Understanding the Security Market Line (SML) | Capital Asset Pricing Model

The security market line (SML) is a visual representation of the capital asset pricing model (CAPM)Capital Asset Pricing Model (CAPM)The Capital Asset Pricing Model (CAPM) is a model that describes the relationship between expected return and risk of a security. CAPM formula shows the return of a security is equal to the risk-free return plus a risk premium, based on the beta of that security. SML is a theoretical representation of the expected returns of assets based on systematic, non-diversifiable risk.

Idiosyncratic risk is not included in the security market line. More broadly, the SML plots the expected market returns for a marketable security at a given level of market risk for the marketable security. The level of risk is determined by the beta of a security against the market.

Theoretically, the “market” refers to all risky assets. In practice, a proxy is typically used. An example of common proxies is the Dow Jones Industrial Average (DJIA), S&P 500 IndexS&P 500 IndexThe Standard and Poor’s 500 Index, abbreviated as S&P 500 index, is an index comprising the stocks of 500 publicly traded companies in the, and the NASDAQ 100. The security market line can also be used to graphically understand the pricing of an asset. However, the security market line is not always applicable in practice, as there are very broad assumptions involved that do not always apply.

Security Market Line Assumptions

Since the security market line is a graphical representation of the capital asset pricing model (CAPM), the assumptions for CAPM also hold for SML. Most commonly, CAPM is a one-factor model that is only based on the level of systematic risk a security is exposed to.

The larger the level of systematic risk, the larger the expected return for the security is – more risk equals more reward. It is a linear relationship and explains why the security market line is a straight line. However, very broad assumptions need to be made for a one-factor model to be upheld. Below are some SML assumptions:

• All market participants are price takers and cannot affect the price of a security.
• The investment horizon for all investors is the same.
• There are no short sales.
• There are no taxes or transaction costs.
• There is only one risk-free asset.
• There are multiple risky assets.
• All market participants are rational.

Components of the SML

The security market line is made up of the risk-free rateRisk-Free RateThe risk-free rate of return is the interest rate an investor can expect to earn on an investment that carries zero risk. In practice, the risk-free rate is commonly considered to equal to the interest paid on a 3-month government Treasury bill, generally the safest investment an investor can make., the beta of the asset related to the market, and the expected market risk premium. The components will yield the expected return of an asset. Additionally, the SML formula can be used to calculate the asset’s risk premium. Below is the formula to calculate the security market line:

Security Market Line = Risk-Free Rate + [Beta * (Expected Market Return – Risk-Free Rate)]

Where:

• Risk-Free Rate – Current risk-free rate
• Beta – Beta of the security to the market
• Expected Market Return – Expected return of all risky assets

Plotting the function for all positive betas, with the constraint of a positive market risk premium (Expected Market Return – Risk-Free Rate), will give the typical security market line. To get the expected risk premium of a security, subtract the first risk-free rate from both sides of the equation. It will produce:

Expected Security Risk Premium = Beta * (Expected Market Return – Risk-Free Rate)

SML and Asset Pricing

The security market line can also be used to determine whether an asset is overpriced or underpriced, given its level of systematic risk, compared to the market. Graphically, if the asset offers a return that is higher than the market’s for a given level of systematic risk, it will be plotted above the security market line. However, if the asset offers a return that is lower than the market’s for a given level of systematic risk, it will be plotted below the security market line.

If an asset is plotted above the security market line, it is underpriced. If an asset is plotted below, it is overpriced. The intuitive reason why an asset that is plotted above the SML is underpriced is that it is giving a return larger than the market, and it is because the cost of buying the asset is not large enough. The return of an asset is directly related to the price at which the asset is bought. Thus, with the security market line, if an asset is providing too large of a return, it means that it is underpriced.

The same intuition holds for when an asset is overpriced. The price of the asset is too high, which eats away at the returns the asset provides and thus, causes the asset to be plotted below the security market line. With the Efficient Market Theory, assets that are plotted above the SML are bought, which increases the demand and the price of the asset, thus decreasing its expected return and bringing it back down to the security market line.

More Resources

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• BetaBetaThe beta (β) of an investment security (i.e. a stock) is a measurement of its volatility of returns relative to the entire market. It is used as a measure of risk and is an integral part of the Capital Asset Pricing Model (CAPM). A company with a higher beta has greater risk and also greater expected returns.
• Expected ReturnExpected ReturnThe expected return on an investment is the expected value of the probability distribution of possible returns it can provide to investors. The return on the investment is an unknown variable that has different values associated with different probabilities.
• Idiosyncratic riskIdiosyncratic RiskIdiosyncratic risk, also sometimes referred to as unsystematic risk, is the inherent risk involved in investing in a specific asset – such as a stock –  the
• Market Risk PremiumMarket Risk PremiumThe market risk premium is the additional return an investor expects from holding a risky market portfolio instead of risk-free assets.