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Risk of Ruin
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Risk of Ruin

  #91 (permalink)
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rosariod View Post
First of all thanks for your help and for your time.

For sure a Monte Carlo Analysis is a good approach to determine the probability of reaching a fraction/multiple of your initial bankroll and I’ve already done it but I would like to find a formula and then, generalizing, apply it to different trading system on the same bankroll.
If I trade k different trading system on the same bankroll with k different f(i)I would like to have a function P(X,n) that give the probability that the bankroll is X fraction after n iterations.
Is it possible to have such function or I have to use Monte Carlo Analysis.

The problems of any model / closed formula are the model assumptions. The great economists have always failed, because they have applied their models without taking into account model limitations.

I have much more confidence in an empirical approach such as the Monte Carlo Analysis, compared to a theoretical approach such as the Kelly formula. If you are interested in applying the Kelly formula to your problems, I suggest that you work through the papers and books below.....


Links to papers on the Kelly Criterion:

http://edwardothorp.com/sitebuildercontent/sitebuilderfiles/Column23understandingthekellycriterion.doc
http://edwardothorp.com/sitebuildercontent/sitebuilderfiles/Good_Bad_Paper.pdf
http://edwardothorp.com/sitebuildercontent/sitebuilderfiles/KellyCriterion2007.pdf
http://edwardothorp.com/sitebuildercontent/sitebuilderfiles/KellySimulationsNew.pdf
http://www.efmaefm.org/0EFMAMEETINGS/EFMA%20ANNUAL%20MEETINGS/2011-Braga/papers/0103.pdf

Further get some elementary knowledge by reading these books ......

Amazon.com: The Doctrine of Chances: Probabilistic Aspects of Gambling (Probability and Its Applications) (9783540787822): Stewart N. Ethier: Books
Amazon.com: The Kelly Capital Growth Investment Criterion: Theory and Practice (World Scientific Handbook in Financial Economic) (9789814293495): Leonard C. MacLean, Edward O. Thorp, William T. Ziemba: Books
Amazon.com: Scenarios for Risk Management and Global Investment Strategies (The Wiley Finance Series) (9780470319246): Rachel E. S. Ziemba, William T. Ziemba: Books


If you think that this is complicated stuff, then you should consider a Monte Carlo Analysis instead.

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A few months off, but Ernie Chan will be doing a webinar on futures.io (formerly BMT) in January that focuses on Capital Allocation and Risk management using Kelly:

https://futures.io/psychology-money-management/23249-webinar-ernest-chan-capital...nt-kelly.html#post264153

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  #93 (permalink)
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OxfordStrat View Post
P. Kaufman offers different formulas in different books. Since the source is the Ralph Vince's book "Portfolio Management Formulas", I consider Vince's formula the correct one (attachment).

I would not consider Kaufman as a reference for the risk of ruin. Ralph Vince certainly is.

The formula that you have attached looks nice, but I believe that it is incorrect. Here are the reasons. If you have a winning percentage, an average winning and average losing trade, this tells you nothing about the dispersion of the trades.

Example: Let us assume that your winning percentage is 60% and that both your average winning and losing trades are 2% of your initial capital.

Scenario 1: all winning trades yield +2.0%, all losing trades yield -2.0%
Scenario 2: 50% of winning trades yield +0.50%, the other 50% of winning trades yield +3.52%, 50% of losing trades yield -0.50%, the other 50% yield - 3.48%

For both scenarios you would have identical input variables for the model put forward by Ralph Vince, so they will both show the same risk of ruin. However, the second scenario produces a higher risk of ruin than the first one. The reason is that the dispersion of the trades around the mean is larger than for the first scenario. The model by Ralph Vince does not take into account the variance of the average winning and losing trade, but only uses the arithmetic mean. I therefore believe that both the models of Perry Kaufman and Ralph Vince are inherently flawed. Unfortunately I am not capable to come up with something better, but for further research I would rather rely on Edward O. Thorpe than Ralph Vincent.


Last edited by Fat Tails; September 23rd, 2012 at 05:04 PM.
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OxfordStrat View Post
With unknown distribution of trades, all formulas are misleading. Plus all the above formulas ignore the dynamic leverage. An example (attachment) is the portfolio of 25 futures markets -- this whale shaped "thing" starts to crack around Risk = 6% (fixed fractional sizing). When you increase the number of markets in portfolio, the "crack" shifts towards left, and when you reduce the number of markets in portfolio, it shifts towards right. I am sure you are aware of this fact, but I am always astonished how many traders have some canned answers like "never risk xx% of portfolio".

I have to admit, I am having a little difficulty understanding this.

Is there a simpler explanation? Or is it simplified as much as possible.

I had a real hard time in calculas for engineers. The instructor spoke with a thick Polish accent, so it was like learning 2 languages simlutaneously.

Do you have an explanation for art majors?

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Accounting for Variance is Scary


Fat Tails View Post
The model by Ralph Vince does not take into account the variance of the average winning and losing trade, but only uses the arithmetic mean. I therefore believe that both the models of Perry Kaufman and Ralph Vince are inherently flawed.

Agreed. Introducing the influence of the variances is conceptually not difficult. I suppose there are several ways do do it.

If I take the PDF document above, and substitute the equations, I get a nice formula for the risk of ruin (RR) as a function of probability of a winning trade, average loss, and average gain. This gives the RR as a function of the mean inputs. We are interested in this, as well as the deviation from the mean due to variance of the inputs. Let's call this the sensitivity of the risk of ruin, or delta-RR.

The value of delta-RR is the sum of the sensitivities of RR due to the variances of each input. The sensitivity of RR due to one input is the standard deviation of that input times the change in RR with respect to that input. As you may know, the "the change in RR with respect to that input" is jsut another way of saying "the derivative of RR with respect to that input" [the vector containing each of the derivatives with respect to each input is a Jacobian, of sorts].

Unfortunately, doing all the math yields fairly lengthy equations. Let me summarize:

Reproducing the first figure for a profit factor of 2, and assuming a standard deviation of 5% for pWin, Lavg%, and profit factor, I get a much different picture. Without taking the 5% standard deviations into account, I calculate a RR of 16% for a Lavg% of 5%. However, assuming the standard deviations, I get a worst-case RR of 68%.

In the figure below, the red line is the same line as the Wavg%/Lavg% = 2.00 line in t he first figure of the pdf. The Blue line is based on the red line calculation, but including 5% standard deviation for pWin, Lavg%, and Wavg%. Note that is with with pWin, Lavg%, and Wavg% all hitting their low mark at the same time. This analysis does not account for the probability that you are unlucky with three statistics simultaneously.
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serac View Post
Agreed. Introducing the influence of the variances is conceptually not difficult. I suppose there are several ways do do it.

If I take the PDF document above, and substitute the equations, I get a nice formula for the risk of ruin (RR) as a function of probability of a winning trade, average loss, and average gain. This gives the RR as a function of the mean inputs. We are interested in this, as well as the deviation from the mean due to variance of the inputs. Let's call this the sensitivity of the risk of ruin, or delta-RR.

The value of delta-RR is the sum of the sensitivities of RR due to the variances of each input. The sensitivity of RR due to one input is the standard deviation of that input times the change in RR with respect to that input. As you may know, the "the change in RR with respect to that input" is jsut another way of saying "the derivative of RR with respect to that input" [the vector containing each of the derivatives with respect to each input is a Jacobian, of sorts].

Unfortunately, doing all the math yields fairly lengthy equations.

Don't hesitate to attach a document with your equations.

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Fat Tails View Post
Don't hesitate to attach a document with your equations.

Well, then. Here you go.

The PDF has my (fairly roough) derivation in Mathematica.

The txt file has the Mathematica output in C. A few minutes of massaging will make it work in C# (I am not at NinjaTrader now, else I would do it).

Attached Thumbnails
Risk of Ruin-deltarr.pdf  
Attached Files
Register to download File Type: txt deltaRRcode.txt (2.0 KB, 39 views)
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sometimes i thought you speak chinese

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  #99 (permalink)
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Great thread.
I think there are two way to get an approximate estimates of risk of ruin, starting from history of past trades: i) using bootstrap, if you think future return/variance space shall be sample of past, ii) using a known PDF, closest to past trades PDF.
I remember an old paper about kelly criterion applied to t-student PDF (R. Osorio, 2008): stock returns PDF seem (?!) close to a 4.5 df t-student.
I have made some attempts using Johnson PDF (it accepts first four stat moments as inputs) but my preference is about bootstrap.
happy new year

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So does anyone actually use kelly ?


So here is one of my strategies and i removed the number of contracts performing scale in and scale out to see what percentage i receive from a base state (of 1 contract). As you can see the numbers are high enough (trend following). It suggests to put 37% of capital at full force however ed thorp suggests when he was doing trend following he would perform at around 1/10 | 1/20 of kelly. If we suggest that the figures are right this would mean 37% / 20 = 1.85% risk per trade at 1/20 .

I'm wondering would it be interesting to segregate an account and throw 10K at it and see what happens.

Anyone using it explicitly in there trading ?

Its more difficult to use in futures due to the leveraged nature but i wonder using spread options maybe a lot better.

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Some interesting reading:

http://www.math.uchicago.edu/~cfm/Chicago_Kelly.ppt

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