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Risk Architecture & Market Regimes

Fortune's Formula

William Poundstone · first published 2005

The story of the Kelly criterion — the formula that turns edge and odds into an exact position size. Bet more and you eventually go broke faster than you compound; bet less and you leave growth on the table.

The big picture

Poundstone traces one formula from Bell Labs through the casinos to Wall Street: the Kelly criterion, which computes the fraction of capital to stake so that long-run compound growth is maximized. The book's core bet is that position size — not entry selection — is where fortunes are actually made and lost, and that there is a mathematically correct answer to "how much", derived from information theory.

Why it matters now: concentrated AI positions with fat right tails are exactly where sizing discipline earns its keep. The same conviction at double the correct size does not double the outcome — it raises the probability of an unrecoverable drawdown.

The Kelly hill — growth rate against position size GROWTH RATE g(f) POSITION SIZE f → f* (FULL KELLY) f*/2 · ~75% OF GROWTH, HALF THE DRAWDOWN 2·f* — ZERO GROWTH RUIN TERRITORY same edge, bigger bet, guaranteed loss f* = (b·p − q) / b  ·  conviction is not a size — edge over odds is
The hill every position sits on: growth peaks at the Kelly fraction, and the same edge compounds into ruin once the stake doubles past it.

The 3 strategic pillars

  1. The formula

    Optimal stake is edge over odds — a precise function of win probability and payoff ratio, not of conviction.

    f* = (b·p − q) / b: p win probability, q = 1−p, b the win/loss payoff ratio. Zero edge → zero position, mechanically.

  2. Overbetting is ruin, not ambition

    Growth as a function of size is a hill: it peaks at Kelly and turns negative at roughly twice Kelly.

    Beyond f* the volatility drag outruns the edge — a bigger bet with the same edge compounds SLOWER, then destroys capital with certainty.

  3. Fractional Kelly in practice

    Because edge estimates are noisy, practitioners run half or quarter Kelly — most of the growth, a fraction of the drawdown.

    Half-Kelly keeps about three quarters of the growth rate while cutting the expected drawdown roughly in half; it also insures against overestimating your own edge.

What a Closelook reader does with it

The working use is a sizing gate after the idea and before the order: estimate win probability and payoff honestly, compute f*, then size at a half or a quarter of it. The mistake it prevents is the most expensive one in a trending market — being right about the theme and still losing money because one oversized position hit its drawdown first. Kelly makes "too big" a computable property instead of a feeling in hindsight.

The bridge to the Closelooknet approach

The Kelly criterion already sits in the Closelooknet glossary as one of the house's working concepts; this book is its full origin story and its casebook of misuse. It pairs directly with the barbell logic of ABR — Kelly says how much total risk the aggressive sleeve can carry, the barbell says where it lives — and with the Directional Alpha framework, whose pattern hit-rates are exactly the p and b inputs the formula asks for. The analog backtester on the asset pages publishes held-rates for structure setups: those percentages drop straight into the pack.

Action-Kit — from theory to practice

Tooling & data

What you needWhere to get itCost
Win rate + payoff ratio for YOUR setup The p and b inputs — from a trade journal or a backtest, never from memory Your own trade log; the asset-page analog backtest publishes held-rates per structure setup Below ~30 observations the inputs are noise — use quarter Kelly or stay at minimum size. Free
Spreadsheet or Python The arithmetic and the growth-vs-size curve The pack covers both; no external service needed Free

The formulas

  • Kelly fraction (discrete bet)

    f* = (b·p − q) / b = p − q/b
    • p — probability of a win
    • q = 1 − p
    • b — average win / average loss

    For even payoffs (b = 1) it reduces to f* = 2p − 1.

  • Kelly fraction (continuous, markets)

    f* ≈ μ / σ²
    • μ — expected excess return of the position
    • σ — its volatility

    The diffusion approximation used for portfolio-style sizing; same hill, same overbetting cliff.

  • Growth rate at stake f

    g(f) = p·ln(1 + b·f) + q·ln(1 − f)
    • f — fraction staked per bet

    g peaks at f*; it crosses zero near 2·f* — the mathematical definition of overbetting.

Applied Pack · free members

Kelly Applied Pack

Edge in, size out: the Kelly sizer with the full growth-vs-size curve, fractional presets and a Monte-Carlo view of what overbetting does to a bankroll.

  • Kelly_Sizer.xlsx — enter win rate and payoff ratio; the sheet computes full/half/quarter Kelly, the growth-rate curve across stake sizes and the 2×Kelly ruin line, all as live formulas
  • kelly_simulator.py — stdlib-only Monte Carlo: simulates bankroll paths at your chosen fractions so the drawdown difference between full and half Kelly is visible, not theoretical
  • README.txt — input sourcing (trade journal, analog held-rates), fractional-Kelly guidance and the educational-use disclaimer

Pack security

Macro-free Excel · plain-text Python you can read before you run it · no installers, no network access — the code works only on files you provide. Served only from closelook.net; we never distribute through download portals or email attachments. How to verify in 30 seconds →

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Closelook publishes a market diary, not investment advice. This condensed read restates the book's ideas in our own words for education — for the author's full argument, go to the source.