Measuring Returns for Long-Short Strategies with Negative P&L
Summary
The document addresses why ordinary percentage returns can become misleading when a long-short strategy’s recorded P&L or value crosses zero. It presents a net asset value approach: account for the value of long holdings, short-sale proceeds, and the current liability from short holdings, then calculate the period return as the change in NAV relative to its starting level. This requires tracking the portfolio’s holdings and financing consistently.
It also describes calculating the long and short legs’ period returns separately, reversing the short-side contribution, and averaging the legs under an equal-weight assumption. A further answer says that market-neutral funds often scale daily profit by total book size, defined as long exposure plus the absolute value of short exposure. These approaches use different return denominators and therefore answer different questions; the suitable measure depends on the strategy’s NAV, weighting, and exposure convention. The document gives no worked resolution for the sample data.
Key ideas
- Raw percentage changes can be nonsensical when the reference P&L value is negative or near zero.
- A portfolio return can be calculated from NAV, including long holdings, short proceeds, and short liabilities.
- Long and short leg returns can be combined period by period under an explicit weighting rule.
- A market-neutral book return may divide daily profit by gross book size.
- Return figures depend on the chosen capital and exposure denominator.
Tags
Full text
# Calculating the returns of a long/short strategy # Calculating the returns of a long/short strategy 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. `2005-02-14 5010 2005-02-15 -23315 2005-02-16 -14371 2005-02-17 -19995 2005-02-18 -17064 2005-02-21 -25018 2005-02-22 736 2005-02-23 -125 2005-02-25 20264` ## Answer by RRG (score 6, accepted) https://quant.stackexchange.com/a/32519 There are two ways to calculate the returns. 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. ## Answer by drx (score 3) https://quant.stackexchange.com/a/73267 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
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.