Financial Risk Manager Part 1

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Explanation:

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.

Explanation:

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

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?

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Last updated: July 15, 2026 at 14:06

Sell 63 futures contracts of the S&P 500 Index

18.5%

Sell 67 futures contracts of the S&P 500 Index

22.2%

Sell 71 futures contracts of the S&P 500 Index

51.9%

Sell 107 futures contracts of the S&P 500 Index

7.4%