Hedging a Bond Portfolio with T-Bond futures

Question

A portfolio manager uses a T-bond futures contract to hedge a bond portfolio over the next 4 months. The portfolio is worth $75 million and will have duration of 5 years in four months. The futures price is 118 and each contract is for $200,000. There are three bonds that can be delivered with durations 7, 8 and 9 years but it is unclear which will be the cheapest to deliver.

1.    If you expect interest rates to rise over the next 4 months, which duration bond will likely be the cheapest to deliver?
2.    What maturity T-bond futures contract should be used to hedge the bond portfolio?
3.    What position of futures contrasts is required?
4.    What adjustment is necessary in one month if you are wrong in your initial assessment that rates would rise; instead you now expect rates to fall?
5.    How will your adjusted position effect the performance of the hedge if long term rates fall more than short term rates

Summary

The question belongs to Finance and it is about Swaps. The question here is about T-bond futures being hedged for 4 months with futures prices being given. Given such a situation, questions such as determining the cheapest bond, the maturity T-bond to be used for hedging, the position of futures contrasts and the adjustments necessary for better positioning the hedge, etc have been given in the solution.

Total Word Count 168