<p>They are related and have very similar implications but they are not the same. I will try to provide simple explanation here for more nuance you can have look at for example <a href="https://mpra.ub.uni-muenchen.de/98945/1/MPRA_paper_98945.pdf" rel="nofollow noreferrer">Mogaji (2019)</a> and sources cited therein.</p>
<p><strong>Uncovered interest rate parity</strong> (UIP) says that the ratio expected exchange rate <span class="math-container">$E_t[S_{t+k}]$</span> to spot exchange rate <span class="math-container">$S_t$</span>, has to be equal to nominal interest rates between home <span class="math-container">$i$</span> and foreign <span class="math-container">$i_f$</span> country.</p>
<p><span class="math-container">$$   \frac{E_{t}(S_{{t+k}})}{S_{t}} = {\frac  {(1+i)}{(1+i_{f})}} \implies E_t [\Delta S] \approx i - i_f$$</span></p>
<p>This is based on the idea that there should be no possibility of arbitrage (riskless profit) in the market resulting from different nominal interest rates.</p>
<p>For example, if interest rate in US would be <span class="math-container">$10\%$</span> and interest rate in UK would be <span class="math-container">$5\%$</span> and if exchange rate would be exactly <span class="math-container">$1{\\\$}=1£$</span>, anyone who could would stop saving in UK and just transfer all their savings into US. However, to do so they have to go through forex market and by creating new demand for USD they should change exchange rate sufficiently enough to eliminate the arbitrage opportunity.</p>
<p>The UIP simply  posits that due to this possibility the ratio between expected exchange rate and spot exchange rate must be equal to the ratio of interest rates otherwise people would start entering forex market and making trades that would force the above parity hold true.</p>
<p><strong>International Fisher effect</strong> (IFE) is based on the idea that ultimately exchange rate must reflect differences in price levels between two countries the expected change in exchange rate must reflect the relative differences in expected inflation rates between two countries (<span class="math-container">$E_t[\pi]$</span> and <span class="math-container">$E[\pi_f]$</span>), since if change in price levels between two countries would not be balanced there would be arbitrages in goods market and violations of the law of one price.  Hence we should have:</p>
<p><span class="math-container">$$E_t[\Delta S_t] \approx E_t[\pi] - E_t[\pi_f]$$</span></p>
<p>Now in turn by Fisher equation the rate of inflation is approximately equal tot he difference between nominal (<span class="math-container">$i$</span>) and real <span class="math-container">$(r)$</span> interest rate <span class="math-container">$e_t[\pi] \approx i-r$</span>. Furthermore, IFE assumes that due to perfect capital mobility the real interest rate must be everywhere equal <span class="math-container">$r=r_f$</span>. Well given these assumptions we will find out that change in the exchange rate should be given by change in nominal interest rates since:</p>
<p><span class="math-container">$$E_t[\Delta S_t] \approx E_t[\pi] - E_t[\pi_f] \approx  i-r - (i_f-r_f) \approx i - i_f$$</span></p>
<p>Hence there are subtle differences between these theories as the mechanisms in UIP and IFE are different. UIP is based on an idea of impossibility of arbitrage in money market. IFE is based on the idea that there cannot be arbitrage in goods market.</p>
<p>Sometimes two different theories might predict the same outcome, this is known in science as <a href="https://en.wikipedia.org/wiki/Observational_equivalence" rel="nofollow noreferrer">observational equivalence</a>. Observational equivalence does not necessarily mean there is no difference between two theories as two different mechanisms can sometimes give rise to same outcome.</p>

CC BY-SA 4.0
2020-11-21T15:11:10.840Z
"UIP is based on an idea of impossibility of arbitrage. IFE is based on the idea that..."---both are no-arbitrage conditions, though, just for different markets: international "money market" vs. goods market.
Michael
CC BY-SA 4.0
2020-11-21T15:14:00.523Z
@Michael you are right I actually mentioned that in the body but screwed the summary - I edited it now. Thanks for your useful comment!
1muflon1
CC BY-SA 4.0
2022-08-24T13:40:39.440Z
A nice answer. I would put *UIP is based on an idea of impossibility of arbitrage in money market. IFE is based on the idea that there cannot be arbitrage in goods market.* in bold.
Richard Hardy
CC BY-SA 4.0
2022-11-09T14:57:48.573Z
Your UIP example contains only the current spot rate and forgets to mention the (expected) future spot rate. (British savers need to convert back to GBP to be able to spend that money in Britain.) The first sentence on IFE is too long and its grammar suffers.
Richard Hardy
CC BY-SA 4.0
2020-11-20T23:15:39.327Z
2020-11-21T15:13:20.930Z
2020-11-21T15:13:20.930Z
1muflon1
<p>IFE says you should expect the same <strong>real</strong> return on domestic and foreign assets. UIP says you should expect the same <strong>nominal</strong> return on domestic and foreign assets.</p>

CC BY-SA 4.0
2023-03-24T05:36:04.853Z
2023-03-24T05:36:04.853Z
Pavel Filip
<p>References:</p>
<p><a href="https://en.wikipedia.org/wiki/International_Fisher_effect" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/International_Fisher_effect</a>
<a href="https://en.wikipedia.org/wiki/Interest_rate_parity#Uncovered_interest_rate_parity" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Interest_rate_parity#Uncovered_interest_rate_parity</a></p>
<p>As far as I can tell, these two are the same. What is the difference? (Is the former a statement without taking expectation over future exchange rate, and thus, a stronger prediction?)</p>

<international-economics>
What is the difference between the international Fisher effect and uncovered interest rate parity?
J Li
# What is the difference between the international Fisher effect and uncovered interest rate parity?

(Asked by: username_0 on 2020-11-20)

References:

<https://en.wikipedia.org/wiki/International_Fisher_effect>
<https://en.wikipedia.org/wiki/Interest_rate_parity#Uncovered_interest_rate_parity>

As far as I can tell, these two are the same. What is the difference? (Is the former a statement without taking expectation over future exchange rate, and thus, a stronger prediction?)

**Tags:** international-economics


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## 2 answers

### Answer by username_1 on 2020-11-20. Score: 4

They are related and have very similar implications but they are not the same. I will try to provide simple explanation here for more nuance you can have look at for example [Mogaji (2019)](https://mpra.ub.uni-muenchen.de/98945/1/MPRA_paper_98945.pdf) and sources cited therein.

**Uncovered interest rate parity** (UIP) says that the ratio expected exchange rate $E\_t[S\_{t+k}]$ to spot exchange rate $S\_t$, has to be equal to nominal interest rates between home $i$ and foreign $i\_f$ country.

$$ \frac{E\_{t}(S\_{{t+k}})}{S\_{t}} = {\frac {(1+i)}{(1+i\_{f})}} \implies E\_t [\Delta S] \approx i - i\_f$$

This is based on the idea that there should be no possibility of arbitrage (riskless profit) in the market resulting from different nominal interest rates.

For example, if interest rate in US would be $10\%$ and interest rate in UK would be $5\%$ and if exchange rate would be exactly $1{\\\$}=1£$, anyone who could would stop saving in UK and just transfer all their savings into US. However, to do so they have to go through forex market and by creating new demand for USD they should change exchange rate sufficiently enough to eliminate the arbitrage opportunity.

The UIP simply posits that due to this possibility the ratio between expected exchange rate and spot exchange rate must be equal to the ratio of interest rates otherwise people would start entering forex market and making trades that would force the above parity hold true.

**International Fisher effect** (IFE) is based on the idea that ultimately exchange rate must reflect differences in price levels between two countries the expected change in exchange rate must reflect the relative differences in expected inflation rates between two countries ($E\_t[\pi]$ and $E[\pi\_f]$), since if change in price levels between two countries would not be balanced there would be arbitrages in goods market and violations of the law of one price. Hence we should have:

$$E\_t[\Delta S\_t] \approx E\_t[\pi] - E\_t[\pi\_f]$$

Now in turn by Fisher equation the rate of inflation is approximately equal tot he difference between nominal ($i$) and real $(r)$ interest rate $e\_t[\pi] \approx i-r$. Furthermore, IFE assumes that due to perfect capital mobility the real interest rate must be everywhere equal $r=r\_f$. Well given these assumptions we will find out that change in the exchange rate should be given by change in nominal interest rates since:

$$E\_t[\Delta S\_t] \approx E\_t[\pi] - E\_t[\pi\_f] \approx i-r - (i\_f-r\_f) \approx i - i\_f$$

Hence there are subtle differences between these theories as the mechanisms in UIP and IFE are different. UIP is based on an idea of impossibility of arbitrage in money market. IFE is based on the idea that there cannot be arbitrage in goods market.

Sometimes two different theories might predict the same outcome, this is known in science as [observational equivalence](https://en.wikipedia.org/wiki/Observational_equivalence). Observational equivalence does not necessarily mean there is no difference between two theories as two different mechanisms can sometimes give rise to same outcome.

> **Comments:**
> **username_2**: "UIP is based on an idea of impossibility of arbitrage. IFE is based on the idea that..."---both are no-arbitrage conditions, though, just for different markets: international "money market" vs. goods market.  
> **username_1**: @username_2 you are right I actually mentioned that in the body but screwed the summary - I edited it now. Thanks for your useful comment!  
> **username_3**: A nice answer. I would put *UIP is based on an idea of impossibility of arbitrage in money market. IFE is based on the idea that there cannot be arbitrage in goods market.* in bold.  
> **username_3**: Your UIP example contains only the current spot rate and forgets to mention the (expected) future spot rate. (British savers need to convert back to GBP to be able to spend that money in Britain.) The first sentence on IFE is too long and its grammar suffers.  

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### Answer by username_4 on 2023-03-24. Score: 0

IFE says you should expect the same **real** return on domestic and foreign assets. UIP says you should expect the same **nominal** return on domestic and foreign assets.


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