Explanation

This is an example of index arbitrage where arbitrage exists if the parity condition between the equity index price and the futures contract price does not hold.

Theoretical Futures Price Calculation:

The parity relationship is: $F_{0,t} = S_0 \times e^{(r - q) \times t}$ Where:

• $S_0 = 3,625$ (current spot index value)
• $r = 5\%$ (risk-free rate)
• $q = 2\%$ (dividend yield)
• $t = 15/12 = 1.25$ years

$F_{0,t} = 3,625 \times e^{(0.05 - 0.02) \times 1.25}$ $F_{0,t} = 3,625 \times e^{0.0375}$ $F_{0,t} = 3,625 \times 1.0382$ $F_{0,t} = 3,763.52$

Arbitrage Strategy:

• Theoretical futures price: USD 3,763.52
• Actual futures price: USD 3,750

Since the actual futures price (3,750) is lower than the theoretical price (3,763.52), the futures contract is undervalued.

Strategy: Buy the undervalued futures contract and sell the overvalued underlying equities (short the index).

This creates a risk-free arbitrage profit because:

1. Buy futures at 3,750 (undervalued)
2. Short sell the index at 3,625
3. At expiration, the futures price converges to the spot price
4. The difference between theoretical and actual futures price represents the arbitrage profit

Options Analysis:

• A: Incorrect - Buying both would not create arbitrage
• B: Correct - Buy futures (undervalued) and sell underlying (overvalued)
• C: Incorrect - Opposite of the correct strategy
• D: Incorrect - Selling both would not create arbitrage