Unit 3 · Level 5 · Quant Foundations
Kelly & the size of edges
The Kelly criterion computes the bet size that maximizes long-run growth for a KNOWN edge. Its lessons: bet zero with no edge; even with an edge, overbetting past Kelly slows long-run growth, and betting far enough past it (about 2× or more) guarantees eventual ruin; and real pros bet fractions of Kelly because edges are estimated, not known. Your 1% rule? A humble fractional Kelly that assumed you might be wrong about everything. It was right to.
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What you get asked
Kelly's most counterintuitive theorem: betting MORE than the optimal fraction…
Despite positive edge on every single bet. Positive edge + oversized bets = ruin. Volatility drag eats the compounding. This is the mathematical tombstone of every over-leveraged genius you've heard of.
Match the sizing regime to its long-run fate
Why fractional? Because your edge estimate has error bars, and the penalty for overbetting is catastrophic while underbetting just means slower. Asymmetry says: round down.
Kelly punishes overconfidence with ruin and rewards ___ with survival. Encode humility in the size.
The math agrees with Formi: the account grows at the speed of your honesty about your own edge.
Volatility drag in one example: +50% then −50% leaves you at…
Arithmetic average: 0%. Geometric reality: −25%. Smoothness is mathematically profitable, not just pretty. This is WHY drawdown control beats return chasing.
Your edge: 60% win rate at 1:1 payoff. What percentage of bankroll does FULL Kelly say to bet?
At even payoff, Kelly = 2p − 1 = 2(0.60) − 1 = 20%. And now forget betting it: pros bet a FRACTION of Kelly, because estimated win rates lie.
The quant translation of everything Formiga taught you about sizing:
Never the fastest rate imaginable. Geometric growth is a marathon where falling = start over. Pace wins. 🐜
The rest of this unit
Kelly, volatility drag, drawdown math: the numbers behind every rule you follow.