Financial Risk Manager Part 1

Explanation

Step 1: Calculate the Z-score

Given:

• Mean (μ) = 17%
• Standard deviation (σ) = 4%
• Target return = 29%

Z-score formula: $Z = \frac{X - \mu}{\sigma}$

$Z = \frac{29 - 17}{4} = \frac{12}{4} = 3$

Step 2: Interpret the Z-score

A Z-score of 3 means the return of 29% is 3 standard deviations above the mean.

Step 3: Find probability from standard normal distribution

We want $P(X > 29) = P(Z > 3)$

From standard normal distribution tables:

• $P(Z \leq 3) = 0.9987$
• Therefore, $P(Z > 3) = 1 - P(Z \leq 3) = 1 - 0.9987 = 0.0013$

Step 4: Convert to percentage

0.0013 = 0.13%

Why other options are incorrect:

• B (0.01): This corresponds to approximately 2.33 standard deviations, not 3
• C (0.13): This is 13%, which is the percentage form (0.13%) but incorrectly expressed as a decimal
• D (0.0525): This corresponds to approximately 1.62 standard deviations

The correct probability is 0.0013 or 0.13%.