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I am using data on the opening, change and closing of short positions, but I am interested in when the profit/losses are made. Hence, I calculated daily the value of the short position by taking the cash gained with increasing the short position minus the current value of the shorts (liability). This results in a PnL, with both positive and negative values. However, now I try to calculate the return based on the PnL values. Problem is that the ordinary (new - old)/(old) won't be of much help when the old value is negative, for example an increase from -2 to +3, (3--2)/-2) = -2.5 while clearly this is an increase.

Does someone know how to handle data in such a situation? Moreover, I am new here, so sorry if I am asking the wrong question.

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If you are analysing the performance of a long/short type of portfolio you typically do not calculate returns of the portfolio value itself. Typically you would calculate your daily pnl in dollar terms and for example calculate the sharpe ratio of that quantity.

The only “return” quantity that truly makes sense for such long/short portfolio is the return on your investment capital. In a long short portfolio, even though at first sight all the long positions are financed by the short ones you still need some capital to maintain your shorts, finance your longs, maintain margins accounts etc... so in other words the investment capital is the money you effectively need to practically run the long/short strategy. Therefore from a portfolio manager perspective the return that makes sense is how much pnl your strategy makes divided by this committed capital.

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  • $\begingroup$ Thank you for reminding me that the Sharpe ratio can also be calculated with absolute values, not only returns. I am looking at it from an academic perspective, hence, it is somewhat of a stylised short only strategy. $\endgroup$
    – Hjalmar
    Dec 27, 2018 at 8:33
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One approach is to simply start with your initial investment and doing a running sum of your PnL (i.e. a sum of all PnLs up until the point of interest). This will be the total portfolio value at a given point. Using those, you can simply use your formula (new - old)/(old) on the total portfolio values.

Note that this is equivalent to dividing the PnL of a period with the previous period's total portfolio value. This is because the PnL of a period is exactly the (new - old) term!

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