<p>Nobody has to loose in an arbitrage. Economic relationships are not necessarily zero-sum (in fact often they will not be zero-sum). For example, if apples in city A are sold for <span class="math-container">${\\\$}5$</span> and apples in city B can be sold for <span class="math-container">${\\\$}8$</span>, and we assume zero transaction cost there will be an arbitrage opportunity to earn <span class="math-container">${\\\$}3$</span> riskless profit per apple by buying apples in city A and selling them in city B. But nobody looses in the transaction.</p>
<p>The apple producers in city A clearly value <span class="math-container">${\\\$}5$</span> more (or at least indifferent) than an apple otherwise they would not trade it and just keep the apple. So giving them <span class="math-container">${\\\$}5$</span> will make them better off (or at least not worse off). Then in city B people who buy apples must value apples more than <span class="math-container">${\\\$}8$</span> they are paying for it otherwise they would just keep the money instead of buying them (or at least they must be again indifferent).</p>
<p>Consequently, when people take advantage of arbitrage opportunities generally speaking nobody looses anything. There must be some other issues present that would turn the problem into zero-sum game.</p>
<p>Regarding the microeconomic implications the main one is that people will take advantage of the arbitrage opportunities until the prices on the markets equalize - in the example above until the prices in both cities would become equal. The law of one price is based on the concept of arbitrage. There might be other implications depending on precise setting where arbitrage occurs, to explore all of them would be beyond the scope of SE answer.</p>

CC BY-SA 4.0
2020-11-27T09:26:52.270Z
One could also argue that if the apple farmers sell an apple for \$5 in city A while they could have sold it for \$8 in city B (with 0 transaction costs), then they incur an opportunity cost of \$3 per apple sold. This makes the interaction zero-sum again.
VARulle
CC BY-SA 4.0
2020-11-27T10:33:02.880Z
@VARulle but in that case there would be no opportunity for arbitrage because then the farmers would not sell the apples for 5, if they are presented with choice to sell it in the other city directly. I think there has to be some extra problem there beyond arbitrage.
1muflon1
CC BY-SA 4.0
2020-11-27T13:42:54.447Z
@1muflon1 then why is arbitrage possible? Obviously the seller *would* sell the apples for $8 in city B so the situation is impossible....... *right*?
Criticize SE actions means ban
CC BY-SA 4.0
2020-11-27T13:45:01.027Z
@user253751 you can assume that seller in city A cannot sell it in city B and then arbitrage is possible - but then there is no opportunity cost for seller A because opportunity cost can only exist if seller A could sell it at city B if they would want to
1muflon1
CC BY-SA 4.0
2020-11-27T13:45:54.173Z
@1muflon1 why can't they sell it in city B? Is there a transaction cost?
Criticize SE actions means ban
CC BY-SA 4.0
2020-11-27T13:47:39.020Z
@user253751 you have to impose that as an assumption if there is transaction cost there would not be any arbitrage at all if the transaction cost is equal to the difference in prices between A and B there is no possibility for risk-less profit or arbitrage. For example you can assume law prevents them from selling in city B
1muflon1
CC BY-SA 4.0
2020-11-27T13:52:00.003Z
@1muflon1 also why doesn't the seller sell all his apples for $7.99 to the arbitrageur?
Criticize SE actions means ban
CC BY-SA 4.0
2020-11-27T13:54:03.750Z
@user253751 for example perfect competition amongst the sellers in the different cities.
1muflon1
CC BY-SA 4.0
2020-11-27T13:59:01.383Z
@1muflon1 sounds like a situation that only government regulation can create
Criticize SE actions means ban
CC BY-SA 4.0
2020-11-27T14:03:33.180Z
@user253751 there can be situations where it can happen without government regulation. However, arbitrage opportunities in real life are really rare. For example,  if you have some unique information about effect of an event on economy there could be an arbitrage opportunity that exists only for you thanks to this information but once you start acting on this you destroy the arbitrage opportunity for yourself - for example let’s assume that  only you know with certainty that there will be cold winter that will make apples more expensive so you start buying them now. For the first apple you
1muflon1
CC BY-SA 4.0
2020-11-27T14:07:00.897Z
but there would be possibility for a risk less profit but as you put extra demand on apples price will eventually move to close the arbitrage opportunity. In real life research shows that arbitrage opportunities rarely last more than few hours. However, long lasting arbitrage can only exist if it is enforced somehow in one way or another.
1muflon1
CC BY-SA 4.0
2020-11-27T14:45:53.007Z
@1muflon1 Arbitrage opportunities with negligible profit are pretty common, though, right? AFAIK, that's how stock prices on different exchanges stay in sync. Some HFT firm somewhere is buying and selling stocks as soon as there's a difference of a fraction of a cent. I'm just saying $3 arbitrage on apples is unrealistic, not all arbitrage.
Criticize SE actions means ban
CC BY-SA 4.0
2020-11-27T14:54:44.057Z
@user253751 it is not clear you can call those arbitrage opportunities because if people are not willing to act on them that means that the profit from them does not cover the cost of them acting. Arbitrage is profit that is left once you account all the costs of doing the arbitrage. Thats why if in the above example there would be transportation cost of 3USD there would not be any arbitrage there because if you need to pay those 3USD to move the good from city A to city B there is no profit. In economics profit does not coincide with accounting profit if there is nonmonetary cost still counts
1muflon1
CC BY-SA 4.0
2020-11-27T14:55:06.957Z
@1muflon1 HFT firms act on them, right?
Criticize SE actions means ban
CC BY-SA 4.0
2020-11-27T14:57:11.930Z
@user253751 right because they have algorithms and enough money to make bulk transactions that reduce their cost on acting them. That is basically the same example as in cities where we assumed the two sellers cant move and sell in other city but the hypothetical 'trader' can move completely freely. Also those arbitrage opportunities lasts only seconds
1muflon1
CC BY-SA 4.0
2020-11-27T14:58:15.167Z
In a *financial market* where shipping costs are effectively zero, counterparties of the arbitrageur are losing money versus a somewhat hypothetical of standard instantaneous mark-to-market of arbitrage-free mid prices. Keep in mind that every transaction away from mid price would generate winners/losers by that standard - transaction costs. Given that dealers’ profits are supposed to generated by skimming transaction costs, this is non-negiligible.
Brian Romanchuk
CC BY-SA 4.0
2020-11-27T15:00:16.917Z
@1muflon1 And in this scenario, the HFT firm is basically acting as a shipping company, adding value to the market by ensuring "goods" (stocks) are available wherever people are willing to buy them and skimming a small profit off the top for shipping. So nobody is really losing, as you said in the answer.
Criticize SE actions means ban
CC BY-SA 4.0
2020-11-27T15:00:22.450Z
@BrianRomanchuk opportunity cost can only exist among options that are in your choice set. If someone is loosing on arbitrage that means that they could have taken the opportunity themselves but did not due to some failure of rationality or other issue. Otherwise you cannot claim that they lost. At least not in terms of economic terminology.
1muflon1
CC BY-SA 4.0
2020-11-27T15:04:50.120Z
Unless you are arguing that financial theory is not applicable to this StackExchange, they lost money on a mark-to-market basis, using standard financial theory. They are transacting at off-market prices.
Brian Romanchuk
CC BY-SA 4.0
2020-11-27T15:08:07.210Z
@BrianRomanchuk financial theory and economics diverge in several areas that is why we have money and personal finance and quantitative finance stacks that are separate from econ stacks. If you want to invoke opportunity cost from econ perspective then there have to be other opportunities for example person A has to have opportunity to sell asset for 5 to intermediary that sells it for 8 or directly for 8 so their choice set was C={5,8}. Then if they sell it to intermediary they have loss of 3 because 5-opportunity cost of 8 =3. But then you need to explain why they took choice 5.
1muflon1
CC BY-SA 4.0
2020-11-27T15:10:14.797Z
@BrianRomanchuk of course here you could invoke irrationality, some laws preventing them from selling it for 8 etc. The point is then that the costs itself orthogonal on whether arbitrage is present or not, what causes the loss is that irrationality, laws other issues that would prevent that agent from making choice of selling for 8 directly. So it would not be arbitrage causing loss but those other characteristics
1muflon1
CC BY-SA 4.0
2020-11-27T18:08:47.303Z
Where did I write “opportunity cost”? They are losing money on a mark-to-market basis. If you are saying that economics does not recognize the concept of a mark-to-market loss, then that just means that the answer provided by economics has no useful content for understanding finance.
Brian Romanchuk
CC BY-SA 4.0
2020-11-27T18:15:15.697Z
@BrianRomanchuk I was not familiar with the term. Regardless, arbitrage is profit from purchase and resale of an asset not profit or loss that is made from  an accounting entry rather than through actual sale. For example, monopoly can make also riskless profit but that is not an arbitrage. In addition, and make an argument that arbitrage itself does not causes losses not that there situations where there is an arbitrage and also some other factor that then creates losses
1muflon1
CC BY-SA 4.0
2020-11-27T00:15:58.740Z
2020-11-27T09:35:34.767Z
2020-11-27T09:35:34.767Z
1muflon1
<p>It's important to distinguish between the effects of arbitrage on: a) the direct parties to arbitrage transactions; b) other agents in the markets in which the arbitrage takes place.</p>
<p>Suppose arbitrageurs buy a good in market A in which its price is \$1 and sell in  market B where its price is \$2. Assume further that in each market those prices have freely come about through the interaction of upward-sloping supply and downward-sloping demand curves. Sellers in market A will not lose by selling to an arbitrageur at \$1 or more, and buyers in market B will not lose by buying from an arbitrageur at \$2 or less.  So there is scope for arbitrage to occur with no loss (and indeed some gain) to the direct parties to arbitrage transactions.</p>
<p>However, if the volume of arbitrage is sufficient to move the prices in the two markets, so that the price in market A becomes more than \$1, and that in market B becomes less than \$2, then there are also consequences for agents who are not parties to the arbitrage transactions, namely, buyers in market A and sellers in market B.  The higher price in market A reduces the consumer surplus to its buyers, while the lower price in market B reduces the producer surplus to its sellers.  Thus there is a welfare loss to both these groups.</p>
<p>This is not to make a case that arbitrage is undesirable or a zero-sum game: its overall effect may well be to raise welfare.  It is only to assert that, even so, it may lower welfare for some groups.</p>

CC BY-SA 4.0
2020-11-28T14:11:21.177Z
2020-11-28T14:11:21.177Z
Adam Bailey
<p>I would note that there is a dispute about the approaches to answer this question. I will give an answer based on finance theory, which may or may not be better placed to be on the quantitative finance board. That said, “finance” is a tag here, so the answer appears to appropriate. Note that I am using an idealised definition of profit that is used in finance and accounting, which might not align with that of economics.</p>
<p>I am using the formal definition of arbitrage - an opportunity to simultaneously enter trades that generate risk-free (supernormal profits). Somewhat equivalently, the ability to enter into a position with zero initial cost, and in all (future) states of the world, the future value of the portfolio is greater than or equal to zero - with strictly positive profits in some states. (My reference is page 80 of Rebonato’s “Interest-Rate Option Models,” but should be in any text on mathematical finance.) Many people use a less formal version of “arbitrage,” but I am referring to the formal definition.</p>
<p>Update: Varian uses the definition I use (or the methamtical equivalent): <a href="https://pubs.aeaweb.org/doi/pdf/10.1257/jep.1.2.55#:%7E:text=If%20no%20arbitrage%20possibilities%20exist,of%20the%20Arrow%2DDebreu%20assets.&amp;text=However%2C%20it%20turns%20out%20that,assets%20than%20states%20of%20nature" rel="nofollow noreferrer">link to Varian article “The Arbitrage Principle in Financial Economics”.</a></p>
<p>(The zero entry cost definition of arbitrage eliminates the issue of defining “excess risk free profits”: one can buy a default-risk free money market instrument and get a “risk-free return”. An arbitrage has to generate a higher return. The zero cost definition eliminates the issue; you sell short the money market instrument to get zero initial investment.)</p>
<p>We then assume that we have observed market quotes at all time, and that we can find a set of theoretical prices from an arbitrage-free model that best fits those prices. For simplicity, I will assume that these are mid-prices. Note that observed prices might have arbitrage opportunities, and there are presumably many fittings. All that matters is that we can find one fitting.</p>
<p>We can then do a mark-to-market of all instruments versus that theoretical fitting at all times. Any time an entity trades away from that mid price, they get a corresponding mark-to-market gain/loss, which is mirrored by their counterparty.</p>
<p>Note that this is an idealised version of how financial accounting treats mark-to-market of securities. In the real world, everything is marked to market (bid, mid, depending on convention) at the close. In this example, the pricing is continuous - to match the simultaneous transactions. It’s also pricing versus an arbitrage-free model that is calibrated/fit against benchmarks, which is also standard practice for the derivatives that represent the bulk of the arbitrage trading. Finally, all entities use the same prices for this hypothetical mark-to-market,   which is needed for trading activity to be zero sum.</p>
<p>When an entity enters into an arbitrage trade, it is clear that the gains/losses of all trades have to add up to a profit. The counter parties will in aggregate generate a loss, but the exact distribution is obviously unknown (unless a single counterparty was willing to arbitrage itself).</p>
<p>This framework also explains how market-makers earn a profit: they hope to continuously be trading at prices on the “correct” side of the mid price, and thus generate continuous trading profits.</p>
<p>In the real world, mark-to-market is not done instantaneously, it is done at the end of the day. Furthermore, the pricing used for the mark-to-market procedure used by different entities need not be the same. (In fact, some entities will not do a daily mark-to-market, such as in held-to-maturity accounting.) This implies that actual trading profit and loss will no longer be exactly zero sum.</p>

CC BY-SA 4.0
2020-11-27T18:33:24.933Z
This answer does not use the word arbitrage in the meaning it has in economics. Following Mankiw Principles of Economics, by definition arbitrage is: " arbitrage, the process
of buying a good in one market at a low price and selling it in another market
at a higher price to profit from the price difference." In general I dont know of any definition of arbitrage within economics (finance of course can have different definition) that would count in profits/losses generated by accounting not trades themselves.
1muflon1
CC BY-SA 4.0
2020-11-27T18:38:02.657Z
As noted, I am using the formal definition from academic finance. Since there is a “Finance” tag, it seems unusual to argue that it is inadmissable.
Brian Romanchuk
CC BY-SA 4.0
2020-11-27T19:02:55.933Z
but MTM profit/losses exist because of the fair value accounting under GAAP they are not caused by arbitrage... they are not real profits and they are not caused by arbitrage they exist in any trades especially high frequency trades even if there is no arbitrage
csilvia
CC BY-SA 4.0
2020-11-27T19:16:39.230Z
@BrianRomanchuk we also have tag for agriculture. As far as I understand tags are often descriptive and I am sure you are well aware that there exists two strands of literature - one I would call finance *proper* and finance or financial economics. Originally it was all finance but I am sure you are aware they diverged in last 80 years or so. Also, I dont have problem with you giving answer with finance *proper* perspective but I also think you are not making clear distinctions here that this is not an economics answer to the issue as OP might think finance is just subset of economics.
1muflon1
CC BY-SA 4.0
2020-11-27T19:17:40.037Z
For example, I dont know if the other comment here is correct or not because my understanding of accounting is based on 1 mandatory undergraduate class, but it even seems that here you are not even using profit in the same meaning as economists do. In economics accounting profit and economic profit are different. Yet you are not warning users about that and since this is economics site I think by default people will assume you are using economics definition of profit. I think if you want to take the finance route here that might be good to explain differences in terminology in general
1muflon1
CC BY-SA 4.0
2020-11-27T20:58:40.897Z
@csilva An arbitrage trade is as I defined: a portfolio with zero entry cost, and guaranteed not to lose money (and gains a profit in some states of the world). This will generate a profit against an idealised mid-market pricing generated by an arbitrage-free model. That does not mean that profits cannot be generated by other means.
Brian Romanchuk
CC BY-SA 4.0
2020-11-27T21:01:08.707Z
@1muflon1 I added a note about the definition of profits. I’m pretty sure papers about arbitrage-free yield curve models show up in economics journals - certainly part of central bank research - and they use the standard mathematical finance definition of arbitrage.
Brian Romanchuk
CC BY-SA 4.0
2020-11-27T21:10:50.413Z
@BrianRomanchuk I don’t know about that I already worked at 2 European central banks (CB) and I never heard arbitrage profit/losses being defined in this way - since that other comment mentioned GAAP I wonder if this just depends on accounting. Also CB have research on yields and other stuff but more from macro/international macro perspective. Granted both jobs were RAs and I was working at CB my focus was either macro-prudential policy and calling recession but even at seminars we had I can recall models of arbitrage profit only in connection to exchange rates where econ meaning is used.
1muflon1
CC BY-SA 4.0
2020-11-28T01:34:13.313Z
@BrianRomanchuk but the MTM is not caused by arbitrage
csilvia
CC BY-SA 4.0
2020-11-28T10:10:23.627Z
My 2c :  the OP mentioned Cryptocurrencies as an example.   This sounds a lot more like financial arbitrage than goods and services arbitrage.  There’s no driving from city A to city B, there’s just awareness and connectivity. Hence, I’m ok with @Brian Romanchuk interpretation.
dm63
CC BY-SA 4.0
2020-11-28T13:36:35.170Z
1moflon1 - it’s an instantaneous mark-to-market, which coincides with the instantaneous transactions of the arbitrage transaction. If you use another accounting system, accounting profit might not coincide with the trading mark-to-market profit. My definition matches the notion of transaction costs of created by trading away from mid.  csilva - I did not write that arbitrage “causes” profit, it is evidence that it happened.
Brian Romanchuk
CC BY-SA 4.0
2020-11-27T18:26:49.367Z
2020-11-28T13:43:04.210Z
2020-11-28T13:43:04.210Z
Brian Romanchuk
<ol>
<li><p>When some entity takes advantage of an arbitrage opportunity, who is losing money? For example, when there are price differences across cryptocurrency exchanges and someone exploits an arbitrage opportunity, who is losing out?</p>
</li>
<li><p>A vaguer question: what are the microeconomic implications of arbitrage?</p>
</li>
</ol>

CC BY-SA 4.0
2020-11-27T13:42:02.697Z
The person who could've sold at the other exchange for more money?
Criticize SE actions means ban
CC BY-SA 4.0
2020-11-27T19:31:49.120Z
In essence, arbitrageurs are paid to transmit information from one market to another.
Rodrigo de Azevedo
CC BY-SA 4.0
2020-11-28T18:40:08.710Z
I've read that crypto currencies suffer from a regulatory problem. Since regulatory bodies act on behalf of the people in a democracy, one might say that the people are losing out if crypto-currencies win out. In fact, Facebook was warned away from creating their own - libra - as I recall.
Mozibur Ullah
<microeconomics><supply-and-demand><competitive-equilibrium><currency-exchange><arbitrage>
Who is losing in an arbitrage?
Sade Ifada
# Who is losing in an arbitrage?

(Asked by: username_0 on 2020-11-26)

1. When some entity takes advantage of an arbitrage opportunity, who is losing money? For example, when there are price differences across cryptocurrency exchanges and someone exploits an arbitrage opportunity, who is losing out?
2. A vaguer question: what are the microeconomic implications of arbitrage?

**Tags:** microeconomics, supply-and-demand, competitive-equilibrium, currency-exchange, arbitrage
> **Comments:**
> **username_1**: The person who could've sold at the other exchange for more money?  
> **username_2**: In essence, arbitrageurs are paid to transmit information from one market to another.  
> **username_3**: I've read that crypto currencies suffer from a regulatory problem. Since regulatory bodies act on behalf of the people in a democracy, one might say that the people are losing out if crypto-currencies win out. In fact, Facebook was warned away from creating their own - libra - as I recall.  

---

## 3 answers

### Answer by username_4 on 2020-11-27. Score: 6

Nobody has to loose in an arbitrage. Economic relationships are not necessarily zero-sum (in fact often they will not be zero-sum). For example, if apples in city A are sold for ${\\\$}5$ and apples in city B can be sold for ${\\\$}8$, and we assume zero transaction cost there will be an arbitrage opportunity to earn ${\\\$}3$ riskless profit per apple by buying apples in city A and selling them in city B. But nobody looses in the transaction.

The apple producers in city A clearly value ${\\\$}5$ more (or at least indifferent) than an apple otherwise they would not trade it and just keep the apple. So giving them ${\\\$}5$ will make them better off (or at least not worse off). Then in city B people who buy apples must value apples more than ${\\\$}8$ they are paying for it otherwise they would just keep the money instead of buying them (or at least they must be again indifferent).

Consequently, when people take advantage of arbitrage opportunities generally speaking nobody looses anything. There must be some other issues present that would turn the problem into zero-sum game.

Regarding the microeconomic implications the main one is that people will take advantage of the arbitrage opportunities until the prices on the markets equalize - in the example above until the prices in both cities would become equal. The law of one price is based on the concept of arbitrage. There might be other implications depending on precise setting where arbitrage occurs, to explore all of them would be beyond the scope of SE answer.

> **Comments:**
> **username_5**: One could also argue that if the apple farmers sell an apple for \$5 in city A while they could have sold it for \$8 in city B (with 0 transaction costs), then they incur an opportunity cost of \$3 per apple sold. This makes the interaction zero-sum again.  
> **username_4**: @VARulle but in that case there would be no opportunity for arbitrage because then the farmers would not sell the apples for 5, if they are presented with choice to sell it in the other city directly. I think there has to be some extra problem there beyond arbitrage.  
> **username_1**: @1muflon1 then why is arbitrage possible? Obviously the seller *would* sell the apples for $8 in city B so the situation is impossible....... *right*?  
> **username_4**: @user253751 you can assume that seller in city A cannot sell it in city B and then arbitrage is possible - but then there is no opportunity cost for seller A because opportunity cost can only exist if seller A could sell it at city B if they would want to  
> **username_1**: @1muflon1 why can't they sell it in city B? Is there a transaction cost?  
> **username_4**: @user253751 you have to impose that as an assumption if there is transaction cost there would not be any arbitrage at all if the transaction cost is equal to the difference in prices between A and B there is no possibility for risk-less profit or arbitrage. For example you can assume law prevents them from selling in city B  
> **username_1**: @1muflon1 also why doesn't the seller sell all his apples for $7.99 to the arbitrageur?  
> **username_4**: @user253751 for example perfect competition amongst the sellers in the different cities.  
> **username_1**: @1muflon1 sounds like a situation that only government regulation can create  
> **username_4**: @user253751 there can be situations where it can happen without government regulation. However, arbitrage opportunities in real life are really rare. For example,  if you have some unique information about effect of an event on economy there could be an arbitrage opportunity that exists only for you thanks to this information but once you start acting on this you destroy the arbitrage opportunity for yourself - for example let’s assume that  only you know with certainty that there will be cold winter that will make apples more expensive so you start buying them now. For the first apple you  
> **username_4**: but there would be possibility for a risk less profit but as you put extra demand on apples price will eventually move to close the arbitrage opportunity. In real life research shows that arbitrage opportunities rarely last more than few hours. However, long lasting arbitrage can only exist if it is enforced somehow in one way or another.  
> **username_1**: @1muflon1 Arbitrage opportunities with negligible profit are pretty common, though, right? AFAIK, that's how stock prices on different exchanges stay in sync. Some HFT firm somewhere is buying and selling stocks as soon as there's a difference of a fraction of a cent. I'm just saying $3 arbitrage on apples is unrealistic, not all arbitrage.  
> **username_4**: @user253751 it is not clear you can call those arbitrage opportunities because if people are not willing to act on them that means that the profit from them does not cover the cost of them acting. Arbitrage is profit that is left once you account all the costs of doing the arbitrage. Thats why if in the above example there would be transportation cost of 3USD there would not be any arbitrage there because if you need to pay those 3USD to move the good from city A to city B there is no profit. In economics profit does not coincide with accounting profit if there is nonmonetary cost still counts  
> **username_1**: @1muflon1 HFT firms act on them, right?  
> **username_4**: @user253751 right because they have algorithms and enough money to make bulk transactions that reduce their cost on acting them. That is basically the same example as in cities where we assumed the two sellers cant move and sell in other city but the hypothetical 'trader' can move completely freely. Also those arbitrage opportunities lasts only seconds  
> **username_6**: In a *financial market* where shipping costs are effectively zero, counterparties of the arbitrageur are losing money versus a somewhat hypothetical of standard instantaneous mark-to-market of arbitrage-free mid prices. Keep in mind that every transaction away from mid price would generate winners/losers by that standard - transaction costs. Given that dealers’ profits are supposed to generated by skimming transaction costs, this is non-negiligible.  
> **username_1**: @1muflon1 And in this scenario, the HFT firm is basically acting as a shipping company, adding value to the market by ensuring "goods" (stocks) are available wherever people are willing to buy them and skimming a small profit off the top for shipping. So nobody is really losing, as you said in the answer.  
> **username_4**: @BrianRomanchuk opportunity cost can only exist among options that are in your choice set. If someone is loosing on arbitrage that means that they could have taken the opportunity themselves but did not due to some failure of rationality or other issue. Otherwise you cannot claim that they lost. At least not in terms of economic terminology.  
> **username_6**: Unless you are arguing that financial theory is not applicable to this StackExchange, they lost money on a mark-to-market basis, using standard financial theory. They are transacting at off-market prices.  
> **username_4**: @BrianRomanchuk financial theory and economics diverge in several areas that is why we have money and personal finance and quantitative finance stacks that are separate from econ stacks. If you want to invoke opportunity cost from econ perspective then there have to be other opportunities for example person A has to have opportunity to sell asset for 5 to intermediary that sells it for 8 or directly for 8 so their choice set was C={5,8}. Then if they sell it to intermediary they have loss of 3 because 5-opportunity cost of 8 =3. But then you need to explain why they took choice 5.  
> **username_4**: @BrianRomanchuk of course here you could invoke irrationality, some laws preventing them from selling it for 8 etc. The point is then that the costs itself orthogonal on whether arbitrage is present or not, what causes the loss is that irrationality, laws other issues that would prevent that agent from making choice of selling for 8 directly. So it would not be arbitrage causing loss but those other characteristics  
> **username_6**: Where did I write “opportunity cost”? They are losing money on a mark-to-market basis. If you are saying that economics does not recognize the concept of a mark-to-market loss, then that just means that the answer provided by economics has no useful content for understanding finance.  
> **username_4**: @BrianRomanchuk I was not familiar with the term. Regardless, arbitrage is profit from purchase and resale of an asset not profit or loss that is made from  an accounting entry rather than through actual sale. For example, monopoly can make also riskless profit but that is not an arbitrage. In addition, and make an argument that arbitrage itself does not causes losses not that there situations where there is an arbitrage and also some other factor that then creates losses  

---

### Answer by username_7 on 2020-11-28. Score: 5

It's important to distinguish between the effects of arbitrage on: a) the direct parties to arbitrage transactions; b) other agents in the markets in which the arbitrage takes place.

Suppose arbitrageurs buy a good in market A in which its price is \$1 and sell in market B where its price is \$2. Assume further that in each market those prices have freely come about through the interaction of upward-sloping supply and downward-sloping demand curves. Sellers in market A will not lose by selling to an arbitrageur at \$1 or more, and buyers in market B will not lose by buying from an arbitrageur at \$2 or less. So there is scope for arbitrage to occur with no loss (and indeed some gain) to the direct parties to arbitrage transactions.

However, if the volume of arbitrage is sufficient to move the prices in the two markets, so that the price in market A becomes more than \$1, and that in market B becomes less than \$2, then there are also consequences for agents who are not parties to the arbitrage transactions, namely, buyers in market A and sellers in market B. The higher price in market A reduces the consumer surplus to its buyers, while the lower price in market B reduces the producer surplus to its sellers. Thus there is a welfare loss to both these groups.

This is not to make a case that arbitrage is undesirable or a zero-sum game: its overall effect may well be to raise welfare. It is only to assert that, even so, it may lower welfare for some groups.


---

### Answer by username_6 on 2020-11-27. Score: 0

I would note that there is a dispute about the approaches to answer this question. I will give an answer based on finance theory, which may or may not be better placed to be on the quantitative finance board. That said, “finance” is a tag here, so the answer appears to appropriate. Note that I am using an idealised definition of profit that is used in finance and accounting, which might not align with that of economics.

I am using the formal definition of arbitrage - an opportunity to simultaneously enter trades that generate risk-free (supernormal profits). Somewhat equivalently, the ability to enter into a position with zero initial cost, and in all (future) states of the world, the future value of the portfolio is greater than or equal to zero - with strictly positive profits in some states. (My reference is page 80 of Rebonato’s “Interest-Rate Option Models,” but should be in any text on mathematical finance.) Many people use a less formal version of “arbitrage,” but I am referring to the formal definition.

Update: Varian uses the definition I use (or the methamtical equivalent): [link to Varian article “The Arbitrage Principle in Financial Economics”.](https://pubs.aeaweb.org/doi/pdf/10.1257/jep.1.2.55#:%7E:text=If%20no%20arbitrage%20possibilities%20exist,of%20the%20Arrow%2DDebreu%20assets.&text=However%2C%20it%20turns%20out%20that,assets%20than%20states%20of%20nature)

(The zero entry cost definition of arbitrage eliminates the issue of defining “excess risk free profits”: one can buy a default-risk free money market instrument and get a “risk-free return”. An arbitrage has to generate a higher return. The zero cost definition eliminates the issue; you sell short the money market instrument to get zero initial investment.)

We then assume that we have observed market quotes at all time, and that we can find a set of theoretical prices from an arbitrage-free model that best fits those prices. For simplicity, I will assume that these are mid-prices. Note that observed prices might have arbitrage opportunities, and there are presumably many fittings. All that matters is that we can find one fitting.

We can then do a mark-to-market of all instruments versus that theoretical fitting at all times. Any time an entity trades away from that mid price, they get a corresponding mark-to-market gain/loss, which is mirrored by their counterparty.

Note that this is an idealised version of how financial accounting treats mark-to-market of securities. In the real world, everything is marked to market (bid, mid, depending on convention) at the close. In this example, the pricing is continuous - to match the simultaneous transactions. It’s also pricing versus an arbitrage-free model that is calibrated/fit against benchmarks, which is also standard practice for the derivatives that represent the bulk of the arbitrage trading. Finally, all entities use the same prices for this hypothetical mark-to-market, which is needed for trading activity to be zero sum.

When an entity enters into an arbitrage trade, it is clear that the gains/losses of all trades have to add up to a profit. The counter parties will in aggregate generate a loss, but the exact distribution is obviously unknown (unless a single counterparty was willing to arbitrage itself).

This framework also explains how market-makers earn a profit: they hope to continuously be trading at prices on the “correct” side of the mid price, and thus generate continuous trading profits.

In the real world, mark-to-market is not done instantaneously, it is done at the end of the day. Furthermore, the pricing used for the mark-to-market procedure used by different entities need not be the same. (In fact, some entities will not do a daily mark-to-market, such as in held-to-maturity accounting.) This implies that actual trading profit and loss will no longer be exactly zero sum.

> **Comments:**
> **username_4**: This answer does not use the word arbitrage in the meaning it has in economics. Following Mankiw Principles of Economics, by definition arbitrage is: " arbitrage, the process of buying a good in one market at a low price and selling it in another market at a higher price to profit from the price difference." In general I dont know of any definition of arbitrage within economics (finance of course can have different definition) that would count in profits/losses generated by accounting not trades themselves.  
> **username_6**: As noted, I am using the formal definition from academic finance. Since there is a “Finance” tag, it seems unusual to argue that it is inadmissable.  
> **username_8**: but MTM profit/losses exist because of the fair value accounting under GAAP they are not caused by arbitrage... they are not real profits and they are not caused by arbitrage they exist in any trades especially high frequency trades even if there is no arbitrage  
> **username_4**: @BrianRomanchuk we also have tag for agriculture. As far as I understand tags are often descriptive and I am sure you are well aware that there exists two strands of literature - one I would call finance *proper* and finance or financial economics. Originally it was all finance but I am sure you are aware they diverged in last 80 years or so. Also, I dont have problem with you giving answer with finance *proper* perspective but I also think you are not making clear distinctions here that this is not an economics answer to the issue as OP might think finance is just subset of economics.  
> **username_4**: For example, I dont know if the other comment here is correct or not because my understanding of accounting is based on 1 mandatory undergraduate class, but it even seems that here you are not even using profit in the same meaning as economists do. In economics accounting profit and economic profit are different. Yet you are not warning users about that and since this is economics site I think by default people will assume you are using economics definition of profit. I think if you want to take the finance route here that might be good to explain differences in terminology in general  
> **username_6**: @csilva An arbitrage trade is as I defined: a portfolio with zero entry cost, and guaranteed not to lose money (and gains a profit in some states of the world). This will generate a profit against an idealised mid-market pricing generated by an arbitrage-free model. That does not mean that profits cannot be generated by other means.  
> **username_6**: @1muflon1 I added a note about the definition of profits. I’m pretty sure papers about arbitrage-free yield curve models show up in economics journals - certainly part of central bank research - and they use the standard mathematical finance definition of arbitrage.  
> **username_4**: @BrianRomanchuk I don’t know about that I already worked at 2 European central banks (CB) and I never heard arbitrage profit/losses being defined in this way - since that other comment mentioned GAAP I wonder if this just depends on accounting. Also CB have research on yields and other stuff but more from macro/international macro perspective. Granted both jobs were RAs and I was working at CB my focus was either macro-prudential policy and calling recession but even at seminars we had I can recall models of arbitrage profit only in connection to exchange rates where econ meaning is used.  
> **username_8**: @BrianRomanchuk but the MTM is not caused by arbitrage  
> **username_9**: My 2c :  the OP mentioned Cryptocurrencies as an example.   This sounds a lot more like financial arbitrage than goods and services arbitrage.  There’s no driving from city A to city B, there’s just awareness and connectivity. Hence, I’m ok with @Brian Romanchuk interpretation.  
> **username_6**: 1moflon1 - it’s an instantaneous mark-to-market, which coincides with the instantaneous transactions of the arbitrage transaction. If you use another accounting system, accounting profit might not coincide with the trading mark-to-market profit. My definition matches the notion of transaction costs of created by trading away from mid.  csilva - I did not write that arbitrage “causes” profit, it is evidence that it happened.  

---

