Financial Risk Manager Part 1
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An equity research analyst forecasts the share price of Equidor Inc.'s stock and the probability of achieving the price target. The forecast made by the analyst is given in the following exhibit.
Exhibit 1: Share Price Forecast
| Probability | Share Price |
|---|---|
| 20% | $32.00 |
| 25% | $28.00 |
| 40% | $34.00 |
| 15% | $38.00 |
What is the variance of Equidor's stock price?
Other
Community
NNikitesh
A
15
B
11
C
16
D
12
Explanation:
Explanation
To calculate the variance of Equidor's stock price, we need to follow these steps:
Step 1: Calculate the Expected Value E(X)
E(X) = Σ [Probability × Share Price]
E(X) = (0.20 × 32) + (0.25 × 28) + (0.40 × 34) + (0.15 × 38) E(X) = 6.4 + 7 + 13.6 + 5.7 = 32.7
Step 2: Calculate Variance
Variance = Σ [Probability × (Share Price - E(X))²]
For each probability-price pair:
-
20% probability,
$32.00: (32 - 32.7)² = (-0.7)² = 0.49 Contribution: 0.20 × 0.49 = 0.098 -
25% probability,
$28.00: (28 - 32.7)² = (-4.7)² = 22.09 Contribution: 0.25 × 22.09 = 5.5225 -
40% probability,
$34.00: (34 - 32.7)² = (1.3)² = 1.69 Contribution: 0.40 × 1.69 = 0.676 -
15% probability,
$38.00: (38 - 32.7)² = (5.3)² = 28.09 Contribution: 0.15 × 28.09 = 4.2135
Step 3: Sum the Contributions
Variance = 0.098 + 5.5225 + 0.676 + 4.2135 = 10.51
However, there seems to be a discrepancy in the provided solution. The solution shows:
- Using E(X) = 33 (not 32.7)
- With E(X) = 33:
- 32: (32-33)² = 1 → 0.20 × 1 = 0.20
- 28: (28-33)² = 25 → 0.25 × 25 = 6.25
- 34: (34-33)² = 1 → 0.40 × 1 = 0.40
- 38: (38-33)² = 25 → 0.15 × 25 = 3.75
- Total = 0.20 + 6.25 + 0.40 + 3.75 = 10.60
Note: The provided solution in the text incorrectly calculates E(X) as 33, but the actual calculation shows 32.7. However, since the answer choices are integers and the solution shows variance ≈ 10.60, the closest integer is 11.
Therefore, the correct answer is B (11).
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