FX-Swap-Implied Yields and Synthetic Funding

A bank in London needs dollars for three months. It could borrow them outright in the interbank market. Or it could hand a counterparty euros today, get dollars back, and agree to reverse the trade in three months at a pre-fixed rate. Nobody called this a loan, but that is exactly what happened — the euros were collateral, and the difference between the two exchange rates was the interest.

That second route is an FX swap, and the interest rate hidden inside it is the FX-swap-implied yield. It matters because that implied rate does not have to equal the rate you'd pay borrowing the currency directly, and the gap between them is one of the most closely watched numbers in short-term funding markets.

Building the trade

An FX swap has two legs, both agreed at once: a near leg, usually spot, and a far leg, a forward, in the opposite direction. Take a desk that needs dollars and has euros. Near leg: sell EUR 100 million, buy USD at spot 1.0850, receiving $108.5 million. Far leg, three months later: buy back EUR 100 million, sell dollars, at the agreed forward rate.

The forward rate is not picked freely — it is set by covered interest parity, which says the forward must offset the interest-rate gap between the two currencies, or a riskless profit would exist. Spelled out:

$$F = S \times \frac{1 + r_{USD} \times t}{1 + r_{EUR} \times t}$$

In words: the forward exchange rate equals the spot rate, scaled up by how much more (or less) interest dollars earn than euros over the life of the swap. If dollar rates are higher than euro rates, the forward dollar price of a euro must be lower than spot, so that nobody can borrow cheap euros, swap into dollars, earn the higher dollar rate, and swap back for a free lunch.

Reading the implied yield back out

Rearranging that same formula the other way is how a trader actually uses it day to day: instead of using known interest rates to find the forward, you take the forward the market is actually dealing at and back out what interest rate it implies.

$$r_{USD}^{implied} = \left(\frac{F}{S} - 1\right) \times \frac{1}{t} + r_{EUR}$$

In words: take the percentage gap between forward and spot, annualize it, and add the euro rate you already know — the result is the dollar rate the swap market is effectively charging you.

Worked example

Spot EURUSD is 1.0850. The 3-month (0.25 year) forward is 1.0800 — dollars have gotten cheaper forward, meaning dollars are the higher-yielding currency. The 3-month euro deposit rate is 3.00%.

1. Forward points. $1.0800 - 1.0850 = -0.0050$, i.e. -50 pips. Dollars trade forward at a discount to euros.
2. Percentage gap. $-0.0050 / 1.0850 = -0.00461$, about -0.461% over the 3 months.
3. Annualize. $-0.00461 \times 4 = -0.0184$, about -1.84% per year — this is how much less the discount says dollars should be trading versus euros in the swap.
4. Implied dollar rate. Because the quote currency (USD) is cheaper forward, dollars are the currency paying the higher rate: $r_{USD} \approx 3.00\% + 1.84\% = 4.84\%$.

If a bank's real cost of borrowing dollars outright in the interbank market is 5.10%, this desk is better off getting dollars synthetically through the FX swap at 4.84% and posting euros as security, rather than borrowing dollars directly.

Worked example: when the arbitrage should not exist, but does

Suppose the same numbers hold, but a US money-market fund is willing to lend dollars directly at only 4.60% — cheaper than the 4.84% implied by the swap. In theory a bank should borrow at 4.60% and have no reason to touch the swap market. In practice, banks are often willing to pay more through the swap than they would to borrow directly, because balance-sheet rules, counterparty limits, or a shortage of who's willing to lend to them make the swap the only channel actually open. That persistent gap between the implied rate and the real cash rate is called the cross-currency basis, and it is a standing signal of dollar funding stress rather than a pure arbitrage waiting to be closed.

What this means in practice

Trading desks quote FX swaps in points, not percentages, because two counterparties can agree on points without agreeing on which day-count convention or interest rate underlies them. But every points quote is secretly an interest-rate market. A corporate treasurer funding an offshore subsidiary, a hedge fund financing a carry trade, and a bank managing its dollar book are all, whether they think of it this way or not, borrowing and lending currencies through the swap curve — and the implied yield tells them whether that channel is cheap or expensive relative to borrowing directly.