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Dollar-Neutral Strategy Returns and the Effect of Dividing by Two

Article Quant Q&A · Author: Plee
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Summary

The discussion explains the return convention for a dollar-neutral long-short position: a long investment in one asset is paired with an equal-dollar short position in another. The question concerns whether the return should be the long asset’s return minus the short asset’s return, or that spread divided by two. The accepted response says the undivided return difference is appropriate when short-sale proceeds finance the long position.

Dividing by two instead expresses the spread relative to the combined gross exposure of the two legs, so it changes the reported return scale under that convention. The response also states that the Sharpe ratio is unchanged by this constant scaling, since both average return and volatility scale together. The exchange is brief and does not define every possible capital or margin denominator; interpreting a reported return therefore requires knowing how the strategy’s capital base is specified.

Key ideas

  • For an equal-dollar long and short, the return difference can be used if short proceeds finance the long leg.
  • Dividing the return spread by two reports it on a different exposure or capital basis.
  • A constant division of returns by two leaves the Sharpe ratio unchanged.
  • Return figures should be interpreted in light of the strategy’s chosen capital denominator.

Tags

EquitiesMean reversionPortfolio construction
Full text
# Calculating Dollar-Neutral Strategy Net Return


# Calculating Dollar-Neutral Strategy Net Return












An example in the book, Quantiative Trading, the net return of a dollar neutral strategy of IGE and SPY is calculated.

```
% net daily returns
(divide by 2 because we now have twice as much capital.)
netRet=(dailyretIGE - dailyretSPY)/2;
```

I don't understand why we divide by 2. We essentially use the short sell from SPY to purchase shares of IGE for the dollar neutral strategy. Wouldn't the net return just be the daily return of IGE - daily return of spy? Hypothetically if I get 100 dollars by short selling spy and i use that to purchase 100$ shares of IGE, if a daily return of IGE is 10% while SPY is 5% then the net return will be 5% of my initial investment of 100 dollars totaling 105 dollars. Why are we dividing by 2?

## Answer by Quantoisseur (score 5, accepted)

https://quant.stackexchange.com/a/58039

Yes, you can just do IGE - SPY if you assume the short finances the long.

The Sharpe ratio will be the same whether or not you divide by 2.

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.