Chapter 8 Index Models
16. Assume that stock market returns do not resemble a single-index structure. An
investment fund analyzes 100 stocks in order to construct a mean-variance efficient portfolio constrained by 100 investments. They will need to calculate ____________ covariances. A) 45 B) 100 C) 4,950 D) 10,000 E) none of the above
Answer: C Difficulty: Moderate Rationale: (n2 - n)/2 = (10,000 - 100)/2 = 4,950 covariances must be calculated.
17. Assume that stock market returns do follow a single-index structure. An investment
fund analyzes 200 stocks in order to construct a mean-variance efficient portfolio constrained by 200 investments. They will need to calculate ________ estimates of expected returns and ________ estimates of sensitivity coefficients to the macroeconomic factor. A) 200; 19,900 B) 200; 200 C) 19,900; 200 D) 19,900; 19.900 E) none of the above
Answer: B Difficulty: Moderate Rationale: For a single-index model, n(200), expected returns and n(200) sensitivity
coefficients to the macroeconomic factor must be estimated.
18. Assume that stock market returns do follow a single-index structure. An investment
fund analyzes 500 stocks in order to construct a mean-variance efficient portfolio constrained by 500 investments. They will need to calculate ________ estimates of firm-specific variances and ________ estimates for the variance of the macroeconomic factor. A) 500; 1 B) 500; 500 C) 124,750; 1 D) 124,750; 500 E) 250,000; 500
Answer: A Difficulty: Moderate Rationale: For the single-index model, n(500) estimates of firm-specific variances must
be calculated and 1 estimate for the variance of the common macroeconomic factor.
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19. Consider the single-index model. The alpha of a stock is 0%. The return on the market
index is 16%. The risk-free rate of return is 5%. The stock earns a return that exceeds the risk-free rate by 11% and there are no firm-specific events affecting the stock performance. The β of the stock is _______. A) 0.67 B) 0.75 C) 1.0 D) 1.33 E) 1.50
Answer: C Difficulty: Moderate Rationale: 11% = 0% + b(11%); b = 1.0.
20. Suppose you held a well-diversified portfolio with a very large number of securities,
and that the single index model holds. If the ó of your portfolio was 0.20 and óM was 0.16, the β of the portfolio would be approximately ________. A) 0.64 B) 0.80 C) 1.25 D) 1.56 E) none of the above
Answer: C Difficulty: Difficult Rationale: s2p / s2m = b2; (0.2)2/(0.16)2 = 1.56; b = 1.25.
21. Suppose the following equation best describes the evolution of β over time: βt = 0.25 + 0.75βt-1 If a stock had a β of 0.6 last year, you would forecast the β to be _______ in the coming
year. A) 0.45 B) 0.60 C) 0.70 D) 0.75 E) none of the above
Answer: C Difficulty: Easy Rationale: 0.25 + 0.75(0.6) = 0.70.
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22. Merrill Lynch estimates the index model for a stock using regression analysis involving
total returns. They estimated the intercept in the regression equation at 6% and the β at 0.5. The risk-free rate of return is 12%. The true β of the stock is ________. A) 0% B) 3% C) 6% D) 9% E) none of the above
Answer: A Difficulty: Difficult Rationale: 6% = a + 12% (1 - 0.5); a = 0%.
23. The index model for stock A has been estimated with the following result:
RA = 0.01 + 0.9RM + eA
2
If σM = 0.25 and RA = 0.25, the standard deviation of return of stock A is _________. A) 0.2025 B) 0.2500 C) 0.4500 D) 0.8100 E) none of the above
Answer: C Difficulty: Difficult Rationale: R2 = b2s2M / s2;0.25 = [(0.81)(0.25)2]/s2; s = 0.4500.
24. The index model for stock B has been estimated with the following result: RB = 0.01 + 1.1RM + eB
2
If σM = 0.20 and RB = 0.50, the standard deviation of the return on stock B is
_________. A) 0.1111 B) 0.2111 C) 0.3111 D) 0.4111 E) none of the above
Answer: C Difficulty: Difficult Rationale: R2 = b2s2M / s2; 0.5 = [(1.1)2(0.2)2]/s2; s = 0.3111.
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25. Suppose you forecast that the market index will earn a return of 15% in the coming year.
Treasury bills are yielding 6%. The unadjusted β of Mobil stock is 1.30. A reasonable forecast of the return on Mobil stock for the coming year is _________ if you use Merrill Lynch adjusted betas. A) 15.0% B) 15.5% C) 16.0% D) 16.8% E) none of the above
Answer: D Difficulty: Difficult Rationale: Adjusted beta = 2/3(1.3) + 1/3 = 1.20; E(rM) = 6% + 1.20(9%) = 16.8%.
26. The index model has been estimated for stocks A and B with the following results: RA = 0.01 + 0.5RM + eA RB = 0.02 + 1.3RM + eB σM = 0.25 σ(eA) = 0.20 σ(eB) = 0.10 The covariance between the returns on stocks A and B is ___________. A) 0.0384 B) 0.0406 C) 0.1920 D) 0.0050 E) 0.4000
Answer: B Difficulty: Difficult Rationale: Cov(RA,RB) = bAbBs2M = 0.5(1.3)(0.25)2 = 0.0406.
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27. The index model has been estimated for stocks A and B with the following results: RA = 0.01 + 0.8RM + eA RB = 0.02 + 1.2RM + eB σM = 0.20 σ(eA) = 0.20 σ (eB) = 0.10 The standard deviation for stock A is __________. A) 0.0656 B) 0.0676 C) 0.2561 D) 0.2600 E) none of the above
Answer: C Difficulty: Difficult Rationale: σA = [(0.8)2(0.2)2 + (0.2)2]1/2 = 0.2561.
28. The index model has been estimated for stock A with the following results: RA = 0.01 + 0.8RM + eA σM = 0.20 σ(eA) = 0.10 The standard deviation of the return for stock A is __________. A) 0.0356 B) 0.1886 C) 0.1600 D) 0.6400 E) none of the above
Answer: B Difficulty: Difficult Rationale: σB = [(.8)2(0.2)2 + (0.1)2]1/2 = 0.1886.
29. Security returns A) are based on both macro events and firm-specific events. B) are based on firm-specific events only. C) are usually positively correlated with each other. D) A and B. E) A and C.
Answer: E Difficulty: Easy Rationale: Stock returns are usually highly positively correlated with each other. Stock
returns are affected by both macro economic events and firm-specific events.
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