CAPM Calculator

How to use the CAPM calculator

Risk-free rate

The risk-free rate is usually the rate of a government bond, such as a 30-year Treasury Bill.

Expected return of the market

This is usually the historical return of a market benchmark such as the S&P 500.

Benchmark	Historical return	Time period of return
S&P 500	7.96%	1957 to 2018
S&P 500	5.90%	1999 to 2019
Dow Jones Industrial Average	5.42%	1896 to 2018
Russell 2000	7.70%	1999 to 2019
MSCI EAFE	4.00%	1999 to 2019

Beta

Beta is the level of the asset return's sensitivity compared to the market. For example:

Beta	Movement
Beta <= −1	Asset moves in opposite direction as the market. Movement is greater than market.
−1 < Beta < 0	Asset moves in opposite direction as the market.
Beta = 0	No correlation between asset and market.
0 < Beta < 1	Asset moves in same direction as market.
Beta = 1	Asset and market are perfectly correlated. Both both in the same direction by the same amount.
Beta > 1	Asset moves in same direction as market. Movement is greater than market.

What is the Capital Asset Pricing Model (CAPM)?

The Capital Asset Pricing Model (CAPM) is a fundamental concept in finance used to determine the theoretically appropriate required rate of return for an asset. It helps investors assess whether a stock is fairly valued by considering its risk relative to the overall market.

The CAPM Formula

The formula for CAPM is:

Expected Return (ER) = Risk-Free Rate (Rf) + Beta (β) * (Expected Market Return (Rm) - Risk-Free Rate (Rf))

Let's break down the components:

Expected Return (ER): This is what the calculator computes – the return an investor should expect for taking on the risk associated with holding the asset.
Risk-Free Rate (Rf): The theoretical return of an investment with zero risk. Typically, the yield on a government bond (like a U.S. Treasury bill) is used as a proxy for the risk-free rate.
Beta (β): A measure of a stock's volatility or systematic risk compared to the overall market.
- β = 1: The asset's price tends to move with the market.
- β > 1: The asset is more volatile than the market.
- β < 1: The asset is less volatile than the market.
- β = 0: The asset's movement is uncorrelated with the market (rare).
- β < 0: The asset tends to move in the opposite direction of the market (also rare).
Expected Market Return (Rm): The anticipated return of the overall market portfolio (e.g., the expected return of a broad market index like the S&P 500).
(Rm - Rf): This part is known as the Market Risk Premium. It represents the excess return the market provides over the risk-free rate as compensation for taking on market risk.

How to Use the Calculator

Enter the Risk-Free Rate (Rf): Input the current yield for a risk-free asset (e.g., 10-year U.S. Treasury bond yield) as a percentage.
Enter the Beta (β): Find the beta value for the specific stock or asset you are analyzing. Financial websites often provide this information.
Enter the Expected Market Return (Rm): Input the return you anticipate for the overall market (e.g., historical average return of the S&P 500) as a percentage.

The calculator will then compute the Expected Return (ER) based on the CAPM formula.

Important Considerations

CAPM is a theoretical model and relies on several assumptions (like rational investors and efficient markets) that may not hold true in reality. Beta can change over time, and estimating the expected market return involves uncertainty. Use CAPM as one tool among others in your investment analysis.

CAPM components

Expected return on asset

The expected return on the asset is what CAPM calculates. This is what an investor expects to earn on the asset over time.

Risk-free rate

The risk-free rate is the return that an investor can expect to receive on a risk-free investment, such as a U.S. Treasury bond. The beta coefficient is a measure of the risk of an asset relative to the overall market. A beta of 1 indicates that the asset's price will move in line with the market, while a beta greater than 1 indicates higher risk and potential for higher returns. A beta less than 1 indicates lower risk and potential for lower returns.

Expected return on the market

The expected return on the market is the return of a market benchmark, such as the S&P 500, Russell 2000, Dow Jones Industrial Average, or another benchmark that encompasses most of the market.

Investors generally use the historical rate of return for the S&P 500, which was 8% between 1957 and 2018.

Beta

An asset's beta measures the risk involved with investing in the asset relative to the market risk and the risk-free rate.

Beta reflects the sensitivity of the asset to the market risk. A beta of 1 signifies that the asset has the same risk as the market. When the market goes up a little, the asset goes up a little. When the market goes down a lot, the asset goes down a lot. The two are perfectly correlated.

A beta of 0 means the asset and the market are not at all correlated. The two move independently of each other.

A positive beta means the asset and the market move in the same direction, while a negative beta means the two move in opposite directions.

Risk premium

The risk premium of the asset is the difference between its expected return and the risk-free rate.

Market premium

The market premium is the difference between the expected return of the market and the risk-free rate.

Conclusion

One of the key assumptions of the CAPM is that investors are rational and will seek to maximize their expected returns while minimizing their risk. This means that they will be willing to accept higher levels of risk if they expect to receive a higher return.

The CAPM has been widely used in finance and has contributed to the development of many other financial models and theories. However, it has also been the subject of criticism, with some arguing that it does not accurately reflect the complexity of financial markets and that it relies on too many assumptions. Despite these criticisms, the CAPM remains an important tool for financial analysts and investors.