What is Arbitrage Pricing Theory (APT)?

Arbitrage Pricing Theory applies to economies that are regulated by the Law of One Price. The Law of One Price states that two identical goods can’t but be sold with the same price. If they sell at different price arbitrage takes up.

Here are the fundamental assumptions of Arbitrage Pricing Theory:

1. Capital Markets are perfectly competitive.
2. Investors always prefer more wealth to less wealth.
3. Perfect competition prevails and there is no transaction cost in the market: frictionless market.

A perfectly competitive market is one where any trader can buy or sell unlimited quantities of the relevant security without changing the security’s price. In an arbitrage portfolio-a set of goods held by an owner in an economy conform to the APT conditions-the investor tries to increase the returns from his portfolio without increasing fund in the portfolio, without spending other money. Moreover, he also likes to keep the risk at the same level. To do so, if the investor got in his portfolio A, B and C securities, to increase returns from his portfolio without further investing he will have to change the proportion of the securities. This means that if A earns him more he will tend to convert B and C in A before spending further money to buy A. Moreover, conversion may occur also to keep the risk constant as B and C might become too risky whereas A becomes less risky to keep. If a seller has one hundred shirts of USA, Brazil and Holland respectively at the beginning of the World Cup and if soccer experts say brazil is in better shape than Holland and USA he will set out selling only American and Dutch shirts, invest the money to buy Brazilian shirts to sell later in the World Cup Final. In the end he will have sold all three hundred shirts, on the contrary if he is left with US or Dutch shirt in the World Cup Final where Holland and USA are eliminated in the quarter final, he will probably be left with some shirts as stock.

There are two models of Arbitrage pricing theory:

1. Two Factor Model, according to Stephen Ross, returns of the securities are influenced by a number of macro economic factors. Among these: growth rate of industrial production, rate of inflation, spread(variability) between short term and long term interest rates and spread(variability) between long-grade and high-grade bonds.
2. According to the Single Factor Model the return is influenced only by the sensitivity, i.e., the responsiveness of a security’s return to a particular factor.