What the book covers

The book discusses five layers of wealth dynamics in a multiplicative world, each with runnable programs:

1. Ensemble average and time average. Why the expected value can be positive while almost every participant loses; Ole Peters’ ergodicity economics and how economists have responded to it.
2. Geometric Brownian motion and volatility drag. Why, by Itô’s lemma, the long-run growth rate is μ − σ²/2, and how leverage turns against compounding through the term −L²σ²/2.
3. The Kelly criterion. The betting fraction that maximises long-run growth, and why full Kelly is still too aggressive when the parameters are uncertain.
4. Absorbing barriers. With rigid spending, how the thickness of a cash buffer changes, non-linearly, the probability of getting through a downturn.
5. Rebalancing and tails. Where Shannon’s demon and the rebalancing bonus come from, and their limits; extreme events under fat-tailed distributions, and when a “barbell” helps and when it merely bleeds slowly.

Chapter 7 reads these modern results beside the ways of managing wealth attributed to Jiran, Fan Li and Bai Gui in Sima Qian’s Shiji, chapter 129, “The Biographies of the Money-Makers”. Chapter 8 offers a four-step checklist for the cash-flow and allocation of a household or a firm, and a pre-registered randomised controlled behavioural experiment.

This book complements 5D Library volume 6 (5DL-B-006), The Economics of Attention: that book also reads the “Money-Makers”, to discuss the scarcity and allocation of attention; this one asks how wealth compounds through time and how to avoid reaching zero.

Claims corrected on checking

Several claims behind this book needed correction or qualification once they were checked. “Almost surely heading to zero” means, mathematically, that wealth tends to zero: almost every path gets ever closer to zero, though none reaches it exactly. Peters’ ergodicity view does not overturn expected utility theory: under multiplicative dynamics, maximising expected logarithmic utility and maximising the time-average growth rate lead to the same decisions; the book also sets out economists’ criticisms of it. In the continuous model, “twice Kelly” brings the long-run growth rate back exactly to the risk-free rate rather than causing immediate ruin; only beyond that does it turn negative. The rebalancing bonus of Shannon’s demon comes from volatility together with the condition that the two holdings grow at similar rates; in a persistent trend buy-and-hold does better, and transaction costs eat part of the bonus. If the high-payoff part of a barbell is priced above fair value, as most option protection is, it bleeds slowly in the long run; its value lies mainly in capping the largest loss, not in raising returns as such. In the “Money-Makers”, “in drought, invest in boats; in floods, invest in carts” belongs to Jiran’s policies; Fan Li is the man who adopted and applied them. Each chapter says so where it arises, and the Editor’s Notes published with the book files collect these points.

How to read the boxes

As in other 5D Library books, different kinds of statement are marked separately.

About this edition

This is version 1.0.0, the first complete edition: a preface and eight chapters, in Chinese and English. Corrections and missing references are welcome through the 5D Library website.