Alpha Definition and Tutorial for Investment Mmodeling

Understanding Alpha for Investments

Intermediate

Alpha is a measure of risk-adjusted performance for individual securities or portfolios relative to a benchmark. It is derived from a regression of returns as the y-variable versus the benchmark as the x-variable. The intercept, where the line crosses the y-axis is the alpha measure. Normally used to evaluate an active portfolio manager, a positive alpha, over long periods such as 3 years, implies positive historical risk-adjusted performance.

Synonym: intercept, constant

For context, recall that active managers seek alpha, which means they hope to achive risk-adjusted returns above a benchmark. The unfortunate part is that most people who evaluate track records of active managers don't understand the math behind the calculation, so they often use active returns as their guide, but active returns don't take risk into consideration. Those at the institutional level fully understand the distinction, and so should you.

In a Sentence

Ken: Help me on the regression again. So a manager with positive alpha of say 1% is a good manager.
Ann: Actually Ken, it just means they 'were' a good manager over that time period.

Video

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Alpha definition for investment modeling (3:53)

Video Script

The script includes two sections where we visualize and demonstrate the calculation of alpha.

Visualize

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

Here we plotted 60 monthly returns on the stock Merck on the y-axis. And 60 monthly returns on the Market plotted on the x-axis for the same time period.

So for this one month, the Market was up 10% and Merck was up 14%.

This line of best fit minimizes the difference between the line and each of the points. That's what linear regression does.

The intercept, or constant, or where the line crosses the y-axis, also in the formula here, is -0.0074%. That is alpha. And the formula for the line, given in y = mx + b format, reads like this: the historical monthly returns for Merck, were best described by a line where you would multiply the Market return by 1.2274 and then subtract 0.0074.

Again, alpha is a measure of risk-adjusted return. So relative to its market-related risk, Merck generated an alpha of -0.0074% per month.

Some people confuse alpha with the term active return, which would simply be subtracting the Market return from the Merck reutrn, and that wouldn't take risk into consideration. Next, let's demonstrate.

Demonstrate

There are four ways to generate regression statistics in Excel.

First, you can use the chart output, but that isn't convenient.

A lot of people use the Data Analysis method, with output like this and alpha is down here described as Intercept.

Third is the function method, where you use the function called =INTERCEPT(). Input the stream of returns for the y-variable first, then comma, then the x-variable and hit Enter.

Fourth is the =LINEST() method which gives added functionality but is too advanced to cover here.

Quiz

Click box for answer.

Because alpha is derived from a regression, a minimum of ___ monthly observations is advised. | 12 or 36 or 90?

36, or 3 years.

Where the line of best fit from a regession crosses the x-axis is the alpha. | True or False?

False, alpha is where the line crosses the y-axis.

Questions or Comments?

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Alpha Definition and Tutorial