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### Arbitrage Definition

Arbitrage refers to subsequent buying and selling of the same type of asset in different markets to benefit from the variety in prices which each market offers. Each market tags a different price to the same or similar assets, making it more appealing to the investor or company. The imperfectly competitive nature of markets is the main reason for the existence of arbitrage. In a perfect competition, all producers must supply at a fixed price.

### A Little More on What is Arbitrage

Arbitrage, which is a necessary force in the market, is the act of buying assets in a market and immediately selling them off in another market at a higher price. Arbitrage exists when there are different market efficiencies, and the margin error is usually small. However, with the advent of technology, traders across different markets are able to know what each market offers for a particular product. This way, using arbitrage becomes harder. However, since these prices are not checked frequently, investors still have a chance of buying and selling off with a profit, provided it is done immediately, possibly within a matter of seconds or minutes.

### Example of A Simple Arbitrage

Arbitrage can be explained in a concise manner using the example given below. Let us assume that a particular Stock CSX is trading at $10.20 on the New York Stock Exchange while trading at $10.00 at Nasdaq at the same time. Now, a trader who discovers this loophole exploits it by buying shares of CSX from Nasdaq at $10, and selling them immediately at $10.20 on the NYSE, thus bagging him or her a profit of $0.20 per stock. This will probably continue till of the stock exchange markets adjusts their price to meet the otherās, or till Nasdaq runs out of stock CSX in its inventory.

### Example of a Complex Arbitrage

In analyzing a complex arbitrage, we shall look at the triangular arbitrage. Though not the most complicated type of arbitrage, it is much more complex than the simple one stated above. In a triangular arbitrage, an individual might choose to convert his or her currency to another in a bank. After that, he or she will proceed with the new currency to a second bank and convert it to another currency. Next, he or she proceeds to a third bank with the new currency and changes it to the first currency, with profits. If the same bank is used, it would have the information of the individual and will adjust its exchange rate to make sure that the individual goes home with what they came with.

Thus, this person deems it best to visit a different bank to convert one currency to another.

Assuming that the individual starts with $5 million. He or she visits three banks A, B, and C, who all have the following exchange rates

- Bank A : USD to EUR = 0. 894
- Bank B: EUR to KWD = 0.34
- Bank C: KWD to USD = 3.3

Using the rates above, youāll first convert the $5 million to euros at 0.894, thus giving you 4,470,000 euros. Now, youāll take that amount to Bank B and convert it to Kuwaiti Dinar at 0.34 dinar for a euro. This would give you 1,519,800 KWD. Next, youāll visit Bank C and convert the KWD to USD at 3.3 dollars per dinar. This would give you 5,015,340 USD. In this case, the extra $15,340 becomes your risk-free arbitrage.

### Reference for āArbitrageā

https://www.investopedia.com/terms/a/arbitrage.asp

https://economictimes.indiatimes.com āŗ Definitions āŗ Equity

https://en.wikipedia.org/wiki/Arbitrage

https://corporatefinanceinstitute.com āŗ Resources āŗ Knowledge āŗ Trading & Investing

https://investinganswers.com/financial-dictionary/world-markets/arbitrage-2171

### Academics research on āArbitrageā

TheĀ **arbitrageĀ **theory of capital asset pricing, **Ross, S. A. (2013). The arbitrage theory of capital asset pricing. InĀ ***Handbook of the Fundamentals of Financial Decision Making: Part I*** (pp. 11-30). **The purpose of this paper is to examine rigorously the arbitrage model of capital asset pricing developed in Ross [13, 14]. The arbitrage model was proposed as an alternative to the mean variance capital asset pricing model, introduced by Sharpe, Lintner, and Treynor, that has become the major analytic tool for explaining phenomena observed in capital markets for risky assets. The principal relation that emerges from the mean variance model holds that for any asset,Ā *i*, its (ex ante) expected returnĀ Ā whereĀ *Ļ*Ā is the riskless rate of interest, is the expected excess return on the market,Ā *E**m*Ā āĀ *Ļ*, andĀ Ā is the beta coefficient on the market, whereĀ *Ļ**m*2Ā is the variance of the market portfolio andĀ Ā is the covariance between the returns on the ith asset and the market portfolio. (If a riskless asset does not exist,Ā *Ļ*Ā is the zero-beta return, i.e., the return on all portfolios uncorrelated with the market portfolio)ā¦

The limits ofĀ **arbitrage**, **Shleifer, A., & Vishny, R. W. (1997). The limits of arbitrage.Ā ***The Journal of finance***,Ā ***52***(1), 35-55. **Textbook arbitrage in financial markets requires no capital and entails no risk. In reality, almost all arbitrage requires capital, and is typically risky. Moreover, professional arbitrage is conducted by a relatively small number of highly specialized investors using other people’s capital. Such professional arbitrage has a number of interesting implications for security pricing, including the possibility that arbitrage becomes ineffective in extreme circumstances, when prices diverge far from fundamental values. The model also suggests where anomalies in financial markets are likely to appear, and why arbitrage fails to eliminate them.

An empirical investigation of theĀ **arbitrageĀ **pricing theory, **Roll, R., & Ross, S. A. (1980). An empirical investigation of the arbitrage pricing theory.Ā ***The Journal of Finance***,Ā ***35***(5), 1073-1103. **Empirical tests are reported for Ross’ [48] arbitrage theory of asset pricing. Using data for individual equities during the 1962ā72 period, at least three and probably four priced factors are found in the generating process of returns. The theory is supported in that estimated expected returns depend on estimated factor loadings, and variables such as the own standard deviation, though highly correlated (simply) with estimated expected returns, do not add any further explanatory power to that of the factor loadings.

**ArbitrageĀ **with fractional Brownian motion, **Rogers, L. C. G. (1997). Arbitrage with fractional Brownian motion.Ā ***Mathematical Finance***,Ā ***7***(1), 95-105. **Fractional Brownian motion has been suggested as a model for the movement of log share prices which would allow longārange dependence between returns on different days. While this is true, it also allows arbitrage opportunities, which we demonstrate both indirectly and by constructing such an arbitrage. Nonetheless, it is possible by looking at a process similar to the fractional Brownian motion to model longārange dependence of returns while avoiding arbitrage.

Covered interestĀ **arbitrage**: Unexploited profits?, **Frenkel, J. A., & Levich, R. M. (1975). Covered interest arbitrage: Unexploited profits?.Ā ***Journal of Political Economy***,Ā ***83***(2), 325-338. **Empirical studies of covered interest arbitrage suggest that the parity condition is not always satisfied and thus implying unexploited profit opportunities. This paper provides a procedure for estimating transaction costs in the markets for foreign exchange and for securities. Allowance for these costs accounts for most of the apparent profit opportunities. It is shown that in addition to transaction costs, demand and supply elasticities in the various markets and lags in executing arbitrage can account for all of the apparent profit opportunities. It is concluded that empirical data are consistent with the interest parity theory and that covered interest arbitrage does not entail unexploited profit opportunities.