Single Index Model

The Single Index Model (SIM) is an asset pricing model, according to which the returns on a security can be represented as a linear relationship with any economic variable relevant to the security.

In case of stocks, this single factor is the market return.

The SIM for stock returns can be represented as follows:

$r_{s}-r_{f}=\alpha +\beta \left ( r_{m} - r_{f}\right )+\varepsilon$

Where:

• Alpha (α) represents the abnormal returns for the stock
• β(r_m − r_f) represents the movement of the market modified by the stock's beta
• ε represents the unsystematic risk of the security due to firm-specific factors.

According to this equation, asset’s returns is influenced by the market (reflected in beta), it has firm specific excess returns (reflected in alpha) and also has firm-specific risk (the residual).