Notes:

The $1$ year Certificates of Deposit pay $1\mathrm{.}95\%$ p$.$a$.$ annually and will be rolled over at

maturity. The $7$ year commercial loans have a duration of $5\mathrm{.}486$ years. The fixed rate

mortgages have a duration of $7\mathrm{.}656$ years. All values are market values and are trading at

par.

Assumption: $30$ days per month; $90$ days per quarter; $360$ days per year.

a$)$ What is the bank$$s duration gap?

a$.-0\mathrm{.}49$ years

b$.+4\mathrm{.}24$ years

c$.0\mathrm{.}94$ years

d$.-2\mathrm{.}81$ years

e$.+3\mathrm{.}69$ years

b$)$ What is the bank$$s interest rate risk exposure $($i$.$e$.$ exposed to rising or falling rates$)?$

c$)$ What is the on$-$balance$-$sheet impact on the bank if all interest rates increase $25$ basis

points? $($i$.$e$.$ suppose $$R$/(1+$R$)$ is equal to an increase of $25$ basis points.$)$

d$)$ Suppose you are a risk manager of the bank. Construct an appropriate swap hedge for

your bank.

i$).$ Specify whether your bank should be a fixed$-$ or variable$-$rate payer in the swap,

and

ii$).$ Calculate the notional of swap, NS$,$ for a perfect hedge. Suppose the fixed side of

the swap has a duration of $12$ years, while the variable side of the swap is floating

on a biennial base.

e$)$ How would you use futures contracts on Canada Bond to hedge your bank$$s interest

rate risk exposure? Specify whether your bank should conduct a long or short hedge.

Justify your strategy.

f$)$ How would you use put option contracts to hedge the interest rate risk exposure of

your bank? That is$,$ should the bank buy or sell put options on Canada Bond?