Forward exchange rate
Encyclopedia
The forward exchange rate (also referred to as forward rate or forward price) is the rate at which a bank
is willing to exchange one currency
for another at some specified future date. The forward exchange rate is a type of forward price
. It is the exchange rate
negotiated today between a bank and a client upon entering into a forward contract
agreeing to buy or sell some amount of foreign currency at a future date. The forward exchange rate is determined by the relationship among the spot exchange rate and differences in interest rates between two countries. Forward exchange rates have important theoretical implications in forecasting future spot exchange rates.
Multinational corporation
s often use the forward market
to hedge
future payables or receivables denominated in a foreign currency against foreign exchange risk by using a forward contract to lock in a forward exchange rate. Hedging with forward contracts is typically used for larger transactions, while futures contract
s are used for smaller transactions. This is due to the customization afforded to banks by forward contracts traded over-the-counter
, versus the standardization of futures contracts which are traded on an exchange
. Banks typically quote forward rates for major currencies
in maturities
of 1, 3, 6, 9, or 12 months, however in some cases quotations for greater maturities are available up to 5 or 10 years.
, and the foreign interest rate. This effectively means that the forward rate is the price of a forward contract, which derives
its value from the pricing of spot contracts and the addition of information on available interest rates.
The following equation represents covered interest rate parity, a no-arbitrage
condition under which investors eliminate exposure to exchange rate risk (unanticipated changes in exchange rates) with the use of a forward contract - the exchange rate risk is effectively covered. The reason for the no-arbitrage condition is that the dollar return
on dollar deposits
, 1+i$, is set equal to the dollar return on euro deposits, F/S(1+ic). If these two returns weren't equal, there would be a potential arbitrage opportunity in which an investor could borrow currency in the country with the lower interest rate, convert to the foreign currency at today's spot exchange rate, and invest in the foreign country with the higher interest rate. Investors will be indifferent to the interest rates on deposits in these countries due to the equilibrium resulting from the forward exchange rate.
where
This equation can be arranged such that it solves for the forward rate:
The forward exchange rate differs by a premium or discount of the spot exchange rate:
where
The equation can be rearranged as follows to solve for the forward premium/discount:
In practice, forward premiums and discounts are quoted as annualized percentage deviations from the spot exchange rate, in which case it is necessary to account for the number of days to delivery as in the following example.
where
For example, to calculate the 6-month forward premium or discount for the euro versus the dollar deliverable in 30 days, given a spot rate quote of 1.2238 $/€ and a 6-month forward rate quote of 1.2260 $/€:
The resulting 0.021572 is positive, so one would say that the euro is trading at a 0.021572 or 2.16% premium against the dollar for delivery in 30 days. Conversely, if one were to work this example in euro terms rather than dollar terms, the perspective would be reversed and one would say that the dollar is trading at a discount against the euro.
and risk neutral
ity, the forward exchange rate is an unbiased predictor of the expected future spot exchange rate. Without introducing a foreign exchange risk premium
(due to the assumption of risk neutrality), the following equation illustrates the unbiasedness hypothesis.
where
is the forward exchange rate at time t
is the expected future spot exchange rate at time t + k
The unbiasedness hypothesis is a well-recognized puzzle among finance researchers. Empirical evidence for cointegration
between the forward rate and the future spot rate is mixed. Researchers have published papers demonstrating empirical failure of the hypothesis by conducting regression analyses
of the realized changes in spot exchange rates on forward premiums and finding negative slope coefficients. These researchers offer numerous rationales for such failure. One rationale centers around the relaxation of risk neutrality, while still assuming rational expectations, such that a foreign exchange risk premium may exist that can account for differences between the forward rate and the expected future spot rate.
The following equation represents the forward rate as being equal to an expected future spot rate and a risk premium (not to be confused with a forward premium):
The current spot rate can be introduced so that the equation solves for the forward-spot differential (the difference between the forward rate and the current spot rate):
Eugene Fama
concluded that large positive correlations of the difference between the forward exchange rate and the current spot exchange rate signal variations over time in the premium component of the forward-spot differential
or in the forecast of the expected change in the spot exchange rate. Fama suggested that slope coefficients in the regressions of the difference between the forward rate and the future spot rate 
, and the expected change in the spot rate 
, on the forward-spot differential 
which are different from 0 imply variations over time in both components of the forward-spot differential: the premium and the expected change in the spot rate. Fama's findings were sought to be empirically validated by a significant body of research, ultimately finding that large variance in expected changes in the spot rate could only be accounted for by risk aversion coefficients that were deemed "unacceptably high."
Other rationales for the failure of the forward rate unbiasedness hypothesis include considering the conditional bias to be an exogenous variable explained by a policy aimed at smoothing interest rates and stabilizing exchange rates, or considering that an economy allowing for discrete changes could facilitate excess returns in the forward market. Some researchers have contested empirical failures of the hypothesis and have sought to explain conflicting evidence as resulting from contaminated data and even inappropriate selections of the time length of forward contracts.
Commercial bank
After the implementation of the Glass–Steagall Act, the U.S. Congress required that banks engage only in banking activities, whereas investment banks were limited to capital market activities. As the two no longer have to be under separate ownership under U.S...
is willing to exchange one currency
Currency
In economics, currency refers to a generally accepted medium of exchange. These are usually the coins and banknotes of a particular government, which comprise the physical aspects of a nation's money supply...
for another at some specified future date. The forward exchange rate is a type of forward price
Forward price
The forward price is the agreed upon price of an asset in a forward contract. Using the rational pricing assumption, for a forward contract on an underlying asset that is tradeable, we can express the forward price in terms of the spot price and any dividends etc...
. It is the exchange rate
Exchange rate
In finance, an exchange rate between two currencies is the rate at which one currency will be exchanged for another. It is also regarded as the value of one country’s currency in terms of another currency...
negotiated today between a bank and a client upon entering into a forward contract
Forward contract
In finance, a forward contract or simply a forward is a non-standardized contract between two parties to buy or sell an asset at a specified future time at a price agreed today. This is in contrast to a spot contract, which is an agreement to buy or sell an asset today. It costs nothing to enter a...
agreeing to buy or sell some amount of foreign currency at a future date. The forward exchange rate is determined by the relationship among the spot exchange rate and differences in interest rates between two countries. Forward exchange rates have important theoretical implications in forecasting future spot exchange rates.
Multinational corporation
Multinational corporation
A multi national corporation or enterprise , is a corporation or an enterprise that manages production or delivers services in more than one country. It can also be referred to as an international corporation...
s often use the forward market
Forward market
The forward market is the over-the-counter financial market in contracts for future delivery, so called forward contracts. Forward contracts are personalized between parties The forward market is the over-the-counter financial market in contracts for future delivery, so called forward contracts. ...
to hedge
Hedge (finance)
A hedge is an investment position intended to offset potential losses that may be incurred by a companion investment.A hedge can be constructed from many types of financial instruments, including stocks, exchange-traded funds, insurance, forward contracts, swaps, options, many types of...
future payables or receivables denominated in a foreign currency against foreign exchange risk by using a forward contract to lock in a forward exchange rate. Hedging with forward contracts is typically used for larger transactions, while futures contract
Futures contract
In finance, a futures contract is a standardized contract between two parties to exchange a specified asset of standardized quantity and quality for a price agreed today with delivery occurring at a specified future date, the delivery date. The contracts are traded on a futures exchange...
s are used for smaller transactions. This is due to the customization afforded to banks by forward contracts traded over-the-counter
Over-the-counter (finance)
Within the derivatives markets, many products are traded through exchanges. An exchange has the benefit of facilitating liquidity and also mitigates all credit risk concerning the default of a member of the exchange. Products traded on the exchange must be well standardised to transparent trading....
, versus the standardization of futures contracts which are traded on an exchange
Exchange (organized market)
An exchange is a highly organized market where tradable securities, commodities, foreign exchange, futures, and options contracts are sold and bought.-Description:...
. Banks typically quote forward rates for major currencies
Hard currency
Hard currency , in economics, refers to a globally traded currency that is expected to serve as a reliable and stable store of value...
in maturities
Maturity (finance)
In finance, maturity or maturity date refers to the final payment date of a loan or other financial instrument, at which point the principal is due to be paid....
of 1, 3, 6, 9, or 12 months, however in some cases quotations for greater maturities are available up to 5 or 10 years.
Forward exchange rate determinants
Covered interest rate parity offers an explanation of what determines forward exchange rates. The forward exchange rate is determined by three known variables: the spot exchange rate, the domestic interest rateInterest rate
An interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender. For example, a small company borrows capital from a bank to buy new assets for their business, and in return the lender receives interest at a predetermined interest rate for...
, and the foreign interest rate. This effectively means that the forward rate is the price of a forward contract, which derives
Derivative (finance)
A derivative instrument is a contract between two parties that specifies conditions—in particular, dates and the resulting values of the underlying variables—under which payments, or payoffs, are to be made between the parties.Under U.S...
its value from the pricing of spot contracts and the addition of information on available interest rates.
The following equation represents covered interest rate parity, a no-arbitrage
Arbitrage
In economics and finance, arbitrage is the practice of taking advantage of a price difference between two or more markets: striking a combination of matching deals that capitalize upon the imbalance, the profit being the difference between the market prices...
condition under which investors eliminate exposure to exchange rate risk (unanticipated changes in exchange rates) with the use of a forward contract - the exchange rate risk is effectively covered. The reason for the no-arbitrage condition is that the dollar return
Rate of return
In finance, rate of return , also known as return on investment , rate of profit or sometimes just return, is the ratio of money gained or lost on an investment relative to the amount of money invested. The amount of money gained or lost may be referred to as interest, profit/loss, gain/loss, or...
on dollar deposits
Demand deposit
Demand deposits, bank money or scriptural money are funds held in demand deposit accounts in commercial banks. These account balances are usually considered money and form the greater part of the money supply of a country.-History:...
, 1+i$, is set equal to the dollar return on euro deposits, F/S(1+ic). If these two returns weren't equal, there would be a potential arbitrage opportunity in which an investor could borrow currency in the country with the lower interest rate, convert to the foreign currency at today's spot exchange rate, and invest in the foreign country with the higher interest rate. Investors will be indifferent to the interest rates on deposits in these countries due to the equilibrium resulting from the forward exchange rate.
where
- F is the forward exchange rate
- S is the current spot exchange rate
- i$ is the interest rate in the US
- ic is the interest rate in a foreign country or currency area (for this example, it is the interest rate available in the EurozoneEurozoneThe eurozone , officially called the euro area, is an economic and monetary union of seventeen European Union member states that have adopted the euro as their common currency and sole legal tender...
)
This equation can be arranged such that it solves for the forward rate:
Forward premium or discount
The equilibrium that results from the relationship between forward and spot exchange rates within the context of covered interest rate parity is responsible for eliminating or correcting for market inefficiencies that would create potential for arbitrage profits. As such, arbitrage opportunities are fleeting. In order for this equilibrium to hold under differences in interest rates between two countries, the forward exchange rate must generally differ from the spot exchange rate, such that a no-arbitrage condition is sustained. Therefore, the forward rate is said to contain a premium or discount, reflecting the interest rate differential between two countries. The following equations demonstrate how the forward premium or discount is calculated.The forward exchange rate differs by a premium or discount of the spot exchange rate:
where
- P is the premium (if positive) or discount (if negative)
The equation can be rearranged as follows to solve for the forward premium/discount:
In practice, forward premiums and discounts are quoted as annualized percentage deviations from the spot exchange rate, in which case it is necessary to account for the number of days to delivery as in the following example.
where
- N represents the maturity of a given forward exchange rate quote
- d represents the number of days to delivery
For example, to calculate the 6-month forward premium or discount for the euro versus the dollar deliverable in 30 days, given a spot rate quote of 1.2238 $/€ and a 6-month forward rate quote of 1.2260 $/€:
The resulting 0.021572 is positive, so one would say that the euro is trading at a 0.021572 or 2.16% premium against the dollar for delivery in 30 days. Conversely, if one were to work this example in euro terms rather than dollar terms, the perspective would be reversed and one would say that the dollar is trading at a discount against the euro.
Unbiasedness hypothesis
The unbiasedness hypothesis states that given conditions of rational expectationsRational expectations
Rational expectations is a hypothesis in economics which states that agents' predictions of the future value of economically relevant variables are not systematically wrong in that all errors are random. An alternative formulation is that rational expectations are model-consistent expectations, in...
and risk neutral
Risk neutral
In economics and finance, risk neutral behavior is between risk aversion and risk seeking. If offered either €50 or a 50% chance of each of €100 and nothing, a risk neutral person would have no preference between the two options...
ity, the forward exchange rate is an unbiased predictor of the expected future spot exchange rate. Without introducing a foreign exchange risk premium
Risk premium
A risk premium is the minimum amount of money by which the expected return on a risky asset must exceed the known return on a risk-free asset, in order to induce an individual to hold the risky asset rather than the risk-free asset...
(due to the assumption of risk neutrality), the following equation illustrates the unbiasedness hypothesis.
where
is the forward exchange rate at time t is the expected future spot exchange rate at time t + k
- k is the number of periods into the future from time t
The unbiasedness hypothesis is a well-recognized puzzle among finance researchers. Empirical evidence for cointegration
Cointegration
Cointegration is a statistical property of time series variables. Two or more time series are cointegrated if they share a common stochastic drift.-Introduction:...
between the forward rate and the future spot rate is mixed. Researchers have published papers demonstrating empirical failure of the hypothesis by conducting regression analyses
Regression analysis
In statistics, regression analysis includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables...
of the realized changes in spot exchange rates on forward premiums and finding negative slope coefficients. These researchers offer numerous rationales for such failure. One rationale centers around the relaxation of risk neutrality, while still assuming rational expectations, such that a foreign exchange risk premium may exist that can account for differences between the forward rate and the expected future spot rate.
The following equation represents the forward rate as being equal to an expected future spot rate and a risk premium (not to be confused with a forward premium):
The current spot rate can be introduced so that the equation solves for the forward-spot differential (the difference between the forward rate and the current spot rate):
Eugene Fama
Eugene Fama
Eugene Francis "Gene" Fama is an American economist, known for his work on portfolio theory and asset pricing, both theoretical and empirical. He is currently Robert R...
concluded that large positive correlations of the difference between the forward exchange rate and the current spot exchange rate signal variations over time in the premium component of the forward-spot differential
or in the forecast of the expected change in the spot exchange rate. Fama suggested that slope coefficients in the regressions of the difference between the forward rate and the future spot rate , and the expected change in the spot rate , on the forward-spot differential which are different from 0 imply variations over time in both components of the forward-spot differential: the premium and the expected change in the spot rate. Fama's findings were sought to be empirically validated by a significant body of research, ultimately finding that large variance in expected changes in the spot rate could only be accounted for by risk aversion coefficients that were deemed "unacceptably high."Other rationales for the failure of the forward rate unbiasedness hypothesis include considering the conditional bias to be an exogenous variable explained by a policy aimed at smoothing interest rates and stabilizing exchange rates, or considering that an economy allowing for discrete changes could facilitate excess returns in the forward market. Some researchers have contested empirical failures of the hypothesis and have sought to explain conflicting evidence as resulting from contaminated data and even inappropriate selections of the time length of forward contracts.