# Analyzing Investment Performance with Alpha & Beta

Sean P. Gilligan, CFA, CPA, CIPM

June 4, 2021

Alpha and beta provide key insights into whether the active management of an investment strategy is truly adding value or merely adjusting the strategy’s exposure to risk. Understanding alpha and beta can help you assess whether a strategy is outperforming on a risk-adjusted basis.

### What is Beta?

Beta measures the sensitivity of a strategy to market movements, which is the most common way to assess the systematic risk of a strategy compared to its benchmark. If the strategy returns move perfectly in sync with the benchmark return, then the strategy’s beta, as compared to that benchmark, is one (i.e., they are perfectly correlated). A beta greater than one means that the strategy is more sensitive (or volatile) than its benchmark while a beta less than one means it is less sensitive (less volatile) than its benchmark. A beta of zero means that the strategy is uncorrelated to the benchmark, while a negative beta means that it is negatively correlated with the benchmark. We will explain this more, but first let’s discuss how it works.

### How to Calculate Beta

Beta is calculated as the covariance of the strategy and the market (benchmark) divided by the variance of the market (benchmark).

If every time the benchmark goes up 1%, the strategy goes up 1.2%, and every time the benchmark goes down 1%, the strategy goes down 1.2%, then the beta is 1.2. This means that the portfolio has increased its systematic risk (perhaps through adding leverage, but otherwise replicating the index). In this case, the portfolio manager has increased the strategy’s systematic risk and volatility as compared to the benchmark, but the manager has not “added alpha.” This strategy will outperform on the upside but will underperform on the downside.

Conversely, if every time the benchmark goes up 1%, the strategy goes up 0.8%, and every time the benchmark goes down 1%, the strategy goes down 0.8%, then the beta is 0.8. This means that the portfolio has decreased its systematic risk (perhaps through adding cash, but otherwise replicating the index). In this case, the portfolio manager has decreased the strategy’s systematic risk and volatility as compared to the benchmark and, as a result, the strategy is expected to underperform the benchmark on the upside and outperform on the downside.

Betas can also be negative; in which case the strategy is negatively correlated with the benchmark and would move in the opposite direction. For example, we would expect a strategy with a beta of -0.5 to go down 0.5% for every 1% increase in the benchmark. Betas can also be zero, indicating that the strategy’s movements are uncorrelated with the movements of the benchmark. Market neutral strategies generally strive to have a beta of zero to eliminate systematic risk from the management of the strategy. This is often achieved through a mix of long and short positions.

### Beta vs. Standard Deviation

When analyzing performance, there are two types of risk: systematic and unsystematic risk. Beta is a measure of systematic risk (i.e., market risk) and standard deviation is a measure of total risk. While beta is focused on correlation with the market or the strategy’s benchmark, standard deviation is focused on the variability of returns. This variability is a combination of systematic risk (market risk) and unsystematic risk (company-specific risk).

Both measures can be used in assessing risk-adjusted returns. Beta is used as the denominator in the Treynor Ratio, which measures how much excess return is generated per unit of systematic risk and is used to show the volatility the investment adds to a fully diversified portfolio. Standard deviation is used as the denominator in the Sharpe Ratio, which helps investors understand their returns as compared to the total risk of the portfolio. In contrast with Treynor, Sharpe is often used to compare fully diversified strategies against each other. For more information on systematic risk verses total risk, check out our article on Investment Performance & Risk Statistics.

### What is Alpha?

Jensen’s alpha measures how much the strategy outperformed its *expected return*, with the expected return determined based on the Capital Asset Pricing Model (CAPM).

### How to Calculate Alpha

To determine if the portfolio manager has “added alpha,” you can calculate Jensen’s alpha for the strategy. Using CAPM, the expected return is determined by the risk-free rate plus the beta-adjusted benchmark return. Specifically:

Jensen’s Alpha is then determined by subtracting the expected return from the actual return. Specifically:

If the portfolio manager is truly “adding alpha” (through stock selection, over/underweighting sectors, etc.) and not just increasing systematic risk in their active management, then the strategy’s Jensen’s alpha should be positive.

A positive Jensen’s Alpha means the manager is consistently beating the market. A negative Jensen’s Alpha means the manager is consistently under-performing. Demonstrating positive alpha over a sustained period of time demonstrates to clients and prospects of the strategy that the active investment decisions made by the portfolio manager resulted in an increased return without increasing systematic risk.

It is important to note that Jensen’s Alpha is part of a regression and usually is accompanied by t-statistics and p-values to test significance levels. In other words, looking at Alpha without testing for statistical significance should be used with caution. If Alpha is positive but not statistically significant, it may not actually mean the manager outperformed on a risk-adjusted basis.

### Why it’s Important to Understand Alpha and Beta

Alpha and beta are widely used statistics that help managers of active investment strategies demonstrate their skill. Comparing strategy returns to benchmark returns without accounting for risk will not provide the full picture. Adjusting for systematic risk will help isolate the return achieved from increasing exposure to the market versus the return that is achieved through investment decisions that increased return without increasing systematic risk exposure.

Adjusting for total risk, rather than only for systematic risk is also important when demonstrating skilled active management. As mentioned earlier, check out Longs Peak’s articles on Investment Performance & Risk Statistics as well as the Sharpe Ratio and the Sortino Ratio to learn more about this.