Forward Premium
A forward premium is the amount by which the forward exchange rate of a currency exceeds its spot rate. A forward premium indicates that the market expects the currency to appreciate, or that the interest rate on the currency is lower than on the other currency.
Definition
The forward premium is the difference between the forward rate and the spot rate, expressed as a percentage of the spot rate, often annualised. If the forward rate is above the spot rate, the currency is at a forward premium; if it is below, the currency is at a forward discount.
The forward premium is related to the interest rate differential between the two currencies through covered interest parity. According to covered interest parity, the forward premium equals the difference between the interest rates on the two currencies, so that arbitrage is unprofitable.
Covered Interest Parity
Covered interest parity is the proposition that the return on a domestic asset equals the return on a foreign asset hedged into domestic currency. If the two returns differ, arbitrageurs can borrow in one currency, invest in the other, and hedge the exchange rate risk, earning a riskless profit.
Covered interest parity implies that the forward premium equals the interest rate differential. The relationship holds closely in normal times, because deviations would be arbitraged away. During periods of stress, deviations can arise, reflecting limits to arbitrage and the balance sheet constraints of financial institutions.
Uncovered Interest Parity
Uncovered interest parity is the proposition that the expected return on a domestic asset equals the expected return on a foreign asset, without hedging. It implies that the expected change in the exchange rate equals the interest rate differential.
Uncovered interest parity does not hold as closely as the covered version. The evidence suggests that high-interest-rate currencies tend to depreciate less than the theory predicts, a pattern known as the forward premium anomaly. The anomaly has been explained by risk premia, by the behaviour of investors, and by limits to arbitrage.
Implications
The forward premium is used in the analysis of exchange rate expectations and of the pricing of currency derivatives. It is used in the hedging decisions of firms, which compare the forward premium with their expectations of the exchange rate.
The forward premium is also relevant to the analysis of carry trades, in which investors borrow in a low-interest-rate currency and invest in a high-interest-rate currency. The carry trade earns the interest rate differential but is exposed to exchange rate risk, and the forward premium provides information about the compensation for that risk.
The Forward Premium and Expectations
The forward premium provides information about the expectations of the market. According to the expectations hypothesis, the forward rate is an unbiased predictor of the future spot rate, so that the forward premium reflects the expected change in the exchange rate.
The expectations hypothesis does not hold exactly. The forward rate is a biased predictor of the future spot rate, and the bias is related to the interest rate differential, a pattern known as the forward premium puzzle. The puzzle suggests that there is a risk premium in the forward market, or that investors behave in ways that the theory does not capture.
The puzzle has been explained by several factors, including the behaviour of investors, the constraints on arbitrage, and the presence of peso problems, in which rare events are not observed in the sample but affect expectations.
The Carry Trade
The carry trade is a strategy of borrowing in a currency with a low interest rate and investing in a currency with a high interest rate. The trade earns the interest rate differential, and it is exposed to the risk that the high-interest-rate currency depreciates.
The carry trade has been profitable on average, which is consistent with the forward premium puzzle. The profitability compensates for the risk of large losses during periods of stress, when the high-interest-rate currency depreciates sharply and the trade is unwound.
The carry trade is used by hedge funds and by other investors, and it can affect the behaviour of exchange rates. The unwinding of carry trades during periods of stress can amplify exchange rate movements and can contribute to financial instability.
Forward Premium and Hedging
Firms use the forward market to hedge their exposure to exchange rates. A firm with a future payment in a foreign currency can buy the currency forward, locking in the exchange rate and eliminating the risk of a change.
The cost or benefit of hedging depends on the forward premium. A firm that buys a currency at a forward premium pays more than the spot rate, while a firm that sells at a forward premium receives more. The forward premium therefore affects the terms on which firms hedge.
The decision to hedge depends on the risk aversion of the firm, on its exposure, and on the cost of hedging. Firms with large exposures and with limited ability to absorb risk are more likely to hedge, while firms that can pass on the cost of exchange rate changes to their customers may choose not to.
Summary
The forward premium is a central concept in the analysis of exchange rates, reflecting the interest rate differential and the expectations of the market. Its relationship with expectations, with the carry trade, and with hedging informs the understanding of currency markets.