# Asset Swaps: Generalization

Swaps can be generalized. An asset swap is an exchange of two series of cash flows. Engineering asset swaps uses a simultaneous sale and purchase of instruments. For example, a client holds a loan and wants to swap Libor against equity index return. The bank could engineer the asset swap by buying the equity index and borrowing floating. The client receives the equity return from the bank and pays to the bank the Libor from its loan.

Fund managers try to track some equity index. One way of doing this is to by buying the underlying portfolio of stocks that replicate the index and constantly adjusting it as the market moves or when new stocks are added or removed from the index, or adjusting is to adjust the fund volume when new funds are received. Using equity swaps is a cost-effective alternative. Under an equity swap, the fund manager receives the equity index return in exchange for a Libor rate over some fixed maturity.

# Mark-to-market Value of an IRS

For an IRS receiving fixed rate and paying floating rate, replication can be seen as lending fixed rate and borrowing same amount long fixed rate and short floating rate. This combines a long fixed rate position and a short floating rate position. The mark-to-market value is the net value of a long bond (loan) minus a short floating rate bond (debt).

The value of a floating rate bond is always par. For example, for one year, with rate *i,* floating, with nominal 1, pays 1 + /, of which present value is final payment discounted to today, or (1 + + /) — 1. The argument is extended to subsequent periods. The value of an IRS is the net value of the two positions. It is zero at inception and becomes positive or negative when fixed is above floating and vice versa. Conceptually, an interest rate swap shows that the market views as equivalent a series of floating rates and a series of fixed swap rate cash flows.

Because a swap can take both positive and negative values when time passes, the one which owns the positive value would lose it if the counterparty defaults. Therefore, it is exposed to credit risk. The modeling of the credit exposure of swaps is discussed in Chapter 44. The situation is similar for a FRA traded OTC.

# Derivatives and P & L

Derivatives are always constructed with prevailing market rates. Contracting a swap receiving the fixed rate will imply receiving the current fixed rate for the selected maturity. Contracting a swap receiving the variable rate will imply receiving the current rate for the selected short maturity of the variable rate, 1 month, 3 month, etc.). Therefore, derivatives influence both the nature of interest rates and the level of interest rates paid or received, hence the earnings (P & L) as well. Both impacts have to be assessed carefully before entering into a derivative transaction.