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Using Daily P&L to Measure an HFT Strategy’s Sharpe Ratio

Article Quant Q&A · Author: Scott Skiles
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Summary

The document addresses a measurement problem for high-frequency trading: a return-based Sharpe ratio can be hard to define when the amount of capital deployed is unclear. The question considers whether posted margin can serve as the capital base or whether a P&L-to-volatility measure is more appropriate.

The accepted response recommends calculating the ratio from daily profit and loss, using mean daily P&L divided by its standard deviation, then annualizing with the square root of the number of trading days. It also gives an opinion about Sharpe levels seen in practice, but supplies no supporting data or definition of the strategy universe behind those figures. The answer’s treatment of risk-free rates and return-based calculations is based on the respondent’s experience, so conventions may differ across firms, strategies, and reporting contexts.

Key ideas

  • Capital deployment can be difficult to define for an HFT strategy, complicating return-based Sharpe calculations.
  • The response recommends using daily P&L mean divided by daily P&L standard deviation.
  • Annualization scales this ratio by the square root of trading days per year.
  • The stated performance benchmarks are anecdotal and lack supporting evidence in the document.

Tags

High-frequency tradingStatisticsRisk management
Full text
# How to measure the Sharpe Ratio of a high frequency trading strategy?


# How to measure the Sharpe Ratio of a high frequency trading strategy?












The Sharpe Ratio is defined as `Sharpe ratio = (Mean portfolio return − Risk-free rate)/Standard deviation of portfolio return`.

Unfortunately, this does not make sense in the context of an HFT strategy. In order to calculate the return of a portfolio, you need to know the amount of capital deployed in an HFT strategy, which is not as straightforward as a portfolio of long/short stocks.

Should you calculate your return for an HFT strategy based on the margin posted for a specific strategy? Or is the inverse of the coefficient of variation `(AvgPnL / StdDev)` the best we can hope for?

## Answer by chrisaycock (score 8, accepted)

https://quant.stackexchange.com/a/41309

Use daily P&L rather than return rate1.

$$ Sharpe = \frac{\mu}{\sigma} $$

To annualize, multiply by the square root of the number of trading days in the year. For US equities, that would be 252.

$$ Annualized\ Sharpe = \frac{\mu}{\sigma} \times \sqrt{252} $$

As for what kind of Sharpe you should target, the lowest I've seen is 5 in practice. A good strategy is more like 8, and the highest end goes into the double digits. The consistency of HFT is incomparable to every other kind of trading strategy.

1In practice, I've never seen returns used to compute the Sharpe, even in low-frequency stat-arb strategies. Also, I've never seen anyone remove the risk-free rate, even if that's what every textbook states.

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.