Alpha vs. Beta: What's the Difference?

Alpha vs. Beta: An Overview

Alpha and beta are two of the key measurements used to evaluate the performance of a stock, a fund, or an investment portfolio.

Alpha measures the amount that the investment has returned in comparison to the market index or other broad benchmark that it is compared against.

Beta measures the relative volatility of an investment. It is an indication of its relative risk.

Alpha and beta are standard calculations that are used to evaluate an investment portfolio’s returns, along with standard deviation, R-squared, and the Sharpe ratio.

Alpha

The alpha figure for a stock is represented as a single number, like 3 or -5. However, the number actually indicates the percentage above or below a benchmark index that the stock or fund price achieved. In this case, the stock or fund did 3% better and 5% worse, respectively, than the index.

An alpha of 1.0 means the investment outperformed its benchmark index by 1%. An alpha of -1.0 means the investment underperformed its benchmark index by 1%. If the alpha is zero, its return matched the benchmark.

Note, alpha is a historical number. It's useful to track a stock's alpha over time to see how it did, but it can't tell you how it will do tomorrow.

Alpha for Portfolio Managers

For individual investors, alpha helps reveal how a public or private stock or fund might perform in relation to its peers or to the market as a whole.

Professional portfolio managers calculate alpha as the rate of return that exceeds the model's prediction or comes short of it. They use a capital asset pricing model (CAPM) to project the potential returns of an investment portfolio.

That is generally a higher bar. If the CAPM analysis indicates that the portfolio should have earned 5%, based on risk, economic conditions, and other factors, but instead the portfolio earned just 3%, the alpha of the portfolio would be a discouraging -2%. 

Formula for Alpha:

$\begin{aligned} &\text{Alpha} = \frac{ \text{End Price} + \text{DPS} - \text{Start Price} }{ \text{Start Price} } \\ &\textbf{where:}\\ &\text{DPS} = \text{Distribution per share} \\ \end{aligned}$​Alpha=Start PriceEnd Price+DPS−Start Price​where:DPS=Distribution per share​

Portfolio managers seek to generate a higher alpha by diversifying their portfolios to balance risk.

Because alpha represents the performance of a portfolio relative to a benchmark, it represents the value that a portfolio manager adds or subtracts from a fund's return. The baseline number for alpha is zero, which indicates that the portfolio or fund is tracking perfectly with the benchmark index. In this case, the investment manager has neither added nor lost any value. 

Beta

Often referred to as the beta coefficient, beta is an indication of the volatility of a stock, a fund, or a stock portfolio in comparison with the market as a whole. A benchmark index (most commonly the S&P 500) is used as the proxy measurement for the market. Knowing how volatile a stock's price is can help an investor decide whether it is worth the risk.

The baseline number for beta is one, which indicates that the security's price moves exactly as the market moves. A beta of less than 1 means that the security is less volatile than the market, while a beta greater than 1 indicates that its price is more volatile than the market.

If a stock's beta is 1.5, it is considered to be 50% more volatile than the overall market.

Like alpha, beta is a historical number.

Beta Examples

Here are the betas for three well-known stocks on November 2021: 

Micron Technology Inc. (MU): 1.27
Coca-Cola Company (KO): 0.64
SPDR S&P 500 ETY (SPY): 1.00

We can see that Micron was 27% more volatile than the market as a whole, while Coca-Cola was 36% less volatile than the broader market. The SPDRs, or SPYs, have a beta of 1.00 because this ETF itself tracks the S&P 500 index.

Acceptable betas vary across companies and sectors. Many utility stocks have a beta of less than 1, while many high-tech Nasdaq-listed stocks have a beta of greater than 1. To investors, this signals that tech stocks offer the possibility of higher returns but generally pose more risks, while utility stocks are steady earners.

While a positive alpha is always more desirable than a negative alpha, beta isn’t as clear-cut. Risk-averse investors such as retirees seeking a steady income are attracted to lower beta. Risk-tolerant investors who seek bigger returns are often willing to invest in higher beta stocks.

Formula for Beta

Here is a useful formula for calculating beta:

$\begin{aligned} &\text{Beta} = \frac{ \text{CR} }{ \text{Variance of Market's Return} } \\ &\textbf{where:}\\ &\text{CR} = \text{Covariance of asset's return with market's return} \\ \end{aligned}$​Beta=Variance of Market’s ReturnCR​where:CR=Covariance of asset’s return with market’s return​

• Covariance is used to measure the correlation in price moves of any two stocks. A positive covariance means the stocks tend to move in lockstep, while a negative covariance means they move in opposite directions.
• Variance refers to how far a stock moves relative to its mean. It is frequently used to measure the volatility of a stock's price over time.