Monte Carlo analysis with strange resultsMonte Carlo analysis with strange results

hanhao · #1 22nd January 2008, 12:24 PM

Monte Carlo analysis with strange results

preliminary testing only looks at one particular instance of an infinite number of random walk paths. It is by no means conclusive. A system will probably generate multiple buy signals on the same day. A trader with sufficient capital for only 1 more trade has to select which signal to buy on. Different trade selections will yield very different final equity results. The results analyzed only accounts for 1 possible instance out of an almost infinite number of trading decision combinations. In order to verify the statistical accuracy of the result, the system would be to be tested exhaustively. This can be achieved by random walking using Monte Carlo analysis. Whenever the system generates multiple trading signals, only one would be chosen at random. This is done 10,000 times. With this, a mean net profit and accuracy together with their corresponding standard deviation can be obtained. After which, a 95% confidence interval can be determined.

now...a typical result would look like this

http://img297.imageshack.us/img297/8241/55816729we5.jpg

Monte Carlo analysis results for net profit
Maximum Profit: $171,061.18 (342.12%)
Average Profit: $142,801.91 (285.60%)
Minimum Profit: $113,469.63 (226.94%)
Standard Deviation: $8,974.64 (17.95%)
Sample Size 10,000

now what i got is this funny curve
http://img297.imageshack.us/img297/6207/76554193td6.jpg
Monte Carlo analysis results for net profit
Maximum Profit: $487,718.13 (975.44%)
Average Profit: $440,281.30 (880.56%)
Minimum Profit: $358,173.52 (716.35%)
Standard Deviation: $48,535.88 (97.07%)
Sample Size 10,000

does anyone knows why?

oxusmorouz · #2 28th January 2008, 04:57 PM

Quote:

Originally Posted by hanhao

Monte Carlo analysis with strange results

preliminary testing only looks at one particular instance of an infinite number of random walk paths. It is by no means conclusive. A system will probably generate multiple buy signals on the same day. A trader with sufficient capital for only 1 more trade has to select which signal to buy on. Different trade selections will yield very different final equity results. The results analyzed only accounts for 1 possible instance out of an almost infinite number of trading decision combinations. In order to verify the statistical accuracy of the result, the system would be to be tested exhaustively. This can be achieved by random walking using Monte Carlo analysis. Whenever the system generates multiple trading signals, only one would be chosen at random. This is done 10,000 times. With this, a mean net profit and accuracy together with their corresponding standard deviation can be obtained. After which, a 95% confidence interval can be determined.

now...a typical result would look like this

http://img297.imageshack.us/img297/8241/55816729we5.jpg

Monte Carlo analysis results for net profit
Maximum Profit: $171,061.18 (342.12%)
Average Profit: $142,801.91 (285.60%)
Minimum Profit: $113,469.63 (226.94%)
Standard Deviation: $8,974.64 (17.95%)
Sample Size 10,000

now what i got is this funny curve
http://img297.imageshack.us/img297/6207/76554193td6.jpg
Monte Carlo analysis results for net profit
Maximum Profit: $487,718.13 (975.44%)
Average Profit: $440,281.30 (880.56%)
Minimum Profit: $358,173.52 (716.35%)
Standard Deviation: $48,535.88 (97.07%)
Sample Size 10,000

does anyone knows why?

Tradesim handles an isolated part of Monte Carlo simulation alone, i.e, it does not generate hypothetical pseudo random trades but merely tests different trade combinations which could have been taken by the user in random in portfolio testing. When the number of trades is low, or when the number of securities used in testing is low, or if there are not enough multiple trades in a given day, that would explain the low degree of dispersion. In fact, tradesim's Monte Carlo simulation hardly qualifies as MCS. A true Monte Carlo simulator should be capable of running hypothetical trades using the given sample of trades and plot n number of permutations.

I've posted an example of a true MCS, taken from Introductory Econometrics.

http://**********.com/files/87254042/MonteCarlo.xls

Applications of MCS in system developing is explained well in Monte Carlo Simulation and System Trading by Volker Butzlaff
There are several instances where the author is cruel to the verbs and adverbs (The book is a German translation) but the book provides certain singular ideas in applications of MCS in trading, often overlooked in most other system development books.

Regards.

uasish · #3 28th January 2008, 05:34 PM

Another Gem of a post to educate us.