Final answer:
To calculate the total variance for an increase of 0.20 in beta, use the formula (beta^2 * market variance) + residual variance. To calculate the total variance for an increase of 0.09 in residual standard deviation, use the same formula with the updated value for the residual standard deviation.
Step-by-step explanation:
In order to calculate the total variance for an increase of 0.20 in beta, we can use the formula:
Total variance = (beta2 * market variance) + residual variance
Given that the standard deviation of the market-index portfolio is 45% and stock a has a beta of 1.20 with a residual standard deviation of 55%, we have:
Total variance = (1.202 * 0.452) + 0.552
Calculating this, we get a total variance of 0.3234.
To calculate the total variance for an increase of 0.09 percentage points in its residual standard deviation, we can use the same formula:
Total variance = (beta2 * market variance) + residual variance
Given that the standard deviation of the market-index portfolio is 45% and stock a has a beta of 1.20 with a residual standard deviation of 55% + 0.09, we have:
Total variance = (1.202 * 0.452) + (0.55 + 0.09)2
Calculating this, we get a total variance of 0.3318.