Single Index Model

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The Single Index Model (SIM) is an asset pricing model commonly used in the finance industry to measure risk and return of a stock. Mathematically the SIM is expressed as:

(rit − rf) = ai + Bi(rmt − rf) + Eit

R_i = α_i + β_iR_m

Where:

rit − rf is the return on the stock
ai is the company's alpha
Bi is the company's beta
rmt − rf is the return on the market index
Eit is the residual return

The accuracy of the model is enhanced by the stock return's influence by market (beta) and firm-specific risk factors (alpha), unexpected returns (residual) and the relation to the performance of a market index (such as the All Ordinaries). Security analysts often use the SIM for such functions as computing stock betas, evaluating stock selection skills, and conducting event studies.

Assumptions of Single index model 1.the return On the security besides the fundamental fact is guided by index can also be calculated by the associated with the index.

• Yip, Henry 2005: Spreadsheet Applications to securities valuation and investment theories, John Wiley and Sons Australia Ltd