Question

Explain the rationale behind the Arbitrage Pricing Theory (APT) model, and discuss its empirical evidence that tests its validity.

Answer 1

Answer:

Arbitrage Pricing Theory (APT) is an asset pricing model which runs on the assumption that asset's returns can be estimated using the linear relationship and a number of macroeconomic variables that capture systematic risk. It is the tool which is used to examine portfolios from the investment point of view to check whether the stocks are mispriced or not. It states how investment reacts to a set of macro-economical factors who degree of reaction is measured by betas and risk premium associated with each of such factors. The APT theory has identified several factors which talks about the relationship of riks premium with a particular security namely inflation, money supply, interest rate etc.
It calculates expected premium with the use of risk free rate, sensitivity of the asset with the factor and the risk premium associated with each factor.

The equation of Arbitrage Pricing Theory is given below:

E(Rp​)=Rf​+ β1​f1​+ β2​f2​+ …+ βn​fn​
where E(Rp​)=Expected return, Rf​=Risk-free return, βn​=Sensitivity to the factor of n, fn​=nth factor price​

Unlike CAPM model, APT is a multi-factor model. This theory is more complex than CAPM model because CAPM model only considers market risk whereas it considers multiple factors.
CAPM assume markets to be efficient whereas APT assumes that securities are mispriced sometimes before it gets stable and gets back to its fair value. Under this theory, arbitrageurs take advantage of the price fluctuations of the securities in the market when they diverge from their fair values.
The factors used in the APT theory are the systematic risk i.e. the risk which cannot be eliminated by diverisification of the portfolio.

For example: Say, the following factors have been identified as the sensitive factors for a particular security say X.
1. Inflation- beta = 0.7, Return = 4%
2. GDP growth- beta = 0.8, Return = 3%
3. Risk Free rate- 4%
Now, using APT we can calculate the expected return of the security as:

Expected Return = 4% + (0.7*4) + (0.8 * 3)  
Expected Return = 8.2%