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

We received a question on YouTube that is helpful in understanding the relationship (and difference) between the Capital Market Line (CML) and the Security Market Line (SML). Related, earlier in the year Akriti1 posted another provider’s (EPP’s) flawed CML/SML practice question that’s typical of a naïve understanding of the CML/CAPM framework: the author presumes the only difference is the X-axis; i.e., total risk (CML) versus systematic risk (SML). As I’ve often said, working with actual datasets tends to force a much deeper understanding of many of these ideas. After I was forced to generate plots with actual data (in a classroom), I quickly came to understand how the CML is an empirical-realistic exercise while the SML is a more theoretical thing. So here is my paraphrase of the question that was asked:

I think it’s a smart question. My reply was the following:

But an illustration might be better, so I quickly added a sheet to our CAPM learning spreadsheet (draft version here, see image below). My spreadsheet is dynamic: you only need to input two assets, their correlation and the riskfree rate. The charts adjust, including I solve for the Market Portfolio (five years ago, I found the analytical solution using mathematica). The plots below happen to assume: For Asset A, μ(A) = +10.0%, σ(A) = 10%. For Asset B, μ(B) =+16.0%, σ(B) = 20.0%. Their correlation, ρ(A,B) = 0.30, and the riskfree rate is 6.0 (primarily to give the plots strong features). The Market Portfolio plots as the red triangle; the Market Portfolio has the highest Sharpe ratio.

The new feature that I added is: you can select the allocation to the Market Portfolio, so that determines your location on the CML. The plot below (left panel) assumes a high-leverage 160.0% allocation the Market Portfolio; it is the orange dot that lies on the CML. There is also plotted a corresponding portfolio on the green PPC: it has the same expected return. Inside the PPC are displayed the risk metrics for this portfolio. In this case, sqrt(18.7%^2 + 10.8%^2) = 21.6% total risk. On the right panel, we see that both of the portfolios on the left locate in the exact same (single) spot on the SML. They both have the same beta of 1.60 per the 160% allocation. And here is the point of the illustration: only portfolios on the CML are “perfectly” well-diversified such that they contain zero specific risk. The portfolio on the PPC offers the same expected return (in this case, +16.5% on both Y axes) and it has the same beta, but it has additional specific risk. In this way, there is a sense in which we can say the portfolios on the green PPC are more diversified as they “get nearer” to the Market Portfolio (which is truly well-diversified and optimal because it has the highest Sharpe ratio, which also means it has zero specific risk). Getting back to the original question, the straight-line CML is also a map to SML/systemic risk but the less efficient portfolios are not.

And this brings me back to my favorite summary distinction of the difference between the CML and SML (and now we can see how the other provider’s question contains a glaring mistake): the CML plots only (the most) efficient portfolios, but the SML plots all portfolios (including inefficient portfolios). I hope that’s interesting!

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Recent Posts

Introduction to the Quantitative Foundation of Risk – Present Value

[caption id="attachment_454805" align="alignright" width="247"]  [/caption] A common question asked by FRM candidates (and people who are considering whether to sit for the FRM exam) is,...

Read More

Week in Financial Education (June 28, 2021)

Welcome to the latest WIFE. For Part 1, we wrote a new set of insurance company practice questions (PQs). I was recently asked how much...

Read More

A Note about Delta-Gamma Value at Risk (VaR) as Taylor Series

Alberto asked a good question here about using the delta-gamma formula to estimate the VaR of an option position. Lu Shu (lushukai) gave an excellent reply...

Read More