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”. 

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

2. 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? What are the sources of risk to an investor who uses stock index futures to hedge an actively managed stock portfolio? 

3. What must be true of the risk of the spot price of an asset if the futures price is an unbiased estimate of the ultimate spot price?