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.

"...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

• 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

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.

"...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

• 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

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.

"...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

• 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