Explanation

Since the returns on the two funds are independent and normally distributed, we can calculate the combined expected return and volatility using portfolio theory.

Step 1: Calculate portfolio weights

• Prudent Fund: USD 50 million
• Aggressive Fund: USD 200 million
• Total assets: USD 250 million
• Weight of Prudent Fund: 50/250 = 0.2 (20%)
• Weight of Aggressive Fund: 200/250 = 0.8 (80%)

Step 2: Calculate combined expected return

$$\mu = w_1 \cdot \mu_1 + w_2 \cdot \mu_2 = 0.2 \cdot 3\% + 0.8 \cdot 7\% = 0.6\% + 5.6\% = 6.2\%$$

Step 3: Calculate combined volatility Since the returns are independent (correlation = 0):

$$\sigma = \sqrt{w_1^2 \cdot \sigma_1^2 + w_2^2 \cdot \sigma_2^2} = \sqrt{0.2^2 \cdot 0.07^2 + 0.8^2 \cdot 0.15^2}$$ $$\sigma = \sqrt{0.04 \cdot 0.0049 + 0.64 \cdot 0.0225} = \sqrt{0.000196 + 0.0144} = \sqrt{0.014596} = 0.121 = 12.1\%$$

Step 4: Calculate Z-statistic for 26% return

$$Z = \frac{X - \mu}{\sigma} = \frac{26\% - 6.2\%}{12.1\%} = \frac{19.8\%}{12.1\%} = 1.64$$

Step 5: Find probability We want P(Z > 1.64) = 1 - P(Z ≤ 1.64) = 1 - 0.95 = 0.05 = 5.0%

Therefore, the probability that the returns on the combined fund will exceed 26% is 5.0%.