Chapter 8 Index Models
Multiple Choice Questions
1. As diversification increases, the total variance of a portfolio approaches ____________. A) 0 B) 1 C) the variance of the market portfolio D) infinity E) none of the above
Answer: C Difficulty: Easy Rationale: As more and more securities are added to the portfolio, unsystematic risk
decreases and most of the remaining risk is systematic, as measured by the variance of the market portfolio.
2. The index model was first suggested by ____________. A) Graham B) Markowitz C) Miller D) Sharpe E) none of the above
Answer: D Difficulty: Easy Rationale: William Sharpe, building on the work of Harry Markowitz, developed the
index model.
3. A single-index model uses __________ as a proxy for the systematic risk factor. A) a market index, such as the S&P 500 B) the current account deficit C) the growth rate in GNP D) the unemployment rate E) none of the above
Answer: A Difficulty: Easy Rationale: The single-index model uses a market index, such as the S&P 500, as a proxy
for the market, and thus for systematic risk.
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4. The Security Risk Evaluation book published by Merrill Lynch relies on the __________ most recent monthly observations to calculate regression parameters. A) 12 B) 36 C) 60 D) 120
E) none of the above Answer: C Difficulty: Easy
Rationale: Most published betas and other regression parameters, including those published by Merrill Lynch, are based on five years of monthly return data.
5. The Security Risk Evaluation book published by Merrill Lynch uses the __________ as a proxy for the market portfolio. A) Dow Jones Industrial Average
B) Dow Jones Transportation Average C) S&P 500 Index D) Wilshire 5000 E) none of the above Answer: C Difficulty: Easy
Rationale: The Merrill Lynch data (and much of the other published data sets) are based on the S&P 500 index as a market proxy.
6. According to the index model, covariances among security pairs are
A) due to the influence of a single common factor represented by the market index
return
B) extremely difficult to calculate C) related to industry-specific events D) usually positive E) A and D Answer: E Difficulty: Easy
Rationale: Most securities move together most of the time, and move with a market index, or market proxy.
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7. The intercept calculated by Merrill Lynch in the regression equations is equal to A) α in the CAPM B) α + rf(1 + β) C) α + rf(1 - β) D) 1 - α
E) none of the above Answer: C Difficulty: Moderate
Rationale: The intercept that Merrill Lynch calls alpha is really, using the parameters of the CAPM, an estimate of a + rf (1 - b). The apparent justification for this procedure is that, on a monthly basis, rf(1 - b) is small and is apt to be swamped by the volatility of actual stock returns.
8. Analysts may use regression analysis to estimate the index model for a stock. When doing so, the slope of the regression line is an estimate of ______________. A) the α of the asset B) the β of the asset C) the σ of the asset D) the δ of the asset E) none of the above Answer: B Difficulty: Moderate
Rationale: The slope of the regression line, b, measures the volatility of the stock versus the volatility of the market.
9. In a factor model, the return on a stock in a particular period will be related to _________.
A) firm-specific events B) macroeconomic events C) the error term D) both A and B E) neither A nor B Answer: D Difficulty: Moderate
Rationale: The return on a stock is related to both firm-specific and macroeconomic events.
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10. Rosenberg and Guy found that __________ helped to predict a firm's beta. A) the firm's financial characteristics B) the firm's industry group C) firm size D) both A and B E) A, B and C all helped to predict betas.
Answer: E Difficulty: Moderate Rationale: Rosenberg and Guy found that after controlling for the firm's financial
characteristics, the firm's industry group was a significant predictor of the firm's beta.
11. If the index model is valid, _________ would be helpful in determining the covariance
between assets K and L. A) βk B) βL C) σM D) all of the above E) none of the above
Answer: D Difficulty: Moderate Rationale: If the index model is valid A, B, and C are determinants of the covariance
between K and L.
12. Rosenberg and Guy found that ___________ helped to predict firms' betas. A) debt/asset ratios B) market capitalization C) variance of earnings D) all of the above E) none of the above
Answer: D Difficulty: Moderate Rationale: Rosenberg and Guy found that A, B, and C were determinants of firms' betas.
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13. If a firm's beta was calculated as 0.6 in a regression equation, Merrill Lynch would state
the adjusted beta at a number A) less than 0.6 but greater than zero. B) between 0.6 and 1.0. C) between 1.0 and 1.6. D) greater than 1.6. E) zero or less.
Answer: B Difficulty: Moderate Rationale: Betas, on average, equal one; thus, betas over time regress toward the mean,
or 1. Therefore, if historic betas are less than 1, adjusted betas are between 1 and the calculated beta.
14. The beta of Exxon stock has been estimated as 1.2 by Merrill Lynch using regression
analysis on a sample of historical returns. The Merrill Lynch adjusted beta of Exxon stock would be ___________. A) 1.20 B) 1.32 C) 1.13 D) 1.0 E) none of the above
Answer: C Difficulty: Moderate Rationale: Adjusted beta = 2/3 sample beta + 1/3(1); = 2/3(1.2) + 1/3 = 1.13.
15. 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 _____________ expected returns and ___________ variances of returns. A) 100, 100 B) 100, 4950 C) 4950, 100 D) 4950, 4950 E) none of the above
Answer: A Difficulty: Moderate Rationale: The expected returns of each of the 100 securities must be calculated. In
addition, the 100 variances around these returns must be calculated.
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