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James Marsden Hurst 1924—2005 Biography and works

Appendix III — Transaction interval according to Hurst

Hurst's theoretical test on 300 securities: why shorter intervals magnify annualized returns and why the curve is not an achievable performance record.

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In plain language — If every trade made money and capital were reinvested, more trades would greatly increase the annualized result. Hurst measures that theoretical potential; he does not measure what a trader actually earned.

Transaction interval and compounding Fig. A III-1 redrawn · historical relationship on the left, ideal arithmetic on the right. The curve measures ideal potential; costs, errors, and execution skill remain outside it. HURST 1970 · APPENDIX III Transaction interval and compounding Fig. A III-1 redrawn · historical relationship on the left, ideal arithmetic on the right CYCLEPEDIA DIAGRAM — EMICICLO AVERAGE OVER 300 STOCKS (NYSE + AMEX) THE COMPOUND INTEREST LAW 500% 1000% 2000% 5 10 20 30 transaction interval — weeks 100% 10k% 1M% 1 2 4 8 interval — weeks (log scale) p = c·(1 + i/q)^NQ Δi = 10% Δi = 20% AT 30 WEEKS ≈400% / yr AT 10 WEEKS ≈1,000% / yr BELOW 10 WEEKS theoretical take-off The curve measures ideal potential; costs, errors, and execution skill remain outside it.
The curve summarizes the relationship reported by Hurst and his compounding interpretation. Tap or select a point to see assumptions and limits.
Select the highlighted points to explore the detail

Sample and measure

Hurst says he selected 300 securities, half from the New York Stock Exchange and half from the American Stock Exchange. For each, he estimates the maximum return available with perfect timing at different average transaction intervals, then aggregates the results.

The measure is therefore a theoretical upper bound built with knowledge of past turning points. It excludes signal error, commissions, spread, slippage, liquidity, tax, and the ability to execute every transaction at the ideal price.

The curve’s shape

In Hurst’s chart, shortening the interval rapidly raises annualized return. He marks a “knee” around 10 to 20 weeks: beyond it the curve is flatter; below it the number of annual reinvestments increasingly dominates the result.

The main shape is explained by compounding. If capital is multiplied by 1 + r after each trade and n trades are completed in a year, the theoretical value is proportional to (1 + r)^n. Small changes in r or n become enormous when multiplied repeatedly.

Why it is not a promise

Perfect retrospective identification of highs and lows uses future information. In practice, shorter intervals increase noise, mistakes, turnover, and costs. Annualizing a theoretical per-trade return also assumes that identical, fully reinvestable opportunities remain available throughout the year.

The useful conclusion is not “trade as often as possible.” It is narrower: decision frequency and reinvestment radically change the scale of reported outcomes. Strategy comparisons must therefore hold horizon, capital, costs, and execution rules constant.

How to test the idea

A modern test would use signals available without future data, realistic costs, liquidity constraints, and a period unseen during design. Per-trade return, trade count, drawdown, and net outcome should be reported separately; a single annualized percentage can conceal all of them.

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