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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:

  1. Estimating daily return per trade: (return of trade)/(number of days that trade was open)
  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?

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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.

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  • $\begingroup$ 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? $\endgroup$
    – Rkl4397qa
    Feb 27 at 9:02
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    $\begingroup$ "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. $\endgroup$
    – user42108
    Feb 27 at 18:43
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    $\begingroup$ "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'. $\endgroup$
    – user42108
    Feb 27 at 18:45
  • $\begingroup$ 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? $\endgroup$
    – Rkl4397qa
    Feb 28 at 16:00
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    $\begingroup$ 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. $\endgroup$
    – user42108
    Mar 1 at 0:23

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