Frm Practice Exam 052711

Financial Risk Manager (FRM®) Examination2011 Practice Exam Part I / Part II 2011 Financial Risk Manager Examination (FRM®) Practice Exam TABLE OF CONTENTS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 2011 FRM Part I Practice Exam 1 Candidate Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . .3 2011 FRM Part I Practice Exam 1 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 2011 FRM Part I Practice Exam 1 Answer Sheet/Answers . . . . . . . . . . . . . . . . . . . . . . . .15 2011 FRM Part I Practice Exam 1 Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17 2011 FRM Part I Practice Exam 2 Candidate Answer Sheet . . . . . . . . . . . . . . . . . . . . . .35 2011 FRM Part I Practice Exam 2 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37 2011 FRM Part I Practice Exam 2 Answer Sheet/Answers . . . . . . . . . . . . . . . . . . . . . . .47 2011 FRM Part I Practice Exam 2 Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49 2011 FRM Part II Practice Exam 1 Candidate Answer Sheet . . . . . . . . . . . . . . . . . . . . . .67 2011 FRM Part II Practice Exam 1 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69 2011 FRM Part II Practice Exam 1 Answer Sheet/Answers . . . . . . . . . . . . . . . . . . . . . . .77 2011 FRM Part II Practice Exam 1 Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .79 2011 FRM Part II Practice Exam 2 Candidate Answer Sheet . . . . . . . . . . . . . . . . . . . . .93 2011 FRM Part II Practice Exam 2 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95 2011 FRM Part II Practice Exam 2 Answer Sheet/Answers . . . . . . . . . . . . . . . . . . . . . .103 2011 FRM Part II Practice Exam 2 Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105 © 2011 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this material in any format without prior written approval of GARP, Global Association of Risk Professionals, Inc. 3 • • Take each practice exam in a quiet place. All rights reserved. Note that the 2011 FRM Examination Part I will contain 100 multiple-choice questions and the 2011 FRM Examination Part II will contain 80 multiple-choice questions. and key learning objectives candidates should refer to the 2011 FRM Examination Study Guide and AIM Statements. In the real world. Hewlett Packard 10B II or Hewlett Packard 20B calculator. and writing instruments (pencils. • • Minimize possible distractions from other people. testing a risk professional on a number of risk management concepts and approaches. You may only use a Texas Instruments BA II Plus (including the BA II Plus Professional). Complete the exam but note the questions answered after the 90 minute mark. core readings. The 2011 FRM Practice Exams I and II have been developed to aid candidates in their preparation for the FRM Examination in May and November 2011. Its questions are derived from a combination of theory. Have only the practice exam. Allocate 90 minutes for the practice exam and set an alarm to alert you when 90 minutes have passed. and “real-world” work experience. Each of the 2011 FRM Practice Exams for Part I contain 25 multiple-choice questions and each of the 2011 FRM Practice Exams for Part II contain 20 multiple-choice questions. The 2011 FRM Practice Exams do not necessarily cover all topics to be tested in the 2011 FRM Examination as the material covered in the 2011 Study Guide may be different from that covered by the 2009 Study Guide. After completing the practice exam. 2. These practice exams are based on a sample of questions from the 2009 FRM Examination and are suggestive of the questions that will be in the 2011 FRM Examination. © 2011 Global Association of Risk Professionals. Global Association of Risk Professionals. Hewlett Packard 12C (including the HP 12C Platinum). erasers) available. as set forth in the core readings. It is illegal to reproduce this material in any format without prior written approval of GARP. Set dates appropriately to give sufficient study/ review time for the practice exam prior to the actual exam. Plan a date and time to take each practice exam. The questions selected for inclusion in the Practice Exams were chosen to be broadly reflective of the material assigned for 2011 as well as to represent the style of question that the FRM Committee considers appropriate based on assigned material. Core readings were selected by the FRM Committee to assist candidates in their review of the subjects covered by the exam. 1 . Questions for the FRM examination are derived from the “core” readings. a risk manager must be able to identify any number of risk-related issues and be able to deal with them effectively. • Use the practice exam Answers and Explanations to better understand correct and incorrect answers and to identify topics that require additional review. Candidates are expected to understand risk management concepts and approaches and how they would apply to a risk manager’s day-to-day activities. The FRM Examination is also a comprehensive examination. For a complete list of current topics. candidates are encouraged to follow these recommendations: 1. Suggested Use of Practice Exams To maximize the effectiveness of the practice exams.2011 Financial Risk Manager Examination (FRM®) Practice Exam INTRODUCTION The FRM Exam is a practice-oriented examination. Inc. It is strongly suggested that candidates review these readings in depth prior to sitting for the exam. candidate answer sheet. • Calculate your score by comparing your answer sheet with the practice exam answer key. The practice exams were designed to be shorter to allow candidates to calibrate their preparedness without being overwhelming. calculator. Consult referenced core readings to prepare for exam. 3. • Follow the FRM calculator policy. Only include questions completed in the first 90 minutes. It is very rare that a risk manager will be faced with an issue that can immediately be slotted into one category. Simulate the test environment as closely as possible. cell phones and study material. Financial Risk ® Manager (FRM ) Examination 2011 Practice Exam PART I / EXAM 1 Answer Sheet . Wrong way to complete 1. 1. 12. Global Association of Risk Professionals. c. 3 8 © 2011 Global Association of Risk Professionals. Inc. It is illegal to reproduce this material in any format without prior written approval of GARP. 15. 10. 7. d. 8. 5. 2. b. 24. 19. 13. 9. a. Correct way to complete 1. 23. 3. 6. 25. b. 16. 4. c. 18. 17. d. 11.2011 Financial Risk Manager Examination (FRM®) Practice Exam a. 21. 22. 20. All rights reserved. 3 . 14. Financial Risk ® Manager (FRM ) Examination 2011 Practice Exam PART I / EXAM 1 Questions . 96.253. All rights reserved. Suppose 400 samples are randomly drawn with replacement from this population.05u2 + 0. and the standard deviation of the observed samples is 30. d. It is illegal to reproduce this material in any format without prior written approval of GARP.12 103. b.29% 1.0%.91% © 2011 Global Association of Risk Professionals. what is the simulated stock price after the second step? a.05. 4. The mean of the observed samples is 508. Assume that a random variable follows a normal distribution with a mean of 50 and a standard deviation of 10. Global Association of Risk Professionals.85% 1.79 98. What is the standard error of the sample mean? a.2011 Financial Risk Manager Examination (FRM®) Practice Exam 1.96% 18. 0. c. 1. and the first two simulated (randomly selected) standard normal variables are ε1 = 0.73% 1. b.1) model is used to forecast the daily return variance of an asset: 2 σn2 = 0.17% 2.15% 24. 5 . The following GARCH(1.47 101. volatility σ = 0. If S0 = 100. d. What percentage of this distribution is between 55 and 65? a. c. c. b.0% and the asset return is -2.92σn-1 n-1 Suppose the estimate of the volatility today is 5. A population has a known mean of 500.02. ε2 = -0.56% 8. d.7.70 3. d.675. Inc.5 15 4. b.015 0. c. Suppose you simulate the price path of stock HHF using a geometric Brownian motion model with drift μ = 0.18 and time step Δt = 0. What is the estimate of the long-run average volatility per day? a.000005 + 0.15 1. Let St be the price of the stock at time t. 3543 -0. “Stalled” and “Defeated” and the stock’s performance into three categories of “increase”.65 for market B. and the factor sensitivities to the global bond factors are 0.45 for market B. this probability is: a. Roy Thomson. -0. a global investment risk manager of FBN Bank. b.7% 6. d. 15. c. The covariance between market A and market B is closest to: a.0089 Global Equity Factor Global Bond Factor Suppose the factor sensitivities to the global equity factor are 0. what the probability that the legislation passed is. All rights reserved. . “constant” and “decrease” and estimates the following events: Passage 20% 10% 60% Stalled 50% 40% 30% Defeated 30% 70% 10% Probability of legislative outcome Probability of increase in stock price given legislative outcome Probability of decrease in stock price given legislative outcome A portfolio manager would like to know that if the stock price does not change in 2011.75 for market A and 0.0132 0.20 for market A and 0.2011 Financial Risk Manager Examination (FRM®) Practice Exam 5. is assessing markets A and B using a twofactor model.113 0. In order to determine the covariance between markets A and B.2% 38. Global Association of Risk Professionals. Based on John’s estimates. John is forecasting a stock’s price in 2011 conditional on the progress of certain legislation in the United States Congress. Inc. Thomson developed the following factor covariance matrix for global assets: Factor Covariance Matrix for Global Assets Global Equity Factor 0. He divides the legislative outcomes into three categories of “Passage”. b. c.0132 Global Bond Factor -0. d.113 0.215 -0.5% 19. It is illegal to reproduce this material in any format without prior written approval of GARP.215 6 © 2011 Global Association of Risk Professionals.6% 22. 000 or less. which fund should he choose? Fund Fund Fund Fund Fund a. c. All rights reserved. II.000 or more.3 A B C D A B C D 9.9 1.3% Volatility 15.000. b.5% Based on the following information.5% 1.8 0.4% 15. Inc.4% 1. 7 .2011 Financial Risk Manager Examination (FRM®) Practice Exam 7.000 or more. one would expect that in one out of: a. 90% confidence level. b. Market Credit Liquidity Operational 8. the portfolio value will decline by USD 5. the portfolio value will decline by USD 5. d. If the daily.000 or less. It is illegal to reproduce this material in any format without prior written approval of GARP.4% Fund Fund Fund Fund © 2011 Global Association of Risk Professionals. Rome Asset Management’s derivative pricing model consistently undervalues call options Swaps with counterparties exceed counterparty credit limit These two risks are most likely to be classified as: a. 90 days.8% Information Ratio 0. 90 days.8% Residual Risk 2. Global Association of Risk Professionals.4% and volatility of 14%. 9.3% 16. the portfolio value will decline by USD 5. Tim is evaluating 4 funds run by 4 independent managers relative to a benchmark portfolio that has an expected return of 7. c. d. c. d. b. the portfolio value will decline by USD 5. value-at-risk (VaR) of a portfolio is correctly estimated to be USD 5. 10 days. 10 days. He is interested in investing in the fund with the highest information ratio that also meets the following conditions in his investment guidelines: • • Expected residual return must be at least 2% Residual risk relative to the benchmark portfolio must be less than 2. Expected Return 9. I. John Diamond is evaluating the existing risk management system of Rome Asset Management and identified the following two risks. 51 and 0. It is illegal to reproduce this material in any format without prior written approval of GARP. d.5% per year and receiving LIBOR annually. d. Basis risk exists when futures and spot prices change by the same amount over time and converge at maturity of the futures contract. d. An airline company hedging exposure to a rise in jet fuel prices with heating oil futures contracts may face basis risk. paying a fixed rate of 7.89 and the volatilities of the equity fund and the futures are 0. the continuously compounded 1-year and 2-year annualized LIBOR rates were 7% per year and 8% per year. Global Association of Risk Professionals.48 per year respectively. b. Instead of selling off his holdings. c. respectively. c. 12. the value of a callable convertible bond to an investor: a. he would rather hedge two-thirds of his market exposure over the remaining 2 months. On Nov 1. Given that the correlation between Jimmy’s portfolio and the S&P 500 index futures is 0. location. . Just after the payment was made at the end of the first year. 13. b. USD -14 USD -4 USD 4 USD 14 million million million million 11. c. The S&P 500 index and its futures with the multiplier of 250 are trading at USD 900 and USD 910.2011 Financial Risk Manager Examination (FRM®) Practice Exam 10. considers locking up the profit from the recent rally. b. Decreases Increases Stays the same Insufficient information to determine. Inc. Sell Sell Sell Sell 250 futures contracts of S&P 500 169 futures contracts of S&P 500 167 futures contracts of S&P 500 148 futures contracts of S&P 500 8 © 2011 Global Association of Risk Professionals. Choices left to the seller about the physical settlement of the futures contract in terms of grade of the commodity. All rights reserved. If the volatility of the interest rate decreases. b. d. Jimmy Walton. c. a fund manager of an USD 60 million US medium-to-large cap equity portfolio. Which of the following statements about basis risk is incorrect? a. A bank had entered into a 3-year interest rate swap for a notional amount of USD 300 million. respectively. chemical attributes may result in basis risk. Basis risk is zero when variances of both the futures and spot process are identical and the correlation coefficient between spot and futures prices is equal to one. what position should he take to achieve his objective? a. The value of the swap at that time was closest to which of the following choices? a. The following bonds are eligible for delivery: Bonds A B C Spot–Price (USD) 102.98 1. d. c. The bonds pay their coupon amount semi-annually on June 30 and December 31.120 USD 0 USD 880 USD 1.80 1 2 3 4 5 -USD 1. the cheapest-to-deliver bond is: a.70 468. It is illegal to reproduce this material in any format without prior written approval of GARP.03 0.20 471. The futures price was USD 500 per unit and the contract size was 100 units per contract. © 2011 Global Association of Risk Professionals.2011 Financial Risk Manager Examination (FRM®) Practice Exam 14.38 Conversion Factor 0. d.30 492. The futures price of the commodity varied as shown below. Global Association of Risk Professionals. The yield curve is upward sloping. c. Alan bought a futures contract on a commodity on the New York Commodity Exchange on June 1. Alan set up a margin account with initial margin of USD 2.59 98. Inc. 9 . b. Futures Price (USD) 497. b. Bond A Bond B Bond C Insufficient information to determine.44 106. What was the balance in Alan’s margin account at the end of day on June 5? Day June June June June June a. You have a short T-Bond interest rate futures position.95 Coupon Rate 4% 5% 3% The futures price is 103 -17/32 and the maturity date of the contract is September 1.710 15.000 per contract and maintenance margin of USD 1000 per contract. With these data. All rights reserved.70 484. d. b.50 and of American put option is USD 10.50 and of American put option is USD 12. 17.56 and of American put option is USD 12.56 and of American put option is USD 10. What is the risk-neutral probability of the stock price going up in a single step? a. The risk-free rate is 10%. The risk-free rate is 12% per annum with continuous compounding.25% 1.5% 57. Value Value Value Value of of of of American American American American call call call call option option option option is is is is USD USD USD USD 6.free rate: a. N(d1) = 0.0 6.457185 and N(d2) = 0. 34. Microsoft’s stock price is currently at USD 22 and no dividend is due during the next 6 months.5% 80.0% 18.76% 3. Further. The stock price can go up or down by 20% each period. Assuming that there is no arbitrage opportunity.0 10 © 2011 Global Association of Risk Professionals. In order to find the no-arbitrage price of the option. b. It is illegal to reproduce this material in any format without prior written approval of GARP.0 5. On the OTC market there are two options available on Microsoft stock: a European put with premium of USD 2.2011 Financial Risk Manager Examination (FRM®) Practice Exam 16. Which of the following values is closest to the Black-Scholes values of these options? a.0 5. Mark uses a two-step binomial tree model.46.25 and an American call option with premium of USD 0.374163. The current stock price is USD 50 and the strike price of the option is USD 52. 0. which of the following choices is closest to the level of the risk. c. Both options have a strike price of USD 24 and an expiration date 3 months from now. d. . Mark is considering writing a 6 month American put option on a non-dividend paying stock ABC. Assume that options on a non dividend paying stock with price of USD 100 have a time to expiry of half a year and a strike price of USD 110.6% 65. Global Association of Risk Professionals. b c. A risk manager for bank XYZ. Inc. c. All rights reserved.52% Insufficient information to determine. d. Mark’s view is that the stock price has an 80% probability of going up each period and a 20% probability of going down. 2011 Financial Risk Manager Examination (FRM®) Practice Exam 19.. An analyst is doing a study on the effect on option prices of changes in the price of the underlying asset. The analyst wants to find out when the deltas of calls and puts are most sensitive to changes in the price of the underlying. Assume that the options are European and that the Black-Scholes formula holds. An increase in the price of the underlying has the largest absolute value impact on delta for: a. b. c. d. Deep in-the-money calls and deep out-of-the-money puts. Deep in-the-money puts and calls. Deep out-of-the-money puts and calls. At-the-money puts and calls. 20. A 5-year corporate bond paying an annual coupon of 8% is sold at a price reflecting a yield-to-maturity of 6% per year. One year passes and the interest rates remain unchanged. Assuming a flat term structure and holding all other factors constant, the bond’s price during this period will have a. b. c. d. Increased Decreased Remained constant Cannot be determined with the data given 21. Which of the following statements is incorrect, given the following one-year rating transition matrix? From/To (%) AAA AA A BBB BB B CCC/C a. b. c. d. AAA 87.44 0.60 0.05 0.02 0.04 0.00 0.08 AA 7.37 86.65 2.05 0.21 0.08 0.07 0.00 A 0.46 7.78 86.96 3.85 0.33 0.20 0.31 BBB 0.09 0.58 5.50 84.13 5.27 0.28 0.39 BB 0.06 0.06 0.43 4.39 75.73 5.21 1.31 B 0.00 0.11 0.16 0.77 7.36 72.95 9.74 CCC/C 0.00 0.02 0.03 0.19 0.94 4.23 46.83 D 0.00 0.01 0.04 0.29 1.20 5.71 28.83 Non Rated 4.59 4.21 4.79 6.14 9.06 11.36 12.52 BBB loans have a 4.08% chance of being upgraded in one year. BB loans have a 75.73% chance of staying at BB for one year. BBB loans have an 88.21% chance of being upgraded in one year. BB loans have a 5.72% chance of being upgraded in one year. © 2011 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this material in any format without prior written approval of GARP, Global Association of Risk Professionals, Inc. 11 2011 Financial Risk Manager Examination (FRM®) Practice Exam 22. You are the risk manager of a fund. You are using the historical method to estimate VaR. You find that the worst 10 daily returns for the fund over the period of last 100 trading days are -1.0%, -.3%, -0.6%, -0.2%, -2.7%, -1.0%, -2.9%, 0.1%, -1.1%, -3.0%. What is the daily VaR for the portfolio at the 95% confidence level? a. b. c. d. -2.9% -1.1% -1.0% -3.0% 23. Consider a bond with par value of EUR 1,000, maturity in 3 years, and that pays a coupon of 5% annually. The spot rate curve is as follows: Term 1 2 3 Annual Spot Interest Rates 6% 7% 8% The value of the bond is closest to: a. b. c. d. EUR EUR EUR EUR 904 924 930 950 24. Assume that portfolio daily returns are independently and identically normally distributed. Sam Neil, a new quantitative analyst, has been asked by the portfolio manager to calculate the portfolio Value-at-Risk (VaR) measure for 10, 15, 20 and 25 day periods. The portfolio manager notices something amiss with Sam’s calculations displayed below. Which one of following VARs on this portfolio is inconsistent with the others? a. b. c. d. VAR(10-day) = USD 316M VAR(15-day) = USD 465M VAR(20-day) = USD 537M VAR(25-day) = USD 600M 12 © 2011 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this material in any format without prior written approval of GARP, Global Association of Risk Professionals, Inc. 2011 Financial Risk Manager Examination (FRM®) Practice Exam 25. For the monthly returns plot of the fund tracked below in 2010, which period had a negative tracking error? a. b. c. d. 1/2009 – 5/2009 6/2009 – 10/2009 1/2009 – 10/2009 None of the above © 2011 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this material in any format without prior written approval of GARP, Global Association of Risk Professionals, Inc. 13 Financial Risk ® Manager (FRM ) Examination 2011 Practice Exam PART I / EXAM 1 Answers . Inc. 20. 18. All rights reserved. 7. Correct way to complete 1. d. 4. It is illegal to reproduce this material in any format without prior written approval of GARP.2011 Financial Risk Manager Examination (FRM®) Practice Exam a. 19. 16. 12. b. 24. 6. c. 9. 23. 13. a. Global Association of Risk Professionals. 3. 17. Wrong way to complete 1. 8. d. b. 3 8 © 2011 Global Association of Risk Professionals. 15 . 1. c. 2. 11. 22. 21. 15. 5. 25. 10. 14. Financial Risk ® Manager (FRM ) Examination 2011 Practice Exam PART I / EXAM 1 Explanations . 5*σ) . ε2 = -0.12 103.18 * 0.56% 8.5*σ) = Prob( X < mean + 1. Chapter 4. 4. All rights reserved.05)) = 101.0. 675 * sqrt(0. Suppose you simulate the price path of stock HHF using a geometric Brownian motion model with drift μ = 0.05 + 0.2417 Topic: Quantitative Analysis Subtopic: Probability Distributions Reference: Damodar N Gujarati.79 98.5*σ < X < mean + 1. Essentials of Econometrics.17% Answer: d.253.1183 S2 = 101.02.9332 . New York: McGraw-Hill. 17 . Chapter 12.02 * 0. Global Association of Risk Professionals. It is illegal to reproduce this material in any format without prior written approval of GARP. Therefore. volatility σ = 0. Explanation: Prob(mean + 0.Prob( X < mean + 0. Let St be the price of the stock at time t. 96. What percentage of this distribution is between 55 and 65? a. S1 = 100 + 100 * (0. and the first two simulated (randomly selected) standard normal variables are ε1 = 0.675.96% 18. © 2011 Global Association of Risk Professionals. c.70 Answer: b. Assume that a random variable follows a normal distribution with a mean of 50 and a standard deviation of 10. 3rd Edition.05)) = 98. what is the simulated stock price after the second step? a.02 * 0.18 and time step Δt = 0. Explanation: In the simulation.1183 + 101.6915 = 0. 80-84. b. c.05. 2. Inc. Value at Risk: the New Benchmark for Managing Financial Risk. 253 * sqrt(0.05 + 0.2011 Financial Risk Manager Examination (FRM®) Practice Exam 1. St is assumed to move as follows over an interval of time of length Δt: ΔSt+i = St+i – 1 (μ Δt + σ εi (Δt)1/2) where εi is a standard normal random variable.4722 Topic: Quantitative Analysis Subtopic: Simulation methods AIMS: Describe how to simulate a price path using a geometric Brownian motion model. 3rd Edition (New York: McGraw-Hill.18 * -0.15% 24.5*σ) = 0. Reference: Jorion (2005).47 101. d. b.1183 * (0. 2006). d. If S0 = 100. pp. b. GARCH model AIMS: Estimate volatility using the GARCH(p. 2009). d.05. Futures.73% 1. 0. (the population mean is irrelevant. Global Association of Risk Professionals. A population has a known mean of 500. . 1. In other words. Suppose 400 samples are randomly drawn with replacement from this population.1) model is used to forecast the daily return variance of an asset: 2 σn2 = 0.0% and the asset return is -2. Explanation: The standard error of the sample mean is estimated by dividing the standard deviation of the sample by the square root of the sample size: sx = s / (n)1/2 = 30 / (400)1/2 = 30 / 20 = 1. 2006). The following GARCH(1. All rights reserved. VL. it follows that VL = 0. it follows that γ = 0. the long-run average volatility per day implied by the model is sqrt(0. Chapter 21. and Other Derivatives. and the standard deviation of the observed samples is 30. c.000167. Options. It is illegal to reproduce this material in any format without prior written approval of GARP. Chapter 4 4. Essentials of Econometrics. What is the estimate of the long-run average volatility per day? a. Inc. b. Because the long-run average variance.q) model.05u2 + 0. What is the standard error of the sample mean? a.91% Answer: a.5.000005 + 0. Because γ = 1− α− β.29%.92σn-1 n-1 Suppose the estimate of the volatility today is 5. 7th Edition (New York: Prentice Hall.2011 Financial Risk Manager Examination (FRM®) Practice Exam 3.7.03. Explanation: The model corresponds to α = 0.0%.15 1.92. Topic: Quantitative Analysis Subtopic: EWMA.5 15 Answer: c. 000167) = 1. and ω = 0. 18 © 2011 Global Association of Risk Professionals.015 0.29% 1. c. can be found by VL = ω / γ . The mean of the observed samples is 508.) Topic: Quantitative Analysis Subtopic: Estimating parameters of distributions AIMS: Define and calculate the standard error of a sample mean Reference: Damodar Gujarati.000005. 3rd Edition (New York: McGraw‐Hill.85% 1. Reference: John Hull. β = 0. d. Global Association of Risk Professionals.3 * 0. 15.3 + 0.2011 Financial Risk Manager Examination (FRM®) Practice Exam 5. d. It is illegal to reproduce this material in any format without prior written approval of GARP. “constant” and “decrease” and estimates the following events: Passage 20% 10% 60% Stalled 50% 40% 30% Defeated 30% 70% 10% Probability of legislative outcome Probability of increase in stock price given legislative outcome Probability of decrease in stock price given legislative outcome A portfolio manager would like to know that if the stock price does not change in 2011.2 * 0.2) = 0. 3rd Edition. this probability is: a. John is forecasting a stock’s price in 2011 conditional on the progress of certain legislation in the United States Congress.6% 22.3 + 0. Based on John’s estimates.2) / (0.2% 38. “Stalled” and “Defeated” and the stock’s performance into three categories of “increase”. c. Explanation: Use Bayes’ Theorem: P(Passage | NoChange) = P(NoChange | Passage) * P(Passage) / P(NoChange) = (0. Chapter 2 (New York: McGraw-Hill. Essentials of Econometrics.5 * 0. 19 .3 * 0. He divides the legislative outcomes into three categories of “Passage”. Inc.7% Answer: c. 2006. All rights reserved. © 2011 Global Association of Risk Professionals.5% 19. what the probability that the legislation passed is. Reference: Damodar Gujarati.222 Topic: Quantitative Analysis Subtopic: Probability Distributions AIMS: Define Bayes’ theorem and apply Bayes' formula to determine the probability of an event. b. Inc. F2) F1 F2 = (0.215 Answer: c.45 for market B. Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk.45)] (-0. 2nd Edition (New York: McGraw‐Hill.20) (0.75) (0. -0.0132 0.20 for market A and 0.45) (0.2 σ2 + (βA.113 0. b. is assessing markets A and B using a twofactor model.0089 Global Equity Factor Global Bond Factor Suppose the factor sensitivities to the global equity factor are 0.0132) = 0. B) = βA.1131 Topic: Foundation of Risk Management Subtopic: Factor models and Arbitrage Pricing Theory AIMS: Calculate a security’s expected excess returns using the APT model and interpret the results. Chapter 7—Expected Returns and the Arbitrage Pricing Theory 20 © 2011 Global Association of Risk Professionals.1 βB.215 -0. It is illegal to reproduce this material in any format without prior written approval of GARP. Thomson developed the following factor covariance matrix for global assets: Factor Covariance Matrix for Global Assets Global Equity Factor 0.1 σ2 + βA.2 βB. Reference: Richard Grinold and Ronald Kahn. 1999).0132 Global Bond Factor -0. d.75 for market A and 0.0089) + [(0. In order to determine the covariance between markets A and B. c. a global investment risk manager of FBN Bank. .65) (0. Roy Thomson. and the factor sensitivities to the global bond factors are 0. Global Association of Risk Professionals.2 βB.75) (0.113 0.1) Cov (F1.1 βB. The covariance between market A and market B is closest to: a. All rights reserved.65) + (0.3543 -0.20) (0.65 for market B.2011 Financial Risk Manager Examination (FRM®) Practice Exam 6.2 + βA.3543) + (0. Explanation: Cov (A. 10% of the time (1 out of 10) the portfolio will lose USD 5. Market Credit Liquidity Operational Answer: d. 10 days. equivalently. All rights reserved. These are types of operational risks Topic: Foundation of Risk Management Subtopic: Creating Value with Risk Management AIMS: Define and describe the four major types of financial risks: market. c. Value-at-Risk: The New Benchmark for Managing Financial Risk. liquidity. John Diamond is evaluating the existing risk management system of Rome Asset Management and identified the following two risks.2011 Financial Risk Manager Examination (FRM®) Practice Exam 7.000 or more.000 or more. 2007). the portfolio value will decline by USD 5. the portfolio value will decline by USD 5. and operational. 3rd Edition (New York: McGraw‐Hill. Chapter 1—The Need for Risk Management 8. Global Association of Risk Professionals. II. b. credit.000.000 or more. 90% confidence level Value at Risk (VaR) of a portfolio is correctly estimated to be USD 5. Chapter 1—The Need for Risk Management © 2011 Global Association of Risk Professionals. Explanation: I is a model failure and II is an internal failure. If the daily. 90% confidence level. 90 days. c. I. one would expect that in one out of: a. the portfolio value will decline by USD 5. value-at-risk (VaR) of a portfolio is correctly estimated to be USD 5. Answer: c. 21 . the portfolio will lose less than USD 5.000. d. Reference: Philippe Jorion. b. Value-at-Risk: The New Benchmark for Managing Financial Risk. the portfolio value will decline by USD 5. Topic: Foundation of Risk Management Subtopic: Creating Value with Risk Management AIMS: Define value-at-risk (VaR) and describe how it is used in risk management Reference: Philippe Jorion. 90 days.000 or less. d. 2007).000 or less. It is illegal to reproduce this material in any format without prior written approval of GARP. one would expect that 90% of the time (9 out of 10). Rome Asset Management’s derivative pricing model consistently undervalues call options Swaps with counterparties exceed counterparty credit limit These two risks are most likely to be classified as: a. Inc.000. 10 days. Explanation: If the daily. 3rd Edition (New York: McGraw-Hill. 9%.4% .3% Volatility 15. Explanation: Information ratio = Expected residual return / residual risk = E(RP – RB) / (RP – RB) Fund A: Expected residual return = 9. Expected Return 9.9 * 2.95%. which does not meet the requirement of minimum residual return of 2%.5% 1. Inc. the information ratio. Portfolio Theory and Performance Analysis (West Sussex. Global Association of Risk Professionals.3% 16.8% Residual Risk 2.7. He is interested in investing in the fund with the highest information ratio that also meets the following conditions in his investment guidelines: • • Expected residual return must be at least 2% Residual risk relative to the benchmark portfolio must be less than 2. which fund should he choose? Fund Fund Fund Fund Fund a.5% = 1.3% . c.9 1.0% / 1.8% = 1. Fund B: Expected residual return = information ratio * residual risk = 0.0% Information ratio = 2.4% Fund Fund Fund Fund Answer: d.8% Information Ratio 0. b.4% = 2. It is illegal to reproduce this material in any format without prior written approval of GARP. d. .11 Both funds B and D meet the requirements.4% 1.4% = 1. Tim is evaluating 4 funds run by 4 independent managers relative to a benchmark portfolio that has an expected return of 7. does not meet residual return of 2% Fund D: This fund also meets both the residual return and residual risk requirements.16%.3 * 1. 2003).2011 Financial Risk Manager Examination (FRM®) Practice Exam 9. All rights reserved. Topic: Foundation of Risk Management Subtopic: Sharpe ratio and information ratio AIMS: Compute and interpret tracking error. Reference: Noel Amenc and Veronique Le Sourd. Fund D has the higher information ratio. Expected residual return = 9.4% = 2. Chapter 4—The Capital Asset Pricing Model and Its Application to Performance Measurement 22 © 2011 Global Association of Risk Professionals. England: John Wiley & Sons.4% and volatility of 14%.4% 15. and the Sortino ratio.3 A B C D A B C D 9.5% Based on the following information. so it meets both requirements Fund C: Expected residual return = information ratio * residual risk = 1.8 0.7. Bfix = USD 300 – USD 295. It is illegal to reproduce this material in any format without prior written approval of GARP. Just after the payment was made at the end of the first year. swaps and options AIMS: Value a plain vanilla interest rate swap based on two simultaneous bond positions. USD -14 USD -4 USD 4 USD 14 million million million million Answer: c. Since the payment has just been made the value of the floating rate is equal to the notional amount. the continuously compounded 1-year and 2-year annualized LIBOR rates were 7% per year and 8% per year. Value of the swap = Bfloating . Options. All rights reserved.5 million Value of the fixed payment = Bfix = 22. Reference: Hull. Explanation: Fixed rate coupon = USD 300 million x 7. Futures and Other Derivatives.08*2) = USD 295. respectively. c. A bank had entered into a 3-year interest rate swap for a notional amount of USD 300 million. Global Association of Risk Professionals. forwards.5 e(-0. paying a fixed rate of 7. d. 7th Edition.5% per year and receiving LIBOR annually.5% = USD 22. Inc. The value of the swap at that time was closest to which of the following choices? a. Chapter 7—Swaps.5 e(-0. 23 .80 = USD 4. b.07)+322. © 2011 Global Association of Risk Professionals.2011 Financial Risk Manager Examination (FRM®) Practice Exam 10.2 million Topic: Financial Markets and Products Subtopic: Futures.80 million Value of the floating payment = Bfloating = USD 300 million. Statement b is incorrect: as it is a correct statement: optionalities left to the seller at maturity gives the seller flexibility resulting in the buyer of the contract facing basis risk. Reference: John Hull. Global Association of Risk Professionals. foreign exchange. b. If the correlation is one then by definition there is no basis risk Topic: Financial Markets and Products Subtopic: Basis Risk AIMS: Define the various sources of basis risk and explain how basis risks arise when hedging with futures. Chapter 4. interest rates. and commodities AIMS: Identify the six factors that affect an option's price and discuss how these six factors affect the price for both European and American options. Answer: c. d. Hedging Strategies Using Futures 12. Basis risk is zero when variances of both the futures and spot process are identical and the correlation coefficient between spot and futures prices is equal to one. Answer: b. 7th Edition. Futures. . Topic: Financial Markets and Products Subtopic: Corporate Bonds. d. Decreases Increases Stays the same Insufficient information to determine. If the volatility of the interest rate decreases.2011 Financial Risk Manager Examination (FRM®) Practice Exam 11. It is illegal to reproduce this material in any format without prior written approval of GARP. Options. 9 24 © 2011 Global Association of Risk Professionals. 7th Edition. Derivatives on fixed‐income securities. Inc. All rights reserved. Basis risk exists when futures and spot prices change by the same amount over time and converge at maturity of the futures contract. Statement c is correct: as it is an incorrect statement: Basis risk exists when futures and spot prices do not change by the same amount over time and possibly will not converge at maturity of the futures contract. equities. location. Choices left to the seller about the physical settlement of the futures contract in terms of grade of the commodity. Explanation: A decrease in the interest rate volatility will decrease the value of embedded call on the bond and increase the value of the convertible bond. Which of the following statements about basis risk is incorrect? a. Options. Statement d is incorrect: as it is a correct statement: The magnitude of basis risk depends mainly on the degree of correlation between cash and futures prices. the value of a callable convertible bond to an investor: a. Chapter 3. An airline company hedging exposure to a rise in jet fuel prices with heating oil futures contracts may face basis risk. c. and Other Derivatives. c. chemical attributes may result in basis risk. b. Explanation: Statement a is incorrect: as it is a correct statement: An Airline company hedging jet fuel with heating oil futures may face basis risk due to difference in the underlying assets. Reference: Hull. Futures and Other Derivatives. Futures Price (USD) 497. Alan bought a futures contract on a commodity on the New York Commodity Exchange on June 1. d. Reference: Hull.89 and the volatilities of the equity fund and the futures are 0. Chapter 3. considers locking up the profit from the recent rally.80 1 2 3 4 5 -USD 1. © 2011 Global Association of Risk Professionals.48 = 0. What was the balance in Alan’s margin account at the end of day on June 5? Day June June June June June a.945 * 40. 7th Edition.000. The S&P 500 index and its futures with the multiplier of 250 are trading at USD 900 and USD 910. Instead of selling off his holdings. Jimmy Walton. d.48 per year respectively. Options. c. he would rather hedge two-thirds of his market exposure over the remaining 2 months. respectively. round up to nearest integer.945 The number of futures contracts is given by N=0. 25 . On Nov 1.30 492. c. Futures and Other Derivatives.51 and 0. what position should he take to achieve his objective? a. The Optimal hedge ratio is given by h = 0. Global Association of Risk Professionals. The futures price was USD 500 per unit and the contract size was 100 units per contract. Sell Sell Sell Sell 250 futures contracts of S&P 500 169 futures contracts of S&P 500 167 futures contracts of S&P 500 148 futures contracts of S&P 500 Answer: c. a fund manager of an USD 60 million US medium-to-large cap equity portfolio. It is illegal to reproduce this material in any format without prior written approval of GARP.000 per contract.51 / 0. compute and interpret the optimal number of futures contracts needed to hedge an exposure.000 per contract and maintenance margin of USD 1. including a “tailing the hedge” adjustment.26 ≈ 167. b.120 USD 0 USD 880 USD 1. The futures price of the commodity varied as shown below. Given that the correlation between Jimmy’s portfolio and the S&P 500 index futures is 0. Topic: Financial Markets and Products Subtopic: Minimum Variance Hedge Ratio AIMS: Define.70 484.20 471. Alan set up a margin account with initial margin of USD 2.000 / (910 * 250) = 166. All rights reserved. Explanation: The calculation is as follows: Two-thirds of the equity fund is worth USD 40 million.2011 Financial Risk Manager Examination (FRM®) Practice Exam 13. b.70 468.710 Answer: d. 14. Inc.89 * 0. .04 Cost of bond C = 98.98) = 0. Cost of delivering = Quoted price – (Current Futures price x Conversion Factor) Cost of bond A = 102. forwards.44 106. 15. and options Reference: Hull. c.70 468.30 492. The yield curve is upward sloping.38 – (103. 7th Edition.38 Conversion Factor 0. 26 © 2011 Global Association of Risk Professionals.98 Cost of bond B = 106. Explanation: Cheapest to deliver bond is the bond with the lowest cost of delivering. Options. b.70 484. Futures and Other Derivatives.59 98.53 x 1. swaps. Global Association of Risk Professionals. Reference: Hull.95 Coupon Rate 4% 5% 3% The futures price is 103 -17/32 and the maturity date of the contract is September 1. d. Options.59 – (103.98 1. Chapter 6.03) = -0. You have a short T-Bond interest rate futures position. The following bonds are eligible for delivery: Bonds A B C Spot–Price (USD) 102. Inc. All rights reserved.44 – (103. Topic: Financial Markets and Products Subtopic: Cheapest to deliver bond.20 471.2011 Financial Risk Manager Examination (FRM®) Practice Exam Explanation: Day June June June June June 1 2 3 4 5 Futures Price 497. 7th Edition. Answer: b.03 0.53 x 0. With these data. Futures and Other Derivatives. It is illegal to reproduce this material in any format without prior written approval of GARP.53 x .02 Hence.80 Daily Gain (Loss) (270) (460) (850) (1250) (290) Cumulative Gain (Loss) (270) (730) (1580) (2830) (3120) Margin Account Balance 1730 1270 420 750 1710 Margin Call 1580 1250 Topic: Financial Markets and Products Subtopic: Futures. Bond A Bond B Bond C Insufficient information to determine. bond B is the cheapest to deliver bond. conversion factors AIMS: Describe the impact of the level and shape of the yield curve on the cheapest‐to‐deliver bond decision.95) = . The bonds pay their coupon amount semi-annually on June 30 and December 31. the cheapest-to-deliver bond is: a. 2011 Financial Risk Manager Examination (FRM®) Practice Exam 16. On the OTC market there are two options available on Microsoft stock: a European put with premium of USD 2.25 and an American call option with premium of USD 0.46. Both options have a strike price of USD 24 and an expiration date 3 months from now. Microsoft’s stock price is currently at USD 22 and no dividend is due during the next 6 months. Assuming that there is no arbitrage opportunity, which of the following choices is closest to the level of the risk- free rate: a. b. c. d. 0.25% 1.76% 3.52% Insufficient information to determine. Answer: c. Explanation: Due to the fact that the American call option under consideration is on the stock which does not pay dividends, its value is equal to European call option with the same parameters. Thus, we can apply put-call parity to determine the level of interest rate. C – P = S – K e-rT 0.46 – 2.25 = 22 – 24 e-0.25r - 23.79 = -24e-0.25r r = 3.52% Topic: Financial Markets and Products Subtopic: American options, effects of dividends, early exercise AIMS: Explain put‐call parity and calculate, using the put‐call parity on a non‐dividend‐paying stock, the value of a European and American option, respectively. Reference: Hull, Options, Futures and Other Derivatives, 7th Edition, Chapter 10 17. A risk manager for bank XYZ, Mark is considering writing a 6 month American put option on a non-dividend paying stock ABC. The current stock price is USD 50 and the strike price of the option is USD 52. In order to find the no-arbitrage price of the option, Mark uses a two-step binomial tree model. The stock price can go up or down by 20% each period. Mark’s view is that the stock price has an 80% probability of going up each period and a 20% probability of going down. The risk-free rate is 12% per annum with continuous compounding. What is the risk-neutral probability of the stock price going up in a single step? a. b. c. d. 34.5% 57.6% 65.5% 80.0% Answer: b. © 2011 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this material in any format without prior written approval of GARP, Global Association of Risk Professionals, Inc. 27 2011 Financial Risk Manager Examination (FRM®) Practice Exam Explanation: b. is correct. pup = (erΔt – d)/(u - d) = (e0.12*3/12 – 0.8)/(1.2 – 0.8) = 57.61% Topic:: Valuation and Risk Models Subtopic: Binomial trees AIMS: Calculate the value of a European call or put option using the one‐step and two‐step binomial model. Reference: John Hull, Options, Futures and Other Derivatives, 7th Edition (New York: Prentice Hall, 2009), Chapter 11. 18. Assume that options on a non dividend paying stock with price of USD 100 have a time to expiry of half a year and a strike price of USD 110. The risk-free rate is 10%. Further, N(d1) = 0.457185 and N(d2) = 0.374163. Which of the following values is closest to the Black-Scholes values of these options? a. b c. d. Value Value Value Value of of of of American American American American call call call call option option option option is is is is USD USD USD USD 6.56 and of American put option is USD 12.0 5.50 and of American put option is USD 12.0 6.56 and of American put option is USD 10.0 5.50 and of American put option is USD 10.0 Answer: a. Explanation: a: is correct. With the given data, the value of a European call option is USD 6.56 and the value of a European put option is USD 11.20. We know that American options are never less than corresponding European option in valuation. Also, the American call option price is exactly the same as the European call option price under the usual Black-Scholes world with no dividend. Thus only ‘a’ is the correct option. Topic: Valuation and Risk Models Subtopic: Black‐Scholes‐Merton model AIMS: Compute the value of a European option using the Black‐Scholes‐Merton model on a non‐dividend‐paying stock. Reference: Hull, Options, Futures and Other Derivatives, 7th Edition, Chapter 13—The Black-Scholes-Merton Model 28 © 2011 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this material in any format without prior written approval of GARP, Global Association of Risk Professionals, Inc. 2011 Financial Risk Manager Examination (FRM®) Practice Exam 19. An analyst is doing a study on the effect on option prices of changes in the price of the underlying asset. The analyst wants to find out when the deltas of calls and puts are most sensitive to changes in the price of the underlying. Assume that the options are European and that the Black-Scholes formula holds. An increase in the price of the underlying has the largest absolute value impact on delta for: a. b. c. d. Deep in-the-money calls and deep out-of-the-money puts. Deep in-the-money puts and calls. Deep out-of-the-money puts and calls. At-the-money puts and calls. Answer: d. Explanation: a: is incorrect. When calls are deep in-the-money and puts are deep out-of-the-money, deltas are NOT most sensitive to changes in the underlying asset. b: is incorrect. When both calls and puts are deep in-the-money, deltas are NOT most sensitive to changes in the underlying asset. c: is incorrect. When both calls and puts are deep out-of-the-money, deltas are NOT most sensitive to changes in the underlying asset. d: is correct. When both calls and puts are at-the-money, deltas are most sensitive to changes in the underlying asset. (Gammas are largest when options are at-the-money) Topic: Valuation and Risk Models Subtopic: Greek Letters AIMS: Define, compute and describe delta, theta, gamma, vega, and rho for option positions. Reference: Hull, Options, Futures and Other Derivatives, 7th Edition, Chapter 17 20. A 5-year corporate bond paying an annual coupon of 8% is sold at a price reflecting a yield-to-maturity of 6% per year. One year passes and the interest rates remain unchanged. Assuming a flat term structure and holding all other factors constant, the bond’s price during this period will have a. b. c. d. Increased Decreased Remained constant Cannot be determined with the data given Answer: b. Explanation: Since yield-to-maturity < coupon, the bond is sold at a premium. As time passes, the bond price will move towards par. Hence the price will decrease. Topic: Valuation and Risk Models Subtopic: Bond prices, spot rates, forward rates AIMS: Discuss the impact of maturity on the price of a bond and the returns generated by bonds. Reference: Bruce Tuckman, Fixed Income Securities, 2nd Edition (Hoboken, NJ: John Wiley & Sons, 2002). © 2011 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this material in any format without prior written approval of GARP, Global Association of Risk Professionals, Inc. 29 BB loans have a 75.44 0.36 12.02 0.85 0.21 + 3.58 5. 2nd Edition.2011 Financial Risk Manager Examination (FRM®) Practice Exam 21.85).00 0.08 0.20 0.78 86.08% chance of being upgraded in one year. The chance of BB loans being downgraded over 1 year is 5.72% chance of being upgraded in one year.46 7. Global Association of Risk Professionals.83 Non Rated 4. The chance of BBB loans being upgraded over 1 year is 4. Chapter 6—The Rating Agencies 30 © 2011 Global Association of Risk Professionals. Which of the following statements is incorrect.31 B 0. 88.83 D 0. Reference: Caouette.39 75. given the following one-year rating transition matrix? From/To (%) AAA AA A BBB BB B CCC/C a. b: is incorrect.06 0.16 0. BBB loans have an 88.43 4.65 2.39 BB 0. Narayanan and Nimmo.94 4.05 0.08 + 0. Inc.00 0. The chance of BB loans staying at the same rate over 1 year is 75.20 5. BB loans have a 5. It is illegal to reproduce this material in any format without prior written approval of GARP.21 4.71 28.00 0.33 0. c: is correct.13 5.73%.95 9.04 0.21 0.79 6.03 0.33 + 5.59 4. Altman.01 0.19 0.27 0.05 0. Managing Credit Risk.09 0.77 7. c.73% chance of staying at BB for one year.74 CCC/C 0.06 0.36 72.04 0.14 9.23 46.04 + 0.21% represents the chance of BBB loans staying at BBB or being upgraded over 1 year. . Topic: Valuation and Risk Models Subtopic: Credit transition matrices AIMS: Define and explain a ratings transition matrix and its elements.21% chance of being upgraded in one year.07 0.50 84.60 0.31 BBB 0.28 0.02 0. b.37 86. d.00 A 0.96 3.27).72% (0. Explanation: a: is incorrect.11 0. d: is incorrect.73 5. AAA 87. All rights reserved.08 AA 7. Answer: c.02 + 0.00 0.52 BBB loans have a 4.29 1.06 11.08% (0.21 1. 2nd Edition (Hoboken.07)^2] + 1050/[(1. -3. -1. FRM questions and answer choices will be structured as to avoid confusion in this matter. Explanation: While some authors differ on the exact point on a discrete distribution at which to define VaR. c. Explanation: Using spot rates.7%.06) + 50/[(1. Chapter 1 © 2011 Global Association of Risk Professionals. -2.000. 23. the value of the bond is: 50/(1. b.37 Topic: Valuation and Risk Models Subtopic: Discount factors. maturity in 3 years.1%.0% Answer: c. -0. NJ: John Wiley & Sons. Global Association of Risk Professionals. 0. b. Fixed Income Securities. yield curves AIMS: Calculate the value of a bond using spot rates. The spot rate curve is as follows: Term 1 2 3 Annual Spot Interest Rates 6% 7% 8% The value of the bond is closest to: a.9%. Topic: Valuation and Risk Models Subtopic: Value‐at‐Risk (VaR) Definition and methods AIMS: Explain the various approaches for estimating VaR. arbitrage. it would be either the fifth worst loss.2011 Financial Risk Manager Examination (FRM®) Practice Exam 22. 2002). d. or some interpolated value in between in this case. c. and that pays a coupon of 5% annually. You are using the historical method to estimate VaR. the sixth worst loss. -2. 31 .0%. You are the risk manager of a fund.1%.2%. -1. Consider a bond with par value of EUR 1. d.1% -1. -2. Reference: Bruce Tuckman. Inc.3%.0%. What is the daily VaR for the portfolio at the 95% confidence level? a.6%.0%.08)^3] = 924. All rights reserved.0% -3. It is illegal to reproduce this material in any format without prior written approval of GARP. -. You find that the worst 10 daily returns for the fund over the period of last 100 trading days are -1. EUR EUR EUR EUR 904 924 930 950 Answer: b. -0.9% -1. c. It is illegal to reproduce this material in any format without prior written approval of GARP. . Value-at-Risk.2011 Financial Risk Manager Examination (FRM®) Practice Exam 24. Assume that portfolio daily returns are independently and identically normally distributed. VAR(10-day) = USD 316M VAR(15-day) = USD 465M VAR(20-day) = USD 537M VAR(25-day) = USD 600M Answer: a. 15. Explanation: Calculate VAR(1-day) from each choice: VAR(10-day) = 316 → VAR(1-day) = 316/sqrt(10) = 100 VAR(15-day) = 465 → VAR(1-day) = 465/sqrt(15) = 120 VAR(20-day) = 537 → VAR(1-day) = 537/sqrt(20) = 120 VAR(25-day) = 600 → VAR(1-day) = 600/sqrt(25) = 120 VAR(1-day) from Answer A is different from those from other answers. Inc. 3rd Edition. VAR from answer A is inconsistent. d. a new quantitative analyst. has been asked by the portfolio manager to calculate the portfolio Value-at-Risk (VaR) measure for 10. b. Sam Neil. Thus. Reference: Jorion. Which one of following VARs on this portfolio is inconsistent with the others? a. 20 and 25 day periods. All rights reserved. The portfolio manager notices something amiss with Sam’s calculations displayed below. Chapter 14 32 © 2011 Global Association of Risk Professionals. Global Association of Risk Professionals. Topic: Valuation and Risk Models Subtopic: Value‐at‐Risk (VaR) Definition and methods AIMS: Explain the various approaches for estimating VaR. 2003). b. 1/2009 – 5/2009 6/2009 – 10/2009 1/2009 – 10/2009 None of the above Answer: d. the information ratio. It is illegal to reproduce this material in any format without prior written approval of GARP. Portfolio Theory and Performance Analysis (West Sussex. Reference: Noel Amenc and Veronique Le Sourd. and the Sortino ratio. England: Wiley. Chapter 4—The Capital Asset Pricing Model and Its Application to Performance Measurement © 2011 Global Association of Risk Professionals.2011 Financial Risk Manager Examination (FRM®) Practice Exam 25. Inc. Explanation: The definition of tracking error is σ(Rp–Rb) where Rp and Rb are the return of the portfolio and benchmark respectively. This value can never be negative. All rights reserved. c. which period had a negative tracking error? a. For the monthly returns plot of the fund tracked below in 2010. d. 33 . Topic: Foundation of Risk Management Subtopic: Tracking error AIMS: Compute and interpret tracking error. Global Association of Risk Professionals. Financial Risk ® Manager (FRM ) Examination 2011 Practice Exam PART I / EXAM 2 Answer Sheet . 17. b. 9. 20. 15. 16. 25. 35 . 10. b. 21. Global Association of Risk Professionals. d. All rights reserved. d. c. c. 1. 18. 12. 4. Correct way to complete 1. 19. 6. 3. 22. 23. Wrong way to complete 1. 7.2011 Financial Risk Manager Examination (FRM®) Practice Exam a. 2. a. 8. It is illegal to reproduce this material in any format without prior written approval of GARP. 5. 3 8 © 2011 Global Association of Risk Professionals. 14. Inc. 24. 13. 11. Financial Risk ® Manager (FRM ) Examination 2011 Practice Exam PART I / EXAM 2 Questions . age and experience. Inc. b. into your model.43% 1. b. In addition you have discovered that the coefficients have low t-statistics but the regression model has a high R2. It is illegal to reproduce this material in any format without prior written approval of GARP. Incorrect standard errors Heteroskedasticity Serial correlation Multicollinearity 2.225.12% 2.521. You incorporated two independent variables. You built a linear regression model to analyze annual salaries for a developed country.95 9.2 and time step Δt = 0. and the first two simulated (randomly selected) standard normal variables are ε1 = -0.01.04% 0. d. Global Association of Risk Professionals. c. What is the standard error of the sample mean? a. The mean of the observed samples is 732. c.2011 Financial Risk Manager Examination (FRM®) Practice Exam 1. c. If S0 = 50.095 0. Upon reading the regression results. -1. 0. you noticed that the coefficient of “experience” is negative which appears to be counter-intuitive.5 95 © 2011 Global Association of Risk Professionals. b. volatility σ = 0. d. A population has a known mean of 750. ε2 = 1. 37 . All rights reserved.7. Suppose you simulate the price path of stock HHF using a geometric Brownian motion model with drift μ = 0. d. and the standard deviation of the observed samples is 60. Let St be the price of the stock at time t. Suppose 4000 samples are randomly drawn with replacement from this population. by what percent will the stock price change in the second step of the simulation? a. What is the most likely cause of these results? a.45% 3. 0% 38. Global Association of Risk Professionals. What is the estimate of the long-run average volatility per day? a. Inc.42% 5. “constant” and “decrease”. He divides the economy’s performance into three categories of “GOOD”.62% 94. d. John is forecasting a stock’s performance in 2010 conditional on the state of the economy of the country in which the firm is based.77σn-1 n-1 Suppose the estimate of the volatility on day n-1 is 2.2011 Financial Risk Manager Examination (FRM®) Practice Exam 4. It is illegal to reproduce this material in any format without prior written approval of GARP. If the state of the economy is NEUTRAL. d. c. He estimates: • • The probability that the state of the economy is GOOD is 20%. d.5% 20.5%. A student has not studied for the exam and just randomly guesses the answers. the asset return was -1.53% 38 © 2011 Global Association of Risk Professionals. The probability that the state of the economy is NEUTRAL is 30%. his supervisor. If the state of the economy is GOOD. If the state of the economy is POOR.000007 + 0.47% 33. 6. • Billy.66% 78. All rights reserved. Suppose that a quiz consists of 10 true-false questions.12u2 + 0. “NEUTRAL” and “POOR” and the stock’s performance into three categories of “increase”.1) model is used to forecast the daily return variance of an asset: 2 σn2 = 0. c. The following GARCH(1. the probability that the stock price increases is 50% and the probability that the stock price decreases is 30%. b.85% 2.21% 1. the probability that the stock price increases is 15% and the probability that the stock price decreases is 70%. John’s best assessment of that probability is closest to: a. . 5. b. the probability that the stock price increases is 80% and the probability that the stock price decreases is 10%.7% 6. 0. c.5% and that on day n-1.80% 1.0% 15. What is the probability that the student will get at least three questions correct? a. b. asks him to estimate the probability that the state of the economy is NEUTRAL given that the stock performance is constant. 95 days.000 or more.5% 42.000. Global Association of Risk Professionals. © 2011 Global Association of Risk Professionals. the portfolio value will decline by USD 10. 95% confidence level. one would expect that in one out of: a. In order to determine the volatility of the investment. Credit spreads widen following recent bankruptcies The bid-ask spread of an asset suddenly widens Which of these can be identified as liquidity risk? a. I only II only I and II Neither 9.5% 24.000 or less. the portfolio value will decline by USD 10. d.20 for the investment.2% 8.2% 37. the portfolio value will decline by USD 10. 95 days. It is illegal to reproduce this material in any format without prior written approval of GARP.2011 Financial Risk Manager Examination (FRM®) Practice Exam 7. b. b. II.01250 Global Equity Factor Global Bond Factor Suppose the factor sensitivity to the global equity factor is 0. value-at-risk (VaR) of a portfolio is correctly estimated to be USD 10.00791 0. The volatility of the investment is closest to: a. John Diamond is evaluating the existing risk management system of Rome Asset Management and identified the following two risks. A global investment risk manager is assessing an investment’s performance using a two-factor model. 11. I.000 or less. d.00791 Global Bond Factor 0. 39 . c. the risk manager developed the following factor covariance matrix for global assets: Factor Covariance Matrix for Global Assets Global Equity Factor 0. d. c.75 for the investment and the factor sensitivity to the global bond factor is 0. c. 20 days. 20 days. the portfolio value will decline by USD 10. If the daily.24500 0. All rights reserved. b. Inc.000 or more. b. 12. what position should he take to achieve his objective? a.1% Residual Risk 2. which fund should he choose? Fund Fund Fund Fund Fund a. d. Sell Sell Sell Sell 40 futures contracts of S&P 500 135 futures contracts of S&P 500 205 futures contracts of S&P 500 355 futures contracts of S&P 500 40 © 2011 Global Association of Risk Professionals.4% 1. c. Inc.100.4% Volatility 14.2 Based on the following information and a risk free rate of 5%. Dane Hudson.55 and 0. d. Which of the following is not a source of basis risk when using futures contracts for hedging? a.4% and volatility of 12%.3 A B C D A B C D 8.4% 17. b.8% Information Ratio 1.5% 1. respectively.8% 19. considers locking up the profit from the recent rally.000 and USD 1. Uncertainty about the exact date when the asset being hedged will be bought or sold. All rights reserved. he would rather hedge his market exposure over the remaining 2 months.5% Fund Fund Fund Fund 11. The need to close the futures contract before its delivery date. b. Instead of selling off his holdings. He is interested in investing in the fund with the highest information ratio that also meets the following conditions in his investment guidelines: I. The S&P 500 index and its futures with the multiplier of 250 are trading at USD 1. II.9 1. The inability of managers to forecast the price of the underlying.3% 16. Expected residual return must be at least 2% The Sharpe ratio must be at least 0. c. c. d. Differences between the asset whose price is being hedged and the asset underlying the futures contract.2011 Financial Risk Manager Examination (FRM®) Practice Exam 10.92 and the volatilities of the equity fund and the futures are 0. On Nov 1. It is illegal to reproduce this material in any format without prior written approval of GARP. Tom is evaluating 4 funds run by 4 independent managers relative to a benchmark portfolio that has an expected return of 6. Expected Return 8.45 per year respectively. . Global Association of Risk Professionals. a fund manager of an USD 50 million US large cap equity portfolio. Given that the correlation between Dane’s portfolio and the S&P 500 index futures is 0.1 0. Bond A Bond B Bond C Insufficient information to determine. You are given the following price history for the September silver futures: Day June 29 June 30 July 1 July 2 July 6 July 7 July 8 Futures Price (USD) 18.72 18. c. b.00 17. 41 . which bond is cheapest-todeliver? a.5 1. The yield curve is upward sloping. d. Each contract size is 5.000 and a maintenance margin of USD 4. The broker requires an initial margin of USD 6. All rights reserved. Global Association of Risk Professionals.62 per ounce. July 2 and July 7 only 1. July July July July 1 only 1 and July 2 only 1. c.500.2011 Financial Risk Manager Examination (FRM®) Practice Exam 13. Inc. It is illegal to reproduce this material in any format without prior written approval of GARP.1 Coupon Rate 4% 5% 3% The futures price is USD 104 and the maturity date of the contract is September 1. Simon purchased two September silver futures contracts. In late June. d.600 -3.100 2. You have a short T-Bond interest rate futures position.60 Conversion Factor 0.69 18.8 1.70 17.62 18.60 Daily Gain (Loss) 0 700 -6.40 99.03 17.000 -1.000 On which days did Simon receive a margin call? a.40 100. With these data. b. The following bonds are eligible for delivery: Bonds A B C Spot–Price(USD) 102. © 2011 Global Association of Risk Professionals.800 -3.000 ounces of silver and the futures price on the date of purchase was USD 18. July 2 and July 8 only 14. The bonds pay their coupon amount semi-annually on June 30 and December 31. short one call.50% 6.50% 5. d.50% What is the 2-year forward rate starting in three years? a. Below is a table of term structure of swap rates Maturity in Years 1 2 3 4 5 Swap Rate 3. Buy one put. All rights reserved.5% per year. Short one put. c. 16. Inc.00% 4. c. It is illegal to reproduce this material in any format without prior written approval of GARP. b. short one unit of spot. The price of a 1-year European call option with strike USD 120 is USD 5 and the price of a European put option with same strike and expiration is USD 25. What strategy exploits an arbitrage opportunity. A stock index is valued at USD 800 and pays a continuous dividend at the rate of 3% per year. and buy six units box-spread. The 6-month futures contract on that index is trading at USD 758. short one call. if any? a. and buy four units of box-spread.02% 17.51% 7. Is the futures contract priced so that there is an arbitrage opportunity? If yes. Global Association of Risk Professionals. 38 40 42 There is no arbitrage opportunity. b. buy one unit of spot. short one unit of spot. There are no arbitrage opportunities. b. The continuously compounded risk free rate is 2. 42 © 2011 Global Association of Risk Professionals.50% 5.2011 Financial Risk Manager Examination (FRM®) Practice Exam 15. A box spread with 1 year to expiration and strikes at USD 120 and USD 150 is trading at USD 20. 4. Buy one put.00% 5. which of the following numbers comes closest to the arbitrage profit you could realize by taking a position in one futures contract? a. . d. and short six units of box-spread. buy one call.50% 4. d. A stock is trading at USD 100. There are no transaction costs or taxes. c. Inc.000 shares of General Motors. Buy 1. What is the risk-neutral probability of the stock price going down in a single step? a. All rights reserved.25 and of American put option is USD 9. The risk-free rate is 8%.0% 68. Buy 10.8% 50. b. c.6164 a.25 and of American put option is USD 0. Which of the following portfolios would have the highest vega assuming all options involved are of the same strikes and maturities? a. 43 .10. b. c. Sell 10. b. c. You are looking to find a no-arbitrage price for a 1 year American call using a two-step binomial tree model for which the stock can go up or down by 25%. Sell 1. Global Association of Risk Professionals.48 9. Assume that options on a non dividend paying stock with price of USD 150 expire in a year and all have a strike price of USD 140. d. 19.00 21. what action must you take on the underlying stock in order to hedge the option exposure and keep it delta neutral? a.000 shares of General Motors.50.7327 and N(d2) = 0. c. d. 22. It is illegal to reproduce this material in any format without prior written approval of GARP.6% 39. d.2011 Financial Risk Manager Examination (FRM®) Practice Exam 18.000 shares of General Motors. d.00 9.3% 20. b. As a risk manager. The delta of the option on one share is 0.000 shares of General Motors. A non-dividend paying stock is currently trading at USD 25. a short in a put. Which of the following values is closest to the Black-Scholes values of these options assuming N(d1) = 0.25 30.48 and of American put option is USD 0.48 and of American put option is USD 30. Long a call Short a put Long a put and long a call A short of the underlying. A trader in your bank has sold 200 call option contracts each on 100 shares of General Motors with time to maturity of 60 days at USD 2. and a long in a call © 2011 Global Association of Risk Professionals. Value Value Value Value of of of of American American American American call call call call option option option option is is is is USD USD USD USD 30. The risk free rate is 10% and you believe that there is an equal chance of the stock price going up or down. 2011 Financial Risk Manager Examination (FRM®) Practice Exam 22.08 AA 7.66 99. AAA 87.02 0.20 0.39 75.25 97.08 0.06 0.21 0.46 7.78 86.21 1. 23.31 B 0. d.00 0.21 0.25 101.52 44 © 2011 Global Association of Risk Professionals.20 9.74 CCC/C 0.83 D Non Rated 0.08% chance of being upgraded in one year.06 5. All rights reserved.65 2.05 0.14 1. USD USD USD USD 95. c.16 0.07 0.00 A 0.36 28.00 0.71 11.36 72.58 5.04 4.59 0. Global Association of Risk Professionals. Which of the following statements is incorrect. b.43 4.28 0.11 0.04 0.83 12.31 BBB 0.00 0. d.02 0.03 0.96 3.44 0.65% chance of staying at AA for one year.06 0.94 4.05 0. The spot rate curve is as follows: Term 1 2 3 Annual Spot Interest Rates 6% 7% 8% The value of the bond is closest to: a.52 ‘AAA’ loans have 0% chance of ever defaulting.79 0. ‘A’ loans have a 13.09 0. given the following one-year rating transition matrix? From/To (%) AAA AA A BBB BB B CCC/C a. It is illegal to reproduce this material in any format without prior written approval of GARP. b.27 0.85 0. ‘BBB’ loans have a 4.39 BB 0. A bond with par value of USD 100 and 3 years to maturity pays 7% annual coupons.33 0.04% chance of receiving a ratings change.77 7.37 86.50 84. .60 0.95 9.73 5.13 5.00 4. Inc.23 46. c.01 4. ‘AA’ loans have a 86.19 0.29 6. d. Global Association of Risk Professionals. 45 . d.2M 316M 412M 25. Sam Neil. What will this be if worst 5 losses in the past 100 trading days are 316M. Theta is always negative for long calls and long puts and positive for short calls and short puts.2011 Financial Risk Manager Examination (FRM®) Practice Exam 24. 385M. Which of the following statements is correct? I. All rights reserved. II. a new quantitative analyst. It is illegal to reproduce this material in any format without prior written approval of GARP. 422M and 485M in USD? a. but this is not true for the Rho of put options. c. The Rho of a call option changes with the passage of time and tends to approach zero as expiration approaches. c. b. has been asked by the portfolio manager to calculate the portfolio 1-day 98% Value-at-Risk (VaR) measure based on the past 100 trading days. b. I only II only I and II Neither © 2011 Global Association of Risk Professionals. USD USD USD USD 31. a. 412M. Inc.6M 41. Financial Risk ® Manager (FRM ) Examination 2011 Practice Exam PART I / EXAM 2 Answers . 24. 3. 4. 5. 18. 15. 47 . 6. Wrong way to complete 1. 2. 1. 17. 11. d. Global Association of Risk Professionals. c.2011 Financial Risk Manager Examination (FRM®) Practice Exam a. 10. b. 23. 3 8 © 2011 Global Association of Risk Professionals. 16. 22. 14. 12. c. All rights reserved. a. 21. Inc. 9. It is illegal to reproduce this material in any format without prior written approval of GARP. b. 7. 8. Correct way to complete 1. 13. 19. 20. 25. d. Financial Risk ® Manager (FRM ) Examination 2011 Practice Exam PART I / EXAM 2 Explanations . Reference: Jorion (2005). Chapter 12. In addition you have discovered that the coefficients have low t-statistics but the regression model has a high R2. 3rd Edition. volatility σ = 0. by what percent will the stock price change in the second step of the simulation? a. (S2 . c. Topic: Quantitative Analysis Subtopic: Linear regression and correlation.2 * 1. Value at Risk: The New Benchmark for Managing Financial Risk. Global Association of Risk Professionals. Suppose you simulate the price path of stock HHF using a geometric Brownian motion model with drift μ = 0. Reference: Damodar Gujarati. hypothesis testing AIMS: Explain the concept of multicollinearity and the implications it has on modeling. Explanation: Age and experience are highly correlated and would lead to multicollinearity. What is the most likely cause of these results? a. St is assumed to move as follows over an interval of time of length Δt: ΔSt+i /St+i–1 = (μ Δt + σ εi (Δt)1/2) where εi is a standard normal random variable. -1. low t-statistics but a high R2 do suggest this problem also. It is illegal to reproduce this material in any format without prior written approval of GARP. © 2011 Global Association of Risk Professionals. Essentials of Econometrics. 49 . Upon reading the regression results. All rights reserved. b and c are not likely causes and are therefore incorrect. Chapter 8 2. Incorrect standard errors Heteroskedasticity Serial correlation Multicollinearity Answer: d. age and experience. In fact. Inc.S1)/S1 = 0. and the first two simulated (randomly selected) standard normal variables are ε1 = -0. b. New York: McGraw-Hill.521. Therefore.2 and time step Δt = 0.225. You incorporated two independent variables.45% Answer: d. d.01. into your model.225 * sqrt(0. Explanation: In the simulation. Answers a. d. You built a linear regression model to analyze annual salaries for a developed country. c. Let St be the price of the stock at time t.12% 2. 3rd Edition. If S0 = 50.2011 Financial Risk Manager Examination (FRM®) Practice Exam 1.43% 1. b. ε2 = 1.01) = 0. you noticed that the coefficient of “experience” is negative which appears to be counter-intuitive.04% 0.0245 Topic: Quantitative Analysis Subtopic: Simulation methods AIMS: Describe how to simulate a price path using a geometric Brownian motion model. 77.00006364. Chapter 4 4. It is illegal to reproduce this material in any format without prior written approval of GARP. d.00006364) = 0. 2009).q) model. Topic: Quantitative Analysis Subtopic: EWMA.) Topic: Quantitative Analysis Subtopic: Estimating parameters of distributions AIMS: Define and calculate the standard error of a sample mean Reference: Damodar Gujarati. Global Association of Risk Professionals.095 0. What is the estimate of the long-run average volatility per day? a. 7th Edition (New York: Prentice Hall.12u2 + 0. and Other Derivatives.000007 + 0.7.11.95 (the population mean is irrelevant. Explanation: The model corresponds to α = 0. the asset return was -1.5% and that on day n-1. 0. What is the standard error of the sample mean? a.95 9. Reference: John Hull. The long-run average variance. b. Because γ = 1− α − β. VL.12. Futures.5 95 Answer: b. and ω = 0. the long-run average volatility per day implied by the model is sqrt(0. β = 0.000007. it follows that VL = 0. All rights reserved. Chapter 21.42% Answer: a.798%. 2006).2011 Financial Risk Manager Examination (FRM®) Practice Exam 3. A population has a known mean of 750. and the standard deviation of the observed samples is 60. The mean of the observed samples is 732.5%. GARCH model AIMS: Estimate volatility using the GARCH(p. can be found with VL = ω /γ. Inc. c. In other words. 3rd Edition (New York: McGraw‐Hill.80% 1. Essentials of Econometrics. Options. b. The following GARCH(1.85% 2. c.21% 1.77σn-1 n-1 Suppose the estimate of the volatility on day n-1 is 2.1) model is used to forecast the daily return variance of an asset: 2 σn2 = 0. 0. . d. Explanation: The standard error of the sample mean is estimated by dividing the standard deviation of the sample by the square root of the sample size: sx = s / (n)1/2 = 60 / (4000)1/2 = 60 / 63 = 0. 50 © 2011 Global Association of Risk Professionals. Suppose 4000 samples are randomly drawn with replacement from this population. it follows that γ = 0. Global Association of Risk Professionals.387 a: b: c: This is the Prob(Constant & Neutral) This is the Prob(Constant) This is the Prob(Neutral | Decrease) Topic: Quantitative Analysis Subtopic: Probability Distributions AIMS: Define Bayes’ theorem and apply Bayes' formula to determine the probability of an event. d.2011 Financial Risk Manager Examination (FRM®) Practice Exam 5. the probability that the stock price increases is 50% and the probability that the stock price decreases is 30%.2 + 0. If the state of the economy is POOR.1 * 0. Chapter 2 (New York: McGraw-Hill. John is forecasting a stock’s performance in 2010 conditional on the state of the economy of the country in which the firm is based. 6.2 * 0. “NEUTRAL” and “POOR” and the stock’s performance into three categories of “increase”. The probability that the state of the economy is NEUTRAL is 30%. Essentials of Econometrics.0% 38. 3rd Edition. c. asks him to estimate the probability that the state of the economy is NEUTRAL given that the stock performance is constant. © 2011 Global Association of Risk Professionals. All rights reserved.5% 20. He estimates: • • The probability that the state of the economy is GOOD is 20%. the probability that the stock price increases is 80% and the probability that the stock price decreases is 10%.15 * 0.3 / (0. It is illegal to reproduce this material in any format without prior written approval of GARP. b. If the state of the economy is GOOD.2 * 0.0% 15. John’s best assessment of that probability is closest to: a. the probability that the stock price increases is 15% and the probability that the stock price decreases is 70%. If the state of the economy is NEUTRAL. 2006.3 + 0. 51 . Reference: Damodar Gujarati. his supervisor. “constant” and “decrease”. Inc.7% Answer: d. Explanation: Use Bayes’ Theorem: P(NEUTRAL | Constant) = P(Constant | Neutral) * P(Neutral) / P(Constant) = 0. He divides the economy’s performance into three categories of “GOOD”.5) = 0. • Billy. 20 for the investment. All rights reserved.5% 42. 52 © 2011 Global Association of Risk Professionals. Inc.62% 94. Global Association of Risk Professionals.47% 33.53% Answer: d Explanation: Calculate for no questions correct. .2011 Financial Risk Manager Examination (FRM®) Practice Exam 6.75 for the investment and the factor sensitivity to the global bond factor is 0.2% 37. 1 question correct.00791 Global Bond Factor 0. and identify common occurrences of each distribution. Christian Menn.05469 = 94. b. and Poisson distribution. d. A global investment risk manager is assessing an investment’s performance using a two-factor model. It is illegal to reproduce this material in any format without prior written approval of GARP. Portfolio Selection and Option Pricing (Hoboken. 5. Reference: Svetlozar Rachev. Binomial distribution.01250 Global Equity Factor Global Bond Factor Suppose the factor sensitivity to the global equity factor is 0. d.24500 0. 11. and Frank Fabozzi. c. Chapter 2— Discrete Probability Distributions 7.2% Answer: c. and 2 questions correct: (10C0 + 10C1 + 10C2)*0. A student has not studied for the exam and just randomly guesses the answers.469% 1 . the risk manager developed the following factor covariance matrix for global assets: Factor Covariance Matrix for Global Assets Global Equity Factor 0. b.0. 2005). NJ: Wiley.66% 78. c. Suppose that a quiz consists of 10 true-false questions.00791 0. What is the probability that the student will get at least three questions correct? a. In order to determine the volatility of the investment.53% Topic: Quantitative Analysis Subtopic: Probability and Probability Distributions AIMS: Describe the key properties of the Bernoulli distribution. The volatility of the investment is closest to: a.510 = 5. Fat-Tailed and Skewed Asset Return Distributions: Implications for Risk Management.510 = (1 + 10 + 45) )*0.5% 24. Value-at-Risk: The New Benchmark for Managing Financial Risk. II.20)2 (0. Topic: Foundation of Risk Management Subtopic: Creating Value with Risk Management AIMS: Define and describe the four major types of financial risks: market. It is illegal to reproduce this material in any format without prior written approval of GARP. I only II only I and II Neither Answer: b. Reference: Richard Grinold and Ronald Kahn. d. Reference: Philippe Jorion.1407) = 37. Chapter 7—Expected Returns and the Arbitrage Pricing Theory 8.00791) = 0. 2nd Edition (New York: McGraw‐Hill. 1999). Inc.2011 Financial Risk Manager Examination (FRM®) Practice Exam Explanation: 2 2 2 2 Var (Inv) = β1 σF1 + β2 σF2 + 2 β1 β2 Cov (F1. 3rd Edition (New York: McGraw‐Hill. and operational. II is liquidity risk. John Diamond is evaluating the existing risk management system of Rome Asset Management and identified the following two risks. liquidity.0125) + 2 (0.5% Topic: Foundation of Risk Management Subtopic: Factor models and Arbitrage Pricing Theory AIMS: Calculate a security’s expected excess returns using the APT model and interpret the results. c.75) (0.75)2 (0. b. All rights reserved.20) (0. 53 . Explanation: I is market risk. I. credit. Global Association of Risk Professionals. Chapter 1—The Need for Risk Management © 2011 Global Association of Risk Professionals. F2) = (0. Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk.1407 σ = sqrt(0.245) + (0. 2007). Credit spreads widen following recent bankruptcies The bid-ask spread of an asset suddenly widens Which of these can be identified as liquidity risk? a. If the daily. 95 days. II. one would expect that in one out of: a.000. equivalently.000 or less. All rights reserved.5% Fund Fund Fund Fund Answer: a. c.4% 1. 54 © 2011 Global Association of Risk Professionals. 2007). which fund should he choose? Fund Fund Fund Fund Fund a. the portfolio value will decline by USD 10.000 or more.1% Residual Risk 2. b. the portfolio value will decline by USD 10. Topic: Foundation of Risk Management Subtopic: Creating Value with Risk Management AIMS: Define value-at-risk (VaR) and describe how it is used in risk management Reference: Philippe Jorion.9 1. Explanation: If the daily.4% and volatility of 12%. He is interested in investing in the fund with the highest information ratio that also meets the following conditions in his investment guidelines: I.1 0.000. Value-at-Risk: The New Benchmark for Managing Financial Risk.4% 17.4% Volatility 14.000.000 or less. 95 days. Chapter 1—The Need for Risk Management 10. c. b. d. 95% confidence level.2011 Financial Risk Manager Examination (FRM®) Practice Exam 9. the portfolio value will decline by USD 10. 5% of the time (1 out of 20) the portfolio will lose USD 10. the portfolio value will decline by USD 10.8% 19. Expected Return 8. d.000 or more. 20 days.3 A B C D A B C D 8. Answer: d. Inc. 95% confidence level Value at Risk (VaR) of a portfolio is correctly estimated to be USD 10. It is illegal to reproduce this material in any format without prior written approval of GARP.5% 1.3% 16. value-at-risk (VaR) of a portfolio is correctly estimated to be USD 10. 20 days. Expected residual return must be at least 2% The Sharpe ratio must be at least 0. the portfolio will lose less than USD 10. Global Association of Risk Professionals.000 or more. Tom is evaluating 4 funds run by 4 independent managers relative to a benchmark portfolio that has an expected return of 6. one would expect that 95% of the time (19 out of 20). . 3rd Edition (New York: McGraw-Hill.8% Information Ratio 1.2 Based on the following information and a risk free rate of 5%. England: John Wiley & Sons. Uncertainty about the exact date when the asset being hedged will be bought or sold.5%)/19. c.1% / 1. It is illegal to reproduce this material in any format without prior written approval of GARP.4% = 0. the information ratio. Fund A has the higher information ratio. Reference: John Hull. Reference: Noel Amenc and Veronique Le Sourd. All rights reserved.183 Both funds A and B meet the requirements. Global Association of Risk Professionals.2011 Financial Risk Manager Examination (FRM®) Practice Exam Explanation: Sharpe Ratio = Return Premium over Risk Free Rate / Volatility = E(RP – Rf) / σ Fund A: Fund B: Fund C: Fund D: Expected residual return = 8. Portfolio Theory and Performance Analysis (West Sussex.16% + 6. Topic: Foundation of Risk Management Subtopic: Sharpe ratio and information ratio AIMS: Compute and interpret tracking error.8% = 1.6. Options. 7th Edition (New York: Pearson.5% .95% Expected residual return = 8. Answer: c. Which of the following is not a source of basis risk when using futures contracts for hedging? a.0%. b. Differences between the asset whose price is being hedged and the asset underlying the futures contract.1% = 0.3 * 1.4% . Explanation: The inability of managers to forecast the price of the underlying is an argument for hedging but does not increase basis risk. Sharpe Ratio = (8.217 Expected residual return = information ratio * residual risk = 1. d. The inability of managers to forecast the price of the underlying. Topic: Financial Markets and Products Subtopic: Basis risk AIMS: Define the various sources of basis risk and explain how basis risk arises when hedging with futures.3% = 0.5% = 1.4% = 2.238 Expected residual return = information ratio * residual risk = 0.1% Information ratio = 2. Futures and Other Derivatives. Chapter 3— Hedging strategies using futures © 2011 Global Association of Risk Professionals.16 Sharpe Ratio = (8. 55 .5%)/16.4% = 2.5% .4% = 2. The need to close the futures contract before its delivery date. 2009). Inc. and the Sortino ratio.4% .9 * 2.5%)/14.4% . Chapter 4—The Capital Asset Pricing Model and Its Application to Performance Measurement 11.16% Sharpe Ratio = (2.6. 2003). he would rather hedge his market exposure over the remaining 2 months.2011 Financial Risk Manager Examination (FRM®) Practice Exam 12. respectively. The S&P 500 index and its futures with the multiplier of 250 are trading at USD 1.124 * 50.000. On Nov 1. c. d. .92 and the volatilities of the equity fund and the futures are 0. 7th Edition. b. Reference: Hull.45 per year respectively. Instead of selling off his holdings. All rights reserved. Explanation: The calculation is as follows: The equity fund is worth USD 50 million.000 / (1. 56 © 2011 Global Association of Risk Professionals. round up to nearest integer. compute and interpret the optimal number of futures contracts needed to hedge an exposure. Topic: Financial Markets and Products Subtopic: Minimum Variance Hedge Ratio AIMS: Define.55 and 0. Inc.100.92 * 0.45 = 1. Global Association of Risk Professionals. Given that the correlation between Dane’s portfolio and the S&P 500 index futures is 0.000 and USD 1. The Optimal hedge ratio is given by h = 0. Dane Hudson. Futures and Other Derivatives. considers locking up the profit from the recent rally. Sell Sell Sell Sell 40 futures contracts of S&P 500 135 futures contracts of S&P 500 205 futures contracts of S&P 500 355 futures contracts of S&P 500 Answer: c.100 * 250) = 204.124 The number of futures contracts is given by N = 1. It is illegal to reproduce this material in any format without prior written approval of GARP.36 ≈ 205. Options.55 / 0. what position should he take to achieve his objective? a. a fund manager of an USD 50 million US large cap equity portfolio. including a “tailing the hedge” adjustment. Chapter 3. 03 17. 2009). 7th Edition (New York: Pearson.72 18. Each contract size is 5. swaps and options AIMS:Describe the rationale for margin requirements and explain how they work. July 2 and July 8 only Answer: b.000 6.800 -3.000 -1. In late June. forwards.900 -9. Global Association of Risk Professionals. Explanation: Here is the complete history of the margin account and margin calls: Day 6/29/2010 6/30/2010 7/1/2010 7/2/2010 7/6/2010 7/7/2010 7/8/2010 Futures Price 18.800 5.60 Daily Gain (Loss) 0 700 -6. b. It is illegal to reproduce this material in any format without prior written approval of GARP.70 17. Simon purchased two September silver futures contracts. July July July July 1 only 1 and July 2 only 1.00 17.69 18. © 2011 Global Association of Risk Professionals.800 -3.62 18. All rights reserved.000 -6. Inc.000 -1.100 2. d. Options.72 18.03 17.000 Cumulative Gain (Loss) 700 -5.000 ounces of silver and the futures price on the date of purchase was USD 18.200 Margin Account Balance 6.00 17. You are given the following price history for the September silver futures: Day June 29 June 30 July 1 July 2 July 6 July 7 July 8 Futures Price (USD) 18. Topic: Financial Markets and Products Subtopic: Futures.700 100 2.60 Daily Gain (Loss) 700 -6.500.200 -10. The broker requires an initial margin of USD 6. 57 .200 -9.000 and a maintenance margin of USD 4.800 4.000 On which days did Simon receive a margin call? a. Reference: John Hull.2011 Financial Risk Manager Examination (FRM®) Practice Exam 13. Futures and Other Derivatives.900 3. July 2 and July 7 only 1.800 Margin Call 0 0 5.600 -3.62 18. c.100 2.600 -3.70 17.900 8.62 per ounce.100 0 0 0 Margin calls happened on July 1 and July 2 only. Chapter 2— Mechanics of Futures Markets.69 18. Topic: Financial Markets and Products Subtopic: Cheapest to deliver bond.40 – (104 x .5% per year. A stock index is valued at USD 800 and pays a continuous dividend at the rate of 3% per year. c. Cost of delivering = Quoted price – (Current Futures price x Conversion Factor) Cost of bond A = 102. The bonds pay their coupon amount semi-annually on June 30 and December 31.5 1. With these data.5) = -55. Options Futures and Other Derivatives. d.40 99.1 Coupon Rate 4% 5% 3% The futures price is USD 104 and the maturity date of the contract is September 1. which of the following numbers comes closest to the arbitrage profit you could realize by taking a position in one futures contract? a. Explanation: Cheapest to deliver bond is the bond with the lowest cost of delivering.8 Hence. conversion factors AIMS: Describe the impact of the level and shape of the yield curve on the cheapest‐to‐deliver bond decision. Chapter 6. 58 © 2011 Global Association of Risk Professionals. b. Inc. 38 40 42 There is no arbitrage opportunity. Answer: b. The 6-month futures contract on that index is trading at USD 758. Bond A Bond B Bond C Insufficient information to determine. c.8) = 19. There are no transaction costs or taxes. d. Answer: b. b. All rights reserved. Reference: Hull.60 Conversion Factor 0. Global Association of Risk Professionals.2011 Financial Risk Manager Examination (FRM®) Practice Exam 14. 15. Is the futures contract priced so that there is an arbitrage opportunity? If yes.40 100.40 – (104 x 1. which bond is cheapest-todeliver? a. The following bonds are eligible for delivery: Bonds A B C Spot–Price(USD) 102. 7th Edition.1) = -14. bond B is the cheapest to deliver bond. The yield curve is upward sloping.2 Cost of bond B = 100. . The continuously compounded risk free rate is 2. You have a short T-Bond interest rate futures position.6 Cost of bond C = 99. It is illegal to reproduce this material in any format without prior written approval of GARP.6 – (104 x 1.8 1. 51% 7.758 = 40 Topic: Financial Markets and Products Subtopic: Futures. b.50% 4.50% 6. 4. and options AIMS: Explain how the discount rates in a plain vanilla interest rate swap are computed. 59 .00% 5.2011 Financial Risk Manager Examination (FRM®) Practice Exam Explanation: With the given data. Explanation: Statement d is correct. d. Futures and Other Derivatives.50% What is the 2-year forward rate starting in three years? a. 7th Edition / Chapter 5—Determination of Futures Prices. 800e(0. given the underlying asset’s price. Global Association of Risk Professionals. 2009). Chapter 4—Interest Rates. Below is a table of term structure of swap rates Maturity in Years 1 2 3 4 5 Swap Rate 3.055^5 / 1. 7th Edition (New York: Prentice Hall. swaps. Options. Reference: John Hull.02% ] Topic: Financial Markets and Products Subtopic: Futures. Options.045^3)^(1/2) . © 2011 Global Association of Risk Professionals.1 = 7.50% 5. It is illegal to reproduce this material in any format without prior written approval of GARP. All rights reserved. forwards.025-0.00% 4. Describe an arbitrage argument in support of these prices. the no-arbitrage futures price should be.03)*0.02% Answer: d. The futures contract could be purchased and the index sold. Arbitrage profit is 798 . with or without short sales and/or consideration to the income or yield of the underlying asset. use the relation: [ (1.50 =798 Since the market price of the futures contract is lower than this price there is an arbitrage opportunity.50% 5. To calculate the 2-year forward rate starting in 3 years. Forwards and Swaps and Options AIMS: Calculate the forward price. c. Futures and Other Derivatives. Inc. 16. Reference: Hull. Explanation: The key concept here is the box-spread. gives you a pay-off of USD 30 at expiration irrespective of the spot price. Chapter 10. if any? a. including bull spread. 60 © 2011 Global Association of Risk Professionals. and buy six units box-spread. b. and Other Derivatives. Global Association of Risk Professionals. and buy four units of box-spread. and diagonal spread. bear spread. short one unit of spot. Buy one put.2011 Financial Risk Manager Examination (FRM®) Practice Exam 17. Options. A box-spread with strikes at USD 120 and USD 150. What strategy exploits an arbitrage opportunity. . There are no arbitrage opportunities. and short six units of box-spread. buy one unit of spot. call is exercised and if it is less than 120. Inc. It is illegal to reproduce this material in any format without prior written approval of GARP. put is exercised. All rights reserved. The net profit is therefore = 180 – 120 = 60. Buy one put. Topic: Financial Markets and Products Subtopic: Trading Strategies using options AIMS: Describe and explain the use and payoff functions of spread strategies. The six spreads will provide a cash flow of 6*30 = 180. c. short one call. Futures. if spot is greater than 120. In either case you end up buying one spot at 120. The price of a 1-year European call option with strike USD 120 is USD 5 and the price of a European put option with same strike and expiration is USD 25. short one call. price of a zero coupon bond with face value of USD 120 can be expressed as 4 units of box spread. Now recall the put call parity relation: p + S = c + price of zero coupon bond with face value of strike redeeming at the maturity of the options Since. Answer: a. the strike is USD 120. d. calendar spread. Strategy A is correct Short one put: +25 Short one spot: +100 Buy one call: -5 Buy six box-spreads: -120 Net cash flow: 0 At expiry. A stock is trading at USD 100. This can be used to close the short position. butterfly spread. Reference: Hull. buy one call. 7th Edition. short one unit of spot. A box spread with 1 year to expiration and strikes at USD 120 and USD 150 is trading at USD 20. Short one put. 7th Edition (New York: Prentice Hall. Explanation: Number of Calls = 200 Contracts * 100 = 20. 2009). Futures. Sell 10.2011 Financial Risk Manager Examination (FRM®) Practice Exam 18.0% 68.3% Answer: b. Options. Reference: John Hull. b. d. A non-dividend paying stock is currently trading at USD 25.000 shares of General Motors. 7th Edition (New York: Prentice Hall. You are looking to find a no-arbitrage price for a 1 year American call using a two-step binomial tree model for which the stock can go up or down by 25%. Futures. Buy 1. c.50.000 shares of General Motors. Reference: John Hull. Answer: a. As a risk manager. The risk free rate is 10% and you believe that there is an equal chance of the stock price going up or down. Explanation: pup = (erΔt – d)/(u . and Other Derivatives.6% 39.000 shares of General Motors. A trader in your bank has sold 200 call option contracts each on 100 shares of General Motors with time to maturity of 60 days at USD 2. All rights reserved. Buy 10.8% 50. c.75% Topic: Valuation and Risk Models Subtopic: Binomial trees AIMS: Calculate the value of a European call or put option using the one‐step and two‐step binomial model. It is illegal to reproduce this material in any format without prior written approval of GARP.000 shares of General Motors.25% pdown = 1 – pup = 39.000 shares in order to keep the position delta neutral. 2009) 19. 22. one needs to buy 10.50 = 10000 shares So.10*6/12 – 0. b. Chapter 11. 61 . Options. Sell 1. what action must you take on the underlying stock in order to hedge the option exposure and keep it delta neutral? a. Topic: Valuation and Risk Models Subtopic: Greek Letters AIMS: Discuss the dynamic aspects of delta hedging. Inc. © 2011 Global Association of Risk Professionals.75)/(1.d) = (e0. and Other Derivatives.75) = 60.000 Calls Hedged by 20000 * .10. d. The delta of the option on one share is 0.25 – 0. What is the risk-neutral probability of the stock price going down in a single step? a. Global Association of Risk Professionals. 25 and of American put option is USD 0. theta. Also.7327 and N(d2) = 0. the American call option price is exactly the same as the European call option price under the usual Black-Scholes world with no dividend.48 9. and Other Derivatives. Reference: Hull. while a straddle increases this exposure. . and rho for option positions. Vega is the sensitivity of a portfolio to volatility.00 Answer: a. gamma. compute and describe delta.00 9. We know that American options are never less than corresponding European option in valuation. 7th Edition. Options. c is a straddle.25 and of American put option is USD 9.25 30. a short in a put. A collar limits exposure to volatility. It is illegal to reproduce this material in any format without prior written approval of GARP. Topic: Valuation and Risk Models Subtopic: Black‐Scholes‐Merton model AIMS: Compute the value of a European option using the Black‐Scholes‐Merton model on a non‐dividend‐paying stock.6164 a. With the given data the value of European call option is USD 30. Inc. The risk-free rate is 8%. Chapter 13—The Black-Scholes-Merton Model 21.2011 Financial Risk Manager Examination (FRM®) Practice Exam 20. d. Which of the following portfolios would have the highest vega assuming all options involved are of the same strikes and maturities? a. Value Value Value Value of of of of American American American American call call call call option option option option is is is is USD USD USD USD 30. and Other Derivatives. Futures. Which of the following values is closest to the Black-Scholes values of these options assuming N(d1) = 0. Chapter 17 62 © 2011 Global Association of Risk Professionals. 7th Edition.48 and of American put option is USD 30. Global Association of Risk Professionals. d is a collar. b. Topic: Valuation and Risk Models Subtopic: Greek Letters AIMS: Define. and a long in a call Answer: c. d.25 and value of European put option is USD 9.48. Explanation: a: is correct. Reference: Hull. Futures. c. b. Assume that options on a non dividend paying stock with price of USD 150 expire in a year and all have a strike price of USD 140. Thus only ‘a’ is the correct option. Long a call Short a put Long a put and long a call A short of the underlying. Explanation: a and b are standard call/put. All rights reserved. Options. c.48 and of American put option is USD 0. vega. 39 BB 0. through consecutive downgrading.01 0. given the following one-year rating transition matrix? From/To (%) AAA AA A BBB BB B CCC/C a.20 5.09 0. It is illegal to reproduce this material in any format without prior written approval of GARP.19 0.85 0.13 5. Altman.11 0.08% chance of being upgraded in one year.36 72. Global Association of Risk Professionals.21 1. c.28 0.73 5. All rights reserved.31 BBB 0.05 0.29 1.06 0. Reference: Caouette. Managing Credit Risk.52 ‘AAA’ loans have 0% chance of ever defaulting.37 86. Chapter 6—The Rating Agencies © 2011 Global Association of Risk Professionals. ‘A’ loans have a 13.79 6.08% Topic: Valuation and Risk Models Subtopic: Credit transition matrices AIMS: Define and explain a ratings transition matrix and its elements.04 0. Which of the following statements is incorrect.94 4.95 9.77 7. ‘AA’ loans have a 86.65% chance of staying at AA for one year.04 0.71 28.16 0.00 0.36 12.46 7.33 0.44 0.00 0. ‘BBB’ loans have a 4. AAA 87.06 11.14 9. 2nd Edition.83 D 0. Explanation: AAA loans can default eventually.31 B 0. Inc.65 2.07 0.23 46.00 0. Answer: a.74 CCC/C 0.65% A → A is 86.06 0.83 Non Rated 4.03 0.00 A 0.02 0.60 0.59 4. AA → AA is 86. 63 . Narayanan and Nimmo. d. b.04% chance of receiving a ratings change.96% BBB → AAA/AA/A (sum) = 4.43 4.05 0. even though they are calculated to not default in one year.39 75.58 5.27 0.50 84.96 3.2011 Financial Risk Manager Examination (FRM®) Practice Exam 22.02 0.20 0.78 86.00 0.08 AA 7.21 4.08 0.21 0. Inc. Explanation: Using spot rates. Reference: Jorion. c. USD USD USD USD 95. USD USD USD USD 31. Global Association of Risk Professionals. d. USD 412M. Value-at-Risk. Sam Neil.25 101. Chapter 14 64 © 2011 Global Association of Risk Professionals.2011 Financial Risk Manager Examination (FRM®) Practice Exam 23. Fixed Income Securities. 422M and 485M in USD? a. A bond with par value of USD 100 and 3 years to maturity pays 7% annual coupons. 2002).66 99.66 Topic: Valuation and Risk Models Subtopic: Discount factors. b. a new quantitative analyst.06) + 7/[(1.07)^2] + 107/[(1. the value of the bond is: 7/(1.25 97. corresponds to the 98th worst return and therefore the 98% 1-day VaR. 2nd Edition (Hoboken. 412M. arbitrage. All rights reserved. 3rd Edition. yield curves AIMS: Calculate the value of a bond using spot rates. Explanation: In the ordered list of 100 trading day returns. It is illegal to reproduce this material in any format without prior written approval of GARP. the 3rd worst loss. Topic: Valuation and Risk Models Subtopic: Value‐at‐Risk (VaR) Definition and methods AIMS: Explain the various approaches for estimating VaR. 385M.52 Answer: b. . c. What will this be if worst 5 losses in the past 100 trading days are 316M.08)^3] = 97.6M 41. NJ: John Wiley & Sons. has been asked by the portfolio manager to calculate the portfolio 1-day 98% Value-at-Risk (VaR) measure based on the past 100 trading days. d.2M 316M 412M Answer: d. Reference: Bruce Tuckman. The spot rate curve is as follows: Term 1 2 3 Annual Spot Interest Rates 6% 7% 8% The value of the bond is closest to: a. Chapter 1 24. b. It is illegal to reproduce this material in any format without prior written approval of GARP. © 2011 Global Association of Risk Professionals. d. 2009). Explanation: Statement I is false—rho of a call and a put will change. gamma. a. Global Association of Risk Professionals. Which of the following statements is correct? I. Reference: John Hull. but this is not true for the Rho of put options. with expiration of time and it tends to approach zero as expiration approaches. 7th Edition (New York: Prentice Hall. Futures and Other Derivatives. theta. All rights reserved. Theta is always negative for long calls and long puts and positive for short calls and short puts. compute and describe delta. b. vega. Statement II is true Topic: Valuation and Risk Models Subtopic: Greek Letters AIMS: Define. The Rho of a call option changes with the passage of time and tends to approach zero as expiration approaches. and rho for option positions. II. c. Inc. Options. 65 .2011 Financial Risk Manager Examination (FRM®) Practice Exam 25. I only II only I and II Neither Answer: b. Financial Risk ® Manager (FRM ) Examination 2011 Practice Exam PART II / EXAM 1 Answer Sheet . 11. Global Association of Risk Professionals. 1.2011 Financial Risk Manager Examination (FRM®) Practice Exam a. 2. 17. 8. 5. 16. 19. 67 . It is illegal to reproduce this material in any format without prior written approval of GARP. Inc. c. 7. 15. 9. 6. 1. a. 20. Correct way to complete 10. b. 1. © 2011 Global Association of Risk Professionals. 18. c. 3 8 13. All rights reserved. d. b. 3. d. 14. Wrong way to complete 12. 4. Financial Risk ® Manager (FRM ) Examination 2011 Practice Exam PART II / EXAM 1 Questions . 084 USD -1.833 USD -2.960 USD -1.285 1. Global Association of Risk Professionals. 1-day VaR of a bank’s portfolio to be USD 1.679 USD -1. d. d. you are concerned that the VaR measure is not providing enough information about tail losses.368 USD -1.484 USD -1. I only II only Both Neither a. 69 .333 USD -2. b. © 2011 Global Association of Risk Professionals.484 using historical simulation with 1000 past trading days. c.228 USD -2. 1-day expected shortfall of the portfolio? a.2011 Financial Risk Manager Examination (FRM®) Practice Exam 1. You decide to re-examine the simulation results and sort the simulated daily P&L from worst to best giving the following worst 15 scenarios: Scenario Rank 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Daily P/L USD -2. When the yield is higher than the coupon rate of a MBS.558 USD -1. Which of following statement about mortgage-backed securities (MBS) is correct? I.319 What is the 99%.347 USD -1. The price of a MBS is more sensitive to yield curve twists than zero-coupon bonds.542 USD -1. the MBS behaves similar to corporate bonds as interest rates change.833 2. USD USD USD USD 433 1. b.751 USD -1.450 USD -1.945 2. After estimating the 99%. Inc. c. II.428 USD -1. It is illegal to reproduce this material in any format without prior written approval of GARP. All rights reserved. Inc. c. b. c.2011 Financial Risk Manager Examination (FRM®) Practice Exam 3.200 loss of USD 303. d. American call option Shout call option European call option Lookback call option 5. c. which of the following options should be the least expensive? a. modified duration of 2. has recently proposed to increase the bank’s liquidity by securitizing existing credit card receivables. It is illegal to reproduce this material in any format without prior written approval of GARP. . The total value of the collateral for the structure is USD 680 million. d. b. a CFO of Bank of Mitsubishi. and the subordinated tranche B bond class is the first loss piece: Exhibit 1. the lockout period is two years.600 gain of USD 607. Edward Art. Assuming equal strike prices and expiration dates. Edward’s proposed securitization includes tranches with multiple internal credit enhancements as shown in Exhibit 1 below. b. Global Association of Risk Professionals.600 gain of USD 303. d. All rights reserved. What would be the change in the value of this portfolio after a parallel rate decline of 20 basis points in the yield curve? a. What is the amount of the prepaid principal paid out to the holders of the junior tranche A bond class? a.53 years and yielding 4.200 4. A fixed-income portfolio with market value of USD 60 million. the underlying credit card accounts have prepaid USD 300 million in principal in addition to regularly scheduled principal and interest payments.7% compounded semiannually. USD USD USD USD 0 million 30 million 120 million 230 million 70 © 2011 Global Association of Risk Professionals. Proposed ABS Structure Bond Class Senior tranche Junior tranche A Junior tranche B Subordinated tranche A Subordinated tranche B Total Par Value USD 270 million USD 230 million USD 80 million USD 60 million USD 40 million USD 680 million At the end of the fourteenth month after the securities were issued. A A A A loss of USD 607. Drawdown on default is assumed to be 60%. Neither gain nor lose value since only expected default losses matter and correlation does not affect expected default losses. d. Assuming the probability of any one bond defaulting is completely independent of what happens to the other bonds in the basket what is the probability that exactly one bond defaults? a. from City Bank I only II only Both Neither 8.06% 3. Capital Bank is concerned about its counterparty credit exposure to City Bank. Global Association of Risk Professionals. a.1% 7.01% 16. b. assuming everything else is unchanged. b. An investor has sold default protection on the most senior tranche of a CDO. It depends on the pricing model used and the market conditions. 2. d. c. The default probability of the loan is assumed to be 2% for the next year and loss given default (LGD) is estimated at 50%. c.2011 Financial Risk Manager Examination (FRM®) Practice Exam 6. Lose significant value since his protection will gain value. d. b. II. Inc. c. d. It is illegal to reproduce this material in any format without prior written approval of GARP. Miller Castello is the head of credit derivatives trading at an investment bank. Which of the following trades by Capital Bank would increase its credit exposure to City Bank? I. A bank has booked a loan with total commitment of USD 50. c. If the default correlation decreases sharply. Gain significant value since the probability of exercising the protection falls. Buying a put option from City Bank Buying a loan extended to Sunny Inc. b. The expected losses for the bank are: a. © 2011 Global Association of Risk Professionals.000 of which 80% is currently outstanding. He is monitoring a new credit default swap basket that is made up of 20 bonds each with a 1% probability of default. USD USD USD USD 380 420 460 500 9. 71 . The standard deviation of LGD is 40% and the standard deviation of the default event indicator is 7%. All rights reserved. the investor’s position will a.5% 30. b. Which of the following are methods of credit risk mitigation? I.737 222. Which of the following statements is/are correct? I. . 1-day) for last 60 trading days Multiplication Factor a. Assuming the return of the bank’s trading portfolio is normally distributed. Management should retain strategic and business risks in which the company has a comparative advantage but diversify risks that can be hedged inexpensively through the capital markets. II. is keen to enhance shareholder value using an enterprise risk management framework.582 134. a large diversified conglomerate. b. c. d.000 USD 25. what is the market risk capital charge of the trading portfolio? VaR (95%. USD USD USD USD 84. 72 © 2011 Global Association of Risk Professionals. d. 1-day) of last trading day Average VaR (95%.2011 Financial Risk Manager Examination (FRM®) Practice Exam 10. a. All rights reserved. The CEO of Merlion Holdings. Global Association of Risk Professionals. c. As a risk manager for Bank ABC. business unit managers must evaluate all major risks in the context of the marginal impact of the project on the firm’s total risk. c. Inc. It is illegal to reproduce this material in any format without prior written approval of GARP. When proposing new projects.594 189.893 USD 40. You are asked to assist senior management to quantify and manage the risk-return tradeoff for the entire firm. Collateral agreements Netting I only II only Both Neither 11. d. Statement I only Statement II only Both statements are correct Both statements are incorrect a.000 2 12. II. Specifically. John is asked to calculate the market risk capital charge of the bank’s trading portfolio under the internal models approach using the information given in the table below. the CEO wants to know which risks to retain and which risks to lay off and how to decentralize the risk-return trade-off decisions within the company. b. . External loss data often exhibits scale bias as operational risk losses tend to be positively related to the size of the institution (i. Which of the following statements about the IRC is/are correct? I. b. Assuming returns of BNA are normally distributed. Daily return for BNA has an estimated volatility of 1. c.629 14. II. the Basel Committee published the consultative document “Guidelines for computing capital for incremental risk in the trading book. The average bid-ask spread is USD 0. In March 2009. It is illegal to reproduce this material in any format without prior written approval of GARP. which has a current stock price of USD 72 (expressed as the midpoint of the current bid-ask spread). Operational risk loss data is not easy to collect within an institution.” The incremental risk charge (IRC) defined in that document aims to complement additional standards being applied to the value-at-risk modeling framework which address a number of perceived shortcomings in the 99%/10-day VaR framework.389 1. d. A bank must calculate the IRC measure at least weekly. using the constant spread approach? a.e.2011 Financial Risk Manager Examination (FRM®) Practice Exam 13. d. c. You are a manager of a renowned hedge fund and are analyzing a 1.469 1. Statement I only Statement II only Both statements are correct Both statements are incorrect 15. b. c. External loss data often exhibits data capture bias as the likelihood that an operational risk loss is reported is positively related to the size of the loss. but doing so may create biases in estimating loss distributions. financial institutions usually attempt to obtain external data. The biases associated with external loss data are more important for large losses in relation to a bank’s assets or revenue than for small losses. a. especially for extreme loss data. what is the estimated liquidity-adjusted daily 95% VaR. © 2011 Global Association of Risk Professionals. d. b. USD USD USD USD 1. or more frequently as directed by its supervisor. Which of the following statements regarding characteristics of external loss data is incorrect? a. External loss data often exhibits truncation bias as minimum loss thresholds for collecting loss data are not uniform across all institutions.16.549 1. Global Association of Risk Professionals. scale of its operations). 73 . All rights reserved. a bank’s IRC model must measure losses due to default and migration over a one-year capital horizon at a 99% confidence level.000 share position in an undervalued but illiquid stock BNA. Inc. For all IRC-covered positions.24%. Therefore. An example of this would include which of the following? a. 74 © 2011 Global Association of Risk Professionals. All rights reserved. The appropriate benchmark-neutral alpha for stock XYZ is: a. b. Global Association of Risk Professionals. Optimistic correlation assumptions embedded in rating agency models. You are the head of the Independent Risk Oversight (IRO) unit of XYZ bank. namely that the agent. many commentators have pointed to the principal-agent problem associated with securitization.10. c. Statement I only Statement II only Both statements are correct Both statements are incorrect 17. c.0 basis points 18. II. the ultimate investor. I.0 basis points 50. b. can have poor incentives to act in the interest of the principal. Model specifications assume that markets are perfectly liquid. d. You want to construct a portfolio so that all of the alphas are benchmark-neutral.3 basis points 56.7 basis points. 44. Stock XYZ has a volatility of 40%. The remuneration of the staff of the IRO unit is dependent on how frequently the traders of XYZ bank use models vetted by the IRO.63.7 basis points 54. It is illegal to reproduce this material in any format without prior written approval of GARP. an information coefficient of 0. and a beta of 1. Which of the existing policies are sources of model risk? a. b. The benchmark has an alpha of 5. c. the originator. Lack of sufficient subordination in securitized mortgage products. The failure of originators to retain sufficient holdings of residual interest risk. d. The lack of liquid hedging instruments in the securitized mortgage market. Inc. . d. Your first task is to review the following existing policies relating to model implementation. an alpha of 60 basis points.2011 Financial Risk Manager Examination (FRM®) Practice Exam 16. When identifying factors that contributed to the recent financial crisis. b. the return on equity (ROE) would be -60%. The ai term measures the extent to which the manager employs greater or lesser amounts of leverage than do his/her peers. I only II only I and II Neither I nor II a. c.20) GRT USD 500 USD 3. In response to the recent crisis.9500 (t = 12. It is illegal to reproduce this material in any format without prior written approval of GARP. d.000 USD 3. 75 .40) 0. Regular dialogue with executive management about the results of stress tests and contingency plans to address such scenarios. Inc. The sensitivity of the GRT fund to the benchmark return is much higher than that of the HCM fund.002) bi 0. II. c. Which of the following statements concerning steps banks can take to improve the value of stress testing exercises is/are correct? I. All rights reserved. which of the following statements is correct? a.2011 Financial Risk Manager Examination (FRM®) Practice Exam 19. the HCM Fund and the GRT Fund. If the GRT Fund were to lose 10% in the next period. He uses a linear regression of each manager’s excess returns (ri) against the excess returns of a peer group (rB): ri = ai + bi * rB + εi The information he compiles is as follows: Fund HCM Initial Equity USD 100 Borrowed Funds USD 0 Total Investment Pool USD 100 ai 0. b. © 2011 Global Association of Risk Professionals. Regular evaluation of a well-defined. Rick Masler is considering the performance of the managers of two funds. rigorous stress testing has been emphasized as an important component of risk measurement and management that has been poorly implemented by many financial institutions in the recent past.500 Based on this information.0150 (t = 4. The regression suggests that both managers have greater skill than the peer group. 20. Global Association of Risk Professionals.0025 (t = 0. common set of scenarios that include a broad range of possible stresses.4500 (t = 10.1) 3. d. Financial Risk ® Manager (FRM ) Examination 2011 Practice Exam PART II / EXAM 1 Answers . 1. 14. Inc. 7. 3. 4. Correct way to complete 10. 77 . b. 17. 5.2011 Financial Risk Manager Examination (FRM®) Practice Exam a. 3 8 13. 8. 1. It is illegal to reproduce this material in any format without prior written approval of GARP. b. 11. 15. a. 9. c. All rights reserved. d. 2. d. 19. 16. 1. © 2011 Global Association of Risk Professionals. 18. Global Association of Risk Professionals. Wrong way to complete 12. 6. c. 20. Financial Risk ® Manager (FRM ) Examination 2011 Practice Exam PART II / EXAM 1 Explanations . 79 .084 USD -1.679 USD -1. d. 1-day expected shortfall of the portfolio? a. Reference: Kevin Dowd.833 USD -2. You decide to re-examine the simulation results and sort the simulated daily P&L from worst to best giving the following worst 15 scenarios: Scenario Rank 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Daily P/L USD -2. b.484 USD -1.428 USD -1. All rights reserved. 2nd Edition (West Sussex. Chapter 2— Measures of Financial Risk © 2011 Global Association of Risk Professionals.2011 Financial Risk Manager Examination (FRM®) Practice Exam 1.319 What is the 99%.484 using historical simulation with 1000 past trading days.450 USD -1. Measuring Market Risk. Explanation: Expected Shortfall = Average of the worst 10 daily P&L = USD 1945.945 2. Global Association of Risk Professionals.228 USD -2. After estimating the 99%.347 USD -1. Inc. c.368 USD -1.558 USD -1. 2005). Topic: Market Risk Measurement and Management Subtopic: Expected shortfall and coherent risk measures AIMS: Explain and calculate expected shortfall (ES). England: Wiley. 1-day VaR of a bank’s portfolio to be USD 1. and compare and contrast VaR and ES.751 USD -1.285 1. USD USD USD USD 433 1.333 USD -2.542 USD -1. you are concerned that the VaR measure is not providing enough information about tail losses. It is illegal to reproduce this material in any format without prior written approval of GARP.833 Answer: c.960 USD -1. which are more sensitive to yield curve twist because of reinvestment risk. This statement is correct.600 gain of USD 607. Inc. Dmod = (-1/P) * (dP/dy). Reference: Tuckman. Chapter 6—Measures of Price Sensitivity Based on Parallel Yield Shifts 80 © 2011 Global Association of Risk Professionals. MBS’ cash flows are like annuities. and Macaulay duration. II. Explanation: I. It is much the same as a normal bond.53 * 60 = 0. the MBS behaves similar to corporate bonds as interest rates change. All rights reserved.53 years and yielding 4.200 Answer: c. 2nd Edition. When yield is higher than MBS’ coupon rate. ΔP = -1 * Δy * Dmod * P = -1 * -0. Global Association of Risk Professionals. What would be the change in the value of this portfolio after a parallel rate decline of 20 basis points in the yield curve? a.0020 * 2. d. Reference: Frank Fabozzi. Explanation: By definition. b. Fixed Income Securities. Which of following statement about mortgage-backed securities (MBS) is correct? I. A fixed-income portfolio with market value of USD 60 million.3036 million Topic: Market Risk Measurement and Management Subtopic: Duration and convexity of Fixed Income Instruments AIMS: Define and calculate yield‐based DV01. Normal bond has a lump sum payment at maturity. Handbook of Mortgage Backed Securities. d. This statement is correct.200 loss of USD 303. c. modified duration of 2. which implies less reinvestment risk.600 gain of USD 303.2011 Financial Risk Manager Examination (FRM®) Practice Exam 2. modified duration. I only II only Both Neither a.7% compounded semiannually. the embedded call option is out of the money. 3. 6th Edition (New York: McGraw-Hill. c. A A A A loss of USD 607. II. b. The price of a MBS is more sensitive to yield curve twists than zero-coupon bonds. 2006). Answer: c. Topic: Market Risk Measurement and Management Subtopic: Mortgages and mortgage‐backed securities AIMS: Describe the various risk associated with mortgages and mortgage backed securities and explain risk based pricing. . It is illegal to reproduce this material in any format without prior written approval of GARP. When the yield is higher than the coupon rate of a MBS. So as a linear approximation. American calls also offer more to the buyer than the European calls. The total value of the collateral for the structure is USD 680 million. The shout call option and lookback call option are clearly wrong. Global Association of Risk Professionals. since they grant more rights to the buyer than the European call option. Assuming equal strike prices and expiration dates. It is illegal to reproduce this material in any format without prior written approval of GARP. has recently proposed to increase the bank’s liquidity by securitizing existing credit card receivables. What is the amount of the prepaid principal paid out to the holders of the junior tranche A bond class? a. Topic: Market Risk Measurement and Management Subtopic: Exotic options AIMS: List and describe the characteristics and pay‐off structure of barrier options.2011 Financial Risk Manager Examination (FRM®) Practice Exam 4. d. Edward’s proposed securitization includes tranches with multiple internal credit enhancements as shown in Exhibit 1 below. USD USD USD USD 0 million 30 million 120 million 230 million Answer: a. c. Explanation: c is correct. the lockout period is two years. All rights reserved. Chapter 24 5. Proposed ABS Structure Bond Class Senior tranche Junior tranche A Junior tranche B Subordinated tranche A Subordinated tranche B Total Par Value USD 270 million USD 230 million USD 80 million USD 60 million USD 40 million USD 680 million At the end of the fourteenth month after the securities were issued. shout options and lookback options Reference: John Hull. Inc. the underlying credit card accounts have prepaid USD 300 million in principal in addition to regularly scheduled principal and interest payments. American call option Shout call option European call option Lookback call option Answer: c. which of the following options should be the least expensive? a. b. and the subordinated tranche B bond class is the first loss piece: Exhibit 1. c. 7th Edition (New York: Prentice Hall. a CFO of Bank of Mitsubishi. Futures. and Other Derivatives. Options. b. 81 . Edward Art. © 2011 Global Association of Risk Professionals. 2009). d. 01)19 = 0.06% 3. 7th Edition (NY: Pearson. Topic: Credit Risk Measurement and Management Subtopic: Structured finance. Explanation: C120p1(1 . Chapter 16. survival probabilities. Credit card prepayments are usually just rolled into new loans (not repaid to bondholders).1% Answer: c. Topic: Credit Risk Measurement and Management Subtopic: Probability of default. tranching and subordination AIMS: Discuss the securitization process for mortgage‐backed securities and asset‐backed commercial paper. d. It is illegal to reproduce this material in any format without prior written approval of GARP. Inc. He is monitoring a new credit default swap basket that is made up of 20 bonds each with a 1% probability of default. market yields. No security tranche will receive principal prepayments until after the 24 months lockout period. recovery rates and cash flows. and Other Derivatives. .0. b. Reference: Christopher Culp. 2009). All rights reserved. Chapter 23—Credit Derivatives 82 © 2011 Global Association of Risk Professionals.01% 16.1652 The right choice is c.01 x (1 . 2006). c.2011 Financial Risk Manager Examination (FRM®) Practice Exam Explanation: d: is correct. Options.5% 30. 2. all principal prepayments within the first two years will be used to fund new loans. Structured Finance and Insurance: The Art of Managing Capital and Risk (Hoboken: John Wiley & Sons. 6. Futures. securitization. Global Association of Risk Professionals.p)19 = 20 x 0. Assuming the probability of any one bond defaulting is completely independent of what happens to the other bonds in the basket what is the probability that exactly one bond defaults? a. given unconditional default probabilities. Reference: John Hull. Miller Castello is the head of credit derivatives trading at an investment bank. loss given default and recovery rates AIMS: Compute the value of a CDS. The securities have a two-year lockout period. Inc. II. Buying a put option from City Bank Buying a loan extended to Sunny Inc. Capital Bank is concerned about its counterparty credit exposure to City Bank. The expected losses for the bank are: a. p. It is illegal to reproduce this material in any format without prior written approval of GARP. Explanation: I. It creates credit risk exposure to Sunny Inc instead. A bank has booked a loan with total commitment of USD 50. II. b. a. c. Drawdown on default is assumed to be 60%.000 of which 80% is currently outstanding. Topic: Credit Risk Measurement and Management Subtopic: Counterparty risk and OTC derivatives AIMS: Describe counterparty credit risk in derivatives markets and explain how it affects valuation. d. Reference: Hull. The standard deviation of LGD is 40% and the standard deviation of the default event indicator is 7%. Buying a put option creates credit risk exposure to City Bank as it is subject to the performance of counterparty City Bank. from City Bank I only II only Both Neither Answer: a. and Other Derivatives. b. City Bank may default to deliver the underlying asset when Capital Bank exercises the option. Global Association of Risk Professionals. © 2011 Global Association of Risk Professionals. Buying a loan extended to Sunny Inc does not create credit risk exposure to City Bank as it is not subject to performance of counterparty City Bank but Sunny Inc. Which of the following trades by Capital Bank would increase its credit exposure to City Bank? I. Options. USD USD USD USD 380 420 460 500 Answer: c.2011 Financial Risk Manager Examination (FRM®) Practice Exam 7. Futures. d. 8. 507. 83 . For example. The default probability of the loan is assumed to be 2% for the next year and loss given default (LGD) is estimated at 50%. c. 7th Edition. All rights reserved. Chapter 22—Credit Risk. Gain significant value since the probability of exercising the protection falls. All rights reserved. . a large number of other names will default. b. Explanation: The Senior tranche will gain value if the default correlation decreases. calculate and interpret expected and unexpected portfolio loss. Standard deviation of the default event indicator = .000 x . Answer: a.5 = 460 Topic: Credit Risk Measurement and Management Subtopic: Expected and unexpected loss AIMS: Define.8 x 50.000 – (0. If the default correlation decreases sharply. An investor has sold default protection on the most senior tranche of a CDO. Lose significant value since his protection will gain value. 2006). the investor’s position will a. Inc. Internal Credit Risk Models. Neither gain nor lose value since only expected default losses matter and correlation does not affect expected default losses.4. securitization. assuming everything else is unchanged. It is illegal to reproduce this material in any format without prior written approval of GARP.02 x 0. Low correlation means that if one name default.000) + {50. Chapter 6—Portfolio Effects: Risk Contributions and Unexpected Losses 9. High correlation means that if one name defaults. c.2011 Financial Risk Manager Examination (FRM®) Practice Exam Explanation: Standard deviation of LGD = 0. It depends on the pricing model used and the market conditions.6 = 46. Reference: Ong. tranching and subordination AIMS: Define securitization and describe the process and the role the participants play. Global Association of Risk Professionals. d. Topic: Credit Risk Measurement and Management Subtopic: Structured finance. A seller of protection on a senior tranche will prefer a small number of highly probable defaults rather that an unlikely large number of defaults so that it becomes less likely that he makes a payment.07 Adjusted Exposure (AE) = Outstanding + (Commitment – Outstanding) x Draw Down on default AE = (0.000 Expected Loss = AE x default probability x LGD = 46. 84 © 2011 Global Association of Risk Professionals.8 x 50000)} x 0. Structured Finance and Insurance: The Art of Managing Capital and Risk (Hoboken: John Wiley & Sons. Chapter 16. Reference: Christopher Culp. it will not affect the default probability of the other names. d. Explanation: Market Risk Capital Charge = MAX(40. 2 x 25.000 x SQRT(10)/1. b.000 USD 25. As a risk manager for Bank ABC. c. 1-day) for last 60 trading days Multiplication Factor a. © 2011 Global Association of Risk Professionals. 2003) 11. a. Global Association of Risk Professionals. Collateral agreements Netting I only II only Both Neither Answer: c. ed.65 x 2.737 222. 1-day) of last trading day Average VaR (95%. Inc. Topic: Operational and Integrated Risk Management Subtopic: Regulation and the Basel II Accord AIMS: Describe and contrast the major elements—including a description of the risks covered—of the two options available for the calculation of market risk: Standardized Measurement Method and Internal Models Approach Reference: “Basel II: International Convergence of Capital Measurement and Capital Standards: A Revised Framework—Comprehensive Version” (Basel Committee on Banking Supervision Publication. June 2006).594 189. John is asked to calculate the market risk capital charge of the bank’s trading portfolio under the internal models approach using the information given in the table below. Topic: Credit Risk Measurement and Management Subtopic: Credit Risk Mitigation AIMS: Describe credit mitigation techniques Reference: Eduardo Canabarro and Darrell Duffie: "Measuring and Marking Counterparty risk" in ALM of Financial Institutions.326. All rights reserved. USD USD USD USD 84. Leo Tilman (London: Euro-money Institutional Investor.2011 Financial Risk Manager Examination (FRM®) Practice Exam 10.893 USD 40.326) = 222893 Candidate is required to convert the VaR (95%. Which of the following are methods of credit risk mitigation? I. c.000 x SQRT(10)/1. what is the market risk capital charge of the trading portfolio? VaR (95%.65 x 2. II. Explanation: Both collateral and netting agreements are methods of mitigating credit risk. Assuming the return of the bank’s trading portfolio is normally distributed.000 2 Answer: d. It is illegal to reproduce this material in any format without prior written approval of GARP. 1-day) to a 95% 10-day VaR. d. 85 .582 134. b. Explanation: In the context of using an ERM framework to decentralize the risk-reward tradeoff in a company. II. All rights reserved. Which of the following statements is/are correct? I. It is illegal to reproduce this material in any format without prior written approval of GARP.549 1. Answer: c. Assuming returns of BNA are normally distributed. d.24%. 4 (2006): 8–20. “Enterprise Risk Management: Theory and Practice.629 Answer: c. Reference: Brian Nocco and René Stulz. c. business unit managers must evaluate all major risks in the context of the marginal impact of the project on the firm’s total risk. d. the CEO wants to know which risks to retain and which risks to lay off and how to decentralize the risk-return trade-off decisions within the company. The average bid-ask spread is USD 0. The CEO of Merlion Holdings. Topic: Foundation of Risk Management Subtopic: Firm-wide risk measurement and management AIMS: Discuss how an ERM program can be used to determine the right amount of risk. Management should retain strategic and business risks in which the company has a comparative advantage but diversify risks that can be hedged inexpensively through the capital markets. When proposing new projects. . Inc. b. You are asked to assist senior management to quantify and manage the risk-return tradeoff for the entire firm.16.2011 Financial Risk Manager Examination (FRM®) Practice Exam 12. USD USD USD USD 1. Global Association of Risk Professionals. 13.” Journal of Applied Corporate Finance 18. using the constant spread approach? a. is keen to enhance shareholder value using an enterprise risk management framework. No. b. Specifically. statements I and II are both correct. c. 86 © 2011 Global Association of Risk Professionals. what is the estimated liquidity-adjusted daily 95% VaR. which has a current stock price of USD 72 (expressed as the midpoint of the current bid-ask spread). a large diversified conglomerate. Daily return for BNA has an estimated volatility of 1. You are a manager of a renowned hedge fund and are analyzing a 1.000 share position in an undervalued but illiquid stock BNA.389 1. Statement I only Statement II only Both statements are correct Both statements are incorrect a.469 1. c. 87 . Inc. the Basel Committee published the consultative document “Guidelines for computing capital for incremental risk in the trading book. England: John Wiley & Sons. All rights reserved.0124) = USD 1469 Liquidity cost = 72.645 * 0.2011 Financial Risk Manager Examination (FRM®) Practice Exam Explanation: The constant spread approach adds half of the bid-ask spread (as a percent) to the VaR calculation: Daily 95% VaR = 72. or more frequently as directed by its supervisor. Topic: Foundation of Risk Management Subtopic: Regulation and the Basel II Accord AIMS: Define the risks captured by the incremental risk charge and the key supervisory parameters for computing the incremental risk charge. 2nd Edition (West Sussex. Which of the following statements about the IRC is/are correct? I.16/72) = 80 LVaR = VaR + LC = 1549 Topic: Operational and Integrated Risk Management Subtopic: Liquidity risk AIMS: Describe and calculate LVaR using the Constant Spread approach and the Exogenous Spread approach. A bank must calculate the IRC measure at least weekly. January 2009) © 2011 Global Association of Risk Professionals. a bank’s IRC model must measure losses due to default and migration over a one-year capital horizon at a 99% confidence level. II. 14. Reference: Dowd. Calculate the capital charge for incremental risk as a function of recent increment risk charge measures.5 * 0. Measuring Market Risk. a bank’s IRC model must measure losses due to default and migration at the 99. b. d. taking into account the liquidity horizons applicable to individual trading positions or sets of positions. for all IRC-covered positions. Global Association of Risk Professionals. Explanation: i is incorrect. Chapter 14. Statement I only Statement II only Both statements are correct Both statements are incorrect Answer: b. A bank must calculate the IRC measure at least weekly.” The incremental risk charge (IRC) defined in that document aims to complement additional standards being applied to the value-at-risk modeling framework which address a number of perceived shortcomings in the 99%/10-day VaR framework.9% confidence interval over a capital horizon of one year. It is illegal to reproduce this material in any format without prior written approval of GARP. In March 2009. ii is correct. or more frequently as directed by its supervisor. a.000 * (0. Specifically. Define the frequency with which banks must calculate the incremental risk charge. 2005). For all IRC-covered positions. Reference: “Guidelines for Computing Capital for Incremental Risk in the Trading Book—Consultative Document” (Basel Committee on Banking Supervision Publication.000 * (1. Therefore. c. Which of the existing policies are sources of model risk? a. II. Topic: Operational and Integrated Risk Management Subtopic: Implementation and model risk AIMS: Explain the issues with the use of both internal and external loss data for modeling loss distributions. b. c. Which of the following statements regarding characteristics of external loss data is incorrect? a. Explanation: The biases associated with external loss data are important for all losses in relation to a bank’s assets or revenue. It is illegal to reproduce this material in any format without prior written approval of GARP. Answer: d. Reference: Falko Aue and Michael Kalkbrener.2011 Financial Risk Manager Examination (FRM®) Practice Exam 15. Global Association of Risk Professionals. You are the head of the Independent Risk Oversight (IRO) unit of XYZ bank. 88 © 2011 Global Association of Risk Professionals. Model specifications assume that markets are perfectly liquid. d.. External loss data often exhibits data capture bias as the likelihood that an operational risk loss is reported is positively related to the size of the loss. “LDA at Work”. Operational risk loss data is not easy to collect within an institution. Deutsche Bank White Paper. The biases associated with external loss data are more important for large losses in relation to a bank’s assets or revenue than for small losses. d. All rights reserved. Inc.e. The remuneration of the staff of the IRO unit is dependent on how frequently the traders of XYZ bank use models vetted by the IRO. External loss data often exhibits scale bias as operational risk losses tend to be positively related to the size of the institution (i. but doing so may create biases in estimating loss distributions. . 2007. Your first task is to review the following existing policies relating to model implementation. I. Statement I only Statement II only Both statements are correct Both statements are incorrect Answer: b. financial institutions usually attempt to obtain external data. especially for extreme loss data. External loss data often exhibits truncation bias as minimum loss thresholds for collecting loss data are not uniform across all institutions. scale of its operations). b. 16. 18. You want to construct a portfolio so that all of the alphas are benchmark-neutral. Inc. Reference: Dowd. It is illegal to reproduce this material in any format without prior written approval of GARP. II. All rights reserved. 17. can have poor incentives to act in the interest of the principal. b. An example of this would include which of the following? a. 382-385.0 basis points Answer: b. Chapter 16.3 basis points 56.10. © 2011 Global Association of Risk Professionals. 2nd Edition—Chapter 14. 2nd Edition (West Sussex. c. c.63*0. Global Association of Risk Professionals. Explanation: To make the alpha benchmark neutral. Optimistic correlation assumptions embedded in rating agency models. England: John Wiley & Sons. 89 . Answer: c.057)] = 0. 44. d. an alpha of 60 basis points. Lack of sufficient subordination in securitized mortgage products. The lack of liquid hedging instruments in the securitized mortgage market. Active Portfolio Management: A Quantitative Approach for Providing Superior Returns and Controlling Risk. This assumption can lead to major error where market liquidity is limited. b. The appropriate benchmark-neutral alpha for stock XYZ is: a. the originator. many commentators have pointed to the principal-agent problem associated with securitization.7 basis points 54. Topic: Risk Management and Investment Management Subtopic: Portfolio construction AIMS: Describe neutralization and methods for refining alphas to be neutral. Stock XYZ has a volatility of 40%. When identifying factors that contributed to the recent financial crisis.60 – (1.0 basis points 50. the ultimate investor. 2005).7 basis points. Reference: Grinold and Kahn. and a beta of 1. an information coefficient of 0. pp. Measuring Market Risk. The benchmark has an alpha of 5. d. the policy itself is regarding compensation and not the model itself. you subtract the product of the beta of the stock and the alpha of the benchmark from the original alpha of the stock [0. Even though this is a risk that can increase exposure to model risk. namely that the agent. The failure of originators to retain sufficient holdings of residual interest risk. Topic: Operational and Integrated Risk Management Subtopic: Implementation and model risk AIMS: Identify and discuss sources of model risk. Incorrect.507.2011 Financial Risk Manager Examination (FRM®) Practice Exam Explanation: I.63. Correct. which of the following statements is correct? a. the return on equity (ROE) would be -60%.” (January 2009). The regression suggests that both managers have greater skill than the peer group. Reference: John Martin. The sensitivity of the GRT fund to the benchmark return is much higher than that of the HCM fund. Inc.40) 0. Topic: Risk Management and Investment Management Subtopic: Risk decomposition and performance attribution AIMS: Describe common features of a performance measurement framework including comparisons with benchmark portfolios and peer groups Reference: Robert Litterman and the Quantitative Resources Group. This indicates that the sensitivity of the GRT fund to the benchmark return is much higher than that of the HCM fund. c. “A Primer on the Role of Securitization in the Credit Market Crisis of 2007. Modern Investment Management: An Equilibrium Approach (Hoboken. Rick Masler is considering the performance of the managers of two funds.20) GRT USD 500 USD 3. the HCM Fund and the GRT Fund. He uses a linear regression of each manager’s excess returns (ri) against the excess returns of a peer group (rB): ri = ai + bi * rB + εi The information he compiles is as follows: Fund HCM Initial Equity USD 100 Borrowed Funds USD 0 Total Investment Pool USD 100 ai 0. It is higher for GRT and lower for HCM.0025 (t = 0. If the GRT Fund were to lose 10% in the next period. Topic: Current Issues in Risk Management Subtopic: Causes and consequences of the current crisis AIMS: Discuss the argument that the traditional originate-to-hold model of credit markets to the originate-todistribute model was a primary driver of the current crisis. b.0150 (t = 4.9500 (t = 12.1) 3.500 Based on this information. 19. d. . It is illegal to reproduce this material in any format without prior written approval of GARP. Answer: d.4500 (t = 10. Explanation: Statement d is correct as can be seen from the bi coefficient. All rights reserved. Chapter 17—Risk Monitoring and Performance Measurement 90 © 2011 Global Association of Risk Professionals. Global Association of Risk Professionals.000 USD 3. The ai term measures the extent to which the manager employs greater or lesser amounts of leverage than do his/her peers. NJ: John Wiley & Sons: 2003).2011 Financial Risk Manager Examination (FRM®) Practice Exam Explanation: Only c is an illustration of the principal-agent problem.002) bi 0. © 2011 Global Association of Risk Professionals. Regular evaluation of a well-defined. b. rigorous stress testing has been emphasized as an important component of risk measurement and management that has been poorly implemented by many financial institutions in the recent past. Haldane. II. Which of the following statements concerning steps banks can take to improve the value of stress testing exercises is/are correct? I. c. Explanation: Both of the statements are correct. Regular dialogue with executive management about the results of stress tests and contingency plans to address such scenarios. All rights reserved.” (February 2009). “Why Banks Failed the Stress Test. It is illegal to reproduce this material in any format without prior written approval of GARP. In response to the recent crisis. Topic: Current Issues in Financial Markets Subtopic: Causes and consequences of the current crisis AIMS: Discuss methods for improving stress testing among financial institutions. I only II only I and II Neither I nor II a. 91 . Reference: Andrew G. Answer: c.2011 Financial Risk Manager Examination (FRM®) Practice Exam 20. Global Association of Risk Professionals. common set of scenarios that include a broad range of possible stresses. d. Inc. Financial Risk ® Manager (FRM ) Examination 2011 Practice Exam PART II / EXAM 2 Answer Sheet . 3. 16. c. 7. 18. c. 1. 19. Inc. 11. It is illegal to reproduce this material in any format without prior written approval of GARP. 8. b. 17. d. 1. 15. 2. 93 . 5. 6. 14. Wrong way to complete 12. © 2011 Global Association of Risk Professionals. 9. Correct way to complete 10. b. 20. 4. 3 8 13. d. Global Association of Risk Professionals. a. All rights reserved.2011 Financial Risk Manager Examination (FRM®) Practice Exam a. 1. Financial Risk ® Manager (FRM ) Examination 2011 Practice Exam PART II / EXAM 2 Questions . 44 years and yielding 6. d.71 6. I only II only Both Neither 3.50 2. barrier USD 95 Down-and-in barrier put.7% compounded semiannually. b. A rise in interest rates increases the duration of a MBS.127. c. All rights reserved. If there is a positive parallel shift in the yield curve of 25 basis points. b.2011 Financial Risk Manager Examination (FRM®) Practice Exam 1. The table below lists the prices of some barrier options on the same stock with a maturity of 1 year and strike of USD 100. II.000 -1. Inc. a. 95 .50 3. A 1-year forward contract on a stock with a forward price of USD 100 is available for USD 1. c. It is illegal to reproduce this material in any format without prior written approval of GARP. b. John Snow’s portfolio has a fixed-income position with market value of USD 70 million with modified duration of 6.755 © 2011 Global Association of Risk Professionals. d.134. USD USD USD USD 2.725 -1. Which of following statement about mortgage-backed securities (MBS) is correct? I. As yield volatility increases. which of the following answers best estimates the resulting change in the value of John’s portfolio? a.21 USD 3.71 Price USD 5. Global Association of Risk Professionals.164. barrier USD 80 a.692 -1. Assuming a continuously compounded risk-free rate of 5% per year what is the price of a European put option on the stock with a strike of USD 100. Option Up-and-in barrier call. c.50. the value of a MBS grows as well.00 3. d. USD USD USD USD -11. d. . b. Changes to interest rates Amount of principal outstanding I only II only Both Neither 5. The proposed securitization includes tranches with multiple internal credit enhancements as shown in Exhibit 1 below. a. George Smith is an analyst in the risk management department and he is reviewing a pool of mortgages. c. It is illegal to reproduce this material in any format without prior written approval of GARP. c. National United Bank has recently increased the bank’s liquidity through securitization of existing credit card receivables. Inc. and the subordinated tranche B bond class is the first loss piece: Exhibit 1. The total value of the collateral for the structure is USD 600 million. the underlying credit card accounts have prepaid USD 300 million in principal in addition to regularly scheduled principal and interest payments. Prepayment risk introduces complexity to the valuation of mortgages. What is the amount of the prepaid principal paid out to the holders of the junior tranche A bond class? a.2011 Financial Risk Manager Examination (FRM®) Practice Exam 4. d. USD USD USD USD 0 million 50 million 120 million 230 million 96 © 2011 Global Association of Risk Professionals. no lockout period. Global Association of Risk Professionals. II. Which of the two factors is generally considered to affect prepayment risk for a mortgage? I. All rights reserved. Proposed ABS Structure Bond Class Senior tranche Junior tranche A Junior tranche B Subordinated tranche A Subordinated tranche B Total Par Value USD 250 million USD 200 million USD 70 million USD 50 million USD 30 million USD 600 million At the end of the fourteenth month after the securities were issued. b. 583 3. II. 97 . c.23% 11. 2. a. Assuming a recovery rate of zero.80% 3.000 Long term debt = 1.500 Expected market value of the firm one year from now = 5. Inc. You are given the following data for a firm: Current market value of firm = 4.2011 Financial Risk Manager Examination (FRM®) Practice Exam 6. c. and the yield on a 1-year zero-coupon corporate bond is 7% per year. It is illegal to reproduce this material in any format without prior written approval of GARP.350 3.612 © 2011 Global Association of Risk Professionals.28% 7. 3. All rights reserved.045 3. The 1-year risk-free rate is 4%. d. b.000 Short term debt = 1. c. Selling a forward contract to the counterparty Selling a call option to the counterparty I only II only Both Neither 8. what is the implied probability of default? a. b.00% 11.300 Annualized volatility of firm’s assets = 22%. d. b. d. what is the distance-to-default one year from now? a. Which of the following two transactions increases counterparty credit exposure? I. According to KMV model. Global Association of Risk Professionals. Of the original balance. Assuming that the individual exposures at default with a counterparty are fixed. b. . the investor’s position will: a. All rights reserved. Given the following information from the bank’s internal credit risk models what is an appropriate loan loss reserve to cover this eventuality? 1-year default probability = 0. USD 20 million has already been drawn and due to deteriorating economic conditions the bank is concerned that the borrower might find itself in a liquidity crisis causing it to draw on the remaining commitment and default. c.400 140. 98 © 2011 Global Association of Risk Professionals. and loss given default. It is illegal to reproduce this material in any format without prior written approval of GARP. USD USD USD USD 210. c. assuming everything else is unchanged. Loss given default can be mitigated by collateral and exposure at default can be mitigated by netting. which of the following statements is correct? a.2011 Financial Risk Manager Examination (FRM®) Practice Exam 9. d.000 117. An investor has sold default protection on the most junior tranche of a CDO. d. Gain value Lose value Neither gain nor lose value It depends on the pricing model used and the market conditions. If the default correlation decreases sharply and changes from a positive to a negative correlation. The probability of default can be mitigated by collateral and exposure at default can be mitigated by netting.35% Drawdown given default = 80% Loss given default = 60% a. 11. b. exposure at default.600 10. Credit risk is a function of the probability of default. The probability of default can be mitigated by netting and exposure at default can be mitigated by collateral. You have been asked by the Chief Risk Officer of your bank to determine how much should be set aside as a loan-loss reserve for a 1-year horizon on a USD 100 million line of credit that has been extended to a large corporate borrower. Global Association of Risk Professionals. b.000 176. d. c. Inc. Loss given default can be mitigated by netting and exposure at default can be mitigated by collateral. which has a current stock price of USD 80 (expressed as the midpoint of the current bid-ask spread). The likelihood that an operational risk loss is reported is positively related to the size of the loss.351 14.10. Which of the following statements regarding characteristics of operational risk loss data and operational risk modeling is correct? a. As a risk manager for Bank ABC is asked to calculate the market risk capital charge of the bank’s trading portfolio under the internal models approach using the information given in the table below. 99 .000 USD 20.076 3. b.000 3 13. c. Assuming returns of BNA are normally distributed. 1-day) for last 60 trading days Multiplication Factor a.594 189. c. It is illegal to reproduce this material in any format without prior written approval of GARP.000 share position in an undervalued but illiquid stock BNA. External loss data often exhibits capture bias as minimum loss thresholds for collecting loss data are uni form across all institutions. c.324 4.737 267.2011 Financial Risk Manager Examination (FRM®) Practice Exam 12. USD USD USD USD 84.471 USD 30.389 2. The average bid-ask spread is USD 0. © 2011 Global Association of Risk Professionals. Operational risk losses tend to be negatively related to the size of the institution. what is the market risk capital charge of the trading portfolio? VaR (95%. All rights reserved.582 134. what is the estimated liquidity-adjusted daily 95% VaR. Inc. Daily return for BNA has an estimated volatility of 1. You are a manager of a renowned hedge fund and are analyzing a 1. d. USD USD USD USD 1. b. d. Global Association of Risk Professionals. 1-day) of last trading day Average VaR (95%. Assuming the return of the bank’s trading portfolio is normally distributed.54%. using the constant spread approach? a. b. Operational risk losses are modeled using techniques that are used in interest rate modeling. d. The benchmark has an alpha of 3. Which of the following statements about the ERM framework is/are correct? I. II.0 basis points 82. The IRO unit of XYZ bank only re-evaluates previously implemented models when a problem is identified. Stock XYZ has a volatility of 30%. and a beta of 1. The IRO unit evaluates and checks the key assumptions of all the models used by XYZ bank. Statement I only Statement II only Both statements are correct Both statements are incorrect 16. I. You are the head of the Independent Risk Oversight (IRO) unit of XYZ bank. The appropriate benchmark-neutral alpha for stock XYZ is: a. d. a large conglomerate is implementing the enterprise risk management (ERM) framework to quantify and manage the risk-return tradeoff for the entire firm. b. Global Association of Risk Professionals. II. d.7 basis points 44.7 basis points.20. Which of the existing policies is/are sources of model risk? a. c. Inc.8 basis points 100 © 2011 Global Association of Risk Professionals.3 basis points 74.2011 Financial Risk Manager Examination (FRM®) Practice Exam 15. The ERM framework tries to minimize the aggregate risk taken by the firm. The performance of each business unit should be evaluated on a stand-alone basis and the unit should be allocated more capital if its net income is positive. an alpha of 90 bps. . an information coefficient of 0. It is illegal to reproduce this material in any format without prior written approval of GARP. a. 30.94. c. You want to construct a portfolio so that all of the alphas are benchmark-neutral. d. Statement I only Statement II only Both statements are correct Both statements are incorrect 17. c. Brisk Holdings. Your first task is to review the following existing policies relating to model implementation. b. All rights reserved. b. 176 0. what will be the reduction in portfolio VaR? a.429 1.3 44. I only II only I and II Neither I nor II © 2011 Global Association of Risk Professionals. c.6 USD 44. b.2011 Financial Risk Manager Examination (FRM®) Practice Exam The next two questions are based on the following information.0 46. Rigorous stress testing has been emphasized as an important component of risk measurement and management that has been poorly implemented by many financial institutions in the recent past. d. 101 .3 USD 46. where ρip denotes the correlation between the return of asset i and the return of the portfolio. It is inappropriate for banks to conduct “reverse” stress tests. It is illegal to reproduce this material in any format without prior written approval of GARP. II.0 38.513 Cannot determine from information provided. d. a. b. d.714 1. USD USD USD USD 15. All rights reserved.6 USD 61. What is β2? a. A risk manager assumes that the joint distribution of returns is multivariate normal and calculates the following risk measures for a 2-asset portfolio: Asset 1 2 Portfolio Position USD 100 USD 100 USD 200 Individual VaR USD 23. c. Global Association of Risk Professionals. Banks do not need to consider potential second round effects of stress scenarios on the broader financial network. c. Let βi = ρip * σi / σp.6 19. If asset 1 is dropped from the portfolio.440 VaR Contribution USD 17.0 USD 61.6 18. Which of the following statements concerning steps banks should consider to improve the value of stress testing exercises is/are correct? I. 0. Inc.6 Marginal VaR 0. σi is the volatility of the return of asset i and σp is the volatility of the return of the portfolio. 20. b. Financial Risk ® Manager (FRM ) Examination 2011 Practice Exam PART II / EXAM 2 Answers . 3 8 13. 11. Wrong way to complete 12. 4. It is illegal to reproduce this material in any format without prior written approval of GARP. b. 2. Inc. d. 7. © 2011 Global Association of Risk Professionals. 1. c. 18. b. 16. 9. Global Association of Risk Professionals. 1. 6. c. 8. 19. 14. 103 . 20. 3. 1. 5.2011 Financial Risk Manager Examination (FRM®) Practice Exam a. Correct way to complete 10. 15. d. a. 17. All rights reserved. Financial Risk ® Manager (FRM ) Examination 2011 Practice Exam PART II / EXAM 2 Explanations . Thus put = USD 5.50 = USD 3.00 3. A 1-year forward contract on a stock with a forward price of USD 100 is available for USD 1. c. Chapter 24 © 2011 Global Association of Risk Professionals. Option Up-and-in barrier call. Global Association of Risk Professionals. Futures.21 USD 3. the value of an up-and-in call is the same as the value of a European call with the same strike price.50 3. Reference: John Hull.71 6. and Other Derivatives. barrier USD 95 Down-and-in barrier put. The table below lists the prices of some barrier options on the same stock with a maturity of 1 year and strike of USD 100.21 .50. d. It is illegal to reproduce this material in any format without prior written approval of GARP. 7th Edition (New York: Pearson 2009).50 Answer: c. Inc. The put-call parity theorem gives put= call . Options. Topic: Market Risk Measurement and Management Subtopic: Exotic options AIMS: List and describe the characteristics and pay-off structures of barrier options.2011 Financial Risk Manager Examination (FRM®) Practice Exam 1. USD USD USD USD 2.71 Price USD 5. b. Explanation: When the barrier is below the strike price. All rights reserved. Assuming a continuously compounded risk-free rate of 5% per year what is the price of a European put option on the stock with a strike of USD 100.71.USD 1. 105 . barrier USD 80 a.forward (with same strikes and maturities). 127. This statement is false.0025 * 6. b. the value of a MBS grows as well. Dmod = (-1/P) * (dP/dy). II. As yield volatility increases.2011 Financial Risk Manager Examination (FRM®) Practice Exam 2.7% compounded semiannually. Explanation: a: is correct. d. Inc.44 * 70 = -1.164. So as a linear approximation.134. As yield volatility increases.000 -1.44 years and yielding 6. If there is a positive parallel shift in the yield curve of 25 basis points. modified duration.692 -1. d. b. which of the following answers best estimates the resulting change in the value of John’s portfolio? a. This statement is true. the value of embedded call option increases. 2nd Edition. Reference: Tuckman. c. It is illegal to reproduce this material in any format without prior written approval of GARP. ΔP = -1 * Δy * Dmod * P = -1 * 0. Explanation: I. c. Topic: Market Risk Measurement and Management Subtopic: Mortgages and mortgage‐backed securities AIMS: Describe the various risk associated with mortgages and mortgage backed securities and explain risk based pricing. Chapter 6—Measures of Price Sensitivity Based on Parallel Yield Shifts 106 © 2011 Global Association of Risk Professionals. USD USD USD USD -11.755 Answer: b. Global Association of Risk Professionals. 2006). Fixed Income Securities. Reference: Frank Fabozzi. . II. and Macaulay duration. I only II only Both Neither Answer: b.127 million Topic: Market Risk Measurement and Management Subtopic: Duration and convexity of Fixed Income Instruments AIMS: Define and calculate yield‐based DV01. John Snow’s portfolio has a fixed-income position with market value of USD 70 million with modified duration of 6.725 -1. A rise in interest rates reduces the prepayments and hence increases the duration of a MBS. Which of following statement about mortgage-backed securities (MBS) is correct? I. Holding MBS is equivalent to holding a similar duration bond and selling a call option. By definition. Handbook of Mortgage Backed Securities 6th Edition (New York: McGraw-Hill. Thus the value of MBS decreases. a. All rights reserved. A rise in interest rates increases the duration of a MBS. 3. 107 . Which of the two factors is generally considered to affect prepayment risk for a mortgage? I. Explanation: Both are factors affecting prepayment Topic: Market Risk Measurement and Management Subtopic: Mortgages and mortgage‐backed securities. Prepayment risk introduces complexity to the valuation of mortgages.2011 Financial Risk Manager Examination (FRM®) Practice Exam 4. 2002). c. Chapter 21— Mortgage‐Backed Securities © 2011 Global Association of Risk Professionals. Changes to interest rates Amount of principal outstanding I only II only Both Neither Answer: c. d. a. All rights reserved. 2nd Edition (Hoboken. Fixed Income Securities. NJ: Wiley & Sons. II. risks in mortgages and mortgage-backed securities AIMS: Describe the impact of interest rate changes on the value of the prepayment option and discuss non‐interest rate factors that may trigger mortgage prepayments. George Smith is an analyst in the risk management department and he is reviewing a pool of mortgages. Global Association of Risk Professionals. Inc. It is illegal to reproduce this material in any format without prior written approval of GARP. Reference: Bruce Tuckman. b. Explanation: USD 50 million is calculated by USD 300 . Reference: Christopher Culp. Structured Finance and Insurance: The Art of Managing Capital and Risk (Hoboken: John Wiley & Sons. . tranching and subordination AIMS: Discuss the securitization process for mortgage‐backed securities and asset‐backed commercial paper. Chapter 16.2011 Financial Risk Manager Examination (FRM®) Practice Exam 5. USD USD USD USD 0 million 50 million 120 million 230 million Answer: b. securitization. d. 2006). the underlying credit card accounts have prepaid USD 300 million in principal in addition to regularly scheduled principal and interest payments. Topic: Credit Risk Measurement and Management Subtopic: Structured finance. It is illegal to reproduce this material in any format without prior written approval of GARP. Since the period is past the lockout period. b. Inc. 108 © 2011 Global Association of Risk Professionals. All rights reserved. Proposed ABS Structure Bond Class Senior tranche Junior tranche A Junior tranche B Subordinated tranche A Subordinated tranche B Total Par Value USD 250 million USD 200 million USD 70 million USD 50 million USD 30 million USD 600 million At the end of the fourteenth month after the securities were issued. c. no lockout period. The total value of the collateral for the structure is USD 600 million. National United Bank has recently increased the bank’s liquidity through securitization of existing credit card receivables. The proposed securitization includes tranches with multiple internal credit enhancements as shown in Exhibit 1 below. and the subordinated tranche B bond class is the first loss piece: Exhibit 1. Global Association of Risk Professionals. What is the amount of the prepaid principal paid out to the holders of the junior tranche A bond class? a.USD 250 = USD 50. the distribution is made. since prepayments are first distributed to the senior tranches. and Other Derivatives. p. Inc. Reference: John Hull. d. d. Explanation: The probability of default (PD) is = 1 .00% 11. II. Assuming a recovery rate of zero. b. It is illegal to reproduce this material in any format without prior written approval of GARP. Futures. Chapter 22— Credit Risk 7.80% 3. c.80% Topic: Credit Risk Measurement and Management Subtopic: Probability of default. Selling an option (for both call and put) does not create credit risk as it is not subject to the performance of the counterparty. Options.28% Answer: a. 7th Edition (NY: Pearson. 507. 2009). loss given default and recovery rates AIMS: Estimate the probability of default for a company from its bond price.((1+risk-free rate)/(1 + corp bond rate)) = 1-((1 + 4%)/(1 + 7%)) = 2. Global Association of Risk Professionals.23% 11. Selling of forward contract creates credit risk exposure to the counterparty as it is subject to the performance of the counterparty. and the yield on a 1-year zero-coupon corporate bond is 7% per year. a. what is the implied probability of default? a.2011 Financial Risk Manager Examination (FRM®) Practice Exam 6. II. b. Topic: Credit Risk Measurement and Management Subtopic: Counterparty risk and OTC derivatives AIMS: Describe counterparty credit risk in derivatives markets and explain how it affects valuation. The 1-year risk-free rate is 4%. Which of the following two transactions increases counterparty credit exposure? I. The option premium has already been collected when the transaction is made and default of the counterparty will have no negative impact on the seller. Reference: Hull. Explanation: I. All rights reserved. 2. and Other Derivatives. Chapter 22—Credit Risk. which may default to pay at expiry date. © 2011 Global Association of Risk Professionals. 109 . Options. Futures. 7th Edition. c. Selling a forward contract to the counterparty Selling a call option to the counterparty I only II only Both Neither Answer: a. You are given the following data for a firm: Current market value of firm = 4. All rights reserved. d. 110 © 2011 Global Association of Risk Professionals.000 Long term debt = 1.22) = 3.35% Drawdown given default = 80% Loss given default = 60% a.400 140. USD USD USD USD 210.500 Expected market value of the firm one year from now = 5.1650)/(5000*0.300 Annualized volatility of firm’s assets = 22%. Given the following information from the bank’s internal credit risk models what is an appropriate loan loss reserve to cover this eventuality? 1-year default probability = 0. Reference: De Servigny and Renault.000 176. Explanation: According to KMV.5*1300 = 1650 Distance to default = (Market value of Asset after 1 year-default point) / Annualized Asset volatility = (5000 . Measuring and Managing Credit Risk.000 Short term debt = 1. It is illegal to reproduce this material in any format without prior written approval of GARP. d.000 117. Global Association of Risk Professionals.2011 Financial Risk Manager Examination (FRM®) Practice Exam 8. According to KMV model. Chapter 3 9. USD 20 million has already been drawn and due to deteriorating economic conditions the bank is concerned that the borrower might find itself in a liquidity crisis causing it to draw on the remaining commitment and default. b.5LT if LT/ST < = 1.583 3. Of the original balance. b. default value X = ST+0. 3.350 3.045 Topic: Credit Risk Measurement and Management Subtopic: Contingent claim approach and the KMV Model AIMS: Describe the Moody’s KMV Credit Monitor Model to estimate probability of default using equity prices. what is the distance-to-default one year from now? a. . c.045 3.5 X = 1000 + 0. You have been asked by the Chief Risk Officer of your bank to determine how much should be set aside as a loan-loss reserve for a 1-year horizon on a USD 100 million line of credit that has been extended to a large corporate borrower.612 Answer: a. Inc.600 Answer: b. c. 000*0. Collateral can’t reduce exposure at default. Loss given default can be mitigated by collateral and exposure at default can be mitigated by netting. This is the amount that the bank should set aside as a loss reserve.6 = USD 176. Options. Netting reduces the settlement amount if the counterparty is in default so that netting reduces exposure at default. and Other Derivatives. Topic: Credit Risk Measurement and Management Subtopic: Expected and unexpected loss AIMS: Define. Topic: Credit Risk Measurement and Management Subtopic: Risk mitigation techniques (including netting. Both of them are independent to netting. exposure at default. c: is correct. and expected default frequency affect the expected and unexpected loss. Chapter 22 Credit Risk © 2011 Global Association of Risk Professionals.400. it can be claimed later so that collateral reduce loss given default. This is the adjusted exposure on default (AE). Explanation: a: is incorrect. 111 . Global Association of Risk Professionals. b.0035*0.80 = USD 84. credit quality. 7th Edition. it can be claimed later so that collateral reduce loss given default.000. 2003). and loss given default. or USD 84. Internal Credit Risk Models: Capital Allocation and Performance Measurement (London: Risk Books. Loss given default can be mitigated by netting and exposure at default can be mitigated by collateral. Probability of default depends on credit events which can’t be controlled by netting because credit events depend on ability to pay and willingness to pay. Credit risk is a function of the probability of default. Probability of default depends on credit events which can’t be controlled by collateral because credit events depend on ability to pay and willingness to pay.2011 Financial Risk Manager Examination (FRM®) Practice Exam Explanation: The risky portion of the asset value at the horizon is Outstanding + (Commitment – Outstanding)*Drawdown Given Default = USD 20. Answer: c. Both of them are independent to collateral.000. and collateral) AIMS: Describe the credit mitigation techniques of netting and collateralization Reference: Hull. Collateral can’t reduce exposure at default. Futures. Inc. respectively. However. c. d. which of the following statements is correct? a. Collateral can be claimed to reduce loss given default.000. Chapter 6—Portfolio Effects: Risk Contributions and Unexpected Losses 10. b: is incorrect. Reference: Michael Ong.000. d: is incorrect. rating triggers.USD 20. The expected loss EL = AE*EDF*LGD.000. The probability of default can be mitigated by netting and exposure at default can be mitigated by collateral. Explain how the recovery rate. The probability of default can be mitigated by collateral and exposure at default can be mitigated by netting.000 + (USD 100.000)*0. calculate and interpret expected and unexpected portfolio loss.000 . All rights reserved.000. Assuming that the individual exposures at default with a counterparty are fixed. However. It is illegal to reproduce this material in any format without prior written approval of GARP. 2011 Financial Risk Manager Examination (FRM®) Practice Exam 11. An investor has sold default protection on the most junior tranche of a CDO. If the default correlation decreases sharply and changes from a positive to a negative correlation, assuming everything else is unchanged, the investor’s position will: a. b. c. d. Gain value Lose value Neither gain nor lose value It depends on the pricing model used and the market conditions. Answer: b. Explanation: The junior tranche will become riskier and more likely to absorb a default since it is now more likely that a single asset default will happen and be absorbed by the junior tranche. This is in contrast to having a high correlation, which would imply a more likely default of many assets at once, and less likely default of any single one. Topic: Credit Risk Measurement and Management Subtopic: Structured finance, securitization, tranching and subordination AIMS: Define securitization and describe the process and the role the participants play. Reference: Christopher Culp, Structured Finance and Insurance: The Art of Managing Capital and Risk (Hoboken: John Wiley & Sons, 2006), Chapter 16. 12. As a risk manager for Bank ABC is asked to calculate the market risk capital charge of the bank’s trading portfolio under the internal models approach using the information given in the table below. Assuming the return of the bank’s trading portfolio is normally distributed, what is the market risk capital charge of the trading portfolio? VaR (95%, 1-day) of last trading day Average VaR (95%, 1-day) for last 60 trading days Multiplication Factor a. b. c. d. USD USD USD USD 84,582 134,594 189,737 267,471 USD 30,000 USD 20,000 3 Answer: d. 112 © 2011 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this material in any format without prior written approval of GARP, Global Association of Risk Professionals, Inc. 2011 Financial Risk Manager Examination (FRM®) Practice Exam Explanation: Market Risk Capital Charge = MAX(30,000 x SQRT(10)/1.65x2.326, 3 x 20,000 x SQRT(10)/1.65 x 2.326) = 267,471 Candidate is required to convert the VaR (95%, 1-day) to a 95% 10-day VaR. Topic: Operational and Integrated Risk Management Subtopic: Regulation and the Basel II Accord AIMS: Describe and contrast the major elements—including a description of the risks covered—of the two options available for the calculation of market risk: Standardized Measurement Method and Internal Models Approach Reference: “Basel II: International Convergence of Capital Measurement and Capital Standards: A Revised Framework—Comprehensive Version” (Basel Committee on Banking Supervision Publication, June 2006). 13. You are a manager of a renowned hedge fund and are analyzing a 1,000 share position in an undervalued but illiquid stock BNA, which has a current stock price of USD 80 (expressed as the midpoint of the current bid-ask spread). Daily return for BNA has an estimated volatility of 1.54%. The average bid-ask spread is USD 0.10. Assuming returns of BNA are normally distributed, what is the estimated liquidity-adjusted daily 95% VaR, using the constant spread approach? a. b. c. d. USD USD USD USD 1,389 2,076 3,324 4,351 Answer: b. Explanation: The constant spread approach adds half of the bid-ask spread (as a percent) to the VaR calculation: Daily 95% VaR = 80,000 * (1.645 * 0.0154) = USD 2026.64 Liquidity cost (LC) = 80,000 * (0.5 * 0.10/80) = 50 LVaR = VaR + LC = 2076.64 Topic: Operational and Integrated Risk Management Subtopic: Liquidity risk AIMS: Describe and calculate LVaR using the Constant Spread approach and the Exogenous Spread approach. Reference: Dowd, Measuring Market Risk, 2nd Edition (West Sussex, England: John Wiley & Sons, 2005), Chapter 14. © 2011 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this material in any format without prior written approval of GARP, Global Association of Risk Professionals, Inc. 113 2011 Financial Risk Manager Examination (FRM®) Practice Exam 14. Which of the following statements regarding characteristics of operational risk loss data and operational risk modeling is correct? a. b. c. d. Operational risk losses tend to be negatively related to the size of the institution. External loss data often exhibits capture bias as minimum loss thresholds for collecting loss data are uniform across all institutions. The likelihood that an operational risk loss is reported is positively related to the size of the loss. Operational risk losses are modeled using techniques that are used in interest rate modeling. Answer: c. Explanation: Statement c is correct: The likelihood that an operational risk loss is reported is positively related to the size of the loss. This is referred to as data capture bias. Topic: Operational and Integrated Risk Management Subtopic: Implementation and model risk AIMS: Explain the issues with the use of both internal and external loss data for modeling loss distributions. Reference: Falko Aue and Michael Kalkbrener, 2007, “LDA at Work”, Deutsche Bank White Paper. 15. Brisk Holdings, a large conglomerate is implementing the enterprise risk management (ERM) framework to quantify and manage the risk-return tradeoff for the entire firm. Which of the following statements about the ERM framework is/are correct? I. II. a. b. c. d. The performance of each business unit should be evaluated on a stand-alone basis and the unit should be allocated more capital if its net income is positive. The ERM framework tries to minimize the aggregate risk taken by the firm. Statement I only Statement II only Both statements are correct Both statements are incorrect Answer: d. Explanation: Statement I is incorrect. Management must avoid a silo approach in its evaluation of the performance of each business unit but should take into account the contributions of each the units to the firm’s total risk. This can be done by assigning a level of additional imputed capital to reflect incremental risk of the project. Statement II is incorrect. The purpose of an ERM program is not to minimize or eliminate the firm’s probability of distress. Rather, it should optimize the firm’s risk portfolio by trading off the probability of large shortfalls and its associated costs and with expected gains from taking strategic and business risks. Topic: Foundation of Risk Management Subtopic: Firm-wide risk measurement and management AIMS: Discuss how an ERM program can be used to determine the right amount of risk. 114 © 2011 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this material in any format without prior written approval of GARP, Global Association of Risk Professionals, Inc. Active Portfolio Management: A Quantitative Approach for Providing Superior Returns and Controlling Risk. Your first task is to review the following existing policies relating to model implementation. c. Chapter 16. England: John Wiley & Sons. Reference: Dowd. Topic: Risk Management and Investment Management Subtopic: Portfolio construction AIMS: Describe neutralization and methods for refining alphas to be neutral. You are the head of the Independent Risk Oversight (IRO) unit of XYZ bank. Reference: Grinold and Kahn. 30. d. Incorrect. II. b.7 basis points. Stock XYZ has a volatility of 30%. I. Models should be reviewed regularly and not just as problems with the model are identified. The appropriate benchmark-neutral alpha for stock XYZ is: a. Which of the existing policies is/are sources of model risk? a.20. and a beta of 1. © 2011 Global Association of Risk Professionals. You want to construct a portfolio so that all of the alphas are benchmark-neutral.828. Inc. II. 2005). Statement I only Statement II only Both statements are correct Both statements are incorrect Answer: a.2011 Financial Risk Manager Examination (FRM®) Practice Exam 16. The benchmark has an alpha of 3.0 basis points 82.8 basis points Answer: d. 115 . an information coefficient of 0. Evaluating and checking key assumptions will reduce model risk. Correct.3 basis points 74. Explanation: I.037)] = 0. Topic: Operational and Integrated Risk Management Subtopic: Implementation and model risk AIMS: Identify and discuss sources of model risk. 17. 382-385. b. All rights reserved.94*0. Global Association of Risk Professionals. Measuring Market Risk. pp.90 – (1. The IRO unit of XYZ bank only re-evaluates previously implemented models when a problem is identified. The IRO unit evaluates and checks the key assumptions of all the models used by XYZ bank. you subtract the product of the beta of the stock and the alpha of the benchmark from the original alpha of the stock [0. It is illegal to reproduce this material in any format without prior written approval of GARP. d. an alpha of 90 bps. 2nd Edition—Chapter 14. c.94.7 basis points 44. Explanation: To make the alpha benchmark neutral. 2nd Edition (West Sussex. 440 VaR Contribution USD 17. d. where ρip denotes the correlation between the return of asset i and the return of the portfolio.USD 46.0 38. b.6 USD 44.6 . incremental VaR and diversified portfolio VaR.0 USD 61.3 USD 46. Inc. What is β2? a. b. Value-at-Risk: The New Benchmark for Managing Financial Risk. Reference: Philippe Jorion. A risk manager assumes that the joint distribution of returns is multivariate normal and calculates the following risk measures for a 2-asset portfolio: Asset 1 2 Portfolio Position USD 100 USD 100 USD 200 Individual VaR USD 23. c. d.3 44.6).6 Marginal VaR 0.714 1. Explanation: a is correct: The new portfolio VAR is that of asset 2 alone (USD 46.2011 Financial Risk Manager Examination (FRM®) Practice Exam The next two questions are based on the following information.6 18. what will be the reduction in portfolio VaR? a.176 0. Answer: b. . Topic: Risk Management and Investment Management Subtopic: Portfolio construction AIMS: Define and distinguish between individual VaR.0 46.513 Cannot determine from information provided. 0. If asset 1 is dropped from the portfolio.0. All rights reserved. It is illegal to reproduce this material in any format without prior written approval of GARP. USD USD USD USD 15. σi is the volatility of the return of asset i and σp is the volatility of the return of the portfolio. which implies a reduction in portfolio VaR of USD 61. 2007). 116 © 2011 Global Association of Risk Professionals. 3rd Edition (New York: McGraw‐Hill.6 Answer: a. Global Association of Risk Professionals. c. Chapter 7—Portfolio Risk: Analytical Methods 19.6 USD 61. Let βi = ρip * σi / σp.429 1.6 = USD 15. and component VaR. compute. Reference: Andrew G. Inc.2011 Financial Risk Manager Examination (FRM®) Practice Exam Explanation: Marginal VaRi = βi * Portfolio VaR / Portfolio Value So. Haldane. Reference: Philippe Jorion. © 2011 Global Association of Risk Professionals. 3rd Edition (New York: McGraw‐Hill. “Why Banks Failed the Stress Test.” (February 2009). and explain the uses of marginal VaR. 2007). d.44 * 200 / 61. βi = Marginal VaRi * Portfolio Value / Portfolio VaR β2 = 0. Explanation: Both statements are incorrect. I—Banks need to examine possible systemic risk implications. Rigorous stress testing has been emphasized as an important component of risk measurement and management that has been poorly implemented by many financial institutions in the recent past. 117 .429 Topic: Risk Management and Investment Management Subtopic: Risk decomposition and performance attribution AIMS: Define. Chapter 7—Portfolio Risk: Analytical Methods 20.6 = 1. Value-at-Risk: The New Benchmark for Managing Financial Risk. a. All rights reserved. Banks do not need to consider potential second round effects of stress scenarios on the broader financial network. Which of the following statements concerning steps banks should consider to improve the value of stress testing exercises is/are correct? I. c. Global Association of Risk Professionals. II. b. Topic: Current Issues in Financial Markets Subtopic: Causes and consequences of the current crisis AIMS: Discuss methods for improving stress testing among financial institutions. II—Banks should stress test for events that can cause major downturns. It is inappropriate for banks to conduct “reverse” stress tests. I only II only I and II Neither I nor II Answer: d. incremental VaR. It is illegal to reproduce this material in any format without prior written approval of GARP. This Page Left Blank . investment management firms.org. and corporations from more than 195 countries.TM Global Association of Risk Professionals 111 Town Square Place Suite 1215 Jersey City. certifications recognized by risk professionals worldwide.Creating a culture of risk awareness. academic institutions.garp.org About GARP | The Global Association of Risk Professionals (GARP) is a not-for-profit global membership organization dedicated to preparing professionals and organizations to make better informed risk decisions. government agencies.719. www. © 2011 Global Association of Risk Professionals. GARP administers the Financial Risk Manager (FRM®) and the Energy Risk Professional (ERP®) exams. Membership represents over 150. 1st Floor 42 Mincing Lane London EC3R 7AE UK + 44 (0) 20 7397 9630 www.garp.000 risk management practitioners and researchers from banks. 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