Answer: Sell 38 futures

## 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.

Author: LeetQuiz .