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Measuring Pairs Trading Performance at the Portfolio Level

Article Quant Q&A · Author: Craig
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Summary

The document asks whether performance statistics such as profit factor and Sharpe ratio should be computed for each leg of a pairs trade separately or for the combined position. Its example shows that the measured profit factor differs depending on whether the two instruments' results are evaluated individually or summed into pair-level results.

The response treats a pair as a small portfolio for risk and performance attribution. Because the legs may have favorable correlation, the combined position can have different return variation and risk-adjusted performance from either asset alone. The appropriate level of measurement follows the strategy's portfolio construction: assess the pair's joint returns when evaluating the pair trade. The document does not specify detailed accounting conventions or how to handle overlapping trades, transaction costs, or capital allocation.

Key ideas

  • A pair's performance statistics differ from statistics calculated separately for its two legs.
  • A pairs trade is a small portfolio, so measure its joint returns for pair-level attribution.
  • Correlation between the legs can change the combined portfolio's return variation and Sharpe ratio.
  • The example does not define conventions for overlapping trades, costs, or capital allocation.

Tags

Pairs tradingStatisticsPortfolio construction
Full text
# Performance Stats of Pairs Trades


# Performance Stats of Pairs Trades












This is something I've been thinking about for a while but I can't reach a clear conclusion. When we calculate, for example, the profit factor for a pairs trading strategy, do we treat each pairs trade as a single result or each of the separate trades on each instrument as a single result? For example, lets say we are trading 2 instruments A and B and we have the following results...

A: -2, 1, 3

B: 1,-2,1

Profit factor for each trade separably -> 5/4

Profit factor for each pair added together -> 4/2

If we treat each pairs trade as a single trade we get a better result, the same would apply when trying to calculate a Sharpe ratio. I guess one could ask the same question of hedged options trades, what do people generally do?

## Answer by Matt Wolf (score 3)

https://quant.stackexchange.com/a/4592

Of course you get through diversification effects different return variation and thus Sharpe ratios depending on whether you calculate the standard deviation on an individual asset or a portfolio standard deviation on a collection of assets. A pairs trade is a small portfolio so with favorable correlation properties you should generally get a better risk adjusted return on the pair than on each asset individually. Market practice is to treat a pair as a portfolio for risk attribution and performance attribution purposes. The whole point of the pairs trade was exactly that, the attempt at capturing a temporary deviation from a presumed co-integration pattern, correct?

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.