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

Lintner further explained that CAPM predicts a tradeoff between systematic risk known as beta and expected return under specific conditions CAPM makes correct forecast about expected return as shown by the formulae below;

E(Ri) = Rf + beta-of-i (Rm - Rf)

Similarities

Both the SIM and CAPM represent market movement of stock. They both further focus on the balanced relationship between the risk and expected return on risky assets. Even the functional form for the expected return is similar for both the two models.

The alpha as show by the symbol α found in both formulae highlights a similarity between the two models. The alpha or the abnormal return of stock of a portfolio is the average of the alphas of the individual securities. For large portfolios the average will be zero, because within the portfolio some stocks have positive alphas whereas some have negative alphas. The average of firm-specific risk diminishes toward zero as the number of securities in the portfolio is increased. Diminishing of risk towards zero is as a result of diversification, which can reduce firm-specific risk. Diversification does not however reduce market risk, to

The Single Index Model leads to a simplification of the portfolio choice model because of the additional assumption that the idiosyncratic components of return are independent across stocks. The market portfolio in the CAPM is not the same as a "market index." In fact, if you use a market index such as the S&P 500 in the single-index model, it is quite unlikely that it will coincide with the tangency portfolio identified by the CAPM. This will become readily apparent when you use the single-index model to analyze real-world data.

The Single Index Model also greatly reduces the computations, since it eliminates the need to calculate the covariance of the securities within a portfolio using historical returns and the covariance of each possible pair of securities in the portfolio. With this equation, only the betas of the individual securities and the market variance need to be estimated to calculate covariance. Hence, the index model greatly reduces the number of calculations that would otherwise have to be made for a large portfolio of thousands of