Everyone (funds, banks, academics, financial information sites etc.) reports the annualized return, standard deviation, and Sharpe ratio. Yet we never get to know what the basis of their computation is:
beginning of period prices?
end of period prices?
I tried to replicate the calculation from Morningstar. They report the following for the S&P500 as of end of August 2020:
annualized returns: 11.15% (10yrs), 10.80% (5yrs), 8.96% (3yrs)
annualized st.dev.: 13.38%, (10yrs), 14.80% (5yrs), 17.51 (3yrs)
Sharpe ratio: 0.92 (10yrs), 0.77 (5yrs), 0.66 (3yrs)
By just dividing
ret/sd, I get considerably lower SR. I am aware that formally one should also take into account the risk-free rate, which however has been close to zero and would have a negative impact anyway (should get yet lower SR).
I tried to replicate the calculation in R, here's my gist. Unfortunately, I cannot find a method that get's me close enough to Morningstar's numbers on all of their reported periods (3/5/10yrs).
My question is what is the industry standard? If there's no standard, then everyone could calculate in whatever way it gets the best results for them (data dredging).