Tuesday, August 31, 2010

The Pain Index : A Measurement of How Hard it is to Trade a System from a Psychological Perspective

It is always said - with very good reason - that the biggest obstacle to trading systems profitably is the trader him or herself. There are many reasons why this is the case but perhaps the large amount of self-sabotaging, the inability to trade through draw down periods and the second-guessing about the profitability of different strategies is what makes unprofitable people turn their accounts into dust in the longer term. It is therefore interesting to ask ourselves if there is a way to measure this psychological hardship and estimate if a given system will or will not be difficult to trade from a mental stand point. It becomes clear that some systems - even if account wiping in the long term - are very psychologically easy to trade while systems that are very robust and long term profitable tend to be extremely hard to trade (and therefore almost never traded).

On today's post I will share with you my solution to this problem - the pain index - which is a measurement of how hard it will be - from a psychological point - to trade any given system. This scale gives us a quantitative way of comparing trading systems and it allows us to easily picture how easy or hard it will be to trade a given strategy in the long term. The lower the pain index, the easier a strategy will be to trade while strategies with a higher pain index reading will be excruciating and tremendously difficult to follow. Now bear in mind that the pain index does NOT tell us anything about profitability and there can be systems with extremely low pain index readings that will wipe accounts (as there are in real life), the pain index merely attempts to measure the psychological pressure on the trader rather than the ultimate effect on the account balance.

When attempting to come up with a measure to calculate how hard it is to trade a given system it became obvious to me that the most important factors were the maximum ten year draw down of a strategy and the maximum draw down period length. Trading systems with higher draw downs or longer draw down periods are harder to trade and the combined effect of these characteristics should be shown in any attempt to calculate the "pain" different strategies cause a trader. However it then became clear that both of these parameters do not have the same effect as deeper draw downs are much more important from a psychological point of view than longer draw down periods. Most traders would be able to bear a 1 year draw down period with a maximum draw down at 5% while doing the same thing with a 30% maximum draw down will be significantly harder.

After doing this analysis I came to the conclusion that maximum draw down should increase difficulty exponentially while draw down period length should do so linearly. Since the above introduces an exponential term I decided to use a logarithmic function (base 10) to normalize the pain index to values that would be between 0 and 10. The formula for the pain index calculation is shown below :

MD = maximum 10 year draw down as a percentage of account equity

MP = maximum 10 year draw down period length in years

pain index = 2*(Log( MD^2 * MP))

The scale goes from 0 to 10 since 0 is a hypothetical system that never loses (a system that would be extremely easy to trade, a system that doesn't exist) while 10 is a system that loses all trades within a ten year period except the last one which takes the account back into profit. So the easiest system to trade is a system that never loses while the hardest system to trade is a system that has a maximum draw down close to 100% and a maximum draw down period length close to 10 years (a system that would be effectively impossible to trade from a psychological standpoint).
As you can see on the above graph which shows the evolution of the unnormalized (without the longarithm) pain index as a function of maximum draw down and draw down period length you can see how deeper draw downs increase the pain index rapidly while the duration of the draw down causes a linear increase. Now pay special attention to the fact that you can have systems with draw downs that can be extremely deep (even close to account wiping) but if their draw down period length is very small (just a few weeks or days) the actual pain index will be low. This is the reason why martingales and scalpers with very bad risk to reward ratios are so successful, even though these systems are dangerous to capital preservation and overall long term profitability they are extremely easy to trade from a psychological stand point since draw downs rarely happen and psychologically challenges will only come very sporadically (and perhaps when they happen the account will be wiped). It is fairly easy now to understand why these systems are tremendously dangerous, very easy to trade from a psychological perspective but extremely dangerous for account equity.

The obvious thing now was to take this new pain index measurement and calculate its value for several Asirikuy systems, risk levels and portfolios to see the actual difficulty to trade the different systems I use in live accounts. The results are actually very interesting and they do reflect the psychological difficulty in trading all these systems. Below you can see a scale showing several examples and their pain index values :

0 - system that never loses (does not exist)

2.59 - Watukushay No.2, Risk 1 EUR/USD

2.93 - Atinalla No.1 Portfolio (Risk 1 on all systems)

3.07 - Teyacanani, Risk 1 EUR/USD

3.60 - Watukushay No.5, Risk 1 USD/CHF

5.08 - Atinalla No.1 Portfolio (Risk 3 on all systems)

5.51 - Kutichiy EUR/USD Risk 1

5.79 - EUR/USD Turtle Trading System (original rules)

5.99 - GBP/USD Kutichiy Risk 1

6.71 - Kutichiy (EUR/USD, GBP/USD, USD/CHF, USD/JPY) (Risk 1 on all instances)

10 - system that loses everytime for ten years except on one trade that takes it to profitability

It is very interesting to see how this indexing falls in line with what we experience with the real live systems. The turtle trading system is extremely difficult to trade while systems like Teyacanani are far easier to use. Since this scale is logarithmic the pain index predicts that it is about 10 thousand times easier to trade teyacanani with a Risk = 1 setting than to trade the Turtle trading system on the EUR/USD. Shorter draw down periods and small maximum draw downs account for this difference. Of course we can also see the effect of increasing risk and how trading Atinalla No.1 on a Risk = 3 is almost 100 times worse psychologically than trading it from a Risk = 1 setting (due to the 3 fold increase in the expected maximum draw down). Overall it seems that systems with pain index levels above 6 start to become extremely hard to trade since they would put enormous psychological pressure on their use both through long and deep draw downs.

I hope that you can use this new pain index measurement to get an idea of how hard it will be to trade your systems from a psychological stand point, it will also help you understand why you have traded systems with unsound trading tactics in the past and how this is justified through the "small pain" that these unprofitable systems cause traders. This also shows that long term profitable systems - especially when aiming for yearly profits above 30% - are extremely hard to trade and why very few people actually achieve long term profitability from automated trading systems.

If you would like to learn more about automated trading and how you too can learn how you analyze systems in depth and come up with reliable long term profit, draw down and worst case scenario targets please consider joining Asirikuy.com, a website filled with educational videos, trading systems, development and a sound, honest and transparent approach automated trading in general . I hope you enjoyed this article ! :o)


Maxim said...


Thanks a lot for finding a mathematical way of expressing the psychological pressure! I agree with your division of pressure to exponential and linear ones.
Could you please post the God gift ATR numbers for risk 1 and 3?


Daniel said...

Hello Maxim,

Thank you for your comment :o) I am glad you agree with the calculation method. I think I will be doing a video on Asirikuy where I will include values for other systems and combinations as well as some calculation examples. Thanks again for your comment Maxim !

Best Regards,


Andrea said...

thanks Daniel, this is very good post.

Daniel said...

Thank you for your comment Andrea :o) Always nice to have you around !

MJFX said...

Hi Daniel,

Seems I did not manage to get it right. I got a negative answer.

Pain index = 2*(Log( MD^2 * MP)) Pain Index = 2*(Log( 42%^2 * 2.5%)) = -4.7
42% drawdown
3 months drawdown period / 10 years=2.5%

Could you please advise?



Daniel said...

Hello MJFX,

Thank you for your comment :o) You're not doing the calculation correctly :

3 months are 0.25 years. Remember that MP is the maximum draw down period length in YEARS.

Pain index = 2*(Log( MD^2 * MP)) Pain Index = 2*(Log( 42%^2 * 0.25)) = 5.28

The pain index for this system is 5.28. I hope this helps !

Best Regards,


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