[R-SIG-Finance] Daily Return of a Leveraged / Shorted Asset

[Patrick Burns]

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
patrick at burns-stat.com
+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
> 
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> 
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