Annualizing Sharpe Ratios When a Strategy Has Inactive Periods

Summary

The document considers how to calculate a daily Sharpe ratio when a strategy is invested during only part of the measurement period. The accepted answer says to include zero returns for periods when the portfolio is not held, then calculate the daily Sharpe ratio over the full sequence and annualize it using the stated trading-day convention. This makes inactivity part of the performance record rather than discarding those observations.

The rationale is that a cash-free or otherwise inactive portfolio has no investment gain in those periods and may incur an opportunity cost relative to the risk-free alternative. The short answer does not specify whether cash earns interest, how the benchmark or risk-free rate is defined, or whether capital is deployed elsewhere while the strategy is inactive. Those choices affect the return series and interpretation, so the suggested treatment assumes that inactive periods should remain in the strategy’s evaluated record and be represented as zero returns under the stated setup.

Key ideas

• Include inactive periods in the return series when evaluating a strategy across the full calendar span.
• The answer represents periods without holdings as zero returns before calculating daily Sharpe.
• Annualization uses the square root of the stated number of trading days.
• The treatment depends on assumptions about cash returns and the opportunity cost of being uninvested.

Tags

# How to calculate Sharpe Ratio if there are gaps in returns?


# How to calculate Sharpe Ratio if there are gaps in returns?












I see a lot of examples, like "We hold long position during whole year, then we calculate daily sharpe ratio and multiply it by SQRT(252) to get the annual one". This example makes sense for me. However, it is not clear, what to do with gaps. Let's say the stock was hold first quarter of the year and the last one, so there is a gap in half of year and, to be fair, there we no losses or gains, we just didn't trade. How to calculate Sharpe Ration in this case. AFAIK, Sharpe Ration should consider this period and the result should degrade, right? I think that daily Sharpe Ratio should be calculated on observations only (2 quarters of a year) and then the multiplier still has to be SQRT(252).

Would you agree? Thanks in advance.

## Answer by phdstudent (score 2, accepted)

https://quant.stackexchange.com/a/22712

You actually need to consider a 0 return on the periods with no holdings (during that period volatility is 0 and you have a negative return due to the opportunity cost of not holding risk free debt). From that you can compute your daily sharpe ratio and then multiply by $252^{0.5}$ as you mention.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.