The manager of a $500 million fixed income portfolio forecasts increase in interest rate. The current portfolio duration is 12. She wants to adjust portfolio duration to 8 by using interest rate futures contracts. The price of the cheapest to deliver futures contract is $100,000 and its duration is 5. The conversion factor for the cheapest to deliver contract is 1.15.

a) how many futures contracts are needed? Should the futures contracts be long or short?

b) if the forecast shows decrease in interest rate and the portfolio manager wants to increase duration to 15, instead, how may futures contracts are needed? Should futures contracts be long or short?