Weighted symmetry
p – Let P define the probability of obtaining a return above the threshold θ (here defined as zero).
ω – Let ω define the ratio of the expected value above the threshold, vis-à-vis the expected value under the threshold θ. Meaning if we set the threshold to zero return, then a value of ω above 1, implies that the average value of positive returns is higher than the average value of negative returns.
From Mar 10 1999 until May 24 2009
Take a look at the Argentinian Merval
p= 0.5163934
ω = 1.3250000
Rolling weighted symmetry
Below i have plottet the evolution of the parameters p and ω.
It is seen that the probability of a positive return is higher than the probability of a negative return. (p>0.5) and that this probability is increasing over time. Going from 0.51 to 0.55.
Further the expected value of these positive returns are higher than the expected negative return, and actualy decreacing over time. From 1.575to 1.255. Now if only i had access to some managed account data…:-)
Then take a look at QQQQ and DIA.
QQQQ
p = 0.5081967
ω = 0.9250000
DIA
p = 0.5327869
ω = 0.8450000
