RE: The Power of Momentum


This is a follow up to (what appears on the surface to be) a simple, effective strategy for trading the U.S. stock market from the Bank of England’s Andrew Haldane, later covered by super-bloggers Felix Salmon and EconomPic.

[growth of $1, logarithmically-scaled]

The graph above is taken directly from Haldane’s paper and shows the result (in red) of going long the S&P 500 when the previous month closed up, and short when it closed down, from 1880 (you can ignore the blue line).

The graph appears to show strong month-to-month momentum in the U.S. market with positive months portending positive months (and vice-versa).

This is the kind of graph that on first blush makes us wonder why we spent all this time developing smart trading strategies when the Holy Grail has been waiting right before our eyes this whole time.

Just one not-so-small problem with the analysis…

Haldane used Robert Shiller’s “Irrational Exuberance” data set for his historical S&P 500 prices.

That’s a problem because when Shiller shows a monthly price for the S&P 500, that price is the average for the month and NOT the month-end (or month-beginning or anything else). In other words, that price isn’t actually knowable until the end of the month (and by then, it’s no longer obtainable).

What if we traded Haldane’s strategy using an actual obtainable price?

Below is the same strategy using the original Shiller data (red) versus the actual month-end close (grey) on the S&P 500 from 1930.

[growth of $1, logarithmically-scaled]

A mighty big difference.

The strategy is a dud, and because I know someone will ask, it’s a dud regardless of whether we trade the last day of the month, the first, or any other.

Lesson learned?

Know your data.

This post shouldn’t be viewed as a black eye for Shiller’s data set, which I use in my own work, or Felix Salmon or EconomPic, whose blogmanship I admire very much.

Just trying to be a little more vertical and keeping the good ideas floating to the top and driving the bad ones to the bottom.

Happy Trading,

. . . . .

To stay up to date with what’s happening at the MarketSci Blog, we recommend subscribing to our RSS Feed or Email Feed.

31 Responses to “RE: The Power of Momentum”

  1. 1 steve

    two points: hard to believe someone of repute could be so shortsighted.
    really nice pickup on your part. THE DEVIL IS IN THE DETAILS!

  2. 2 Carl

    Good catch.

    Did you try using the Average Price to make the decision (which would be known at the end of the month) and the Close price for the transaction? Or did you use Close for decision/Close for transaction? I wonder how much of the return is dependent on the indicator vs the price.


    • 3 MarketSci

      RE to Carl: good question. I used the month-end close for the decision and for the transaction.

      But I tested the other possibility as well (average price for the decision, month-end for the transaction) and it fared even worse. Much worse.


      • 4 Carl

        If much worse means negative, or even close, you may have developed a nice hedging formula! Imagine staying out of the markets all those months and only going in the others… LOL

  3. 5 codes

    What if you only trade the strategy when the price is at the average or within a tight range of the average. And then just for fun – what if you traded the strategy within a tight range of the average price on even years with below average tempatures in the previous year?

    • 6 codes

      BTW, Great catch. Thank you

    • 7 MarketSci

      RE to codes: good question (err, the first part =)…I’d have to code it up to say for sure (and I’ve put that on the to do list), but we’re straying so far from Haldane’s intention that we’re really talking about an entirely different widget.


      • 8 codes

        It would be interesting to see how that one plays out. The first one that is : )

        Given the math I think you may have something here. Please keep us informed. Thx

  4. 9 Andrew

    Nice catch. That’s why I am such a fan of this blog.

    But, why is the avg price of the month so bad? Who says you wouldn’t be a gradual net-buyer accumulating shares over the course of several days/weeks during the month? All in or all out in a single trading day that I think everyone would trade it.

    • 10 MarketSci

      RE to Andrew: there’s nothing necessarily wrong with targeting the average price of the month, but I should mention that when I’ve tested such an approach with (actual) long-term strategies (like the Golden Cross) it hasn’t significantly helped or hurt performance.


    • 11 Frank


      the problem with that approach is that you don’t know during the month if the month will be up or down on a month-end basis (you always know with hindsight only), so being a net-buyer means you’re always assuming (before the fact) the month will be up, not down, otherwise you’d have to be a gradual net-seller, not a net-buyer.

      That is a pophecy (month up or down) recorded after the fact, a classic example of hindsight bias.


  5. 12 blink

    “going long the S&P 500 when the previous month closed up, and short when it closed down”

    Don’t understand exactly…if I go long on 31st, do you mean:
    C>O (this month Closed higher than this month Open)
    C>Ref(C,-1) (This month Closed higher than previous month Close)

    • 13 MarketSci

      RE to Blink: good question. I’m using close-to-close [C>Ref(C,-1)]. I should also note if you’re trying to reproduce these results that I used the S&P 500 price index (which investors follow) to determine if the month closed up or down, but used dividend-adjusted data to determine returns. michael

  6. 14 Craig


    You are a hero. Congratulations. I was sure this study stank, just based on the failure to account for transactional fees (and the ridiculous branding of a one-month technical analysis as the “value” strategy)–but I had no idea how utterly unsound the methodology was. It amounts to nothing more than “buy if the market is about to go up, and sell if the market is about to go down.” Did Haldane even realize that? Because it pretty much comes down to mendacity or incompetence at this point. He owes you a letter of appreciation, and the world a public retraction–but I wouldn’t hold my breath.

    • 15 MarketSci

      RE to Craig: thanks for the kind words, but I wouldn’t be so hard on Haldane. Shiller (for all of the good things he’s done) doesn’t do enough to make it clear on the dataset that the S&P 500 price is the average price and I’m sure that’s led to thousands of misguided studies like this one. Haldane’s just happened to catch my attention. michael

  7. 16 Aly Somji

    Thanks for alerting us blog readers, Michael.

    Always appreciate your work.


  8. michael-

    nice catch, but i’d love to take a look at the data using actual S&P 500 TR index data. any way you can share it going back to 1930? if so, please email it to me:

    econompicdata at


  9. 18 George

    At first I was sceptical about your refute. But you are right Micheal. If one takes a look at page 29 and scrutinize chart 7 and chart 8. Both show the same momentum strategy. Chart 7 is for US (SP500), chart 8 is for UK (FTSE). The same momentum strategy shows no real profit for the FTSE in chart 8. I don’t understand, how Haldene couldn’t notice this huge divergence.
    And the paper is going to a conference…. Eh. How was it possible that nobody noticed this huge mistake? It tells a lot about the current publishing climate. If you are a big guy (publishing in the name of the Bank of England), you can publish anything. Thank you for your revelation.

  10. I guess after looking at the performance charts you intuitively guessed something was wrong with the data and went to look at it…. I had the same feeling, but not the same patience.

    • 20 MarketSci

      Almost…I looked at the chart and said “have I really been so blind this whole time that this super-simple uber-effective strategy has just been staring me in the face”? It was more of a “questioning my very existence” kind of thing…

      …then I tested it and remembered why I exist =)


  11. 21 Crosby

    This article has two obvious flaws: (i) Contrary to what has been written here, it is much more sensible to use the ‘average’ for the month than to use the last day. [It is well known that Institutional and Mutual Fund investors adjust their holdings to finish a month looking ‘good’ by buys/sells on the last day. This happens particularly at the end of quarters or years.] So, last-day values are probably the ‘least’ meaningful of the whole month.
    (ii) If MarketSci had used 1940 for instance (rather than 1930) as the starting year, the situation and conclusion would have been completely different. The returns in the first few years are of major importance in the success of an investment portfolio (as Jim Otar has shown). If you look carefully at the first ten years starting at 1940, instead of the 1930 chosen, you would find that the grey and red lines would be barely distinguishable. This is an old ploy of the Mutual Fund world – selecting a starting point which favors the point it is promoting. Beware of staring dates!

    • 22 MarketSci

      RE to Crosby: it’s pretty clear based on your comment that you didn’t understand the point of this post in the slightest. I would strongly suggest a reread.

      This post is showing that Haldane’s research was flawed mathematically, that his results couldn’t be reproduced in the real world under any conditions. It doesn’t matter if you start in 1930, or 1940, or 2009, math is math.

      MarketSci is the farthest thing imaginable from the “mutual fund world” and to imply that this post is somehow slanted to favor anything other than the facts is incorrect and unjustified.

      My apologies for the snarkiness of my response but it irks me when I receive such confident comments from commenters who obviously have not taken the time to actually read the post.


  12. 24 Crosby

    My apologies: Michael, I think you may have misunderstood both my points due to my careless writing. In (i) I was trying to say that the Closing Price is probably the least reliable datum point to use – because it has been ‘influenced’ artificially by very big investors who have to produce good-looking end-of-month data (such as have Managers of Mutual Funds, Pension Plans etc.). In (ii) I was only trying to point out that the starting year of a portfolio makes a tremendous difference: and it seems to me that if you had started in 1940, where your grey line hits a minimum, it would have looked so much more positive than your line for 1930. However, when referring to Mutual Funds in point (ii), I’m sorry it read as if I were pointing at you rather than making a general observation about the Fund industry publishing with ‘selected’ dates.

    • 25 MarketSci

      RE to Crosby: I appreciate the points of clarification, but unfortunately the points above don’t in any way change the conclusion of the post.

      1. You can’t trade Haldane’s approach using the average price because you don’t know the average price until AFTER it’s unobtainable. The “real world” variation of his strategy that I’ve shown significantly underperforms regardless of whether month-end, month-beginning, or any other date is used (as I mention in the post). To say month-end is the least reliable data point (though I disagree with you) is a moot issue. It doesn’t work across the board.

      2. Had I started at the worst of the 1930/40’s drawdown, of course the lines would have been closer together, but the “real world” strategy would have still underperformed Haldane’s by a wide, wide margin (2.8% vs 7.2% annually).


  13. 26 Frank


    excellent posting, as always.

    In case you didn’t notice, I checked Haldane’s approach using the end-of-period prices (not the average price, of course) for different time frames (daily, weekly, quartely, semiannual and annual), in oder to figure out what didn’t work on a monthly basis could very well work using different time frames.

    Besides the fact that with respect to compound returns the daily follow-through clearly came on top, the semiannual strategy (Haldane’s approach, but not on a monthly but on a semiannual basis) outperformed Haldane’s monthly approach by a wide margin, came close to a buy-and-hold approach (with respect to compound returns), but beats a buy-and-hold approach with respect to (a significantly lower) maximum drawdown and time in drawdown.

    Each frequency had it’s high time, e.g. the weekly momentum strategy between 1960 and 1972 (but gave back all of its gains and some thereafter), the semiannual strategy went parabolic at the end of the 90th, and so on.


  14. Excellent post. You have the ability to explain complex things in an easy to understand manner. I look forward to your next post.

  15. 28 Chronos Phenomena

    If I buy a share at market close everyday, what will be the average price Of My holding?

    • 29 MarketSci

      RE to Chronos: something approaching the “average price” (actually a little less than the average if buying in equal dollar amounts), but you still couldn’t follow Haldane’s strategy because you wouldn’t know which way to trade (long or short) until after the month had ended. michael

  16. 30 Chronos Phenomena

    Right…. I thought that the strategy says go long if average price in previous month gained relative to second previous month… (the only tradable way)…

    Don’t understand how somebody can talk about non tradable strategy ?!?!?!


  1. 1 Tuesday links: trust and confidence Abnormal Returns

Leave a Reply

Please log in using one of these methods to post your comment: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s