Aligning ETF Return and Volatility Calculations Across Periods
Summary
The question concerns calculating a five-year return and standard deviation for an ETF from daily adjusted closing prices. Its proposed approach computes volatility separately for each year and averages those annual figures, while compounding the yearly returns. The response points out that return conventions matter: a period return is commonly expressed as the change in value relative to the starting value, though alternatives exist.
The central guidance is to align the data frequency and measurement horizon. Daily volatility should be paired with daily expected returns, while a five-year return should be compared with a risk measure calculated over a matching five-year period. Published figures can differ because providers make different choices about definitions, sampling frequency, and time periods. The answer does not specify a universal provider convention or derive a single exact calculation, so matching a website requires identifying the methodology behind its displayed statistics.
Key ideas
- A simple period return is commonly measured as the change in value divided by starting value.
- Match daily volatility with daily expected returns when comparing risk and reward.
- Align the measurement period for return with the period used for its risk statistic.
- Published ETF statistics can differ because providers use different calculation choices.
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# How to calculate 5 years return & STD for ETF? # How to calculate 5 years return & STD for ETF? I want to calculate by-myself 5 year return & STD for SPY ETF. What I did: - Downloaded to Excel from yahoo finance historical data for the ETF (daily Adj. Close) from `1/1/start_year to 1/1/start_year+5`. - (A) Calculated for each year in Excel `STDEV.P` based on daily closed prices. (B) Calculated for each year return by `end_year_price/start_year_price`. - (A) Simple Arithmetic `Average` for the STD based on yearly STD's I have from above. (B) `Geomean` for the return based on yearly returns I have from above (compound average). Problem: The numbers far away from the figures we can find in Morningstar, yahoo finance etc. (Assume I work correct from the perspective of using numbers, percentages, +/-1, *100 etc...) Question: This is a Math exercise not a real world finance one. Does from pure mathematical point of view I have mistakes? Which means that the deviations from the figures published in yahoo finance can be explained with taxes, dividends etc. real economic world. OR: I have mathematical mistakes and this is not the way how to compute this figures (in such case - I would like to know how what are the mistakes). Thanks, ## Answer by RndmSymbl (score 1) https://quant.stackexchange.com/a/22115 I believe a few things need to be said here. First, returns are usually calculated (END_VALUE-BEGIN_VALUE)/BEGIN_VALE. There are other ways, but this is what is usually used, and much arguments can be had on what "value" actual is. Second, data frequency should be aligned so daily standard deviation should be aligned to daily expected returns. Third, the periods for the measures should be aligned so that a 5 year return is matched by a 5 year standard deviation. Now that should get you on the right track. However, since in these three decisions alone much discretion has to be applied it is expected that your calculations do not match what you see on a web site, unless you are able to infer their choice.
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