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How the Capital Market Line Differs from the Security Market Line

Article Quant Q&A · Author: S.Rana
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Summary

The discussion distinguishes the Security Market Line (SML), which relates expected return to beta, from the Capital Market Line (CML), which relates expected return to total risk for combinations of the risk-free asset and the market portfolio. In the CAPM equilibrium framing, securities and portfolios are expected to lie on the SML; a security above or below it may indicate mispricing relative to its required return. The SML therefore does not select only efficient portfolios.

The CML represents portfolios formed from the risk-free asset and the market, with the market portfolio at the tangency point. The answer explains that these combinations are efficient and have better risk-return tradeoffs than risky portfolios away from the tangent point, while clarifying that the CML does not include every efficient risky portfolio on the frontier. These relationships depend on the model's equilibrium assumptions; the document is a conceptual explanation and supplies no empirical test.

Key ideas

  • The SML relates expected return to beta, a measure of systematic risk.
  • Under CAPM equilibrium, securities and portfolios are expected to lie on the SML regardless of portfolio efficiency.
  • The CML relates expected return to total risk for combinations of the risk-free asset and the market portfolio.
  • CML portfolios are efficient, but the CML does not contain every efficient risky portfolio.
  • A security above or below the SML may represent mispricing relative to its required return in the equilibrium framework.

Tags

Portfolio constructionRisk managementStatistics
Full text
# Relationship between CML and SML


# Relationship between CML and SML












I am referring to the book Sharpe et al. (1998), Investments, 6th Edition. I am trying to wrap my head around some lines from the book, pertaining to Security Market Line. It reads:

> Earlier it was established that the expected return of a portfolio is a weighted average of the expected returns of component securities, where the proportions invested are the weights. Therefore every portfolio plots on the SML because every security plots on SML. To put it more broadly, not only every security but also every portfolio must plot on the upward sloping straight line in a diagram with expected return on vertical axis and beta on horizontal axis. So efficient portfolios plot on both CML and SML, although inefficient portfolios plot on the SML but below CML.

I understand the first two sentences. A portfolio is a convex combination of the individual securities and hence I can imagine that a line that plots individual securities on a standard deviation-expected return plane will also contain the portfolio made out of the securities. What I can infer from the above paragraph is that efficiency and inefficiency has nothing to do with plotting of SML since all portfolios will lie on it. However, CML plots only efficient sets. Is this correct? I seem to have some issues with understanding the relationship. I would be great help if someone could help me with it. Thanks a lot!

## Answer by AdB (score 2, accepted)

https://quant.stackexchange.com/a/44474

In equilibrium, all securities and portfolios (i.e. convex combinations of securities) lie on the SML, which plots expected return as a function of beta. Note that outside of equilibrium, if a security was undervalued, it would lie above the SML and vice versa.

The efficient frontier consists of all efficient portfolios, i.e. all portfolios that yield the maximum expected return given their standard deviation of return. Basically, for every point along the sigma-axis, it is the topmost portfolio - or equivalently, for every point along the expected return-axis, it is the leftmost portfolio.

The CML is the combination of all portfolios for which the sharpe ratio is maximized (i.e. the risk-adjusted excess return is the largest). This will always be a combination of the risk free security and the market (tangent) portfolio. Hence, the CML will intersect the second axis at the risk free rate and go through the market (tangent) portfolio. It is important to note that all portfolios on the CML offer a superior risk-reward profile to any portfolio on the efficient frontier. This is evident when drawn out, since the CML is above or to the left of the efficient frontier at all points (except for the tangent portfolio).

Hence, while all portfolios on the CML are efficient, the CML does not contain all efficient portfolios.

## Answer by Smirti Bam Thakuri (score 0)

https://quant.stackexchange.com/a/50343

Such a wonderful and insightful post. Thank you for sharing.

Capital Market Line shows the relationship between the expected return on efficient portfolio and their total risk.

Security Market Line shows the relationship between the required return on individual security as a function of systematic, non-diversifiable risk.

Check out this. CML VS SML

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.