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Choosing Risk Neutrality and Capital Weights for Pairs Trades

Article Quant Q&A · Author: Vladimir Belik
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Summary

The document asks how to divide capital between the long and short legs of a pairs trade and whether using a hedge ratio implies equal dollar allocations. Its answer explains that the appropriate split depends on which exposures a trader wants the portfolio to offset and which source of return the trade is intended to capture.

Dollar neutrality uses equal dollar values on both sides to reduce sensitivity to broad market direction. Other approaches size positions to offset beta, volatility, industry, or country exposures. These methods define neutrality differently, so a hedge ratio alone does not settle the capital allocation question. The discussion offers conceptual alternatives but no worked sizing example, estimation procedure, or evidence comparing their performance; the suitable choice depends on the manager’s risk objective.

Key ideas

  • Dollar neutrality balances the dollar value of the long and short positions.
  • Beta neutrality sizes the legs to offset their market beta exposures.
  • Volatility, industry, and country exposures can also guide the construction of a hedge.
  • The desired capital split depends on which risks the trader seeks to neutralize.

Tags

Pairs tradingEquitiesRisk managementPosition sizing
Full text
# What is the proper capital split/allocation between the long and short in a pairs trade?


# What is the proper capital split/allocation between the long and short in a pairs trade?












I am trying to understand the following. If I have $100, how do I determine how much to allocate to the long and short of a pairs spread?

You might say "use the hedge ratio you calculate, as that will tell you the number of shares of stock B to long/short for every share of stock A". The hedge ratio, though, is basically the "average" ratio between the prices of A and B. Therefore, by following the hedge ratio, won't my allocation always be 50/50? I have heard this is not optimal.

Is there any other way of splitting the capital?

## Answer by AlRacoon (score 4, accepted)

https://quant.stackexchange.com/a/70308

There are many different approaches to creating a portfolio comprising long-short pairs trades. Many take the approach of market neutrality. They attempt to create a portfolio that is insensitive to market direction and isolate the effect of the narrowing of the spread between the pairs.

Your description is an attempt to be market neutral by being dollar neutral. In other words, they take the same dollar value of the long position and the short position.

Others have a different definition of market neutrality, such as Beta neutrality. In this case they would take a Beta weighted value of each position such that the Beta of their long position would be offset by the Beta of their short position.

Others attempt to create a portfolio that is industry neutral, country neutral etc. And still others might take a volatility weighted off-setting positions to create a portfolio that is volatility neutral.

As you can see, the approach to creating a long short portfolio is dependent on what disparity of risks the portfolio manager is trying to exploit and what risks the portfolio manager is attempting to neutralize through the hedge, as well as that portfolio manager's definition of that risk.

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.