Answer: 0.87

## 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] 1. For 62.15: (62.15 - 61.842)² = (0.308)² = 0.094864 Contribution: 0.33 × 0.094864 = 0.031305 2. For 60.75: (60.75 - 61.842)² = (-1.092)² = 1.192464 Contribution: 0.39 × 1.192464 = 0.465061 3. 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: 1. (62.15 - 61.84)² = (0.31)² = 0.0961 × 0.33 = 0.031713 2. (60.75 - 61.84)² = (-1.09)² = 1.1881 × 0.39 = 0.463359 3. (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.

Author: Nikitesh Somanthe