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Answer: Sell 71 futures contracts of the S&P 500 Index
## Explanation **C is correct.** The optimal hedge ratio is calculated using the formula: \[ h = \rho \times \frac{\sigma_P}{\sigma_F} \] Where: - \( \rho \) = correlation coefficient = 0.89 - \( \sigma_P \) = volatility of equity portfolio = 0.51 - \( \sigma_F \) = volatility of futures = 0.48 \[ h = 0.89 \times \frac{0.51}{0.48} = 0.9456 \] **Portfolio value to hedge:** Two-thirds of USD 60 million = USD 40,000,000 **Futures contract value:** S&P 500 futures price × multiplier = 2,120 × 250 = USD 530,000 **Number of futures contracts:** \[ N = h \times \frac{\text{Portfolio value}}{\text{Futures contract value}} \] \[ N = 0.9456 \times \frac{40,000,000}{530,000} \] \[ N = 0.9456 \times 75.4717 \] \[ N = 71.3679 \approx 71 \text{ contracts (rounded to nearest integer)} \] Since the manager wants to hedge against potential market decline, they should **sell** 71 futures contracts to lock in profits.
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On November 1, the fund manager of a USD 60 million US mid-to-large cap equity portfolio, considers locking in the profit from a recent market rally. The S&P 500 Index is trading at 2,110. The S&P 500 Index futures with a multiplier of 250 is trading at 2,120. Instead of selling the holdings, the fund manager would rather hedge two-thirds of the market exposure over the remaining 2 months. Given that the correlation between the equity portfolio and the S&P 500 Index futures is 0.89 and the volatilities of the equity portfolio and the S&P 500 futures are 0.51 and 0.48 per year, respectively, what position should the manager take to achieve the objective?
A
Sell 63 futures contracts of the S&P 500 Index
B
Sell 67 futures contracts of the S&P 500 Index
C
Sell 71 futures contracts of the S&P 500 Index
D
Sell 107 futures contracts of the S&P 500 Index
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