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Appendix II — Commonality according to Hurst

Hurst's historical DJIA–S&P 500 comparison, with observation kept separate from the generalization he drew from it.

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In plain language — Hurst overlaid two broad indexes and observed that many turns looked alike. That supports a common market component, but it does not establish that every individual stock moves in the same way.

Appendix II · from similarity to commonality Synthetic diagram of the DJIA–S&P 500 comparison; it does not reproduce the original plate’s data. Observation, inference, and proof are three different steps. HURST 1970 · APPENDIX II Appendix II · from similarity to commonality Synthetic diagram of the DJIA–S&P 500 comparison; it does not reproduce the original plate’s data CYCLEPEDIA DIAGRAM — EMICICLO DJIA S&P 500 1949 1961 OBSERVATION co-movement historical plate 1949–1961 HURST’S INFERENCE commonality extension to securities BOUNDARY hypothesis, not law modern replication needed Observation, inference, and proof are three different steps.
Synthetic curves explaining the comparison, not the original data. Tap or select an area to distinguish observation, inference, and sample limits.
Select the highlighted points to explore the detail

The comparison

Hurst compares the DJIA and S&P 500 from 1949 to 1961 using weekly data. He uses logarithmic prices and a normalization factor to make amplitude comparable. In the published plate, many fluctuations in the two aggregates appear close in timing and shape.

That observation is plausible for indexes sharing an economic environment and some constituents. It is not a test on independent companies: both are US portfolios, their constituents overlap, and diversification can suppress stock-specific movement.

From observation to inference

Hurst uses the resemblance to support commonality: part of price movement would be shared by many stocks. He then extends the signature studied on the DJIA to a larger share of the market and argues that company fundamentals are not the main cause of the index oscillations he observes.

Those latter statements are the author’s interpretations, not results generated automatically by the chart. Similar indexes demonstrate a strong common component; on their own, they neither identify its cause nor quantify what remains specific to each stock.

A modern check

Today the question would be addressed by separating market, sector, and security returns, then measuring rolling correlation and stability across regimes. It would require non-overlapping samples, international indexes, and out-of-sample tests. A common structure that changes with regime, weights, or composition should not be mistaken for an immutable wave.

The useful lesson is methodological: always distinguish what the comparison shows from what its author concludes. That distinction makes a historical source usable without turning it into doctrine.

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