Funds Investing

There are two ways that a swap position can be interpreted: (1) as a package of forward/ futures contracts, and (2) as a package of cash flows from buying and selling cash market instruments.

Package of Forward Contracts Consider the hypothetical interest-rate swap described earlier to illustrate a swap. Let’s look at party X’s position. Party X has agreed to pay 10% and receive six-month LIBOR. More specifically, assuming a $50 million notional principal amount, X has agreed to buy a commodity called six-month LIBOR for $2.5 million This is effectively a six-month forward contract in which X agrees to pay $2.5 million in exchange for delivery of six-month LIBOR. If interest rates increase to 11%, the price of that commodity (six-month LIBOR) is higher, resulting in a gain for the fixed-rate payer, who is effectively long a six-month forward contract on six-month LIBOR. The floating-rate payer is effectively short a six- month forward contract on six-month LIBOR. There is therefore an implicit forward contract corresponding to each exchange date.

Consequently, interest-rate swaps can be viewed as a package of more basic interest-rate control tools, such as forwards. The pricing of an interest-rate swap will then depend on the price of a package of forward contracts with the same settlement dates in which the underlying for the forward contract is the same index.

Although an interest-rate swap may be nothing more than a package of forward contracts, it is not a redundant contract, for several reasons. First, maturities for forward or futures contracts do not extend out as far as those of an interest-rate swap; an interest-rate swap with a term of 15 years or longer can be obtained. Second, an interest-rate swap is a more transactionally efficient instrument. By this we mean that in one transaction an entity can effectively establish a payoff equivalent to a package of forward contracts. The forward contracts would each have to be negotiated separately. Third, the interest-rate swap market has grown in liquidity since its establishment in 1981; interest-rate swaps now provide more liquidity than forward contracts, particularly long-dated (i.e., long-term) forward contracts.

Package of Cash Market Instruments To understand why a swap can also be interpreted as a-package of cash market instruments, consider an investor who enters into the following transaction:

• Buy $50 million par of a five-year floating-rate bond that pays six-month LIBOR every six months.
• Finance the purchase by borrowing $50 million for five years on terms requiring 10% annual interest rate paid every six months.

The cash flows for this transaction are shown in Exhibit 25-1. The second column of the table shows the cash flow from purchasing the five-year floating-rate bond. There is a $50 million cash outlay and then 10 cash inflows. The amount of the cash inflows is uncertain because they depend on future LIBOR. The next column shows the cash flow from borrowing $50 million on a fixed-rate basis. The last column shows the net cash flow from the entire transaction. As the last column indicates, there is no initial cash flow (no cash inflow or cash outlay). In all 10 six-month periods, the net position results in a cash inflow of LIBOR and a cash outlay of $2.5 million. This net position, however, is identical to the position of a fixed-rate payer/floating-rate receiver.

It can be seen from the net cash flow in Exhibit 25-1 that a fixed-rate payer has a cash market position that is equivalent to a long position in a floating-rate bond and a short position in a fixed-rate bond—the short position being the equivalent of borrowing by issuing a fixed-rate bond.

What about the position of a floating-rate payer? It can be easily demonstrated that the position of a floating-rate payer is equivalent to purchasing a fixed-rate bond and financing that purchase at a floating rate, where the floating rate is the reference interest rate for the swap. That is, the position of a floating-rate payer is equivalent to a long position in a fixed-rate bond and a short position in a floating-rate bond.

EXHIBIT 25^-1 CASH FLOW FOR THE PURCHASE^-OF A FIVE^-YEAR FLOATING^-RATE BOND FINANCED BY BORROWING ON A FIXED^-RATE BASIS

Transaction: Purchase for $50 million a five-year floating-rate bond: floating rate = LIBOR, semiannual pay; borrow $50 million for five years: fixed rate = 10%, semiannual payments

The subscript for LIBOR indicates the six-month LIBOR as per the terms of the floating-rate bond at time t.

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