APPENDIX 6A: CURRENCY OPTION VALUATION
7.2 SWAPS AS PORTFOLIOS OF FORWARD CONTRACTS
You’ve taken a fast-track job as a junior analyst with International Notions Com- pany, Inc. It’s your first day on the job and Hiromi Ito, Notions’ CFO, brings you into her office to discuss the currency exposure of Notions’ operations. You only get one chance to make a first impression, and you are eager to demonstrate that your time at school was well spent.
Ito: ‘‘I want to get your opinion on a persistent problem that we face here at Notions. We have sales in more than 140 countries worldwide. Yet 70 percent of our research and development expenses, the bulk of our production
0 100 200 300 400
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
$6 trillion
(1%) derivatives
$3 trillion (1%)
Interest rate derivatives
$465 trillion (83%) CDSS
$30 trillion (5%)
and swaps
$58 trillion (10%)
FIGURE 7.1 Notional Amounts Outstanding in OTC Derivatives Markets ($ trillions).
Sources: International Swap Dealers Association (www.isda.org) and Bank for International Settlements (www.bis.org).
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expenses, and all of our interest expenses are in dollars. Our dividends also are paid in dollars. I’m particularly concerned about our exposure to the countries of the European Union. A high percentage of our sales come from these countries, yet our operating and financial expenses are largely in dollars.
What do you suggest?’’
(Okay. . .now what was it that you studied in school? Think fast! Ah, yes. A currency swap might be just the thing. Stepping into the breach, you suggest a dollar-for-euro currency swap.)
You: ‘‘Well, we might consider a currency swap for euros. We could swap our dollar debt for euro debt on the same amount of notional principal and thereby convert some of our dollar expenses to euro expenses. Our counterparty would pay the dollar interest payments on our debt and we would pay the euro interest payment on a comparable amount of euro debt. This would form a hedge against revenues from countries in the European Union.’’
Ito: ‘‘Hmm. . .and who do you propose as a counterparty?’’
You: ‘‘This should be a fairly standard financial transaction, so I’d suggest an international bank making a market in currency swaps. I have a classmate in the swaps department at UBS in New York. I’m sure she could give us a quote.’’
Ito: ‘‘What if they default on their side of the deal?’’
You: ‘‘We’d stop paying them as soon as they stopped paying us. At most, we’d be out a few months’ interest on the notional principal.’’
Ito: ‘‘If Notions loses any money on this deal, we’ll also be out one junior analyst!’’
How do you respond? Whatisthe default risk of a swap contract?
A swap is a portfolio of forward contracts of different maturity dates.
Ms. Ito’s question is most easily answered by comparing the swap contract with a futures contract. Futures are nothing more than a bundle of consecutive one-day forward contracts in which changes in wealth due to changes in exchange rates are marked-to-market each day. Swaps are also a bundle of forward contracts. But instead of being laid end-to-end as renewable one-day forwards contracts, a swap is a bundle ofsimultaneousforward contracts, each with a different maturity date.
Suppose a domestic firm borrows an amount Xd in a T-period nonamortizing loan with periodic (fixed or floating rate) interest payments Cdt =idtXd throughout the life of the loan.
Domestic currency loan
–C1d –C2d –(CTd+Xd) +Xd
If the company has a need to hedge revenues from a foreign subsidiary, it can swap this domestic currency loan for a foreign currency loan of equal value (Xft=Xdt/Sdt/f) paying interest payments Cft=iftXf. If the principal being received is set equal in value to the principal being paid, there is no reason to exchange the principal amounts, and the principal is called notional principal. Rather than exchange the full amount of the interest payments, only the difference check need be exchanged. This difference check is equal to (Cdt −CftSdt/f) after translating the foreign currency interest payment into domestic currency at the prevailing spot rate.
The net cash flows look as follows:
Net cash flows of a currency swap
+C1d +C2d +CTd
–C1fS1d/f –C2fS2d/f –CTfSTd/f
This is equivalent to a portfolio of T forward contracts each with successively longer maturities.
One-period forward contract
Two-period forward contract T-period forward contract
(C1d – C
1fS1d/f)
(C2d – C2fS2d/f)
(CTd – C
TfSTd/f) Currency swaps are essentially bundles of currency forward contracts of different maturities. Ms. Ito’s concern is at least partially justified because swap contracts, like forward contracts, are subject to default risk. Although the risk and consequences of default are somewhat more than in a comparable futures contract with a futures exchange clearinghouse, they are far less than for straight debt.
A futures contract reduces default risk relative to a forward contract by: (1) requiring a margin, (2) having an exchange clearinghouse as the counterparty, and (3) marking-to-market daily. Swaps can be compared with futures along these same three dimensions. First, swaps do not generally require a performance bond, such as a margin requirement, and this tends to give swaps slightly more default risk than comparable futures contracts. Second, a commercial or investment bank making a market in swaps is generally the counterparty. To the extent that the bank is more prone to default than a clearinghouse, this may slightly increase default risk. Third, whereas the entire gain or loss on a futures contract is marked-to-market daily, the performance period between payments is longer (e.g., six months) than in a futures contract and only the current interest payment is settled in a swap. The default risk of a swap contract thus falls somewhere between the risk of a comparable futures contract (which is negligible) and the risk of the longest maturity forward contract in the swap contract.
Swaps are far less risky than straight debt because if one side defaults, the other side is released from its obligations as well. Further, the entire principal is not at risk as it is in a loan because of the exchange of actual or notional principals at the beginning and at the end of the contract. The interest payments are less at risk than in straight debt, because the difference check depends on the difference between the interest rates rather than on the level of one of the interest rates. For these reasons, currency and interest rate swaps are far less risky than comparable straight debt.1