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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.

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    $\begingroup$ 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. $\endgroup$ – phdstudent Jan 12 '16 at 11:45
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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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