SYNTHETIC RISK-FREE RATE 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? If so, how? (You dont have to show it is an arbitrage, just say the strategy.)