Similarities And Differences Between The Single Index Model And Capital Asset Pricing Model

Outline the similarities and differences between the Single Index Model (SIM) and the Capital Asset Pricing Model (CAPM). Justify which of the two models makes a better assessment of return of a security (25 marks).

To reduce a firm’s specific risk or residual risk a portfolio should have negative covariance or rather it should have no variance at all, for large portfolios however calculating variance requires greater and sophisticated computing power. As such, Index models greatly decrease the computations needed to calculate the optimum portfolio. The use of such Index models also eliminates illogical or rather absurd results. The Single Index model (SIM) and the Capital Asset Pricing Model (CAPM) are such models used to calculate the optimum portfolio.

Sharpe (1963) defined SIM as an asset pricing model which is purely arithmetical. The returns on a security can be represented as a linear relationship with any economic variable relevant to the security, for example in stocks the single factor is the market return. According to Sharpe the Single index model for return on stocks is shown by the formulae shown below;

Rs-Rf = α + β (Rm- Rf) +ε. α or alpha represents abnormal returns for stock.

Β (Rm − Rf) represents the markets movement. ε represents the unsystematic risk of the security.

The equation above shows the relationship or correlation equation between two variables. These variables are (Rs- Rf) and (Rm-Rf) as such. This equation as such must always be