Security Market Line (Slope, Formula)

What is the Security Market Line (SML)?

Security market line (SML) is the graphical representation of the Capital Asset Pricing Model (CAPM) and gives the expected return of the market at different levels of systematic or market risk. It is also called ‘characteristic line’ where the x-axis represents beta or the risk of the assets and y-axis represents the expected return.

Security Market Line Equation

The Equation is as follows:

SML: E(R_i) = R_f + β_i [E(R_M) – R_f]

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
β_i is a non-diversifiable or systematic risk. It is the most important factor in SML. We will discuss this in detail in this article.
E(R_M) is expected return on market portfolio M.
E(R_M) – R_fis known as Market Risk Premium

The above equation can be graphically represented as below:

Characteristics

Characteristics of Security Market Line (SML) are as below

SML is a good representation of investment opportunity cost which provides the combination of 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 market risk premium which is: (E(R_M) – R_f). Higher the market risk premium steeper the slope and vice-versa
All the assets which are correctly priced are represented on SML
The assets which are above the SML are undervalued as they give the higher expected return for a given amount of risk.
The assets which are 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%. Consider two securities one with a beta coefficient of 0.5 and other with the beta coefficient of 1.5 with respect to the market index.

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

Expected return for Security A as per security market line equation is as per below

E(R_A) = R_f + β_i [E(R_M) – R_f]
E(R_A) = 5 + 0.5 [14 – 5]
E(R_A) = 5 + 0.5 × 9 = 9.5%

Expected return for Security B:

E(R_B) = R_f + β_i [E(R_M) – R_f]
E(R_B) = 5 + 1.5 [14 – 5]
E(R_B) = 5 + 1.5 × 9 = 18.5%

Thus, as can be seen above Security A has lower beta thus, it has lower expected return while security B has higher beta coefficient and has the higher expected return. This is in line with general finance theory of higher risk higher expected return.

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Slope of Securities Market Line (Beta)

Beta (slope) is an important 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 as compared to the market as a whole. The market can be considered as 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 market and beta less than 1 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 with respect to the market, however, beta does not remain constant with time.

Advantages

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

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

These are the major 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 can have even shorter-term duration thus causing volatility
Market return is the long-term return from a market index which includes both capital and dividend payments. Market return could be negative which is generally countered by using 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 beta coefficient can vary with time. There can be macroeconomic changes like GDP growth, inflation, interest rates, unemployment etc. which can change the SML.
Major 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 portfolio lies above and below the line respectively. A risk-averse investor’s investment is more often to lie close to y-axis or the beginning of the line whereas risk-taker investor’s investment would lie higher on the SML. SML provides a good method for comparing two investments or securities, however, the same depends on assumptions of market risk, risk-free rates, and beta coefficients.