Strategic Risk Taking: A Framework for Risk Management

Appendix 2: Derivation of the Arbitrage Pricing Model

Like the capital asset pricing model, the arbitrage pricing model begins by breaking down risk into firm-specific and market risk components. As in the capital asset pricing model, firm-specific risk covers information that affects primarily the firm, whereas market risk affects many or all firms. Incorporating both types of risk into a return model, we get the following.

R      =      E(R)      +      m      +      ε

where R is the actual return, E(R) is the expected return, m is the market-wide component of unanticipated risk, and ε is the firm-specific component. Thus, the actual return can be different from the expected return, either because of market risk or firm-specific actions. In ...