ch01 JWBK035-Vince February 22, 2007 21 : 43 Char Count= 0
36 THE HANDBOOK OF PORTFOLIO MATHEMATICS
ABCDEFG
col C col C col D
X Y X–X avg Y–Y avg times squared squared
col D1
2 1 1.2 0.3 0.36 1.44 0.09
1 2 0.2 1.3 0.26 0.04 1.69
− 11 −1.8 0.3 −0.54 3.24 0.09
3 −12.2−1.7 −3.74 4.54 2.89
2 3 1.2 2.3 2.76 1.44 5.29
− 12 −1.8 1.3 −2.34 3.24 1.69
− 2 − 1 −2.8 −1.7 4.76 7.84 2.89
− 3 − 2 −3.8 −2.7 10.26 14.44 7.29
1 −30.2−3.7 −0.74 0.04 13.69
− 21 −2.8 0.3 −0.84 7.84 0.09
3 −22.2−2.7 −5.94 4.84 7.29
1 3 0.2 2.3 0.46 0.04 5.29
1 1 0.2 0.3 0.06 0.04 0.09
2 1 1.2 0.3 0.36 1.44 0.09
3 2 2.2 1.3 2.86 4.84 1.69
3 3 2.2 2.3 5.06 4.84 5.29
− 13 −1.8 2.3 −4.14 3.24 5.29
2 −11.2−1.7 −2.04 1.44 2.89
− 12 −1.8 1.3 −2.34 3.24 1.69
3 −12.2−1.7 −3.74 4.84 2.89
3
avg=0.8 avg=0.7 Totals= 0.8 73.2 68.2vice versa.Negative correlation readings below−.25 to−. 30 imply that big
losses tend to be followed by bigwins and vice versa.
There are a couple of reasons whyitisimportant to use both the runs
test and the linear correlation coefficient togetherin lookingfor depen-
dency/correlation between trades.The firstis that futures tradingsystem
trades (i.e., the profits and losses) do not necessarily conform to a Normal
Probability Distribution.Rather, they conform pretty much to whatever the
distributionis that futures prices conform to, whichis as yet undetermined.
Since the runs test assumes a Normal Probability Distribution, the runs test
is only as accurate as the degree to which the system trade P&Ls conform
to the Normal Probability Distribution.
The second reason for usingthe linear correlation coefficientin con-
junction with the runs testis that the linear correlation coefficientis af-
fected by the size of the trades.It not onlyinterprets to what degree like
begets like or like begets unlike,it also attempts to answer questions such