Whether to Include Flat Days in Sharpe Ratio Calculations
Summary
The document presents competing views on calculating a strategy’s Sharpe ratio when it has no open positions. Some responses argue for excluding such days because they have no realized strategy return and including zero or forward-filled observations could alter the measured return pattern. Another response argues that including zero-return days preserves the strategy’s average return per unit of calendar time, which matters when annualizing performance. A further point is that excluding flat days while using a nonzero risk-free rate can overstate the Sharpe ratio.
The discussion does not resolve the disagreement with a single rule. The appropriate return series depends on what performance is meant to represent, including whether the statistic should reflect returns over elapsed time and how the risk-free rate is handled. The answers are brief forum opinions, not a formal derivation or empirical comparison, so the document offers a measurement issue to consider rather than a definitive calculation procedure.
Key ideas
- Including zero-return days measures performance across elapsed calendar time.
- Excluding flat days changes the return sample and may affect both the mean and volatility estimates.
- The risk-free rate can affect whether excluding days without positions is appropriate.
- The document presents conflicting recommendations and does not establish one universal convention.
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Full text
# Sharpe ratio in days with no open positions
# Sharpe ratio in days with no open positions
Should I include or not the days a strategy has no open positions (thus no returns) in the Sharpe ratio calculation?
## Answer by chrisaycock (score 7, accepted)
https://quant.stackexchange.com/a/7014
No, don't include them. Otherwise you'll just wind-up with zero-value returns (or worse, forward-filled returns), which will make your Sharpe ratio reflect a performance that didn't actually occur.
## Answer by Matt Wolf (score 4)
https://quant.stackexchange.com/a/7018
If you really think about the actual meaning of Sharpe ratios then you should come to the right conclusion yourself:
- It is a measure of excess risk-adjusted return (whether realized or unrealized)
In that you obviously only want to calculate actual returns. You do not have any actual returns on days with no open positions. Hence, why would you want to include such days?
=> The core thought here is to only measure the nature of the returns not whether returns occurred or not.
## Answer by Arbitrage Technologies (score 2)
https://quant.stackexchange.com/a/76380
its fundamental to include the zero in pnl returns when compute a sharpe or an information ratio.
the mean of returns u compute in numerator tells u the average returns per units of time.
lets say u dont include the zeros (days with no trades).
Then, that mean, will tell u that each day, you strategy returns is on average 10 basis points. now lets says you want to extrapolate the average return of the strat for 5 year. the, u will multiply 5 * 252 * 10...
but in reality u will never reach those 5 * 252 * 10 in five years because the 10 basis points didnt took into account real time spent, i mean, the days with no trades!
the same reflexion apply for stdev on the denominator.
## Answer by feetwet (score -1)
https://quant.stackexchange.com/a/14033
Remember that Sharpe ratio includes a risk-free rate of return ("RFR").
Unless the RFR is zero, then excluding days when you have no position is not correct and will technically overstate your Sharpe ratio.
And if you're using a RFR of zero then what you're actually providing is the signal-to-noise ratio. (Although yes, I acknowledge that in recent years the RFR is practically zero. But that doesn't justify these other incorrect answers.)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.