Momentum is Price Breakout

Lately, there is a tendency to associate momentum, relative strength or cross-sectional, to quantitative analysis and label absolute momentum as technical analysis. Nothing can be further from the truth. Momentum is a trivial concept that is based on breakouts above a past price. At the same time, absolute momentum is much broader in scope than relative despite recent efforts to relate them.

Let us consider for example the price rate of change (ROC) used in relative strength momentum models:

ROC(n) = (C – Cn)/Cn       (1)

Basically, this is the arithmetic return over n periods. Note that the denominator is always positive and therefore, ROC(n) changes sign when (C-Cn) changes sign. There is nothing new in this as it is known to traders for ages. The result is that the following two strategies are equivalent:

  • Looking at sign changes  of n-period returns, (C-Cn)/Cn
  • Looking at a breakout of price C above or below the price n-periods ago, Cn

A backtest should convince a skeptic.  Consider the following trading system

Trading System 1:

Buy when ROC(close, 200) > 0
Sell when ROC(close, 200) < 0

Basically, this system buys a security when the trailing 200-period return turns positive and sells it when it turns negative.

Also consider the following trading system:

Trading System 2:

Buy when (Close - Close of 200 days ago) > 0
Sell when (Close - Close of 200 days ago) < 0

We will use adjusted SPY data since inception to 07/29/2015, starting capital of $100,000, fully invested equity at the open of the day following the signal and $0.01 commission per share.

Below are the equity curves. They are identical, as expected (click to enlarge)


Trading System 1


Trading System 2

Note that the performance of both systems is below buy and hold during strong uptrends of 1990s and 2010s. The systems trade-off performance during strong uptrends for reduced risks during downtrends.

Next, it is also a fact known for ages that an indicator that uses the change in direction of a moving average with period n is equivalent to ROC(n) or (C-Cn), as described above.  Consider the following system:

Trading System 3:

Buy  when (MA(n) - MA(n) of one period ago) > 0
Sell when (MA(n) - MA(n) of one period ago) < 0

Trading system 3 generated identical results with the two systems considered before. This is because of the following equivalence

MA(n) – MA(n)  of one period ago = (C – Cn)/n    (2)

Actually, this is also a price breakout system with the rule divided by n, something that does not affect the sign changes.

Let us next consider the performance of the ROC(200) versus a long-only 50-200 moving average crossover system in SPY with same data and backtest parameters as before.

Parameter ROC(200)
Trading System 1
50-200 crossover
Long -only
CAR 8.83% 10.11%
Max. DD -29.17% -19.39%
Win rate 41.30% 80%
Sharpe 0.32 0.56
Trades 46 10

It may be seen that the 50-200 crossover performance is superior but this comes at a severe reduction of sample size, from 46 to 10 trades. Trading rules with small trade samples may be curve-fitted. The main trade-off is between low and high win rate. As the win rate drops below 50%, trading systems become susceptible to large drawdown levels and possibly ruin. Therefore, this is something to keep in mind:

Small trade samples trade-off significance for performance

This is the “curse of trading system development.” As one attempts to increase performance in longer timeframes, samples decrease, leading to lower significance. This problem can be solved by utilizing ultra fast timeframes, with the requirements imposed, and making a transition from directional trading to market making (HFT). This is what some markets participants have done. Those who still trade longer timeframes face issues of significance with their systems.


I have shown in this blog that momentum is simply a price breakout and therefore a technical analysis rule, actually a trivial one. Therefore, any claims that momentum falls under quantitative trading and other rules, such as moving average crossovers, fall under technical analysis, is false. Then, I showed with an example that trading rules that employ moving average crossovers are much different than those employing momentum. The simple explanation for that is that moving averages smooth volatility and thus generate smaller trade samples, trading-off significance for performance.

Finally, there can be no generalizations about trading rules. Although at an abstract level all trading rules can be placed within a certain framework, it is performance that matters. Results in trading are judged by performance and whether rules are similar or different is not really important. Most everything about trading rules is already known since the 1980s and even before that. What is now important is how to conceive new rules that are not influenced much by data-snooping and not to re-classify trading rules by assigning to them new names.

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6 Responses to Momentum is Price Breakout

  1. Bo says:


    I really like this: "As one attempts to increase performance in longer timeframes, samples decrease, leading to lower significance." My solution to this problem is to apply the system to as many instruments as you can. While for one particular market, the results are not significant due to reduced sample size. If the same rules are applied to many different markets, then overall sample size will be greatly increased. In fact I found the correlation actaully helps to increase the robustness of the system. It also helps to dynamiclly size the trade. Another good thing is it helps to truly stress test your system. One example this year is: while the trend following system will not long EURCHF as the vol is too low before the peg was broken, it might very well give a long trade in say NZDCHF. By adding this cross pair into your system, you could get a much realistic picture of how system behaves when a black swan event happens.

    Great article again.


    • Hello Bo. I also apply the test on "comparable securities". Here is an example:


      P.S. Sorry for late reply but my spam filter was sending most messages to spam folder, I just found out.

  2. David Chamness says:

    The term breakout usually means that price has made a new high or low beyond all past closes in a window. A 50 day upside breakout means the price closed above ALL of the closing prices over the past 50 days.

    Using the word "breakout" to say that price is above one price from n days ago, and then saying that breakout is the same as momentum simply redefines breakout as momentum. The usual meaning of breakout is a more extreme occurrence than price crossing above or below one number from n days ago.

    • You are correct in the sense of classical TA. However, you can always consider a hypothetical resistance level at price Cn and call a breakout a move of price C above it. In quant analysis the resistance levels is the zero line and the breakouts occur above and below it. Thus, in this sense I see no problem in using the term "breakout" despite what it usually means in classical technical analysis, which btw is followed by a diminishing group of old timers and noise traders.

      Best regards.

  3. david varadi says:

    hi Michael, i definitely agree with the last point– it is annoying that academics (or authors in general) that write papers get the credit for inventing things simply because they wrote a paper on it. Practitioner research definitely leads publishing (Thorpe had the same option pricing formula as Black Scholes nearly 10 years in advance)–unfortunately from a credibility perspective to the investor (and even advisor audience) academic papers that validate a concept provide the necessary stamp of approval. For some reason running tons of regressions (already a quantitatively flawed procedure) and having a PhD with no trading experience (or quantitative testing/development experience) is the only way to rubber stamp a concept. Sadly most academic research involves re-branding or re-labelling existing ideas and being the first to publish a paper on it (or more dangerously the studies that combine two or more separate anomalies written about separately)–suddenly you are a brilliant quantitative innovator and considered respectable among academic circles and other asset managers.
    Like most human endeavours most people want to invest in what is commonly considered acceptable (validated by academic research), and do not wish to be the guinea pigs for a new idea. As a result the very best strategies and research are done for the benefit of either high frequency/prop trading, hedge funds and private traders where there is less pressure to conform. Even large hedge funds face pressure to demonstrate that they are exploiting commonly known anomalies. Perception is reality. Research must reflect that to some extent. For others, research is simply a marketing or publishing exercise to draw attention. Sometimes members in the latter category lack an understanding of the difference between research and marketing, while others know exactly what they are doing and unfortunately can fool the unwary.
    (the strawman argument is poorly understood but very important–you need a good sample size during a modern period with good data — of course if you publish a research paper without using the long-term data no one takes you seriously : ( )
    david varadi

    • Thanks for the post David. Sad story about Thorpe. There is a lot of stealing of ideas by the academic crowd and they never give credit except to their own circles. As far as paper on trading models, some of them sound like they discovered the whole thing. It is pathetic. For example, these guys from Columbia that took all the credit for momentum premium, which in my opinion is a data-mined anomaly mainly due to 1990s bull run, just analyzed what thousands have been doing for many years.


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