CAPM provides a framework for measuring the systematic risk of an individual security and relate it to the systematic risk of a well-diversified portfolio. The risk of individual securities is measured by β (beta). Thus, the equation for security market line (SML) is: E(Rj) = Rf + [E(Rm) – Rf] βj
Where E(Rj) is the expected return on security j, Rf the risk-free rate of interest, Rm the expected return on the market portfolio and βj the undiversifiable risk of security j. βj can be measured as follows:
βj = Cov (Rj, Rm)
= σj σm Cor jm
= σj Cor jm
In terms of Equation 2, the undiversifiable (systematic) risk (βj) of a security is the product of its standard deviation (σj) and its correlation with the market portfolio divided by the market portfolio’s standard deviation. It can be noted that if a security is perfectly positively correlated with the market portfolio, then CML totally coincides with SML.
Equation 1 shows that the expected rate of return on a security is equal to a risk-free rate plus the risk-premium. The risk-premium equals to the difference between the expected market return and the risk-free rate multiplied by the security’s beta. The risk premium varies directly with systematic risk measured by beta.
The figure above illustrates the security market line. For a given amount of systematic risk (β), SML shows the prevailing rate of return. A security’s beta of 1 indicates an average level of systematic risk. If the security’s beta is greater than 1, then it implies the security’s returns fluctuate more than the market returns. On the other hand, a beta less than 1 means that the security’s returns are less sensitive to the changes in the market returns.
Asset Pricing Theory
The purpose of Asset Pricing Theory is to understand the pricing of risk. That involves two things:
1. Recognizing risk categories, the ability to...
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