Topic Swap

$4.$ A commercial bank has $$100$ million of four$-$year maturity floating$-$rate loans yielding the T$-$bill rate plus $3$ percent. These loans are financed with $$100$ million of four$-$year maturity fixed$-$rate deposits costing $8$ percent. The commercial bank can issue four$-$year variable$-$rate deposits at the T$-$bill rate plus $1$ percent. A savings bank has $$100$ million of four$-$year maturity mortgages with a fixed rate of $14$ percent. They are financed with $$100$ million of four$-$year maturity CDs with a variable rate of the T$-$bill rate plus $2$ percent. The savings bank can issue four$-$year long$-$term debt at $11$ percent.

a$.$ Discuss the type of interest rate risk each FI faces.

b$.$ Propose a swap that would result in each FI having the same type of asset and liability cash flows.

c$.$ Assume swap rate of $9\%$ fixed for Libor $+1\%$ variable. Diagram the cash flows. Then show that this swap would be acceptable to both parties.

d$.$ The realized T$-$bill rates over the four$-$year contract period are as follows:

$\backslash$table$[[$End of Year$],[1],[2],[3],[4]]$

$\backslash$table$[[$T$-$bill Rate$],[1\mathrm{.}75\%$