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?
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TTanishq
A
12.45
B
10.51
C
16.324
D
12.213
Explanation:
The variance is calculated using the formula: Var(X) = E(X²) − [E(X)]²
Step 1: Calculate E(X) - Expected Value E(X) = 0.20(32) + 0.25(28) + 0.40(34) + 0.15(38) = 6.4 + 7.0 + 13.6 + 5.7 = 32.7
Step 2: Calculate E(X²) - Expected Value of Squares E(X²) = 0.20 × 32² + 0.25 × 28² + 0.40 × 34² + 0.15 × 38² = 0.20 × 1024 + 0.25 × 784 + 0.40 × 1156 + 0.15 × 1444 = 204.8 + 196 + 462.4 + 216.6 = 1,079.8
Step 3: Calculate Variance Var(X) = E(X²) − [E(X)]² = 1,079.8 − (32.7)² = 1,079.8 − 1,069.29 = 10.51
The variance of Equidor's stock price is 10.51, which corresponds to option B.
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