[dc]T[/dc]raders and investors are often unprepared for the variability of their trading results. This is difficult on many fronts. First, and most obviously, perhaps you won’t make as much money as you “should” from trading your system, or maybe you will make a lot more. Maybe your system will seem to stop working for a time. (And if so, how will you separate “for a time” from a more serious permanent breakdown in the methodology?) This variability can also make evaluation your results very difficult, and can hide the truth of your and your systems performance. Consider the following trading system.

- Risks a fixed amount R per trade. For the purposes of this discussion, R = $2,000.
- Losses are always exactly -1.0R and wins are always +1.2R.
- The system wins 50% of the time, loses 50% of the time, and has no breakeven trades.
**The expectancy of this system is positive, and is 0.1.**(Win percentage * Average win) – (Loss percentage * Average loss) = 1.2 * 0.5 – 1.0 * 0.5 = 0.1.- This means that for every dollar risked, on average, we receive that dollar back, plus another $0.10. Over a finite time span, results can be much more variable than this would suggest.

Now, assume that you have to trade the system and assume that you will trade it for 250 consecutive trades with a $100,000 starting account, risking $2,000 per trade. What results do you expect? On average you “should” end up with a total account value of $150,000 at the end of 250 trades, but how sure are you? Could you lose money trading this positive expectancy system?

Take a look at the following chart, which shows the results of 100 traders trading 250 trades of the exact same system. (A useful way to think about this is to think that these traders were maybe working in parallel alternate universes. Each run is completely independent of the others.) No trader made any mistakes or errors. The only difference was the random distribution of wins and losses, with a 50% probability on each individual trade. The blue arrow shows the expected value of the system, and we see that many of the traders ended up in that neighborhood, but results, as they say, vary. Some traders doubled their money, and one, out of this sample of 100, very consistently lost money even though he made no mistakes and was trading a positive expectancy system. That is a critical point–no one made any mistakes here. No one held a loser past its stop point, no one got emotional and took “bad trades”, and no one made any execution errors. The variability in these results is all due to normal statistical fluctuation–the slings and arrows of outrageous fortune, as the Bard said–and your own trading (and backtesting) will be subject to the same laws of nature. We’ll explore this in more depth in future blog posts, but, for now, spend some time trying to consider the performance of the top and bottom group of traders, the different impressions they might have had of the system and of their own performance.

Takeaway #1: our long-term success as traders depends more than anything on the degree to which we understand and accept how much randomness is involved, and the way in which we plan for and react to the inevitable random fluctuations in our results.

Takeaway #2: you’d have to be nuts to risk 2% of your account on each trade using a system where the expectancy is 0.2%. Which leads to an interesting question: what is the maximum acceptable per-trade risk expressed as a multiple of expectancy?

#1: Yes, I think that is a very important point.

#2: Maybe. My book includes a chapter looking at different risk levels for this particular system, and 2% is not outrageous… you just have to be prepared to accept that there will be some extreme variability. There are some answers to this question, and I’ll explore them in a future blog post.

According to the Kelly Criterion, bet size should be about 1% for this strategy.

There are issues with Kelly in actual trading, but this theoretical example is a case where you could apply Kelly. The Kelly number is quite a bit higher than 1% in this case though.

I thought for a 50/50 system Kelly says bet nothing.

That is if the return and losses matched as well

I find this to be the most discouraging part of trading. How many trades do you need to be able to assume at P95/99 that your system is profitable at all, expectancy > 0.1, >0.15 etc.

Even worse if you trade different set-ups. Maybe you are profitable on a few and not on others.

Even worse, and as Adam mentions, what about your errors (positive/negative), learning curve, moods/flow and others that will influence your trades over a time frame affecting the statistical significance of your results so far…

This is very tough and I find it even hard when I am overall positive and then see a few set-ups not working at all, although they looked as “brilliant” as the ones before…

Good points here, and you’re asking many of the right questions, in my opinion. (I think thinking in terms of confidence intervals is one useful path.) I’ll probably use some of your question in a future post. Thank you!

The blog post is already 2 years old, but I have to come back on it…

I re-created your results in a MC analysis and it would see around 7% of all traders end up losing. But beyond that, there is another aspect which makes things even more challenging… let’s call it streakiness. I introduced a new factor, basically if your last 10 trades were net positive you’d had a 60/40 probability ratio on the next trade and if they were net negative it was 40/60, with the same pay-outs. The mean value does not change, but the extremes do. The probability of a negative return after 250 trades was now around 20% – on a profitable system after a decent number of trades…

I worked on a system which performed very well over the past 8 years, but I am somewhat reluctant to put it into practice after seeing it under-perform in the 07-09 bear market.

Hi irdoj75.

Can’t tell about the usefulness of your specific system -unfortunately- but, your analysis makes sense as long as some bias is assumed; I mean, after having a bad series of trades, proper psychology would invite you to take a break and start from scratch so, there’s probably no reason no assume worse odds (40%) in that case. In a similar manner, assuming better odds (60%) after a series of successful trades somehow implies accepting the “hot hand” theory which, I believe has been proven to have no statistical grounds at all.

In any case, under a conservative scenario, I’d probably be biased myself towards modelling the downside (40% success after a bad streak…a very real situation for newbies like me) but not the upside (so 50% success rate max. in all cases). Other traders would think differently but, Adam’s approach was the statistically neutral one.

Good stuff. Regards.

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That’s the nature of trading. Not everyone has the volume or patience for duration.

Great post. One part of the system here is that the wins are always 1.2R and never higher than that. A system with a 50% win rate and no outsized wins time to time definitely will pose some serious drawdowns ( > 10 consecutive losers), compounded by small execution errors, etc. If the average win is 1.2R, but there’s a possibility of outsized wins, would that 1 out of 100 loser still happen?

The -1.0 and 1.2 assumptions are simplifications, but they could also be averages. In other words, if the wins varied in size with a mean of 1.2, you’d have substantially the same outcome. We’ll look at some variations of this concept in future posts, but, even with outsized wins, you can still have very severe drawdowns. The message is the same: most people are unprepared for the kind of variability we’ll see in trading returns. Thanks for your question and your kind words on the post.

short answer: yes. if the 1.2 and 1.0 were means instead of fixed sizes, the results would be more or less the same, though with more variability.

I know this is a year old discussion Adam, however, why would the 1.0 side of the equation be a mean? For purposes of the discussion, we have a stop, it’s 1.0 and we don’t touch it. Ignoring jumped stops, why can’t we have outsided wins and keep our losses at 1.0?

Isn’t manipulating the balance of the series, ALL our trades this year, the whole point of this profession?

Now how does that change the result?

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what if the traders do not risk a fixed R = $2k per trade, instead, the trader risk 1% of his account for each trade? Does any of those traders will still lose money?

I think you emailed me (or someone emailed with virtually the same question). I addressed this in considerable detail in my book. The losses would be less, but some of the runs did end up negative. Money management, by itself, isn’t an edge. Even with an edge, you can get unlucky.