# How to compute returns of a Pairs Trading Strategy with different holding periods?

I am currently working on a project where I am testing a Pairs Trading Strategy based on Cointegration. In this strategy I am considering to trade a couple of hundred stock pairs every day over a time frame of 3 years. According to this strategy I am holding my trades open until either the take profit condition (revert to mean of spread) or stop loss condition (spread exceeding [mean + 3* standard deviation]) holds. This means that some trades might be open a couple of days, others might be open for weeks or even months.

My question is now: How can i calculate the returns of my overall strategy?

I know how to calculate the returns per trade but when aggregating returns over a certain time period or over all traded pairs I have problems.

Let's say I am trying to calculate returns over 1 year. I could take the average of all the trade returns or calculate sum(profits per trade of each pair)/sum(invested or committed capital per trade), both of these would only give me some average return values.

Most of my single trades are profitable but in the end I am trying to show how profitable my whole trading strategy is, so I would like to compare it to some benchmark, but right now I don't really know how to do that.

One idea I had, was to possibly estimate the average daily return of my trading strategy by:

2. Taking the average of all the daily returns per trade

Then finally I would compare it to the average daily return of an index over the same time frame. Does this make any sense or what would be a more appropriate approach?

A more appropriate approach is to sum your PNL each day across all of your positions and calculate the return for the book as a whole (assuming I understand your question correctly).

Return should be based on your bankroll/AUM/capital allocation, not your notional positions.

• Thanks a lot for your answer! That makes sense to me. So, just to clarify: On days that I do not close any trades, I would have return =0% and only on the days where I actually close trades I have return values? If I understand your answer correctly, that way I could compare it to the daily return of an index as a benchmark, correct? How would I approach comparing the performance of my strategy over a longer time frame - say a quarter? Do I take cumulative (daily) returns over the quarter or can I only work with the average of the daily return values over the quarter? Commented Feb 27, 2021 at 9:02
• "On days that I do not close any trades, I would have return =0%" - no, you will have MTM PNL each day (which will likely be non-zero). The value of your positions will be changing while the trades are open. Commented Feb 27, 2021 at 18:43
• "I could compare it to the daily return of an index as a benchmark, correct?" - which index and why? If you have a (possibly) market-neutral strategy, why is an index the appropriate benchmark? Loosely speaking, your benchmark should be a 'substitute good'. Commented Feb 27, 2021 at 18:45
• Thanks for the explanations! That makes sense. So I am assuming from the trades that we close, we carry on their profit and the investment? How can I measure how much return I would have made, if I would have invested 100k into this strategy? Is it even possible because in the end (lets say after 3 years) we would have all our profits divided by all our ever made investments on trades? This would again be just an average over all our trades that happened, right? Commented Feb 28, 2021 at 16:00
• I'd suggest something like the HFRX Equity Market Neutral index might be more appropriate. hfr.com/hfrx-indices-index-descriptions#. But arguably depends on what the strategies' stated aims are, what their risk factor exposures are, etc. Commented Mar 1, 2021 at 0:23