Risk Architecture & Market Regimes
Fortune's Formula
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 3 strategic pillars
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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.
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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.
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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 need | Where to get it | Cost |
|---|---|---|
| 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
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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.
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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.
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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
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Educational templates — a research diary companion, not investment advice.
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.