This post was prompted by Michael Covel’s interview Traders’ Magazine in which he claims that trend followers don’t try to make predictions. This idea that trend followers do not forecast returns is widely and frequently repeated. It is also complete nonsense.
Every trading strategy makes forecasts^{1}. Whether these forecasts are explicit or hidden behind entry/exit rules is irrelevant. All the standard trend following systems can trivially be converted into a forecasting model that predicts returns, because they are fundamentally equivalent.
The specific formulation of the trend following system doesn’t matter, so I’ll keep it simple. A typical trend following indicator is the Donchian channel, which is simply the nbar highest high and lowest low. Consider a system that goes long when price closes above the 100day Donchian channel and exits when price closes below the 50day Donchian channel.
This is the equity curve of the system applied to crude oil futures:
This system can trivially be converted to a forecasting model of the form
the dependent variable y is returns, and x will be a dummy variable that takes the value 1 if we are in a trend, and the value 0 if we are not in a trend. How do we define “in a trend”? Using the exact same conditions we use for entries and exits, of course.
We estimate the parameters and find that α ≃ 0, and β = 0.099% (with pvalue 0.013). So, using this trend following forecasting model, the expected return when in a trend is approximately 10bp per day, and the expected return when not in a trend is zero. Look ma, I’m forecasting!
Even without explicitly modeling this relationship, trend followers implicitly predict that trends persist beyond their entry point; otherwise trend following wouldn’t work. The model can easily be extended with more complicated entry/exit rules, short selling, the effects of volatilitybased position sizing, etc.
Footnotes
Presenting the similarity between multiple time series in an intuitive manner is not an easy problem. The standard solution is a correlation matrix, but it’s a problematic approach. While it makes it easy to check the correlation between any two series, and (with the help of conditional formatting) the relation between one series and all the rest, it’s hard to extract an intuitive understanding of how all the series are related to each other. And if you want to add a time dimension to see how correlations have changed, things become even more troublesome.
The solution is multidimensional scaling (the “classical” version of which is known as Principal Coordinates Analysis). It is a way of taking a distance matrix and then placing each object in N dimensions such that the distances between each of them are preserved as well as possible. Obviously N = 2 is the obvious use case, as it makes for the simplest visualizations. MDS works similarly to PCA, but uses the dissimilarity matrix as input instead of the series. Here’s a good take on the math behind it.
It should be noted that MDS doesn’t care about how you choose to measure the distance between the time series. While I used correlations in this example, you could just as easily use a technique like dynamic time warping.
Below is an example with SPY, TLT, GLD, SLV, IWM, VNQ, VGK, EEM, EMB, using 252 day correlations as the distance measure, calculated every Monday. The motion chart lets us see not only the distances between each ETF at one point in time, but also how they have evolved.
Some interesting stuff to note: watch how REITs (VNQ) become more closely correlated with equities during the financial crisis, how distant emerging market debt (EMB) is from everything else, and the changing relationship between silver (SLV) and gold (GLD).
Here’s the same thing with a bunch of sector ETFs:
To do MDS at home: in R and MATLAB you can use cmdscale(). I have posted a C# implementation here.
When I was first starting out a couple of years ago I didn’t really track my performance beyond the simple report that IB generates. Eventually I moved on to excel sheets which grew to a ridiculous and unmanageable size. I took a look at tradingdiary pro, but it wasn’t flexible or deep enough for my requirements.
So I wrote my own (I blogged about it here): on the one hand I focused on flexibility in terms of how the data can be divided up (with a very versatile strategy/trade/tag system), and on the other hand on producing meaningful and relevant information that can be applied to improve your trading. Now I have ported it to WPF and removed a bunch of proprietary components so it can be open sourced. So…
I’m very happy to announce that the first version (0.1) of the QUSMA Performance Analytics Suite (QPAS) is now available. For an overview of its main performance analysis capabilities see the performance report documentation.
The port is still very fresh so I’d really appreciate your feedback. For bug reports, feature requests, etc. you can either use the GitHub issue tracker, the google group, or the comments on this post.
While the IB flex statements provide enough data for most functionality, QPAS needs additional data for things like charting, execution analysis, and benchmarking. By default it uses QDMS, but you can use your own data source by implementing the IExternalDataSource interface.
Currently the only supported broker is Interactive Brokers, but for those of you who do not use them, the statement importing system is flexible: see the Implementing a Statement Parser page in the documentation for more.
I should note that in general I designed the application for myself and my own style of trading, which means that some features you might expect are missing: no sector/factor attribution for stock pickers, no attribution stats for credit pickers, dailyfrequency calculation of things like MAE/MFE (so any intraday trades will show zero MAE/MFE), and no optionsspecific analytics. All these things would be reasonably easy to add if you feel like it (and know a bit of C#), though.
Features:
 Highly detailed performance statistics
 Expost risk analytics
 Benchmarking
 Execution analytics
 Trade journal: annotate trades with rich text and images
Requirements:
Screenshots:


Performance overview


Pertrade stats


Monte Carlo simulation, with equity curve confidence intervals and max drawdown distribution


Benchmarking


Execution analysis


Expected shortfall


Trade annotations with rich text and images


Trade overview


Maximum adverse excursion (MAE)


Relative capital usage by strategy


Performance by instrument


Average cumulative returns per day