Measuring Portfolio Returns for Pairs Trades with Unequal Holding Periods
Summary
The document asks how to assess a cointegration-based pairs strategy when trades overlap and remain open for different lengths of time. It questions whether to average trade returns, divide each trade return by its holding days, or compare aggregated trade profits with committed capital. Those approaches can describe individual trades or produce averages, but they do not by themselves establish the return earned by the overall strategy over a calendar period.
The answer recommends calculating the portfolio’s profit and loss across all open positions each day, then computing the book’s return using bankroll, assets under management, or allocated capital as the denominator. This creates a time series of strategy returns that can be compared with a benchmark over matching dates. The guidance is concise and assumes the analyst has defined capital allocation and position valuation consistently; the document does not specify treatment of fees, financing, idle cash, or risk-adjusted comparisons.
Key ideas
- Aggregate profit and loss across all open positions at each daily valuation point.
- Calculate book returns using bankroll, assets under management, or allocated capital as the denominator.
- Different trade holding periods make averages of per-trade returns difficult to interpret as portfolio performance.
- A daily portfolio return series can be aligned with a benchmark over the same period.
- The answer does not specify costs, financing, or capital-allocation conventions.
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# How to compute returns of a Pairs Trading Strategy with different holding periods? # 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: - Estimating daily return per trade: (return of trade)/(number of days that trade was open) - 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? ## Answer by user42108 (score 2, accepted) https://quant.stackexchange.com/a/61386 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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