Final answer:
To calculate the total variance of Stock A after an increase in beta, the new beta is squared, the market variance is calculated as the square of the market standard deviation, and these values are combined with the square of the residual standard deviation to find the result.
Step-by-step explanation:
The question pertains to calculating the total variance for a stock given an increase in its beta. The beta of a stock is a measure of its volatility in relation to the market, and residual standard deviation is the standard deviation of the stock's returns that is not explained by the market's movements. To calculate the total variance of Stock A after its beta changes, the formula used would be:
Total Variance = β2 * Market Variance + Residual Variance
Given the original beta (2.20) and the increase (0.20), the new beta would be 2.40. With the market-index portfolio's standard deviation of 15%, the market variance is (0.15)2. Stock A's residual standard deviation is 25%, so the residual variance is (0.25)2. Plugging these into the formula:
Total Variance = 2.402 * (0.15)2 + (0.25)2
After calculating, you round the total variance to four decimal places to get the final answer. This explanation helps students understand the impact of beta on a stock's volatility relative to the market.