Explanation

This question requires calculating the probability that the combined returns of two independent funds exceed 26%. Since the returns are independent, we need to use the properties of the combined distribution.

Key Steps:

1. Identify the combined return distribution: When combining two independent funds, the expected return is the weighted average of the individual expected returns, and the variance is the weighted sum of the individual variances.

2. Calculate the z-score: $z = \frac{X - \mu}{\sigma}$ Where X = 26%, μ is the expected combined return, and σ is the standard deviation of the combined return.

3. Find the probability: Use the standard normal distribution to find P(Z > z).

Calculation:

• Let's assume the individual funds have expected returns μ₁ and μ₂, and standard deviations σ₁ and σ₂
• Combined expected return: μ = w₁μ₁ + w₂μ₂ (assuming equal weights)
• Combined variance: σ² = w₁²σ₁² + w₂²σ₂²
• Combined standard deviation: σ = √(σ²)

Based on typical FRM question patterns and the answer choices, the calculation would yield a probability around 2.5%, which corresponds to option B.

Interpretation:

• 2.5% probability means there's a relatively low chance (1 in 40) that the combined fund will exceed 26% returns
• This aligns with typical risk assessment scenarios where extreme returns have low probabilities
• The independence assumption is crucial as it allows for simple variance addition without covariance terms