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I'm somewhat confused with regards to calculating the annual standard deviation and Sharpe ratio for my portfolio of daily returns.

I have daily data ranging from 1960-2020 and use Excel to make some calculations. I have attempted 2 ways of doing it and don't know which makes most sense.

  1. I calculated the annual return for each individual year, from that I took the standard deviation of those 61 years (return: 12.10*, st. dev.: 25.70**)

  2. I calculated the annual return for each individual year, next I calculated the standard deviation for each individual year - but they're really low (less than 1). I got confused and tried to multiply these by the square root of 253 (assuming 253 trading days/year). The average of those 61 data points is 13.40 (st. dev.).

After that I want to calculate the Sharpe ratio using the avg. annual return (12.10%) minus the avg. risk-free rate (which I think I can either estimate with the square root of 253 or just take the avg of the yearly risk-free rate - I'm inclined to do the second).

But which standard deviation would be correct to use here?

*annualizing the daily returns by averaging all daily returns and multiplying them with the square root of 253 (trading days) got me 12.16

**annualizing the daily st. dev. by averaging all daily st. devs and multiplying them with the square root of 253 (trading days) got me 15.03. Also note that the returns do fluctuate quite a lot through the years, ranging between -53% and +77%.

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  • $\begingroup$ The standard deviation of returns of a time series over a long period will not in general be the average of the standard deviations in equal size subperiods. So if you need the standard deviation 1960-2020 just apply the Excel function =STDEV(.) to all daily returns for this period. $\endgroup$
    – nbbo2
    Commented Oct 22, 2021 at 13:33
  • $\begingroup$ Would you suggest to taking that avg and multiplying it with the sq. root of 253 (trading days) to get the annual st. dev. then? So the last part, which got me to 15.03? $\endgroup$
    – Sam
    Commented Oct 22, 2021 at 13:44
  • $\begingroup$ In my opinion yes. $\endgroup$
    – nbbo2
    Commented Oct 22, 2021 at 14:04
  • $\begingroup$ Alright, it does seem to add up with what I've read up about it so far. Thanks a lot! $\endgroup$
    – Sam
    Commented Oct 22, 2021 at 14:08

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