# Duration based hedging strategies

• Considering a situation where an asset that is interest rate dependant is hedged using an interest rate futures contract
• In such cases the number of contracts to hedge is given by the equation below:

• FC        Contract price for interest rate futures
• DF     Duration of asset underlying futures at maturity
• P      Value of portfolio being hedged
• DP     Duration of portfolio at hedge maturity
• When hedges are constructed using interest rates it is important to note that interest rate and futures prices move in opposite directions . So if one is expecting to lose money when the interest rate falls, one should long futures contracts so that they can hedge their losses by gains in futures prices

Example

An investor has invested $10m in government bonds and is expecting the interest rates to rise in the next 6 months so he decides to hedge himself by interest rate futures. It is currently June and he decides to use the December T bond futures contract for the hedge. If the current futures price is 97.2345 and the duration of the portfolio of government bonds at the end of 6 months is 7.1 years. The duration of the cheapest to deliver T-bond in December is given as 9.121 years. What position should the investor take in the futures contract? How many futures contract should long / short for the hedge if each contract is for the delivery of$100,000 face value.

Solution

The number of contracts that should be shorted is: