Market model

This relationship is sometimes called the single-index model. The market model says that the return on a security depends on the return on the market portfolio and the extent of the security's responsiveness as measured, by beta. In addition, the return will also depend on conditions that are unique to the firm. Graphically, the market model can be depicted as a line fitted to a plot of asset returns against returns on the market portfolio.

 Mathematically it is expressed as:

where:

r_it is return to stock i in period t

r_f is the risk free rate (i.e. the interest rate on treasury bills)

r_mt is the return to the market portfolio in period t

α_i is the stock's alpha, or abnormal return

β_i is the stocks's beta, or responsiveness to the market return

Note that r_it − r_f is called the excess return on the stock, r_mt − r_f the excess return on the market

ε_it is the residual (random) return, which is assumed normally distributed with mean zero and standard deviation σ_i

These equations show that the stock return is influenced by the market (beta), has a firm specific expected value (alpha) and firm-specific unexpected component (residual). Each stock's performance is in relation to the performance of a market index.