Financial Risk Manager Part 1
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Assuming that mutual fund returns are normally distributed and using a z-table, what is the correct probability of earning a return in excess of 20%?
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NNikitesh
A
1.60% for Fund Y
B
5.78% for Fund Z
C
0.62% for Fund X
D
11.6% for Fund Y
Explanation:
The correct answer is C) 0.62% for Fund X.
Step-by-step explanation:
-
Calculate z-values for each fund:
- Fund X: z = (20% - 15%) / 2% = 5% / 2% = 2.5
- Fund Y: z = (20% - 15.20%) / 3% = 4.8% / 3% = 1.60
- Fund Z: z = (20% - 14%) / 4% = 6% / 4% = 1.50
-
Use z-table to find cumulative probabilities:
- For z = 2.5: Cumulative probability = 99.38% (probability of return ≤ 20%)
- For z = 1.60: Cumulative probability = 94.52%
- For z = 1.50: Cumulative probability = 93.32%
-
Calculate probability of return > 20%:
- Fund X: 100% - 99.38% = 0.62%
- Fund Y: 100% - 94.52% = 5.48%
- Fund Z: 100% - 93.32% = 6.68%
-
Compare with given options:
- Option A (1.60% for Fund Y) is incorrect - actual probability is 5.48%
- Option B (5.78% for Fund Z) is incorrect - actual probability is 6.68%
- Option C (0.62% for Fund X) is correct
- Option D (11.6% for Fund Y) is incorrect
Key concept: When returns are normally distributed, the z-score measures how many standard deviations a value is from the mean. The z-table gives the cumulative probability from negative infinity to that z-value. To find the probability of exceeding a value, subtract the cumulative probability from 100%.
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