The Capital Asset Pricing Model


The capital asset pricing model helps investors assess the required rate of return on a given asset by measuring sensitivity to risk.

When considering assets for diversification in an investment portfolio, investors and financiers use various tools to project the required rate of return and risk of a given investment. This means that investors are on the lookout for ways to minimize risk, maximize returns, and invest intelligently in well-priced assets. The key assumption is that the market will self-correct to adjust each investment option's expected return to the relative risk of investing.


The Capital Asset Pricing Model

The capital asset pricing model (CAPM) can be a useful tool for measuring the ratio between risk and return on a given investment. This model measures a given asset's sensitivity to systematic risk (or market risk) about the expected return compared to a theoretical risk-free asset.


How CAPM Works

This sounds complicated, but it's simpler than it seems. All this means is that the CAPM tries to measure the risk the market will offer the asset compared to the risk-free rate and make sure the expected return will offset that risk. To understand this concept, there are a few variables that are useful to identify upfront:

  • E(Ri) is an expected return on security.

  • E(RM) is an expected return on market portfolio M.

  • β is a non-diversifiable or systematic risk.

  • RM is a market rate of return.

  • Rf is a risk-free rate.


There are many ways to rearrange the relationship between these variables to derive meaningful information. Like all equations, depending on what you know, you can solve for what you do not know.

For basic CAPM calculations, you want to solve for the expected return on a security, which looks like this:

\(E(R_i)=R_f+β_i(E(R_m)−R_f)\)


Security Market Line

By rearranging these variables, you can also look at the concept of the security market line (SML), which underlines a security's relationship with systematic risk and respected return in a graphical format. This is written as:

\(SML:E(R_i)=R_f+β_i[E(R_M)−R_f]\)

The security market line is illustrated in this graph, where an assets expected return can be visualized.

Security Market Line This graph illustrates the security market line, which visualizes an asset's expected return.


Risk and Return

A final application of the CAPM variables in relation to one another is in deriving a ratio that illustrates the relationship between risk and return. On the left side of the equation below, you have an assessment of the overall risk relative to a risk-free asset. On the right side, you have the overall return (similarly relative to a risk-free asset). This can be written as follows:

\(\dfrac{E(R_i)−R_f}{βi}=E(R_m)−Rf​\)

Investors can utilize the CAPM equation and its various implications to assess various market investment opportunities to diversify a portfolio and identify undervalued assets.

Key Points

  • Investors use various tools to determine the overall expected return and relative risk of a security in the broader financial markets.

  • One such tool is the capital asset pricing model (CAPM), which essentially distills the required rate of return applied to the risks (both of which are relative to the risk-free rate).

  • By utilizing the variables involved in a CAPM calculation, an investor can also determine the risk to return ratio alongside the security market line (a graphical representation of the asset's risk and return).

  • By utilizing the CAPM equation, investors can determine when an asset is undervalued, and balance a portfolio for the best prospective return on the lowest possible risk.

Term

  • Capital Asset Pricing Model – an equation that assesses the required rate of return on a given investment based upon its risk relative to a theoretical risk-free asset.

Source: Boundless Finance, https://ftp.worldpossible.org/endless/eos-rachel/RACHEL/RACHEL/modules/en-boundless-static/www.boundless.com/finance/textbooks/boundless-finance-textbook/introduction-to-the-cost-of-capital-10/approaches-to-calculating-the-cost-of-capital-89/index.html
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