Buyers invest to gain a return on their money. However, what they actually seek are higher returns than they would gain in so-called “risk-free” investments. This return over and above such risk-adjusted returns comprise what investment professionals call “alpha.” Determining this measure means learning how to calculate a stock’s alpha.

Defining Alpha

To be sure, the average investor does not think of returns in this academic fashion. While they may understand the difference between low and high risk, few attempt to quantify it. Indeed, factors of both a predictable and unpredictable nature ultimately determine a stock price. That factor alone dissuades most average investors from attempting to quantify alpha.

Economist Michael Jensen changed this when he created the alpha equation in 1968. With the equation, investors gained a method for evaluating fund managers. For this reason, the equation is sometimes called “Jensen’s Index” or “Jensen’s Alpha.” Jensen defined how to calculate a stock’s alpha as follows:

α = Rp – [Rf + (Rm-Rf)*β]

Where:

α = Alpha

Rp = Portfolio return

Rf = Risk-free rate

Rm = Market return

β = Beta

Of these, portfolio return, the actual rate of increase of a group of stocks, is the only one of these statistics that one can consider self-explanatory. About all I can add is adding such a number makes measuring alpha a backward-looking exercise.

Understanding Risk-free Rates and Market Return

As for the risk-free rate, one can argue that this is a misnomer. Inflation and the outside possibility of government collapse stand as examples of risks to risk-free rates. However, for explanatory purposes, we shall define “risk-free” by Treasury bills defined by a time period. This means we would use a one-year Treasury for determining a one-year return, or a five-year T-bill if calculating a return over five years.

Like the risk-free rate, one can calculate market return based on several factors. Asset classes usually define this choice. Within the realm of U.S. stocks, the average return of the S&P 500 would likely stand as the most appropriate choice. Some will argue for sector-based market returns in select cases. Since industrial stocks often lag the S&P, one can argue for a sector-based index when measuring such a portfolio. However, most investors want to ultimately beat the S&P, so they should look to that index in almost every stock market-based case.

Beta Defined

Another factor that plays a key role in knowing how to calculate a stock’s alpha is beta. Beta attempts to measure the risk or volatility of a stock. A measure of one denotes average risk. In practice, most professionals consider the S&P 500, or its index fund, the SPDR S&P 500 ETF (NYSEARCA:SPY) to hold a beta of one. Also, if researching online, different research sites could show different betas for the same stock. This happens because each site defines beta by different time periods.

Even without time variances, betas in stocks vary greatly. Johnson & Johnson

(NYSE:JNJ) holds a AAA credit rating and has increased its dividend every year for 55 years. Due to this level of stability, it holds a beta of 0.54. This means it is only 54% as risky as the S&P. It also means investors expect it to produce 54% as much return as the index. Increased risk adds to the beta. E-commerce giant Amazon.com (NASDAQ:AMZN) attained a beta of 1.72, meaning a 72% higher-than-average rate for both risk and return. While it enjoys high growth, its price-to-earnings (PE) of over 250 adds to the risk.

Final Thoughts on How to Calculate a Stock’s Alpha

Jensen’s definition of alpha allows investors to evaluate portfolio performance. It incorporates what an investor would earn without risk. It also considers the risk of investments and the overall market measure to truly determine who bests the performance of the market.

Although few average investors use this to evaluate performance, it can quantify the performance of oneself or that of their manager. By knowing how to calculate a stock’s alpha, investors can know the meaning of and strive for true outperformance.

As of this writing, Will Healy did not hold a position in any of the aforementioned stocks. You can follow Will on Twitter at @HealyWriting.