You wish to hedge your exposure to interest rates by using a duration based hedging strategy. To this you need to use 30 year Treasury bond futures. The bond currently available to deliver is detailed below
Years until maturity Annual coupon
17 9%
Treasury bond futures contracts are available with 6 months to expiry, the current zero rate curve is flat at 5% per annum semi-annually compounded. Bonds pay a semi-annual coupon and has just gone ex-coupon so the accrued interest will be exactly the size of the coupon. The conversion factor is the price of the delivered bond ($1 par value) to yield 6 percent.

Assume that you have a bond portfolio of size $1bn with Macaulay duration 10.98.

Each futures contract is for 1,000 bonds.

The fair futures price is $110.24.

1. How many futures contracts should you enter into to hedge your position? This is in order to match the duration of your portfolio with the futures contracts.

If the zero rate curve remains flat but instantaneously decreases to 4% p.a semi-annually compounded the value of your portfolio rises to $1.109 bn. You will need to calculate the new value of bond and also the new futures price to answer part 1

2. Calculate how effective your hedge was in this scenario. Give reasons why this may be the case.