Position Sizing, Risk of Ruin, Drawdowns and Portfolio Construction

A trading system with a genuine edge can still go broke, and one with a modest edge can compound for decades. The difference is how much is bet each time and how the bets are combined. That is the second factor of the book's edge equation, survival: sizing and leverage such that the worst plausible sequence of outcomes does not end the game. The mathematics is old. John L. Kelly Jr. of Bell Labs showed in 1956 that a gambler with an edge maximises the long-run growth of capital by betting a fixed fraction of wealth proportional to that edge ("A New Interpretation of Information Rate", Bell System Technical Journal, July 1956), and Edward Thorp carried the idea from blackjack to warrants and options ("Optimal Gambling Systems for Favorable Games", Review of the International Statistical Institute, 1969; Princeton Newport Partners). The arithmetic of loss is older still: a 50% drawdown needs a 100% gain to recover, a 90% drawdown a 900% gain. What sizing cannot do is make an estimate of edge more accurate. Full Kelly on an overestimated edge is over-betting, and over-betting at twice the true Kelly fraction has an expected growth rate of zero. The blow-ups this KB documents — Long-Term Capital Management in 1998, LJM Partners in February 2018 (~80% lost in days, Shared facts), Optionsellers.com in November 2018, Archegos in March 2021 — were sizing failures before they were anything else: each held positions whose plausible worst case was larger than the capital behind them. Meanwhile the businesses that survive longest, from the Turtle rules of 1983 (risk a fixed fraction of equity per unit of volatility) to the multi-manager platforms that cut a manager's capital after a drawdown of a few percent (Millennium, Citadel — reported, verify), are built around explicit, dull rules for how much to risk. This section covers fixed-fractional and volatility-targeted sizing, Kelly and fractional Kelly, risk of ruin, drawdown arithmetic, what stop-losses do and do not do, correlation and diversification across systems, and risk parity. The companion worked example combines three stylized systems — trend, short-volatility carry and mean reversion — and shows how much of a portfolio's apparent safety depends on what happens in the few weeks when they all lose together.