The standard deviation of the market-index portfolio is 30%. Stock A has a beta

Question

The standard deviation of the market-index portfolio is 30%. Stock A has a beta of 1.50 and a residual standard deviation of 40%.

a. Calculate the total variance for an increase of 0.10 in its beta. (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Total variance             %-Squared

b. Calculate the total variance for an increase of 3.35% in its residual standard deviation. (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Total variance            %-Squared

Explanation / Answer

Variance of market = (Standard Deviation of market)2 = (30)2 = 900

Residual Variance = (Residual Standard Deviation)2 = (40)2 = 1600

a) New beta = 1.50 + 0.10 = 1.60

Total Variance = Beta2 x Variance of market + Residual Variance = (1.60)2 x 900 + 1600 = 3904

b) Beta = 1.50

Residual Variance = (Residual Standard Deviation)2 = (40+3.35)2 = 1879.2225

Total Variance = Beta2 x Variance of market + Residual Variance = (1.50)2 x 900 + 1879.2225 = 3904

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