Blog Article

Subcribe to the Bionic Turtle Blog

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!

Recent Posts

Man at computer

GARP FRM Pass Rate Information

Professionals who use our services are able to pass the FRM exam at a highly successful rate. Our customers often come to us with little knowledge of how to study for their Global Association of Risk Professionals (GARP) Financial Risk Manager (FRM) certification, yet, they see results after...

Read More
Laptop, coffee, pad and pen, and phone

Spot Rates


Spot prices are a basic building block in finance, but they are tricky when the commodity is money. When the commodity is money, spot prices are called spot rates (a.k.a., spot interest rate). A spot price is simply the market’s current price to buy or sell a commodity for immediate delivery...

Read More
Typing at laptop

What Is a Z Table?


Functions based on the normal distribution are easy to retrieve in code or excel, so we do not really need z tables anymore, in practice. But we still want to understand the z table. Why? Because the popular exam calculators (TI BA II+ and HP 12c) do not include z table functionality...

Read More

What Your Colleagues Are Saying

I took the exam in Sydney and had a similar feeling about the exam being more qualitative (but no less rigorous). However, I felt I was better prepared thanks to the BT's relentless focus on throwing real life examples and methods.

Jagan G.

I subscribed to BT for my Part 1 FRM exam and just wanted to say thanks for the depth and breadth of the study materials and practice questions. I found out that I scored in the top quartile of every topic and I absolutely could not have done this without using BT - I spent many, many hours going over the practice questions and answers! I wanted to express my appreciation and gratitude to your team for your hard work in creating these materials. Thanks!

Shu C.

The BT scripts, practice questions, global topic drills and mock exams were a great help in understanding the concepts (which I could already apply on the job!) and where structured in such a manner that the breadth and depth where optimal for exam preparation - clearly the exam would have been a catastrophe without BT!

Ivan J.

Passed first time. Happy all the hard work paid off. BT was the right choice. Thanks David and Nicole for your work and commitment.

John D.

Passed! 1,4,1,2,1,4! Thank you David and Nicole for your efforts! Thank you BT! Couldn't have done it otherwise. I'm a mechanical engineer who had a career in petroleum services, then I decided to switch career to financial risk management. Passed part 1 from the first time with top quartiles and passed part 2 from the first time as well. All with BT! BT is always the recommendation I give to people aiming at the FRM designation! Thank you again!

Feras S.

Passed Part I and Part II first time - absolutely could not have done it without BT. Like a few others I didn't even both buying the GARP books for Part II and went solely with BT materials. Just read, answered questions, watched videos, read, more questions, and... more questions! All the practice question taking looked to pay off. Thanks again Bionic Turtle for a great curriculum. Keep up the fantastic work!

John D.

Looking for the best FRM® Exam Prep?