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

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 matches the benchmark.

Note that 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%. 

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. 

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​

This formula will provide insight into how well an asset will perform against its benchmark by including its return. For example, if the alpha were zero, it would indicate that the asset's performance is equal to its benchmark.

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.

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​

In this formula, 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. 

Key Differences

Let’s summarize the main differences between alpha and beta. Note that in a given trading scenario, there may be fewer or greater considerations, and not every difference may be material in any given investment position. 

• Measurement Focus: Alpha focuses on the excess return of an investment compared to its expected return given its level of risk. Meanwhile, beta focuses on measuring the sensitivity of an investment's returns to changes in the market. Beta is more concerned about being a comparison against the broader market, while alpha focuses on a specific risk level.
• Calculation Method: It goes without saying that each has a different way of being calculated. Alpha is formulated using the capital asset pricing model (CAPM) formula which considers an investment's actual return, risk-free rate, and beta. Beta, on the other hand, is calculated through regression analysis, which compares the historical returns and variances of an investment against the returns of a market index. 
• Risk Assessment: Alpha does not directly assess risk; instead, it evaluates performance relative to risk-adjusted expectations. On the other hand, beta directly measures an investment's riskiness. Higher beta values signify higher systematic risk, while lower values suggest lower risk.
• How It’s Applied: Alpha is specific to individual investments or portfolios. Beta, however, is commonly used to assess the risk of entire asset classes or portfolios, providing a broader perspective on market exposure.
• Market Sensitivity: Alpha is not directly tied to market movements. Instead, it evaluates performance relative to market expectations. Beta directly measures an investment's sensitivity to market movements. High-beta investments tend to amplify market movements.
  

Alternatives to Alpha and Beta

In addition to differences between alpha and beta, there are similar yet different alternative options you can use to evaluate your portfolio. Let’s quickly cover these common alternatives to alpha and beta.

• Sharpe Ratio: The Sharpe ratio measures the risk-adjusted return of an investment or portfolio. It compares the excess return of the investment over the risk-free rate to its volatility (standard deviation of returns). A higher Sharpe ratio indicates better risk-adjusted performance.
• Sortino Ratio: Similar to the Sharpe ratio, the Sortino ratio measures risk-adjusted returns. However, it’s just going to care about the downside risk. It does this by looking only at the standard deviation of negative returns.
• Treynor Ratio: The Treynor ratio evaluates the risk-adjusted performance of an investment relative to its systematic risk as measured by beta. It is calculated by dividing the excess return of the investment over the risk-free rate by its beta. The higher the Treynor ratio, the better the risk-adjusted performance relative to market risk.
• Jensen's Alpha: Jensen's Alpha is similar to traditional alpha but is calculated using a different method. It measures the excess return of an investment relative to its expected return based on its beta and the risk-free rate. Jensen's Alpha is used to assess whether a portfolio manager has added value through active management after you’ve adjusted for some market risk.
• R-squared: R-squared measures the percentage of a fund's movements that can be explained by movements in its benchmark index. It provides insight into how closely the fund's performance tracks the benchmark. A higher R-squared indicates a stronger correlation between the fund and its benchmark.
• Tracking Error: Tracking error measures the standard deviation of the difference between the returns of a portfolio or fund and its benchmark index. It quantifies how closely the portfolio's returns track the benchmark's returns. A lower tracking error indicates better alignment with the benchmark.
  

The Bottom Line

Alpha measures a portfolio's performance relative to a benchmark index. This helps indicate the value added by the portfolio manager's investment decisions. Beta, on the other hand, measures the portfolio's volatility or systematic risk in relation to the market. It's used to know how much the portfolio's returns are expected to change in response to market movements.

Correction—July 17, 2024: This article previously used a return formula for the alpha formula. The correct alpha formula has now been included.