# Understanding the Security Market Line

## Defining the Security Market Line

The security market line displays the expected rate of return of a security as a function of systematic, non-diversifiable risk.

#### LEARNING OBJECTIVE

• Describe the Security Market Line

#### KEY POINTS

• The security market line is the theoretical line on which all capital investments lie. Investors want higher expected returns for more risk.
• On a graph, the line has risk on its horizontal axis (independent variable) and expected return on the vertical axis (dependent variable).
• Assuming a linear relationship between risk and return, the assumption is that the y-intercept is the return on a risk-free investment (the risk free rate), and the slope is the premium on risk in terms of expected returns.
• Given two investments with the same expected return, investors would always choose less risk. Someone with opposite preferences might better be called a gambler.

#### TERMS

• line of credit

source of debt extended to a government, business or individual by a bank or other financial institution

• market risk

the potential for loss due to movements in prices in a system of exchange

• security market line

Security market line (SML) is the representation of the capital asset pricing model. It displays the expected rate of return of an individual security as a function of systematic, non-diversifiable risk (its beta).

• diversifiable risk

the potential for loss which can be removed by investing in a variety of assets

• beta

Average sensitivity of a security's price to overall securities market prices.

the amount by which expected rate of return of the exchange system exceeds the risk-free interest rate

The security market line, also known as the "characteristic line", is the graphical representation of the capital asset pricing model. It is a hypothetical construct based on a world of perfect information. In the absence of perfect information, we can more or less assume historical data will give us an accurate expectation of what kind of returns and risk to expect with a particular investment of capital. The security market line graphs the systematic, non-diversifiable risk (stated in terms of beta) versus the return of the whole market at a particular time, and shows all risky marketable securities. The security market line is defined by the equation:

$\mathrm{SML}: E\left(R_{i}\right)=R_{f}+\beta_{i}\left[E\left(R_{M}\right)-R_{f}\right]$

The equation that defines the security market line.

Look at the equation and remember that old formula of a line: $y = mx + b$. In this case it looks rearranged, like $y = b + mx$, but the real question is what do the slope and y-intercept actually represent?

The Y-intercept of the SML is equal to the risk-free interest rate. Recall that the risk-free interest rate is the theoretical rate of return of an investment with no risk of financial loss. When used in portfolio management, the SML represents the investment's opportunity cost -- i.e., investing in a combination of the market portfolio and the risk-free asset. All the correctly priced securities are plotted on the SML. The assets that lie above the line are undervalued because for a given amount of risk, theyyield a higher return. The assets below the line are overvalued because for a given amount of risk, they yield a lower return.

The slope of the SML is equal to the market risk premium and reflects the risk return trade off at a given time. The idea of a security market line follows from the ideas asserted in the last section, which is that investors are naturally risk averse, and a premium is expected to offset the volatility of a risky investment. In a perfect world, with perfect information, any capital investment is on the security market line. The idea of a security market line is important for understanding the capital asset pricing model. Let's look at the line again:

The Security Market Line: This is an example of a security market line graphed. The y-intercept of this line is the risk-free rate (the ROI of an investment with beta value of 0), and the slope is the premium that the market charges for risk.