Wall Street sells the Arithmetic Mean. "This fund returns 20% per year on average!" But Vince shows that the Arithmetic Mean is a lie for traders who reinvest. If you lose 50% one year and gain 50% the next, your arithmetic average is 0%—but your geometric reality is a .
He famously proved this using a simple coin-toss game. Imagine a 60% win-rate system where you win $2 for every $1 you risk. Statistically, it’s a gold mine. Yet, if you bet a fixed 50% of your capital every trade, you will eventually go broke despite the positive edge. The math guarantees it.
Raw Optimal ( f ) often tells a trader to risk 20%, 30%, or even 50% of their capital on a single trade. While mathematically optimal for logarithmic utility , this leads to massive drawdowns (sometimes 70% or more) before hitting the exponential growth curve. Wall Street sells the Arithmetic Mean
Instead, it is a dense, equation-laden, mind-bending journey into the mathematics of survival.
In 1990, he wrote the warning label for gambling disguised as investing. Today, it remains the blueprint for exponential growth. You cannot predict the next trade. But with Portfolio Management Formulas, you can mathematically ensure you survive the next hundred trades. And in the futures, options, and stock markets, survival is the only thing that matters. He famously proved this using a simple coin-toss game
A deep dive into the 1990 classic that taught Wall Street that how much to trade is more important than what to trade.
This was the bombshell of 1990. Portfolio Management Formulas was the manual for defusing that bomb. While the book covers a vast landscape of statistical mechanics, three concepts form its backbone. 1. The ( f ) Concept (Optimal Fixed Fraction) Before Vince, traders used the Kelly Criterion. Kelly is great for bet sizing on a binary outcome (horse racing, blackjack). But markets are not binary; they have continuous distributions of outcomes (e.g., a stock can move 1%, 5%, or -20%). Yet, if you bet a fixed 50% of
Vince’s formulas force the trader to optimize for the . He argues that a system with a lower arithmetic average but less variance will make you richer over 100 trades than a system with a high arithmetic average and high variance. 3. The Risk of Ruin (Exact Calculations) Prior to Vince, "Risk of Ruin" was a vague concept. Analysts used simple formulas: "If you risk 2% per trade, you have a 0.5% chance of ruin." Vince laughed at this.