# Errata (eg, FRM Handbook) or Key Exam Issue

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1. ### Questions

Hi asja, Re: Does it mean that the question/answer posted here are copied directly from handbook, therefore may contain error, until you vet them? I guess I will just wait for the pdf then… Yes, exactly correct, they are merely copied until I vet them... Re: If your time is limit, IMHO you may focus more on the Note. (I know this is a sensitive topic. By no means I want to push, I only...
Hi asja, Re: Does it mean that the question/answer posted here are copied directly from handbook, therefore may contain error, until you vet them? I guess I will just wait for the pdf then… Yes, exactly correct, they are merely copied until I vet them... Re: If your time is limit, IMHO you may focus more on the Note. (I know this is a sensitive topic. By no means I want to push, I only...
Hi asja, Re: Does it mean that the question/answer posted here are copied directly from handbook, therefore may contain error, until you vet them? I guess I will just wait for the pdf then… Yes, exactly correct, they are merely copied until I vet them... Re: If your time is limit, IMHO...
Hi asja, Re: Does it mean that the question/answer posted here are copied directly from handbook, therefore may contain error, until you vet them? I guess I will just wait for the pdf then… ...
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2. ### Focus Review Exercise 1

Hi, David, Thank you so much. I got it. I thought I missed some important concept as during the focus review, everyone seems understanding completely.
Hi, David, Thank you so much. I got it. I thought I missed some important concept as during the focus review, everyone seems understanding completely.
Hi, David, Thank you so much. I got it. I thought I missed some important concept as during the focus review, everyone seems understanding completely.
Hi, David, Thank you so much. I got it. I thought I missed some important concept as during the focus review, everyone seems understanding completely.
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2
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3. ### Zero Coupon Bond (5th Ed, p11)

This question, motivated by a forum query, is a variation on an example given in the FRM Handbook (page 11); the spreadsheet contains solutions for both. I thought this would give practice on several bond ideas. Question: Consider a 10-year zero-coupon Treasury bond with face value of $100 trading at a yield of 5%. Questions: a. What is the bond's price under (i) annual, (ii)... This question, motivated by a forum query, is a variation on an example given in the FRM Handbook (page 11); the spreadsheet contains solutions for both. I thought this would give practice on several bond ideas. Question: Consider a 10-year zero-coupon Treasury bond with face value of$100 trading at a yield of 5%. Questions: a. What is the bond's price under (i) annual, (ii)...
This question, motivated by a forum query, is a variation on an example given in the FRM Handbook (page 11); the spreadsheet contains solutions for both. I thought this would give practice on several bond ideas. Question: Consider a 10-year zero-coupon Treasury bond with face value of $100... This question, motivated by a forum query, is a variation on an example given in the FRM Handbook (page 11); the spreadsheet contains solutions for both. I thought this would give practice on... Replies: 0 Views: 3 4. ### Return on Bank Equity pages 682,683 Hi JY - I am frankly confused by both examples (?!) ... I do agree with you, Jorion's funding of the$100 with $92 or$98 does seem inconsistent with a more typical approach; i.e., to fully fund the asset with deposits, so that there is a clean "spread ... that's how Crouhy does it for RAROC: if $1,000 loan, fund with$1,000 deposits ... the only possibility I can figure is perhaps he has...
Hi JY - I am frankly confused by both examples (?!) ... I do agree with you, Jorion's funding of the $100 with$92 or $98 does seem inconsistent with a more typical approach; i.e., to fully fund the asset with deposits, so that there is a clean "spread ... that's how Crouhy does it for RAROC: if$1,000 loan, fund with $1,000 deposits ... the only possibility I can figure is perhaps he has... Hi JY - I am frankly confused by both examples (?!) ... I do agree with you, Jorion's funding of the$100 with $92 or$98 does seem inconsistent with a more typical approach; i.e., to fully fund the asset with deposits, so that there is a clean "spread ... that's how Crouhy does it for RAROC:...
Hi JY - I am frankly confused by both examples (?!) ... I do agree with you, Jorion's funding of the $100 with$92 or $98 does seem inconsistent with a more typical approach; i.e., to fully fund... Replies: 1 Views: 2 5. ### relationship between CF and maturity/coupon? This looks like a duplicate of this: http://www.bionicturtle.com/forum/viewthread/2387/ David This looks like a duplicate of this: http://www.bionicturtle.com/forum/viewthread/2387/ David This looks like a duplicate of this: http://www.bionicturtle.com/forum/viewthread/2387/ David This looks like a duplicate of this: http://www.bionicturtle.com/forum/viewthread/2387/ David Replies: 1 Views: 4 6. ### EXAMPLE 4.1: FRM EXAM 2003—QUESTION 40 Question: In the geometric Brown motion process for a variable S, I. S is normally distributed. II. dln(S) is normally distributed. III. dS/S is normally distributed. IV. S is lognormally distributed. a. I only b. II, III, and IV c. IV only d. III and IV Answer: b. Both dS/S or dln(S) are normally distributed. As a result, S is lognormally distributed. The only incorrect answer... Question: In the geometric Brown motion process for a variable S, I. S is normally distributed. II. dln(S) is normally distributed. III. dS/S is normally distributed. IV. S is lognormally distributed. a. I only b. II, III, and IV c. IV only d. III and IV Answer: b. Both dS/S or dln(S) are normally distributed. As a result, S is lognormally distributed. The only incorrect answer... Question: In the geometric Brown motion process for a variable S, I. S is normally distributed. II. dln(S) is normally distributed. III. dS/S is normally distributed. IV. S is lognormally distributed. a. I only b. II, III, and IV c. IV only d. III and IV Answer: b. Both dS/S or... Question: In the geometric Brown motion process for a variable S, I. S is normally distributed. II. dln(S) is normally distributed. III. dS/S is normally distributed. IV. S is lognormally... Replies: 0 Views: 9 7. ### EXAMPLE 4.2: FRM EXAM 2002—QUESTION 126 Question: Consider that a stock price S that follows a geometric Brownian motion dS = aSdt + bSdz, with b strictly positive. Which of the following statements is false? a. If the drift a is positive, the price one year from now will be above today’s price. b. The instantaneous rate of return on the stock follows a normal distribution. c. The stock price S follows a lognormal... Question: Consider that a stock price S that follows a geometric Brownian motion dS = aSdt + bSdz, with b strictly positive. Which of the following statements is false? a. If the drift a is positive, the price one year from now will be above today’s price. b. The instantaneous rate of return on the stock follows a normal distribution. c. The stock price S follows a lognormal... Question: Consider that a stock price S that follows a geometric Brownian motion dS = aSdt + bSdz, with b strictly positive. Which of the following statements is false? a. If the drift a is positive, the price one year from now will be above today’s price. b. The instantaneous rate of... Question: Consider that a stock price S that follows a geometric Brownian motion dS = aSdt + bSdz, with b strictly positive. Which of the following statements is false? a. If the drift a is... Replies: 0 Views: 5 8. ### EXAMPLE 4.3: FRM EXAM 1999—QUESTION 18 Question: If S1 follows a geometric Brownian motion and S2 follows a geometric Brownian motion, which of the following is true? a. ln(S1 + S2) is normally distributed. b. S1 × S2 is lognormally distributed. c. S1 × S2 is normally distributed. d. S1 + S2 is normally distributed. Answer: b. Both S1 and S2 are lognormally distributed since dln(S1) and dln(S2) are normally distributed.... Question: If S1 follows a geometric Brownian motion and S2 follows a geometric Brownian motion, which of the following is true? a. ln(S1 + S2) is normally distributed. b. S1 × S2 is lognormally distributed. c. S1 × S2 is normally distributed. d. S1 + S2 is normally distributed. Answer: b. Both S1 and S2 are lognormally distributed since dln(S1) and dln(S2) are normally distributed.... Question: If S1 follows a geometric Brownian motion and S2 follows a geometric Brownian motion, which of the following is true? a. ln(S1 + S2) is normally distributed. b. S1 × S2 is lognormally distributed. c. S1 × S2 is normally distributed. d. S1 + S2 is normally distributed. Answer:... Question: If S1 follows a geometric Brownian motion and S2 follows a geometric Brownian motion, which of the following is true? a. ln(S1 + S2) is normally distributed. b. S1 × S2 is... Replies: 0 Views: 1 9. ### EXAMPLE 4.4: FRM EXAM 1999—QUESTION 19 Question: Considering the one-factor Cox, Ingersoll, and Ross term-structure model and the Vasicek model: I. Drift coefficients are different. II. Both include mean reversion. III. Coefficients of the stochastic term, dz, are different. IV. CIR is a jump-diffusion model. a. All of the above are true. b. I and III are true. c. II, III, and IV are true. d. II and III are true. ... Question: Considering the one-factor Cox, Ingersoll, and Ross term-structure model and the Vasicek model: I. Drift coefficients are different. II. Both include mean reversion. III. Coefficients of the stochastic term, dz, are different. IV. CIR is a jump-diffusion model. a. All of the above are true. b. I and III are true. c. II, III, and IV are true. d. II and III are true. ... Question: Considering the one-factor Cox, Ingersoll, and Ross term-structure model and the Vasicek model: I. Drift coefficients are different. II. Both include mean reversion. III. Coefficients of the stochastic term, dz, are different. IV. CIR is a jump-diffusion model. a. All of the... Question: Considering the one-factor Cox, Ingersoll, and Ross term-structure model and the Vasicek model: I. Drift coefficients are different. II. Both include mean reversion. III.... Replies: 0 Views: 4 10. ### EXAMPLE 4.5: FRM EXAM 1999—QUESTION 25 Question: The Vasicek model defines a risk-neutral process for r , which is dr = a(b− r )dt + σdz, where a, b, and σ are constant, and r represents the rate of interest. From this equation we can conclude that the model is a a. Monte Carlo-type model b. Single-factor term-structure model c. Two-factor term-structure model d. Decision tree model Answer: b. This model postulates only... Question: The Vasicek model defines a risk-neutral process for r , which is dr = a(b− r )dt + σdz, where a, b, and σ are constant, and r represents the rate of interest. From this equation we can conclude that the model is a a. Monte Carlo-type model b. Single-factor term-structure model c. Two-factor term-structure model d. Decision tree model Answer: b. This model postulates only... Question: The Vasicek model defines a risk-neutral process for r , which is dr = a(b− r )dt + σdz, where a, b, and σ are constant, and r represents the rate of interest. From this equation we can conclude that the model is a a. Monte Carlo-type model b. Single-factor term-structure model ... Question: The Vasicek model defines a risk-neutral process for r , which is dr = a(b− r )dt + σdz, where a, b, and σ are constant, and r represents the rate of interest. From this equation we can... Replies: 0 Views: 2 11. ### EXAMPLE 4.6: FRM EXAM 1999—QUESTION 26 Question: The term a(b− r ) in the previous question represents which term? a. Gamma b. Stochastic c. Reversion d. Vega Answer: c. This represents the expected return with mean reversion. Question: The term a(b− r ) in the previous question represents which term? a. Gamma b. Stochastic c. Reversion d. Vega Answer: c. This represents the expected return with mean reversion. Question: The term a(b− r ) in the previous question represents which term? a. Gamma b. Stochastic c. Reversion d. Vega Answer: c. This represents the expected return with mean reversion. Question: The term a(b− r ) in the previous question represents which term? a. Gamma b. Stochastic c. Reversion d. Vega Answer: c. This represents the expected return with mean reversion. Replies: 0 Views: 1 12. ### EXAMPLE 4.7: FRM EXAM 1998—QUESTION 24 Question: Which of the following is a shortcoming of modeling a bond option by applying Black-Scholes formula to bond prices? a. It fails to capture convexity in a bond. b. It fails to capture the pull-to-par phenomenon. c. It fails to maintain put-call parity. d. It works for zero-coupon bond options only. Answer: b. The model assumes that prices follow a random walk with a constant... Question: Which of the following is a shortcoming of modeling a bond option by applying Black-Scholes formula to bond prices? a. It fails to capture convexity in a bond. b. It fails to capture the pull-to-par phenomenon. c. It fails to maintain put-call parity. d. It works for zero-coupon bond options only. Answer: b. The model assumes that prices follow a random walk with a constant... Question: Which of the following is a shortcoming of modeling a bond option by applying Black-Scholes formula to bond prices? a. It fails to capture convexity in a bond. b. It fails to capture the pull-to-par phenomenon. c. It fails to maintain put-call parity. d. It works for zero-coupon... Question: Which of the following is a shortcoming of modeling a bond option by applying Black-Scholes formula to bond prices? a. It fails to capture convexity in a bond. b. It fails to... Replies: 0 Views: 1 13. ### EXAMPLE 4.8: FRM EXAM 2000—QUESTION 118 Question: Which group of term-structure models do the Ho-Lee, Hull-White and Heath, Jarrow, and Morton models belong to? a. No-arbitrage models b. Two-factor models c. Lognormal models d. Deterministic models Answer: a. These are no-arbitrage models of the term structure, implemented as either one-factor or two-factor models. Question: Which group of term-structure models do the Ho-Lee, Hull-White and Heath, Jarrow, and Morton models belong to? a. No-arbitrage models b. Two-factor models c. Lognormal models d. Deterministic models Answer: a. These are no-arbitrage models of the term structure, implemented as either one-factor or two-factor models. Question: Which group of term-structure models do the Ho-Lee, Hull-White and Heath, Jarrow, and Morton models belong to? a. No-arbitrage models b. Two-factor models c. Lognormal models d. Deterministic models Answer: a. These are no-arbitrage models of the term structure, implemented... Question: Which group of term-structure models do the Ho-Lee, Hull-White and Heath, Jarrow, and Morton models belong to? a. No-arbitrage models b. Two-factor models c. Lognormal models d.... Replies: 0 Views: 1 14. ### EXAMPLE 4.9: FRM EXAM 2000—QUESTION 119 Question: A plausible stochastic process for the short-term rate is often considered to be one where the rate is pulled back to some long-run average level. Which one of the following term-structure models does not include this characteristic? a. The Vasicek model b. The Ho-Lee model c. The Hull-White model d. The Cox-Ingersoll-Ross model Answer: b. Both the Vasicek and CIR models... Question: A plausible stochastic process for the short-term rate is often considered to be one where the rate is pulled back to some long-run average level. Which one of the following term-structure models does not include this characteristic? a. The Vasicek model b. The Ho-Lee model c. The Hull-White model d. The Cox-Ingersoll-Ross model Answer: b. Both the Vasicek and CIR models... Question: A plausible stochastic process for the short-term rate is often considered to be one where the rate is pulled back to some long-run average level. Which one of the following term-structure models does not include this characteristic? a. The Vasicek model b. The Ho-Lee model c.... Question: A plausible stochastic process for the short-term rate is often considered to be one where the rate is pulled back to some long-run average level. Which one of the following... Replies: 0 Views: 4 15. ### EXAMPLE 4.10: FRM EXAM 2004—QUESTION 28 Question: Which of the following statements about American stock options is false? a. American options can be exercised at or before maturity. b. American options are always worth at least as much as European options. c. American options can easily be valued with Monte Carlo simulation. d. American options can be easily valued with binomial trees. Answer: c. American options cannot... Question: Which of the following statements about American stock options is false? a. American options can be exercised at or before maturity. b. American options are always worth at least as much as European options. c. American options can easily be valued with Monte Carlo simulation. d. American options can be easily valued with binomial trees. Answer: c. American options cannot... Question: Which of the following statements about American stock options is false? a. American options can be exercised at or before maturity. b. American options are always worth at least as much as European options. c. American options can easily be valued with Monte Carlo simulation. ... Question: Which of the following statements about American stock options is false? a. American options can be exercised at or before maturity. b. American options are always worth at least as... Replies: 0 Views: 1 16. ### EXAMPLE 4.11: FRM EXAM 1999—QUESTION 8 Question: Several different estimates of the VAR of an options portfolio were computed using 1,000 independent, log-normally distributed samples of the underlyings. Because each estimate was made using a different set of random numbers, there was some variability in the answers. In fact, the standard deviation of the distribution of answers was about$100,000. It was then decided to rerun...
Question: Several different estimates of the VAR of an options portfolio were computed using 1,000 independent, log-normally distributed samples of the underlyings. Because each estimate was made using a different set of random numbers, there was some variability in the answers. In fact, the standard deviation of the distribution of answers was about \$100,000. It was then decided to rerun...
Question: Several different estimates of the VAR of an options portfolio were computed using 1,000 independent, log-normally distributed samples of the underlyings. Because each estimate was made using a different set of random numbers, there was some variability in the answers. In fact, the...
Question: Several different estimates of the VAR of an options portfolio were computed using 1,000 independent, log-normally distributed samples of the underlyings. Because each estimate was...
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17. ### EXAMPLE 4.12: FRM EXAM 1998—QUESTION 34

Question: You have been asked to find the value of an Asian option on the short rate. The Asian option gives the holder an amount equal to the average value of the short rate over the period to expiration less the strike rate. To value this option with a one-factor binomial model of interest rates, what method would you recommend using? a. The backward induction method, since it is the...
Question: You have been asked to find the value of an Asian option on the short rate. The Asian option gives the holder an amount equal to the average value of the short rate over the period to expiration less the strike rate. To value this option with a one-factor binomial model of interest rates, what method would you recommend using? a. The backward induction method, since it is the...
Question: You have been asked to find the value of an Asian option on the short rate. The Asian option gives the holder an amount equal to the average value of the short rate over the period to expiration less the strike rate. To value this option with a one-factor binomial model of interest...
Question: You have been asked to find the value of an Asian option on the short rate. The Asian option gives the holder an amount equal to the average value of the short rate over the period to...
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18. ### EXAMPLE 4.13: FRM EXAM 1997—QUESTION 17

Question: The measurement error in VAR, due to sampling variation, should be greater with a. More observations and a high confidence level (e.g., 99%) b. Fewer observations and a high confidence level c. More observations and a low confidence level (e.g., 95%) d. Fewer observations and a low confidence level Answer: b. Sampling variability (or imprecision) increases with (1) fewer...
Question: The measurement error in VAR, due to sampling variation, should be greater with a. More observations and a high confidence level (e.g., 99%) b. Fewer observations and a high confidence level c. More observations and a low confidence level (e.g., 95%) d. Fewer observations and a low confidence level Answer: b. Sampling variability (or imprecision) increases with (1) fewer...
Question: The measurement error in VAR, due to sampling variation, should be greater with a. More observations and a high confidence level (e.g., 99%) b. Fewer observations and a high confidence level c. More observations and a low confidence level (e.g., 95%) d. Fewer observations and a...
Question: The measurement error in VAR, due to sampling variation, should be greater with a. More observations and a high confidence level (e.g., 99%) b. Fewer observations and a high...
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19. ### EXAMPLE 4.14: FRM EXAM 1999—QUESTION 29

Question: (Data-intensive) Given the covariance matrix, (FORMULA GOES HERE) let = XX, where X is lower triangular, be a Cholesky decomposition. Then the four elements in the upper left-hand corner of X, x11, x12, x21, x22, are, respectively, a. 3.0%, 0.0%, 4.0%, 2.0% b. 3.0%, 4.0%, 0.0%, 2.0% c. 3.0%, 0.0%, 2.0%, 1.0% d. 2.0%, 0.0%, 3.0%, 1.0% Answer: c. This involves a...
Question: (Data-intensive) Given the covariance matrix, (FORMULA GOES HERE) let = XX, where X is lower triangular, be a Cholesky decomposition. Then the four elements in the upper left-hand corner of X, x11, x12, x21, x22, are, respectively, a. 3.0%, 0.0%, 4.0%, 2.0% b. 3.0%, 4.0%, 0.0%, 2.0% c. 3.0%, 0.0%, 2.0%, 1.0% d. 2.0%, 0.0%, 3.0%, 1.0% Answer: c. This involves a...
Question: (Data-intensive) Given the covariance matrix, (FORMULA GOES HERE) let = XX, where X is lower triangular, be a Cholesky decomposition. Then the four elements in the upper left-hand corner of X, x11, x12, x21, x22, are, respectively, a. 3.0%, 0.0%, 4.0%, 2.0% b. 3.0%,...
Question: (Data-intensive) Given the covariance matrix, (FORMULA GOES HERE) let = XX, where X is lower triangular, be a Cholesky decomposition. Then the four elements in the upper...
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20. ### EXAMPLE 5.1: FRM EXAM 2002—QUESTION 56

Question: Consider a forward contract on a stock market index. Identify the false statement. Everything else being constant, a. The forward price depends directly on the level of the stock market index. b. The forward price will fall if underlying stocks increase the level of dividend payments over the life of the contract. c. The forward price will rise if time to maturity is...
Question: Consider a forward contract on a stock market index. Identify the false statement. Everything else being constant, a. The forward price depends directly on the level of the stock market index. b. The forward price will fall if underlying stocks increase the level of dividend payments over the life of the contract. c. The forward price will rise if time to maturity is...
Question: Consider a forward contract on a stock market index. Identify the false statement. Everything else being constant, a. The forward price depends directly on the level of the stock market index. b. The forward price will fall if underlying stocks increase the level of dividend...
Question: Consider a forward contract on a stock market index. Identify the false statement. Everything else being constant, a. The forward price depends directly on the level of the stock...
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