Forward Premium / Discount Calculator
Compute the annualised forward premium or discount of a currency: (forward − spot) ÷ spot × (360 ÷ days) × 100%, to see if it trades rich or cheap to spot.
Input Data
Results
At a glance:Forward premium/discount measures a currency's annualised premium or discount in the forward market vs spot: annualised = (forward − spot) ÷ spot × (360 ÷ days) × 100%. Positive = forward premium (forward richer), negative = forward discount (forward cheaper). It is mainly driven by the interest-rate differential (interest rate parity), not a forecast: the lower-rate currency usually shows a forward premium, the higher-rate a forward discount, by about the rate gap. Annualising makes maturities comparable; used for hedging-cost and carry-trade analysis.
Formula
Annualised = (forward − spot) ÷ spot × (360 ÷ days) × 100%.
Positive = forward premium; negative = forward discount.
$$$\\dfrac{F - S}{S} \\times \\dfrac{360}{\\text{Days}} \\times 100\\%$$$$$() ()$$$$$\\dfrac{7.85 - 7.8}{7.8} \\times \\dfrac{360}{90} \\approx 2.56\\%$$$How to Use
- Enter the spot and forward rates.
- Enter the forward term in days.
- View the annualised forward premium/discount.
Annualised forward premium/discount at different quotes
| Spot | Forward | Days | Direction | Annualised |
|---|---|---|---|---|
| 7.8000 | 7.8500 | 90 | Premium | +2.5641% |
| 7.8000 | 7.7500 | 90 | Discount | −2.5641% |
| 100.0000 | 101.0000 | 180 | Premium | +2.0000% |
Case Studies
Case 1: Compute the annualised forward premium
Currency pair spot S = 7.8, 90-day forward F = 7.85. Annualised premium?
= (7.85 − 7.8) ÷ 7.8 × (360 ÷ 90) × 100% = 0.006410 × 4 × 100% ≈ 2.5641%. Positive → forward premium.
Interpretation: (F−S)/S gives the 90-day premium (~0.64%); × (360÷90 = 4) annualises it. Annualising matters because maturities are not directly comparable (90-day 0.64% vs 180-day 0.64% differ in cost); annualised it is 'x% per year', comparable with rates and other maturities. The ~2.56% premium usually matches the ~2.56% rate differential.
Case 2: Premium set by rate gap, not a forecast
Misconception: forward premium means 'market expects appreciation'. By IRP it is set by the rate differential. Suppose currency A rate 1%, B rate 3.5%, gap 2.5%.
To stop arbitrage (borrow low A, convert to high B, earn the gap risk-free), the forward must make high-rate B show a ~2.5% forward discount and low-rate A a ~2.5% premium, offsetting the gap — matching Case 1's ~2.56%.
Interpretation: so the high-rate currency is forward-discounted (cheaper) — seemingly odd but the arbitrage necessity: if it did not depreciate forward to offset the interest edge, everyone would carry-trade until the forward adjusted. The premium/discount is a mirror of the rate gap, a pricing from arbitrage, not a prediction. Use it for hedging cost, carry-trade fairness and parity checks. Sign depends on quote direction; in stress it may deviate from pure rates. Educational/estimation only.
FAQ
What are forward premium and discount, and how computed?
Spot is the rate for immediate trade; forward is the rate agreed for future delivery. The gap is the forward premium/discount. Forward premium: forward > spot (richer later); forward discount: forward < spot (cheaper later). To compare maturities it is annualised: (forward − spot) ÷ spot × (360 ÷ days) × 100%. Example: spot 7.8, 90-day forward 7.85 → (7.85−7.8)÷7.8×(360÷90)×100% ≈ 2.5641%. Sign matters: positive premium, negative discount. Note the sign depends on the quote direction (foreign per local or vice versa) — confirm the convention first.
Is the forward premium a market forecast? What drives it?
A common and important misconception: the forward rate is NOT a forecast of the future spot, but mainly reflects the interest-rate differential — interest rate parity (IRP). Arbitrage logic: with one sum you can (A) earn currency A interest, or (B) convert to B, earn B interest, convert back at the forward. For the two to yield equally (no risk-free arbitrage), the forward must adjust to offset the rate gap. So: the lower-rate currency shows a forward premium; the higher-rate a forward discount, by about the rate differential. Counter-intuitive — a high-rate currency 'depreciates' forward — because otherwise everyone borrows low, lends high, arbitraging until the forward adjusts. Thus the forward premium/discount is a mirror of the rate gap, a pricing from arbitrage, not a prediction. See also the interest-rate-parity calculator.
What is it used for in practice?
Several uses: (1) estimate FX hedging cost — when a firm locks a forward to avoid future rate risk, the premium/discount is the hedge's price; a selling currency at a forward discount means locking a lower future price (the discount is the hedge cost), a premium may add gain. Annualising shows the hedge's annualised cost rate. (2) analyse carry-trade fairness — since it ≈ the rate gap, check whether the market forward fairly reflects rates and how much FX risk an unhedged carry trade bears. (3) check quote fairness / arbitrage — compare the theoretical premium from the rate gap with the market's; a clear deviation implies (covered) arbitrage (though transaction costs often absorb it in mature markets). (4) read market stress — in tension, some currencies' forward premium/discount deviate from pure rates (basis), signalling funding or safe-haven demand. It is the bridge between FX and rates; pair with the currency-forward and carry-trade calculators.
Covered vs uncovered interest parity, and relation to forward premium?
The forward premium rests on interest rate parity (IRP), which has covered and uncovered versions. Covered IRP (CIRP): the version this calculator maps to — a risk-free arbitrage equilibrium. If you convert to earn higher interest and simultaneously lock the forward to convert back (covered, hedged), the return should equal holding the local currency. For that, the forward must adjust so the premium/discount equals the rate gap. Because it is hedged, CIRP is a 'must hold' pricing (in mature, low-friction markets); the forward premium ≈ rate gap is its conclusion. Uncovered IRP (UIRP): no forward lock — assumes investors bear FX risk on expected future spot; it says the high-rate currency is expected to depreciate by the gap, equalising expected returns. The difference: UIRP is about expectation and bearing risk, not an arbitrage-guaranteed equality, and empirically often fails (high-rate currencies need not depreciate as expected — the source of carry-trade profits and risks). Summary: forward premium (this calculator) is CIRP's direct expression (hedged, risk-free rate gap); UIRP is about unhedged expected returns (carry-trade background). Hedge with covered (clear lock cost); carry trade means betting UIRP fails, bearing unhedged FX risk.
Practical use for hedging and cross-border investing?
The forward premium/discount bridges FX and rates, useful for corporate finance, cross-border investing and FX trading. (1) Estimate the annualised hedging cost/gain — a HK firm expecting to pay euros in six months locks a forward buy; if EUR is at a forward premium vs HKD, the locked future buy price is above spot, the premium is the hedge cost. Annualising shows the hedge's annualised cost rate (e.g. 2.5%) for budgeting vs unhedged risk. (2) Analyse carry-trade fairness/risk — since premium ≈ rate gap, an unhedged carry trade's interest gain equals the high-rate currency's forward discount, reminding you the gain has an FX-risk 'price' already priced by the forward market. (3) Check quote fairness/arbitrage — compare theoretical premium (from rate gap) with the market's; clear deviation implies (covered) arbitrage, though costs absorb it. (4) Read stress — in tension, USD's forward premium/discount can deviate from pure rates (basis), signalling funding/safe-haven demand. For HK investors, HKD and USD are tightly linked (Linked Exchange Rate), so premiums are usually small; but for EUR/JPY/CNY assets or trade, the forward premium is the core hedging-cost tool. Sign depends on quote direction; educational/estimation only, not advice.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.