Jensen's Alpha Definition, Quiz and Tutorial for Investment Modeling

Understanding Jensen's Alpha

Intermediate

Jensen's Alpha is a risk-adjusted return measure used for the evaluation of portfolios. The calculation requires a linear regression of the benchmark returns as the x-variable and the portfolio returns as the y-variable. Alpha is the intercept or the point where the line of best fit crosses the y-axis. It was named after Michael Jensen who used it to study mutual fund performance.

Synonyms: alpha, ex-post alpha, Jensen's measure, Jensen ratio

When inputs are provided, a simplification of the Jensen's Alpha regression can be performed using the following formula.

Jensen's Alpha = Port - [RF + Beta * (RM - RF)]

Where:

Beta = Regression-derived beta of portfolio and market excess returns
Port = Average portfolio return
RF = Average risk-free return
RM = Average market or benchmark return

A Jensen's Alpha calculation can also be performed to analyze portfolio performance by using a multifactor model like the Fama-French three factor model.

As with any backward-looking evaluation of portfolio performance the results are highly dependent on the timeframe selected. Whether it be three years of monthly periods, or five years, it's important for the investment analyst to attempt to capture full market cycles and regime-changes in style and size factors.

In a Sentence

Kay: Am I slow? Don't alpha and Jensen's Alpha get you the same result?
Jim: Yes. We typically see Jensen's on tests because they can't expect you to run a regression by hand.

Video

This video can be accessed in a new window or App , at the YouTube Channel or from below.

Jensen's Alpha definition for investment modeling (4:31)

Video Script

The script includes two sections where we visualize and demonstrate the concept of Jensen's Alpha.

Visualize

We're sitting right here in Excel and this is a snippet from our boot camp course.

Here we are focused on portfolios and specifically evaluating the historical (ex-post) performance of portfolios.

This method is called returns-based performance analysis, meaning we are taking monthly returns as the input. Holdings-based performance analysis uses holdings and provides more detail, but is too complex to cover here.

First, we need to create a portfolio. In this section we have a Market portfolio, like an index, or benchmark, with these weights to four stocks. And another called Portfolio which is actively managed, with these weights. Active weights refer to the differences.

Here we have returns calculated over a 60-month period, totals and averages, based on data on the Returns tab. Let's focus on the second row, average arithmetic. The Portfolio beat the Market by 0.08% per month.

While not required for Jensen's Alpha, we compute the standard deviation of monthly returns here, and note that the Portfolio had higher volatility.

Next, the regression, as shown in this chart, the 60 monthly returns on the Market plotted on the x-axis, with the Portfolio return on the y-axis. So from the regression we get the measures alpha and beta here.

So Jensen's Alpha is 0.285% per month of positive outperformance after taking into consideration the risk of the portfolio relative to the benchmark.

It is hard to see, but it corresponds with where the line crosses the y-axis.

Next, let's focus on this cell in blue and demonstrate.

Demonstrate

There are four ways to generate regression statistics in Excel, and the function method is the one we will use for Jensen's Alpha.

In this cell, type =INTERCEPT open parenthesis, the y-range of 60 returns listed here, comma, then the x-range, closed parenthesis and Enter.

There you have it, a small positive alpha. You can test whether it is significant using other statistics, and would be a good idea to think about the cost of active management as part of further portfolio analysis. (Note: Here we used the long method to focus on the concept. On tests and in textbooks, it is common to be given inputs such as beta, risk free, and returns on the Portfolio and Market)

Quiz

Click box for answer.

Which risk-adjusted return measure takes into consideration market-related risk instead of absolute risk. | Jensen's Alpha or Sharpe Ratio?

Jensen's Alpha, because it uses beta instead of standard deviation.

With a beta of 1.10 and an average portfolio return of 10% when the Benchmark return was 11% and Risk Free was 2%, what was the Jensen's Alpha measure? | -1.90%, -0.20%, 0.20%, 1.90%?

-1.90%

Questions or Comments?

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Jensen's Alpha Definition and Tutorial