The average liquidity (and capitalization) of ensemble falls down from a) to d). For each ensemble the mean, standart deviation, skewness and kurtosis of the distribution of dayly return was calculated for each trading day. The time distribution of these quantities was considered. The following regularities were observed:
1) The average standart deviation increases by decreasing the capitalization. ( d(i) in your model).
2) The higher values of kurtosis are less probable for the stocks with higher capitalization (this proves your point).
3) The autocorrelation of standart deviation as a function of time decreases with increasing the cap.
Actually, 2) is equivalent to 3) and vice versa: nonzero kurtosis implyes the volatility clustering effect (and deviation of detrended returns from Gaussian distribution).
существенные отличия не для всех, а только для существенно отличающися по стоимости.
It seems that your model is drastically depends on liquidity. In paper
it was proved that the liquidity (measured as a price impact of a single trade executed at NYSE) is the monotonic function of mean market capitalization (see fig.2 of the paper, where the price shift for 20 groups of stocks sorted by market cap are plotted).
So the more liquid the stock is, the more stable the results of the trendfollowing systems are. My approach is a little bit different: I exploit the deviation of the stock return from Gaussian distribution. So I profit more from less liquid stocks (allowing, of course, more severe drawdowns and higher risk). Probably I shall become a trendfollower someday (after losing all the money J
