# How CAPM and Beta Determine a Stock’s Expected Return

According to the CAPM, a stock’s expected return is positively related to its beta. But what does this mean, and how can investors use this information to make better investment decisions? In this article, we will explain the concepts of CAPM and beta, and how they can help investors estimate the risk and return of different stocks.

## What Is CAPM?

CAPM stands for Capital Asset Pricing Model, which is a widely used method for pricing risky securities and for generating estimates of the expected returns of assets, particularly stocks. The CAPM formula is as follows:

���=��+�����(���−��)ERi​=Rf​+betai​(ERm​−Rf​)

where:

• ���ERi​ = expected return of investment
• ��Rf​ = risk-free rate
• �����betai​ = beta of the investment
• (���−��)(ERm​−Rf​) = market risk premium

The CAPM formula shows that the expected return of a stock is equal to the risk-free rate plus a risk premium, which is based on the beta of that stock. The risk-free rate is typically equal to the yield on a 10-year US government bond, which represents the minimum return that investors can expect from investing in a safe asset. The market risk premium is the difference between the expected return on the market (usually the S&P 500 index) and the risk-free rate, which represents the extra return that investors demand for investing in a risky asset.

## What Is Beta?

Beta is a measure of the volatility — or systematic risk — of a stock or portfolio compared to the market as a whole. Beta indicates how much a stock’s returns tend to move with the market. A stock with a beta of 1.0 has the same level of systematic risk as the market, and its returns tend to move in sync with the market. A stock with a beta higher than 1.0 has more systematic risk than the market, and its returns tend to be more volatile than the market. A stock with a beta lower than 1.0 has less systematic risk than the market, and its returns tend to be less volatile than the market.

Beta can be calculated by dividing the covariance of a stock’s returns and the market’s returns by the variance of the market’s returns over a specified period2. Alternatively, beta can be obtained from various sources, such as financial websites or databases.

## How CAPM and Beta Relate to Each Other

The CAPM and beta are related because they both capture the concept of systematic risk, which is the risk that affects all stocks in the market due to factors such as economic cycles, interest rates, inflation, political events, etc. Systematic risk cannot be eliminated by diversification, and investors expect to be compensated for taking on this risk in the form of higher returns.

The CAPM shows that the expected return of a stock is positively related to its beta, meaning that stocks with higher betas have higher expected returns than stocks with lower betas. This is because stocks with higher betas are more exposed to systematic risk, and therefore require higher risk premiums to attract investors. Conversely, stocks with lower betas have lower expected returns than stocks with higher betas, because they are less exposed to systematic risk, and therefore require lower risk premiums.

For example, suppose that the risk-free rate is 2%, the expected return on the market is 10%, and two stocks have betas of 0.5 and 1.5 respectively. Using the CAPM formula, we can calculate their expected returns as follows:

• Stock A (beta = 0.5): ���=2ERA​=2
• Stock B (beta = 1.5): ���=2ERB​=2

As we can see, stock B has a higher expected return than stock A because it has a higher beta. This means that stock B is more risky than stock A, and investors demand a higher return for investing in it.

## How Investors Can Use CAPM and Beta

Investors can use CAPM and beta to estimate the expected return of different stocks, and compare them with their actual or required returns. This can help investors decide whether a stock is overvalued or undervalued, and whether it fits their risk preferences and portfolio objectives.

For example, suppose that an investor has a required rate of return of 12%, and is considering investing in two stocks with betas of 0.8 and 1.2 respectively. Assuming that the risk-free rate is 2% and the expected return on the market is 10%, we can calculate their expected returns using CAPM as follows:

• Stock C (beta = 0.8): ���=2ERC​=2
• Stock D (beta = 1.2): ���=2ERD​=2

Based on these calculations, we can see that stock C has an expected return lower than the investor’s required return, and therefore is not a suitable investment for the investor. Stock D has an expected return closer to the investor’s required return, but still slightly lower, and therefore may not be an attractive investment for the investor either. The investor may need to look for stocks with higher betas and expected returns, or lower their required rate of return.

Alternatively, suppose that the investor knows the actual or historical returns of the two stocks, and wants to compare them with their expected returns using CAPM. Assuming that the actual returns of the two stocks are 9% and 12% respectively, we can calculate their difference from their expected returns as follows:

• Stock C (beta = 0.8): ���−���=9ARC​−ERC​=9
• Stock D (beta = 1.2): ���−���=12ARD​−ERD​=12

Based on these calculations, we can see that both stocks have actual returns higher than their expected returns using CAPM, and therefore are undervalued according to the model. This means that the stocks offer higher returns than what their level of risk would suggest, and therefore are attractive investments for the investor.

## Limitations of CAPM and Beta

While CAPM and beta are useful tools for estimating the expected return and risk of stocks, they also have some limitations that investors should be aware of. Some of these limitations are:

• CAPM and beta are based on historical data, which may not reflect the future performance or risk of stocks.
• CAPM and beta assume that investors are rational, risk-averse, and hold diversified portfolios, which may not be true in reality.
• CAPM and beta rely on a single measure of risk (beta), which may not capture all the sources of risk that affect a stock, such as unsystematic risk, liquidity risk, or event risk.
• CAPM and beta assume that the market is efficient, meaning that all relevant information is reflected in stock prices, which may not be true in reality.
• CAPM and beta may not be applicable to all types of stocks, such as those with negative or very high betas, or those that do not follow the market trends.

Therefore, investors should use CAPM and beta with caution, and supplement them with other methods of analysis and valuation, such as fundamental analysis , technical analysis , or discounted cash flow analysis . Investors should also consider their own personal factors, such as their risk tolerance , time horizon , and investment goals , when making investment decisions.

## Conclusion

According to the CAPM, a stock’s expected return is positively related to its beta. This means that stocks with higher betas have higher expected returns than stocks with lower betas, because they have more systematic risk and require higher risk premiums. Investors can use CAPM and beta to estimate the expected return and risk of different stocks, and compare them with their actual or required returns. This can help investors decide whether a stock is overvalued or undervalued, and whether it fits their risk preferences and portfolio objectives. However, investors should also be aware of the limitations of CAPM and beta, and use them with caution and in conjunction with other methods of analysis and valuation. 