Suppose cocoa is trading in the market at $1. The one-year forward price is $1.70.

1. Roughly sketch the payoff diagrams of the forward, the underlying, and the bond (at maturity).

2. Replicate the payoff of the bond with a portfolio with the forward and cocoa. Illustrate the replication graphically.

Note that you have created a synthetic bond, i.e. you can use this portfolio to borrow and lend at the risk-free rate without trading in the bond directly.

3. Suppose there is no storage cost/convenience yield. Using your answer above, find the 1-year risk-free rate.

4. Compare the rate you found above to the actual 1-year Treasury rate. Are your answers the same? If you could trade in actual Treasuries, could you construct an arbitrage?