Ralph Vince - Portfolio Mathematics

ch01 JWBK035-Vince February 22, 2007 21 : 43 Char Count= 0

28 THE HANDBOOK OF PORTFOLIO MATHEMATICS

degree of certainty.We have seen that the area under the curve of the Nor-

mal Probability Function at 1 standard deviation on either side of the mean

equals 68% of the total area under the curve.So we take our Z score and

convertit to a confidence limit, the relationshipbeingthat the Z scoreis

how many standard deviations and the confidence limitis the percentage

of area under the curve occupied at so many standard deviations.

Confidence Limit Z Score

99.73% 3. 00

99% 2. 58

98% 2. 33

97% 2. 17

96% 2. 05

95.45% 2. 00

95% 1. 96

90% 1. 64

85% 1. 44

80% 1. 28

75% 1. 15

70% 1. 04

68.27% 1. 00

65%. 94

60%. 84

50%. 67

Withaminimum of 30 closed trades we can now compute our Z scores.

We are tryingto determine how many streaks of wins/losses we can ex-

pect from agiven system.Are the win/loss streaks of the system we are

testinginline with what we could expect?If not,is there a high enough

confidence limit that we can assume dependency exists between trades,

thatis, the outcome of a trade dependent on the outcome of previous

trades?

Here, then,is how to perform the runs test, how to find a system’s

Z score:

1.You will need to compile the followingdata from your run of trades:

A.The total number of trades, hereafter called N.

B.The total number of winningtrades and the total number of losing

trades.Now compute what we will call X.X= (^2) Total Number of
WinsTotal Number of Losses.
C.The total number of runsin a sequence.We’ll call thisR.