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70. The index model for stock A has been estimated with the following result:
RA = 0.01 + 0.94RM + eA
If M = 0.30 and R2A = 0.28, the standard deviation of return of stock A is _________.
A. 0.2025
Difficulty: Difficult
71. Suppose you forecast that the market index will earn a return of 12% in the coming year.
Treasury bills are yielding 4%. The unadjusted 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%
Difficulty: Difficult
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72. The index model has been estimated for stocks A and B with the following results:
RA = 0.01 + 0.8RM + eA
RB = 0.02 + 1.1RM + eB
M = 0.30 (eA) = 0.20 (eB) = 0.10
The covariance between the returns on stocks A and B is ___________.
A. 0.0384
Difficulty: Difficult
73. If a firm’s beta was calculated as 1.35 in a regression equation, Merrill Lynch would state
the adjusted beta at a number
A. less than 1.35
B. between 0.0 and 1.0.
Difficulty: Moderate
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74. The beta of a stock has been estimated as 1.4 by Merrill Lynch using regression analysis
on a sample of historical returns. The Merrill Lynch adjusted beta of the stock would be
___________.
D. 1.0
E. none of the above
Difficulty: Moderate
75. The beta of a stock has been estimated as 0.85 by Merrill Lynch using regression analysis
on a sample of historical returns. The Merrill Lynch adjusted beta of the stock would be
___________.
A. 1.01
B. 0.95
Difficulty: Moderate
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76. Assume that stock market returns do not resemble a single-index structure. An investment
fund analyzes 125 stocks in order to construct a mean-variance efficient portfolio constrained
by 125 investments. They will need to calculate _____________ expected returns and
D. 15,625, 15,625
E. none of the above
Difficulty: Moderate
77. Assume that stock market returns do not resemble a single-index structure. An investment
fund analyzes 125 stocks in order to construct a mean-variance efficient portfolio constrained
by 125 investments. They will need to calculate ____________ covariances.
A. 90
B. 125
Difficulty: Moderate
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78. Assume that stock market returns do not resemble a single-index structure. An investment
fund analyzes 132 stocks in order to construct a mean-variance efficient portfolio constrained
by 132 investments. They will need to calculate ____________ covariances.
A. 100
B. 132
Difficulty: Moderate
79. Assume that stock market returns do follow a single-index structure. An investment fund
analyzes 217 stocks in order to construct a mean-variance efficient portfolio constrained by
217 investments. They will need to calculate ________ estimates of expected returns and
________ estimates of sensitivity coefficients to the macroeconomic factor.
A. 217; 47,089
Difficulty: Moderate
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80. 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
750 investments. They will need to calculate ________ estimates of firm-specific variances
and ________ estimates for the variance of the macroeconomic factor.
D. 124,750; 750
E. 562,500; 750
Difficulty: Moderate
81. Consider the single-index model. The alpha of a stock is 0%. The return on the market
index is 10%. The risk-free rate of return is 5%. The stock earns a return that exceeds the risk-
free rate by 5% and there are no firm-specific events affecting the stock performance. The
of the stock is _______.
A. 0.67
B. 0.75
Difficulty: Moderate
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82. Suppose you held a well-diversified portfolio with a very large number of securities, and
that the single index model holds. If the of your portfolio was 0.24 and M was 0.18, the
of the portfolio would be approximately ________.
A. 0.64
Difficulty: Difficult
83. Suppose you held a well-diversified portfolio with a very large number of securities, and
that the single index model holds. If the of your portfolio was 0.14 and M was 0.19, the
of the portfolio would be approximately ________.
D. 1.56
E. none of the above
Difficulty: Difficult
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84. Suppose the following equation best describes the evolution of over time:
t = 0.30 + 0.70t-1
If a stock had a of 0.82 last year, you would forecast the to be _______ in the coming
year.
A. 0.91
B. 0.77
Difficulty: Easy
85. The index model has been estimated for stocks A and B with the following results:
RA = 0.03 + 0.7RM + eA
RB = 0.01 + 0.9RM + eB
M = 0.35 (eA) = 0.20 (eB) = 0.10
The covariance between the returns on stocks A and B is ___________.
A. 0.0384
B. 0.0406
Difficulty: Difficult
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Short Answer Questions
86. Discuss the advantages of the single-index model over the Markowitz model in terms of
numbers of variable estimates required and in terms of understanding risk relationships.
For a 50 security portfolio, the Markowitz model requires the following parameter estimates:
n = 50 estimates of expected returns;
n = 50 estimates of variances;
(n2 – n)/2 = 1,225 estimates of covariances;
1,325 estimates.
For a 50 security portfolio, the single-index model requires the following parameter
estimates:
n = 50 estimates of expected excess returns, E(R);
Difficulty: Moderate
87. Discuss the security characteristic line (SCL).
The security characteristic line (SCL) is the result of estimating the regression equation of
the single-index model. The SCL is a plot of the typical excess returns on a security over the
risk-free rate as a function of the excess return on the market. The slope of the SCL is the beta
Difficulty: Moderate
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88. Discuss the “adjusted betas” published by Merrill Lynch in Security Risk Evaluation.
Over time, security betas move toward 1, as the average beta of all securities is 1 and
variables regress toward the mean. Thus, if a historic beta has been greater than 1, the chances
are that in the future, this beta will be less than the historic beta. The opposite relationship will
be observed if the historic beta has been less than one. Merrill Lynch uses the following
Difficulty: Easy