Derive a One-Year Forward Rate From Interest Rates

[Fairman]

Derive a One-Year Forward Rate From Interest Rates

Spot EUR/USD is 1.1000. The one-year interest rate in dollars is 5 percent, and in euros is 3 percent. What does covered interest parity imply for the one-year forward rate?

Use the formula: forward equals spot times one plus the quote currency rate, divided by one plus the base currency rate. Here, the quote is the dollar, the base is the euro.

Forward = 1.1000 times 1.05 divided by 1.03. The ratio 1.05 over 1.03 is 1.01942. So forward is 1.1000 times 1.01942, about 1.1214.

That puts the forward above spot, which is the correct direction. The dollar has the higher interest rate, so dollars should trade at a forward discount, and the euro at a forward premium. EUR/USD forward above spot means the euro is more expensive in dollars at the forward date. Correct: the euro, with the lower interest rate, trades at a forward premium.

The forward premium is 1.1214 minus 1.1000, about 214 pips, or 1.94 percent, roughly the 2 percent interest difference.

Now relate to swap. A trader long EUR/USD earns the euro rate and pays the dollar rate, a net cost of about 2 percent a year. Over a day, 2 percent of 110,000 dollars notional divided by 365 is about 6.0 dollars per lot. That matches the typical size of negative swaps on long EUR/USD, before broker markups.

The forward is not a forecast. It is arithmetic from interest rates.

Exercise: compute the one-year forward for another pair using current policy rates.

[FXS HongKong Scalper]

Correct calculation, and the direction is the part people get wrong most often. The higher-yielding currency trades at a forward discount, so the dollar being worth less in the forward than spot is consistent with the dollar paying more interest.

One practical note: the 1.1214 result implies about 214 forward points. That's the same economics as the swap you pay or earn holding spot EURUSD for a year, before the broker markup. So someone holding long EURUSD in this scenario pays roughly 2 percent a year in swap, and the higher forward is the market's way of compensating for exactly that cost.

[Fairman]

The direction of the forward is the part people most often get backwards, so it's worth restating simply. The currency with the higher interest rate trades at a forward discount. Here the dollar pays 5 percent and the euro 3 percent, so a dollar held for a year earns more, and the forward price compensates by making dollars cheaper in the future. EUR/USD forward at about 1.1214 means each euro costs more dollars a year from now. If it didn't, a bank could borrow euros, convert to dollars, earn the higher rate, and lock in a riskless profit with a forward contract.

[Amanhasnoname]

I only really understood forward points when I compared the formula with the swap numbers on my own platform. I took a EURUSD long, worked out the interest difference for one night, and then checked it against the swap my broker showed in the contract specification. The theoretical figure was a bit under what I was actually charged, and the gap was the broker's markup, which in my case was close to a third of the total.

The calculation in the post gives about 214 points for a year, which spread over the days works out to a small daily number. For a scalper holding trades for minutes that cost is irrelevant, but I noticed it matters on the Wednesday rollover, when the swap is charged three times for the weekend. I now close or reduce anything I do not want to carry through that night.

One more practical habit is checking the swap before opening any trade I plan to hold for days, because on some crosses the sign flips between long and short and it changes which side I prefer.

[Fairman]

The swap calculation ties the theory to something every retail trader sees. A long EUR/USD position effectively borrows dollars at the dollar rate and holds euros at the euro rate, so it pays the 2 percent difference. On 110,000 dollars of notional, that's about 2,200 dollars a year, or about 6 dollars a day. Brokers add a markup on both sides, so the actual swap on a long will be more negative, and the swap on a short will be less positive than the pure differential suggests. Comparing a broker's swap table with this calculation shows how large their markup is.

[Fairman]

The statement that the forward isn't a forecast is important. Many traders see a forward above spot and assume the market expects EUR/USD to rise. It doesn't. The forward simply reflects the interest rate difference, so that neither currency offers a riskless advantage. In practice, studies have found that high yielding currencies have often not depreciated as much as forwards imply, at least over some periods, which is the basis for the carry trade. But that tendency is unreliable and can reverse sharply, as carry traders have learned during periods of market stress.

[Fairman]

It's worth trying the calculation for a pair where the base currency has the higher rate. If USD/JPY spot is 150, with dollar rates at 5 percent and yen rates near 0.5 percent, the forward is 150 times 1.005 divided by 1.05, about 143.6. The forward is below spot because the dollar, the base, pays more. A long USD/JPY position earns positive swap in that case. The formula is the same; only the direction changes depending on which side has the higher rate. Has anyone here checked their broker's swap rates against this kind of calculation? I'd be curious how large the markups were.