Security Market Line: Definition, Formula and Example

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  • 29 Nov 2023
Security Market Line: Definition, Formula and Example

Key Highlights

  • The Security Market Line (SML) is a graphical or visual representation of the capital asset pricing model (CAPM).

  • The SML is an upward slope. It shows the expected return of securities for different levels of risk.

  • The assets that appear above the SML are considered overvalued. It suggests that the expected returns of the assets are higher than the justified required returns.

  • The assets that lie below the SML are undervalued. It suggests that the expected returns of the assets are lower than the justified required returns.

The Security Market Line (SML) is a chart of the expected rate of return and risks associated with different securities traded in the market. SML is a visual representation of the capital asset pricing model (CAPM), which shows the systematic or market risks associated with assets. The x-axis and y-axis make up the security market line. The y-axis shows the assets' projected return, whereas the x-axis shows the assets' beta or risk. Another name for the security market line (SML) is the characteristic line.

The stocks lying above the SML are undervalued. This is because the necessary return of these stocks is larger than what the capital asset pricing model justifies. Similarly, the stocks trading below the security market line are overpriced due to their lower necessary return compared to the fair-value return suggested by the CAPM. So, they have a higher price.

The following are some of the assumptions of SML:

  • There is no possibility of any short-selling.
  • Every investor follows the same investment timeline.
  • There are several high-risk securities.
  • Everybody in the market acts reasonably.
  • All market participants are price takers. They cannot affect the price of the assets.
  • There are no fees or taxes associated with these transactions.

After going through the SML definition, let us understand its formula. The equity risk premium (ERP), beta (β), and risk-free rate (rf) make up the three parts of the SML calculation.

  • Risk Free Rate (rf): The return on risk-free securities, typically the government's 10-year Treasury bonds.

  • Beta (β): In comparison to the market, beta (β) represents the volatility or systematic risk of an asset or portfolio. The market may be seen as a universal asset basket or as an indicative market index.

The stock and the market are both equally risky if beta equals 1. An asset is considered riskier than the market if its beta value is higher than 1. Conversely, it's less risky than the market if its beta value is less than 1.

  • Equity Risk Premium (ERP): It is the extra return obtained from investing in public shares above the risk-free rate, calculated as the difference between the expected market return and the risk-free rate.

To determine the expected return on the investment, multiply the equity risk premium (ERP) with the security's beta. Then add the risk-free rate (rf) to the result obtained.

Expected Return, E(Ri) = Risk Free Rate + β (Market Return – Risk Free Rate)

E( ri ) = rf + ßi [ E( rm ) - rf ]

The equity risk premium (ERP) is determined by deducting the risk-free rate (rf) from the market return. It is sometimes referred to as the "market risk premium."

Equity Risk Premium (ERP) = Market Return - Risk Free Rate

Let’s determine if the following assets are overpriced or undervalued. Assume that the risk-free rate is 4.5% and the equity risk premium is 6%. Their beta coefficient and necessary rate of return using the dividend discount model are as follows:

Stock Beta Observed Return
A1.27%
B1.410%
C1.611%
D1.813%

The justified rate of return for each stock is as follows.

Stock Beta Required Return (DDM) Formula Required Return as per CAPM
A1.15%4.50%+1.2 × 6%11.7%
B1.37%4.50%+1.4 × 6%12.9%
C1.29%4.50%+1.6 × 6%14.1%
D1.911%4.50%+1.8 × 6%15.3%

When using SML or CAPM, the beta of a security is a crucial statistic. This is because it shows an asset's systematic or non-diversifiable risk. Beta is also an important metric used to calculate the market average. Market participants typically assess the securities in an investment portfolio using the security market line (SML) to find the amount of risk and expected return in the underlying portfolio.

Similar types of securities may also be compared using SML. A security's risks and returns are determined by its position on the SML chart. An undervalued investment appears above the security market line. This indicates that it has lower risks and higher returns.

The following are the major benefits of the security market line.

1. Simple to use: Using the security market line makes it easy to calculate expected returns from assets.

2. Comparison of diversified portfolios: It is simpler to compare two diversified portfolios since the model ignores unsystematic risk. It assumes that the portfolio is well-diversified.

3. Considers Systematic Risk: In contrast to other models, such as the Dividend Discount Model (DDM) and the Weighted Average Cost of Capital model, the SML takes into account systematic risk.

The limitations of the SML include the following.

  1. The yield on short-term government securities is known as the risk-free rate. However, volatility might arise because the risk-free rate is subject to fluctuations over time. It also has a shorter duration.

  2. The market return is the long-term return on an index that includes dividends and capital gains. Positive long-term returns often offset negative market returns.

  3. Market returns are determined by historical performance. However, SML line doesn’t take into account the past performance of assets.

  4. The beta coefficient and the market risk premium can change over time. The SML is subject to macroeconomic fluctuations in GDP growth, inflation, interest rates, unemployment, and other factors.

  5. The beta coefficient is an important factor in SML. However, it can be challenging to forecast the beta accurately. So, you may fail to consider the appropriate assumptions for calculating beta. In that case, the validity of predicted returns using SML will not be reliable.

Conclusion

The securities market line is a good method for figuring out an asset's returns. SML is a chart for the expected rate of return and risks associated with an asset. It is a visual representation of the capital asset pricing model. It is easy to calculate. In addition, it doesn’t consider the unsystematic risk. So, investors can also compare diversified portfolios. Yet. there are some drawbacks to this model. The risk-free rate can change with time. Moreover, it can be difficult to find the beta coefficient properly. So, it's essential to take into account other indicators while investing in an asset.

FAQs on Security Market Line

Use the risk-free rate () as the starting point on the Security Market Line.

Yes, the Security Market Line is useful indicator to analyse individual securities. You can compare the expected returns of the assets with the expected returns as per the CAPM.

Securities appearing above the SML are usually considered overvalued. This is because it is expected to offer returns higher than what is justified by its systematic risk

If a security appear below the SML then it is expected to provide returns lower thanthe justified required rate. So, it is undervalued.

The SML keeps changing based on changes in risk-free rate and the expected return.

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