$1.($Hedging with Forwards$)$ An FI holds a $15-$year, $$10$ million par value bond that is priced at

$104$ with a yield to maturity of $7$ percent. The bond has a duration of eight years and the FI plans

to sell it after two months.

The FI$$s market analyst predicts that interest rates will be $8$ percent at the time of the desired sale.

Because most other analysts are predicting no change in rates, two$-$month forward contracts for

$15-$year bonds are available at $104.$ The FI would like to hedge against the expected change in

interest rates with an appropriate position in a forward contract.

What will this position be$?$ Show that if rates rise $1$ percent as forecast, the hedge will protect the

FI from loss.