Level I (Questions 120)
FRM 2010 Practice Questions
–
Vol. I
By David Harper, CFA FRM CIPM www.bionicturtle.com
FRM 2010
LEVEL I (QUESTIONS 120)
1 www.bionicturtle.com
Table of Contents
Question 1: Simulation methods [quantitative] 2
Question 2: Jensen’s Alpha measure [foundations]
3 Question 3: Creating Value [foundations] 4 Question 4: Market Structure [products] 6 Question 5: Bonds DV01 [valuation] 7 Question 6: Mean & standard deviation [valuation] 9 Question 7: Simple regression model [quantitative] 10 Question 8: Null hypothesis [quantitative] 12 Question 9: Hypothesis testing [quantitative] 14 Question 10: Option delta [valuation] 16 Question 11: Estimate of invoice price [products] 18 Question 12: Hedge [products] 20 Question 13: Market/Credit/Operational risk [foundation] 22 Question 14: Models for estimating volatility [quantitative] 24 Question 15: Duration of the bond [valuation] 26 Question 16: Diversification for a VaR [valuation] 28 Question 17: Probability [quantitative] 30 Question 18: Bonds [valuation] 33 Question 19: Duration and convexity [valuation] 35 Question 20: Historical simulation [valuation] 37
FRM 2010
LEVEL 1 (QUESTIONS 120)
2 www.bionicturtle.com
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copy and also violates GARP’s ethical standards.
Some of the questions may have a followup explanation. This would be located on the forum: http://www.bionicturtle.com/forum/viewforum/45/
Question 1: Simulation methods [quantitative]
Which of the following statements about simulation is invalid?
a)
The historical simulation approach is a nonparametric method that makes no specific assumption about the distribution of asset returns. b)
When simulating asset returns using Monte Carlo simulation, a sufficient number of trials must be used to ensure simulated returns are risk neutral. c)
Bootstrapping is an effective simulation approach that naturally incorporates correlations between asset returns and nonnormality of asset returns, but does not generally capture autocorrelation of asset returns. d)
Monte Carlo simulation can be a valuable method for pricing derivatives and examining asset return scenarios.
[Please note: the additional, followup questions were written by David Harper. The goal is to explore the topic in greater depth.]
1.2. Which VaR simulation approach can incorporate (handle) heavytailed or skewed asset returns?
1.3. Briefly explain Linda Allen’s hybrid approach.
1.4. What is the motive and advantage of Jorion’s QMC method?
Answer: B
Explanation:
Risk neutrality has nothing to do with sample size. Topic: Quantitative Analysis, Subtopic: Simulation methods. Reference: Jorion, chapter 12. 1.2 Which VaR simulation approach can incorporate (handle) heavytailed or skewed asset returns? All VaR methods, including both HS and MCS, can incorporate nonnormal returns! 1.3 The
hybrid approach blends HS and EWMA for the weighting scheme; Linda Allen’s hybrid is
still essentially a SIMULATION approach as a parametric form does not describe returns. 1.4 quasi Monte
Carlo (QMC) are faster, producing an “error that shrinks at a faste
r rate,
proportional to close to 1/K rather than 1/SQRT(k)”
FRM 2010
LEVEL 1 (QUESTIONS 120)
3 www.bionicturtle.com
Question 2: Jensen’s Alpha measure [foundations]
Portfolio Q has a beta of 0.7 and an expected return of 12.8%. The market risk premium is 5.25%. The riskfree rate is 4.85%. Calculate
Jensen’s
Alpha measure for Portfolio Q.
a)
7.67% b)
2.70% c)
5.73% d)
4.27%
2.2. What is the portfolio’s Treynor measure?
2.3. Are Jensen’s and Treynor related?
2.4. What is the portfolio’s Sharpe measure?
2.5. What is a criticism of Jensen’s alpha?
2.6. Is Jensen’s alpha the same as Grinold’s alpha?
Answer: D (4.27% or 4.28%).
Explanation:
Jensen’s alpha is defined by: E(RP ) − RF = αP + βP(E(RM) − RF);
αP = E(RP ) − RF

βP(E(RM) − RF) = 0.128
 0.0485  0.7 * (0.0525 + 0.0485  0.0485)= 0.0427 a. Incorrect. Forgets to subtract the riskfree rate for the excess market return. b. Incorrect. Forgets to multiply the excess market return by beta. c. Incorrect. Forgets to subtract the riskfree rate for both excess market return and excess portfolio return. d. Correct. 2.2 Treynor measure = (12.8%  4.85%) / 0.7 = 0.114 2.3. Yes, both assume CAPM such that an exact linear relationship exists between them! 2.4. Not enough information! We need portfolio volatility.
2.5 Says Amenc, “The Jensen measure is subject to the same criti
cism as the Treynor measure: the result depends on the choice of reference index. In addition, when managers practice a market timing strategy, which involves varying the beta according to anticipated movements in the market, the Jensen alpha often becomes negative, and does not then reflect the real
performance of the manager.”
2.6 No, Grinold’s alpha (think “hedge fund alpha”) is a generalized version of Jensen’s alpha.