Choosing Return Frequency and Conventions for Sharpe Ratio Reporting
Summary
The document examines why published annualized returns, standard deviations, and Sharpe ratios can be difficult to reproduce. It raises choices that affect the calculation, including sampling frequency, price timing, and simple versus logarithmic returns, then describes an attempt to match a financial data provider’s reported S&P 500 figures. The accepted response says monthly arithmetic returns are a common reporting convention, while daily Sharpe ratios are also valid and may reveal behavior that monthly data smooths over.
The discussion cautions that annualized return is not necessarily the mean return used in the original Sharpe formulation, and that provider-specific definitions can differ. It also notes that small discrepancies can arise from calculation choices, data differences, and missing observations. Another response points to investment performance reporting standards and regulations, whose requirements can depend on the reporting context. The exchange does not settle every convention or reproduce the provider’s numbers; it emphasizes documenting definitions and avoiding false precision when comparing reported ratios.
Key ideas
- Monthly arithmetic returns are described as a common basis for reported Sharpe ratios.
- Daily and monthly Sharpe ratios can convey different information about strategy returns.
- Using annualized or geometric returns in place of average periodic returns can change the calculation.
- Data and definition differences can prevent exact replication of a provider’s reported metrics.
- Performance reporting requirements may vary by standard and jurisdiction.
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Full text
# Industry or academic standard frequency to report the return, standard deviation, and Sharpe ratio? # Industry or academic standard frequency to report the return, standard deviation, and Sharpe ratio? 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) 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). ## Answer by Chris (score 2, accepted) https://quant.stackexchange.com/a/58251 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. ## Answer by pyCthon (score 2) https://quant.stackexchange.com/a/58242 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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