The standard deviation of the market-index portfolio is 20%. Stock A has a beta of 2.50 and a residual standard deviation of 30%. a. Calculate the total variance for an increase of 0.25 in its beta. (Do not round intermediate calculations. Round your answer to the nearest whole number.) b. Calculate the total variance for an increase of 7.75% in its residual standard deviation.

Answer and Explanation:

Given:

Market-index portfolio (σ) = 20% = 0.20

β = 2.50

Residual standard deviation (e) = 30% = 0.30

A. Total variance for an increase of 0.25 beta = ?

B. Total variance for an increase of 7.75% (0.0775) in its residual standard deviation = ?

Computation:

A. Total variance = Systematic Variance + Residual Variance

Total variance = β²σ² + e²

Total variance = (2.50 + 0.25) ² (0.20) ² + (0.30) ²

Total variance = (2.75) ² (0.20) ² + (0.30) ²

Total variance = (7.5625) (0.04) + 0.09

Total variance = (0.3025) + 0.09

Total variance = 0.3925

B. Total variance = Systematic Variance + Residual Variance

Total variance = β²σ² + e²

Total variance = (2.50) ² (0.20) ² + (0.30 + 0.0775) ²

Total variance = (2.50) ² (0.20) ² + (0.3775) ²

Total variance = (6.25) (0.04) + 0.14250625

Total variance = (0.25) + 0.14250625

Total variance = 0.3925