Suppose that the futures price for December 2020 delivery is $111 per $100 par value, and that the only three possible T-bond prices in December are $110, $111, and $112. If the investor currently holds 200 bonds, each with par value $1,000, he would take short position in two contracts, each for $100,000 par value. Protecting the value of a portfolio with sort futures positions is called short hedging.

a. Calculate the portfolio value as a function of the bond price in December. What is your findings from this calculation?

b. Suppose that T-bonds will be priced at $110, $111, or $112 in two months. Show that the cost in December of purchasing $200,000 par value of T-bonds net of the profit/loss on two long T-bond contract will be $222,000 regardless of the eventual bond price.