Final answer:
To find the variance of a portfolio consisting of $3,500 in stock A and $6,500 in stock B, we can calculate the weighted average return and variance for each stock, and then combine them. The overall variance of the portfolio is approximately 0.683%.
Step-by-step explanation:
To find the variance of a portfolio consisting of $3,500 in stock A and $6,500 in stock B, we need to calculate the weighted average return and the weighted average variance for each stock, and then combine them.
Stock A has a return of 15% in a boom and 8% in a normal economy, so the weighted average return is (0.15 * 0.15) + (0.85 * 0.08) = 0.1285 or 12.85%.
The variance of stock A is (0.15 - 0.1285)^2 * 0.15 + (0.08 - 0.1285)^2 * 0.85 = 0.014695.
Stock B has a return of 9% in a boom and 6% otherwise, so the weighted average return is (0.15 * 0.09) + (0.85 * 0.06) = 0.0705 or 7.05%.
The variance of stock B is (0.09 - 0.0705)^2 * 0.15 + (0.06 - 0.0705)^2 * 0.85 = 0.00153075.
To calculate the overall variance of the portfolio, we multiply the weight of each stock by its respective variance and sum them up. The overall variance is (0.35 * 0.014695) + (0.65 * 0.00153075) = 0.00683 or 0.683%.