Lies, Damned Lies, and Average Returns

by Sep 1, 2016All Articles, Technical Analysis

Mark Twain popularised a famous saying that he attributed to the British Prime Minister Benjamin Disraeli: “There are three kinds of lies: lies, damned lies, and statistics”. As I’ve been focused so heavily on Signal Testing throughout 2016, I’ve been learning more and more about average returns. I want to change that quote to “lies, damned lies, and average returns”. I’ll explain why, and how we can fix the problem in a moment. First I need to explain a bit of the history that led us to build the Optuma Signal Tester.

The Signal Tester journey started for me in 2014 when I was running some backtests on RRG angles. I’d been thinking of the RRG as a compass and I wanted to know if a tradeable system existed by executing from different angles on the RRG (see my “Buying out-performers is too late” research paper for those results).


My first test, with an account size of $10,000, gave me some good results. Great! Let’s see what happens if I increase the capital to $100,000. Surely I would get a proportional lift in the results? What actually happened is that the results went down! What the? That didn’t make sense. On came the programming hat. I started to dig and look at what was happening.

I Got Lucky

It turned out that in the initial test I was victim to one of the fundamental flaws of backtesting. My position size was out of proportion with the starting capital. This meant that on a day where I had six signals, I only had enough capital to take three. Adding the extra capital meant that more signals (in this case the bad ones) were considered. Another term for this is “Path Dependency”. That is, my result is dependant on picking the right “path”—or combination—through so many rules.

In trading that’s life. We usually can’t take every signal. At this stage of my research though, I wanted to know if the signal was good (or at least better than others I’d been using). The more I thought about it, the more I realised that traditional backtesting (including the way we do it in Optuma) is taking a Buy Signal, a Sell Signal, position sizing, starting capital, pyramiding rules, stop losses and targets (let alone leverage), and throwing it all together to see what we get. That’s just way too many axis of freedom in one single test to be scientifically valid.

Bring On The Innovation

I wanted to know whether my signal was good or not. To get that answer, I needed to build the Optuma Signal Tester. This was great. It found every single instance of the signal and measured the returns over the 30 days following the signal. It then averaged up the returns to give me a wonderful average return number. Whoo-hoo, High-5’s all ‘round! At this point I was quite pleased with myself. I showed what we had done to Kirk Northington and Carson Dahlberg of ND Research in Charlotte, NC. These guys are the absolute world-leaders at taking Technical Analysis and thinking about it in a Quantitative way. I wanted to get their opinion on the Signal Tester.

Oh Boy! It really was one of those times where they smiled, patted me on the head (well, not literally, that would have been weird) and said, “Great Start, but what’s behind the average?”  Huh? They patiently explained that an average is made up of lots of results, but our confidence in achieving the average needs to be explored. It’s easy to forget that an average is made up of lots of values. Talk about a BFO (Blinding Flash of the Obvious). It’s so easy to forget that summary statistics are a guide, not a certainty.

The spread of those values determines how valid the average is. For example, these two number sets have the same average (49,50,51) and (0, 50, 100), but the first series gives us much more confidence that the next value will be close to the average. The second set will get the same average, but the volatility is huge.

Anscombe’s Quartet

As a reference of how dangerous statistics can be, you should have a look at Anscombe’s quartet. It does a great job of explaining how four sets of values can give the exact same summary statistical results. It’s obvious to us that the results are different, but that information is hidden by the statistics.

Anscombe’s Quartet

The key point is that we need to look into the results to see what the results are made up of. If there is only one thing you take away from this post, please let it be that you need to be suspicious when someone quotes you an average return from tests or trading results. Sure— they may have a 10% average return from their RIA—but what is the spread of the trades? Did they just get lucky on one big trade? Or are they consistently getting returns with a low spread?


You need to be suspicious when someone quotes you an average return from tests or trading results

Armed with that revelation, we set about designing the new updated Signal Tester.

We’ll cover a lot of the different sections over the next few weeks, but by far the most important inclusion is the Profit Analysis chart which lets us look inside the average returns.

mv_01_Sep_2016_img4This chart takes all of the returns for each of the signals and puts them into half percent buckets. It then counts how big each “bucket” is and plots it.

In the Profit Analysis chart, we want to see a “High and Tight” distribution. This is telling us that there is a significant number of signals that are supporting the average. If the distribution was “low and wide” then we know that the likelihood of future signals landing near the average is very low.

Won’t Both Produce The Average?

It could be argued that over time you will eventually get the same result if it was High and Tight or Low and Wide. My response would be that a Signal that has a High and Tight profit analysis is going to make it a lot easier to sleep at night. Particularly if you are managing someone else’s money. It is more important to have a high probability of making small profits, than it is to make one big profit (Lottery Trading). I want signals that give me a much higher probability of hitting the average every time I enter a trade. If a new signal can get me the same result with half the volatility—I’m taking it!

The other thing I want to see is the peak of the distribution skewed to the right. This one is slightly. That’s telling me that every time I take this signal, I am more likely to turn a profit than a loss.

Next time we’ll dig into the Statistics on the Signal Tester. I hope you now understand why I now group “average returns” with lies and damned lies. The average return is an important number that helps compare one system versus another, but there is important information that can be hidden behind the average. My hope is that being armed with this knowledge will help you avoid being duped, and also help you examine your own strategies in a new way.

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Mathew Verdouw, CMT, CFTe

Mathew Verdouw, CMT, CFTe

CEO / Founder Optuma

As a Computer Systems Engineer, Mathew started Market Analyst (now Optuma) within 18 months of completing his degree. From that point on, Mathew has made it his mission to build the very best software tools available.

Since 1996 Mathew has been learning about all aspects of financial analysis, and in 2014 earned the CMT designation (Chartered Market Technician). In 2015, he was also awarded the CFTe designation. In 2017, Mathew started to teach the required content for the CMT exams at He is the only person in the world who teaches all three levels due to his broad exposure to all forms of financial analysis.

As someone who has dedicated his life to find better ways to analyse financial markets, Mathew is set to drive innovation in this sector for many years to come.


  1. David Williams

    Great stuff Matthew.

    How do you determine the exit in the signal tester? It’s not very flexible entering this.

    • Mathew Verdouw, CMT, CFTe

      Hi David, Thanks for that.

      The thing with the signal tester is that there is no exit (until it runs out of time), my goal with it is to look at the signal in complete isolation from all other rules (including exits). With those results I can make much better decisions about how to set up my strategy. For instance, if the main result plot shows me a sharp initial rise and then it flattens after 10 days, I can determine that I should have a 10 day time stop on this since I have a higher probability of returns by exiting and finding other opportunities.
      So armed with this knowledge, I can start to plan whether my exit should be a different signal, a time stop or a price target. I can also determine what my position size should be based on the number of signals I am getting, if I only get one signal a month, then “load the boat”. I can then take all of that knowledge into the BackTester and run some meaningful tests.

      The Signal Tester does not replace the Back Tester but it is a powerful first step.

      All the best


      • David Williams

        Ok Thanks Matthew.

        I’ve been running the signal tester on a weekly system and for 4 weeks before, 52 weeks after so it’s a bit harder to judge an optimal timeframe there. Perhaps I would be better off using the backtester.

      • Mathew Verdouw, CMT, CFTe

        Hi David,

        Is your hold time typically a year? If so, then setting it up like that makes sense. Trending strategies, which are slower to enter but catch larger trends, need the longer hold periods. It would be more a set and forget strategy where you only periodically monitor the positions. There is not usually a lot of Alpha in that though as it is generally catching the whole market trends. With our Optex Bands that we released in Optuma, we were looking for mean-reversions that would give us significant Alpha for a short period (7 days seems to be the best). We intend to create a Testing Course on that really digs in to understanding all these concepts.

        I do agree that a Backtest is probably better for the really long tests, but only once you are sure that your signal is making sense.

        All the best


      • David Williams

        Thanks Matthew. I will ride a trend until it hits my stop – why get out early if it’s trending and building profits. Some really good moves can run for years. Let your profits run and cut your losses short.

        And yes – I was wanting to use the signal tester to validate my scanning criteria and then use my usual trading rules to manage a trade and use the backtester. For instance I was running a test using varying EMA’s and HighestHigh values to determine the best/most profitable combination. I was doing this in the signal tester over a 1 year period after the signal – so given I can’t set a real stop in the tester I would be better off running it over 1 month after signal. I can then introduce other criteria and finally use the back tester.

        Thanks for your reply which I had missed until now.

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