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I attended a workshop a year ago, at which I
presented some research 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.
It may be of use in suggesting new features for
proprietary or commercial trading analysis software,
for example TradeStation or Rina or ProSizer or Inside
Edge or Adaptrade MSA or StockWave or even, for that
matter, Wealth-Lab.
BEWARE, this is a 7.5 megabyte Adobe Acrobat (.pdf)
document file. It'll take a while to download.
It's too bad the omega-list doesn't have a file
manager / archive where such things can be uploaded
and stored "permanently".
Because the file is so big, I'm only going to keep
it up on the web through the end of October, 2006.
Then it's coming off. If you want it, or think you
may want it someday, grab it now while you can.
After 10/31/06, it's gone. If you are reading this
email on a date after 10/31, my condolences to you.
Here's the Abstract of the paper:
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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.
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The paper is temporarily located at
http://www.mjohnson.com/monte_temp/MC_resampling_Nbars.pdf
-- Mark Johnson
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