Technical Paper on Monte Carlo Simulation by Mark Johnson
Posted: Thu Feb 15, 2007 10:40 am
Mark Johnson presented a paper on Monte Carlo Simulations to a workshop a little over a year ago. He subsequently posted the paper to the Austin Association of Financial Traders mailing list. I asked his permission to post this paper here.
Mark was the one to suggest the mechanism we used in Trading Blox to maintain the serial correlation characteristics for Monte Carlo simulations and this paper covers that subject as well as a few others.
You may find the PDF file for the paper here:
http://www.tradingblox.com/Files/MC_res ... _Nbars.pdf
- Forum Mgmnt
The text from Mark's email to the AAFT group follows:
__________________________________________________
I attended a workshop a year ago, at which I presented a fairly detailed (35 pages), fairly technical (49 graphs) research paper called
Monte Carlo Resampling of Equity Curves using N-Bar Segments
Distribution was initially limited to the workshop attendees only, but that embargo is now lifted. So I'm releasing the article to a much wider audience. The paper is pretty technical and assumes the reader already has had some exposure to, or practical experience with, Monte Carlo analysis in trading. If that's you, then you might well enjoy the article.
BEWARE, this is a 7.5 megabyte Adobe Acrobat (.pdf) document file. It'll take a while to download. [NOTE: I removed the reference here to the location of the file since we are hosting it on our servers - Forum Mgmnt]
Here's the Abstract:
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The equity curve produced by historical simulation of a mechanical trading system is resampled, creating many new equity curves having (it is hoped) the same probability of occurrence as the simulated one. Statistics such as CAGR%, MaxDD%, Longest Drawdown, Sharpe's Information Ratio, etc. are computed for each of the new equity curves. Cumulative probability distributions are then created, showing the probability that, for example, CAGR% is greater than or equal to 40% per year.
Conventionally, the simulated equity curve is resampled using a sample length of 1 bar. However, this decision is sometimes criticized because it effectively destroys any serial correlation that may be present in the original (simulated) equity curve. The present work explores the use of N-bar samples (1 <= N <= 20 bars) in the resampling process, to preserve any serial correlation that may exist.
The investigation produced four main results: 1. At least ten million resampled bars are needed to guarantee convergence of the Monte Carlo results. In the examples shown here, ~3000 new equity curves with 4100 bars per curve. 2. Serial correlation is present in the historical equity curve, however only for 1-bar lags. (Today's equity value is somewhat correlated to yesterday's, but not to the equity value of any day before
that). 3. The amount of serial correlation in the equity curve varies as the number of instruments in the simulated portfolio is changed, *which is unexpected*. 4. Pure reversal systems that are always in the market, and "choosy" systems that are only in the market a small percentage of the time, exhibit approximately the same amount of serial correlation.
------------ --------- -------
Mark was the one to suggest the mechanism we used in Trading Blox to maintain the serial correlation characteristics for Monte Carlo simulations and this paper covers that subject as well as a few others.
You may find the PDF file for the paper here:
http://www.tradingblox.com/Files/MC_res ... _Nbars.pdf
- Forum Mgmnt
The text from Mark's email to the AAFT group follows:
__________________________________________________
I attended a workshop a year ago, at which I presented a fairly detailed (35 pages), fairly technical (49 graphs) research paper called
Monte Carlo Resampling of Equity Curves using N-Bar Segments
Distribution was initially limited to the workshop attendees only, but that embargo is now lifted. So I'm releasing the article to a much wider audience. The paper is pretty technical and assumes the reader already has had some exposure to, or practical experience with, Monte Carlo analysis in trading. If that's you, then you might well enjoy the article.
BEWARE, this is a 7.5 megabyte Adobe Acrobat (.pdf) document file. It'll take a while to download. [NOTE: I removed the reference here to the location of the file since we are hosting it on our servers - Forum Mgmnt]
Here's the Abstract:
------------ --------- ---
The equity curve produced by historical simulation of a mechanical trading system is resampled, creating many new equity curves having (it is hoped) the same probability of occurrence as the simulated one. Statistics such as CAGR%, MaxDD%, Longest Drawdown, Sharpe's Information Ratio, etc. are computed for each of the new equity curves. Cumulative probability distributions are then created, showing the probability that, for example, CAGR% is greater than or equal to 40% per year.
Conventionally, the simulated equity curve is resampled using a sample length of 1 bar. However, this decision is sometimes criticized because it effectively destroys any serial correlation that may be present in the original (simulated) equity curve. The present work explores the use of N-bar samples (1 <= N <= 20 bars) in the resampling process, to preserve any serial correlation that may exist.
The investigation produced four main results: 1. At least ten million resampled bars are needed to guarantee convergence of the Monte Carlo results. In the examples shown here, ~3000 new equity curves with 4100 bars per curve. 2. Serial correlation is present in the historical equity curve, however only for 1-bar lags. (Today's equity value is somewhat correlated to yesterday's, but not to the equity value of any day before
that). 3. The amount of serial correlation in the equity curve varies as the number of instruments in the simulated portfolio is changed, *which is unexpected*. 4. Pure reversal systems that are always in the market, and "choosy" systems that are only in the market a small percentage of the time, exhibit approximately the same amount of serial correlation.
------------ --------- -------