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Answer: Buy silver in the spot market and enter into a 6-month forward contract to sell silver.
## Explanation The relationship between the forward price and spot price of an investment asset with no income and no applicable storage costs can be evaluated with the basic no-arbitrage formula: \[ F = S(1 + R)^T \] Where: - \( F \) = Forward price - \( S \) = Spot price - \( R \) = Risk-free interest rate - \( T \) = Time to maturity **Given values:** - Spot price \( S = 24.70 \) - Forward price \( F = 25.00 \) - Risk-free rate \( R = 2\% = 0.02 \) - Time \( T = 0.5 \) years (6 months) **Calculate theoretical forward price:** \[ F_{theoretical} = 24.70 \times (1 + 0.02)^{0.5} = 24.70 \times (1.02)^{0.5} = 24.70 \times 1.00995 = 24.95 \] **Comparison:** - Actual forward price = 25.00 - Theoretical forward price = 24.95 Since the actual forward price (25.00) is **greater than** the theoretical forward price (24.95), the forward contract is **overpriced**. This creates an arbitrage opportunity. **Arbitrage strategy:** 1. Borrow money at the risk-free rate 2. Buy silver in the spot market at $24.70 3. Enter into a forward contract to **sell** silver at $25.00 4. At maturity, deliver the silver and receive $25.00 5. Repay the loan with interest: $24.95 6. Profit = $25.00 - $24.95 = $0.05 per ounce **Why other options are incorrect:** - **A**: There IS an arbitrage opportunity since the forward is overpriced - **B**: Selling spot and buying forward would result in a loss - **D**: Buying spot and buying forward doesn't create an arbitrage position The correct arbitrage strategy is to **buy silver in the spot market and enter into a 6-month forward contract to sell silver** (Option C).
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A portfolio manager at an investment fund specializing in trading precious metals is evaluating the current pricing conditions in the silver market. The manager observes that the spot price of silver is USD 24.70 per ounce and a 6-month forward contract is quoted at USD 25.00 per ounce. If the annually compounded risk-free interest rate is 2%, and assuming no lease rate, no storage costs, and no convenience yield, which of the following trades should the manager make to earn an arbitrage profit?
A
There is no arbitrage opportunity in the silver market.
B
Sell silver in the spot market and enter into a 6-month forward contract to buy silver.
C
Buy silver in the spot market and enter into a 6-month forward contract to sell silver.
D
Buy silver in the spot market and enter into a 6-month forward contract to buy silver.