A Traditional Interest Rate Swap Has a Notional Capital of 100

question 31

Essay

A traditional interest rate swap has a notional capital of 100 and exchange LIBOR (the floating leg) against 6% (fixed leg). At maturity of the swap there is no capital exchange as the same notional capital of 100 is "exchanged" on both legs. Assume that the swap has a five-year maturity.
A company needs to create an immediate cash flow to offset an immediate loss and decides to use an amortizing swap. Its off-balance sheet items are accounted at their book or historical values. The floating leg is LIBOR, paid quarterly, with a notional capital of 100. The fixed leg also has a notional capital of 100, however, there is only an initial cash flow of X on the fixed leg of the amortizing swap and no other cash flow (zero coupons). Hence, there is no capital exchanged at maturity of the swap (capital identical on both legs). The swap is priced (the value of X is set) so that the initial swap value is zero.
The company enters the amortizing swap to pay floating and receive fixed. In other words, its cash flows on the swap are as follows:
$\bullet$ Receive X at time 0.
$\bullet$ Pays LIBOR every quarter for five years.
$\bullet$ No cash flow at maturity.
a. Why is the amortizing swap interesting for this company, which wants to window-dress an immediate loss? How will it impact its future earnings?
b. The term structure is flat at 6%. What should be the "fair" value of X?
c. The company expects a loss of 10 million, what should be the notional capital of the amortizing swap that should be contracted?
d. Assume now that the company must value all off-balance sheet items at their market value. What would happen to the value of the swap immediately after the payment of X is received by the company? Are amortizing swaps useful in deferring losses with this accounting convention?

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