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Bootstrap Testing of Pairs Trading Returns Against Random Pairs

Article Quant Q&A · Author: Laura
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Summary

The document explains a bootstrap comparison designed to test whether pairs trading returns reflect pair-specific reversion or simply the tendency of recent losers to rebound and recent winners to fall. On each historical date when a selected pair opens, the comparison substitutes securities drawn from the same prior-month return deciles as the respective members of the actual pair. It then compares the simulated pairs’ returns with the actual strategy’s returns and repeats the sampling across the trading dates to assess how much performance may be explained by this broader reversal effect.

The response describes the logic and suggests repeating the random selection many times before aggregating results. The evidence provided is an explanation of the paper’s quoted procedure, not a fresh empirical test or a full implementation recipe. It does not specify all sampling details, such as whether random securities can recur or how to handle overlapping trades, and the bootstrap comparison alone does not establish that a strategy will perform similarly out of sample.

Key ideas

  • A bootstrap benchmark can help distinguish pair-specific returns from general reversal effects.
  • Random comparison securities are selected from the same prior-month return deciles as each traded stock.
  • Repeated resampling shows how results vary across alternative random selections.
  • The comparison should preserve the historical dates on which the actual pairs opened.

Tags

EquitiesPairs tradingMean reversionBacktestingStatistics
Full text
# Bootstrap Method for Assessing Pairs Trading Performance


# Bootstrap Method for Assessing Pairs Trading Performance












After reading this paper I tried to replicate it. I almost done, but I am stuck on the section 3.6 where the author constructs a random pair (how he constructs this?) for Assessing Pairs Trading Performance by using a Bootstrap Method.

Pairs Trading: Performance of a Relative-Value Arbitrage Rule

"In particular, we conduct a bootstrap where we compare the performance of our pairs to random pairs. The starting point of the bootstrap is the set of historical dates on which the various pairs open. In each bootstrap we replace the actual stocks with two random securities with similar prior one-month returns as the stocks in the actual pair. Similarity is defined as coming from the same decile of previous month's performance. The difference between the actual and the simulated pairs returns provides an indication of the portion of our pairs return that is not due to reversion. We bootstrapped the entire set of trading dates 200 times."

Any help??

I trully apreciate a help.

There is Any other way to assess the performance of a pairs trading strategy?

Thanks

LAura

## Answer by Magic is in the chain (score 2, accepted)

https://quant.stackexchange.com/a/48962

Assume on a date t, your pair trading strategy said trade the pair: A and B, say go long A, and short B. By definition of the pair strategy, it is very likely that the price of A declined whereas that of B increased in the previous period; so from pair trading perspective, A is cheaper, whereas B is expensive. So we buy A and sell expensive B, expecting A to go up, and B to decline.

Now what the quoted paragraph is trying to do is to check whether the return of the pair trading strategy is actually coming from negative auto-correlation, which as per the article you quoted is well documented, and roughly amount to: what goes down, goes up, and vice versa!

To test this hypothesis, they rank the return of the stocks in the previous month (just prior to trading date t), and group it into declines. Now you can replace A and B by random stocks from their respective deciles. So stocks in the decile of A would most likely have declined in the previous month, otherwise they won’t be in the same decile, and the stocks in the same decile as B would have increased in value. If this alternative strategy produces the return of the pair trading then you would have reason to believe that the return of the pair trading is actually coming from negative auto correlation in returns, and labelled pair trading.

You can repeat the randomness in the above, say 200 times, so each time the algorithm will hopefully pick different stocks from the respective deciles of A and B, and you will get more confidence, in the sense that the finding are more robust and not solely driven by one random set of stocks.

You can apply the above logic to all trading dates, which is straightforward, and then aggregate the results.

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.