The label changes the question
A calendar-year change uses specified year-boundary observations. A holding-period change follows a chosen entry to a chosen exit. A strong annual endpoint can coexist with a difficult path inside that year.
The final displayed year may be partial. A year-to-date observation must name its actual end date and must not be presented as a completed calendar year.
Compound the path, not the percentages
For successive annual returns, multiply the growth factors. Adding returns or averaging them does not reproduce the endpoint wealth factor. The compound annual growth rate translates that endpoint into a constant annual rate over the stated number of complete years.
Arithmetic mean and compound annual growth rate answer different questions. Their difference is not a data error. Negative factors, missing years and incomplete horizons need explicit handling.
Formula: Cumulative factor = product of (1 + r) over the complete years. CAGR = factor^(1 / number of years) -1.
Complete windows and overlapping samples
A ten-year window needs ten consecutive eligible annual observations under the selected definition. Missing years cannot be filled with zero. A recent entry with less than ten years of history is incomplete, not a failed investment.
Rolling windows often share most of their observations. Their counts are not independent trials. A percentage of historical windows is not automatically a forecast probability.
Use annual research on its own clock
The century reading and annual studies keep reported research returns, country identities, local currencies and available years separate from daily fund-era paths. They do not manufacture a century of daily index prices.
The JST-derived material is provided for the recorded noncommercial research use with its required attribution and share-alike conditions. See the source notice before reusing it.