Answer-first summary for fast verification
Answer: Cash and carry: Buy the commodity at the current spot price and short the futures contract for a future profit of about \$0.250
**Correct answer: B** First compute the no-arbitrage theoretical forward/futures price: \[ F_0 = S_0 e^{rT} = 30 \cdot e^{0.01 \cdot 0.5} \] \[ F_0 \approx 30 \cdot 1.0050125 = 30.1504 \] The observed six-month forward price is **$30.40**, which is **higher** than the theoretical no-arbitrage price. That means the forward is overpriced. ### Arbitrage strategy: cash-and-carry - Buy the commodity today at $30 - Finance the purchase at the risk-free rate - Short the forward contract at $30.40 - At maturity, deliver the commodity into the forward and receive $30.40 - Repay the loan: $30 e^{0.005} \approx 30.1504$ ### Arbitrage profit \[ 30.40 - 30.1504 \approx 0.2496 \approx 0.250 \] So the correct arbitrage is **cash and carry** with profit of about **$0.250**.
Author: Manit Arora
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Q-707.3. The spot price of commodity, , is currently `F(0) = S(0)\exp(rT)F(0)=S(0)*(1+r)^TrF(0, 0.5), is \`30.40`, then which of the following is the CORRECT arbitrage trade (i.e., trade that exploits the arbitrage opportunity)?
A
There is no arbitrage opportunity
B
Cash and carry: Buy the commodity at the current spot price and short the futures contract for a future profit of about `$0.25`0
C
Cash and carry: Buy the commodity at the current spot price and short the futures contract for a future profit of about `$1.39`0
D
Reverse cash and carry: Sell short the commodity at the current spot price and buy the futures contract for a future profit of about `$0.14`0
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