Explanation

To determine the optimal hedge ratio and number of futures contracts, we use the minimum variance hedge ratio formula:

$h^* = \rho \times \frac{\sigma_S}{\sigma_F}$

Where:

• $\rho$ = correlation coefficient = 0.77
• $\sigma_S$ = standard deviation of spot price (bronze) = 2.6%
• $\sigma_F$ = standard deviation of futures price (copper) = 3.2%

$h^* = 0.77 \times \frac{2.6\%}{3.2\%} = 0.77 \times 0.8125 = 0.625625$

Now, calculate the number of futures contracts:

$N = h^* \times \frac{Q_S}{Q_F}$

Where:

• $Q_S$ = quantity of spot position = 1,000 mt
• $Q_F$ = quantity per futures contract = 25 mt

$N = 0.625625 \times \frac{1000}{25} = 0.625625 \times 40 = 25.025$

Since the company is selling bronze in the future (short spot position), they need to take an opposite position in futures to hedge. Therefore, they should sell futures contracts.

Rounded to the nearest whole number: 25 contracts

However, the provided option mentions "Sell 38 futures" which doesn't match our calculation. Let me verify if there's additional information:

Looking at the calculation again, the hedge ratio is: $h^* = 0.77 \times \frac{2.6}{3.2} = 0.625625$

Number of contracts: $N = 0.625625 \times \frac{1000}{25} = 25.025 \approx 25 \text{ contracts}$

Since the company is selling bronze (short spot), they should sell futures to hedge. Therefore, the correct answer should be Sell 25 futures, but the only option provided is "Sell 38 futures" which appears to be incorrect based on the calculation.