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Asset Allocation Models Based on Moving Averages Are Dumb

Asset allocation models based on moving averages are dumb in the sense that they cannot adjust to changing market conditions. They are also risky because they reflect wishful thinking. Below is my analysis for open-minded individuals who place reason over hype.

Asset allocation models based on moving averages are usually sold on the basis of historical outperformance of the S&P 500 total return at reduced risk. However, the longer-term backtests shown are often based on non tradable indexes, such as the S&P 500, the MSCI EAFE, NAREIT and also on difficult-to-trade for the retail crowd assets, such as fixed income, commodities and gold.  Why is that a problem?

Before I answer this question I want to emphasize that I am not disputing the existence of the momentum premium and the benefits of asset allocation. What I am disputing is the evidence provided to convince the retail crowd that these can be exploited easily. I list a few reasons for this below:

  • Before 1993 (SPY inception) it was difficult for a retail investor to track the S&P 500 index. An index tracking portfolio was required to minimize transaction cost and that was an art and science known only to investment banks.
  • Products for tracking developed stock markets, bonds, gold and commodities appeared after 2000. Before that it was difficult for the retail crowd to effectively allocate to these assets without using derivatives or other securities or funds.
  • Some have argued that transaction cost is not important due to the infrequent rebalancing of allocation schemes based on monthly data but, in reality, there was continuous rebalancing of the underline indexes. For example, any backtests on S&P 500 index before SPY was available implicitly assume rebalancing of index tracking portfolios. Note that although the math of index tracking was exciting, this approach lost its appeal in the 1990s due to high transaction cost and tracking error problems.
  • More importantly, most asset allocation and momentum systems presented in the literature are data-mined and conditioned on price series properties that may not be present in the future. Showing robustness to moving average variations is not enough to prove that such methods are not artifacts of data-mining bias.

In this blog I will concentrate on two of the above issues. First I will show through a randomization study that a moving average model lacks intelligence and then I will explain why such models are based on wishful thinking.

Moving average crossover models are dumb

One way to show that a trading model is dumb is by demonstrating that it underperforms a sufficiently large percentage of random models that have similar properties. For the purpose of this study we will consider adjusted SPY monthly data that reflect total S&P 500 return in the period 01/1994 to 07/2015. The “dumb model” is a 3-10 moving average crossover system, i.e., a system that fully invests in SPY when the 3-month moving average crosses above the 10-month moving average and exits the position when the opposite occurs. This is a popular moving average crossover used in some widely publicized asset allocation methods.  This system has generated 8 long trades in SPY since 01/1994 and has outperformed buy and hold by about 110 basis points at a much lower maximum drawdown. The rules of the system are as follows

If monthly MA(3) > monthly MA(10)  buy at the next open
Exit at the next open if  MA(3) < monthly MA(10) 

The equity curve of this system is shown below:


Below are some key performance statistics of this system:

Parameter SPY System SPY B&H
CAR 10.42% 9.31%
Max. DD -15.28% -50.80%
Sharpe 0.57
Win rate 87.50%
Profit factor 266
Payoff ratio 38
Trades 8
Commission $0.02/share $0.02/share

It may be seen that the timing models generated about 110 basis points of annual excess return as compared to buy and hold but at a much lower drawdown.

I just want to emphasize at this point that the job of every serious trading system developer is not to try to find support for the result of a backtest but instead to try to discredit it. Unfortunately, exactly the opposite happens in most publications. For example, varying the moving averages and claiming that because the system remains profitable it is robust, is not enough. We will consider in the second part of this blog an example but first we will test this system for intelligence.

One way of testing a system for possessing intelligence is through a suitable randomization of performance. For this particular moving average system, we will randomize performance by generating random moving average crossovers for each entry point that range from 1 to 8 for the fast and from 2 to 20 for the slow. We will consider only those systems with slow ma > fast ma. In addition we will randomize the entry point by tossing a coin and we will require that in addition to the crossover condition, heads show up. On top of that, the exit will be set to a number of bars that are randomly sampled between 5 and 55. Note that the average number of months in a position for the original system was 25.

Each random run is repeated 20,000 times and the CAR is calculated. Then the cumulative frequency distribution of CAR is plotted as shown below:


The CAR of 10.42% of the original 3-10 crossover system results in a p-value of 0.117. This p-value is not low enough to reject the null hypothesis that the system is not intelligent. in fact, the system generated lower return than about 12% of the random systems, as shown by the vertical red line on the above chart.

Note that well curve-fitted systems always result in low p-value and that makes this method not very robust in general. However, this method provided in this case an initial indication that the 3-10 moving average crossover system in SPY lacks intelligence. Again, this is because 12% random system performed better than the original system. However, there is another more practical way of showing that this system is data-mined, dumb and that its performance is based on wishful thinking.

Moving average crossover models are based on wishful thinking

The reason for this is that these models assume that the past will remain similar to the future. In the case of the SPY system, the model assumes that uptrends and downtrends will be smooth enough and come in V-shapes with no protracted periods of sideways price action. We do not know if this will be the case in the U.S. stock market in the future but relying on such assumptions is wishful thinking. One can get a taste of what may happen to an account that invests with such a model by a backtest on EEM data from 01/2010 to 07/2015, a period of 5 1/2 years during which the emerging markets ETF moved for all practical purposes sideways.  Below is the backtested equity curve:


Below are some performance details:

Parameter EEM system EEM B&H
CAR -7.64% +0.21%
Max. DD -35.28% -29.12%
Return -35.22% +1.14%

It may be seen that the 3-10 moving average crossover system based on monthly data performed exceptionally bad during the sideways market period, losing 35.22% as opposed to a gain of 1.14% for the buy and hold.

Can the U.S. stock market move sideways for an extended period of time? I cannot answer this question. My point here was that moving average crossover systems on monthly data, the types used in some asset allocation models, assume V-shaped reversals from downtrends to uptrends with no protracted choppy action in between. Therefore, the future performance of such systems is based on wishful thinking. These systems are dumb and risky.


Ninety nine percent of systems in the trading literature are data-mined. There is nothing wrong with that in principle except the fact that data-mined systems are 99.999% or more curve-fitted on market conditions. It is an art and a science to distinguish those that are not from the many that are and in fact this is the trading edge, it is not the system. Nowadays, a computer can generate hundreds of systems per minute. Proving that systems are intelligent is the true edge, not their generation. This will remain an art and science that no mechanical process will ever be able to accomplish for all cases.

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  1. Fred Dobbs


    I don't know how much you can rely on testing something like the SPY system you present that only showed 8 trades even after you do a simulation. The EEM slice of time you present is only 5.5 years, which is a very short period. One can always find short periods like that, but they may not represent long run expectations.

    Have the seen this paper by Zakamulin? He tests a number of different MA methods on the S&P Composite index on over 158 years of data. Yes, I know costs are not included, but the results are very strong and low-cost index funds are available now. His conclusion is: "Whereas over very long-term horizons the market timing strategy is almost sure to outperform the market on a risk-adjusted basis, over more realistic medium-term horizons the market timing strategy is equally likely to outperform as to underperform. Yet we find that the average outperformance is greater than the average underperformance." He also has another paper on robustness testing of MAs.

    • Hi Fred,

      "I don't know how much you can rely on testing something like the SPY system you present that only showed 8 trades even after you do a simulation."

      I did not present the system. This system is a part of some well-known allocation methods (ex. Faber).

      "The EEM slice of time you present is only 5.5 years, which is a very short period."

      Do you think that 5.5 years of devastating losses is a short period of time? This is a recent market unlike studies that go back when there were no cars, computers, even electricity or telephones and people moved around on horses. I wonder why an sane person would pay attention to these studies that only reflect data-mining bias and wishful thinking.

      "Have the seen this paper by Zakamulin?"

      I have learnt over the years to rely on my own work. There are many issues with backtests, many assumptions and data-mining bias. I started backtesting systems in the mid 1980s unlike some authors who only discovered backtesting in the last few years. Backtesting is more of an art than a science.

      MAs are a dangerous indicator for market timing. Performance deteriorates fast during sideways and fast markets. Relying on MAs is indistinguishable from gambling with money. Outperformance is due to luck as a general rule.

      "over more realistic medium-term horizons the market timing strategy is equally likely to outperform as to underperform"

      This is wishful thinking, it is not science. But before that he concludes:

      "Third, we did find support for the claim that one can beat the market by timing it. Yet the chances for beating the market depend on the length
      of the investment horizon"

      A truly amazing revelation. 🙂 It says something about timing EEM with MAs in the last 5.5 years.

      Fred, it boils down to this: very long backtests fool naive market researchers due to stock market structural bias. Rules play no role. See for example:


  2. Bo

    I agree with you that moving average cross over systems are largely random. A trend following system based on this will do very poorly on equity indices in the past three years even though the underline equity indices themself are doing very well. A very long back test only ensure that you are more likely to run into a period where this strategy does extremly well so as to lift the overall metrics to a good level. It does not say anything about goinng forward it would work or not. It's unknow. The best I think we can do is to apply this kind of systems equally on a variety of uncorrelated assets. For example, while trend following does not work on equity indices in the past three years, it seems to work very well on currencies.

    Again great article!

  3. Hello Bo,

    "The best I think we can do is to apply this kind of systems equally on a variety of uncorrelated assets."

    I think this is the key but one problem is that correlation varies and instruments may get correlated during certain period. CTAs have struggled in recent years although their trend-following methods still carry a positive skew from the 1990s. Take a look at performance here in the last 5 years.

    Note that 2011, 2012 and 2013 marked the first two and three consecutive losing streaks for CTAs. Remember that CTAs mostly use MAs and other similar longer-term indicators.


  4. stefan

    hi michael,

    thx for your analysis. i read it with a lot of interest, because some time ago i was advicing friends of mine to an asset allocation system with ma. they are just getting started with their jobs and so they wanted to know what to do with their money. as i did read some ma and ma with asset allocation studies i thought this would be a good way to go (implemented with ETFs, yes i know ETFs are no holy grail). i want to express that expection of an investment is one important point, like the possible risk (i told them that if you cant take a 50% drawdown you should not start investing in stocks, with or without ma's) in deciding what to do for my friends, but also there is an effort factor. if you have a job and not much time/interest in investing your possibilities are llimited. you can simply go buy and hold, buy fonds (i do think that the probability that a fond beats buy and hold is pretty low) or do some very simply strategie (like ma's), which hopefully gives you a realistic chance for outperformance versus buy and hold after several years. so my question: do you think my advice for my friends using such a ma asset allocation is a good/bad advice, do you know of possible alternative strategies or do you have other ideas to this topic ?

    thx, stefan

    • Hello Stefan,

      Offering investment advice is a much more complex and involved process than providing market analysis. For that one must use the services of a qualified professional. This blog is not the proper place for that.


  5. Dyson

    Most asset allocation models based on technical indicators are data-mined while no sufficient analysis is made to determine their robustness. Any future performance prospects of asset allocation models using moving average crossovers are founded on wishful thinking.

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