What is the Security Market Line (SML)?

The security market line (SML) is the Capital Asset Pricing Model (CAPMCAPMThe Capital Asset Pricing Model (CAPM) defines the expected return from a portfolio of various securities with varying degrees of risk. It also considers the volatility of a particular security in relation to the market.read more). It gives the market’s expected return at different levels of systematic or market risk. 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.

Security Market Line Equation

The Equation is as follows:

SML: E(Ri) = Rf + βi [E(RM) – Rf]

In the above security market line formula:

  • E(Ri) is the expected return on the securityRf is the risk-free rate and represents the y-intercept of the SMLβi is a non-diversifiable or systematic risk. It is the most crucial factor in SML. We will discuss this in detail in this article.E(RM) is expected to return on market portfolio M.E(RM) – Rf  is known as Market Risk Premium

The above equation can be graphically represented as below:

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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-versaAll 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.

Security Market Line 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 indexMarket IndexA market index tracks the performance of a diverse selection of securities that make up a significant part of the financial market. It serves as an indicator of the overall financial market condition by listing the historical and real-time trends in different market segments. read more.

Now let’s understand the security market line example, calculating the expected returnCalculating The Expected ReturnThe Expected Return formula is determined by applying all the Investments portfolio weights with their respective returns and doing the total of results. Expected return = (p1 * r1) + (p2 * r2) + ………… + (pn * rn), where, pi = Probability of each return and ri = Rate of return with probability. read more for each security using SML:

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

  • E(RA) = Rf + βi [E(RM) – Rf]E(RA) = 5 + 0.5 [14 – 5]E(RA) = 5 + 0.5 × 9 = 9.5%

Expected return for Security B:

  • E(RB) = Rf + βi [E(RM) – Rf]E(RB) = 5 + 1.5 [14 – 5]E(RB) = 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 coefficientBeta CoefficientThe beta coefficient reflects the change in the price of a security in relation to the movement in the market price. The Beta of the stock/security is also used for measuring the systematic risks associated with the specific investment.read more 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:

βi = Cov(Ri , RM)/Var (RM) = ρi,M * σi / σM

  • Cov(Ri , RM) is the covarianceCovarianceCovariance is a statistical measure used to find the relationship between two assets and is calculated as the standard deviation of the return of the two assets multiplied by its correlation. If it gives a positive number then the assets are said to have positive covariance i.e. when the returns of one asset goes up, the return of second assets also goes up and vice versa for negative covariance.read more of the asset i and the marketVar (RM) is the variance of the marketρi,M is a correlation between the asset i and the marketσi is the standard deviation of asset iσi 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.

Advantages

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 portfolioThe model assumes the portfolio is well diversified hence neglects the unsystematic riskUnsystematic RiskUnsystematic risk refers to risk that is generated in a specific company or industry and may not be applicable to other industries or the economy as a whole.  There are two types of unsystematic risk: business risk and financial risk.read more making it easier to compare two diversified portfoliosCAPM or SML considers the systematic risk, which is neglected by other models likes the Dividend Discount ModelDividend Discount ModelThe Dividend Discount Model (DDM) is a method of calculating the stock price based on the likely dividends that will be paid and discounting them at the expected yearly rate. In other words, it is used to value stocks based on the future dividends’ net present value.read more (DDM) and Weighted Average Cost of Capital ( + [Cost of Debt * % of Debt * (1-Tax Rate)]” url=”https://www.wallstreetmojo.com/weighted-average-cost-capital-wacc/”]WACC”WACC””The) 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 premiumMarket Risk PremiumThe market risk premium is the supplementary return on the portfolio because of the additional risk involved in the portfolio; essentially, the market risk premium is the premium return investors should have to make sure to invest in stock instead of risk-free securities.read more 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.

Security Market Line (SML) Video

Conclusion

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 respectivelyAbove And Below The Line RespectivelyAbove the line are items that appear above the company’s gross profit value on its income statement. In contrast, below the line represents items shown below the gross profit value of the company in its income statement.read more. 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. 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.

This article is a guide to the Security Market Line. Here we discuss the security market line formula and the practical example, importance, advantages, and limitations of SML. You can learn more about Valuations from the following articles –

  • Risk Premium FormulaDCFTop Valuation Interview QuestionsValuation Analyst