Purchasing Power Parity Theorem

Introduction

The concept of purchasing power parity claims that the equilibrium for the exchange rate of two currencies is attained if they have the same ability to buy a fixed quantity of goods. If the purchasing power parity theorem holds, then the exchange rate of two countries should be equal to the ratio of prices of a fixed volume of goods in these countries. With inflation, the exchange rate needs to be adjusted in order to retain the purchasing power parity. The paper seeks to establish if an arbitrage opportunity exists between the United States and the United Kingdom. In the calculations, the United States shall be the foreign country while the United Kingdom will be the domestic country. Further, the review will cover a period of 6 years between January 2009 and December 2014. The data used and all the calculations are presented in the attached excel file. In the analysis, it was established that no-arbitrage condition exists between the two countries. The findings suggest that the purchasing power parity theorem holds.

Arbitrage opportunity

The calculations in the excel file aim at estimating the values of forwarding exchange. The results show that there is no numerical difference between the forward exchange rate and the spot rate. This is because if the differences between these two rates are rounded off to four decimal places, then the values are zero for all the months. This implies that the values of the two exchange rates are equal (Mankiw 2014). The graph presented below shows the trend of spot, forward exchange rate, and the difference between the rates.

In the graph, it can be noted that the line for forwarding exchange rate is superimposed on the line for a spot rate. Also, the line graph for the differences is at zero. This implies that the values of the two rates are equal. It also shows that there is no opportunity for arbitrage. An arbitrage opportunity arises as a result of differences in quotes of the exchange rate. Such differences allow traders to take advantage of different rates offered by different brokers. It is worth mentioning that this condition is a state of equilibrium and it will leave an investor indifferent about which country to invest in (Becker 2013).

Reasons no-arbitrage arbitrage condition

In the discussion above, it is established that the no-arbitrage condition exists. An arbitrage condition presents an opportunity of earning a profit that is free of risk after deducting the costs that are related to the transactions. A number of reasons explain why this condition exists. The first reason is the lack of an opportunity to promptly buy at low price and sell at a high price. As mentioned in the section above, the spot and forward exchange rates between the British Pound and the US Dollar was equal during the six year period. Therefore, a trader cannot buy low in one currency and sells high in another currency. The findings affirm that the law of one price holds. The law states that the price of a given commodity will remain the same, irrespective of the country, when the exchange rate is taken into account. This law is similar to the purchasing power parity theorem (Silver 2010).

The concept of purchasing power theorem can hold under certain assumptions. The first assumption is that there should be a competitive market for the commodities in the United Kingdom and the United States. The competitive market will allow commodities to trade freely in the market. This assumption eliminates the availability of market imperfections such as the existence of monopoly and other imperfect forms of market structures. The second assumption of this theorem is that it applies to commodities that are movable only. This is based on the fact that movable goods can be traded in across different countries because they can be shipped from one market to another. Therefore, immobile commodities such as land are left out. From a theoretical point of view, the Balassa-Samuelson effect outlines that some commodities cannot be transacted (Winston & Albrigh 2011). The inability to transact arises from the differences in the consumption patterns. For instance, a country in which most of the operations are labor intensive may find it difficult to exchange labor with a country whose operations are capital intensive. The nature of production has a potential of affecting the prices of commodities being compared in these countries. Such commodities limits the application of the theorem. Since no arbitrage condition exists between these countries, it indicates that all commodities can be traded or exchanged between the countries (Kwok 2008).

The third assumption is that there are no other costs that are incurred when carrying out the transaction. Examples of these costs are shipping, transaction and taxation. These costs have a potential of eliminating the similarity in prices between the two countries. However, this assumption is impractical unless the transactions are carried out electronically. Another assumption is that there is no barrier to the exchange of commodities between the two countries. This allows for free flow of commodities. In real life, countries usually impose trade barriers with other countries for a number of reasons. However, since the law of one price holds between these two countries, it implies that this assumption is fulfilled (Ignatiuk 2009).

Theories allude that when an arbitrage opportunity exits, then the law of one price does not hold. Therefore, an arbitrageur will make profits. However, this will not persist for long because the prices will eventually converge in the two markets. The rate of convergence usually depends on the efficiency of the markets (Winston & Albrigh 2011). More efficient markets will converge at a higher rate than less efficient markets. Therefore, the situation between the United Kingdom and the United States market can be as a result of convergence of the prices. There is also the assumption of perfect substitutability of assets or securities of the two countries. This implies that the assets or the securities in one country will be as good as those in another country. With this assumption, a trader will find it easy to buy or sell the assets in either of the countries (Munzer 2009).

Another reason that can explain the existence of the no arbitrage condition is that similar assets or securities that have matching cash flow are quoted in same price in the two countries. This implies that when the intrinsic value of these assets are estimated, then they will be found to be equal irrespective of their geographical location. Further, another factor that can contribute to the no arbitrage condition is that if the future prices of assets are well-known, then the assets will trade at future prices (Winston & Albrigh 2011). However, these future prices are converted to the present value using the risk free interest rates. This will eliminate the possibility of buying using lower prices and selling them in the future at higher prices. The no arbitrage condition also exists because of the availability of perfect information between the countries. It is worth mentioning that the United States and the United Kingdom are some of the highly developed economies in the world. These countries have developed financial market where information flows freely and is readily available to all stakeholders. Therefore, the trades are able to get information that relates to prices of assets and securities easily. In such markets, the traders do not have to make a choice between the rate of making a sale and their bottom line (Winston & Albrigh 2011).

Further, the no arbitrage condition exists in the two markets because of the high risks that are associated with arbitrage. Examples of these risks are liquidity, mismatch, execution, and counter-party risks among others. The risks arise from the fact that for an arbitrage condition to exist, then the all transactions need to be executed at the same time (Taylor 2013). A delay in the execution can result in massive losses. In highly developed economies such as the United States and the United Kingdom, this may be quite difficult and risky. These risks will make a trader to incur hefty losses. Thus, traders will shy away from taking advantage of arbitrage opportunities.

In summary, the paper evaluated if an arbitrage opportunity exists between the United States and the United Kingdom. The results show that no arbitrage condition exists between the countries. The reasons why this condition does not exist are also discussed.

References

Becker, J 2013, Making money with statistical arbitrage: generating alpha in sideways markets with this option strategy, Anchor Academic Publishing, Germany.

Ignatiuk, A 2009, The principles, practice and problems of purchasing power parity theory, Books on Demand Publishers, Germany.

Kwok, Y 2008, Mathematical models of financial derivatives, Springer Science & Business Media, USA.

Mankiw, N 2014, Principles of economics, Cengage Learning, USA.

Munzer, M 2009, Purchasing power parity – its theoretical perspective and empirical evidence, GRIN Verlag, Germany.

Silver, M 2010, IMF applications of purchasing power parity estimates, International Monetary Fund, USA.

Taylor, M 2013, Purchasing power parity and real exchange rates, Routledge, USA.

Winston, W & Albrigh, S 2011. Practical management science, Cengage Learning, USA.