Financial Risk Manager Part 1
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Assume you're a financial risk manager at an investment management firm where you're given the task to estimate the dispersion of a specific equity price around its forecasted value. As a financial risk manager, calculate the variance of equity value using the data provided in the following table.
| Probability | Equity Value |
|---|---|
| 0.33 | $62.15 |
| 0.39 | $60.75 |
| 0.28 | $63 |
Other
Community
NNikitesh
A
0.87
B
0.93
C
0.75
D
0.78
Explanation:
Explanation
To calculate the variance of equity value, we need to follow these steps:
Step 1: Calculate the Expected Value (Mean)
The expected value E(X) is calculated as the weighted average of equity values:
E(X) = Σ [Probability × Equity Value]
E(X) = (0.33 × 62.15) + (0.39 × 60.75) + (0.28 × 63) E(X) = 20.5095 + 23.6925 + 17.64 E(X) = 61.842
Step 2: Calculate Variance
Variance = Σ [Probability × (Equity Value - Expected Value)²]
-
For 62.15: (62.15 - 61.842)² = (0.308)² = 0.094864 Contribution: 0.33 × 0.094864 = 0.031305
-
For 60.75: (60.75 - 61.842)² = (-1.092)² = 1.192464 Contribution: 0.39 × 1.192464 = 0.465061
-
For 63: (63 - 61.842)² = (1.158)² = 1.340964 Contribution: 0.28 × 1.340964 = 0.375470
Step 3: Sum the Contributions
Variance = 0.031305 + 0.465061 + 0.375470 = 0.871836 ≈ 0.87
Step 4: Verify with the Provided Calculation
The solution shows:
Variance = 0.33(62.15 - $61.84)² + 0.39(60.75 - $61.84)² + 0.28(63 - $61.84)²
Using rounded expected value of 61.84:
- (62.15 - 61.84)² = (0.31)² = 0.0961 × 0.33 = 0.031713
- (60.75 - 61.84)² = (-1.09)² = 1.1881 × 0.39 = 0.463359
- (63 - 61.84)² = (1.16)² = 1.3456 × 0.28 = 0.376768
Total = 0.031713 + 0.463359 + 0.376768 = 0.87184 ≈ 0.87
Therefore, the correct answer is A. 0.87.
Key Concept
Variance measures the dispersion of a random variable around its expected value. In financial risk management, it quantifies the uncertainty or risk associated with an asset's value.
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