OK, so you want to know if your new strategy is performing to expectations, right?


There is a simple way, and a complicated way. Today I'll look at the simple way.

The only data you need for this is the average trade, or average daily result. It you have the standard deviation of this value, then you can do even more.

All you do plot your results, along with the equation "n * avg" where n is the trade number/day, and avg is the average value. You'll get a chart like this:





So, if you are above the average line, your strategy is doing better than you thought. If below, your strategy is worse.

This chart becomes really useful as time goes on. Over 30 or more periods, you'd expect the strategy to be right around the average line. That is how I use it. For each strategy I am tracking, I simply plot the results with the average line. I do this every month. Then, at a quick glance, I know the general state of the strategy. Here is an example of a strategy I have been running live a few years. I consider this "good performance, as expected." Note how it rubber bands around the average line.






This is nice, but it doesn't convey a lot of information, especially early on. To get more insight, add 2 lines for the +/- standard deviation curves:

Upper curve: n*avg + sqrt(n)*(std dev)*X
Avg curve: n*avg
Lower curve: n*avg - sqrt(n)*(std dev)*X


What this tells you is that roughly 68% (X=1) or 95% (X=2) of the time, your equity curve should be within the upper or lower bands. That is a pretty good range of performance. If it is outside of those bands, maybe there is something going on with your strategy.


Here is what my Combine system looks like with X=2 bands:





The most interesting point here is that bottom curve. Look as it starts negative, and stays negative. Imagine that! A winning (positive expectancy) system can still have negative results for quite a while. Pure random chance (the order of trade results) can lead a winning system to appear to be a losing system.

Of course, over time, the positive expectancy starts to dominate, and the lower curve should turn positive.

This has HUGE implications for the trader who "tweaks" his method if, after 5 trades, he is not showing a profit. He may well have just changed a winning system!

Here is a great quote that explains it better than I can. It is from the book "Trading Bases:"

"Well, if you had the opportunity to invest in a venture with a positive expected value, like ownership of a roulette wheel, would you prefer to own it for one hour or nine and a half hours? Funny things can happen in one hour; there is no guarantee of a profit even with the house edge. But over nine and a half hours, the natural fluctuations inherent in the game will smooth out, and the chances of losing money will be very small, approaching zero over time."

The dotted red average line in Fig. 2 appears to be a straight line, which is exactly what I'd expect it to be.
The black average line in Fig. 1 and 3, however, appears to have a changing slope. Is it because your X axis is Trade Day, whereas n in your n*avg formula is actually Trade Number?

Trovatore 

The dotted red average line in Fig. 2 appears to be a straight line, which is exactly what I'd expect it to be. The black average line in Fig. 1 and 3, however, appears to have a changing slope. Is it because your X axis is Trade Day, whereas n in your n*avg formula is actually Trade Number?

Good Catch. I had the wrong curve representing the "average" line (it was the Monte Carlo simulation average line.)

Here is the corrected version.

Sorry for the confusion.

kevinkdog 

Good Catch. I had the wrong curve representing the "average" line (it was the Monte Carlo simulation average line.) Here is the corrected version. Sorry for the confusion.

Thanks, it's very clear now.
One more question, if I may ask. If you find after a reasonably large number of trades that the actual line tends to rubber band not around the average line but rather around a less favorable line (but still inside the 95% or even the 68% range), how do you decide whether you are just being unlucky or you maybe got the expectancy wrong (i.e. it rubber bands around a true expectancy which is different from how you had assessed it during your system development and walk-forward testing)?

Trovatore 

Thanks, it's very clear now. One more question, if I may ask. If you find after a reasonably large number of trades that the actual line tends to rubber band not around the average line but rather around a less favorable line (but still inside the 95% or even the 68% range), how do you decide whether you are just being unlucky or you maybe got the expectancy wrong (i.e. it rubber bands around a true expectancy which is different from how you had assessed it during your system development and walk-forward testing)?

That is a very good question. Many times, the historical walkforward performance (what I plot as the "average" line) is not what you get in real life - usually there is some degradation, which like you said is really a change in expectancy. This would show up as a shallower sloped "average" line.

Another thing could happen too. The market could change at some point, which might have a dramatic impact on your system. Say for example we go into a super low (or super high) volatility mode - one that had never been seen historically. Your system's performance may not be close at all to that average line.


So, the question becomes: how can you tell when the system you are trading is statistically different than the system you historically tested? Given my aerospace quality assurance and engineering background, I can tell you what I do, but there are many other ways to do it too.

I use something called Statistical Process Control (SPC). It helps you determine when a process (trading system) goes out of control, and gives you indications that corrective action (stop trading, change strategy, etc) is necessary.

SPC can be really complicated, and there are books and courses out there that can explain it much better than I ever could.

I hope this explains it a little bit. In the situation you are describing, as long as the real time equity line was still within the upper and lower line, I'd probably keep trading it as is.

hi Kevin,

i think i have some confusion on your average curve ( "line" ) - Why not should it be of variable slope, i mean i feel it should not be of constant slope. As the time/trades passes , with each trade your average gona be change.

devdas 

hi Kevin, i think i have some confusion on your average curve ( "line" ) - Why not should it be of variable slope, i mean i feel it should not be of constant slope. As the time/trades passes , with each trade your average gona be change.

The "average" line is from the historical database of trades, so I calculate it before I start trading live. Therefore, it never changes. That let's me compare by real performance to my walkforward testing performance.

You bring up a great point. You could have the "average" line include current trades, then it would change as you suggest. You could also plot a running average of the last X trades. There are a lot of different ways to do it, especially if you wanted to incorporate recent performance.

Day 12, Heading the Wrong Way...

A good overnight trade, overwhelmed by the big loser day trade.

Passing the Combine is, at this point, probably not going to happen without some divine intervention.

I was hoping that even if I did not pass the Combine, that at least I'd be profitable. That would encourage me to trade it live. So far, I'm not seeing that, either. I'm at the 15th percentile so far. This means that the Combine performance is at the bottom end of my expectations for it. Pretty poor.


On the positive side, I have absolutely no desire to "cheat" or to do something silly (like go for broke, double size, etc). My discipline is pretty resolute - I'll stick to the system until the end...

Kevin have you been able to identify any particular market conditions or variables of your strategy development that account for the current underperformance? Do you think that the strategy will revert to the mean if implemented on a larger time scale? thanks.

chambemk 

Kevin have you been able to identify any particular market conditions or variables of your strategy development that account for the current underperformance? Do you think that the strategy will revert to the mean if implemented on a larger time scale? thanks.

Thanks for the great question. I was hoping this would come up.

I love analyzing data. Looking for trends, clues, etc. to trading performance is always fun.

BUT, my feeling is that analyzing current Combine results would be a big mistake.

Why? Simply put, not enough data. I've had 12 days of results. That is nowhere near enough to analyze and make any type of conclusions, especially when those decisions may recommend changes.

If the strategy is good, it will revert to the mean. But it may take 30-50 days to show that. That is one reason why I wait to trade a new system with real money.

If the strategy is not good, I'll probably abandon it, rather than try to figure out why it failed. My experience is that analysis doesn't necessarily help (you can always look back in hindsight and come up with a reason). As for market conditions, it should work on all markets, since I tested over all markets.

In the next few days I'll show a real world example of this. The first 100 days of that strat were pretty bad, but after that - the strategy took off.