Question: You are given a 30-year bond with yield y. The yield curve is flat and will have only parallel shifts. You have a liquid 3-month Eurodollar contract at your disposition. You can also borrow and lend at a rate of 5% initially.
a. Using the long bond and the Eurodollar contract, construct a delta-hedged portfolio that is immune to interest rate changes.
b. Now suppose you observe the following interest rate movements over a period of 1 year:
{0.06, 0.04, 0.06, 0.04, 0.06, 0.04}
These observations are each 2 months apart. What are your convexity gains from a long volatility position?