The Missing Billionaires

An Economist Best Book of the Year

"Making Money and Keeping It" – The Wall Street Journal

Over the past century, if the wealthiest families had spent a reasonable fraction of their wealth, paid taxes, invested in the stock market, and passed their wealth down to the next generation, there would be tens of thousands of billionaire heirs to generations-old fortunes today. The puzzle of The Missing Billionaires is why you cannot find one such billionaire on any current rich list. There are a number of explanations, but this book is focused on one mistake which is of profound importance to all investors: poor risk decisions, both in investing and spending. Many of these families didn’t choose bad investments– they sized them incorrectly– and allowed their spending decisions to amplify this mistake.

The Missing Billionaires book offers a simple yet powerful framework for making important lifetime financial decisions in a systematic and rational way. It's for readers with a baseline level of financial literacy, but doesn’t require a PhD. It fills the gap between personal finance books and the academic literature, bringing the valuable insights of academic finance to non-specialists.

Part One builds the theory of optimal investment sizing from first principles, starting with betting on biased coins. Part Two covers lifetime financial decision-making, with emphasis on the integration of investment, saving and spending decisions. Part Three covers practical implementation details, including how to calibrate your personal level of risk-aversion, and how to estimate the expected return and risk on a broad spectrum of investments.

The book is packed with case studies and anecdotes, including one about Victor’s investment with LTCM as a partner, and a bonus chapter on Liar’s Poker. The authors draw extensively on their own experiences as principals of Elm Wealth, a multi-billion-dollar wealth management practice, and prior to that on their years as arbitrage traders– Victor at Salomon Brothers and LTCM, and James at Nationsbank/CRT and Citadel.

Whether you are young and building wealth, an entrepreneur invested heavily in your own business, or at a stage where your primary focus is investing and spending, The Missing Billionaires: A Guide to Better Financial Decisions is your must-have resource for thoughtful financial decision-making.

Foreword xiii

Preface xvii

About the Authorsxxi

Acknowledgments xxiii

Chapter 1: Introduction: The Puzzle of the Missing Billionaires 1

Section I: Investment Sizing 13

Chapter 2: Befuddled Betting on a Biased Coin 15

Chapter 3: Size Matters When It’s for Real 27

Chapter 4: A Taste of the Merton Share 41

Chapter 5: How Much to Invest in the Stock Market? 49

Chapter 6: The Mechanics of Choice 67

Chapter 7: Criticisms of Expected Utility Decision-making 103

Chapter 8: Reminiscences of a Hedge Fund Operator 117

Section II: Lifetime Spending and Investing 127

Chapter 9: Spending and Investing in Retirement 129

Chapter 11: Spending Like You Won’t Live Forever 165

Section III: Where the Rubber Meets The Road 173

Chapter 12: Measuring the Fabric of Felicity 175

Chapter 13: Human Capital 193

Chapter 14: Into the Weeds: Characteristics of Major Asset Classes 201

Chapter 15: No Place to Hide: Investing in a World with No Safe Asset 235

Chapter 16: What About Options? 245

Chapter 17: Tax Matters 265

Chapter 18: Risk Versus Uncertainty 275

Section IV: Puzzles 285

Chapter 19: How Can a Great Lottery Be a Bad Bet? 287

Chapter 20: The Equity Risk Premium Puzzle 291

Chapter 21: The Perpetuity Paradox and Negative Interest Rates 297

Chapter 22: When Less Is More 303

Chapter 23: The Costanza Trade 309

Chapter 24: Conclusion: U and Your Wealth 319

Bonus Chapter: Liar’s Poker and Learning to Bet Smart 327

Cheat Sheet 335

A Few Rules of Thumb 340

Endnotes 343

Suggested Reading 357

References 359

Index 373

"...a smart and sophisticated primer on quantitative risk-management techniques."
—The Wall Street Journal

"A compelling book dealing with an important and neglected question in finance: not what to buy or sell, but how much. Even sophisticated professionals tend to answer this question badly, leading to lost fortunes. But financial theory provides the answer. Mathematical but not excessively so, this will appeal to anyone with an interest in markets."
—The Economist Best Books of 2023, December 9-15, 2023

"The most important investment decision is not 'what' but 'how much.' If you ever hear a professional investor talk about a trade that taught them a lot, prick up your ears. Usually, this is code for 'a time I lost an absolutely colossal amount of money,' and you are in for one of the better stories about how finance works at the coalface. On this front, Victor Haghani is a man to whom it is worth listening. Now, along with his present-day colleague James White, he has written a book that aims to spare other investors his mistakes . . . The Missing Billionaires . . . examines what its authors argue is a much more important—and neglected—question than picking the right investments to buy or sell: not 'what' but 'how much.'"
—The Economist Buttonwood column "Size Matters," September 21, 2023

Victor Haghani has 40 years' experience working and innovating in the financial markets, and has been a prolific contributor to academic and practitioner finance literature. He founded Elm Wealth in 2011 to help clients, including his own family, manage and preserve their wealth with a thoughtful, research-based, and cost-effective approach that covers not just investment management but also broader decisions about wealth and finances. Victor started his career at Salomon Brothers in 1984, where he became a Managing Director in the bond-arbitrage group, and in 1993 he was a co-founding partner of Long-Term Capital Management. He lives in London and Jackson Hole, Wyoming.

James White has spent two decades working in finance, covering the gamut of quantitative research, market-making, investing, and wealth management. He is currently the CEO of Elm Wealth, and previously has held research, trading, and executive roles at PAC Partners, Citadel, and Bank of America. He lives in Philadelphia.

Over the past century, if the wealthiest families had spent a reasonable fraction of their wealth, paid taxes, invested in the stock market, and passed their wealth down to the next generation, there would be tens of thousands of billionaire heirs to generations-old fortunes today. The puzzle of the missing billionaires is why you cannot find one such billionaire on any current rich list. There are a number of explanations, but this book is focused on one which is of profound importance to all investors: poor risk decisions, both in investing and spending. Many of these families didn’t choose bad investments—but they sized them incorrectly, and allowed their spending decisions to amplify this mistake.

This book offers a simple yet powerful framework for making important lifetime financial decisions in a systematic and rational way. It’s for readers with a baseline level of financial literacy, but doesn’t require a PhD. It fills the gap between personal finance books and academic literature, bringing the valuable insights of academic finance to non-specialists.

You will learn about the theory of optimal investment sizing from first principles. These ideas will then be extended to problems in lifetime financial decision-making, with emphasis on the integration of investment, saving and spending decisions. Throughout, attention will be paid to practical implementation details, including how to calibrate your personal level of risk-aversion, and how to estimate the expected return and risk on a broad spectrum of investments. Finally, you will see how a series of fascinating financial puzzles can be unlocked with the new framework and tools that have been acquired.

The book is packed with case studies and anecdotes, including one about Victor’s investment with LTCM as a partner, and a bonus chapter on Liar’s Poker. The authors draw extensively on their own experiences as principals of Elm Wealth, a multi-billion-dollar wealth management practice, and prior to that on their years as quantitative researchers and arbitrage traders.

Whether you are young and building wealth, an entrepreneur invested heavily in your own business, or at a stage where your primary focus is investing and spending, The Missing Billionaires: A Guide to Better Financial Decisions is your must-have resource for thoughtful financial decision-making.

Praise for The Missing Billionaires

“How much investment risk should I take? How much should I spend, and how much should I save? We all want answers to these questions, and financial economists have them, but the answers need to be translated into practical language. That’s exactly why you should read this enjoyable and insightful book, to understand and apply the best thinking about risk-taking and lifetime financial planning.”
—John Y. Campbell, Morton L. and Carole S. Olshan Professor of Economics at Harvard University

“Through years of dialogue with Victor and James, I have put into practice the ideas described in this book, and to great effect. They present a framework which encompasses many of the important principles I have learned through my nearly four decades of trading experience. The Missing Billionaires should be required reading at every bank, hedge fund and investment firm focused on enduring success.”
—Alan Howard, Founder of Brevan Howard

“This book provides a thought-provoking, straightforward introduction to some of the most important questions in personal finance, and an engaging, non-technical description of some of the answers provided by financial economists over the past fifty years.”
—Robert C. Merton, MIT Sloan School of Management Distinguished Professor of Finance, Nobel Laureate in Economic Sciences

“Haghani and White persuasively explain that to make good decisions under uncertainty, not only must we think probabilistically, but also we must apply those probabilities to the appropriate objective function. Thinking beyond the plight of the ‘missing billionaires,’ perhaps human history would have followed a gentler and more peaceful path if our leaders had made decisions with the ideas of this book in mind.”
—Philip E. Tetlock, Annenberg University Professor at the University of Pennsylvania, and co-founder of The Good Judgment Project

"This is a marvelous book that importantly extends the literature on financial decision-making. The authors creatively weave together the essence of practical considerations with insightful academic theory. One of a small handful of books that is timeless and should be read and reread over a lifetime for enjoyment and substance."
—Gary P. Brinson, CFA, Author, and Founder of Brinson Partners

"The missing billionaires in the book's title allude to the difficulty of keeping already-made fortunes. Believing that nobody should get rich twice, Victor and James arm investors with lessons galore, drawn from their long practitioner careers. Yet the core lessons come from academia, and this wonderful book gives the best shot for Expected Utility and lifecycle models to finally become widely used in real-world investment decision-making. Uniquely, this book puts position sizing in the center, showing through many illustrations how 'too much of a good thing' can be just too much."
—Antti Ilmanen, Principal at AQR Capital, Author of Expected Returns

"The Missing Billionaires addresses a topic that gets far too little attention in the investment community: how much to invest. The book is a terrific blend of theory, practice, and stories from the front lines. This is must-reading for anyone seeking to invest and spend wisely."
—Michael Mauboussin, Author and Head of Consilient Research, Morgan Stanley

"I enjoyed and learned from Victor and James' book on incorporating uncertainty directly into making better financial decisions. Rightly so, for them, risk is front and center. This book is a great education for all of us, seamlessly marrying sophisticated theory with applications, demonstrating the beauty of a risk architecture that combines specificity with illuminating implementations into the lifetime wealth management problem."
—Myron S. Scholes, Frank E. Buck Professor of Finance, Emeritus, Stanford Graduate School of Business, Nobel Laureate in Economic Sciences