FX · X6 · 9 min
Forwards and covered interest parity
Work out a forward exchange rate from today’s rate and two interest rates, and say which currency trades at a discount.
In the news: A surprise rate decision from the Bank of England or the Fed moves every sterling–dollar forward rate.
The essentials
- Outright forward
- An exchange rate agreed today for an exchange on a later date. It is set by spot and the two currencies’ interest rates, so it says nothing about where traders expect spot to go.
- Covered interest parity
- Converting now and depositing, or depositing and selling forward, must pay the same, or someone makes a riskless profit. So at spot 1.2500, with sterling at 5% and dollars at 3%, one year forward is 1.2262.
- Forward premium and discount
- The higher-yielding currency trades at a forward discount and the lower-yielding one at a . With sterling rates above dollar rates, the GBP/USD forward sits below spot.
- Forward points
- The forward minus spot, in . Roughly spot × rate gap × time: 1.27 × 0.75% × 91 ÷ 360 is about 24 pips; with sterling deposits counting 365 days, nearer 22.
- Points quoted two ways
- Bigger number first (35/33): subtract from spot, as the first currency is at a discount. Smaller first (20/22): add. Spot 1.3000/1.3002 with points 35/33 gives a forward of 1.2965/1.2969.
Covered interest parity
F = S × (1 + r_terms × d/B_terms) ÷ (1 + r_base × d/B_base); points = F − S
- S
- spot, in terms currency per unit of base
- r
- deposit rate for each currency, as a decimal
- d
- days from spot to the forward date
- B
- day basis: 365 for sterling, 360 for dollars and euros
How it works
1. Two ways to get dollars in a year
To have dollars in a year, you can change pounds now and deposit the dollars, or deposit the pounds and change them later. With pounds earning 5% a year, dollars 3%, and £1 = $1.25 today: route A changes £100 now to $125 and deposits the dollars; route B deposits the pounds, getting £105 in a year, and changes them then.
2. A rate fixed today
Route B needs an exchange rate for a year’s time. If you agree that rate today, both routes are free of risk, so they must pay the same: £105 × F = $128.75, which gives F = 1.2262. A rate agreed now for an exchange later is a , or .
3. The rule and its name
As a formula: forward = spot × (1 + dollar rate) ÷ (1 + sterling rate). This is : the forward is set by spot and the two interest rates, because any other rate would hand someone a riskless profit.
4. The higher-yielder trades at a discount
In the example the forward, 1.2262, is below spot, 1.2500. Sterling pays more interest, and is worth less for later delivery: it trades at a forward discount, and the dollar at a . The lower forward takes back sterling’s extra interest.
5. Forward points
Dealers quote the gap between the forward and spot in pips: the . Here 1.2262 − 1.2500 = −0.0238, or −238 points. A quick estimate is spot × rate gap × time: 1.25 × (3% − 5%) × 1 = −0.025, about −250.
6. Shorter periods and day counts
For less than a year, scale each rate by the days. Sterling deposits count days out of 365; dollar and euro deposits out of 360. For 91 days at 4.50%, £1 grows to 1 + 0.045 × 91 ÷ 365 = £1.01122.
7. Points quoted two ways
Dealers quote forward points as a bid and an offer. If the bigger number comes first, as in “35/33”, subtract them from spot: the first currency is at a discount. If the smaller comes first, as in “20/22”, add them. Spot 1.3000/1.3002 with points 35/33 gives a forward of 1.2965/1.2969.
8. Not a forecast
A forward discount doesn’t mean traders expect sterling to fall. The forward is arithmetic on spot and the two interest rates. When a central bank surprises the market, rates change and every forward moves with them, whatever happens to spot.
Try it
Move the two interest rates and the time. When sterling pays more interest, its forward rate sits below spot.
- Forward, 3m
- 1.2670
- Forward points
- −29.8
- Sterling trades at
- A discount
| Tenor | Outright forward | Forward points |
|---|---|---|
| 1 week | 1.2698 | −2.3 |
| 1 month | 1.2690 | −9.9 |
| 2 months | 1.2680 | −20.0 |
| 3 months | 1.2670 | −29.8 |
| 6 months | 1.2641 | −58.9 |
| 9 months | 1.2613 | −87.4 |
| 1 year | 1.2584 | −115.6 |
Sterling deposits earn more over 3 months, so sterling trades at a forward discount: the forward gives 29.8 pips fewer dollars per pound than spot, which takes back the extra interest. The higher-yielding currency trades at a forward discount.
Route 1: deposit pounds, sell them forward
£1,000,000 at 4.50% → £1,011,219, sold at 1.2670 → $1,281,236
Route 2: sell pounds now, deposit dollars
£1,000,000 at 1.2700 → $1,270,000, at 3.50% → $1,281,236
Worked example
GBP/USD spot is 1.2700. For 91 days, sterling deposits pay 4.50% (counted out of 365) and dollar deposits 3.75% (out of 360).
- Dollar growth: 1 + 0.0375 × 91 ÷ 360 = 1.0094792.
- Sterling growth: 1 + 0.0450 × 91 ÷ 365 = 1.0112192.
- Forward: 1.2700 × 1.0094792 ÷ 1.0112192 = 1.26781.
- Points: 1.26781 − 1.2700 = −0.00219, or −21.9 pips.
- Sterling pays more interest, so it trades at a forward discount.
About 1.2678: 22 pips below spot.
Check yourself
8 quick questions on the explanation above.
Practice
New numbers every set. Misses and guesses go into your review deck.
In the interview
Answer out loud in under a minute, then compare.
Why isn’t the forward rate the market’s forecast?
Sterling rates are above dollar rates. Is GBP/USD at a forward premium or a discount?
Walk me through the arbitrage that pins down the forward.
Remember
F = S × (1 + r_terms × t) ÷ (1 + r_base × t)
The higher-yielding currency trades at a forward discount of about the rate gap times time: the forward evens out the interest, it doesn’t forecast spot.