1991issue C011-2

Weekly close-to-close volatility as a horizon filter

A weekly historical-volatility reading is a market-regime label used to score later directional tests. Editorial view: treat that label as an evaluation design, not a market call, until absolute daily aggregation, exponential smoothing, a full-standard-deviation band, and several look-ahead windows are compared side by side.

Historical volatility in this workflow is a weekly series built from absolute close-to-close percent changes and then judged as unusually high or low against its own mean and dispersion.
A market-regime label only says a reading sits above or below a chosen standard-deviation band, so a later directional test can be read in a high-volatility or low-volatility context.
Exponential smoothing is a 33-percent recursive average of that weekly series, treated as roughly comparable to a five-week window and scored against the unsmoothed index.
Extremes were marked with one-standard-deviation and two-thirds bands and scored over the next week, five weeks, 13 weeks, 26 weeks, and the following year.

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Current trackHistorical volatility analysis47 readings Exponential smoothing117 readings

A weekly label is an evaluation design

This archive article walks through a weekly historical-volatility workflow as an evaluation design. The first product is a market-regime label, not a forecast. A later directional test is scored only after that label is in place.

Editorial view: a weekly volatility reading should not be treated as a market call until absolute daily aggregation, exponential smoothing, a full-standard-deviation band, and several look-ahead windows are compared side by side.

Start from the absolute daily change

A weekly historical-volatility index can be formed by taking each session's absolute percent change in a major industrial average, scaling that change by 1,000, and averaging the scaled values over the week.

That building block is the absolute-daily-change: the unsigned percent move from one session close to the next, scaled by 1,000 so the weekly average is a usable number. Historical volatility, in this usage, is the weekly series of those values, later judged as unusually high or low against its own mean and dispersion.

Hold the unsmoothed week next to a 33-percent smooth

That weekly series can be converted to a 33-percent exponential smooth, presented as roughly comparable to a five-week average. Exponential smoothing here is a 33-percent recursive average of the weekly series, scored against the unsmoothed index.

Both the unsmoothed weekly index and the exponential smooth were scored on every week of a 10-year sample. Editorial view: scoring both constructions keeps an explicit quantitative baseline in view when the regime labels are marked.

Use a standard-deviation band as the regime cut

Extreme readings were marked with two alternative bands: one standard deviation from the mean and two-thirds of one standard deviation from the mean. A standard-deviation-band is that cutoff, used to mark unusual high and low points.

A market-regime is the label that a reading sits above or below the chosen band. The band does not replace the later directional test. It only supplies the high-volatility or low-volatility context for that test.

Score the same reading on five evaluation horizons

Those extremes were tested as directional calls over the next week, the next five weeks, 13 weeks, 26 weeks, and the following year. Each window is an evaluation-horizon: the forward span over which a regime reading is scored as a directional test.

Within that comparison, the exponentially smoothed series and the full-standard-deviation band were treated as the stronger of the two construction pairs that were tested.

Inspect the close-to-close record for a lasting rise

The same close-to-close series was inspected for a lasting rise in day-to-day volatility after program trading became more common. The plotted record was presented as not showing such a rise, while an intradaily effect was left open.

Editorial view: that inspection describes the weekly close-to-close record in the archive sample. It is not a statement about current markets, and it does not settle what happens inside a session.

DJIA weekly close-to-close volatility, 1981–1990

Day-to-day DJIA volatility as a 33 percent exponential of absolute close-to-close percent change times 1,000. The series stays near the mean until the 1987 crash spike, then settles without a lasting rise. Values were read from the plotted curve, not a table.DJIA · 1W · 1981-01-01T00:00:00.000Z to 1990-12-31T00:00:00.000Z

Merrill multiplies absolute daily DJIA close-to-close percent change by 1,000, averages each week, then applies a 33 percent exponential (about a five-week average). Dashed lines are mean and plus or minus one standard deviation. Digitized from the printed plot; weekly ticks are denser than the recovered sample.

Educational research material, not investment advice. Historical source context does not establish present-day performance.

6 of 31 in the Historical volatility analysis track

19951-14 pp.Next on Historical volatility analysisA modified volatility construction for weeks-to-months regimesHistorical volatility is the standard deviation of an asset's rates of return. Implied volatility is the input that makes an option pricing model match the traded price, and the two estimates can differ.

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