How to calculate 3-factor (Fama-French) and 1-factor (CAPM) alpha

/How to calculate 3-factor (Fama-French) and 1-factor (CAPM) alpha

How to calculate 3-factor (Fama-French) and 1-factor (CAPM) alpha

Wow, Turnkey Analyst and I have been buried at Turnkey Analyst working on a variety of research projects and hanging out with our families over the holidays.

Sorry about being MIA.

To kick off the new year we wanted to show the world how to calculate “alpha,” as it is traditionally understood.

Our guess is that a large potion of market participants have no clue what alpha really is, but want to learn!

We’re here to help!

Below is a video that describes how to calculate alpha:

Here is the source file for the video tutorial:

how to calculate alpha

  • The views and opinions expressed herein are those of the author and do not necessarily reflect the views of Alpha Architect, its affiliates or its employees. Our full disclosures are available here. Definitions of common statistics used in our analysis are available here (towards the bottom).
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About the Author:

Wes Gray
After serving as a Captain in the United States Marine Corps, Dr. Gray earned a PhD, and worked as a finance professor at Drexel University. Dr. Gray’s interest in bridging the research gap between academia and industry led him to found Alpha Architect, an asset management that delivers affordable active exposures for tax-sensitive investors. Dr. Gray has published four books and a number of academic articles. Wes is a regular contributor to multiple industry outlets, to include the following: Wall Street Journal, Forbes,, and the CFA Institute. Dr. Gray earned an MBA and a PhD in finance from the University of Chicago and graduated magna cum laude with a BS from The Wharton School of the University of Pennsylvania.
  • Phil

    I’ve got one question on the Legg Mason Value Trust point not having alpha when you control for size and control for low price to book.

    You make the point that even if we’re not controlling for risk, we’re controlling for something that could be replicated with a low cost index fund or a mechanical strategy, so there’s no real alpha.

    But in 1981 (start of Legg Mason Value Trust), was anyone saying that there was this well known small stock and price to book outperformance? (At the very least, there weren’t index funds based on those strategies). If they weren’t, I think you do a disservice to Legg Mason.

    Think of it this way – what if Fama-French decide that there is this new anomaly called the “magic formula outperformance” where if you pick companies with high ROIC and low EV/EBITDA you outperform the market. So it’s now a four factor model. Then they use that four factor model and test the non-arbitrage and non-special situation performance of Gotham Capital. And when they do that, it might look like Gotham Capital showed no non-arbitrage and no non-special situation alpha, because anyone could have mechanically ranked the stocks according to the magic formula starting back in 1990 or whenever.

    The point is – no one did. I think Legg Mason Value Trust should get some credit for the identification of excess return (putting aside whether there was risk associated with that), and I don’t think can be criticised after the fact for generating the excess return, even if it was just because they looked at low price to book companies.

  • Hi Phil,

    This is an excellent comment regarding a potential “look-ahead” bias when analyzing the performance of fund managers over time (especially a manager with a long term track record such as Legg Mason).

    Here is a quick analysis:

    1: The “size” and “value” anomaly were known before the start of the Legg Mason Value Trust. For example, Banze (1981 Journal of Financial Economics) highlights the size anomaly, and Stattman (1980 Journal of Financial Economics) documents the value anomaly.

    2: As was mentioned in the video, when analyzing managers it is important to benchmark them against your nearest opportunity costs, AT THE TIME.

    Historically, quantitative small cap and value portfolios with “index-like” fees were not available until the late 90’s and early 00’s. Of course, today, exposure to various factors are everywhere and extremely cheap.

    So you are correct to point out that for the case of the Legg Mason Value Trust, in their early years of operation, they were smartly exposing investors to various return-enhancing strategies (maybe risk, maybe alpha) at a reasonable fee, considering there were no other alternatives offering similar exposures at lower costs. This argument is harder to make in the later years of the sample when the nearest opportunity costs become cheaper and easier to access.

    Regardless, with the advent of liquid, tax-efficient, low-cost ETFs and mutual fund companies giving investors cheap access to various exposures, it is getting harder and harder for active managers to justify fees, without evidence for sustainable alpha. Of course, the investment management business is like any other industry–they don’t just sell a good or service, they can also sell an image/brand/lifestyle. If the world only desired product, Kellogg Corn Flakes would have gone out of business and we’d only see generic “toasty flakes” on the shelves. So I’m not sure the “branded” investment products will ever go away, nor should they.

  • Thanks Dr Gray.

    I take your point. Looking forward, if we’re confident the LMVT only gives us access to the low price to book outperformance (and we should given the regression results), there are cheaper ways to do that.

    Great video by the way – I’ll have to find other data sets of long term investors to check their alpha. I love the website too.

  • George

    Wes, great video – thanks for the demonstration! What is you take on Carhart’s Four Factor Model? I’ve seen this 4-factor model used on some investment web sites because they like the add’l control factor for momentum.

  • I used this method to try to measure Whitney Tilson’s alpha. As you’ll see in the post, there’s just not enough data points. Any pointers on whether I’m interpreting the p-value correctly?

  • Hi Phil,
    I think your analysis is sound. The problem–as you mentioned–is a small sample. With small samples it is very hard to distinguish between luck and skill with any sort of reliability. From a point estimate standpoint it certainly seems like Tilson has a little alpha, but it is hard to distinguish that ‘alpha’ from luck/noise in the data.

  • Thanks. I updated my post to link back here – thanks for the video. It was incredibly helpful.

  • ttobrien99

    Hi Dr. Gray,

    I also appreciated the video. Question: I regressed one of our funds’ excess returns for 2011 on the excess returns of our benchmark. The alpha that resulted was negative, although insignificant. We soundly outperformed our benchmark in 2011 (by 10 percentage points). Now, I know that it’s possible that 10 ppts may not translate into a statistically significant outperformance, but I don’t understand how the sign on the alpha can be negative.

    Any thoughts on this?

    Thanks, Tim

  • Tim, email me and I’ll help you out

  • Paul Forde

    Hey Phil,

    If I wanted to analyse a fund using the Carhart model with a momentum factor can I just added the variables used in the regression.

  • Yep, just add MOM and run a 4 factor regression.