Currency Swaps

A US manufacturer wants to fund a new plant in Japan. It could borrow yen directly from a Japanese bank — but its credit is far better known, and far more cheaply priced, in the US dollar bond market. So it does something that looks strange at first: it borrows $10 million in dollars, the currency it doesn't actually need, and then enters a currency swap to convert that dollar liability into a yen one. By the time the swap is done, the company is paying yen interest on a yen amount, funded by a dollar bond it never has to think about again until it matures.

A currency swap looks like the interest-rate swap from earlier in this module in almost every way — a schedule of periodic exchanges, a fixed or floating rate on each side — with one change that turns out to matter enormously: the two legs are denominated in different currencies, and this time the principal really is exchanged, both at the start and at the end.

The structure: three exchanges, not one

A plain-vanilla fixed-for-fixed currency swap between a USD payer and a JPY payer involves:

That last point is the crux of the whole instrument, and it's why a currency swap carries real currency risk even though the exchange rate used for principal is fixed in the contract: fixing the rate does not fix the real economic value of what's being exchanged, since the value of a fixed number of yen, in dollar terms, moves with the market every single day.

Worked example: three years of cash flows

Our manufacturer's swap: initial exchange \$10\text{m} \leftrightarrow \text{¥}1{,}500\text{m} at S_0 = 150 ¥/\$; USD fixed rate 4.00\% annually, JPY fixed rate 1.20\% annually; three-year term. The company pays JPY interest, receives USD interest (which it uses to service the dollar bond it actually issued).

Date Company pays Company receives
Inception $10,000,000 ¥1,500,000,000
Year 1 ¥18,000,000 $400,000
Year 2 ¥18,000,000 $400,000
Year 3 ¥18,000,000 + ¥1,500,000,000 $400,000 + $10,000,000

The yen interest is 1{,}500{,}000{,}000 \times 0.012 = \text{¥}18{,}000{,}000 per year; the dollar interest is 10{,}000{,}000 \times 0.04 = \$400{,}000 per year. Notice the two interest legs aren't remotely comparable in size — ¥18 million and $400,000 are simply the market rates for each currency, applied to principal amounts that were equivalent only at the moment they were set. At maturity the original principal comes back exactly, letting the company retire its dollar bond with the $10 million it receives from the swap — the currency swap has done its job of converting a dollar liability into a yen one for three years, cleanly.

Valuation: the difference of two bonds, in a common currency

Exactly as with an interest-rate swap, decompose each leg into a bond. The USD leg is a dollar-denominated bond B_{\$}, discounted on the USD curve; the JPY leg is a yen-denominated bond B_{\text{¥}}, discounted on the JPY curve. The only new step is converting one of them into the other's currency at today's spot rate S before subtracting:

V_{\text{receive-\$, pay-¥}} = B_{\$} - \frac{B_{\text{¥}}}{S},

where S is quoted as yen per dollar, so dividing the yen bond's value by S converts it into dollars. (Unlike the interest-rate swap case, the floating leg — if there is one — still reprices to par at each reset in its own currency; the FX conversion is a separate step layered on top.)

Revalue our manufacturer's swap exactly one year in. Suppose the yen has strengthened: spot has moved from 150 to S = 140 ¥/\$. The USD discount curve is flat at 4.50%, the JPY discount curve flat at 0.50% (a realistic gap — yen rates have historically sat far below dollar rates). Two years remain.

B_{\$} = 400{,}000\,e^{-0.045(1)} + \left(400{,}000 + 10{,}000{,}000\right)e^{-0.045(2)} \approx \$9{,}887{,}272, B_{\text{¥}} = 18{,}000{,}000\,e^{-0.005(1)} + \left(18{,}000{,}000 + 1{,}500{,}000{,}000\right)e^{-0.005(2)} \approx \text{¥}1{,}520{,}790{,}900.

Converting the yen bond at today's spot and subtracting:

V_{\text{receive-\$, pay-¥}} = 9{,}887{,}272 - \frac{1{,}520{,}790{,}900}{140} \approx 9{,}887{,}272 - 10{,}862{,}792 = -\$975{,}520.

The company's swap has lost nearly a million dollars of value — because the yen strengthened. The company is contractually obligated to hand back ¥1.5 billion at maturity, and that fixed number of yen is now worth more dollars than when the deal was struck. This is exactly the currency risk a currency swap does not remove: it removes interest-rate mismatch, but the company is left, for three years, effectively short the yen.

See the FX sensitivity

Holding the two bonds' own-currency values fixed, the swap's dollar value moves with the spot rate through simple division — a hyperbola, not a straight line, because it's the yen bond's value divided by S, not multiplied.

As S rises (the yen weakens, since more yen now buy one dollar), the yen bond is worth fewer dollars, and the receive-dollar party's position improves. As S falls (the yen strengthens), that party's position deteriorates — exactly the move that hurt our manufacturer above.

The modern currency swap market traces to a single, celebrated 1981 deal arranged by Salomon Brothers between IBM and the World Bank. IBM was sitting on old Swiss-franc and Deutschmark debt taken out years earlier, back when those currencies were strong against the dollar; by 1981 the dollar had rallied hard, and IBM would have loved to lock in the currency gain but didn't want the hassle and expense of unwinding the actual bonds. The World Bank, meanwhile, needed to keep raising Swiss francs and Deutschmarks to fund its lending programs abroad, but was running into the practical limits of how much debt those markets would absorb from a single frequent issuer — while it could still borrow dollars easily. Salomon's structure let the World Bank issue new dollar debt (which it could place easily) and swap the proceeds into francs and marks matching IBM's outstanding obligations, while IBM effectively ended up with dollar exposure. Both sides got the currency they actually wanted, neither had to touch its existing bonds, and the deal is now credited as the birth of the swap market as we know it today.

It's tempting to assume that at maturity, the two sides simply "true up" at whatever the exchange rate happens to be that day. They don't — the final exchange happens at S_0, the rate fixed in the contract at inception, exactly as described above. This is precisely why a currency swap carries real FX risk for its full life: if it instead re-exchanged at the prevailing spot rate, both principal legs would always be worth the same amount in either currency, and the FX risk would vanish entirely. The whole point of fixing the rate contractually is that it does not track the market — so whichever side is contracted to hand over the currency that has since strengthened is handing over something worth more, in real terms, than what they originally received.

A related trap: don't assume currency-swap payments net against each other the way interest-rate swap payments do. Because the two legs are denominated in different currencies, there is nothing to net (you cannot subtract yen from dollars) — both legs are typically paid in full, in their own currency, every period. This also means the notional is genuinely at risk on both the interest legs and, at the two exchange dates, the full principal — a materially larger and longer-lived exposure to a counterparty's default than a same-currency interest-rate swap ever creates, which is exactly the subject of the next lesson.