Capital Market Line Definition and Tutorial for Investment Modeling

Capital Market Line

Intermediate

Capital Market Line is a theoretical concept from the Capital Asset Pricing Model used to derive investor allocations to two assets: a Risk-Free asset like a T-Bill and the Market Portfolio of risk assets. It connects the Risk-Free asset return on the y-axis to the Efficient Frontier at the Market Portfolio. Portfolio allocations below the Market Portfolio imply lending (or buying bonds) and above imply borrowing (using leverage) to buy additional positions of the Market Portfolio. Where the client's Indifference Curve meets the line is at the Optimal Portfolio.

Synonym: CML

For context, this theory provides a way to group all investable assets into two groups, "risk-free" and "risky". After setting expected returns for each, it becomes easy to grasp the trade-off between the two in terms of return and risk. That's why the Capital Market Line has had such an influential impact on how most people invest, whether they know it or not.

In a Sentence

Jim: My client understands the Capital Market Line and...
Ken: Sorry Jim, is says right here in our ADV, clients cannot use leverage.

Video

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Capital Market Line definition for investment modeling (5:19)

Video Script

The script includes two sections where we visualize and demonstrate the concept of the Capital Market Line.

Visualize

We're sitting in Excel, and this is a snippet from our boot camp course.

There we cover all of the curves, lines and dots shown here in one 40-minute video, but because most people can't sit still that long, we break it out into eleven 4-5 minute videos, just like this one. I'll provide a link to boot camp video if you'd like the whole story. (See the tutorial Ace Your Portfolio Theory Exam instead).

Ok, we have a chart, with expected return on the y-axis and expected risk on the x-axis. The 'expected' timeframe assumes we've taken 'historical' data as input, run a regression to generate 'expected' return and risk.

The curves and dots on the right represent advancements in Modern Portfolio Theory, covered elsewhere, and Capital Market Theory, or CAPM, developed in the 1960s, shifted the conversation to the left here.

Academic theories require that we hold other variables constant, with assumptions and here is a list of MPT assumptions to review later. We could tack on another set for Capital Market Theory and if you'd like more than this quick-and-dirty summary reach out to me for in-depth readings.

Demonstrate

Let's demonstrate and focus on this definition. The Capital Market Line connects the Risk-Free Asset return, rf2 on the y-axis, to the Efficient Frontier dark green curve, at the Market Portfolio, labeled M2 here. At rf2 an investor allocates 100% in Treasury Bills. At M2, the investor allocates 100% to the Market Portfolio. The investor wouldn't choose point A because she would get more bang for her buck where the line's slope is the steepest. Ponder that for a second.

Think about it this way, an investor seeking a higher return must take risk, and move up this line. Each step of the way adding risky assets 25%, 50%, 75%, 100%. Think about buying T-Bills just as if you are lending to the government. You could keep going, past M2 and have maybe 200% invested in the Market Portfolio, with 100% of borrowed money. That's a difficult concept, but is possible, yet uncommon.

Capital Market Theory demonstrated how investors could choose between these two assets exclusively, selecting an allocation that matches her tolerance for risk, thereby shifting this light green indifference curve, which was over here for the MPT examples, up and down the Capital Market Line. Risk-averse investors here, and risk-seeking investors here.

Quiz

Click box for answer.

If the risk-free rate was equal to the expected Market rate there would be no reason to invest in stocks? | True or False?

True, theoretically.

What would the slope of the Captial Market Line be if you expected T-bills to return 0% and a basket of risky assets to return 8% with a standard deviation of 16%? | 0.25, 0.50, 1.00 or 1.50?

0.50, a rise of 8 divided by run of 16.

Questions or Comments?

Still unclear on the Capital Market Line? Leave a question in the comments section on YouTube or check out the Quant 101 Series, specifically Ace Your Portfolio Theory Exam.

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Capital Market Line Definition and Tutorial