# Capital Market Line and the Efficient Frontier

**Capital Market line**, Security Market Line, Capital Allocation LIne and Efficient frontier. These are some of the common terms you will come across when learning about modern portfolio theory. It can be confusing when you are faced with such similar terms as the *capital market line* and the capital allocation line. You may ask yourself is the security market line the same thing as the __capital market line__? Hopefully we will be able to clarify some of these things in this article and allow you to differentiate your capital market line from your capital allocation line.

**Securities Market Line (SML)**

One of the important ideas that you will come across when learning about the CAPM is the Securities Market Line (SML). The securities market line is a graphical representation of the CAPM model. Along the x-axis of the graph we have the Beta, while on the y-axis we have the expected return for a given level of risk. The idea is that any security that falls exactly at any point on the line is fairly valued. If the security is at any point above the line we would basically know that the security is undervalued as it offers a greater return for the given level of risk. If the security is below the line we know that the security is overvalued as the return it offers is not adequate for the given level of risk. You can see a image below which shows the security market line, the red line is the plot of the securities market line in the diagram below.

## Capital Market Line and the Efficient Frontier

One of the big advances in finance was modern portfolio theory (MPT) which tried to fit portfolio selection around a quantitative framework. The work on MPT won several of its creators Nobel prizes in the field of economics. MPT uses statistical techniques to achieve portfolio diversification and thereby reduce risk – essentially in a mean - variance framework. The aim of course if to construct an efficient portfolio that maximises yield whilst reducing risk. This would lead to any number of portfolios that can be constructed based on different weights – call this our set of all possible portfolios. What the efficient frontier is trying to do is determine the best possible combination of assets in a portfolio that maximises the expected level of returns for a given level of risk (as defined by volatility / standard deviation). In effect the efficient frontier gives a very formal relationship between risk and returns. Any portfolio that is below the efficient frontier line is deemed to be sub-optimal – this is quite intuitive as any point below will offer the same return for greater risk or same risk and less return. This leads to 2 formal definitions:

1) Maximise expected return for a given level of volatility

2) Minimise volatility for a given level of returns

The set of optimal portfolios that we get from all the possible combinations of portfolios in the risk-return is known as the efficient frontier. You can see a very clear illustration below where the lighter pinkish area is the set of all possible portfolios and the dark red line is the actual efficient frontier.

### Capital Allocation Line

Investors can make a choice of how they allocate funds between the risk free asset and the risky portfolio. This can range from all assets in the risk free asset to all (or more than all with leverage) in the risky portfolio. When we plot this in a graphical fashion we get a linear line with mean on the Y axis and the volatility on the x axis. Note that the line is linear as the risk free asset has no volatility. The important point to take away here is that each risky portfolio will have its own capital allocation line. The capital allocation line that lies at a tangent to the efficient frontier and is the highest possible line is known as the Capital Market line (because it is the market portfolio). Given the mean-variance criterion all investors will hold their portfolio in the same weights as the market portfolio (and hence lie on the capital market line).

### Capital Market Line

Now that we understand the efficient frontier we can talk about the capital market line. The capital market line (CML) is used to illustrate the allocation between the market portfolio (the portfolio that consists of the risky assets from above) and the risk-free asset. If we decided to invest purely in the risk free asset we would have no risk, from here we can draw a line up changing the allocation between the risky portfolio and the risk-free asset to get a whole set of returns with a given level of risk. This would be a linear line with the intercept at the Y-axis being at the risk free interest rate level. Where this line intercepts with the efficient frontier would be deemed the optimal allocation between the risky portfolio and the risk-free asset. This can be seen quite clearly in the diagram below.

That explains how to construct an optimal portfolio in order to minimise risk and maximise returns for a given set of assets. These concepts are rooted in quantitative analysis and use concepts like mean , standard deviation , correlation etc to construct an optimum portfolio. One of the common criticisms of the CAPM model is that the distribution is assumed to be normal. Of course in actual reality distribution is far from being normal and we will see extreme events (fat tails) quite often in the market. However this model still remains an important theoretical underpinning of modern finance despite the criticisms.

You can download the Excel file below, which will take you through the construction of an efficient portfolio in a 2-asset environment and fit the capital market line to it. All the other concepts that we have gone through upto now in this blog – volatility , portfolio volatility , correlation etc will be relevant, so in case you need a refresher just go back to those posts and refresh yourself.

Download the spreadsheet with the capital market line and the efficient frontier here.

Suggested Reading

How to set up a 3 asset Capital Market Line with efficient frontier.

Criticisms of the Modern Portfolio Theory Approach

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