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Should I include or not the days a strategy has no open positions (thus no returns) in the Sharpe ratio calculation?

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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.

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Thank you Chris. Then how should I anualize the Sharpe ratio? Can I still use square_root(250)? –  Victor P Jan 18 '13 at 16:43
    
@VictorP Correct. –  chrisaycock Jan 18 '13 at 16:43
    
This is not obvious to me even though I do just that myself (use sqrt(250)). Why couldn't you argue that one should use sqrt(days_in_the_market_per_year)? –  klon Jan 19 '13 at 0:00
    
@klon You are correct; use the number of days in the market that you trade in. Perhaps Victor's market has 250 days. US equities is 252 days, which is what I use. –  chrisaycock Jan 19 '13 at 1:28
    
@chrisaycock Sorry, I wasn't clear. I meant why not sum up the days you actually have open positions over the year and square root that sum. What would be the argument against that? Well obviously it would be a different measure.. –  klon Jan 19 '13 at 15:54
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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.

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