Re: Position trading 100+ futures markets times 8 systems

[Bob Fulks <omegalist@xxxxxxxxxxxx>]

At 11:24 AM 4/16/2008, Mark Johnson wrote:

>But what does appear to be true, at least in my own
>research, is that the correlation coefficients between
>the equity curves of different markets traded with the
>same mechanical system, are Quite Low.  

The reason for this is quite simple to understand.

If you apply a trading system that goes long, short, and flat to a 
price curve, it will trade at different points in time on different 
commodities. So the resulting equity curves will tend to be less 
highly correlated than are the price curves. The resulting correlation 
actually become very low for commodities, which tend to not be too 
highly correlated to begin with.

And with uncorrelated equity curves the variance of the portfolio 
returns tends to decrease directly as the number of equity curves 
increases. So the standard deviation of the portfolio decreases as the 
square root of the number of equity curves and the Sharpe Ratio 
increases as the square root of the number of equity curves.

So trading 100 commodities could improve the basic Sharpe Ratio of the 
trading system by a factor of 10 - very significant.

So even a pretty mediocre basic trading system can be used to generate 
a very smooth equity curve at the portfolio level.

Trading 200 commodities would increase this to a factor of 14 - a 40% 
increase over 100.

Trading 300 commodities would increase this to a factor of 17 - a 20% 
increase over 200.

So the benefit decreases fairly rapidly but the transaction costs 
increase linearly with the number of equity curves so there should be 
an optimum number of commodities to trade using this method.

Bob Fulks