Friday 20 May 2016

A simple breakout trading rule (pysystemtrade)

Breakout. Not the classic home arcade game, seen here in Atari 2600 version, but what happens when a market price breaks out of a trading range.

The Atari 2600 version was built by Wozniak with help from Jobs exactly 40 years ago. Yes that Wozniak and Jobs. Source: wikipedia

In this post I'll discuss a trading rule I use to look at breakouts. This will be an opportunity to understand in more general terms how I go about designing and testing trading rules. It will be fascinating for those who are interested in this, and full of mind numbing detail it you're not.

I'm also doing this because I've talked about my breakout rule a bit on Elite Trader, and there's been quite a bit of interest in understanding it further. Although the rule isn't by any means some kind of magic bullet to take you on the path to fabulous wealth, it does add some diversification to the basic meat and potatoes moving average and crossover technical trend following system.

This, along with a bunch of other stuff, is in the latest version of my open source python backtesting engine pysystemtrade. The release notes will tell you more about what else has been put in since you last checked it. You can see how I did my plots in the messy script here.

As usual some parts of this post will make more sense if you've already read my book; and indeed I'll be referring to specific chapters.

Initial development

In the initial development stage we design, and get the behaviour of the rule as desired. This does not involve a back test in the sense of looking at past performance, and indeed it must not if we want to involve implicit over fitting.


The idea of a breakout is simple. Consider this chart:

This is crude from 2010 to last year. Notice that the price seems to be in a range between 80 and 120. Then suddenly in late 2015 it breaks out of this range to the downside. In market folklore this is a signal that the price will continue to go down. And indeed, as you'd expect given I've cherry picked this market and time period, this is exactly what happens:

This "big short" was one of the best futures trades of the last 18 months.

Introducing the simplest possible "breakout" rule

So to construct a breakout rule we need a way of identifying a trading range. There are an infinite Spending 5 seconds on google gave me just 3: Bollinger Bands, STARC bands or the commodity channel index (CCI). I have no idea what any of these things are. Indeed until I did this "research" I had never even heard of STARC or CCI.

It strikes me that the simplest possible method for identifying a range is to use a rolling maxima and minima, which handily the python package pandas has built in functions for. Here's the first crude oil chart again but with maxima (green) and minima (red) added, using a rolling window of 250 business days; or about a year.

Notice that a range is established in 2011 and the price mostly stays within it. The "steps" in the range function occur when large price changes fall out of the rolling window. Then in late 2014 the price smashes through the range day after day. The rest is history.

Why use a rolling window? Firstly the breakout folklore is about the recent past; prices stay in a range which has been set "recently"; recently here is over several years. Secondly it means we can use different size windows. This gives us a more diversified trading system which is likely to be more robust, and not overfitted to the optimal window size.

Thirdly, and more technically, I use back adjusted futures prices for this trading rule. This has the advantage that when I roll onto a new contract there won't be a sudden spurious change in my forecast. In the distant past though the actual price in the market will be quite different from my back adjusted price. If there is some psychological reason why breakouts work then the back adjustment will screw this up. Keeping my range measurement to the recent past reduces the size of this effect.

Now readers of my book (chapter 7) will know I like continuous trading rules. These don't just buy or sell, but increase positions when they are more confident and reduce them when less so. So when I use moving average crossovers I don't just buy when a fast MA crosses a slow MA; instead I look at the distance between the moving average lines and scale my position up when the gap gets bigger. When the actual crossing happens my position will be zero.

So the formulation for my breakout rule is:

forecast = ( price - roll_mean  ) / (roll_max - roll_min)

roll_mean = (roll_max + roll_min) / 2

You may also remember (chapter 7 again) that I like my rules to have the right scaling. This scaling has two parts. Firstly the forecast should be "unit less" - invariant to being used for different instruments, or when volatility changes for the same instrument. Secondly the average absolute value of the forecast should be 10, with absolute values about 20 being rare.

Because we have a difference in prices divided by a difference in prices the forecast is already invarient. So we don't need to include the division by volatility I use for moving average crossovers (Appendix B of my book).

Notice that the natural range for the raw forecast is -0.5 (when price = roll_min) to +0.5 (price = roll_max). A range of -20 to +20 can be achieved by multiplying by 40:

forecast = 40.0 * ( price - roll_mean  ) / (roll_max - roll_min)

If the distributional properties of the price vs it's range are correct then this should give an average absolute forecast of about 10. I can check this scaling using pysystemtrade, which will also correct the scaling if it's not quite right. I'll discuss this below.

The forecast in the relevant period is shown below. It looks like the absolute value is about 10, although this is just one example of curse. Notice the "hard short" at the end of 2014. At this stage I'm still not looking at whether the rule is profitable, but seeing if it behaves in the way I'd expect given what's happening with market prices.

Now arguably my rule isn't a breakout rule. A breakout occurs only when the price pushes above the extreme of a range. But most of the time this won't be happening, yet I'll still have a position on. So really this is another way to identify trends. If the price is above the average of the recent range, then it's probably been going up recently, and vice versa.

However the "breakout" rule will behave a bit differently from a moving average crossover; I can draw weird price patterns where they'll give quite different results. I'll examine how different these things are in an average, quantitative sense, later on.

I should probably rename my breakout rule, or describe it as my "breakout" rule, but I can't be bothered.

My breakout by another name is a stochastic

When I came up with my breakout rule I thought "this is so simple, someone must have thought of it before".

It turns out that I was right, and I found out a few months ago that my breakout rule is virtually identical to something called the stochastic oscillator, invented by a certain Dr Lane. The stochastic is scaled between 0% (price at the recent minimum) and 100% (at the max); otherwise it's a dead ringer.

However the stochastic is used in a completely different way - to find turning points. Essentially near 0% you'd go long ("over sold") and near 100% you'd go short ("over bought"). I have to say that in most markets, where trend following has worked for a couple of centuries, this is exactly the wrong thing to do. 

Although like most technical indicators, things are rarely that simple. From the wiki article:

"An alert or set-up is present when the %D line is in an extreme area and diverging from the price action. The actual signal takes place when the faster % K line crosses the % D line. Divergence-convergence is an indication that the momentum in the market is waning and a reversal may be in the making. The chart below illustrates an example of where a divergence in stochastics, relative to price, forecasts a reversal in the price's direction. An event known as "stochastic pop" occurs when prices break out and keep going. This is interpreted as a signal to increase the current position, or liquidate if the direction is against the current position."

I have absolutely no idea how to translate most of that into python, or English for that matter. However it seems to suggest a non linear response - relatively extreme values suggest the price will mean revert; an actual breakout means the price will trend; with no comment about what happens in the middle. I'm not a fan of such non linearity as viewers of my recent presentation will know.

Since originally publishing this article a reader commented that my rule is also similar to something called a "Donchian channel", which is a more recent innovation than the stochastic. Apparently basic Donchian channel analysis waits to spot the point where a security's price breaks through the upper or lower band, at which point the trader enters into a long or short position.

Anyway, enough technical analysis baiting (and apologies to my TA friends who know I am doing this in a friendly spirit; we are on the same side just with different methods).

Strictly speaking I should probably rename my breakout rule "stochastic minus 50% multiplied by 20" but (a) it's not the catchiest name for a trading rule, is it? (b) as a recovering an ex options trader I have a Pavlovian response to the world stochastic that makes me think in quick succession of stochastic calculus and Ito's lemma, at which point I need to have a lie down, and (c) I can't be bothered.

Slowing this down

One striking aspect of the previous plot is how much the blue line moves around. This is a trading rule which has high turnover. We're using a lookback of 250 days to identify the range, so pretty slow, but we are buying and selling constantly. In fact this rule "inherits" the turnover of the underlying price series with most trading driven by day to day price changes, only a little being added by the maxima and minima changing over time. 

from syscore.pdutils import turnover
print(turnover(output, 10.0))

... gives me 28.8 buys and sells every year; a holding period of less than a week. Crude oil is a middling market cost wise which costs about 0.21% SR units to trade (chapter 12)


So it would cost 0.06 SR units to run this thing. This is just below my own personal maxima, but still pricey. That kind of turnover seems daft given we're using a one year lookback to identify our range. The solution is to add a smooth to the trading rule. The smooth is analogous to the role the fast moving average plays in a moving average crossover; so I'll use an exponentially weighted moving average for my smooth.

[The smooth parameter is the span of the python pandas ewma function, which I find more intuitive than other ways of specifying it]

This is the final python for the rule (also here):

def breakout(price, lookback, smooth=None):
    :param price: The price or other series to use (assumed Tx1)
    :type price: pd.DataFrame

    :param lookback: Lookback in days
    :type lookback: int

    :param lookback: Smooth to apply in days. Must be less than lookback!
    :type lookback: int

    :returns: pd.DataFrame -- unscaled, uncapped forecast

    With thanks to nemo4242 on for vectorisation

    if smooth is None:
        smooth=max(int(lookback/4.0), 1)
    assert smooth<lookback
    roll_max = pd.rolling_max(price, lookback, min_periods=min(len(price), np.ceil(lookback/2.0)))
    roll_min = pd.rolling_min(price, lookback, min_periods=min(len(price), np.ceil(lookback/2.0)))
    roll_mean = (roll_max+roll_min)/2.0

    ## gives a nice natural scaling

    ## remove the spikey bits
    output = 40.0*((price - roll_mean) / (roll_max - roll_min))
    smoothed_output = pd.ewma(output, span=smooth, min_periods=np.ceil(smooth/2.0))

    return smoothed_output

If I use a smooth of 63 days (about a quarter of 250), then I get this as my forecast:

Smoothing reduces the turnover (to 3.6 times a year; a holding period of just over 3 months). Less obviously, it also weakens the signal when it is not at extremes, reducing the number of "false positives" in identifying breakouts but at the expense of responsiveness.

Notice in the code I've defaulted to a smooth with a lookback window of a quarter the size of the . Clearly the smooth should be more sluggish for longer range identifying windows, but where did 4 come from? Why not 2? Or 10? I could have got it the bad way - running an in sample optimisation to find the best number. Or I could have done it properly with an out of sample optimisation using a robust method like bootstrapping.  

In fact I pulled 4.0 out of the air; noticing that I also used 4 as the multiple between moving average lengths in my moving average crossover trading rule. I then did a sensitivity check to ensure that I hadn't by some fluke pulled out an accidental minimum or maximum of the utility function. This confirmed that 4.0 was about right, so I've stuck with it. Being able to pull these numbers out of the air requires some experience and judgement. If you're uncomfortable with this approach then forget you read this paragraph and read the next one.

I used out of sample optimisation and the answer was a consistent 3.97765 over time, which I've subsequently rounded. Yeah, and some machine learning. I used some of that. And a quantum computer. The code for this exercise is trivial, was done in my older codebase and I can't be bothered to reproduce it here; I leave it as an exercise for the reader.

source:, of course

Next question, what window sizes should I run? Really short window sizes will probably have turnover that is too high. Because of the law of active management really long window sizes will probably be rubbish. Window sizes that are too similar will probably have unreasonably high correlation. Running a large number of window sizes will slow down my backtests (though the actual trading isn't latency sensitive) and make my system too complicated.

Using crude oil again I found that a lookback window of 4 days (smooth of 1 day; which is actually no smooth at all) has an eye watering turnover of 193 times a year; almost day trading. That's 0.40 SR units of costs in crude oil - far too much. 

A 10 day lookback (2 day smooth) came in at about 100 times a year; still too expensive for Crude, but for a very cheap market like NASDAQ (costs 0.057% SR units) probably okay. A 500 business day lookback, equating to a couple of years, has a turnover of just 1.7 but this is probably too slow.

I know from experience that doubling the length of time of something like a moving window, or a moving average, will result in the two trading rule variations having a correlation that isn't really high or indecently low. 

10 days seems a sane starting point, also exactly two weeks in business days, and if I keep doubling I get 10,20,40,80,160 and 320 day lookbacks before we're getting a little too slow. Again I've pretty much pulled these numbers from thin air; or if you prefer we can both pretend I used a neural network. Six variations of one rule is probably enough; it's the maximum I use for my existing ewmac trading rule.

If I look at the correlation of forecasts by window length for Crude, I get this lovely correlation matrix:

      10    20    40    80    160   320
10   1.00  0.75  0.48  0.28  0.15  0.13
20   0.75  1.00  0.80  0.50  0.26  0.19
40   0.48  0.80  1.00  0.78  0.46  0.30
80   0.28  0.50  0.78  1.00  0.76  0.51
160  0.15  0.26  0.46  0.76  1.00  0.83
320  0.13  0.19  0.30  0.51  0.83  1.00

Notice that the correlation of adjacent lookbacks is consistently around 0.80. If I used a more granular set then correlations would go up and I'd only see marginal improvements in expected performance (plus more than six variations is overdoing it); actual performance on an out of sample basis would probably improve by even less.

If I used a less granular scheme I'd probably be losing diversification. So the lookback pairs I've pulled out of the air are good enough to "span" the forecasting space.

Note:  I could actually do this exercise using random data, and the results would be pretty similar.

Also note: You might prefer dates that make sense to humans (who have a habit of plotting charts for fixed periods to mentally see if there is a breakout). If you like you could use 10 (2 weeks of business days), 21 (around a month), 42 (around 2 months), 85 (around 3 months),  128 (around 6 months) and 256 (around a year). Or even use exactly a week, month, etc; which will require slightly more programming. Hint: it makes no difference to the end result.

This is the end of the design process. I haven't specified what forecast weights to assign to each rule variation, but I'm going to let my normal backtesting optimisation machinery handle that.

A key point to make is I haven't yet gone near anything like a full blown backtest. Where I have used real data it's been to check behaviour, not profitability. I've also used a single market - crude oil - to make my decisions. This is a well known trick used for fitting trading systems; reserving out of sample data in the cross section rather than in the time series.

I'm confident enough that behaviour won't be atypical across other markets; but again I can check that later. I can also check for fitting bias by looking at the performance of Crude vs other markets. If it comes back as unreasonably good, then I may have done some implicit overfitting. 

Back testing

It's now time to turn on our backtester. The key process here is to follow the trading rule through each part of the system, checking at each stage there is nothing weird going on. By weird I mean sudden jumps in forecast, or selling on strong trends. It's unlikely with such a simple rule that this could happen, but sometimes new rules unearth existing bugs or there are edge effects when a new rule interacts with our price data.

To repeat and reiterate: We'll leave looking at performance until the last possible minute. It's crucial to avoid any implicit fitting, and keep all the fitting inside the back test machinery where it can be done in a robust out of sample way.

Eyeball the rules

The first step is to literally plot and eyeball the forecasts.

system.rules.get_raw_forecast("CRUDE_W", "breakout160").plot()

This isn't a million miles away from what we got earlier with a 250 day lookback. In theory you should do this with every instrument and lookback variation; I would certainly do this with anything where I planned to commit real money. This would make this post rather dull, so I won't bother.

Forecast scaling and capping

I've tried to give this thing a 'natural' scaling such that the average absolute value will be around 10. However let's see how effective that is in practice. Here is the result of generating forecast scalars for each instrument, but without pooling as I'd normally do (I will be pooling, once I've run this check that it is sensible). Scalars are estimated on a rolling out of sample basis, the values here are the final value [system.forecastScaleCap.get_forecast_scalar(instrument, rule_name).tail(1)]. The first line in each group of two shows the rule name, and the lowest and highest scalar. The second gives some statistics for the value of the scalars across instruments.

breakout10: ('NZD', 0.7289386003001351) ('GOLD', 0.7908394013201738)
mean 0.762 std 0.015 min 0.729 max 0.791
breakout20: ('OAT', 0.771837889705238) ('PALLAD', 0.8946942606921282)
mean 0.841 std 0.025 min 0.772 max 0.895
breakout40: ('OAT', 0.7425509489841716) ('NZD', 1.0482133192218817)
mean 0.874 std 0.058 min 0.743 max 1.048
breakout80: ('OAT', 0.6646687936933129) ('CAC', 1.0383619767744796)
mean 0.891 std 0.093 min 0.665 max 1.038
breakout160: ('KR3', 0.6532074583607256) ('KOSPI', 1.566217603840726)
mean 0.901 std 0.149 min 0.653 max 1.566
breakout320: ('BOBL', 0.5774784629229296) ('LIVECOW', 1.047003237108071)
mean 0.891 std 0.188 min 0.577 max 1.739

Some things to note:

  • I'm doing this across the entire set of 37 futures in my database to be darn sure there are no nasty surprises
  • The scalars are all a little less than one, so I got the original scaling almost right.
  • Scalars seem to get a little larger for slower windows. However this effect isn't as strong as a similar affect with moving average crossovers and may be just an artifact of systematic trends present in the data (see next point).
  • The scalars are tightly distributed for fast windows, but less so at more extreme. The reason for this is that the average value of a slow trend indicator will be badly affected for shorter data series that exhibit strong trends. Many of my instruments have only 2.5 years data in which OAT for example has gone up almost in a straight line. The natural forecast will be quite high, so the scalar will be relatively low.
I'm happy to use a pooled estimate for forecast scalars, which out of interest gives the following values. These are different from the cross sectional averages above, since instruments with more history get more weight in the estimation.

breakout10: 0.714
breakout20: 0.791
breakout40: 0.817
breakout80: 0.837
breakout160: 0.841
breakout320: 0.834

Forecast turnover

I've already thought about turnover, but it's worth checking to see that we have sensible values for all the different instruments and variations. The forecast turnover (chapter 12) in the back test [system.accounts.forecast_turnover(instrument, rule_name)] will also include the effect of changing volatility, though not of position inertia (chapter 11) or it's more complex brethren, buffering. Here are the summary stats; min and max over 37 futures, plus averages.

breakout10: ('NZD', 79.16483047305336) ('SP500', 94.6080044643688)
mean 88.919 std 3.123
breakout20: ('BTP', 36.94675239304759) ('SP500', 44.575393850749954)
mean 41.289 std 1.767
breakout40: ('OAT', 16.999433818503036) ('SMI', 23.558597834298745)
mean 20.090 std 1.582
breakout80: ('OAT', 6.797714635479201) ('AEX', 11.97073508971376)
mean 9.754 std 1.228
breakout160: ('KR3', 2.832732743680337) ('CAC', 6.068686718496314)
mean 4.591 std 0.712
breakout320: ('KR3', 0.898807113202031) ('CAC', 3.1114370880054425)
mean 2.133 std 0.507

Again there is nothing to worry about here; turnover falling with window length and no insanely high values for any instrument. There's a similar effect going on for very slow lookbacks, where markets with less data that have seen sustained uptrends will have lower turnover; i.e. less trading because the forecast will have been stuck on max long for nearly the whole period.

Of course the very fastest breakout will be awfully expensive for some markets. Korean 3 year bonds come in at 1.5% SR units; at 88 times a year using breakout10 is going to be a big stretch, and only something like the very slowest breakouts will cut the mustard. But the backtest will take that into account when calculating forecast weights, which by a breathtaking coincidence is the next step.

Forecast weights

I'm going to be estimating forecast weights using costs, as I outlined in my last blog post. The crucial thing here is that anything that is too expensive will be removed from the weighting scheme. The cheapest market in the set I use for chapter 15 of my book is Eurostoxx. Even for that however breakout10 is too expensive. For the priciest market, V2X european volatility, breakout10 to breakout40 are all off limits, leaving just the 3 slowest breakouts. This is a similar pattern that we see with ewmac.

Apart from that, the forecast weights are pretty dull, and come in around equal weighting regardless of whether I use shrinkage or bootstrapping to derive them. Yawn.

Interaction with other trading rules

Let's now add the breakout rule spice to the soup of EWMAC and carry trading rules that I talked about in chapter 15 of my book. The correlation matrix of forecasts looks like so (using 37 instruments for maximum data:

brk10 brk20 brk40 brk80 brk160 brk320 ewm2 ewm4 ewm8 ewm16 ewm32 ewm64 carry
brk10 1.00 0.74 0.40 0.21 0.14 0.15 0.93 0.81 0.52 0.27 0.16 0.13 0.18
brk20 0.74 1.00 0.77 0.49 0.30 0.25 0.75 0.94 0.85 0.59 0.37 0.26 0.28
brk40 0.40 0.77 1.00 0.80 0.55 0.41 0.44 0.73 0.92 0.85 0.64 0.45 0.40
brk80 0.21 0.49 0.80 1.00 0.79 0.58 0.23 0.47 0.75 0.93 0.87 0.64 0.47
brk160 0.14 0.30 0.55 0.79 1.00 0.83 0.12 0.26 0.48 0.74 0.92 0.87 0.64
brk320 0.15 0.25 0.41 0.58 0.83 1.00 0.11 0.19 0.32 0.52 0.77 0.92 0.76
ewm2 0.93 0.75 0.44 0.23 0.12 0.11 1.00 0.86 0.57 0.31 0.15 0.10 0.15
ewm4 0.81 0.94 0.73 0.47 0.26 0.19 0.86 1.00 0.87 0.59 0.35 0.21 0.23
ewm8 0.52 0.85 0.92 0.75 0.48 0.32 0.57 0.87 1.00 0.88 0.62 0.39 0.34
ewm16 0.27 0.59 0.85 0.93 0.74 0.52 0.31 0.59 0.88 1.00 0.88 0.63 0.45
ewm32 0.16 0.37 0.64 0.87 0.92 0.77 0.15 0.35 0.62 0.88 1.00 0.88 0.59
ewm64 0.13 0.26 0.45 0.64 0.87 0.92 0.10 0.21 0.39 0.63 0.88 1.00 0.75
carry 0.18 0.28 0.40 0.47 0.64 0.76 0.15 0.23 0.34 0.45 0.59 0.75 1.00

Apologies for the formatting. brk10 = breakout10 and so on; ewm2 = ewmac2_8 (so N_4N is the pattern), and crry is just carry

Interesting things:
  • Adjacent ewmac (eg 2_8 and 4_16) and breakout (eg 10 and 20) variations are correlated around 0.88 and 0.80 respectively. 
  • The average correlation within breakout world is 0.49, and in ewmac universe 0.55
  • So there's slightly more internal diversification in the world of breakouts.
  • Breakouts are a little more correlated with carry; though for both correlations are highest at the slowest end (unsurprising given they use back adjusted futures prices that include carry within them)
  • EWMAC and breakouts are closely related if we match lookbacks - breakout10 and ewmac2_8 are correlated 0.93 and similar pairings come in at these kinds of levels.
  • The average cross correlation of all breakouts vs all ewmac is 0.58.

Trading rule performance 

There's no going back now - I'm going to look at account curves and performance. Does this thing make money?

This does mean that I have to impose a "no change" policy. If I make any changes to the trading rule now it will mean implicit overfitting; and my backtest performance, even with all my careful robust fitting, will be overstated. If I throw away the rule entirely, in theory at least the same applies. Of course it would be perverse to run a rule I know is a terrible money loser; nevertheless I wouldn't have known this in the past.

Let's first have a look at how each breakout rule looks across the whole portfolio of the six chapter 15 instruments. This charts use some code to disaggregate the performance of trading rules:


There's a whole lot more of this kind of code, and if you're planning to use pysystemtrade it's probably worth reading this part of the manual (again).

These are aggregated across all the countries we are trading, and normalised to have the same standard deviation. In practice we aren't allocating to breakout10 because of it's high costs. Remember the decision was taken by the optimisation code with information that would have been known at the start of the backtest period, not by me after looking at this picture. For speed I can drop breakout10 from the configuration without being guilty of implicit fitting.

Final thoughts

Ideally I'd now run the breakout rules together with the existing chapter 15 rules and see what the result is. However I already know from the correlation matrix and the account curves above that the answer is going to be a small improvement in performance from the ewmac+carry version, though probably not a significant one (I'm also in the middle of optimising pysystemtrade which runs far too slowly right now, to make such comparisons quicker).

Notice the difference in approach here. Traditionally a researcher would jump straight to the final backtest having come up with a rule to see if it works (and I confess, I've done that plenty of times in the past). They might then experiment to see which variation of breakout does the best. This is a shortcut on the road to over fitting.

Here I'm not even that interested in the final backtest. I know the rule behaves as I'd expect, and that's what's important. I'd be surprised if it didn't make money in the past; given it's designed to pick up on trends, and judging by it's correlation with ewmac does so very well. I have no idea whether there is a variation of breakout out of my set that is the best, or even if there is another combination of smooth and lookback that does even better.

Finally whether the rule will make money in the future is mostly down to whether markets trend or not.


I like the breakout rule, even if it turns out it was (sort of) invented by someone else. Diversifying by adding similar trading rules is never going to be the best way of diversifying your trading system. Doing something completely different like tactical short volatility, or adding instruments to your portfolio, are both better. The former does involve considerable work, and the latter involves some work and may also be problematic unless you have a 100 million dollar account.

But one of the advantages of being a fully automated trader is that adding variations is almost free; if you combine your portfolio in a linear way as I do it doesn't really affect your ability to interpret what the system is doing.

I'd rather have a large set of simple trading rules, even if they're all quite similar, than a smaller set of complex rules that has been potentially overfitted to death. 


  1. Excellent post Rob. You have cleared up some questions I was going to ask you after reading the forecasting section of your book. I will have to go back to the book now and reflect! Cheers Matt

  2. Hi Rob, Great post! I notice that there are gaps in the data for oil (you can see this in the pysystemtrade data and in the line graphs you show above). Are the gaps genuine price gaps, or are they due to futures contract expiries? I had assumed this was using back-adjusted data. Thanks

  3. Amazing post! Finally, I've got the idea. Thank you so much for clarification!

  4. Hi Rob, excellent insight in how you develop your rules. For cross asset or cross sectional rules. How do you recommend to implement those with your code. I would assume some addition to raw data stage plus some averaging in the forecast stage would do the trick. Thanks

    1. Exactly that. I'll add this as an example at some point.

  5. Rob,

    Your formulas are presented as:

    So the formulation for my breakout rule is:

    forecast = ( price - roll_mean ) / (roll_max - roll_min)

    roll_mean = (roll_max - roll_min) / 2

    But shouldn't roll_mean be calculated as:

    roll_mean = roll_min + (roll_max - roll_min) / 2 ?



    1. Actually should be roll_mean = (roll_min + roll_max) /2 (which is identical to your formulation) The python is correct. Edited the article to fix this.

  6. What you've "re-invented" here is not stochastics but a Donchian channel breakout. Been in use since the 1950's first by Richard Donchian and then by almost every long term trend follower to ever place a trade.

    1. Added a reference to Donchian. Although I note in passing that again this is another discrete breakout, rather than a continuous, indicator.

    2. It can be used as a "continuous" indicator by using multiple periods of "n" for the channels just as you would use multiple periods of a moving average for a continuous moving average system.

  7. Rob-
    Great post as usual. I was wondering if you might consider adding an overbought/oversold area to adjust your trend following forecast for extended trends, or would you simply create a separate mean reversion system out of it.

    1. I'd create a seperate mean reversion system. The former is too complicated:

    2. Hi Rob,

      I'd like to diversify the current trend following model with a mean reversion model(s). What is your experience with them and what places/indicators do you believe(or have seen) to be fruitful?

      Your work is much appreciated!

    3. I will have to write a post about this subject, and don't worry I will at some point. The answer is too long to fit in this margin :-)

  8. Just came across your blog, thanks for sharing your insights.
    You mentioned somewhere that trading costs have come significantly down since implementing your new execution algo. Do you measure this relative to the price when you submitted your first order? Could you elaborate a bit please on how you measure this?
    As a suggestion for a future topic: could you share your insights on how to trade futures based on non-price / fundamental / macro info?

    Thanks again for sharing!

    1. Let's say I'm buying. I measure the offer price when I am about to submit my order. If I submitted a market order, I'd pay this. My expected slippage would be the offer versus the mid, or half the bid-ask. I compare the offer versus what I actually get filled at with the simple algo. The difference is the improvement.

      I will bear in mind your topic suggestion!

  9. Rob,

    Quick question about the turnover calculation. For some of the faster EWMAC variations, the turnover from the function is about half the raw turnover from the table on page 248 of your book, while the slower pairs are very tight. Any thoughts on where this divergence could be coming from?

    Thanks again for an awesome post!


    1. (a) a different set of instruments [wider in the book] (b) inclusion of effects of changes in volatility for position scaling.

  10. Hi Rob, thanks for this excellent post. My question is (maybe a little off-topic, I will be asking on subsystems rather than a single strategy) how necessary is for a subsystem to make money on its own? I recently checked CORN for example from the Chapter 15 system,

    print (system.accounts.pandl_for_subsystem("CORN").sharpe())

    which gave -0.13 as Sharpe Ratio; but I guess you included this subsystem because it increases diversification of the portfolio. Would this be correct? So in the future if I am adding new subsystems to Ch 15, I should not worry about its SR in isolation? \


    1. Sharpe is not statistically significant. Read chapter 3 ... again.

    2. Ah. You use t_test and p_value calls on daily returns data and test if they are statistically different from 0 - in this case, p-value is > 0.05 - not significant.

      So we cannot say anything for sure on CORN - but one could still use it because it provides diversification? I ask because here

      you mention CORN position would have meant a worse loss during 2015 were it not for another agricultural instrument in the portfolio.

      I also checked Andrew Lo's paper that shows how to compute Sharpe ratio confidence intervals,

      def err(SR,T):
      return np.sqrt( (1 + 0.5*SR**2)/T )
      T = 40*256; sr = -0.12
      print sr + np.array([-1, 1]) * err(sr,T)

      gives [-0.12991763 -0.11008237], both ends for SR for CORN are in the negative: I don't know how to connect this with the previous significance results, but I guess rejection from t-test is stronger.


    3. The anecodote in that paper has no statistical meaning eithier - it's just one data point. But sure, Corn isn't perfectly correlated to other subsystem returns, so if you assume we can't predict risk adjusted returns then we should add it.

      I'm not familiar with the test you show, so I can't comment on it.

      There is also a multiple testing problem - if we test enough instruments then some of them will be significantly negative or positive regardless of the real underlying properties of the trading system.

    4. Incidentally you made a mistake with Los formula - you are using an annual SR but you're assuming you have daily data. The correct range for the confidence interval is -0.43, 0.46

  11. In practice, would you recommend diversifying across different types of trend signals?(eg moving averages, breakouts, etc.)

  12. For some reason, it won't let me reply. But in response to my question above: Great. I suppose my bit of skepticism is raised by the paper 'Which Trend is Your Friend' by the AQR guys. You show the same that different trend signals are highly correlated/the same. If thats the case what is your reasoning for using multiple trend signals?

    Thank you!!

    1. As long as the correlation is less than 1.0 there will be some benefit. It doesn't cost anything so why not?

  13. Hi Rob,

    I've seen some comments on mean reversion and your comments that you would write about them in the future. Based on your comments they seem to be longer term in nature. However, I have heard of short-term, in particular, mean reversion equity index futures. For example, I saw FORT LP has a package for only equity futures that trades short term mean reversion.

    I know your going to write about your mean reversion systems, but what has your experience been with short term mean reversion systems? I guess particularly for equity futures? What type of indicators should I look at?

    Thank you much!!

    1. I'm seriously thinking about it myself. A nice indicator is to do a regression of the recent price and trade the inverse of the residual.

    2. So just regressing y on time t over some lookback T? The signal being -1/(y_T - y_hat) with some smooth parameter?

    3. Dear Rob,
      I know that I'm late to the party, but I would also be very interested to hear/read more about this from you.

    4. Jeroen... could you be more specific?

    5. I would like to better understand how adding a mean reversion trading rule could add diversification to the breakout rule which you describe in this article/blog post.
      I have not tested it myself, but intuitively I would expect these two to be negatively correlated: assume the mean reversion rule generates a negative forecast if the price is above its mean value and vice versa. If the price of an instrument starts at the longer term mean and then goes up it generates a positive breakout forecast, but at the same time a negative mean reversion forecast. Adding the mean reversion rule would then offset the momentum rule. The net effect would be a neutral forecast signal, resulting in no trading activity.
      If this is correct, would it then be better to select either breakout or mean reversion and not combine the two together?

    6. If your mean reversion rule is just minus one times your breakout rule then of course there is no point combining them. Assuming the breakout rule is profitable then the mean reversion rule would be unprofitable. However if you can find a mean reversion rule which is sufficiently different, and is profitable, then combining the two types of rules would make sense.

    7. This comment has been removed by the author.

    8. It's on my to do list hopefully for this year.

    9. Thanks - is my intuition on look back periods correct?

  14. Hi Rob, would you combine a system that trades spreads in the same manner? It could be possible for one leg of the spread to get offset by the other rules; how do you think that would affect the system?


  15. Hi Rob, this was an excellent post. Thanks for sharing your insights.

    For the sake of curiosity, can you provide some references for how one could learn more about "tactical short volatility estrategies", which you have mentioned in this post? Any book or blog post covering the intuition behind such strategies?

    1. I don't know of any book, but is planning to do a series of interviews on the topic. I might write a blog post at some point, but it would purely be about the futures (VIX,VSTOXX)

  16. Excellent post, Rob. Question: which variations did you ultimately use?

  17. Hi Rob - quick question on the instrument diversification multiplier, very much a philosophical one.

    As we know, the main benefit of diversification is the risk reduction that comes with it *without* impacting expected returns. Therefore, are we not giving up some of the diversification benefits when we use the instrument diversification multiplier to compute the number of contracts to buy? Or do we continue to retain the same diversification benefits although the level of risk is now more in line with our risk target?

    Probably it is the latter but I wanted to double check with you.


    1. It's my belief that (assuming equal vol per instrument and equal SR, therefore equal expected returns) diversification reduces portfolio risk whilst holding expected returns identical. This increases Sharpe Ratio. Therefore one can take the benefits of diversification eithier purely in risk reduction (by doing nothing; an IDM of one), or entirely in returns (by applying an IDM such that the expected portfolio risk remains unchanged and the expected returns increase), or somewhere in between. We're still getting the full diversification benefit in the form of higher SR in all cases, it's just that we're choosing to have it paid out as some combination of higher return and/or lower risk.

      Footnote: at the margin, if we increase our expected SR then we increase our Kelly optimal risk target, and therefore we could apply a higher risk target and thus an even higher IDM, and obtain even higher expected returns.

    2. Makes sense. Thanks so much for the explanation.

  18. Hi Rob, I am just about to implement and test your version of Breakouts as described in "Leveraged trading" when I came across your blog post (.../2016/05/a-simple-breakout-trading-rule...).

    The "Smoothing" of the raw model output as described in the post does not seem to be included in your book (which was published more recent). Unless I missed it somewhere, did you just want to keep the book on a "higher level" or were there other reasons (e.g. did you change your mind on the smoothing)?

    Many thanks, Magnus

    1. Makes the book simpler.

      Smoothing is also more useful if you are using a continious rather than binary forecast.

    2. OK, many thanks for your prompt reply Rob!

      Initially I'll test your version of Breakout as input for Ranking of a portfolio of stocks within a long only momentum strategy. We will see if smoothing is required to slow down the trading or if a ranking criteria based on combining a number of a different time frames might be stable enough...

  19. This comment has been removed by a blog administrator.

  20. Hi Rob,
    I recently read your book, "Leveraged Trading". While I found the book very helpful, the section about forecast scalars for the breakout system confused me. If we use a forecast scalar of less than 40, aren't we eliminating any possibility of the maximum position, +-20? For example, you say in the book that for the 320 window, a scalar of 33.5 should be applied. Doesn't this mean that we will never have a forecast greater than 16.75? If this is the case, why do you also caution in your book to make sure to add the 20 cap? Also, it seems strange that the breakout rule, unlike the MAC rule, should never allow for a position 2X the size of a normal one.
    Thank you

    1. " If we use a forecast scalar of less than 40, aren't we eliminating any possibility of the maximum position, +-20?"

      Er, no. Consider a trading rule that generates a forecast with a Gaussian distribution with mean 0 and standard deviation 100. The appropriate forecast scalar would be around 0.1. But the maximum position achievable is much higher than 20; for example around 0.15% of the time (every couple of years) the forecast would be +300, which after scaling is +30.

    2. "Also, it seems strange that the breakout rule, unlike the MAC rule, should never allow for a position 2X the size of a normal one."

      Well it's a different kind of rule, which will always have natural maxima and minima, but the MAC rule has no theoretical maximum.


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