A security is currently trading at $97. It will pay a coupon of $5 in two months. No other payouts are expected in the next six months. Assume continuous compounding at 12%. If the 6-month forward price is $92, what you should do now to create an arbitrage opportunity?

I. Do nothing. There is no arbitrage opportunity.
II. Sell the short spot at $97.
III. Borrow $97 for six months at 12%, and buy the security at $97.
IV. Invest $97 for six months at 12%.
V. Invest $4.901 for two months at 12%.
VI. Investment $92.099 for six months at 12%.
VII. Buy the forward at $92.
VIII. Sell the forward at $92.

Correct Answer: II, V, VI, and VII

According to the previous question, the forward should be worth $97.794 but it's priced at $92. You should buy the forward at $92, short-sell the security at $97, invest the PV ($4.901) of the coupon for two months at 12%, and invest the rest of the proceeds (97 - 4.901 = 92.099) for six months at 12%. In two months, you can use the cash inflow of $5 from the investment in V to pay the coupon due to the shorted security. In six months, you receive the cash from the six month investment (92.099 x e^{(0.12 x 6/12)} = $97.794), pay the delivery price of $92 on the forward to get the security, and use it to close the short spot position. The risk-free profit will be 97.794 - 92 = $5.794.