Question

Bank of America has $100 million of floating rate loans yielding the T-bill rate plus 4%. These loans are finances with $100 million of fixed rate deposits costing 6%. Citigroup has $100 million of mortgages with a fixed rate of 11%, which are financed by $100 million of CDs with a variable rate of T-bill plus 3%. Describe a swap that would be acceptable to both parties. Does this remove all the interest rate risk? How much does each bank make?

Answer 1

1) Bank of America (BOA) has floating rate loans yielding the T-Bill rate plus 4% which are financed by Fixed rate Deposits of 6%. In this case if the T-bill rate decreases to less than 2%, BOA stands to lose money. Similarly Citigroup has fixed rate mortgages at 11% which are financed by T-Bill plus rate 3%. In this case too in case, T-bill rate increase by more than 8% Citigroup stands to lose. Therefore the interest rate risk is high. To hedge risk both the banks have to enter into a swap agreement.

Assuming swap of deposits, the margin for both Banks would be as per below table.

Bank	Amt ($)	Mortgage rate	Deposit rate after swap	Margin
BOA	100 million	T Bill plus 4%	T bill plus 3%	1%
Citigroup	100 million	11%	6%	5%
	Total

A swap which gives both the banks equal margin would be acceptable to both parties. In that case

a) Citigroup would offer BOA floating rate of T-Bill plus 3% less 2% i.e T-bill rate +1%

b) BOA would offer fixed rate of 6% plus 2% i.e fixed rate of 8%.

By doing so both banks hedge themselves against any loss due to movements in T-bill rate and their margins will be protected.

Bank	Amt ($)	Mortgage rate	Deposit rate after swap	Margin
BOA	100 million	T Bill plus 4%	T bill plus 1%	3%
Citigroup	100 million	11%	8%	3%
	Total			6%

Hence by doing so both the banks remove all interest rate risk due to movement in T-Bill rate. Each bank will make 3% on $100 million i.e $3 million p.a,