Interest Rate Parity

Covered interest rate parity is enforced by a four-leg trade that has no net cash outlay and no residual currency exposure. An investor borrows one currency, converts the proceeds at spot, invests in the second currency's money market for the same tenor, and simultaneously sells the maturing foreign proceeds forward. Because every leg is contracted today, the terminal payoff is known with certainty. If it exceeds the cost of the initial borrowing, the trade is riskless profit, and dealers will bid the forward rate until the gap closes.

The resulting condition, written with the quote convention of price currency per unit of base currency, is that the forward rate equals the spot rate multiplied by the ratio of one plus the price-currency interest rate for the period to one plus the base-currency interest rate for the period. Money market rates are annualised, so each must be scaled by the actual day count over the relevant basis, typically 360 days, before being applied.

Dealers do not quote outright forwards for most tenors; they quote forward points, the difference between the forward and the spot rate expressed in pips. Rearranging the parity condition, forward points equal the spot rate multiplied by the interest rate differential for the period divided by one plus the base-currency rate for the period. When the base currency carries the higher rate, the differential is negative and the points are negative: the base currency trades at a forward discount.

This is why the FX swap market, not the deposit market, is the primary channel through which institutions raise foreign currency. A European bank needing dollars typically sells euros spot against dollars and simultaneously buys them back forward, paying the implied dollar rate embedded in the forward points. The forward curve is therefore a direct reading of relative money market pricing, and the cross-currency basis measures the extent to which it deviates from clean parity.

Uncovered interest rate parity replaces the contracted forward rate with the expected future spot rate: the high-yield currency is expected to depreciate by roughly the interest rate differential, leaving expected returns equal across currencies. Unlike its covered counterpart, this condition is not enforced by arbitrage, because the investor bears unhedged currency risk. It is a statement about expectations and risk neutrality, not a pricing identity.

Empirically, uncovered parity fails badly over short and medium horizons. High-yield currencies have historically tended to appreciate, or at least depreciate by less than the differential, generating positive average carry trade returns punctuated by sharp drawdowns during risk-off episodes. This forward rate bias means the forward rate is a poor forecaster of the future spot rate, though evidence for convergence toward parity strengthens over multi-year horizons.

Candidates should be able to move fluently in three directions: compute a forward rate from spot and two money market rates, back out an implied interest rate from a quoted forward, and test a set of quoted rates for an arbitrage opportunity. Accuracy depends almost entirely on discipline with conventions. Identify which currency is the base and which is the price currency before touching the arithmetic, apply the correct day count to each annualised rate, and remember that the price-currency rate belongs in the numerator.

The second skill is directional reasoning without a calculator. Given only that one currency's rates rise relative to another's, a candidate should immediately state whether that currency moves to a forward premium or discount, whether forward points widen or narrow, and what the change implies for the hedged return of a foreign bond portfolio. Linking parity to the mark-to-market of a hedged position is a frequent application in later curriculum levels.