Arbitrage simply means finding two things that are essentially the same and buying the cheaper and selling, or selling short the more expensive. “Buying an asset in one market and simultaneously selling an identical asset in another market at a higher price. Sometimes these will be identical assets in different markets, for instance, shares in a company listed on both the London Stock Exchange and New York Stock Exchange.”(Economist) “Formally, theoreticians define an arbitrage as a trading strategy that requires the investment of no capital, cannot lose money, and has a positive probability of making money.” (Riskglossary)
Law of One Price:
The Law of one price says that a commodity will sell for the same price regardless of where it is purchased. “An economic rule which states that in an efficient market, a security must have a single price, no matter how that security is created. For example, if an option can be created using two different sets of underlying securities, then the total price for each would be the same or else an arbitrage opportunity would exist”. (Investor Words) Thus the concept ‘Law of One Price” relates to “the impact of market arbitrage and trade on the identical commodities that are exchanged in two or more markets”. (EH.Net)
Role of Arbitrage and Law of One Price in a Market-based System
An efficient stock market is one in which stock prices fully reflect available information. According to Andrei Shleifer (2000) there are three determinants of market efficiency. They are (1) Rationality, (2) independent deviations from rationality, (3) arbitrage. Of these determinants arbitrage plays a dominant role in making the stock market more efficient.
The stock market consists of both irrational amateurs and rational professional investors. Based on their irrational thinking some times the amateurs may carry the stocks either above or below their efficient prices. This irrational thinking comes as a result of their emotions about the valuation of the stocks. The professionals on the other hand do not react on the basis of their emotions but evaluate the market information coolly and clearly and make their investment decisions. This way the professionals have more confidence than that of the amateurs. This enables the professional to take larger risks on certain stocks even knowing that such stocks are mispriced, while the amateurs might take risk for a smaller sum. Here ‘Arbitrage’ comes into place. Arbitrage generates profit from the simultaneous purchase and sale of different but substitute securities. If the arbitrage of professionals dominates the speculation of amateurs markets would still be efficient. This is one of the determinants of market efficiency. (Ross Wasterfield Jaffe) The role and purpose of arbitrage can thus be regarded as maintaining the efficiency of the stock market.
The Law of one price is also known as the theory of ‘Purchasing Power Parity’ “The general idea behind purchasing power parity is that a unit of currency should be able to buy the same basket of goods in one country as the equivalent amount of foreign currency, at the going exchange rate, can buy in a foreign country, so that there is parity in the purchasing power of the unit of currency across the two economies.” (Alan M. Taylor and Mark P. Taylor 2004)
Thus under ‘law of one price’ the same asset must be traded at the same price in all markets. When the law of one price does not hold good the arbitrageur will indulge in:
- (1) Buying the assets in the market where it is selling at a cheaper price and selling it or short selling it simultaneously in another market where the price is higher.
- (2) Delivering the assets to the contracted buyer and collect the higher prices.
- (3) Paying the contracted seller in the market where the asset is sold cheap and thereby make a huge margin simply by the difference in the prices in the different markets.
Hence the law of one price is important to keep the equilibrium in a market based system.
‘One Price’ of an Asset
An asset represents a financial instrument that has a current purchase price and one or more future pay offs and a ‘bond’ is a simplest form of an asset. The bond has a definite future monetary payoff regardless of its state in the future. However in the case of stocks there is no certainty of payoffs, since there are different factors acting on the value of the shares. The payoffs depend on the state of nature that emerges in future. Similarly other assets have different payoffs. Despite the differences in payoffs and structures the financial assets transfer purchasing power among different parties.
“Buying an asset implies we are transferring purchasing power from the present to some future state; selling or short-selling an asset implies we are transferring purchasing power from some future state to the present. Regardless of the type of financial asset – stocks, bonds, options, etc. – all of them involve at least these time-and-state spanning properties.” (History of Economic Thought)
The assets are traded in the asset market and hence the asset market becomes the place where the prices of assets are determined. One of the important aspects of financial theory is the determination of asset prices and there are some competing theories developed in this direction.
According to Dybvig and Ross, (1987)” the one concept that unifies all of finance” is the condition that in the equilibrium position of the asset market the asset prices are such that there is no place of practicing any arbitrage. As already explained ‘arbitrage’ implies buying financial assets at a low price and selling them at higher price at the same time so that the earning from the sale transaction pays off the cost of buying the stocks.
However in principle ‘absence of arbitrage’ presupposes the existence of the individual rationality of a single agent.
The absence of arbitrage opportunities requires the existence of the following things in the market system.
- There exists the ‘law of one price’ for the assets having same return.
- The prices of all assets with the same riskless return should have the same price.
Hence when we adopt the ‘law of one price’ there can not be any transactions to purchase and short sell a single asset make a margin in the process of entering into the transaction. But for achieving this position the second condition that the prices of all assets within the same class of risk should be having ‘one price’. This is a part of ‘Arbitrage Pricing Theory’ which is an equilibrium model based on individuals arbitraging across multiple factors. (James Van Horne)
Reference:
- Alan M. Taylor and Mark P. Taylor (2004) ‘The Purchasing Power Parity Debate ‘NBER Working Papers
- http://www.econ.ucdavis.edu/faculty/amtaylor/papers/w10607.pdf
- Andrei Shleifier (2000) ‘Inefficient Markets: An Introduction to Behavioural Finance’ Oxford United Kingdom
- Dybvig P.H and Ross S.A.(1987) “Arbitrage”, in Eatwell, Milgate and Newman, editors, The New Palgrave: Finance New York: Norton.
- Economist ‘Arbitrage’
- http://www.economist.com/research/Economics/searchActionTerms.cfm?query=arbitraged
- EH.Net Encyclopedia ‘The Law of One Price’
- http://eh.net/encyclopedia/article/persson.LOOP
- Investor Words ‘Law of one Price’
- http://www.investorwords.com/2725/law_of_one_price.html
- James C. Van Horne ‘Financial Management Policy’ Edition XII Prentice Hall of India Private Limited
- History of Economic Thought ‘Arbitrage and Equilibrium’
- http://cepa.newschool.edu/het/essays/sequence/arbitrage.htm
- Riskglossary ‘Arbitrage’
- http://www.riskglossary.com/link/arbitrage.htm
- Ross A.Stephen, Westerfield A. Tandolph Jaffe Jaffrey ‘Corporate Finance’ Edition VII Tata-McGrawhill Publishing Company Ltd
