Default risk and innovations in the design of interest rate swaps - includes appendix - Security Design Special Issue

Financial Management (Financial Management Association), Summer, 1993 by Keith C. Brown, Donald J. Smith

Beyond its ability to reduce default risk, another key property of this "marking" procedure is that the overall internal rate of return on a swap-linked variable rate funding structure is relatively invariant to the exact swap rate that prevails on each future settlement date. This follows directly from the trade-off that is created between making (receiving) a swap unwind payment and then adjusting the remainder of the agreement to a lower (higher) rate. Consequently, no matter what path interest rates follow in the future, the swap unwind payment -- and subsequent resetting of the fixed rate on the "new" swap -- always link the process back to the conditions in the market at date 0. This point is illustrated by the following example and documented more thoroughly in the Appendix.

B. A Numerical Example

Suppose that a corporation has just issued a two-year, floating-rate note (FRN) with a par value of $10 million, calling for semiannual interest payments based on the London Interbank Offer Rate (LIBOR). Because this firm presumably would prefer a known cost of funds but now would be exposed to rising rates, it can convert its new debt into the equivalent of a fixed-rate issue via the swap market. This can be accomplished by entering a pay-fixed, two-year (i.e., four settlement period) swap against six-month LIBOR with a notional principal of $10 million. That is, as floating-rate payments are required on its FRN, the firm will receive an equal amount from its swap counterparty in exchange for cash flows based on the fixed swap rate. Letting the current fixed rate for such an agreement be [F.sub.0, 4] = 9.00%, Exhibit 2 summarizes the data necessary to illustrate the mechanics of the procedure outlined above.(5)

Panel A specifies one possible pattern for swap fixed rates on each future settlement date. Note that with each successive settlement date, the maturity of the swap is reduced by six months to match the remaining maturity on the underlying note. Panel B shows the calculations of the periodic cash flows associated with these assumptions, including both the fixed payments on the existing swap and the liquidation value of the remainder of that swap.(6) For example, on date 1 the economic value of the existing agreement is [V.sub.0] = -$69,049, a negative amount since the firm is obligated to pay 9.00% when the current market rate is only [F.sub.1, 3] = 8.50%. The corporation would have to pay its counterparty that amount to close out the existing agreement. In addition, the fixed payment due on that date is $450,000, given the initial fixed rate of 9.00%. Finally, Panel C computes the corporation's synthetic funding cost, expressed as the internal rate of return of the combined FRN/swap transaction.

This example highlights two important attributes of the mark-to-market swap. First, and most importantly, notice that when measured to the basis point the internal rate of return on the aggregate position is 9.00%. Of course, this is the same net funding rate that the firm would have had if it could have found a counterparty willing to accept 9.00% as a fixed rate on a plain vanilla swap with otherwise comparable terms. Thus, when viewed solely in terms of the cost of funds over the entire two years, the plain vanilla and mark-to-market swap structures achieve the same result. Second, unlike the plain vanilla swap, which would have required constant settlement payments of $450,000, the mark-to-market scheme generates highly variable cash flows from period to period. The exact payment pattern will depend on the path of the fixed rates on the sequence of replacement swaps, which in practice could come from the market maker's own quote sheet or as the median of a set of quotes from competing swap dealers. We should stress, though, that the plain vanilla swap keeps the periodic cash flows constant at the expense of creating default risk exposure for one counterparty or the other. The whole point of the mark-to-market structure is to eliminate this exposure on each settlement date by converting it to an obligatory cash payment.