IGNOU : M.COM : MCO 7 : UNIT 4 : Q - 4. Explain in brief the ideas of Arbitrage Pricing Theory.

Ans. Arbitrage Pricing Theory

Arbitrage pricing theory is one of the tools used by the investors and portfolio managers. The capital asset pricing theory explains the returns of the securities on the basis of their respective betas. According to the previous models, the investor chooses the investment on the basis of expected return and variance. The alternative model developed in asset pricing by Stephen Ross is known as Arbitrage Pricing Theory. The APT theory explains the nature of equilibrium in the asset pricing in a less complicated manner with fewer assumptions compared to CAPM.

Arbitrage : Arbitrage is a process of earning profit by taking advantage of differential pricing for the same asset. The process generates riskless profit. In the security market, it is of selling security at a high price and the simultaneous purchase of the same security at a relatively lower price. Since the profit earned through arbitrage is riskless, the investors have the incentive to undertake this whenever an opportunity arises. In general, some investors indulge more in this type of activities than others. However, the buying and selling activities of the arbitrager reduces and eliminates the profit margin, bringing the market price to the equilibrium level. The assumptions:

1. The investors have homogenous expectations.

2. The investors are risk averse and utility maximisers.

3. Perfect competition prevails in the market and there is no transaction cost.

The APT theory does not assume (1) single period investment horizon, (2) no taxes, (3) investors can borrow and lend at risk free rate of interest, and (4) the selection of the portfolio is based on the mean and variance analysis. These assumptions are present in the CAPM theory.

The APT Model : According to Stephen Ross, returns of the securities are influenced by a number of macro economic factors. They are: growth rate of industrial production, rate of inflation, spread between long term and short term interest rates and spread between low-grade and high grade bonds. The arbitrage theory is represented by the equation:

Ri = λo + λ1 bi1 + λ2 bi2 ….. + λj bii

Ri = average expected return

λ1 = sensitivity expected return to bi1

bi1 = the beta co-efficient relevant to the particular factor

Whatever be the number of factors built into the model, two securities with the same factor betas, should provide the same expected return. If not, arbitrage (i.e., the process of buying the cheaper and selling the expensive) will take place and security prices adjust themselves. The investors will try to realize arbitrage profits, if there is disequilibrium and adjust their portfolios and the security prices are driven to equilibrium.

Carrying further their piece of research work, Richard Roll and Stephen Ross believed that there are five specific factors that capture systematic risk of a portfolio of securities. They are:

i) Changes in the expected inflation

ii) Unanticipated changes in inflation

iii) unanticipated changes in industrial production

iv) unanticipated changes in the yield differential between low and high grad securities (known to be default risk premium).

v) unanticipated changes in the yield differential between long term and short term bonds (known to be the term structure of interest rates).