Learn the stock market in 7 easy steps. Get spreadsheets & eBook with your free subscription!

How to Use Jensen’s Alpha to Measure True Investor Performance

Measuring investment returns is something that everyone looks to do when they start investing in the markets. The search for “alpha,” or market-beating investment returns, is the goal of every investor.

One of the easiest ways to determine your investment return or alpha is the Jensen’s Alpha method. The use of this formula will enable any investor to measure their returns versus its portfolio and the market.

Mohnish Pabrai has returned fantastic returns over his investing career, one of my favorite investors, a 16% return from 1995 to 2015.

The stock market returns, including dividends over the last 100 years, have been over 10% annually, which is a great benchmark for long-term investors to try to achieve.

A tool like Jensen’s Alpha can help us determine our results against any benchmark.

In today’s post, we will learn:

  • What is Jensen’s Alpha?
  • Jensen’s Alpha vs. Sharpe Ratio
  • What Does a Negative Jensen’s Alpha Mean?
  • How to Calculate Jensen’s Alpha with Real-World Examples

Okay, let’s dive in and learn more about Jensen’s Alpha.

What is Jensen’s Alpha?

Jensen’s Alpha, also known as Jensen’s measure, is a risk-adjusted performance measure representing the average return on our portfolios or investments.

The Jensen’s Alpha formula was first introduced in 1968 by Michael Jensen, a well-renown economist who specialized in financial economics.

Jensen’s Alpha aims to determine the extra returns of a portfolio or investment, including stocks, bonds, or any other investment type.

The formula measures the investor’s return compared to the capital asset pricing model, or CAPM model. They are using measures of the investment’s beta and the average market return.

We could also look at this metric as simply alpha.

Let’s back up a moment to define alpha for those unfamiliar with that term.

Investment returns use greek symbols to highlight different types of returns. Alpha is the measurement of outperformance of a return compared to a particular benchmark. And Beta is the measurement of risk, and Delta is a measurement used in options to track pricing changes.

For example, many investors use the S&P 500 as their benchmark to measure their returns. If an investor refers to beating their benchmark, they are returning alpha for their clients or themselves.

But, for our purposes, we are looking at our portfolio returns or Alpha, but the good news is there is no need for knowledge of statistics or higher-algebra to determine our returns.

As investors, we use measurements to check the performance of our investments. The reason for this, as we buy and sell investments, we need a benchmark to measure our progress.

Looking at our investments in a vacuum doesn’t tell us much unless it is tied to another benchmark or related to those returns, to accurately analyze our returns or investment manager’s returns.

An investor must look at the total return and risk associated with those investments to determine if the returns compensate us for that implied risk.

A great example to illustrate, suppose we are looking at two investments with 15% returns; any rational investor would invest in the investment with less risk.

We can use Jensen’s alpha formula to measure the investment’s return versus the risk level.

If Jensen’s alpha is positive, that tells us the investment is returning excess returns. A positive value tells us that our investment is “beating the market” with our stock-picking skills. Yeah us!

Jensen’s Alpha vs. Sharpe Ratio

Measuring risk is an important part of the evaluation in investing. There are no risk-free investments or assets, and the ability to measure the risk of an investment is a key to avoid losing money.

Buffett’s rule number one is never losing money, and measuring any investment risk helps you heed that rule.

Two of the more common methods of measuring those risks are Jensen’s alpha and the Sharpe ratio.

Both of these methods are useful in stocks, as well as mutual funds or ETFs.

The Sharpe ratio, as well as Jensen’s alpha, help show historical volatility. All of this helps us investors pick which stocks or funds will fit our investment goals and the risks we are willing to take to achieve those goals.

Modern Portfolio Theory tells us that risk ties closely to returns; I believe that risk is more associated with losing money. Buffett agrees.

The Sharpe ratio, developed by economist William Sharpe, is a risk-adjusted measurement of returns.

We calculate the Sharpe ratio by subtracting the risk-free return, defined as a US Treasury bond, from the investment return rate. And then dividing that all by the standard deviation of return for that investment.

The Sharpe ratio highlights how an investment earns its returns, which is useful in comparing investment returns with similar historical returns.

For example, if Walmart and Amazon have ten-year returns of 10%, and Walmart has a Sharpe ratio of 1.5, Amazon has a Sharpe ratio of 1.30.

As conservative investors, we would choose Walmart, because according to the higher Sharpe ratio, Walmart would have higher risk-adjusted returns.

Jensen’s alpha offers the ability to compare returns on a risk-adjusted basis, but the alpha formula compares those returns concerning a benchmark.

For investors wishing to use benchmarks to measure returns, Jensen’s alpha is the choice for them. If Walmart shows a 2% alpha, that indicates that Walmart is beating its benchmark by 2%. So the higher the alpha, the better.

According to the formula, the higher the alpha, the better stock-picking or fund-picking by the investor or manager.

What Does a Negative Jensen’s Alpha Mean?

According to the various benchmarks, measuring alpha is a great way to determine if our investments are doing well.

A positive alpha indicates the investment is outperforming its benchmark and is earning excess returns. For example, if Walmart is earning 2% alpha, it beats its benchmark by 2%. So if you invest $100 in Walmart versus the benchmark of the S&P 500, then Walmart will earn 2% more returns than the S&P 500.

Let’s put that in numbers to help illustrate.

If you invest $1000 in Walmart for five years and it returns 12% over that period, Walmart will return you $1762, or $762 on our $1000 investment.

On the other hand, if your investment of $1000 in the S&P 500 over five years, with a return of 10%, would return $1,611, or $611 on our $1000 investment.

The above simple example shows us how we would earn an extra $151 over that five years with an alpha of 2%.

Now, what if the alpha was negative?

That would indicate that the investment is underperforming compared to the benchmark or earning less on our investment than in the benchmark.

Returning to our above example, Walmart earned 8%, instead of the 12%, now the investment alpha is a negative 2%.

For our $1000 investment, we would earn $1,469 over the five years or $469 for our investment. I was comparing that to the investment in the S&P 500 yields $142 less than if we invested in the S&P 500 instead.

Negative alpha doesn’t always indicate that our investment is losing money; as you can see from the above example, we still made money on the investment. The only issue is that it didn’t beat the benchmark or generate alpha.

Do you sell the investment if it doesn’t generate alpha?

Negative alpha over a longer stretch might indicate an underlying weakness in the investment. Either our thesis is incorrect, the market is still not recognizing the potential of the investment, or that we are wrong about our company’s analysis, and it is not as strong as we first thought.

Measuring our portfolio’s performance based on alpha is a great tool, but it is one of our tools. And basing our decisions on one tool is not the best idea. Rather it is better to use alpha as a guide, along with our goals, to make decisions.

Measuring alpha is available for both individual investments, as well as portfolio management.

Not every investment we buy will create alpha. Remember that Warren Buffett doesn’t pick every winner; not all of his picks generate alpha.

No investor or manager will achieve alpha with every single pick or portfolio creation. Instead, it is the effort to achieve alpha that is the goal, with increasing alpha to help raise all the ships.

Okay, let’s move on and determine how to measure alpha in our investments, either individual or portfolio.

How to Calculate Jensen’s Alpha with Real-World Examples

First, let’s look at the formula to calculate Jensen’s alpha below:

Where inputs for the formula are:

Portfolio return = return of investment or portfolio
Risk-free rate = risk-free rate of return
Beta = beta of investment or portfolio during the measured period
Market return = return of the benchmark, i.e., S&P 500

For example, let’s pick a couple of stocks from Warren Buffett’s portfolio to see how those returns generate alpha.

The first company I would like to look at is Apple (AAPL). To find our inputs, I will use a combination of the following websites:

Okay, now that we know where to go, I will pull together some numbers for us for Apple.

Apple’s

  • Beta – 1.29
  • Annual return – 76.21%
  • S&P return – 13.48%
  • Risk-free rate – 0.87%

Okay, now we can plug in our inputs to the formula.

Apple alpha = 76.21% – {0.87% + 1.29 * (13.48% – 0.87%)}
Apple alpha = 76.21% – 17.14% = 59.07%

So, that tells us that Apple has earned 59.07% alpha compared to the S&P 500 for the last year. That is outstanding, to say the least.

Let’s look at another example; say Coca-Cola (KO).

Coke:

Beta0.58
Annual return(1.03)%
S&P 500 annual return13.48%
Risk-Free rate0.87%


Now, we can plug all the above numbers into the formula.

Coke alpha = -1.03% – {0.87% + 0.58 * (13.48% – 0.87%)}
Coke alpha = -1.03% – 8.18% =  -9.21%

The formula above tells us that Coke is losing alpha; when comparing it to the S&P 500, Coke’s returns are less than the S&P 500 during that period.

Let’s try another one for giggles.

Wells Fargo (WFC) was battered during the pandemic and has not returned to pre-pandemic levels.

Wells Fargo:

Beta1.08
Annual return(52.98)%
S&P 500 annual return13.48%
Risk-free rate0.87%


Wells Fargo alpha = -52.98% – {0.87% + 1.08 * (13.48% – 0.87%)}
Wells Fargo alpha = -52.98% – 14.48% = (67.46)%

The above formula tells us that Wells Fargo is earning less than the benchmark and is losing money as an investment.

After looking at a company underperforming the benchmark, we need to consider why Wells Fargo is underperforming. And then decide whether those reasons merit selling that investment or holding for a longer period.

If we analyze Buffett’s portfolio performance over the last three years, we can see that he has returned over 11.08% over that time, compared to 14.89% of the S&P 500.

If we assume a beta of 1 and a risk-free rate of 2, we get an alpha of (3.81)% over that time. And if we look over a longer period, we see that he is not generating alpha until 15 years out.

3-year(3.81)%
5-year(1.37)%
10-year(2.56)%
15-year1.23%


Analyzing another value investor, David Tepper, who runs the Appaloosa Investment portfolio, he has generated alpha, as shown below:

3-year3.17%
5-year1.91%
10-year12.49%


One of the great ways to track the different fund managers’ performances is to follow their returns via 13F filings, which you can either find on SEC.gov or using a site like whalewhisdom.

As our final tally, let’s look at an ETF fund to determine how much alpha it might generate. The fund I would like to look at is the Vanguard Total Stock Market fund or VTI.

The current market price is $184.22, and the beta is 1.01. The fund has total returns of 18.05% for the year, versus S&P returns of 14.45%, which gives us an alpha of 3.46% (on today’s risk-free rate of 0.87%).

Okay, after all those examples, I hope that we have a handle on how to calculate alpha for our investments, be they individual picks or portfolios.

Final Thoughts

Every investor strives to earn better returns, either through picking stocks, bonds, or ETFs. Whether they are a retail investor, investing on their own, or a fund manager, generating alpha compared to a benchmark is always the goal.

Most investors use the big stock exchanges as their benchmarks, S&P 500, Dow Jones, or Nasdaq. But we can use other metrics as well, such as:

  • Other gurus portfolios such as Buffett, Pabrai, or Dalio
  • Other benchmarks such as a 60/40 portfolio construction
  • Or trying to outdo yourself

Measuring those returns by using a simple formula such as Jensen’s alpha is a great way to measure your performance against those benchmarks.

Investors are a funny bunch; they all talk about generating great returns and beating a benchmark; it’s almost like looking to see who hits the longest home run.

Instead of focusing on the goal of beating another investor to gain bragging rights, focus on another goal, such as earning alpha for yourself.

The whole goal is to invest with the risk you are comfortable with and earn the returns you want compared to that risk.

Buffett talks a lot about sleeping well at night because he is comfortable with the level of risk he has in his portfolio. And the returns he has generated over his 50+ year investment career allow him that comfort.

With that, we are going to wrap up our discussion today concerning measuring alpha with Jensen’s alpha formula.

As always, thank you for taking the time to read this post, and I hope you found something valuable on your investing journey.

If I can be of any further assistance, please don’t hesitate to reach out.

Until next time, take care and be safe out there,

Dave