Derive a forward rate from the two interest rates and explain a currency's forward premium or discount
The idea
Covered interest rate parity ties the forward rate to spot and the interest differential, because otherwise investors could borrow, convert, invest and hedge for a riskless profit. With quotes as price/base, F = S x (1 + i_price x t)/(1 + i_base x t), where t is the fraction of a year, often days/360. If the price currency has the higher rate, the forward exceeds spot and the base currency trades at a forward premium. Under covered parity, the higher-rate currency trades at a forward discount. Forward points are (F - S) scaled to the last quoted decimal, usually x 10,000, so +35 points on 1.2500 gives 1.2535. As a percentage, the premium or discount is F/S - 1. The forward is not a forecast; it simply reflects the interest differential.
A practice question
Under covered interest parity, the currency with the lower interest rate will trade at a:
- forward premium — correct
- forward discountWhy not: A forward discount applies to the higher-rate currency, offsetting its interest advantage.
- forward rate equal to spotWhy not: Forward equals spot only when the two interest rates are identical.
If the low-rate currency did not appreciate in the forward market, investors could borrow it, invest in the high-rate currency and hedge at no cost. The forward premium removes that arbitrage.
A harder one
Spot USD/GBP is 1.2600 (dollars per pound). One-year rates are 4.0% in the US and 5.0% in the UK. The one-year forward rate and the pound's forward position are:
- 1.2721, pound at a premiumWhy not: This puts the UK rate in the numerator; the price currency's rate (USD) belongs on top.
- 1.2480, pound at a discount — correct
- 1.2480, pound at a premiumWhy not: The forward is right, but it is below spot, so the pound buys fewer dollars forward, a discount.
F = S x (1 + i_USD)/(1 + i_GBP) = 1.2600 x 1.04/1.05 = 1.2480. The higher-rate pound trades at a forward discount that offsets its interest advantage.
The hardest tier
Spot CHF/USD is 0.9000 (francs per dollar) and the one-year forward is 0.8820. If the one-year USD rate is 5.0%, the CHF rate implied by covered interest parity is closest to:
- 3.00%Why not: Subtracting the 2% forward discount from 5% is only the linear approximation of the parity relationship.
- 2.90% — correct
- 7.14%Why not: This inverts the forward-to-spot ratio, implying the franc is the higher-rate currency when its forward premium says otherwise.
F/S = (1 + i_CHF)/(1 + i_USD), so 1 + i_CHF = (0.8820/0.9000) x 1.05 = 0.98 x 1.05 = 1.029, giving 2.90%. The dollar's 2% forward discount reflects its higher interest rate.
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