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The recent threads about "7%" and SilverDragon's thread about an auto meltdown got me thinking,

I'd like to do some research/study to illustrate (and prove to myself) which risk equivalents are more prone to larger drawdowns. Maybe I'll discover I was mistaken and there's no difference.

I refer to "risk equivalents" as systems that have the same overall outcome but different (win%*R:R) factor.

I'd like to show whether or not, an increasing (or decreasing factor) has any effect on potential drawdowns.

I guess there's a couple of ways to do this....

If we could do a sample set of 10,000 trades, then we could Monte Carlo and either determine what the mean and median drawdown is for each system with varying factors,

OR we could calculate the probability of a $10k drawdown for each system.

I'm thinking that the average drawdown will be the same, but the drawdown volatility (how wide a shot group) will be higher for systems that feature low win rates, but high R/R ratio, as those systems feature a large percentage of losers that can string together easily during large sample sets.

"A dumb man never learns. A smart man learns from his own failure and success. But a wise man learns from the failure and success of others."

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For Estimating Drawdowns Information on the Variance of Returns is Required

You just mentioned win rate and R-multiple. This does not tell you anything on the dispersion or variance of the results, so it is basically not sufficient to study drawdowns.

For example, if you have 50% winners with a R-Multiple of 1, then the expectancy is zero. But that expectancy could be the results of trades of -20 points and + 20 points, or - 2 points and + 2 points, which is certainly not the same in terms of drawdowns.

Comparing Win Rate and R-Multiple for Equal Expectancy

I understand that you want to understand, whether win rate or R-Multiple have a larger impact on drawdowns and risk-adjusted returns. To find this out you do not need Monte-Carlo simulations, but can use our simple model for Bernoulli distributions.

A Monte-Carlo simulation is needed, if you add information on the variance or if you study a real series of trades with more than two different outcomes.

An example with zero expectancy is difficult to be used for any model, as the time to reach a target will be infinity. It is a non-sense in terms of risk-adjusted returns.

I will do a quick simulation for a Bernoulli distribution with a second post.

The following 3 users say Thank You to Fat Tails for this post:

I'm just trying to get a sense if there's any drawdown advantages to equivalent outcome systems......

In essence, I'd like to verify or compare if a system that's 33% win rate and a 2:1 RR, has more potential for extreme drawdowns than a system that's 66% win rate and has a 1:2 RR.

I realize that they're a zero outcome, I was trying to avoid disparity with the performances.

Choose whatever Risk and Reward values you like, whole numbers, etc.

So to compare the drawdown potential for system that features a 33.333% win rate, and risks $100 to make $200,

vs. a system that features a 50% win rate, risks $100 to make $100

vs. a system that features a 66% win rate, risks $200 to make $100

Over the course of 10,000 trades, all of these systems should perform relatively closely (in terms of net profit) and ideally, they should be near zero....

I just want to see, if moving to either side of the 50% win rate, creates a propensity for more volitile drawdown results.....

In essence, does featuring a lower win rate with a higher RR give you less drawdown risk than a higher win rate with lower RR?

"A dumb man never learns. A smart man learns from his own failure and success. But a wise man learns from the failure and success of others."

I'm just speculating (with my intuition, which may be wrong) but I'm suspecting that a higher win rate with a smaller RR ratio wil feature a drawdown distribution that's tall, with skinny tails, and a lower win rate system with high RR ratio will feature a more broad distribution with fat tails.

I may be wrong, we may find that the distribution is the same....or reversed.

"A dumb man never learns. A smart man learns from his own failure and success. But a wise man learns from the failure and success of others."

Obviously, the value in this, is recognizing whether or not you're more likely to see out of tolerance drawdowns on low win rate systems or high win rate systems.

The 2nd order implications are trader psychology. Van Tharp discusses in length the human necessity to be "right" more often than not, even though in trading, that's often not a tendency for success.

We've also heard numerous times that the majority of successful (long term) traders feature approaches that have a less than 50% win rate with some RR ratio higher than 1.

The 3rd order effect is drawdown fatigue.....and peak/peak times for profit peaks.

I've developed systems that I rejected, simply based upon the fact that I know myself and I'm more likely to lose discipline and patience with a system that features extended (time) drawdowns and extended periods between profit peaks. Not many people can trade consistently with a max peak to peak time of more than a couple of weeks.....when you start talking about months....that's asking a lot to endure without going stir crazy and changing something. In essence, it makes the execution more difficult because of human factors.

"A dumb man never learns. A smart man learns from his own failure and success. But a wise man learns from the failure and success of others."

(1) I have an account with $ 50,000. I will trade until I have reached my target account size of $ 100,000. My risk tolerance is 0.1% for a drawdown of 50%, which I consider being equivalent to ruin.

(2) I am reinvesting returns, which translates into fixed-fracitonal position sizing.

(3) I will trade a simple system, which will only produce two results. Either there will be a winning trade with profit X or a losing trade with loss Y. I will call P the probability of a winning trade and Q = 1 - P the probability of a losing trade. The R-Multiple X/Y is obtained by dividing the profit of a winning trade by the loss of a losing trade. I am therefore sticking with a Bernoulli distribution, which can easily be modeled.

(4) I will NOT take into account slippage and commissions in a first step, as I only want to study the impact of win rate and R-Multiple on the risk-adjusted returns.

(5) I will compare 3 trading systems, which have identical expectancy, but different win rates and R-Multiples.

System A :

average win 10 points
average loss 10 points
win rate 60%
expectancy per trade = 0.6 * 10 points - 0.4 *10 points = 2 points

System B :

average win 20 points
average loss 10 points
win rate 40%
expectancy per trade = 0.4 * 20 points - 0.6 * 10 points = 2 points

System C :

average win 30 points
average loss 10 points
win rate 30%
expectancy per trade = 0.3 * 30 points - 0.7 * 10 points = 2 points

For the model I will further assume that 1 point has a value of $ 5 (such as for YM), but this is not important.

Results:

The results are based on the acceptable risk of ruin. Depending on observerd drawdowns I am allowed to leverage the position such that the probability of a drawdown of $ 25,000 is equal to 1%.

System A:

I am allowed to trade 36 contracts for an accepted loss per trade of 3.6%. I should reach my target account after 97 trades.

System B :

I am allowed to trade 18 contracts for an accepted loss per trade of 1.8%. I should reach my target account after 193 trades.

System C:

I am allowed to trade 12 contracts for an accepted loss per trade of 1.2%. I should reach my target account after 289 trades.

This means that the system A - due to a lower frequency of losing trades - produces smaller draw downs and can therefore be traded with a higher leverage than the other two systems.

The following 9 users say Thank You to Fat Tails for this post:

Yes!! I've found that my best looking systems from backtesting are skewed towards larger R:R and lower win rate. And then when I think through the scenario of trading them I know I would struggle to stick with them for the exact reason you point out - how long can you hold your breath 'underwater'?

know thyself

The following user says Thank You to mokodo for this post:

So if I were to graphically depict this so that they lay person could understand more easily, it would look something
like a skewed distribution for system A that's tall with a skinny tail, a skewed distribution for system B that's shorter with a fatter tail and a skewed distribution for C even shorter with a fatter tail?

In summary, the odds of experiencing greater than 3 sigma drawdown are higher with a low win rate system (compared to a higher win rate system) that produces similar/exact profits?

"A dumb man never learns. A smart man learns from his own failure and success. But a wise man learns from the failure and success of others."

I have always had a problem with a 3-sigma event. As we know, sigma stands for the standard deviation, which is a concept that makes sense, if returns are normally distributed. However, if we built a trading system, the last thing we want is that normal distribution, which tells us that in the end we will have just paid commissions.

The notion of a R-Multiple even implies, that the returns are not symmetrical, so I do not want to use a measure which calculates a mean variance irrespectively whether the deviation from the mean is positive or negative. The actual risk depends on the variance of the losing trades and not on the variance of the winning trades.

A drawdown is the result of a series of N trades. The worst case is N losses, which produce the maximum drawdown. If we execute 100 trades, it is not very likely to have 100 losers, so the worst case scenario is not really interesting. What we can do is

brute force method: produce a simulation of all possible trade sequences of the 100 trades (switch on your PC and come back next year)
Monte-Carlo method: select trade sequences at random and draw them

In both cases eliminate the lowest percentile, if you can live with a 1% probability that your maximum acceptable drawdown is actually hit. The worst remainig case is your bottom line. You can now leverage to adjust it to your maximum acceptbale draw down.

Now to your question with the distribution. All three systems are Bernoulli distributions, so they are quite boring to depict. You will only get two columns one for the wins (always the same amount) and one for the losses (always the same amount).

What you had in mind was probably the distribution of a series of N trades. If N becomes a large number, then you may deduct from the Central Limit Theorem that the distribution of the sum or the mean of the sample population approaches a normal distribution.

You don't have any luck here, there are no Fat Tails to come to your rescue. The difference between a series of N trades for the models A, B and C is not that one is more skewed than the other, they are not skewed at all. The difference comes with the variance of returns of a series of N trades. System A has the lowerst variance allowing for higher leverage.