Answer: 5.0%

The question involves the concept of combining two portfolios, Prudent Fund and Aggressive Fund, with the aim of estimating the probability that the combined portfolio's returns will exceed 26%. Given that the returns of both funds are normally distributed and independent, the analyst can use the properties of normal distributions to calculate the combined expected mean return and volatility. The combined expected mean return (μ) is calculated by taking a weighted average of the individual mean returns, where the weights correspond to the proportion of each fund's assets in the combined portfolio. For Prudent Fund with a mean return of 3% and Aggressive Fund with a mean return of 7%, the combined mean return is calculated as follows: \[ \mu = (0.2 \times 3\%) + (0.8 \times 7\%) = 6.2\% \] The combined volatility (σ) is calculated by taking a weighted sum of the individual volatilities (standard deviations), squared and then taking the square root. For Prudent Fund with a standard deviation of 7% and Aggressive Fund with a standard deviation of 15%, the combined volatility is calculated as follows: \[ \sigma = \sqrt{(0.2^2 \times 0.07^2) + (0.8^2 \times 0.15^2)} = 0.121 = 12.1\% \] To find the probability that the returns on the combined fund will exceed 26%, the analyst uses the Z-statistic, which is the number of standard deviations an outcome is from the mean. The Z-statistic is calculated as: \[ Z = \frac{26\% - 6.2\%}{12.1\%} \approx 1.64 \] Using standard normal distribution tables or a calculator, the probability that a Z-score is greater than 1.64 is found to be 1 - 0.95 = 0.05, or 5.0%. Therefore, the probability that the combined portfolio's returns will exceed 26% is closest to 5.0%, which corresponds to option C.

Author: LeetQuiz Editorial Team