Question

Consider a $25 million bond portfolio having a modified duration of 7.5. Its manager would like to immunize the portfolio against interest rate risk using T-Bond futures. The futures contract price is 110-10 and the cheapest to deliver bond has a modified duration of 10. Determine the appropriate hedging transaction: (and why)

A. Buy 170 US T-Bond futures contracts

B. Sell 170 US T-Bond futures contracts

C. Buy 302 US T-Bond futures contracts

D. Sell 302 US T-Bond futures contracts

E. Buy 750 US T-Bond futures contracts

F. Sell 750 US T-Bond futures contracts

Answer #1

Number of contracts required for hedge = (P*Dp) / (Fc * DF)

Where P is Portfolio value

Dp = Duration of portfolio

Fc =Futures Price

Df =Duration od asset underlying the futures contract ie Duration o cheapest to deliver

N = 25,000,000 *7.5 / ((110+2/32)*1000*10) = 169.97 = 170

Short poistion in 170 T-bond futures is required to hedge. If interest rates goes up, gain will be made on short futures but loss on bonds. If rates goes down it will be vice versa

Ans B

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