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Choosing a Return Denominator for Market-Neutral Sharpe Ratios

Article Quant Q&A · Author: sigirisetti
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Summary

Market-neutral long–short portfolios can produce positive profit and loss while having little or no net invested capital, making a conventional return denominator unclear. The document presents two ways to define returns for Sharpe ratio analysis: divide profit and loss by the portfolio’s total notional, or divide it by the cash tied up to satisfy margin requirements.

Margin-based returns can use changing daily margin or a larger, fixed cash reserve set aside to meet margin calls. For a portfolio of such positions, allocating capital by sub-portfolio risk budgets is described as a related approach. The central practical point is that the Sharpe ratio is scale-invariant when the return series and its volatility use the same denominator. The note offers no empirical comparison or universal convention, so the chosen basis should be stated clearly and applied consistently.

Key ideas

  • A market-neutral portfolio may have near-zero net capital, so net investment is a problematic return denominator.
  • Use total long–short notional as a denominator to measure the sub-portfolio’s profit and loss contribution.
  • Alternatively, calculate returns against cash committed to margin, using daily margin or a fixed reserve.
  • The Sharpe ratio is unchanged by consistent rescaling of returns and volatility.

Tags

StatisticsRisk managementPortfolio construction
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# How to calculate the Sharpe ratio for market neutral strategies?


# How to calculate the Sharpe ratio for market neutral strategies?












Suppose I am long one stock and short an index in a ratio effectively making market beta as zero and I close the position with some positive P&L.

How should I calculate the return for the portfolio above? How do I effectively calculate the Sharpe ratio for above long-short and market neutral portfolios?

## Answer by rhaskett (score 3, accepted)

https://quant.stackexchange.com/a/15206

There is no universally accepted answer for the main problem here which is the denominator for the return calculation is zero or near zero. There are a few common solutions to this issue.

The most simple solution is to use the total portfolio notional as the divisor for the PnL. This can be considered the PnL contribution of that long/short sub-portfolio to the total portfolio.

Another common but more complicated solution is based on capital locked up. To get into long/short positions or portfolios of these positions you often have to post some margin or a margin on a portfolio of these positions. The return is than calculated against the cash locked up to meet the margin. Now the margin varies from day-to-day so you can use this daily number or in real life more commonly you use a constant number larger than the actual margin which is buffer you have set aside to meet this margin. For portfolios of these positions this is similar to risk-budgeting which approximately proportions the cash locked up for each sub-portfolio.

The nice thing the Sharpe ratio will be very similar no matter which method is used. As long as the returns and volatility are both be calculated using the same scale it doesn't matter if the scale is large or small for a ratio.

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.