Why does the same question have three answers on the same day?
Every statistic in this course was computed over a window, and the window was a choice. This lesson makes the choice visible by asking one question three ways on one date — 3 September 2026 — and reading the three answers.
Volatility, measured 2026-09-04
Annualised standard deviation of SPY.US's daily returns, ending 3 September 2026:
| Window | Volatility |
|---|---|
| Last 20 trading days | 8.1% |
| Last 60 trading days | 13.0% |
| Last 250 trading days | 12.8% |
| Last 10 years | 18.0% |
| Last 20 years | 19.4% |
Five windows, five numbers, one market on one day. None is wrong. The 20-day figure describes a quiet late summer; the 20-year figure carries 2008 and 2020; the 250-day figure is the one an options desk would compare with implied volatility. Asked "what is SPY's volatility?", the only defensible reply is "over what window?".
Correlation, same day
Correlation of SPY.US and TLT.US daily returns, ending 3 September 2026: last 60 days +0.32, last 250 days +0.23, last 1,000 days +0.15, full twenty years −0.31. The shorter the window, the more it reflects the current regime; the longer, the more it averages regimes that have ended. The stocks-and-bonds lesson's table was this fact laid out by calendar year.
Return, same day
SPY.US total return to 3 September 2026: one year +21.4%, three years +78.6%, five years +82.6%, ten years +315.7%. Annualised, the three-year figure is the highest and the five-year the lowest — the same fund, the same end date, and a ranking that depends entirely on whether the window starts before or after a bad year. A fund's "5-year return" on a factsheet is a window's return, and the window moves every month.
The rule
Short windows are timely and noisy; long windows are stable and stale. Neither is right, and the choice should follow the use. For a volatility to size tomorrow's position, short — the clustering lesson said yesterday is the best forecast. For a correlation to design an allocation that will be held for years, long, and then stress-tested on the crisis subset from the tails lesson. For a mean return, as long as exists, and then the standard error, which will say it was not long enough.
And always: state the window beside the number. A statistic without its window is a number without a meaning.
The provider's windows
/technical/{ticker}?function=stddev&period=20 returns a rolling 20-period standard deviation of the price, in price units — 4.31 for SPY.US on 3 September 2026, against a close of 773. That is a different object from the return volatility in the table: it measures how far the price wandered from its 20-day average, in dollars, and it is not annualised. function=volatility returns a rolling return volatility. Both carry their window in the period parameter, which is the one plain thing about a technical indicator: it says what it looked at.
In the data
One pull, /eod/SPY.US?from=2006-09-01&to=2026-09-03&fmt=json, and the table is five slices of its tail. The correlation rows are the same pull for TLT.US joined on date. /technical/SPY.US?function=volatility&period=20&from=2026-08-01&to=2026-09-03 gives the provider's version of the first row for comparison.
Try it now
- Here are the 21 sessions that make the 20-day row, and the 21 ending 31 March 2020. Reproduce the 20-day row from the first: twenty daily log returns, their standard deviation, times √252. Computed on 28 September 2026, dividing by 19 (the sample standard deviation) gives 8.3% and dividing by 20 gives the table's 8.1%, so write down which you used. Then compute the same figure for March 2020 and write it beside the 8.1%. The 250-day row is the identical computation on 251 closes.
Measure one, three and five years back from the last bar. Rank them annualised, and name the year that decides the ranking.