ch01 JWBK035-Vince February 22, 2007 21 : 43 Char Count= 0
30 THE HANDBOOK OF PORTFOLIO MATHEMATICS
4.Take the square root of the answerin number 3.For our example this
would be:
√
392. 727272 = 19. 817347775.Divide the answerin number 2 by the answerin number 4.Thisis the Z
score.For our example this would be:18/19. 81734777 =. 9082951063- Confidence Limit=^1 −(2∗(X∗.^31938153 −Y∗.^356563782
+(X∗Y∗ 1. 781477937 −Y^2 ∗ 1. 821255978
- 821255978 +Y^2 ∗X∗ 1 .330274429)∗ 1
/
- 821255978 +Y^2 ∗X∗ 1 .330274429)∗ 1
√
EXP(Z^2 )∗ 6 .283185307))
where: X= 1 .0/(((ABS(Z))*.2316419) + 1.0).
Y=X∧ 2.
Z=The Z score you are convertingfrom.
EXP( )=The exponential function.
ABS( )=The absolute value function.Thiswillgive you the confidence limit for the so-called“two-tailed”
test.To convert this to a confidence limit for a“one-tailed”test:Confidence Limit= 1 −(1−A)/ 2where: A=The“two-tailed”confidence limit.If the Z scoreisnegative, simply convertit to positive (take the abso-
lute value) when findingyour confidence limit.Anegative Z scoreimplies
positive dependency, meaningfewer streaks than the Normal Probability
Function wouldimply, and hence that wins beget wins and losses beget
losses.A positive Z scoreimplies negative dependency, meaningmore
streaks than the Normal Probability Function wouldimply, and hence that
wins beget losses and losses beget wins.
As longas the dependencyis at an acceptable confidence limit, you
can alter your behavior accordingly to make better tradingdecisions, even
though you do not understand the underlyingcause of the dependency.
Now,if you could know the cause, you could then better estimate when the
dependency wasin effect and whenit was not, as well as when a changein
the degree of dependency could be expected.
The runs test will tell youif your sequence of wins and losses con-
tains more or fewer streaks (of wins or losses) than would ordinarily be
expectedin a truly random sequence, which has no dependence between