Capital Market Line (CML) vs Security Market Line (SML)

In this post I address one common question students have about the capital asset pricing model (CAPM). Under the standard assumptions and in the presence of a risk free investment, the capital asset pricing model can be described using two equations.

The first one, the capital market line, gives the set of efficient portfolios. It is described in the return and standard deviation space. The standard deviation measures total risk in this setting. When a risk free asset is available, every efficient portfolio would be a combination between the risk free investment and the market portfolio. The market portfolio is the tangency portfolio from a line that starts from the risk free rate and is tangent to the efficient frontier of only risky assets (the upper part of the hyperbola formed by optimal combinations of only risky assets). The capital market line only describes optimal portfolios. Optimal portfolios are diversified. So, for example, holding only one stock would not be part of the capital market line. All mean variance investors would hold an optimal portfolio. However, the capital market line does not help you price anything that is not optimal. In other words, it is good for saying what an investor would hold, but it is not good at describing assets in general.

The second relationship is more interesting. It links returns to the market beta. The market beta is a measure of systematic risk. This relationship must hold for EVERY ASSET. It does not matter whether that asset is diversified or not. Both an individual stock and an optimal portfolio should be somewhere in that line. This line is famously described by the equation E(r)-rf=beta*[E(rm)-rf]. Where r describes the return of a particular asset, rf the return of the risk free rate, rm the return on the market portfolio and beta the sensitivity of the asset to market risk. This equation is very important for asset pricing and, also, for corporate finance, since given the beta of any asset (the level of systematic risk) we can backout the expected return.