Capital Asset Pricing Model (CAPM) is a theory developed by economist William Sharpe in 1970 that details the relationship between the expected return and the risk of investing in a particular investment. The theory utilizes a formula that calculates the expected return of a security based on its level of risk, detailed below.
His theory states that an investment contains two types of risk:
- Systematic Risk
- Refers to market risk that affects all investors. It includes macroeconomic conditions, inflation, interest rate changes and economic direction. Systematic risk cannot be diversified.
- Non-Systematic Risk
- Refers to risk that is unique to a business or industry. Adding low correlation funds into your portfolio will allow you to fully diversify your portfolio. Modern Portfolio Theory states that rational investors can eliminate non-systematic risk by diversifying their portfolio.
The model is based on systematic risk, also known as non-diversifiable risk. It mentions that the expected return on a security is determined by taking the risk-free rate, usually the yield on a government bond, plus a risk premium. The risk premium is the rate of return that is greater than the risk free rate. Investors who are looking to take above average risk needed to be compensated in the form of a risk premium.
Capital Asset Pricing Model Formula
Re = Rf + βa ∗ (Rm − Rf)
Re = Expected return on a security
Rf = Risk-free rate
βa = Beta of the security
Rm = Expected return of the market (Rm−Rf) = market risk premium
The Capital Asset Pricing Model Formula (CAPM) allows you to calculate the expected return on a security based on its level of risk. The formula involves taking the risk free rate plus the beta multiplied by the difference between the rate of return on the market and the risk free rate.
What is Beta?
Beta measures the systematic risk of an asset in relation to the over all movement of the market. By definition, a beta is usually equal to 1. If the beta is lower than 1, this means that the particular stock is a defensive stock and less volatile than its peers. If the beta is greater than 1, this is a risky stock. Remember that systematic risk cannot be diversified away by adding more uncorrelated securities to the portfolio.
Example of CAPM Formula
Below we’re going to calculate the expected return of Company A given the following information. The risk free rate in the market is currently 5% and the market return is 10%. If Company A has a stock beta of 1.5, what would be it’s expected return?
12.5% = 5% + 1.5 ∗ (10% − 5%)
The expected return on company A would be 12.5%. The higher the beta, the more correlated a particular security will be to the overall market. In this example, the beta is 1.5 which is positively correlated. How would the equation look like if the beta was 0.5?
Limitations with Capital Asset Pricing Model
Capital Asset Pricing Model has often been criticized due to the fact that it’s based on assumptions. The formula states that a riskier asset will generate higher return but this is not always the case. A riskier asset could also generate lower returns. In addition, CAPM uses historical data to predict expected future results. Past returns are not indicative of future returns and historical volatility may not reflect the future. Another point of criticism is that CAPM does not account for changes in the risk free rate. It assumes that the rate will remain constant over time.
Even though it has its limitations, CAPM formula continues to be widely used throughout the financial community, particularly for pricing risky securities and determining expected future return.