I'm not following your notation, so I don't

really understand your question. But I have

one comment that might help.

When you short an asset, you are really reversing

time in terms of returns. What we normally think

of as time t-1 is really the "buy time" and time t

is the "sell time".

Patrick Burns

[hidden email]
+44 (0)20 8525 0696

http://www.burns-stat.com(home of "The R Inferno" and "A Guide for the Unwilling S User")

David St John wrote:

> 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]]

>

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