<p>There is an arbitrage argument for UIP because under UIP forward rate must be equal to expected exchange rate so the same arbitrage arguments from CIP can be extended to UIP (under its strict assumptions). You will find it in most international macroeconomics or finance textbooks. For example, according to Nelson Mark's International Macroeconomics and Finance:</p>
<blockquote>
<p>If foreign exchange participants are risk neutral, they
care only about the mean value of asset returns and do not care at all
about the variance of returns. Risk-neutral individuals are also willing to take unboundedly large positions on bets that have a positive
expected value. Since <span class="math-container">$F_{t} − S_{t+1}$</span> is the profit from taking a position in
forward foreign exchange, under risk-neutrality expected forward speculation profits are driven to zero and the forward exchange rate must,
in equilibrium, be market participant's expected future spot exchange
rate</p>
<p><span class="math-container">$$F_{t} = E_{t}(S_{t+1}). (1.6)$$</span></p>
<p>Substituting (1.6) into (1.2) [result given from covered interest parity where instead of expected exchange rate you have forward rate] gives the uncovered interest parity condition
<span class="math-container">$$ 1 + i_t = (1 + i_t^* )\frac{E_t[S_{t+1}]}{S_t}. (1.7)$$</span>
If (1.7) is violated, a zero-net investment strategy of borrowing in one
currency and simultaneously lending uncovered in the other currency has a positive payoff in expectation. We use the uncovered interest
parity condition as a first-approximation to characterize international
asset market equilibrium, especially in conjunction with the monetary
model (chapters 3, 10, and 11). However, as you will see in chapter 6,
violations of uncovered interest parity are common and they present an
important empirical puzzle for international economists.</p>
</blockquote>
<p>The in text square brackets contain my clarifications. So as the above passages show there is an arbitrage argument in UIP. You can find further sources and more detailed explanations in the textbook itself.</p>

CC BY-SA 4.0
2020-07-29T13:16:17.797Z
Thanks for the recommendation, I'll pick that book up in the next few days! The part that interests me though is why "expected forward speculation profits are driven to zero". If the exchange rate appreciates more than it should according to (1.7), then an onslaught of rational investors will raise the rate even higher instead of pushing it down to its fair value. In replication-based arbitrage this price increase would lower returns and thereby diminish profit opportunities but this mechanism doesn't apply here because the interest rate is a relative return by definition.
Steven
CC BY-SA 4.0
2020-07-29T13:21:51.270Z
@Steven the UIP hold only under strict assumptions, including that agents are all risk neutral and homogenous - you cant divorce the UIP from those assumptions because that is how you derive it.Those assumptions are not realistic and that is how its empirical failure is usually excused in the literature
1muflon1
CC BY-SA 4.0
2020-07-29T13:44:21.510Z
Yeah, the most critical empirical issue is definitely the negligence of a risk premium, but thinking strictly inside the bounds model, I don't see why investors flocking to a currency that delivers excess returns violates any of the pertaining assumptions. Could you clarify where my thought experiment overstepped the theoretical boundaries?
Steven
CC BY-SA 4.0
2020-07-29T13:51:02.633Z
@Steven but if UIP holds the currency cannot offer any excess returns due to the equation 1.7 which is the UIP. The argument there is precisely the same argument as the arbitrage argument in CIP because under UIP expected exchange rate must be exactly equal to the forward rate. Hence if there are any arbitrage opportunities they would instantly disappear. Of course, in real world you can have investors flocking to currency and finding ways how successfully exploit it, but in the real world people have heterogeneous risk appetites, information, transaction costs etc which violate UIP
1muflon1
CC BY-SA 4.0
2020-07-29T14:01:36.773Z
I agree with you on every point, my question is what the microeconomic mechanics of "if there are any arbitrage opportunities they would instantly disappear" are. The argument of no free lunches makes sense, but is not a sufficient explanation for why a single investor is to undertake any action that would mitigate excess earnings potentials (under the assumption that all investors are risk-neutral).
Steven
CC BY-SA 4.0
2020-07-29T14:13:06.163Z
@Steven it’s literary the same as with CIP except you don’t use the futures but just the current and future expected exchange rate itself. For example, if interest rate in EU is 5% and in US 10% then when people start borrowing in EU and investing in US the exchange rate changes in order to make the expected returns equal as to invest in US you have to sell EUR and buy USD furthermore you face the same issue when you will want to convert the money from USD back to the EUR. In the end the trading of currency itself eliminates the arbitrage due to losses/gains made through forex market.
1muflon1
CC BY-SA 4.0
2020-07-29T15:10:19.947Z
In that example the USD would appreciate and without any speculative capital outflows from the US hold its new value indefinitely. UIP however predicts a gradual depreciation, which (to my knowledge) can only be facilitated through a gradual capital outflow. Why would anyone be motivated to withdraw capital if uncle Sam gives them 5% on top of what they would get at home?
Steven
CC BY-SA 4.0
2020-07-29T15:19:23.667Z
@Steven you have to go through exchange rate twice because otherwise there is no way how to use the money in your country of origin. Hence, USD will appreciate when you will start investing in the US and depreciates when you will try to get your money back. If you never convert your USD denominated earnings into EUR then exchange rate does not move but then you wont get the riskless profit.
1muflon1
CC BY-SA 4.0
2020-07-29T16:25:27.750Z
Sounds reasonable but is not part of the assumptions made by UIP. The exchange rate should still depreciate from t=0 to t=1 even if all investors decide to leave their funds invested until t=2. One theory I had from the start (that would be consistent with your point) is that only interest returns are assumed to be withdrawn to the funding currency as it accumulates, but that's not really waterproof either because the rate depreciation should not depend on the size of the foreign investment position in the investment currency.
Steven
CC BY-SA 4.0
2020-07-29T16:28:24.323Z
@Steven Every model has assumptions and from those assumptions you draw results. Part of an assumptions of UIP is that markets are perfect. The above result is a result that occurs when you have perfect markets due to supply-demand interactions. The exchange rate has to adjust because the demand for the currencies change - thats just part of the mechanics of the model
1muflon1
CC BY-SA 4.0
2020-07-29T16:50:24.737Z
No disagreement on the general points, but the basket of assumptions that the perfect market encompasses doesn't include one that says that all capital has to be withdrawn after one period. I haven't yet found evidence why the SD equilibrium would change (as it should) when I construct an economy purposefully so that there's no incentive to (which is really just a stylized model of reality). Not sure whether we're getting anywhere though, so thanks for your time :)
Steven
CC BY-SA 4.0
2020-07-29T16:55:31.783Z
@Steven well but you have to withdraw them to enjoy them rational person would not let money sit on some US account to never ever use them for the rest of the life. If you make that kind of assumptions on agent behavior that they don’t care about using the money then the exchange will be higher forever but then the people are not getting anything out of it
1muflon1
CC BY-SA 4.0
2020-07-29T17:00:51.183Z
I am not sure that "no positive expectation under risk neutrality" is the same as "no arbitrage".  An arbitrage argument leads to Covered Interest Parity, but Uncovered Interest Parity is rather different, and no Central Bank lowers interest rates in the belief this will lead to a medium term appreciation in the value of its currency
Henry
CC BY-SA 4.0
2020-07-29T17:03:32.897Z
@Henry I agree it is different because of the expectations involved but you can extend the logic of CIP to UIP because under UIP $E[S]=F$. Also I agree that central banks don’t do that but UIP also does not hold empirically this is purely theoretical discussion here
1muflon1
CC BY-SA 4.0
2020-07-30T10:02:52.760Z
@1muflon1 That's completely reasonable in reality, but UIP cannot possibly hinge on the assumption that investors withdraw just the right amount of capital to devalue the currency just the right amount for it to balance out exactly the interest rate differential.
Steven
CC BY-SA 4.0
2020-07-30T10:32:31.773Z
@Steven but that is not an assumption it’s part of the result. For example, it’s part of the result in classic supply demand model that producers produce exactly the same quantity as supplier. That’s not assumption that’s a result. The mechanism is exactly the same as with simple Econ 101 supply demand model. If there is any profit to be made by investing in US people will do so in such amount that the new demand forces exchange rate to eliminate that profit opportunity and in the model it happens instantly (in real life of course there can be lucky person acting before others notice)
1muflon1
CC BY-SA 4.0
2020-07-30T10:40:18.780Z
@Steven for example imagine that in US you can invest 1USD that will yield return of 4USD and in EU you can invest 1EUR that in the same amount of time yields 2EUR and original exchange is 1EUR=1USD. Every single rational person in such case would try to invest in US but as they go to forex market the currency sellers will realize there is increased demand and this demand must be such that the new exchange rate will be 2EUR=1USD eliminating any risk less profit. If that would not be the case market would not be in equilibrium. You will get exactly the reverse problem when transferring back
1muflon1
CC BY-SA 4.0
2020-07-30T10:44:54.063Z
@Steven in addition the above is an extreme case to illustrate the point as equation 1.7 shows it’s not even necessary for exchange rate to move into the position that eliminates arbitrage twice as what matters is the ratio of $E[S]/S$
1muflon1
CC BY-SA 4.0
2020-07-30T12:03:46.193Z
@1muflon1 I see your point that that the withdrawal amount (or whichever mechanism directly causes the depreciation) is endogenous and agree that this is probable. However this exact endogeneity is what I'm looking for, because the (endogenous) variable that causes the depreciation is not (yet) part of the UIP equation.
Steven
CC BY-SA 4.0
2020-07-30T12:11:07.833Z
@Steven it is. On forex market (as in any single market) both price and quantity are jointly determined (i.e. endogenous). On forex market for any exchange pair for example USD-EUR the exchange rate is the price. Since we assume perfect market without any restrictions the exchange rate (i.e. price) must be exactly such that there is no excess demand. If there is any arbitrage opportunity to be have by investing in US then the demand for USD will shift to the right. The reason why it shifts in an exact amount to eliminate arbitrage is that until the demand shifts enough
1muflon1
CC BY-SA 4.0
2020-07-30T12:12:55.573Z
@Steven there is still incentive for people to demand more in order to profit from it. Only once exchange rate is exactly such that there is no arbitrage opportunity left people will stop demanding higher and higher quantities of USD. It is literary your econ 101 supply demand explanation.
1muflon1
CC BY-SA 4.0
2020-07-31T11:45:59.563Z
@1muflon1 I think I just got your point :D It's because the effective interest rate differential declines until it is 0 at maturity of the forward, right? CIP requires the difference between the F and S to be arbitraged away, so for an infinitesimal addition of time, there's an infinitesimal small arbitrage opportunity. In reality, it's only arbitraged as soon as it's large enough to cover transaction costs. Is that correct?
Steven
CC BY-SA 4.0
2020-07-31T12:14:55.567Z
@Steven yes pretty much except if you get revenue that just large enough to cover transaction costs it would not qualify as arbitrage - but that’s just semantics
1muflon1
CC BY-SA 4.0
2020-07-31T14:11:13.737Z
Thanks for bearing with me then haha. Follow-up question in this case would be why only the spot rate depreciates and why the forward doesn't appreciate. Can you enlighten me on that one too?
Steven
CC BY-SA 4.0
2020-07-31T14:13:58.177Z
@Steven I just used extreme case to show the point if you read my comments carefully you will see that in one of them I mention combination of them can occur as well but I did not focus on that because I thought it would just add more confusion what matters in the model in the end is just that $E[S]/S$ that is the whole ratio will be such that it prevents the arbitrage
1muflon1
CC BY-SA 4.0
2020-07-31T14:39:43.103Z
But how does $E[S]=F$ hold true if the adjustment can go both ways?
Steven
CC BY-SA 4.0
2020-07-31T14:40:24.907Z
@Steven yes that will always hold under the assumptions of the model (although of course not in reality)
1muflon1
CC BY-SA 4.0
2020-07-31T15:13:20.420Z
The forward is fixed at time t though, so how does fit with the adjustment until T going both ways?
Steven
CC BY-SA 4.0
2020-07-31T15:16:50.193Z
@Steven no the F is determined by what people expect the exchange rate will be in the future - it’s fixed at time t the same way as any price is fixed at any time t but that does not mean it’s fixed at any arbitrary level
1muflon1
CC BY-SA 4.0
2020-07-31T20:22:52.297Z
But we you assume that from t to T no new information arises and expectations don't change for other reasons either; thus the only reason that price moves is the interest rate differential?
Steven
CC BY-SA 4.0
2020-07-31T20:26:52.093Z
@Steven yes. If the interest rates are not equal, prices (exchange rate and its expectation) adjust in order to make the equation 1.7 hold and if no new information or changes occur then they stay fixed until something changes further down the road.
1muflon1
CC BY-SA 4.0
2020-07-29T12:43:45.270Z
2020-07-29T15:23:24.037Z
2020-07-29T15:23:24.037Z
1muflon1
<p>From a real world perspective, “interest rate parity” always holds - so long as you take into account the cross-currency basis swap spread. (Basis swaps are typically ignored in simple academic models, but are important for cross-currency funding). Forward points are set based on the theoretical relationship, with a bid-offer spread. Any market maker that is off market would be mercilessly arbitraged, and would be looking for a new job. There is no debate about this, that’s how market makers operate.</p>
<p>The only room for research questions are the following.</p>
<ul>
<li>Are forwards an accurate measure of market participants forecasts for currency values? Given that the basis and interest rate market pricing is determined by fixed income investors who often cannot trade foreign exchange, there is no way of surveying “investors” properly. Cross-currency basis swaps are a funding instrument, and are priced based on funding flows. Meanwhile, the primary driver of short-term rates is rate expectations. As such, currency relative valuation does not show up in the instruments determining forward-spot spreads, other than via the indirect route of central bank reactions to currency movements.</li>
<li>Are forward points offer “good predictions” (however defined) of the future spot rate? That’s where most of the literature ends up, but I think it is safe to say that currency forwards have little useful information about future currency movements. One thing to note is the realised volatility in currencies is often much larger than the deviation of spot and forward, so it’s equivalent to saying that currencies can go up or down.</li>
</ul>

CC BY-SA 4.0
2020-07-31T11:11:50.863Z
2020-07-31T12:08:10.310Z
2020-07-31T12:08:10.310Z
Brian Romanchuk
<p>The key idea behind UIP is that as for all common financial instruments, the &quot;law of no free lunch&quot; should also hold for currencies. However it differs from traditional replication-based no-arbitrage conditions like CIP in that there is no obvious argument for why the exploitation of opportunities when it does not hold true necessarily depletes all such opportunities, thereby making &quot;free lunches&quot; rare in a world of rational investors.</p>
<p>Concretely, the currency of a country with a relatively higher interest rate needs to gradually depreciate to offset the positive earnings potential. What mechanism drives this gradual depreciation?</p>
<p>I've heard that there are models on this issue but have not been able to locate the literature.</p>
<p>Thanks for all suggestions!</p>

CC BY-SA 4.0
2020-07-29T12:12:11.990Z
What's wrong with expected free lunches?
Giskard
CC BY-SA 4.0
2020-07-29T12:12:26.163Z
To clarify, are you asking for literature or an explanation?
Giskard
CC BY-SA 4.0
2020-07-29T12:17:24.703Z
@Giskard The fact that UIP (under risk-neutrality) expects there to be no free lunches, but there is no obvious arbitrage argument like for a mispriced forward contract.
Steven
CC BY-SA 4.0
2020-07-29T12:18:55.813Z
@Giskard Both :) I'd love to read the source material, but I'd also appreciate an explanation if you don't happen to be familiar with the literature I'm searching for
Steven
<interest-rate><exchange-rates><arbitrage>
Microeconomic rationale for UIP (uncovered interest rate parity)
Steven
# Microeconomic rationale for UIP (uncovered interest rate parity)

(Asked by: username_0 on 2020-07-29)

The key idea behind UIP is that as for all common financial instruments, the "law of no free lunch" should also hold for currencies. However it differs from traditional replication-based no-arbitrage conditions like CIP in that there is no obvious argument for why the exploitation of opportunities when it does not hold true necessarily depletes all such opportunities, thereby making "free lunches" rare in a world of rational investors.

Concretely, the currency of a country with a relatively higher interest rate needs to gradually depreciate to offset the positive earnings potential. What mechanism drives this gradual depreciation?

I've heard that there are models on this issue but have not been able to locate the literature.

Thanks for all suggestions!

**Tags:** interest-rate, exchange-rates, arbitrage
> **Comments:**
> **username_1**: What's wrong with expected free lunches?  
> **username_1**: To clarify, are you asking for literature or an explanation?  
> **username_0**: @Giskard The fact that UIP (under risk-neutrality) expects there to be no free lunches, but there is no obvious arbitrage argument like for a mispriced forward contract.  
> **username_0**: @Giskard Both :) I'd love to read the source material, but I'd also appreciate an explanation if you don't happen to be familiar with the literature I'm searching for  

---

## 2 answers

### Answer by username_2 on 2020-07-29. Score: 0 | Accepted answer

There is an arbitrage argument for UIP because under UIP forward rate must be equal to expected exchange rate so the same arbitrage arguments from CIP can be extended to UIP (under its strict assumptions). You will find it in most international macroeconomics or finance textbooks. For example, according to Nelson Mark's International Macroeconomics and Finance:

> If foreign exchange participants are risk neutral, they
> care only about the mean value of asset returns and do not care at all
> about the variance of returns. Risk-neutral individuals are also willing to take unboundedly large positions on bets that have a positive
> expected value. Since $F\_{t} − S\_{t+1}$ is the profit from taking a position in
> forward foreign exchange, under risk-neutrality expected forward speculation profits are driven to zero and the forward exchange rate must,
> in equilibrium, be market participant's expected future spot exchange
> rate
>
> $$F\_{t} = E\_{t}(S\_{t+1}). (1.6)$$
>
> Substituting (1.6) into (1.2) [result given from covered interest parity where instead of expected exchange rate you have forward rate] gives the uncovered interest parity condition
> $$ 1 + i\_t = (1 + i\_t^\* )\frac{E\_t[S\_{t+1}]}{S\_t}. (1.7)$$
> If (1.7) is violated, a zero-net investment strategy of borrowing in one
> currency and simultaneously lending uncovered in the other currency has a positive payoff in expectation. We use the uncovered interest
> parity condition as a first-approximation to characterize international
> asset market equilibrium, especially in conjunction with the monetary
> model (chapters 3, 10, and 11). However, as you will see in chapter 6,
> violations of uncovered interest parity are common and they present an
> important empirical puzzle for international economists.

The in text square brackets contain my clarifications. So as the above passages show there is an arbitrage argument in UIP. You can find further sources and more detailed explanations in the textbook itself.

> **Comments:**
> **username_0**: Thanks for the recommendation, I'll pick that book up in the next few days! The part that interests me though is why "expected forward speculation profits are driven to zero". If the exchange rate appreciates more than it should according to (1.7), then an onslaught of rational investors will raise the rate even higher instead of pushing it down to its fair value. In replication-based arbitrage this price increase would lower returns and thereby diminish profit opportunities but this mechanism doesn't apply here because the interest rate is a relative return by definition.  
> **username_2**: @Steven the UIP hold only under strict assumptions, including that agents are all risk neutral and homogenous - you cant divorce the UIP from those assumptions because that is how you derive it.Those assumptions are not realistic and that is how its empirical failure is usually excused in the literature  
> **username_0**: Yeah, the most critical empirical issue is definitely the negligence of a risk premium, but thinking strictly inside the bounds model, I don't see why investors flocking to a currency that delivers excess returns violates any of the pertaining assumptions. Could you clarify where my thought experiment overstepped the theoretical boundaries?  
> **username_2**: @Steven but if UIP holds the currency cannot offer any excess returns due to the equation 1.7 which is the UIP. The argument there is precisely the same argument as the arbitrage argument in CIP because under UIP expected exchange rate must be exactly equal to the forward rate. Hence if there are any arbitrage opportunities they would instantly disappear. Of course, in real world you can have investors flocking to currency and finding ways how successfully exploit it, but in the real world people have heterogeneous risk appetites, information, transaction costs etc which violate UIP  
> **username_0**: I agree with you on every point, my question is what the microeconomic mechanics of "if there are any arbitrage opportunities they would instantly disappear" are. The argument of no free lunches makes sense, but is not a sufficient explanation for why a single investor is to undertake any action that would mitigate excess earnings potentials (under the assumption that all investors are risk-neutral).  
> **username_2**: @Steven it’s literary the same as with CIP except you don’t use the futures but just the current and future expected exchange rate itself. For example, if interest rate in EU is 5% and in US 10% then when people start borrowing in EU and investing in US the exchange rate changes in order to make the expected returns equal as to invest in US you have to sell EUR and buy USD furthermore you face the same issue when you will want to convert the money from USD back to the EUR. In the end the trading of currency itself eliminates the arbitrage due to losses/gains made through forex market.  
> **username_0**: In that example the USD would appreciate and without any speculative capital outflows from the US hold its new value indefinitely. UIP however predicts a gradual depreciation, which (to my knowledge) can only be facilitated through a gradual capital outflow. Why would anyone be motivated to withdraw capital if uncle Sam gives them 5% on top of what they would get at home?  
> **username_2**: @Steven you have to go through exchange rate twice because otherwise there is no way how to use the money in your country of origin. Hence, USD will appreciate when you will start investing in the US and depreciates when you will try to get your money back. If you never convert your USD denominated earnings into EUR then exchange rate does not move but then you wont get the riskless profit.  
> **username_0**: Sounds reasonable but is not part of the assumptions made by UIP. The exchange rate should still depreciate from t=0 to t=1 even if all investors decide to leave their funds invested until t=2. One theory I had from the start (that would be consistent with your point) is that only interest returns are assumed to be withdrawn to the funding currency as it accumulates, but that's not really waterproof either because the rate depreciation should not depend on the size of the foreign investment position in the investment currency.  
> **username_2**: @Steven Every model has assumptions and from those assumptions you draw results. Part of an assumptions of UIP is that markets are perfect. The above result is a result that occurs when you have perfect markets due to supply-demand interactions. The exchange rate has to adjust because the demand for the currencies change - thats just part of the mechanics of the model  
> **username_0**: No disagreement on the general points, but the basket of assumptions that the perfect market encompasses doesn't include one that says that all capital has to be withdrawn after one period. I haven't yet found evidence why the SD equilibrium would change (as it should) when I construct an economy purposefully so that there's no incentive to (which is really just a stylized model of reality). Not sure whether we're getting anywhere though, so thanks for your time :)  
> **username_2**: @Steven well but you have to withdraw them to enjoy them rational person would not let money sit on some US account to never ever use them for the rest of the life. If you make that kind of assumptions on agent behavior that they don’t care about using the money then the exchange will be higher forever but then the people are not getting anything out of it  
> **username_3**: I am not sure that "no positive expectation under risk neutrality" is the same as "no arbitrage".  An arbitrage argument leads to Covered Interest Parity, but Uncovered Interest Parity is rather different, and no Central Bank lowers interest rates in the belief this will lead to a medium term appreciation in the value of its currency  
> **username_2**: @Henry I agree it is different because of the expectations involved but you can extend the logic of CIP to UIP because under UIP $E[S]=F$. Also I agree that central banks don’t do that but UIP also does not hold empirically this is purely theoretical discussion here  
> **username_0**: @1muflon1 That's completely reasonable in reality, but UIP cannot possibly hinge on the assumption that investors withdraw just the right amount of capital to devalue the currency just the right amount for it to balance out exactly the interest rate differential.  
> **username_2**: @Steven but that is not an assumption it’s part of the result. For example, it’s part of the result in classic supply demand model that producers produce exactly the same quantity as supplier. That’s not assumption that’s a result. The mechanism is exactly the same as with simple Econ 101 supply demand model. If there is any profit to be made by investing in US people will do so in such amount that the new demand forces exchange rate to eliminate that profit opportunity and in the model it happens instantly (in real life of course there can be lucky person acting before others notice)  
> **username_2**: @Steven for example imagine that in US you can invest 1USD that will yield return of 4USD and in EU you can invest 1EUR that in the same amount of time yields 2EUR and original exchange is 1EUR=1USD. Every single rational person in such case would try to invest in US but as they go to forex market the currency sellers will realize there is increased demand and this demand must be such that the new exchange rate will be 2EUR=1USD eliminating any risk less profit. If that would not be the case market would not be in equilibrium. You will get exactly the reverse problem when transferring back  
> **username_2**: @Steven in addition the above is an extreme case to illustrate the point as equation 1.7 shows it’s not even necessary for exchange rate to move into the position that eliminates arbitrage twice as what matters is the ratio of $E[S]/S$  
> **username_0**: @1muflon1 I see your point that that the withdrawal amount (or whichever mechanism directly causes the depreciation) is endogenous and agree that this is probable. However this exact endogeneity is what I'm looking for, because the (endogenous) variable that causes the depreciation is not (yet) part of the UIP equation.  
> **username_2**: @Steven it is. On forex market (as in any single market) both price and quantity are jointly determined (i.e. endogenous). On forex market for any exchange pair for example USD-EUR the exchange rate is the price. Since we assume perfect market without any restrictions the exchange rate (i.e. price) must be exactly such that there is no excess demand. If there is any arbitrage opportunity to be have by investing in US then the demand for USD will shift to the right. The reason why it shifts in an exact amount to eliminate arbitrage is that until the demand shifts enough  
> **username_2**: @Steven there is still incentive for people to demand more in order to profit from it. Only once exchange rate is exactly such that there is no arbitrage opportunity left people will stop demanding higher and higher quantities of USD. It is literary your econ 101 supply demand explanation.  
> **username_0**: @1muflon1 I think I just got your point :D It's because the effective interest rate differential declines until it is 0 at maturity of the forward, right? CIP requires the difference between the F and S to be arbitraged away, so for an infinitesimal addition of time, there's an infinitesimal small arbitrage opportunity. In reality, it's only arbitraged as soon as it's large enough to cover transaction costs. Is that correct?  
> **username_2**: @Steven yes pretty much except if you get revenue that just large enough to cover transaction costs it would not qualify as arbitrage - but that’s just semantics  
> **username_0**: Thanks for bearing with me then haha. Follow-up question in this case would be why only the spot rate depreciates and why the forward doesn't appreciate. Can you enlighten me on that one too?  
> **username_2**: @Steven I just used extreme case to show the point if you read my comments carefully you will see that in one of them I mention combination of them can occur as well but I did not focus on that because I thought it would just add more confusion what matters in the model in the end is just that $E[S]/S$ that is the whole ratio will be such that it prevents the arbitrage  
> **username_0**: But how does $E[S]=F$ hold true if the adjustment can go both ways?  
> **username_2**: @Steven yes that will always hold under the assumptions of the model (although of course not in reality)  
> **username_0**: The forward is fixed at time t though, so how does fit with the adjustment until T going both ways?  
> **username_2**: @Steven no the F is determined by what people expect the exchange rate will be in the future - it’s fixed at time t the same way as any price is fixed at any time t but that does not mean it’s fixed at any arbitrary level  
> **username_0**: But we you assume that from t to T no new information arises and expectations don't change for other reasons either; thus the only reason that price moves is the interest rate differential?  
> **username_2**: @Steven yes. If the interest rates are not equal, prices (exchange rate and its expectation) adjust in order to make the equation 1.7 hold and if no new information or changes occur then they stay fixed until something changes further down the road.  

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### Answer by username_4 on 2020-07-31. Score: 0

From a real world perspective, “interest rate parity” always holds - so long as you take into account the cross-currency basis swap spread. (Basis swaps are typically ignored in simple academic models, but are important for cross-currency funding). Forward points are set based on the theoretical relationship, with a bid-offer spread. Any market maker that is off market would be mercilessly arbitraged, and would be looking for a new job. There is no debate about this, that’s how market makers operate.

The only room for research questions are the following.

* Are forwards an accurate measure of market participants forecasts for currency values? Given that the basis and interest rate market pricing is determined by fixed income investors who often cannot trade foreign exchange, there is no way of surveying “investors” properly. Cross-currency basis swaps are a funding instrument, and are priced based on funding flows. Meanwhile, the primary driver of short-term rates is rate expectations. As such, currency relative valuation does not show up in the instruments determining forward-spot spreads, other than via the indirect route of central bank reactions to currency movements.
* Are forward points offer “good predictions” (however defined) of the future spot rate? That’s where most of the literature ends up, but I think it is safe to say that currency forwards have little useful information about future currency movements. One thing to note is the realised volatility in currencies is often much larger than the deviation of spot and forward, so it’s equivalent to saying that currencies can go up or down.


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