Question

Recall the Capital Asset Pricing Model: Rs=Rf+?(Rm−Rf). What does the parameter β represent here and why is it multiplied by the market risk premium?

Answer 1

The CAPM model is used for calculating the required rate of return on security on the basis of the systematic risk which is signified by β.

The parameter β (beta), is a measure of how much risky the security is when comparing it to the market and the CAPM model determined how much higher return the security must generate in order to compensate for the higher risk of the stock as compared to the market. In short, β signifies the volatility of return of the security in comparison to the entire market. A beta is found out by regression with respect to the market data.

A higher beta signifies more risk and hence demand higher returns. Eg. β=1, signifies that the security is as volatile as the market and hence the required return will be equal to the market return. Rs=Rf+Rm−Rf = Rm

β>1, signifies that the security is more volatile than the market and hence the required return will be higher than the market return. Rs=Rf+2(Rm−Rf) ==> Rs= 2Rm−Rf

Accordingly, β<1, signifies that the security is less volatile than the market and hence the required return will be lesser than the market return.

The market risk premium (Rm−Rf), is the return expected from the market above the risk-free rate. Since, a market has higher risk than a risk-free security, the market premium is the addition return that is needed to be generated over and above the risk-free rate in order to compensate for the additional risk. As the volatility increases (higher Beta), signifies that the security demand a higher premium over the risk-free rate and this premium is directly proportional to beta ( since beta is calculated with respect to the market premium). Hence, multiplying the security β with the market risk-premium returns the premium the security demands over the risk-free rate.