 # Security Market Line – SML By Yuriy Smirnov Ph.D.

## Definition

The security market line (SML) is a visual representation of the capital asset pricing model or CAPM. It shows the relationship between the expected return of a security and its risk measured by its beta coefficient. In other words, the SML displays the expected return for any given beta or reflects the risk associated with any given expected return.

## Equation

As was mentioned above, the security market line is based on the following CAPM equation

E(Ri) = RF + βi × (E(RM) - RF)

where E(Ri) is an expected return of a security, RF is a risk-free rate, βi is a security’s beta coefficient, and E(RM) is an expected market return.

## SML Graph

The x-axis of the SML graph is represented by the beta, and the y-axis is represented by the expected return. The value of the risk-free rate is the beginning of the line. 1. The zero-beta security will have the expected return equal to the risk-free rate. The expected return of zero-beta portfolio also equals the risk-free rate.
2. The slope of the security market line is determined by the market risk premium (RPM), which is the difference between the expected market return and the risk-free rate. The higher the market risk premium, the steeper the slope and vice versa.
3. The SML is not fixed and can change the slope and y-axis intersection over time. It depends on changes in interest rates, risk-return trade-off.
4. If the beta coefficient of the given security changes over time, its position on the line will also change.

The shift of SML can also occur when key economical fundamental factors change, such as a change in the expected inflation rate, GDP, or unemployment rate.

## Example

Let’s assume the current risk-free rate is 4.75%, and the expected market return is 15.50%. Thus, the SML equation will be as follows:

E(Ri) = 4.75 + βi × (15.50 - 4.75) = 4.75 + 10.75 × βi

Suppose that Security A has a beta of 0.6, and Security B has a beta of 1.2. The expected return of Security A is 11.20%, and the expected return of Security B is 17.65%.

E(RA) = 4.75 + 10.75 × 0.6 = 11.20%

E(RB) = 4.75 + 10.75 × 1.2 = 17.65%

So, lower risk (lower beta) means lower expected return and vice versa. ## Limitations of use

The security market line has the same limitations as CAMP because it is based on the same assumptions. Real markets conditions can’t be characterized by strong efficiency because market participants have different abilities to lend or borrow money at a risk-free rate, and transaction costs are different. Thus, in the real world, the position of a given stock can be above or below the SML as shown in the figure below. So, the graph shown on actual values of betas, and expected returns of stocks look like a set of points rather than a single line. Stocks above the line are undervalued because investors require a higher return for a given risk (beta) than the CAPM assessment. If stocks are below the security market line, they are overvalued, which means investors require a lower return for a given risk than was assessed by the CAPM.