I feel like an idiot asking this but i haven't found the answer anywhere.
I have backtestest a paris trading strategy, while calculating the returns of the strategy I run into some problems when the P&L just gets more negative. Lets take for example the data above. From 2005-02-16 to 2005-02-17 the arithmetic return is 39.13% or for the dates 2005-02-23 to 2005-02-24 the return is -16311.20% which isn't right obviously. So my question is how do I calculate the returns when I have a P&L which allows negative negative values.
One way is to calculate the net asset value (NAV) of your portfolio.
For the long side the NAV is the value of your stock holdings.
For the short side the initial NAV is zero since the cash proceeds from the sale balances the liabilities of the short holdings.
The portfolio NAV is hence initially equal to the value of the long holdings.
At a future date the short NAV is equal to the initial cash proceed from the sale minus the current liability of the short position, which is the negative value of the stocks that are shorted. The portfolio NAV is hence the value of the long stocks + cash proceeds from the sales - value of the short stocks. To find the return $R(t_1,t_2)$ between dates $t_1$ and $t_2$ one takes $R(t_1,t_2) = NAV(t_2)/NAV(t_1) -1 $.
Another way is to calculate the period return (say one week) of the long stocks and the negative returns of the short stocks and average them (assuming equal weighting) giving the long/short return over the period.
I worked in long-short neutral fund. For a long-short neutral strategy, typically in practice book size is assumed to be long size + abs(short size). So daily return would be daily profit / book size as defined