Security market line

The CML defines the relationship between total risk and expected return for portfolios consisting of the risk-free asset and the market portfolio. The capital asset pricing model identifies the security return net of the risk -free rate as proportional to the expected net market return, where beta serves as the constant of proportionality. As a consequence of this relationship. all securities in equilibrium plot along a straight line called the security market line(SML). Since the unsystematic risk tends to be diversified away by the construction of an efficient portfolio, it is desirable to develop an alternative to CML. Which will use beta as the independent variable and will accommodate both portfolio and SML is a linear relationship between expected return and beta or systematic risk on which both portfolios and individual securities can lie whereas capital market line(CML).is a linear relationship between the expected return of a portfolio and the total risk associated with it. It generates a line on which an efficient portfolio can lie figure first presents a SML which has beta as the independent variable and the expected return of portfolios and individual securities as the dependent variable.
The SML has a positive slope .indicating that the expected return increases with risk(beta). By definition, the risk of a riskless asset, T, is zero Therefore, T is the point at which the SML crosses the vertical axis, the Y-intercept point. The beta of the market portfolio which measures the systematic risk of the market relative to itself, is 1 lie to the left of M on the SML and are called defensive securities and portfolios with a beta of less than 1 lie to the left of M on the SML and are called defensive securities. Likewise, securities with a beta of more than 1 are riskier than the market and are called aggressive securities. In addition. The expected return of a security on the SML is determined by the riskless rate plus a systematic risk premium which is proportional to its beta.

 

Symbolically,
\tilde{R_{i}}=T+\beta _{im}(\tilde{R_{m}}-T)
The use of the SML as a decision tool can be illustrated with a numerical illustration.Now we are in a position to compare the expected return for an individual security with the expected return for the market portfolio.For this ,it is useful to deal with returns in excess of the riskless rate.The excess return is simply the expected return less the riskless return.The expected excess return on a security’s non-market characteristics equals the pure interest rate if it priced correctly,the expected excess return on the market component will thus be zero.The expected excess return will then come entirely from the market component of its return.

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