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.