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| {{Distinguish|forward rate|forward price}}
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| The '''forward exchange rate''' (also referred to as '''forward rate''' or '''forward price''') is the [[exchange rate]] at which a [[commercial bank|bank]] agrees to exchange one [[currency]] for another at a future date when it enters into a [[forward contract]] with an investor.<ref name="Madura 2007">{{Cite book | title = International Financial Management: Abridged 8th Edition | author = Madura, Jeff | year = 2007 | publisher = Thomson South-Western | location = Mason, OH | isbn = 0-324-36563-2}}</ref><ref name="Eun & Resnick 2011">{{Cite book | title = International Financial Management, 6th Edition | author = Eun, Cheol S. | author2 = Resnick, Bruce G. | year = 2011 | publisher = McGraw-Hill/Irwin | location = New York, NY | isbn = 978-0-07-803465-7}}</ref><ref name="Levi 2005">{{Cite book | title = International Finance, 4th Edition | author = Levi, Maurice D. | year = 2005 | publisher = Routledge | location = New York, NY | isbn = 978-0-415-30900-4}}</ref> [[Multinational corporation]]s, banks, and other [[financial institution]]s enter into forward contracts to take advantage of the forward rate for [[hedge (finance)|hedging]] purposes.<ref name="Madura 2007" /> The forward exchange rate is determined by a parity relationship among the [[spot exchange rate]] and differences in [[interest rate]]s between two countries, which reflects an [[economic equilibrium]] in the [[foreign exchange market]] under which [[arbitrage]] opportunities are eliminated. When in equilibrium, and when interest rates vary across two countries, the parity condition implies that the forward rate includes a premium or discount reflecting the interest rate differential. Forward exchange rates have important theoretical implications for forecasting future spot exchange rates. [[Financial economics|Financial economists]] have put forth a hypothesis that the forward rate accurately predicts the future spot rate, for which [[empirical evidence]] is mixed.
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| ==Introduction==
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| The forward exchange rate is the rate at which a commercial bank is willing to commit to exchange one currency for another at some specified future date.<ref name="Madura 2007" /> 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 in the future.<ref name="Eun & Resnick 2011" /><ref name="Levi 2005" /> Multinational corporations and financial institutions often use the [[forward market]] to hedge future [[accounts payable|payable]]s or [[accounts receivable|receivable]]s 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 (finance)|over-the-counter]], versus the standardization of futures contracts which are traded on an [[exchange (organized market)|exchange]].<ref name="Madura 2007" /> Banks typically quote forward rates for [[hard currency|major currencies]] in [[maturity (finance)|maturities]] of one, three, six, nine, or twelve months, however in some cases quotations for greater maturities are available up to five or ten years.<ref name="Eun & Resnick 2011" />
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| ==Relation to covered interest rate parity==
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| [[interest rate parity#Covered interest rate parity|Covered interest rate parity]] is a no-arbitrage condition in foreign exchange markets which depends on the availability of the forward market. It can be rearranged to give the forward exchange rate as a function of the other variables. The forward exchange rate depends on three known variables: the spot exchange rate, the domestic interest rate, and the foreign interest rate. This effectively means that the forward rate is the price of a forward contract, which [[derivative (finance)|derives]] its value from the pricing of [[spot contract]]s and the addition of information on available interest rates.<ref name="Feenstra & Taylor 2008">{{Cite book| title = International Macroeconomics | author = Feenstra, Robert C. | author2 = Taylor, Alan M. | year = 2008 | publisher = Worth Publishers | location = New York, NY | isbn = 978-1-4292-0691-4}}</ref>
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| The following equation represents covered interest rate parity, a condition under which investors eliminate exposure to foreign exchange risk (unanticipated changes in exchange rates) with the use of a forward contract – the exchange rate risk is effectively ''covered''. Under this condition, a domestic investor would earn equal returns from investing in domestic assets or converting currency at the spot exchange rate, investing in foreign currency assets in a country with a different interest rate, and exchanging the foreign currency for domestic currency at the negotiated forward exchange rate. Investors will be indifferent to the interest rates on deposits in these countries due to the equilibrium resulting from the forward exchange rate. The condition allows for no arbitrage opportunities because the [[rate of return|return]] on domestic [[demand deposit|deposits]], 1+''i<sub>d</sub>'', is equal to the return on foreign deposits, ''F/S''(1+''i<sub>f</sub>''). If these two returns weren't equalized by the use of a forward contract, there would be a potential arbitrage opportunity in which, for example, 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.<ref name="Feenstra & Taylor 2008" />
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| :<math>(1+i_d) = \frac {F} S (1+i_f)</math>
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| where | |
| :''F'' is the forward exchange rate
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| :''S'' is the current spot exchange rate
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| :''i<sub>d</sub>'' is the interest rate in domestic currency
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| :''i<sub>f</sub>'' is the interest rate in foreign currency
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| This equation can be arranged such that it solves for the forward rate:
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| :<math>F = S \frac {(1+i_d)} {(1+i_f)}</math>
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| ==Forward premium or discount==
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| 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.<ref name="Madura 2007" /><ref name="Eun & Resnick 2011" />
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| The forward exchange rate differs by a premium or discount of the spot exchange rate:
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| :<math>F = S(1 + P)</math>
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| where
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| :''P'' is the premium (if positive) or discount (if negative)
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| The equation can be rearranged as follows to solve for the forward premium/discount:
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| :<math>P = \frac {F} S - 1</math>
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| 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.<ref name="Eun & Resnick 2011" />
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| :<math>P_N = (\frac {F} S - 1) \frac {360} d</math>
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| where
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| :''N'' represents the maturity of a given forward exchange rate quote
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| :''d'' represents the number of days to delivery
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| 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 $/€:
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| :<math>P_6 = (\frac {1.2260} {1.2238} - 1) \frac {360} {30} = 0.021572 = 2.16%</math>
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| 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.
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| ==Forecasting future spot exchange rates==
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| ===Unbiasedness hypothesis===
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| The unbiasedness hypothesis states that given conditions of [[rational expectations]] and [[risk neutral]]ity, the forward exchange rate is an unbiased predictor of the 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.<ref name="Levi 2005" /><ref name="Delcoure et al. 2003">{{Cite journal | title = The Forward Rate Unbiasedness Hypothesis Reexamined: Evidence from a New Test | journal = Global Finance Journal | volume = 14 | issue = 1 | year = 2003 | pages = 83–93 | author = Delcoure, Natalya | author2 = Barkoulas, John | author3 = Baum, Christopher F. | author4 = Chakraborty, Atreya | url = http://www.sciencedirect.com/science/article/pii/S1044028303000061 | accessdate = 2011-06-21 | doi=10.1016/S1044-0283(03)00006-1}}</ref><ref name="Ho 2003">{{Cite journal | title = A re-examination of the unbiasedness forward rate hypothesis using dynamic SUR model | journal = The Quarterly Review of Economics and Finance | volume = 43 | issue = 3 | year = 2003 | pages = 542–559 | author = Ho, Tsung-Wu | url = http://www.sciencedirect.com/science/article/pii/S1062976902001710 | accessdate = 2011-06-23 | doi=10.1016/S1062-9769(02)00171-0}}</ref><ref name="Sosvilla-Rivero & Park 1992">{{Cite journal | title = Further tests on the forward exchange rate unbiasedness hypothesis | journal = Economics Letters | volume = 40 | issue = 3 | year = 1992 | pages = 325–331 | author = Sosvilla-Rivero, Simón | author2 = Park, Young B. | url = http://www.sciencedirect.com/science/article/pii/016517659290013O | accessdate = 2011-06-27 | doi=10.1016/0165-1765(92)90013-O}}</ref>
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| :<math>F_t = E_t(S_{t + k})</math>
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| where
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| :<math>F_t</math> is the forward exchange rate at time ''t''
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| :<math>E_t(S_{t + k})</math> is the expected future spot exchange rate at time ''t + k''
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| :''k'' is the number of periods into the future from time ''t''
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| The empirical rejection of 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.<ref name="Delcoure et al. 2003" /><ref name="Moffett et al. 2009">{{Cite book | title = Fundamentals of Multinational Finance, 3rd Edition | author = Moffett, Michael H. | author2 = Stonehill, Arthur I. | author3 = Eiteman, David K. | year = 2009 | publisher = Addison-Wesley | location = Boston, MA | isbn = 978-0-321-54164-2}}</ref><ref name="Villanueva 2007">{{Cite journal | title = Spot-forward cointegration, structural breaks and FX market unbiasedness | journal = International Financial Markets, Institutions & Money | volume = 17 | issue = 1 | year = 2007 | pages = 58–78 | author = Villanueva, O. Miguel | url = http://www.sciencedirect.com/science/article/pii/S1042443105000764 | accessdate = 2011-06-22 | doi=10.1016/j.intfin.2005.08.007}}</ref> Researchers have published papers demonstrating empirical failure of the hypothesis by conducting [[regression analysis|regression analyses]] of the realized changes in spot exchange rates on forward premiums and finding negative slope coefficients.<ref name="Zivot 2000">{{Cite journal | title = Cointegration and forward and spot exchange rate regressions | journal = Journal of International Money and Finance | volume = 19 | issue = 6 | year = 2000 | pages = 785–812 | author = Zivot, Eric | url = http://www.sciencedirect.com/science/article/pii/S0261560600000310 | accessdate = 2011-06-22 | doi=10.1016/S0261-5606(00)00031-0}}</ref> 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 future spot rate.<ref name="Diamandis et al. 2008">{{Cite journal | title = Testing the forward rate unbiasedness hypothesis during the 1920s | journal = International Financial Markets, Institutions & Money | volume = 18 | issue = 4 | year = 2008 | pages = 358–373 | author = Diamandis, Panayiotis F. | author2 = Georgoutsos, Dimitris A. | author3 = Kouretas, Georgios P. | url = http://www.sciencedirect.com/science/article/pii/S1042443107000212 | accessdate = 2011-06-23 | doi=10.1016/j.intfin.2007.04.003}}</ref>
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| The following equation represents the forward rate as being equal to an future spot rate and a risk premium (not to be confused with a ''forward premium''):<ref name="Fama 1984">{{Cite journal | title = Forward and spot exchange rates | journal = Journal of Monetary Economics | volume = 14 | issue = 3 | year = 1984 | pages = 319–338 | author = Fama, Eugene F. | url = http://www.sciencedirect.com/science/article/pii/0304393284900461 | accessdate = 2011-06-20 | doi=10.1016/0304-3932(84)90046-1}}</ref>
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| :<math>F_t = E_t(S_{t + 1}) + P_t</math>
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| 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):
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| :<math>F_t - S_t = E_t(S_{t + 1} - S_t) + P_t</math>
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| [[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 <math>F_t - S_t</math> 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 <math>F_t - S_{t + 1}</math>, and the expected change in the spot rate <math>E_t(S_{t + 1} - S_t)</math>, on the forward-spot differential <math>F_t - S_t</math> which are different from zero imply variations over time in both components of the forward-spot differential: the premium and the expected change in the spot rate.<ref name="Fama 1984" /> 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."<ref name="Sosvilla-Rivero & Park 1992" /><ref name="Diamandis et al. 2008" /> Other researchers have found that the unbiasedness hypothesis has been rejected in both cases where there is evidence of risk premia varying over time and cases where risk premia are constant.<ref name="Chatterjee 2010">{{Cite thesis | title = Three essays in forward rate unbiasedness hypothesis | publisher = Utah State University | date = 2010 | pages = 1-102 | author = Chatterjee, Devalina | url = http://digitalcommons.usu.edu/etd/644 | accessdate = 2012-06-21}}</ref>
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| Other rationales for the failure of the forward rate unbiasedness hypothesis include considering the conditional bias to be an [[exogeny|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.<ref name="Diamandis et al. 2008" /> Economists demonstrated that the forward rate could serve as a useful proxy for future spot exchange rates between currencies with [[liquidity premium|liquidity premia]] that average out to zero during the onset of floating exchange rate regimes in the 1970s.<ref name="Cornell 1977">{{Cite journal | title = Spot rates, forward rates and exchange market efficiency | journal = Journal of Financial Economics | volume = 5 | issue = 1 | year = 1977 | pages = 55–65 | author = Cornell, Bradford | url = http://www.sciencedirect.com/science/article/pii/0304405X77900290 | accessdate = 2011-06-28 | doi=10.1016/0304-405X(77)90029-0}}</ref> Research examining the introduction of [[endogenous]] breaks to test the structural stability of cointegrated spot and forward exchange rate time series have found some evidence to support forward rate unbiasedness in both the short and long term.<ref name="Villanueva 2007" />
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| ==See also==
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| *[[Foreign exchange derivative]]
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| ==References==
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| {{Reflist|2}}
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| {{good article}}
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| [[Category:Financial economics]]
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| [[Category:Financial terminology]]
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| [[Category:Foreign exchange market]]
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| [[Category:International finance]]
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Hi there, I am Andrew Berryhill. To perform lacross is something I really appreciate doing. Distributing manufacturing has been his profession for some time. Ohio is where my home is but my spouse desires us to move.
Here is my blog post ... phone psychic readings