Dear All,

In the literature, it seems to be popular / standard to use the percentage
change:
d(t) = x(t)-x(t-1) / x(t-1)
To define the 'return' of an asset being held with position s(t) as:
r(t) = ln(1+s(t)d(t))

This is already problematic, even if s(t) takes on values of only 1, -1, 0,
since you could be short on a day when d(t)>1.  It's especially problematic
when s(t) is allowed to take on any real (possibly bounded, possibly
normalized) value corresponding to a more or less leveraged / cautious
position.

So, is there some reason why the measure:
r(t) = ln(1+s(t)d(t))
Is preferable to the more obvious, never undefined (for nonzero prices):
s(t)ln(x(t)/x(t-1))
???

Thanks,
-David

	[[alternative HTML version deleted]]

