ch01 JWBK035-Vince February 22, 2007 21 : 43 Char Count= 0
38 THE HANDBOOK OF PORTFOLIO MATHEMATICS
Evenif a system showed dependency to a 95% confidence limit for all val-
ues of a parameter, that confidence limitis hardly high enough for us to
assume that dependency doesin fact exist between the trades of agiven
market/system.
Yet the confidence limits and linear correlation coefficients are tools
that should be used, because on rare occasions they may turn up a dia-
mondin the rough, which can then possibly be exploited.Furthermore,
and perhaps moreimportantly, theyincrease our understandingof the en-
vironmentinwhich we are tryingto operate.
On occasion, particularlyin longer-term tradingsystems, you will en-
counter cases where the Z score and the linear correlation coefficientindi-
cate dependency, and the dependency holds up across markets and across
optimizeable parameter values.In such rare cases, you can take advantage
of this dependency by either passingcertain trades or alteringyour com-
mitment on certain trades.
By studyingthese examples, you will better understand the subject
matter.−10, 10,−1, 1
Linear Correlation=−. 9172
Z score= 1 .8371 or 90 to 95% confidence limit that like begets unlike.
10,−1, 1,− 10
Linear Correlation=. 1796
Z score= 1 .8371 or 90 to 95% confidence limit that like begets unlike.10,−10, 10,− 10
Linear Correlation=− 1. 0000
Z score= 1 .8371 or 90 to 95% confidence limit that like begets unlike.−1, 1,−1, 1
Linear Correlation=− 1. 0000
Z score= 1 .8371 or 90 to 95% confidence limit that like begets unlike.1, 1,−1,− 1
Linear Correlation=. 5000
Z score=−.6124 or less than 50% confidence limit that like begets like.100,−1, 50,−100, 1,− 50
Linear Correlation=−. 2542
Z score= 2 .2822 or more than 97% confidence limit that like begets unlike.Theturning points testis an altogether different test for dependency.
Goingthrough the stream of trades, a turningpointis countedif a trade
is for agreater P&L value than both the trade beforeit and the trade after