Measuring Returns on Short Positions with Negative P&L
Summary
A short position’s cash flows and liability can produce a marked value or P&L that crosses from negative to positive. Applying the ordinary percentage-change formula directly to that signed series can give a misleading result, so the discussion considers alternative ways to define performance.
One answer recommends tracking dollar P&L and assessing it with measures such as the Sharpe ratio, or dividing P&L by the capital committed to operate the long/short strategy. Another proposes adding period P&L to initial capital to form a running portfolio value, then calculating returns from that value. The distinction is that a meaningful return needs a defined capital base. The discussion gives no worked calculation or guidance on choosing committed capital, and the running-value approach depends on an appropriate starting investment and portfolio valuation.
Key ideas
- Percentage changes on signed P&L can be misleading when values cross zero.
- Dollar P&L can be analyzed directly with performance measures such as the Sharpe ratio.
- A return for a long/short strategy can be defined relative to the capital needed to run it.
- Accumulated P&L plus initial capital provides a portfolio value series for calculating period returns.
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Full text
# Short position returns with negative NAV # Short position returns with negative NAV 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. ## Answer by Ezy (score 2) https://quant.stackexchange.com/a/43226 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. ## Answer by AdB (score 0) https://quant.stackexchange.com/a/43213 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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