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Alpha definition and tutorial

A term often confused with active return provides a much more complete picture of long-term performance.
  1. Define - Define alpha for investments.
  2. Context - Use alpha in a sentence.
  3. Video - See the video.
  4. Script - Read the transcript.
  5. Quiz - Test your knowledge.
by Paul Alan Davis, CFA, July 1, 2016
Updated: December 20, 2018
While alpha can apply to individual securities and portfolios, it is most relevant for evaluating portfolio managers.

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Understanding Alpha for Investments


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

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.


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

Alpha definition for investment modeling (3:53)

Video Script

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


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.


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.


Click box for answer.

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


Questions or Comments?

Still unclear on alpha? Leave a question in the comments section on YouTube or check out the Quant 101 series.

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