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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:

  • daily returns?

  • weekly returns?

  • quarterly returns?

  • monthly returns?

  • beginning of period prices?

  • end of period prices?

  • simple returns?

  • log returns?

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).

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Insofar as a standard exists, it would be a Sharpe ratio from monthly returns using arithmetic rather than log returns.

As a rule of thumb, arithmetic returns should always be used in any kind of reporting since log returns are an approximation (and one we tolerate for ease of use despite being slightly off, particularly for larger moves).

Also return is calculated as the average over interval and for given frequency not the geometric (or annualized return) return, per Sharpe's original paper. Morningstar uses their own definition which doesn't adhere to this.

Monthly is a kind of frequency standard, but daily Sharpe is a completely valid stat and will provide slightly different information. I typically calculate both but more frequently use monthly Sharpe as a quick reference for quality of strategy. Large deviations between the two suggest there are/may be things going on intra-month that isn't being accounted for at the monthly level.

Small differences in calculation can occur for any of a number of reasons (eg, small calc differences, data discepancies, missing data, etc), so trying to 'match' a calculation is sort of a fool's errand unless you need an exact match for some reason.

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The question isn't simply answered and the short answer is it depends on a number of factors.

The GIPS standard for investment managers is the only performance reporting standard AFAIK and it can be found here:

https://www.cfainstitute.org/en/ethics-standards/codes/gips-standards/firms

There are certain rules and requirements depending on the frequency you wish to report and other factors. There are also regulatory requirements which can vary (SEC, AIFMD exc.. exc..).

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