Financial Risk Manager Part 1

Explanation

To find the probability of earning a return in excess of 20% for each mutual fund, we need to calculate the z-score for each fund and use the z-table to find the corresponding probability.

Z-Score Formula:

$Z = \frac{\text{Desired Return} - \text{Mean Return}}{\text{Standard Deviation}}$

Calculations:

Fund X:

• Mean = 25%, Std. Dev. = 2%
• $Z = \frac{20\% - 25\%}{2\%} = \frac{-5\%}{2\%} = -2.5$
• P(Z < -2.5) ≈ 0.0062 (from z-table)
• P(X > 20%) = 1 - P(Z < -2.5) = 1 - 0.0062 = 0.9938 = 99.38%

Fund Y:

• Mean = 24.8%, Std. Dev. = 3%
• $Z = \frac{20\% - 24.8\%}{3\%} = \frac{-4.8\%}{3\%} = -1.6$
• P(Z < -1.6) ≈ 0.0548 (from z-table)
• P(Y > 20%) = 1 - P(Z < -1.6) = 1 - 0.0548 = 0.9452 = 94.52%

Fund Z:

• Mean = 26%, Std. Dev. = 4%
• $Z = \frac{20\% - 26\%}{4\%} = \frac{-6\%}{4\%} = -1.5$
• P(Z < -1.5) ≈ 0.0668 (from z-table)
• P(Z > 20%) = 1 - P(Z < -1.5) = 1 - 0.0668 = 0.9332 = 93.32%

Analysis of Options:

• Option A (1.60% for Fund Y) - Incorrect, this is approximately P(Z < -1.6) not P(Y > 20%)
• Option B (94.52% for Fund Z) - Incorrect, this is actually the probability for Fund Y
• Option C (99.38% for Fund X) - CORRECT - Matches our calculation for Fund X
• Option D (11.6% for Fund Y) - Incorrect, this doesn't match any of our calculated probabilities

Therefore, the correct answer is C - 99.38% for Fund X.