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Asset Allocation, Quantitative trading

Fooled by Dividend-Induced Upward Drift

The bulk of reported backtest results involving securities that pay dividends are based on adjusted data. The dividend-induced drift has a special effect on momentum models, relative or absolute. In many cases users of such models believe that their risk-adjusted returns are due to timing ability of the models when in fact they are being fooled by an upward drift due to dividend adjustments.

Update [08/10/2015]: A specific example is given in another post. If you would like to post a comment about adjusted vs. unadjusted data use the comment section of that post.

Quantitative trading is primarily about time-series analysis and then about hitting the backtest button to get performance results. However, most trading system developers do not go through the preliminary steps to understand the data series they are dealing with. As a result, the financial blogosphere is bombarded daily with unrealistic results of momentum models, relative or absolute, based on backtests that do not correspond to actual prices of the past, i.e., they are based on unrealistic market conditions.

Enter the Chaos

I have talked about the “chaos” adjusted data has caused in technical analysis in a series of articles. You can find the articles in my archive by searching for the keyword “chaos”. Here is a link to the last one in the series.

This is not even funny: How many traders, professionals or even funds have been fooled by adjusted data? It is hard to say. One thing I know from personal experience is that it took many years for people to find out that the two most popular backtesters used in the 1990s had major flaws, often producing unrealistic results. This may have to do with the “Ostrich effect” cognitive bias: Most people just wish that there are no problems with what they do. But always keep in mind this:

If finance, more than often very good results are probably due to a flawed process

Examples

I will provide two examples below using adjusted and unadjusted TLT data, an ETF that is popular and it is being used in all sorts of momentum rotation and trend-following systems for asset allocation. The first system to backtest is a 50-200 moving average crossover, as follows:

Buy  if 50-day MA >  200-day MA
Sell if 50-day MA <  200-day MA

Equity is fully invested and commission is set to $0.01/share. The backtest period is from inception of TLT on 07/30/2002 to 12/31/2008, as shown on the chart below, where TLT is the adjusted series and $TLT at the bottom chart the unadjusted one:

TLT_20150805

Notice the strong uptrend in the adjusted TLT price series. This is only due to dividend adjustments. The actual series, shown on the bottom chart, does not exhibit a strong uptrend.

Accordingly, the results of the backtest of the 50-200 moving average crossover system vary widely. The adjusted data produce a Sharpe ratio of 0.35 where for the unadjusted it is only o.02. Note that in actual trading you buy actual prices, not adjusted. In case dividends are paid during the holding period of a trade, then performance must be adjusted accordingly but that will not be due to some timing ability of the system used to enter the trades and this is the main point made here.

The above chart tells an ugly story, i.e., how traders with a backtesting program can get fooled by dividend-induced upward drift into thinking that they have a superb timing model.

Let us now look at a popular timing model used in absolute momentum allocation schemes that involves a 1-10 crossover on monthly data, as follows:

Buy  if close of this month >  10-month MA
Sell if close of this month <  10-month MA

Below is the chart of adjusted and unadjusted series with the results for this backtest:

TLT_20150805_M

Here the variation is more pronounced and performance on actual data is negative, as opposed to a large CAR on adjusted data. The positive CAR on the adjusted series only reflects the upward drift from future price adjustments. Actually, past results depend on future dividend adjustments. If you are a system developer and you do not realize how severe this effect is, then you ought to consider it. Do your models really have timing ability or are you being fooled by a dividend-induced drift?

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Charting program: Amibroker
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27 Comments

  1. Comment by post author

    I will be closing down the comment section of this article today because I will post another article in the next few days illustrating the effects of adjusted data on the reliability and significance of backtest results.

    This is what it boils down to as stated in a comment by Matt:

    “Because price adjustments are made proportionately, I think that most indicators will in fact produce nearly identical results regardless of how many adjustment factors have been applied. ”

    However, backtest results show exactly the opposite. The main reason is that the above statement ignores the holding period. It is true that most short-term variations will be small. But variations when the holding period gets large will be large and this is obvious to anyone with a backtesting program.

    Quantitative trading is also hard because different people often have a different reference frame. I appreciate all comments and input because it helps me improve the way I clarify my own views.

  2. Smruti Behera

    Hi Michael, a very thought provoking article. I get your main point that dividend adjusted and unadjusted series will give wildly different results. But you also mention that using dividend adjusted data exposes the backtest to lookahead bias. That's the part I cannot reconcile with my tests. As long as you are not using absolute levels, I don't see how there is a lookahead bias. I tested this by downloading S&P 500 total return data from Dec 1995 to Dec 1999 and Dec 1989 to Dec 2014. Obviously these two series are different (for the overlapping period) but they differ by a constant factor. So mathematically the moving average formulae should be equivalent (and they are). What am I missing here?

    • Comment by post author

      Hello Smruti,

      Good points. Note that the adjusted prices you download today are already adjusted "all the way", i.e., as of last dividend payment, for example in Yahoo! finance. With historical data as of today, for example, that are adjusted for dividends, price series in the past are influenced by future dividends. This affects the timing of the entry and exit signals and corresponding returns. In my backtests in the article, the timing of the signals is different as well as the number of trades.

      Let us say we are actually back in time on 01/1999 and we get a signal on adjusted data. There is a adjustment factor in the data due to dividends. When we backtest in 2015, the adjustment factor is different because of the future dividends after 01/1999. This causes a different entry signal that would have not been obtained on 01/1999. A steeper trend appears to be in place but in 01/1999 that was not in place. The trade gains are different due to this change. This is what I mean by forward looking.

      Michael

  3. Alonso

    Michael thanks for another interesting article.Please do not let those who either unintentionally due to their limiting comprehension ability or lack of understanding of the subject or intentionally try to upset you. Alonso.

  4. David

    If you use unadjusted data, what about stock splits? Surely unadjusted data has many discrepancies. Thanks for the insight.

    • Comment by post author

      Good point David. If there are spits data must be adjusted but relative returns stay invariant under the transformation because C/Cn stays invariant as both numerator and denominator are divided by same constant. Therefore, backtests are good as long as they do not refer to point exits or absolute price levels.

      On the other hand, in futures where the rollover introduces a fixed displacement of all prices in points, first differences stay invariant (C-Cn) and backetsts are good as long as they make no reference to percentage gains.

      I have talked about the above in my out-of-print book in 2000 but the concepts are easy to understand if one is willing to do some test examples.

      Michael

  5. Tonio

    How about calculating the buy/sell signals with unadjusted data but consider the adjusted data for the returns obtained (equity curve)?

    • Comment by post author

      Hello Tonio,

      This is a good way of doing it as I alluded here:

      "In case dividends are paid during the holding period of a trade, then performance will increase but that will not be due to some timing ability of the system used to enter the trades and this is one of the points made here.""

      Some people misunderstood the post completely. This post was not about ignoring dividends but about the timing ability of some trend-following models and how it is affected by adjusted price series. Some quants remove the drift due to dividends before backtesting and their purpose is to see whether the signals of the models have timing ability. By doing that they do not mean to ignore dividends and their impact on equity curve as some wrongly thought. Their only purpose is to see whether a model is intelligent enough to capture returns before dividends.

      Michael

  6. evo34

    Oh my, you are ignorant. Dividends are money. They exist. They buy cars. If your system got paid a dividend, then you count it. Just as if you have a short system that has to *pay* a dividend, you count it against your PnL. All that "upward drift" occurs because you (the long system trader) got paid the same amount it drifted.

    I really cannot believe I had to write this. It feel like this is an April Fools post.

    • Comment by post author

      Please read the article before posting knee-jerk reactions.

      "Also keep in mind that in actual trading you buy actual prices, not adjusted. In case dividends are paid during the holding period of a trade, then performance will increase but that will not be due to some timing ability of the system used to enter the trades and this is one of the points made here."

      Also understand that when you trade in 2005 you do not have dividends from 2014 to adjust the series. Is this so hard to understand?

      You do not understand the article. This is about longer-term trading in daily data with 200-ma and monthly data with 10-ma. The small changes due to dividends do not affect MA values in monthly data. The objective of the article was to show that future dividends accumulate to create an upward drift in the past data that is artificial and when you backtest after many years you get unrealistic results.

      Try to be more polite and do not post comments before you read carefully.

    • Duke

      LoL. Did you read anywhere in this good article the author saying that dividends are not good and he won't take them? What's the matter with you, have you lost it completely? April Fools will be your day everyday when you attribute stories you make up in your mind to articles of reputable authors.

  7. Alex

    Great article Michael!

    I recently downloaded the demo of your Price Action Lab software and I'm impressed with it. I was wondering whether I should use it with adjusted or non-adjusted data and then this article raised some good points against the former. What do you recommend for use with your program?

    Alex

    • Comment by post author

      Hello Alex,

      For short-term trading systems it makes no much difference as dividend adjustments do not matter much but in case of momentum price patterns on monthly data (see recent feature added to the software) extra steps may be required to establish the significance of the model and its timing ability.

      Michael

  8. Rich

    Using unadjusted prices is equivalent to never receiving the dividends you are entitled to as a long only investor. This is incorrect. Prices are adjusted in order to make prior prices consistent with the current price for backtesting purposes.

    • Comment by post author

      Rich, see my answer to Alexander above. Also if you have time take a look at my "Chaos" articles. You can always add dividends afterwards as Alexander said. The point is whether the timing of the signals models was realistic.

      • Rich

        Ok, it seems you meant the dividend adjustment alters the trend. That was not at all how I understood you article. Regardless, it essential that you adjust for dividends when calculating your equity curve, even if you do not adjust for signal generation. But if you don't use adjusted prices for signal generation you are going to get jumps in the signal on ex-div dates, which is unlikely to be desirable.

        Asset total return prices really do have an upward bias, why do you want to arbitrarly offset this upward trend? In your TLT example the adjusted price version is achievable in real trading. The unadjusted one is not (unless you give away your dividends to charity).

        • Comment by post author

          OK, I will try to make this as simple as possible:

          Let us say that we are back in 2005. The signals generated by a crossover in 2005 and actual data in TLT do not correspond to signals generated in the same security when doing a backtest in 2015 due to adjustments.

          "Regardless, it essential that you adjust for dividends when calculating your equity curve, even if you do not adjust for signal generation."

          Yes, you can do that afterwards but if you do backtests based on adjusted data they may not correspond to what would have been achieved in the past had you traded actual data. You may get misleading results. I think the examples I presented show that clearly.

          I don't think I can say that in a simpler way. You will have to do some tests yourself do see the difference.

          Example: In unadjusted data there is a trade from 09/15/2004 to 11/03/2005 with 1.59% return.

          The equivalent trade in adjusted data is from 08/23/2004 to 11/21/2005 with a 11.06% return. This variation cannot correspond to dividends received at that time, i.e., the backtests based on adjusted data are unrealistic.

  9. James

    Great article. Very sound advice!

  10. Alexander Kurguzkin

    When calculating Sharpe ratio for the strategy using unadjusted data you then have to add dividends to returns. I don't think in the long run there will be much difference.

    • Comment by post author

      True for passive investing but the point of the article concerns the ability of models to time entries. Specifically, the drift due to dividend adjustments creates a trend when there is none and these models could face whipsaw and losses. Thus, in hindsight, some of these models work due to future adjustments, something that is equivalent to forward looking.

      Example: In unadjusted data there is a trade from 09/15/2004 to 11/03/2005 with 1.59% return.

      The equivalent trade in adjusted data is from 08/23/2004 to 11/21/2005 with a 11.06% return. This variation cannot correspond to dividends received at that time, i.e., the backtests based on adjusted data are unrealistic.

      Is Cyprus hot these days btw?

      Michael

      • Matt

        Hi Michael,

        During the time period of your trade using unadjusted data, the dividends would have amounted to about 5.5% of the entry price. However, because the entry signal using unadjusted data occurred 3 weeks after the entry signal using adjusted data, you missed out on a 1.5% gain at the start of the trade. Similarly, the different exit dates caused the unadjusted trade to miss out on another 2.4% of gains at the end of the trade. So in fact, 1.59% (unadjusted trade gain) + 9.4% (dividends and signal differences) is very close to the 11.06% gains shown for the trade using adjusted prices.

        Whether you choose to calculate your indicators using adjusted or unadjusted data for live trading is a personal choice. However, as long as you follow the same rules in your back testing that you do in your live trading, I think that the results will be a fair representation of what would have happened if you'd actually traded your strategy over the back test period.

        • Comment by post author

          Hello Matt,

          I do not dispute your calculations for matching performance. Actually what you have shown is how to adjust results based on unadjusted data to match results based on adjusted data.

          However, the main point of this article was that dividends impose a drift and the performance obtained is often wrongly attributed to the timing ability of the trading models. The purpose of using the unadjusted data was to show that the model fails when the trend is not in place. The purpose of the post was not to choose between adjusted and unadjusted data although it may appeared as such.

          Then, things are not that simple. As I commented below,

          "Let us say we are actually back in time on 01/1999 and we get a signal on adjusted data. There is a adjustment factor in the data due to dividends. When we backtest in 2015, the adjustment factor is different because of the future dividends after 01/1999. This causes a different entry signal that would have not been obtained on 01/1999. A steeper trend appears to be in place but in 01/1999 that was not the place. The trade gains are different due to this change. This is what I mean by forward looking."

          What do you think?

          Michael

          • Matt

            So if I understand correctly, your main point is that the entry and exit signals generated by back testing against adjusted price data could not possibly have been generated in real time, nor even by a back test run on a different date when the dividend adjustment factors were different.

            Because price adjustments are made proportionately, I think that most indicators will in fact produce nearly identical results regardless of how many adjustment factors have been applied. My experience bears this out. The company I work for used to update its price-adjusted database once a month. As a sanity check, we would run the same back test against both an existing database and the updated database, and then check for trade discrepancies. The discrepancies that we found were almost always due to intentional or unintentional changes in the price data, for example because the data supplier had previously included bad price quotes which were now corrected. This process actually allowed us to alert the data supplier when there was an inconsistency in their data.

            As pointed out elsewhere in the comments to your post, the one place that you *must* use unadjusted data is if your model uses absolute price or volume thresholds, such as "price greater than $10" or "at least 1M shares average volume".

          • Comment by post author

            Hi Matt,

            "So if I understand correctly, your main point is that the entry and exit signals generated by back testing against adjusted price data could not possibly have been generated in real time"

            That was not the main point of the post. The main point was that dividends induce drifts in price series and trend-following models appear to capture price returns when in fact they capture dividends.

            "Because price adjustments are made proportionately, I think that most indicators will in fact produce nearly identical results regardless of how many adjustment factors have been applied. "

            In hindsight yes, But if you do proper backtests with incremental adjustments of dividends starting from the past and not from the future then you will see discrepancies.

            "the one place that you *must* use unadjusted data is if your model "

            Again, I am surprised by the level of misunderstanding of this post's message. The post was not about a choice of data. The post only showed that when there is no upward drift due to dividends, some trend-following systems based on moving averages get whipsawed because they have no timing ability.

            But yes, there are discrepancies when using adjusted data that do not correspond to trades that would have actually been taken. All you have to do is run proper tests to see them.

    • Comment by post author

      Just to clarify further I agree with the dividend adjustment as I wrote:

      "In case dividends are paid during the holding period of a trade, then performance will increase but that will not be due to some timing ability of the system used to enter the trades and this is one of the points made here."

      So my point was that some attribute performance to timing ability of models but in reality it is the dividends that contribute to it and not the systems.

      Michael