Q$1$a$)$ A bank with $20-$year $$1$ million face value bond as asset

$$ Market value of the bond: $$97$ per $$100$ face value

$$ Duration of the bond: $9$ years

$$ Current interest rate: $8\%$

$$ If the bank manager receives a forecast that interest rate will increase by $2\%$ from $8\%$ to $10\%$ in the next $3$ months, would there be a capital gain or loss from the bond position?

Q$1$b$)$ To hedge, the manager enters into a forward contract to sell $20-$year bonds for delivery in $3$ months$$ time. Suppose that the manager can find a buyer willing to

pay $$97$ per $$100$ face value of $20-$year bond for delivery in $3$ months$$ time.

$$ If the interest rate forecast proves to be true in $3$ months$$ time:

$$ Bond position:

$$ Forward position: