SWAPS

Warehousing In practice, it is unlikely that two companies will contact a financial institution at exactly the same time and want to take opposite positions in exactly the same swap. For this reason, most large financial institutions are prepared to warehouse interest rate swaps. This involves entering into a swap with one counterparty, then hedging the interest rate risk until a counterparty wanting to take an opposite position is found.

The Comparative Advantage Argument An explanation commonly put forward to explain the popularity of swaps concerns comparative advantages. Consider the use of an interest rate swap to transform a liability. Some companies, it is argued, have a comparative advantage when borrowing in fixedrate markets, while other have a comparative advantage in floating-rate markets. When obtaining a new loan, it makes sense for a company to go to the market where it has a comparative advantage. This may lead to a company borrowing fixed when it wants floating, or vice versa. The swap is used to transform the different types of liabilities. The total apparent gain from a interest rate swap agreement is always a b  , where a is the difference between the interest rates facing the two companies in fixed-rate markets, and b is the difference between the interest rates facing the two companies in floating-rate markets.

Criticism of the Comparative Advantage Argument Why should the spreads between the rates offered to A and B be different in fixed and floating markets? Now that the swap market has been in existence for some time, we might reasonably expect these types of differences to have been arbitraged away. The reason why spread differentials appear to continue to exist may be due in part to the nature of the contracts available to companies in fixed and floating market. In the floating-rate market, the lender usually has the opportunity to review the floating rates avery six months. If the creditworthiness of A or B has declined, the lender has the option of increasing the spread over LIBOR that is charged. In extreme circumstances the lender can refuse to roll over the loan at all. The providers of fixed-rate finance do not have the option to change the terms of the loan in this way. The spreads between the rates offered to A and B are a reflection of the extent to which B is more likely to default than A. During the next six months there is very little chance that either A or B will default. As we look further ahead, defult statistics show that the probability of a default by a company with a low credit rating (such as B) increases faster than the probability of a default by a company with a high credit rating (such as A). This is why the spread between the five-year rates is greater than the spread between the six-month rates.

Valuation of Interest Rate Swaps If we assume no possibility of default, an interest rate swap can be valued either as a long position in one bond combined with a short position in another bond, or as a portfolio of forward rate agreements. Relationship of Swap Value to Bond Prices Although the principal is not exchanged, we can assume without changing the value of the swap that at the end of its life, A pays B the notional principal of $100 million and B pays A the same notional principal. The swap is then the same as an arrangement in which: 1. Company B has lent the financial institution $100 million at the six-month LIBOR rate. 2. The financial institution has lent company B $100 million at a fiex rate of 5.015% per annum. The value of the swap to the financial institution is therefore the difference between the values of two bonds. Suppose that it is now time zero and that under the terms of a swap, a financial institution receives fixed payments of k dollars at times t i n i 1   and makes floating payments at the same times. Define: : value of swap to financial institution : value of fixed-rate bond underlying the swap : value of floating-rate bond underlying the swap : notional principal in swap agreement fix fl V B B Q It follows that: V B B   fix fl It is customary to discount the cash flows in a swap at LIBOR rates. The implicit assumption is that the risk associated with swap cash flows is the same as the risk associated with the cash flows on a loan in the interbank market. A LIBOR zero-coupon yield curve is usually calculated from Eurodollar futures quotes and swap quotes. For this purpose it is assumed that a swap entered into at the average of the bid and offer quote has a value of zero. The floating-rate bond underlying such a swap is worth par. It follows that the fixed-rate bond is also worth par. These are known as par yield bonds. The bootstrap procedure described in Section 4.1 is used to determine the zero-coupon yield curve from Eurodollar futures quotes and these par yield bonds. This zero-coupon yield curve defines the appropriate discount rates to use in evaluating equation V B B   fix fl for an existing swap.