Understanding Alpha vs Beta in Investing

When it comes to portfolio management, two of the most important metrics to understand are alpha and beta. Alpha is often used to identify investment skill, while beta is used to measure the relative risk, or volatility, of an investment or portfolio. Together, both alpha and beta can combine to help you understand if you are getting the returns you might expect for the amount of risk in your portfolio.

What is Alpha?

Alpha is the “excess return” above or below what is predicted by models that take into account the risk level of a portfolio. A positive excess return would be characterized as outperformance by a manager or investor, while a negative excess return would be underperformance. For example, if you were managing a portfolio of large cap U.S. stocks and your portfolio had the same level of volatility as the S&P 500, but your portfolio earned 15% while the S&P 500 was up 10%, the extra 5% return would be the alpha. Conversely, if your portfolio return was 5% and still had the same level of volatility as the S&P 500, you would have negative alpha, or underperformance, of 5%.

However, different portfolios often have different levels of volatility. In order to understand if investors are getting better returns that adequately compensate them for the amount of risk they are taking, then we need to factor in beta. Another way to understand this would be to consider a portfolio that that was twice as volatile as the S&P 500 but achieved the same return. In this case, it’s clear that the investor did not get compensated for taking on more risk because they got the same return as a less risky portfolio (the S&P 500 in this case). In this case, they would have underperformed on a risk-adjusted basis.

What is Beta?

Beta is a measure of how volatile a portfolio (or an individual security) is relative to its benchmark. If the portfolio moves up and down at the same rate as the benchmark, it has a beta of 1. If the portfolio is half as volatile as the benchmark, the beta is 0.5. And if the portfolio is twice as volatile as the benchmark, it has a beta of 2.

Most people just memorize the definitions of alpha and beta, but to truly understand how they relate to evaluating portfolio performance we can turn to the Capital Asset Pricing Model.

The Capital Asset Pricing Model (CAPM)

Alpha and beta come from the Capital Asset Pricing Model. The Capital Asset Pricing Model is almost always referred to by it’s acronym, CAPM (pronounced “Cap-ehm”). It is one of the foundations of portfolio management. It provides a model for understanding the returns an investor might expect for a given level of risk.

While it might look intimidating, the formula for the Capital Asset Pricing Model is actually relatively easy to follow if we break down each component:

• E(Rp) = Rf + β(Rm − Rf)

Let’s break down each term, and then explain how they fit together.

• E(Rp) is the Expected Return of the Portfolio
• Rf is the Risk-Free Rate (Note that it appears twice)
• β is Beta
• Rm is the Return of the Market (The benchmark)
• Rf, the risk-free rate, is the return associated with treasury bills. This represents the theoretical return an investor can get without assuming any risk.

The term in brackets (Rm − Rf) can be read as “the market return minus the risk-free rate”, and is sometimes called the “market premium”. This is the extra return an investor gets for taking on the risk of investing in the market versus a risk-free investment of treasury bills.

Let’s now plug in some numbers to see how we can assess portfolio management skill.

Let’s say the market returned 10% and the risk free rate was 3%. Our portfolio was 25% more volatile than the market, so that means our beta was 1.25. According to the CAPM formula, our expected portfolio return E(Rp) is:

• E(Rp) = 3% + 1.25(10% − 3%)           

This works out to 11.75%. Again, this means that given the relative volatility of our portfolio versus the overall market, we would have expected a return of 11.75%. The actual return of our portfolio above or below this would be the “excess return” which can be positive or negative, and is the alpha.

If our actual portfolio return was 11.75%, then we can say we got the return expected for the level of risk we took and our alpha was zero. But if our actual portfolio return was 12.5%, then the alpha would have been +0.75%.

Conversely, if we only matched the market return of 10%, even though our portfolio was 25% riskier (as measured by the volatility), then we would have negative alpha of 2.5%. We could then say that, given the level of risk that we took in our portfolio we did not get enough return and we underperformed on a risk-adjusted basis.

Understanding how to use Alpha and Beta

You don’t have to memorize the CAPM formula or know how to calculate alpha and beta on your own.

Beta will show up on most stock quotes and all you really need to know is that a beta of 1 means the security in question tends to move up and down at the same level as the benchmark index. Betas below one indicate less volatile securities, and betas greater than one indicate more volatile securities. Beta can also be calculated for you for your overall portfolio with using portfolio management tools.

Alpha is essentially used to tell you if a portfolio has outperformed or underperformed a benchmark given the level of risk in the portfolio. It’s possible to have a positive alpha (indicating skill) if the return of a portfolio is lower than the benchmark, but the risk of the portfolio is much less than the risk of the benchmark. It’s also possible to have a negative alpha (indicated underperformance from a risk-adjusted perspective) even though a portfolio had a higher return than its benchmark. This would be because the portfolio took on too much risk in order to get that extra return. Overall, positive alpha represents outperformance on a risk-adjusted basis, and negative alpha represents underperformance on a risk-adjusted basis.