Arbitrage pricing theory

APT relies on the assumption that asset returns in the market are determined by macroeconomic and firm-specific factors, and asset returns are generated by the following linear factor model:

Equation 1

Here, E(r_i) is the expected return of asset i, F_j stands for the unexpected change of the jth factor, and β_ij shows the ith security's sensitivity for that factor, while e_i is the return caused by unexpected firm-specific events. So represents the random systemic effect, and e_i represents the non-systemic (that is idiosyncratic) effect, which is not captured by the market factors. Being unexpected, both and e_i have a zero mean. In this model, factors are independent of each other and the firm-specific risk. Thus, asset returns are derived from two sources: the systemic risk of the factors that affect all assets in the market and the non-systematic risk that impacts only that special firm. A non-systemic risk can be diversified by holding more assets in the portfolio...