# Security Market Line (SML)

Last Updated :

21 Aug, 2024

Blog Author :

Wallstreetmojo Team

Edited by :

Ashish Kumar Srivastav

Reviewed by :

Dheeraj Vaidya

Table Of Contents

## What Is A Security Market Line (SML)?

*The security market line (SML) is the Capital Asset Pricing Model (CAPM). It gives the market's expected return at different systematic or market risk levels. It is also called the 'characteristic line' where the x-axis represents the asset's beta or risk, and the y-axis represents the expected return.*

SML gives the graphical representation of the Capital asset pricing model to give expected returns for systematic or market risk. Fairly priced portfolios lie on the SML, while undervalued and overvalued portfolios lie above and below the line respectively. A risk-averse investor's investment tends to lie closer to the y-axis than the beginning of the line, whereas a risk-taker investor's investment would lie higher on the SML.

##### Table of contents

### Security Market Line Explained

The security market line is a financial concept where the capital asset pricing model is shown in the form of a graph along with beta, which is the systematic risk. The systematic risk is the one that cannot be diversified and affects the entire financial market as a whole. The line acts as a guidance to investors and analysts who can take investment decisions based on it because it determines the return that can be expected form it based on the risk compared to the overall market.

In other words, it can be said that the concept is a method to assess the risk and return level of an investment graphically in order to decide whether the investment is worth or feasible. The opportunity becomes attractive if the return as per the SML is more than the current return levels. The opposite proves that the investment is not worth the risk.

SML provides an exemplary method for comparing two investment securities; however, the same depends on assumptions of market risk, risk-free rates, and beta coefficients. It is also called the Characteristics Line in the financial market. It assumes that every investor needs a compensation for the risk they take, also known as the risk premium and the time value of money, which explains that the value of a sum is more than what it will be at a future date.

However, it cannot be assumed as the only tool to asses or evaluate an investment opportunity. It should be used in conjunction with other tools to get a precise understanding.

### Characteristics

Characteristics of the Security Market Line (SML) are as below

- SML is a good representation of investment opportunity cost, which combines the risk-free asset and the market portfolio.
- Zero-beta security or zero-beta portfolio has an expected return on the portfolio, which is equal to the risk-free rate.
- The slope of the Security Market Line is determined by the market risk premium, which is: (E(RM) – Rf). Higher the market risk premium steeper the slope and vice-versa
- All the assets which are correctly priced are represented on SML.
- The assets above the SML are undervalued as they give a higher expected return for a given amount of risk.
- The assets below the SML are overvalued as they have lower expected returns for the same amount of risk.

### Formula

Let us try to understand the formula used for the calculation.

The Equation is as follows:

**SML**: E(R_{i}) = R_{f} + β_{i}

In the above security market line formula:

- E(R
_{i}) is the expected return on the security - R
_{f}is the risk-free rate and represents the y-intercept of the SML. It shows tge return that the investor will get from any risk free investment. A perfect example is a government bond that is taken as a benchmark and compared with other risky investments. - β
_{i}is a non-diversifiable or systematic risk. It is the most crucial factor in SML and measures the fluctuation or volatility of the security as compared to the market. We will discuss this in detail in this article. - E(R
_{M}) is expected to return on market portfolio M. - E(R
_{M}) – R_{f }is known as Market Risk Premium, which is the difference between the expected market return and risk free rate. It is the extra return that the investor will expect for taking the risk of investing in that security and not going for the risk free investment.

### Graph

The above equation can be graphically represented as below:

The graph shows that in the x-axis, there is systematic risk and in the y-axis there is expected return. At the level of risk-free rate of return, we can see that the SML intersects the y-axis. The slope of this line is identified as the market risk premium.

When the beta is 1, as shown in the x-axis, the market is able to earn an expected return of Rm, shown in the y-axis. As the level of beta increases, the level of risk also increases and rises more than the market average. If the beta is less, then the investment has a risk level lower than the market. Therefore, as per the graph, we can conclude that on the SML, all securities or investments are properly priced. There is no undervaluation or overvaluation. But if the risk and return is plotted on the graph and it is above the SML, it is worth investing since the return is more than the risk, which indicates that the security is underpriced. Similarly if the investment is overpriced, then it will show below the SML, indicating risk is more than return. It is better to avoid such investment.

### Security Market Line (SML) Explained in Video

### Example

Let us try to understand the concept with the help of a suitable example.

Let the risk-free rate be 5%, and the expected market return is 14%. Then, consider two securities, one with a beta coefficient of 0.5 and the other with a beta coefficient of 1.5, concerning the market index.

Now let's understand the security market line example, calculating the expected return for each security using SML:

The expected return for Security A as per the security market line equation is as per below.

- E(R
_{A}) = R_{f}+ β_{i} - E(R
_{A}) = 5 + 0.5 - E(R
_{A}) = 5 + 0.5 × 9 = 9.5%

Expected return for Security B:

- E(R
_{B}) = R_{f}+ β_{i} - E(R
_{B}) = 5 + 1.5 - E(R
_{B}) = 5 + 1.5 × 9 = 18.5%

Thus, as can be seen above, Security A has a lower beta; therefore, it has a lower expected return while security B has a higher beta coefficient and has a higher expected return. Consequently, it aligns with the general finance theory of higher risk and higher expected return.

### The Slope of the Securities Market Line (Beta)

Beta (slope) is an essential measure in the Security Market Line equation. Thus let us discuss it in detail:

Beta is a measure of volatility or systematic risk or a security or a portfolio compared to the market. The market can be considered an indicative market index or a basket of universal assets.

If Beta = 1, then the stock has the same level of risk as the market. A higher beta, i.e., greater than 1, represents a riskier asset than the market, and a beta less than one represents risk less than the market.

The formula for Beta:

β_{i} = Cov(R_{i} , R_{M})/Var (R_{M}) = ρ_{i,M} * σ_{i} / σ_{M}

- Cov(R
_{i}, R_{M}) is the covariance of the asset i and the market - Var (R
_{M}) is the variance of the market - ρ
_{i,M}is a correlation between the asset i and the market - σ
_{i}is the standard deviation of asset i - σ
_{i}is the standard deviation of the market index

Although beta provides a single measure to understand the volatility of an asset concerning the market, beta does not remain constant with time.

### Importance

Since the SML is a graphical representation of CAPM, the advantages and limitations of SML are the same as that of the CAPM. Let us look at the benefits:

- Easy to use: SML and CAPM can be easily used to model and derive expected returns from the assets or portfolio
- The model assumes the portfolio is well diversified hence neglects the unsystematic risk making it easier to compare two diversified portfolios
- CAPM or SML considers the systematic risk, which is neglected by other models likes the Dividend Discount Model (DDM) and Weighted Average Cost of Capital (WACC) model.

These are the significant advantages of the SML or CAPM model.

### Limitations

Let us have a look at the limitations:

- The risk-free rate is the yield of short-term government securities. However, the risk-free rate can change with time and have an even shorter duration, thus causing volatility.
- The market return is the long-term return from a market index that includes capital and dividend payments. The market return could be negative, which is generally countered by long-term returns.
- Market returns are calculated from past performance, which cannot be taken for granted in the future.
- The slope of SML, i.e., market risk premium and the beta coefficient, can vary with time. Macroeconomic changes like GDP growth, inflation, interest rates, unemployment, etc., can change the SML.
- The significant input of SML is the beta coefficient; however, predicting accurate beta for the model is difficult. Thus, the reliability of expected returns from SML is questionable if proper assumptions for calculating beta are not considered.

Thus, it is always better to assess the advantages and limitations of any financial concept thoroughly so as to take important and informed financial decisions.

### Recommended Articles

This article is a guide to what is Security Market Line(SML). We explain it with formula, graph, slope, example, importance and limitations. You can learn more about Valuations from the following articles –