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
