Equity curves

[Gooly <gooly@xxxxxx>]

Hi List,

there were some posts about the evaluation of equity curves and one metioned 
Chande with his relation of Final Equity divided by the Error of the linear 
regression. Another post mentioned the sharp ratio, which is s.th. simular 
devided by the non-risk-interest-rate.

I may be wrong and would be glad if s.o. points to my failor, but I think that 
both aren't the best methods if you want to impove a system by optimizing 
parameters.

In the specific case of optimizing ne system within one or more markets the 
input of the (allways same!!) non-risk-interest-rate in the evaluation of the 
outcome does not give you any additional information, it just changes the 
number. Only if you compare different types of investment this sharp ratio 
makes sense - no?

And Chande relation - if used to optimize - does not leed you to the best 
system, I think. Here an example:
lets assume this equity curve: (1 trd = 1000 and 4 trds = 0, ..)
1000,1000,1000,1000,1000,2000,2000,2000,2000,2000,
	3000,3000,3000,3000,3000,4000,4000,4000,4000,4000,
	5000,5000,5000,5000,5000,6000,6000,6000,6000,6000,7000));
This leeds to this from the linear regression:
'Final Equity: 7000  Eqt/Err: 2406 slope: 197.58  intercept: 451.61 
Error: 290.99  No.Trades: 31'
Chande's relation is 2406

now this one: (1 trd = 5000, 1 trd = -1000, 3 trd = 0, 1 trd = 6000, ...)
5000,4000,4000,4000,4000,10000,9000,9000,9000,9000,
	15000,14000,14000,14000,14000,20000,19000,19000,19000,19000,
	25000,24000,24000,24000,24000,30000,29000,29000,29000,29000,35000));
This much better result leeds (from lienar regression) to
Final Equity: 35000 Eqt/Err: 1956  slope: 987.9   intercept: 1483.87  
Error: 1789.08   No.Trades: 31'
Chande's relation here is 1956, much less so you would reject this version.

I think if you optimize a system, then you try to find those parameters that 
finds better the correct enter- and exits times and - I think - it happens 
that what is shown in the above two equity curves, some trades are much 
better, some a little worse and you try to get form curve-1 to curve-2. But 
Chande "won't let you do that".

Additionally to that I myself found that not the systems with a maximized 
Eqt/Err-relation performed better in different markets but those that where 
optimized by maximizing the final Equity did.

Refutations appreciated, ...

carl