Daily Return of a Leveraged / Shorted Asset
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 [[alternative HTML version deleted]]
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