We often hear the terms alpha and beta when talking about investments. These are two different measures that are part of the same equation derived from a linear regression. Don't worry if that sounds too complicated, we'll explain it all in this article.

### Key Takeaways

- Alpha and beta are two different parts of an equation used to explain the performance of stocks and investment funds.
- Beta is a measure of volatility relative to a benchmark, such as the S&P 500.
- Alpha is the excess return on an investment after adjusting for market-related volatility and random fluctuations.
- Alpha and beta are both measures used to compare and predict returns.

## The Equation

If equations make your eyes glaze over, you can just skip this part. On the other hand, we can go straight to the equation if you know some algebra or ever took a class covering regressions in college. The basic model is given by:

- y = a + bx + u

Where:

- y is the performance of the stock or fund.
- a is alpha, which is the excess return of the stock or fund.
- b is beta, which is volatility relative to the benchmark.
- x is the performance of the benchmark, which is often the S&P 500 index.
- u is the residual, which is the unexplained random portion of performance in a given year.

## Defining Beta

Beta is a measure of volatility relative to a benchmark, and it's actually easier to talk about beta first. It measures the systematic risk of a security or a portfolio compared to an index like the S&P 500. Many growth stocks would have a beta over 1, probably much higher. A T-bill would have a beta close to zero because its prices hardly move relative to the market as a whole.

Beta is a multiplicative factor. A 2X leveraged S&P 500 ETF has a beta very close to 2 relative to the S&P 500 by design. It goes up or down twice as much as the index in a given period of time. If beta is -2, then the investment moves in the opposite direction of the index by a factor of two. Most investments with negative betas are inverse ETFs or hold Treasury bonds.

What beta also tells you is when risk cannot be diversified away. If you look at the beta of a typical mutual fund, it's essentially telling you how much market risk you're taking.

It's crucial to realize that high or low beta frequently leads to market outperformance. A fund with lots of growth stocks and high beta will usually beat the market during a good year for stocks. Similarly, a conservative fund that holds bonds will have a low beta and typically outperform the S&P 500 during a poor year for the market.

If a stock or fund outperforms the market for a year, it is probably because of beta or random luck rather than alpha.

## Defining Alpha

Alpha is the excess return on an investment after adjusting for market-related volatility and random fluctuations. Alpha is one of the five major risk management indicators for mutual funds, stocks, and bonds. In a sense, it tells investors whether an asset has consistently performed better or worse than its beta predicts.

Alpha is also a measure of risk. An alpha of -15 means the investment was far too risky given the return. An alpha of zero suggests that an asset has earned a return commensurate with the risk. Alpha of greater than zero means an investment outperformed, after adjusting for volatility.

When hedge fund managers talk about high alpha, they're usually saying that their managers are good enough to outperform the market. But that raises another important question: when alpha is the "excess" return over an index, what index are you using?

For example, fund managers might brag that their funds generated 13% returns when the S&P returned 11%. But is the S&P an appropriate index to use? The manager might invest in small-cap value stocks. These stocks have higher returns than the S&P 500, according to the Fama and French Three-Factor Model. In this case, a small-cap value index might be a better benchmark than the S&P 500.

There is also a chance that a fund manager just got lucky instead of having true alpha. Suppose a manager outperforms the market by an average of 2% during the first three years of the fund without any extra market-related volatility. In that case, beta equals one, and it might look like alpha is 2%.

However, suppose the fund manager then underperforms the market by 2% over the next three years. It now looks like alpha equals zero. The original appearance of alpha was due to sample size neglect.

Very few investors have true alpha, and it typically takes a decade or more to be sure. Warren Buffett is generally considered to have alpha. Buffett focused on value investing, dividend growth, and growth at a reasonable price (GARP) strategies during his career. A study of Buffett's alpha found that he tended to use leverage with high-quality and low-beta stocks.

## The Bottom Line

Alpha and beta are both risk ratios that investors use as tools to compare and predict returns. They're significant numbers to know, but one must check carefully to see how they are calculated.