Financial Risk Manager Part 1

Explanation

To solve this problem, we need to calculate the probability that returns exceed 29% when returns are normally distributed. However, the question is incomplete as it doesn't provide the mean (μ) and standard deviation (σ) of the returns distribution.

Standard Approach

For a normally distributed random variable X ~ N(μ, σ²):

1. Calculate the z-score: z = (X - μ) / σ
2. Find the probability: P(X > 29%) = 1 - P(X ≤ 29%) = 1 - Φ(z)

Using the Standard Normal Table

The standard normal table provided gives cumulative probabilities P(Z ≤ z) for z-values from 0.0 to 3.6.

Analysis of Options

• Option A (0.0013): This corresponds to P(Z > 3.0) = 1 - 0.9987 = 0.0013
• Option B (0.01): This corresponds to P(Z > 2.33) ≈ 0.01
• Option C (0.13): This corresponds to P(Z > 1.13) ≈ 0.13

Conclusion

Without the specific mean and standard deviation values, we cannot determine the exact probability. However, based on typical financial return distributions and the options provided, Option A (0.0013) is the most reasonable answer as it represents a very small probability, which would be appropriate for returns significantly above the mean in a normal distribution.

Note: In a complete problem, you would need the mean and standard deviation to calculate the exact z-score and find the corresponding probability from the standard normal table.