Math Questions

H

HFStartup

I took the daily performance of my fund and doubled the daily gain or loss per day. I then applied the same statistical metrics to these doubled figures as I do for the original values. Logically, I would have thought that the metrics also would have doubled. For example, I would have expected a figure of .084% to go .168%. However, what I found was that the figure went to .277%. This "exageration" occurred throughout all of the metrics I applied. In addition, I found an even greater "exageration" when I tripled the numbers. I would expect this condition would grow more extreme as I continue multiplying the original figures...

My questions are:

1. Does this phenomena have a name?

2. What is the cause of it, in simple, layman's terms?

Thank you for your assistance.
 
HFstartup

if you can please give more details of some numbers and calc. methodology, it will be much easier to explain the mathematical reasoning behind it. Thanks
 
Have a look at this thread and how Acrary demonstrates that Expectancy doesn't improve consistency:

http://www.elitetrader.com/vb/showthread.php?s=&threadid=33654

One series of studies I did was to find out what were the important factors in consistency. I did tests on size of expectation, % wins, profit factor, number of trades within a timeframe, and the effect of dispersion of trades (std. deviation) has on the results. For instance, here's a run for a daytrader that does 10 trades a day with 70% wins and makes $500 on each win and loses $500 on each loss. As you can see this is quite profitable at the 50% level (the average over time). However you can also see that after the 80% level the trader actually loses money. So for a daytrader with these numbers they only have a 80% chance of achieving their goal of consistent profitability on a daily basis. If that level of confidence is ok, then they have a example to use going forward.

Model name daytrade
# of trades in series 10
% of trades that are winners 70
Mean of winning trades 500
Std. Dev. of winning trades 0
Mean of losing trades 500
Std. Dev. of losing trades 0

Outcome Profit Factor Max DD
1% level 5,000.00 10.00 0
5% level 4,000.00 9.00 -500
10% level 4,000.00 9.00 -500
20% level 3,000.00 4.00 -500
30% level 3,000.00 4.00 -500
40% level 2,000.00 2.33 -500
50% level 2,000.00 2.33 -1,000
60% level 2,000.00 2.33 -1,000
70% level 1,000.00 1.50 -1,000
80% level 1,000.00 1.50 -1,000
90% level 0.00 1.00 -1,500
95% level -1,000.00 0.67 -2,000
99% level -2,000.00 0.43 -2,500
Expected outcome 1,950.00
Expectancy 200

Now what happens if that daytrader decides he wants 95% level of confidence so that he'll accpect one losing day per month. What changes would he make? If he doubles his expectation does that help? As you can see from this run, he still only has about 80% confidence level with double the expectancy on each trade.

Model name daytrade
# of trades in series 10
% of trades that are winners 70
Mean of winning trades 1000
Std. Dev. of winning trades 0
Mean of losing trades 1000
Std. Dev. of losing trades 0

Outcome Profit Factor Max DD
1% level 10,000.00 10.00 0
5% level 8,000.00 9.00 -1,000
10% level 8,000.00 9.00 -1,000
20% level 6,000.00 4.00 -1,000
30% level 6,000.00 4.00 -1,000
40% level 4,000.00 2.33 -1,000
50% level 4,000.00 2.33 -1,000
60% level 4,000.00 2.33 -2,000
70% level 2,000.00 1.50 -2,000
80% level 2,000.00 1.50 -2,000
90% level 0.00 1.00 -3,000
95% level 0.00 1.00 -4,000
99% level -4,000.00 0.43 -5,000
Expected outcome 4,000.00
Expectancy 400
 
As requested, I have attached the spreadsheet example to this post to include all formulas. An example of what specifically confuses me is the relationship between cells D2, K2 and R2, however this trend can be observed to occur throughout almost all of the metrics.

Any thoughts are appreciated.

Thanks.
 

Attachments

Thanks, Joman. The thread you listed was an excellent suggestion and I have been reading it for hours. Thank you.

Quote from Joman:

Have a look at this thread and how Acrary demonstrates that Expectancy doesn't improve consistency:

http://www.elitetrader.com/vb/showthread.php?s=&threadid=33654

One series of studies I did was to find out what were the important factors in consistency. I did tests on size of expectation, % wins, profit factor, number of trades within a timeframe, and the effect of dispersion of trades (std. deviation) has on the results. For instance, here's a run for a daytrader that does 10 trades a day with 70% wins and makes $500 on each win and loses $500 on each loss. As you can see this is quite profitable at the 50% level (the average over time). However you can also see that after the 80% level the trader actually loses money. So for a daytrader with these numbers they only have a 80% chance of achieving their goal of consistent profitability on a daily basis. If that level of confidence is ok, then they have a example to use going forward.

Model name daytrade
# of trades in series 10
% of trades that are winners 70
Mean of winning trades 500
Std. Dev. of winning trades 0
Mean of losing trades 500
Std. Dev. of losing trades 0

Outcome Profit Factor Max DD
1% level 5,000.00 10.00 0
5% level 4,000.00 9.00 -500
10% level 4,000.00 9.00 -500
20% level 3,000.00 4.00 -500
30% level 3,000.00 4.00 -500
40% level 2,000.00 2.33 -500
50% level 2,000.00 2.33 -1,000
60% level 2,000.00 2.33 -1,000
70% level 1,000.00 1.50 -1,000
80% level 1,000.00 1.50 -1,000
90% level 0.00 1.00 -1,500
95% level -1,000.00 0.67 -2,000
99% level -2,000.00 0.43 -2,500
Expected outcome 1,950.00
Expectancy 200

Now what happens if that daytrader decides he wants 95% level of confidence so that he'll accpect one losing day per month. What changes would he make? If he doubles his expectation does that help? As you can see from this run, he still only has about 80% confidence level with double the expectancy on each trade.

Model name daytrade
# of trades in series 10
% of trades that are winners 70
Mean of winning trades 1000
Std. Dev. of winning trades 0
Mean of losing trades 1000
Std. Dev. of losing trades 0

Outcome Profit Factor Max DD
1% level 10,000.00 10.00 0
5% level 8,000.00 9.00 -1,000
10% level 8,000.00 9.00 -1,000
20% level 6,000.00 4.00 -1,000
30% level 6,000.00 4.00 -1,000
40% level 4,000.00 2.33 -1,000
50% level 4,000.00 2.33 -1,000
60% level 4,000.00 2.33 -2,000
70% level 2,000.00 1.50 -2,000
80% level 2,000.00 1.50 -2,000
90% level 0.00 1.00 -3,000
95% level 0.00 1.00 -4,000
99% level -4,000.00 0.43 -5,000
Expected outcome 4,000.00
Expectancy 400
More...
 
You'll notice that the overall % return of "Actual" is 0.05069%
and the % return of "2x Actual" is 0.101386% or, 2 times Actual's return. That works because they both use the same starting value and every day's $ value return was doubled for "2x Actual".
What you did in D2 and K2 is not 2x because there are many % returns during the time period that are not 2x because of the reason given above by dtrader. For example, J20's 3.87% is not 2x C20's 1.86% because Actual was using with 214,268.07 and 2x Actual is using 205,705.25.
If you want K2 to be 2x D2 you'd want to double the percentage returns of each day, not double the dollar amounts.
 
I see your point, Monstimal. I can't believe I didn't catch that by myself but I thank you for pointing it out. Pretty obvious to me now.

Thanks again.

Quote from monstimal:

You'll notice that the overall % return of "Actual" is 0.05069%
and the % return of "2x Actual" is 0.101386% or, 2 times Actual's return. That works because they both use the same starting value and every day's $ value return was doubled for "2x Actual".
What you did in D2 and K2 is not 2x because there are many % returns during the time period that are not 2x because of the reason given above by dtrader. For example, J20's 3.87% is not 2x C20's 1.86% because Actual was using with 214,268.07 and 2x Actual is using 205,705.25.
If you want K2 to be 2x D2 you'd want to double the percentage returns of each day, not double the dollar amounts.
More...
 
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