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How do I go from daily to annual sharpe?

Say I have an asset with average daily return of 0.1% and a daily return standard deviation of 1%.

My daily sharpe ratio is 0.1%/1% = 0.1

Now let me annualize, assuming 365 trading days. 0.1% daily return is (1+0.1%)^365 - 1 = 44% per year. (fixed, thanks commentors). While 1% sd becomes 1%*sqrt(365) = 19.1% annualized.

My annual sharpe is 44/19.1 = 2.30

Now I think that's not correct, because others calculate yearly return linearly as 0.1% * 365 instead of compounding (1.01)^365-1 but I don't see how that makes sense.

Thanks, Paul

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    $\begingroup$ It is unusual to compound the expected return. Instead the standard practice is that the return annualized is set to 365*0.1%. And since returns are usually measured per trading day it is standard to use 252 (the number of trading days) rather than 356 (the number of calendar days per year) as well. This is more about conventions than "what is right". $\endgroup$
    – nbbo2
    Commented Aug 1, 2021 at 16:12
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    $\begingroup$ One thing you didn't do is subtract 1 from your compounded annualized return. $\endgroup$
    – AlRacoon
    Commented Aug 1, 2021 at 16:31
  • $\begingroup$ The asset trades 365 days. Why would it be a linear 0.1%*365 rather than the compounding returns of ((1+0.1%)^365 -1) ? Doesn't make any sense to me $\endgroup$
    – Paul
    Commented Aug 2, 2021 at 9:58
  • $\begingroup$ Hi: Atleast to me, it doesn't seem "fair" to compound the return and then leave the standard deviation alone. If one was going to compound the return, then it feels like the standard deviation should be based off of the compounded returns also. A second point is that, whether one compounds or not really depends on whether the returns made in one day are being re-invested the next day. If not, then the returns shouldn't be compounded. $\endgroup$
    – mark leeds
    Commented Aug 2, 2021 at 11:51
  • $\begingroup$ Hi mark. We have a fixed amount of money invested, that grows/shrinks each day by the daily return. No money is taken out or put in. The returns are compounding. The standard deviation on a sample can't compound? I don't understand how you could calculate it differently. $\endgroup$
    – Paul
    Commented Aug 2, 2021 at 16:52

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I think standard is to do sqrt(365) * daily Sharpe ratio

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    $\begingroup$ right ( or sqrt(252 ) but Paul was asking why isn't compounding used when going from daily to annual. I was saying that, if one compounds and doesn't handle the denominator change in the daily return, then this would overstate the numerator in the resuiting sharpe ratio. So, I don't think compounding is necessarily wrong but it would need to be done with care. Also, the compounded series results in a different return series so the volatility of the return series would change also. $\endgroup$
    – mark leeds
    Commented Aug 3, 2021 at 16:23

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