1. 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 rated and so decided to hedge with a T bond futures contract. The cheapest to deliver bond have a project duration at maturity of 114 years. Their conversion factor is 1.1529 and at their current price the future 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.

1. Based on above data, compute the optimal hedge ratio.
2. Based on the interest rate expectations, should they take a short or long position?
3. The optimal number of contract to hedge with future contract is for $100,000 of bond?
4. Based on this compute the optimal number of future contract to hold. The closing future contract price is 89-16. Based on this how did the future position perform?