A portfolio manager holds a bond portfolio worth $10 million with a modified duration of 6.8 years, to be hedged for three months. The current futures price is 93-02, with a notional of $100,000. We assume that its duration can be derived from that of the cheapest-to-deliver bond, which is 9.2 years.2
To be consistent, all of these values should be measured as of the hedge horizon date. So, the portfolio and futures durations are forecast to be 6.8 and 9.2 years in three months. The $10 million should be the forward value of the portfolio, although in practice it is often taken from the current value.
Compute
i) The dollar value of the futures contract notional
ii) The number of contracts to buy/sell for optimal protection