Capital Asset Pricing Model

Updated: April 12, 2022

The Capital Asset Pricing Model (CAPM) provides a way to calculate the expected return of an investment based on the time value of money and the systematic risk of the asset. Put simply, CAPM estimates the price of a high-risk stock by linking the relationship between the risk of the stock, and the expected return.

CAPM is very commonly used in finance to price risky securities and calculating an expected return on those assets when considering the risk and cost of capital.

The systematic risk and unsystematic risk are two kinds of risks that most investors face. When we talk about a risk that causes low or negative returns and risks of the financial system where the whole economy goes down, we are referring to systematic risk. For example, an economic recession is a systematic risk.

When we add additional investments to a portfolio, we are able to mitigate such risks. For instance, since there are particular events that may affect it, a portfolio of 100-stocks is less prone to the negative performance of one company.

Risk specific to a particular investment, on the other hand, refers to unsystematic risk. A major disruption in the company’s supply chain, an unfavorable court ruling affecting the company, etc. would be examples of unsystematic risk. By adding additional investments to a portfolio, you can still mitigate such risks.

The capital asset pricing model doesn’t provide any reward for taking on unsystematic risk since it can be eliminated through diversification. The required return is measured based on the level of systematic risk inherent in a specific investment.

Capital Asset Pricing Model Formula

$$ER_{i} = R_{f} + B_{i} (ER_{m} - R_{f})$$

  • ERi = Expected return of investment
  • Rf = Risk-free rate
  • Bi = Beta of the investment
  • (ERm – Rf) = Market risk premium

You must first understand the risk of an investment to fully understand the capital asset, pricing model. A loss of investment to the investor is possible from individual securities since it carries a risk of depreciation.  With additional risk, an investor expects to realize a higher return on their investment since some securities have more risk than others.

The risk-free rate in the CAPM formula accounts for the time value of money – that money available at the present time is worth more than the same amount in the future due to its current earning capacity. The other components of the formula focus on the additional risk taken on by the investor.

The beta of the investment is a way to measure and account for how much risk this particular investment will add to the portfolio relative to the market. If a stock is riskier than the overall market, it will have a beta that is higher than 1 and a beta of less than 1 would assume that the investment will reduce the overall risk of the portfolio.

Once you have the beta, you multiply it by the market risk premium (the return expected from the market that is above the risk-free rate). This value is then added to the risk-free rate to give you the final expected rate of return for the asset.

Capital Asset Pricing Model Example

Daphne wants to calculate the expected rate of return for security for her work as a freelance investment banker. Pedro has the following figures to calculate CAPM: the risk-free rate is 4%, the expected return of the market is 12%, and the systematic risk b of the security is 1.3.

$$Expected\: Return = 4\% + 1.3 (12\% - 4\%) = 14.4%$$

So what does this mean to the potential investor? If the expected return they are looking for is equal to or less than 14.4%, then this is a good option for them to invest in.

Capital Asset Pricing Model Conclusion

When calculating the capital asset pricing model, the below points are worth bearing in mind as a quick recap of what it is, why it’s used, and how to use it:

  • The relationship between the systematic risk of investment and the required return is established by the capital asset pricing model. 
  • Systematic risk and unsystematic risks are two kinds of risks investors face.
  • Systematic risk is a downfall of the whole economy and causes low or negative returns.
  • Unsystematic risk is a risk related to one specific investment. 
  • Diversification can eliminate unsystematic risk, you cannot get any reward from the CAPM for using it.
  • The risk of investment must be understood fully. 
  • There are some terms you need to know to calculate the expected rate of return: RF- risk-free rate, RM- expected return of the market, and b-systematic risk. 
  • The rate that is assumed to have no risk involved in an investment is called the risk-free rate. 
  • The risk premium of the particular security and the risk-free rate are the two components you can break the capital asset pricing model formula to.
  • The overall market’s risk can be determined by subtracting the market return from a risk-free return in the CAPM formula.
  • The individual stock’s risk can be determined by multiplying the beta times this risk of the market.
  • The risk of individual security related to the market is called beta. 
  • Epsilon is considered to be the error in the regression, and
  • Alpha is considered to be the risk-free rate. 

Capital Asset Pricing Calculator

You can use the CAPM calculator below to work out your own expected return by entering the risk-free rate, the beta, and the market return rate.

Frequently Asked Questions

What is the capital asset pricing model?

The CAPM is a model that calculates the expected rate of return for an investment, given the risk of that investment. In other words, it determines how much extra compensation an investor needs to receive for taking on additional risk.

Why do we use the capital asset pricing model?

The CAPM is one of the most commonly used models for calculating expected rates of return, and it helps investors understand the relationship between risk and reward. It can help them determine whether a particular investment is worth taking on additional risk for the potential higher return.

How do you calculate the capital asset pricing model?

The CAPM equation is:

E(R)i = Rf + (ERm - Rf) Where: ERi = Expected return of investment Rf = Risk-free rate Bi = Beta of the investment (ERm – Rf) = Market risk premium

What is an example of how to use the capital asset pricing model?

Let's say you're interested in investing in a security that has a beta of 1.5. You would plug these numbers into the equation: E(R)i = Rf + (ERm - Rf) E(R)i = 4% + (12% - 4%) E(R)i = 14% So, the expected rate of return for this investment would be 14%.

What are the risks and rewards associated with the capital asset pricing model?

The biggest risk associated with the CAPM is that it's based on historical data, and therefore doesn't always accurately predict future returns. Another risk is that not all risks can be accounted for by the model, such as company-specific risks. The main reward of the CAPM is that it allows investors to quantify the risk/reward relationship for a particular investment.