<p>Because of exchange rate and uncovered interest rate parity (UIP). By the UIP the following relationship should hold between nominal interest rates and exchange rates:</p>
<p><span class="math-container">$$ (1+i_{t}^$) = \frac{E_t(S_{t+1})}{S_t}(1+i_{t}^€)$$</span></p>
<p>In short, the ratio of expected future nominal exchange rate (<span class="math-container">$E_t(S_{t+1})$</span>) and current nominal exchange rate (<span class="math-container">$S_t$</span>) should make the interest rates in US (<span class="math-container">$i^{\\\$}$</span>) and Eurozone (<span class="math-container">$i_{t}^€$</span>), equivalent eliminating any arbitrage opportunities.  If the equality above would not hold, then there indeed would be an opportunity for an arbitrage, but as soon as people would take advantage of the arbitrage opportunity trading on forex markets would move exchange rate to the proper position. You can learn more details on intuition behind UIP in Copeland Exchange Rates and International Finance.</p>
<p>In real life the above equation will sometimes be violated but empirical evidence shows trading typically eliminates arbitrage opportunities very fast. Usually within hours or days, or few weeks at the most save for some special circumstances (see discussion in Nelson International Macroeconomics and Finance in first chapter).</p>
<p>In addition, to the above mentioned UIP which may not always hold there is also related concept of covered interest rate parity (CIP) where expected future exchange rate is replaced with value of futures for the exchange rate and thus given by:</p>
<p><span class="math-container">$$ (1+i_{t}^$) = \frac{F_{t}}{S_t}(1+i_{t}^€)$$</span></p>
<p>When it comes to intuition and mechanism of the model there is not much difference between UIP and CIP but evidence shows CIP is being violated less frequently (again see the Nelson reference above). This is precisely because value of future contracts is easier to measure and thus any possible arbitrage will closed much sooner or even prevented altogether by movements in price of futures.</p>

CC BY-SA 4.0
2021-04-29T14:13:26.680Z
Only violation of CIP can result in arbitrage. Violation of UIP would mean profits with positive expected value, but since there is risk, this is not arbitrage. Also, in real life $E_t(S_{t+1})$ is not precisely known, as no one declares expectations.
Giskard
CC BY-SA 4.0
2021-04-29T14:23:10.070Z
1) no actually you can talk of arbitrage even under UIP because just because there are expectations there that does not mean one is not able to make riskless profit. In fact, if the above UIP holds with equality then there is possibility for risky profits due to the fact that it is about expected value. If it won't hold with equality then there is possibility for not just risky but also riskless profit since risks can be hedged 2) you are right IRL E(S_t+k)  is not precisely known but one can use proxies. I am not claiming the UIP is useful for trading but it explains the mechanism
1muflon1
CC BY-SA 4.0
2021-04-29T14:32:46.240Z
@Giskard I added explanation of CIP as well, but in literature people do talk about arbitrage even with UIP since you can always eliminate risk by hedging and thus get risk less profits but only if the equality holds because otherwise the hedging strategies that completely eliminate risk will leave you with no profit (see the previous comment - sorry I forgot to tag you there)
1muflon1
CC BY-SA 4.0
2021-04-29T15:37:45.843Z
"*I am not claiming the UIP is useful for trading but it explains the mechanism*" This feels contradictory to me. Also, I got the notification for both of your comments, even the untagged one.
Giskard
CC BY-SA 4.0
2021-04-29T15:57:39.937Z
@Giskard I don’t think it’s a contradiction. Consider a person playing pool. For such person knowing all physical formulas that govern motion of a ball and that offer explanation why ball moves and how it pushes other balls is useless. A pool player does not need to know physics to play pool. But if a billiard player wants to understand why those balls move then the player needs to consult the physical formulas that explain mechanism. However, knowledge of the mechanism does not make one better pool player. The reason why physical formulas and the formula above would be useless is
1muflon1
CC BY-SA 4.0
2021-04-29T16:01:24.583Z
Exactly the same. A) different values might be hard to measure since pool rules presumably don’t allow for precise measuring devices and in economics it might be due to lack of data and so forth. B) even having all the data at hand it might be too difficult to act on them - a billiard player might not know how to put precise force under precise angle to move ball as the formula would demand a trader might not have access to some trading strategies that would allow full hedge. But none of this means the formulas do not offer accurate description physical/economic mechanisms respectively
1muflon1
CC BY-SA 4.0
2021-04-29T16:11:05.310Z
Sorry, but I always disliked "proof by analogy". This is a mathematical equation. Either it directly corresponds to the trader not being able to profit from arbitrage or it does not. I think it does not, as you also need a bunch of additional assumptions, such as perfect hedging at no loss of expected value.
Giskard
CC BY-SA 4.0
2021-04-29T14:04:30.013Z
2021-04-29T14:31:57.663Z
2021-04-29T14:31:57.663Z
1muflon1
<p>Why can I not borrow $1B of EUR at EURIBOR (pays me 50bps per year), convert it to USD (also pays me 50bps per year), lend it out at LIBOR, and collect a 1% spread? Am I missing somethign obvious?</p>
<p><a href="https://www.euribor-rates.eu/en/current-euribor-rates/" rel="nofollow noreferrer">EURIBOR</a>
and <a href="https://tradingeconomics.com/united-states/interbank-rate" rel="nofollow noreferrer">LIBOR</a></p>

CC BY-SA 4.0
2021-04-29T14:11:28.603Z
Are you a bank, or how come you can get loans at such low rates? Or are you asking how come banks do not do this?
Giskard
CC BY-SA 4.0
2021-04-29T14:58:37.287Z
The [EUR/USD exchange rate](https://fred.stlouisfed.org/series/DEXUSEU) is likely to change by more than 1% over a year, so there is risk involved here when you need to pay off your initial loan
Henry
<interest-rate><banking><nonexpert>
How is it not arbitrage that EURIBOR (EUR) is around -0.5% and LIBOR (USD) is around 0.5%?
Derek Fulton
# How is it not arbitrage that EURIBOR (EUR) is around -0.5% and LIBOR (USD) is around 0.5%?

(Asked by: username_0 on 2021-04-29)

Why can I not borrow $1B of EUR at EURIBOR (pays me 50bps per year), convert it to USD (also pays me 50bps per year), lend it out at LIBOR, and collect a 1% spread? Am I missing somethign obvious?

[EURIBOR](https://www.euribor-rates.eu/en/current-euribor-rates/)
and [LIBOR](https://tradingeconomics.com/united-states/interbank-rate)

**Tags:** interest-rate, banking, nonexpert
> **Comments:**
> **username_1**: Are you a bank, or how come you can get loans at such low rates? Or are you asking how come banks do not do this?  
> **username_2**: The [EUR/USD exchange rate](https://fred.stlouisfed.org/series/DEXUSEU) is likely to change by more than 1% over a year, so there is risk involved here when you need to pay off your initial loan  

---

## 1 answers

### Answer by username_3 on 2021-04-29. Score: 1 | Accepted answer

Because of exchange rate and uncovered interest rate parity (UIP). By the UIP the following relationship should hold between nominal interest rates and exchange rates:

$$ (1+i\_{t}^$) = \frac{E\_t(S\_{t+1})}{S\_t}(1+i\_{t}^€)$$

In short, the ratio of expected future nominal exchange rate ($E\_t(S\_{t+1})$) and current nominal exchange rate ($S\_t$) should make the interest rates in US ($i^{\\\$}$) and Eurozone ($i\_{t}^€$), equivalent eliminating any arbitrage opportunities. If the equality above would not hold, then there indeed would be an opportunity for an arbitrage, but as soon as people would take advantage of the arbitrage opportunity trading on forex markets would move exchange rate to the proper position. You can learn more details on intuition behind UIP in Copeland Exchange Rates and International Finance.

In real life the above equation will sometimes be violated but empirical evidence shows trading typically eliminates arbitrage opportunities very fast. Usually within hours or days, or few weeks at the most save for some special circumstances (see discussion in Nelson International Macroeconomics and Finance in first chapter).

In addition, to the above mentioned UIP which may not always hold there is also related concept of covered interest rate parity (CIP) where expected future exchange rate is replaced with value of futures for the exchange rate and thus given by:

$$ (1+i\_{t}^$) = \frac{F\_{t}}{S\_t}(1+i\_{t}^€)$$

When it comes to intuition and mechanism of the model there is not much difference between UIP and CIP but evidence shows CIP is being violated less frequently (again see the Nelson reference above). This is precisely because value of future contracts is easier to measure and thus any possible arbitrage will closed much sooner or even prevented altogether by movements in price of futures.

> **Comments:**
> **username_1**: Only violation of CIP can result in arbitrage. Violation of UIP would mean profits with positive expected value, but since there is risk, this is not arbitrage. Also, in real life $E_t(S_{t+1})$ is not precisely known, as no one declares expectations.  
> **username_3**: 1) no actually you can talk of arbitrage even under UIP because just because there are expectations there that does not mean one is not able to make riskless profit. In fact, if the above UIP holds with equality then there is possibility for risky profits due to the fact that it is about expected value. If it won't hold with equality then there is possibility for not just risky but also riskless profit since risks can be hedged 2) you are right IRL E(S_t+k)  is not precisely known but one can use proxies. I am not claiming the UIP is useful for trading but it explains the mechanism  
> **username_3**: @Giskard I added explanation of CIP as well, but in literature people do talk about arbitrage even with UIP since you can always eliminate risk by hedging and thus get risk less profits but only if the equality holds because otherwise the hedging strategies that completely eliminate risk will leave you with no profit (see the previous comment - sorry I forgot to tag you there)  
> **username_1**: "*I am not claiming the UIP is useful for trading but it explains the mechanism*" This feels contradictory to me. Also, I got the notification for both of your comments, even the untagged one.  
> **username_3**: @Giskard I don’t think it’s a contradiction. Consider a person playing pool. For such person knowing all physical formulas that govern motion of a ball and that offer explanation why ball moves and how it pushes other balls is useless. A pool player does not need to know physics to play pool. But if a billiard player wants to understand why those balls move then the player needs to consult the physical formulas that explain mechanism. However, knowledge of the mechanism does not make one better pool player. The reason why physical formulas and the formula above would be useless is  
> **username_3**: Exactly the same. A) different values might be hard to measure since pool rules presumably don’t allow for precise measuring devices and in economics it might be due to lack of data and so forth. B) even having all the data at hand it might be too difficult to act on them - a billiard player might not know how to put precise force under precise angle to move ball as the formula would demand a trader might not have access to some trading strategies that would allow full hedge. But none of this means the formulas do not offer accurate description physical/economic mechanisms respectively  
> **username_1**: Sorry, but I always disliked "proof by analogy". This is a mathematical equation. Either it directly corresponds to the trader not being able to profit from arbitrage or it does not. I think it does not, as you also need a bunch of additional assumptions, such as perfect hedging at no loss of expected value.  

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