Final answer:
The total variance of Stock A, after an increase of 0.25 in its beta, is calculated using the formula for total variance in a diversified portfolio. The calculated total variance is 0.2500, rounded to four decimal places.
Step-by-step explanation:
The subject of the question is within the field of Business, specifically concerning portfolio analysis in finance. To calculate the total variance of stock A after an increase of 0.25 in its beta, we need to apply financial formulas that include market risk and the specific risk of the stock.
The formula for the total variance of a stock that is part of a diversified portfolio is:
Total Variance = (β² × Market Variance) + Residual Variance
Given the increase in beta, Stock A's new beta would be β = 1.75 + 0.25 = 2. The market variance is the square of the market-index portfolio's standard deviation, which is 20%, so Market Variance = 0.20² = 0.04. The residual variance is the square of the stock's residual standard deviation, so Residual Variance = 0.30² = 0.09.
Plugging the values into the formula, we get:
Total Variance = (2² × 0.04) + 0.09 = (4 × 0.04) + 0.09 = 0.16 + 0.09 = 0.25
Therefore, the total variance of Stock A after an increase of 0.25 in its beta is 0.2500, rounded to four decimal places.