SML and CML Comparison The beta coefficient of an asset can be expressed as a fu
ID: 2714724 • Letter: S
Question
SML and CML Comparison The beta coefficient of an asset can be expressed as a function of the asset's correlation with the market as follows: b i = rho I m sigma i/sigma M Substitute this expression for beta into the Security Market Line (SML), equation below. SML: n = rRF + (rm - rRF)bi = rRF + (RMM)bi This results in an alternative form of the SML. Compare your answer to part a with the Capital Market Line (CML), equation below. CML: gamma p = gamma RF + (gamma M^-gamma RF/sigma M) sigma p What similarities are observed? What conclusions can be drawn?Explanation / Answer
A line used in the capital asset pricing model to illustrate the rates of return for efficient portfolios depending on the risk-free rate of return and the level of risk (standard deviation) for a particular portfolio.
The CML is derived by drawing a tangent line from the intercept point on the efficient frontier to the point where the expected return equals the risk-free rate of return.
The CML is considered to be superior to the efficient frontier since it takes into account the inclusion of a risk-free asset in the portfolio. The capital asset pricing model (CAPM) demonstrates that the market portfolio is essentially the efficient frontier. This is achieved visually through the security market line (SML).
The line that graphs the systematic, or market, risk versus return of the whole market at a certain time and shows all risky marketable securities.
The SML essentially graphs the results from the capital asset pricing model (CAPM) formula. The X-axis represents the risk (beta), and the Y-axis represents the expected return. The market risk premium is determined from the slope of the SML.
It is a useful tool in determining if an asset being considered for a portfolio offers a reasonable expected return for risk. Individual securities are plotted on the SML graph. If the security's risk versus expected return is plotted above the SML, it is undervalued since the investor can expect a greater return for the inherent risk. And a security plotted below the SML is overvalued since the investor would be accepting less return for the amount of risk assumed.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.