Question: 7. Another way to write a duration-based hedge ratio is as follows: Hedge Ratio = CF ctd X (P b X D b ) (1+YTM

7. Another way to write a duration-based hedge ratio is as follows:

Hedge Ratio = CF_ctd X (P_b X D_b) (1+YTM_ctd) where

(P_f X D_f ) (1+YTM_b)

CF = conversion factor for CTD bond

P_b = price of bond portfolio as percentage of par

D_b = duration of bond portfolio

P_f = price of futures contract as percentage of 100%

D_f = duration of CTD bond for futures contract

YTM_ctd = Yield to Maturity of CTD bond

YTM_b = Yield to Maturity of the portfolio (average)

A bond portfolio manager holds a government bond portfolio with a face value of $10 million that is currently worth a market value of $9.7 million. The manager is concerned about future rising interest rates and so decides to hedge with a T-Bond futures contract. The cheapest to deliver bonds have a projected duration at maturity of 11.14 years. Their conversion factor is 1.1529 and at their current price the futures price is 90-22. The projected average duration of the bond portfolio is 9.0 years. Current Yield to Maturity is 7.8% on the portfolio and 7.1% on the CTD bond.

a. Based on the above data, compute the optimal hedge ratio.

b. Based on the interest rate expectations, should they take a short or long position?

c. The optimal number of contracts to hedge with is given by:

Number of contracts = HR X (Portfolio par value/value of futures contract)

Where each futures contract is for $100,000 of bonds.

Based on this, compute the optimal number of futures contracts to hold.

d. The closing futures contract price is 89-16. Based on this, how did the futures position perform?

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