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| The '''international Fisher effect''' (sometimes referred to as '''Fisher's open hypothesis''') is a hypothesis in [[international finance]] that suggests differences in [[nominal interest rate]]s reflect expected changes in the spot [[exchange rate]] between countries.<ref name="Buckley 2004">{{Cite book | title = Multinational Finance | author = Buckley, Adrian | year = 2004 | publisher = Pearson Education Limited | location = Harlow, UK | isbn = 978-0-273-68209-7}}</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> The hypothesis specifically states that a spot exchange rate is expected to change equally in the opposite direction of the interest rate differential; thus, the [[currency]] of the country with the higher nominal interest rate is expected to depreciate against the currency of the country with the lower nominal interest rate, as higher nominal interest rates reflect an expectation of [[inflation]].<ref name="Eun & Resnick 2011" /><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>
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| ==Derivation of the international Fisher effect==
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| The international Fisher effect is an extension of the [[Fisher effect]] hypothesized by American economist [[Irving Fisher]]. The Fisher effect states that a change in a country's expected inflation rate will result in a proportionate change in the country's interest rate,<ref name="Eun & Resnick 2011" /><ref name="Mishkin 2006">{{Cite book | title = Economics of Money, Banking, and Financial Markets, 8th edition | author = Mishkin, Frederic S. | year = 2006 | publisher = Addison-Wesley | location = Boston, MA | isbn = 978-0-321-28726-7}}</ref> such that the Fisher effect:
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| :<math>(1 + i_\$) = (1 + \rho_$) \times E(1 + \pi_$)</math>
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| can be arranged as
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| :<math>i_\$ = \rho_\$ + E(\pi_\$) + \rho_\$E(\pi_\$) \approx \rho_\$ + E(\pi_\$)</math>
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| where
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| :<math>i_$</math> is the nominal interest rate
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| :<math>\rho_$</math> is the [[real interest rate]]
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| :<math>E(\pi_$)</math> is the expected inflation rate | |
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| The hypothesis suggests that the expected inflation rate should equal the difference between the [[real versus nominal value (economics)|nominal]] and real interest rates in any given country,<ref name="Saunders & Cornett 2009">{{Cite book | title = Financial Markets and Institutions, 4th Edition | author = Saunders, Anthony | author2 = Cornett, Marcia Millon | year = 2009 | publisher = McGraw-Hill/Irwin | location = New York, NY | isbn = 978-0-07-338229-6}}</ref> such that:
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| :<math>E(\pi_$) = \frac {(i_$ - \rho_$)} {(1 + \rho_$)} \approx i_$ - \rho_$</math>
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| where
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| :<math>$</math> could be substituted with any country's currency
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| Assuming the real interest rate is equal across two countries due to [[capital mobility]], such that <math>\rho_$ = \rho_c</math>, substituting the aforementioned equation into the expectations form of [[relative purchasing power parity]] results in the formal equation for the international Fisher effect:
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| :<math>E(e) = \frac {(i_$ - i_c)} {(1 + i_c)} \approx i_$ - i_c</math>
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| where
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| :<math>E(e)</math> is the expected rate of change in the exchange rate
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| This equation can be rearranged as:
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| :<math>E(e) = \frac {(1 + i_$)} {(1 + i_c)} - 1</math>
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| ===Relation to interest rate parity===
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| Combining the international Fisher effect with [[interest rate parity#Uncovered interest rate parity|uncovered interest rate parity]] yields the following equation:
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| :<math>\frac {E(S_{t+k})} {S_t} - 1 = \frac {(i_$ - i_c)} {(1 + i_c)} = E(e)</math>
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| where
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| :<math>E(S_{t+k})</math> is the expected future spot exchange rate
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| :<math>S_t</math> is the spot exchange rate
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| Combining the international Fisher effect with [[interest rate parity#Covered interest rate parity|covered interest rate parity]] yields the equation for [[forward exchange rate#Unbiasedness hypothesis|unbiasedness hypothesis]], where the forward exchange rate is an unbiased predictor of the future spot exchange rate.:<ref name="Eun & Resnick 2011" />
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| :<math>\frac {F_{t,T}} {S_t} - 1 = \frac {(i_$ - i_c)} {(1 + i_c)} = E(e)</math>
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| where
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| :<math>F_{t,T}</math> is the [[forward exchange rate]].
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| ===Example===
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| Suppose the current [[spot exchange rate]] between the United States and the United Kingdom is 1.4339 USD/GBP. Also suppose the current interest rates are 5 percent in the U.S. and 7 percent in the U.K. What is the expected spot exchange rate 12 months from now according to the international Fisher effect? The effect estimates future exchange rates based on the relationship between nominal interest rates. Multiplying the current spot exchange rate by the nominal annual U.S. interest rate and dividing by the nominal annual U.K. interest rate yields the estimate of the spot exchange rate 12 months from now:
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| :<math>$1.4339 \times \frac {(1 + 5%)} {(1 + 7%)} = $1.4071</math>
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| To check this example, use the formal or rearranged expressions of the international Fisher effect on the given interest rates:
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| :<math>E(e) = \frac {(5% - 7%)} {(1 + 7%)} = -0.018692 = -1.87%</math>
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| :<math>E(e) = \frac {(1 + 5%)} {(1 + 7%)} - 1 = -0.018692 = -1.87%</math>
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| The expected percentage change in the exchange rate is a depreciation of 1.87% for the GBP (it now only costs $1.4071 to purchase 1 GBP rather than $1.4339), which is consistent with the expectation that the value of the currency in the country with a higher interest rate will depreciate.
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| ==References==
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| {{Reflist}}
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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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Greetings! I am Myrtle Shroyer. His wife doesn't like it the way he does but what he really likes performing is to do aerobics and he's been performing it for quite a while. For a whilst I've been in South Dakota and my parents reside nearby. Bookkeeping is my profession.
Also visit my page: std testing at home