Statistics and psycology

Richbynature

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In order to ensure that I maintain some form of objectivity in trading I analyse my results statistically (i.e. with a mind to understanding how much 'randomness', or things beyond my control day to day can play a part).

I have attached 3 files. The point of these is to find objective mathematical ways of comparing cummulative results a trader obtains against what might be expected given certain assumptions about our "average" performance (a term that is difficult to define in practice).

I invite you to play with / inspect these files and give feedback if you would like to. They are a source of calm to me as I can absolutely measure the how's, why's and wherefore's of my results.

How do you use statistics constructivesly in analysing your trading?

Attachment 1. Trading results simulation - how welll am I doing?
This is probably the simplest of the 3 files. Here simply plotted is the result of a series of trades with initially defined probabilities. An interesting point is that the curves can overlap and diverge quite differently depending on the random numbers generated. So it's hard to gauge how successful we are as traders in the short term - agree / disagree? You can "run" the simulation by pressing "Delete" in any empty cell.

Attachment 2. Prob lose calculator
So a simple extension of the above file is to start to think about the probabilities of drawdowns. This attachment asks the question "how long might I expect to trade for in order to make a profit given my assumption of my expected win percentage?" The data given answer the question of no. trades to be profitable, which = 1 - probability of being in a loss. You can alter cell E5 to play with the graph. We all suffer drawdowns and periods of loss - this quantifies the probability of going a number of trades before we are "out of loss". Eventually, we all have the worst day of our lives, it's good to know how many bad days we might have prior to that so as to get a measure of luck / randomness at play!

Attachment 3. Equity curves based on probabilities
This one is conceptually most difficult / messy, but is really just an extension of 2 with a simulation output as a graph. Column A creates an output that has a positive expectation (i.e. on average it is > 1) but that has a non zero probability of being less that 0 (i.e. in some time periods a trader would expect to lose money, true?). Column B creates a summation over time (so the row numbers might be thought of as days / weeks / years depending on how you want to model your trading - graphed for you). Row 4 counts across upto 21 (had to stop somewhere!) and measures "number of overlapping timeframes". So if you click in D6 you'll see that A6&7 are summed. All of column D does this. Column E sums over 2 time boundaries (3 results in Column A), and so on, across the spreadsheet. Total drawdown occurs over any period of time across the whole lifespan of a trader (i.e. the minimun value in the cell calculated) and is given in AA18 (again, hitting "Delete" in an empty cell will run the formula for you). The most negative numbers will probably be in Column D, the least in Column X. However, the biggest drawdowns are 'hidden in clear view, in the middle somewhere'! And it's that drawdown that kills traders. The value given in AA18 varies and gives the drawdown relative to A6, the input "average". You can play with A6 to compare with your strategy if you want to.

The point is simple: your strategy will have it's worst run culminating on 1 day - is it and are you robust enough to withstand it?

If there are errors in these files, please say so. However, my purpose is to stimulate discussion on statistics. Once we know what is random, we can focus on what is real. What is real can be affected, the rest is a waste of energy and time. Time is limited.

Do stats help you keep a clear sense of perspective when you trade?

http://www.bbc.co.uk/iplayer/episode..._Joy_of_Stats/
 

Attachments

  • Trading results simulation - how welll am I doing.xls
    205 KB · Views: 400
  • Prob lose calculator.xls
    30 KB · Views: 356
  • Equity curves based on probabilities.xls
    1.5 MB · Views: 788
One thing I see a lot is that over 80% of the trader think that they are better than the average trader. Now it's up to you to find the mistake in this calculation :)
 
One thing I see a lot is that over 80% of the trader think that they are better than the average trader. Now it's up to you to find the mistake in this calculation :)

Ofcourse this WOULD be possible if there was a highly skewed distribution with the very worst traders being truly dire (and non-symmetrically the best being only slightly better than the median). In reality the bottom end is truncated by "account empty" and the upper end is not, so I guess you are correct in your statement but the data doesn't exist to prove it. George Soros and Warren Buffet are examples of those who shift the average way up.
 
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