary least squares (OLS) regression to estimate the sensitivity of a stock'sreturn to the return on the S&P 500. This OLS procedure is designed ethethesquare of the sum of differences between the actual and estimated S&P 500 returns.square of the sum of differences between the actual and estimated stock returns.sum of differences between the actual and estimated squared S&P 500 returns.sum of squared differences between the actual and estimated stock returns.Using the prior 12 monthly returns, an analyst estimates the mean monthly return of stock XYZ to be -0.75%with a standard error of 2.70%.ONE-TAILED T-DISTRIBUTION TABLEDegrees of 2.179Using the t-table above, the 95% confidence interval for the mean return is between:a.b.c.d.3.-6.69% and 5.19%-6.63% and 5.15%-5.60% and 4.10%-5.56% and 4.06%Using data from a pool of mortgage borrowers, a credit risk analyst performed an ordinary least squaresregression of annual savings (in GBP) against annual household income (in GBP) and obtained the followingrelationship:Annual Savings 0.24 * Household Income - 25.66, R² 0.50Assuming that all coefficients are statistically significant, which interpretation of this result is correct?a.b.c.d.ForForForForthis sample data, the average error term is GBP -25.66.a household with no income, annual savings is GBP 0.an increase of GBP 1,000 in income, expected annual savings will increase by GBP 240.a decrease of GBP 2,000 in income, expected annual savings will increase by GBP 480. 2015 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this materialin any format without prior written approval of GARP, Global Association of Risk Professionals, Inc.7

2015 Financial Risk Manager (FRM ) Practice Exam4.A risk analyst is estimating the variance of stock returns on day n, given by, using the equationwhereandrepresent the return and volatility on day n-1, respectively.If the values of α and β are as indicated below, which combination of values indicates that the variancefollows a stable GARCH (1,1) process?a.b.c.d.αααα β 0.9090730.9255730.9255730.925573The following information applies to questions 5 and 6.A portfolio manager holds three bonds in one of his portfolios and each bond has a 1-year default probability of15%. The event of default for each of the bonds is independent.5.What is the probability of exactly two bonds defaulting over the next year?a.b.c.d.6.What is the mean and variance of the number of bonds defaulting over the next year?a.b.c.d.81.9%5.7%10.8%32.5%MeanMeanMeanMean 0.15, variance 0.320.45, variance 0.380.45, variance 0.320.15, variance 0.38 2015 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this materialin any format without prior written approval of GARP, Global Association of Risk Professionals, Inc.

2015 Financial Risk Manager (FRM ) Practice Exam7.A risk manager is evaluating a portfolio of equities with an annual volatility of 12.1% per year that is benchmarked to the Straits Times Index. If the risk-free rate is 2.5% per year, based on the regression results given inthe chart below, what is the Jensen's alpha of the portfolio?y 0.4936x 3.7069R2 0.5387a.b.c.d.8.0.4936%0.5387%1.2069%3.7069%An investment advisor is analyzing the range of potential expected returns of a new fund designed to replicate the directional moves of the BSE Sensex Index but with twice the volatility of the index. The Sensex hasan expected annual return of 12.3% and volatility of 19.0%, and the risk free rate is 2.5% per year. Assumingthe correlation between the fund’s returns and that of the index is 1, what is the expected return of the fundusing the capital asset pricing model?a.b.c.d.18.5%19.0%22.1%24.6% 2015 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this materialin any format without prior written approval of GARP, Global Association of Risk Professionals, Inc.9