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"Portfolio Management":Beta coefficient
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Questions 1:
The correlation between the historical returns of Stock A and Stock B is 0.75. If the variance of Stock A is 0.16 and the variance of Stock B is 0.09, the covariance of returns of Stock A and Stock B is closest to:
A 、 0.01.
B、 0.09.
C 、0.16.
Questions 2:
An asset has an annual return of 19.9%, standard deviation of returns of 18.5%,
and correlation with the market of 0.9. If the standard deviation of returns on
the market is 15.9% and the risk-free rate is 1%, the beta of this asset is closest
to:
A 、 1.02.
B 、 1.05.
C 、 1.16
View answer resolution
【Answer to question 1】B
【analysis】
B is correct. Cov(A,B) = ρABσAσB = 0.75 × 0.4 × 0.3 = 0.09
A is incorrect. Variance is used instead of standard deviation. Covariance is incorrectly calculated as 0.75 × 0.16 × 0.09 = 0.0108.
C is incorrect. Covariance is incorrectly calculated as [(0.4 × 0.3)/0.75] = 0.16.
【Answer to question 2】B
【analysis】
B is correct.
A is incorrect because it calculates the Sharpe ratio instead of beta: (19.9% – 1.0%)/18.5% = 1.02.
C is incorrect because it is the ratio of the standard deviation of the asset to the standard deviation of the market: (18.5%/15.9%) = 1.16.
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