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The Missing Billionaires: A Guide to Better Financial Decisions
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 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 A Guide to Better Financial Decisions is your must-have resource for thoughtful financial decision-making.
416 pages, Hardcover
Published September 6, 2023
536 people are currently reading
2611 people want to read
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October 10, 2024
Aprender de errores ajenos, sobre todo los catastróficos, siempre traerán un elemento de sabiduría. Por ello, luego de la quiebra del Hedge Fund Long Term Capital Management (LTCM) en 1998, Victor Haghani – uno de los socios fundadores – dedicó un tiempo considerable en cómo evitar un resultado similar cuando se gestiona un portafolio de inversión. Esta búsqueda lo llevó a fundar una firma de asesoría, Elm Wealth, junto a su socio James White. En ella, crearon un sistema propio (Dynamic Index Investing), poniendo al riesgo como pilar en la toma de decisiones.
El libro The Missing Billionaires (2023) responde a la pregunta de por qué vemos tantas familias con altos patrimonios que no logran conservar su riqueza de manera intergeneracional. Un dicho bien conocido es que es más difícil preservar la riqueza que construirla. Otras personas sugieren que ambos estadios requieren habilidades diferentes, las cuales son difíciles de transferir. De hecho, los autores narran la historia de la familia “Vanderbilt”, identificando dos puntos comunes en lo que ven en la actualidad: 1) dimensionamiento incorrecto de cuanto invertir; y 2) gasto recurrente que no refleja las fluctuaciones del patrimonio del inversionista a lo largo del tiempo.
Cabe resaltar que gran parte de los libros en finanzas subrayan la importancia en qué invertir (acciones, bonos, alternativos), dejando de lado un tópico no menos relevante: cuánto invertir en cada uno. La propuesta del libro es guiar esta última decisión sobre un marco de referencia unificado. La lección: buenas oportunidades de inversión con un mal “sizing” pueden resultar en una pérdida permanente del capital, sobre todo cuando operamos en un entorno de incertidumbre y consideramos el efecto negativo de la volatilidad.
Si bien el libro no es para una lectura cómoda en la playa y requiere conocimiento intermedio de estadística y matemática, la información presentada es muy valiosa, con un uso concreto sin quedarse en lo teórico. Ejemplos: (i) por qué el objetivo fundamental del inversionista no debe ser maximizar el nivel de patrimonio absoluto sino el crecimiento anual compuesto de éste en el tiempo (con demostración matemática incluida); (ii) tomar en cuenta la función de utilidad esperada del inversionista y cómo su forma influye en el nivel de bienestar; (iii) la fórmula de “Merton” y el criterio de “Kelly” pueden ser un gran punto de partida para la distribución óptima de portafolio.
El libro The Missing Billionaires (2023) responde a la pregunta de por qué vemos tantas familias con altos patrimonios que no logran conservar su riqueza de manera intergeneracional. Un dicho bien conocido es que es más difícil preservar la riqueza que construirla. Otras personas sugieren que ambos estadios requieren habilidades diferentes, las cuales son difíciles de transferir. De hecho, los autores narran la historia de la familia “Vanderbilt”, identificando dos puntos comunes en lo que ven en la actualidad: 1) dimensionamiento incorrecto de cuanto invertir; y 2) gasto recurrente que no refleja las fluctuaciones del patrimonio del inversionista a lo largo del tiempo.
Cabe resaltar que gran parte de los libros en finanzas subrayan la importancia en qué invertir (acciones, bonos, alternativos), dejando de lado un tópico no menos relevante: cuánto invertir en cada uno. La propuesta del libro es guiar esta última decisión sobre un marco de referencia unificado. La lección: buenas oportunidades de inversión con un mal “sizing” pueden resultar en una pérdida permanente del capital, sobre todo cuando operamos en un entorno de incertidumbre y consideramos el efecto negativo de la volatilidad.
Si bien el libro no es para una lectura cómoda en la playa y requiere conocimiento intermedio de estadística y matemática, la información presentada es muy valiosa, con un uso concreto sin quedarse en lo teórico. Ejemplos: (i) por qué el objetivo fundamental del inversionista no debe ser maximizar el nivel de patrimonio absoluto sino el crecimiento anual compuesto de éste en el tiempo (con demostración matemática incluida); (ii) tomar en cuenta la función de utilidad esperada del inversionista y cómo su forma influye en el nivel de bienestar; (iii) la fórmula de “Merton” y el criterio de “Kelly” pueden ser un gran punto de partida para la distribución óptima de portafolio.
January 23, 2024
4 out of 5, really liked it. It's hard to go with 5 for me after reading all these things about fat-tailed.
The title of the book raises the question, what happened to all the billionaires and what they sucked at so that they have their fortunes disappeared. Then, through the rest of the book it tries to help you to learn how not to suck in the same way.
If you haven’t heard about the Kelly criterion, Sharpe ratios, the mighty Expected Utility function or if you went bust by using leverage because some told you to do so, this book will help you a lot. The way it introduces the new terms and discusses outcomes is straightforward and precise. Beware, this books includes some equations and mentions variance, variability and a few others. If you’re afraid of some math though, I’m not sure you should deal with money anyways so 🤷
Big kudos for:
1. covering options from the point of leverage and showing that two items (bonds, stock) is sufficient for a usual person to manage their exposures according to the risk preference
2. showing that personal income potential should be taken into considerations when planning
3. providing needed graphics, especially when discussing fat-skewed distributions and risk preference
The last thing is that after reading Taleb’s work, one might not be a fan of getting into the normal distributions for stock. Still, the barrelled approach (T-bones and stock) is some common denominator (NNT and his fans, don't kill me for this simplification).
The title of the book raises the question, what happened to all the billionaires and what they sucked at so that they have their fortunes disappeared. Then, through the rest of the book it tries to help you to learn how not to suck in the same way.
If you haven’t heard about the Kelly criterion, Sharpe ratios, the mighty Expected Utility function or if you went bust by using leverage because some told you to do so, this book will help you a lot. The way it introduces the new terms and discusses outcomes is straightforward and precise. Beware, this books includes some equations and mentions variance, variability and a few others. If you’re afraid of some math though, I’m not sure you should deal with money anyways so 🤷
Big kudos for:
1. covering options from the point of leverage and showing that two items (bonds, stock) is sufficient for a usual person to manage their exposures according to the risk preference
2. showing that personal income potential should be taken into considerations when planning
3. providing needed graphics, especially when discussing fat-skewed distributions and risk preference
The last thing is that after reading Taleb’s work, one might not be a fan of getting into the normal distributions for stock. Still, the barrelled approach (T-bones and stock) is some common denominator (NNT and his fans, don't kill me for this simplification).
December 21, 2023
An intriguing premise underpins the raison de'etre for this book; if you look at the billionaires around over 20th century, there are far fewer of them or their descendants than you would expect had they managed that wealth wisely. The reasons for that number in the many; changing times, descendants could have frittered it away in folly and sloth, wealth erosion that comes from the estate being caught up in legal battles... The authors instead chose to concentrate on the wealth erosion that comes from poor sizing of investment pots that amplify the financial mistakes made by the would-be billionaires. This also applies to the other 99%.
The book builds a lot on financial theory centering on probability and optimization before going into the real world examples. I felt it spent too much time on theory and very little on real world experiences and as such on most occasion it reads like an assigned literature for some class. This is hardly the book that you read at an airport lounge as you wait for your flight. In their defence the authors issue a caveat that you need a baseline understanding of finance but do not necessarily need a PHD. They are right, you need a proper baseline before you get into this. As it is, it would greatly benefit finance professionals especially those involved in investment decision making. It would also benefit a tenacious "lay person" who doesn't mind going on reddit to find out what some concepts mean, I also saw tiktok is helpful on providing good results on search queries. Google should be your last option. Happy hunting
The book builds a lot on financial theory centering on probability and optimization before going into the real world examples. I felt it spent too much time on theory and very little on real world experiences and as such on most occasion it reads like an assigned literature for some class. This is hardly the book that you read at an airport lounge as you wait for your flight. In their defence the authors issue a caveat that you need a baseline understanding of finance but do not necessarily need a PHD. They are right, you need a proper baseline before you get into this. As it is, it would greatly benefit finance professionals especially those involved in investment decision making. It would also benefit a tenacious "lay person" who doesn't mind going on reddit to find out what some concepts mean, I also saw tiktok is helpful on providing good results on search queries. Google should be your last option. Happy hunting
April 12, 2024
Not a bad book, but it tries to take too much out of a relatively simple framework not unfamiliar to any economist (utility maximization, if you're curious). Could be an Excel spreadsheet + 50 page handbook.
June 8, 2024
Haghani y White abordan muy profundamente la cuestión de cuánto invertir de tal manera que se evite la ruina financiera, bajo la premisa de que los grandes millonarios del pasado han fallado mayoritariamente en la pregunta del "cuánto invertir", mas que en la pregunta de "en qué invertir". El libro tiene una perspectiva muy marcada desde las finanzas personales y wealth management, que es la práctica a la que se dedican Haghani y White en la actualidad.
Un dato importante y que le brinda relevancia a los aprendizajes es que Haghani fue socio fundador de Long Term Capital Management, famosísimo hedge fund que tuvo retornos exhorbitantes desde su creación en 1994 hasta abril de 1998, para después quebrarse espectacularmente en octubre de 1998. Esta experiencia de Haghani marca una buena parte de los aprendizajes del libro.
La cuestión de la asignación y distribución óptima de portafolio es abordada con herramientas que existen hace décadas en distintos papers de autores que marcaron la historia de la economía y las finanzas (e.g., Arrow, Fama, Kahneman, Merton, Samuelson, Sharpe, entre otros), pero cuya aplicabilidad en un sentido estricto de finanzas personales quizás no se había logrado divulgar de manera satisfactoria. Incluso, la principal herramienta que usan los autores es precisamente de Economía 101: Utilidad esperada.
A pesar de lo abstracto que resulta trabajar con los valores que arroja una función de utilidad, en la primera sección del libro los autores brindan muy buenas herramientas para descubrir la función de utilidad propia y la mejor manera de usarlo como punto de comparación, siempre en el marco de decisiones financieras importantes. También exploran cómo escoger el porcentaje óptimo de tu patrimonio por invertir en un producto dado, de tal manera que maximice tu utilidad esperada en función de los riesgos asumidos (i.e., el risk-adjusted return).
Las otras 3 secciones del libro construyen gradualmente a partir de los conceptos clave de la sección 1. Puntualmente muy interesantes, según el tipo de inversionista que sea el lector, los capítulos de la sección 3, relacionados con impuestos, capital humano, inversiones en derivados, e inversiones con una alta incertidumbre de por medio.
El libro, a pesar del esfuerzo divulgativo que hacen los autores, sigue siendo relativamente complejo y exhaustivo, y solo se le saca provecho con buen tiempo para profundizar en algunos conceptos, y con una hoja de Excel abierta para llevar rápidamente a la práctica, con el portafolio propio, los conceptos que se abordan.
Un dato importante y que le brinda relevancia a los aprendizajes es que Haghani fue socio fundador de Long Term Capital Management, famosísimo hedge fund que tuvo retornos exhorbitantes desde su creación en 1994 hasta abril de 1998, para después quebrarse espectacularmente en octubre de 1998. Esta experiencia de Haghani marca una buena parte de los aprendizajes del libro.
La cuestión de la asignación y distribución óptima de portafolio es abordada con herramientas que existen hace décadas en distintos papers de autores que marcaron la historia de la economía y las finanzas (e.g., Arrow, Fama, Kahneman, Merton, Samuelson, Sharpe, entre otros), pero cuya aplicabilidad en un sentido estricto de finanzas personales quizás no se había logrado divulgar de manera satisfactoria. Incluso, la principal herramienta que usan los autores es precisamente de Economía 101: Utilidad esperada.
A pesar de lo abstracto que resulta trabajar con los valores que arroja una función de utilidad, en la primera sección del libro los autores brindan muy buenas herramientas para descubrir la función de utilidad propia y la mejor manera de usarlo como punto de comparación, siempre en el marco de decisiones financieras importantes. También exploran cómo escoger el porcentaje óptimo de tu patrimonio por invertir en un producto dado, de tal manera que maximice tu utilidad esperada en función de los riesgos asumidos (i.e., el risk-adjusted return).
Las otras 3 secciones del libro construyen gradualmente a partir de los conceptos clave de la sección 1. Puntualmente muy interesantes, según el tipo de inversionista que sea el lector, los capítulos de la sección 3, relacionados con impuestos, capital humano, inversiones en derivados, e inversiones con una alta incertidumbre de por medio.
El libro, a pesar del esfuerzo divulgativo que hacen los autores, sigue siendo relativamente complejo y exhaustivo, y solo se le saca provecho con buen tiempo para profundizar en algunos conceptos, y con una hoja de Excel abierta para llevar rápidamente a la práctica, con el portafolio propio, los conceptos que se abordan.
July 29, 2024
3.5 stars!
July 11, 2024
The perfect blend of all my finance-related interests, everything that I'm looking for in an investing book. I see the world thru the same lens as the authors - financial economics, expected utility, portfolio theory, (somewhat) mathematical finance with a touch of discretionary finance.
Most financial advisors don't use EUT (nor do I think they've even heard of it tbh), and frankly there must be a reason for that. There is a large mismatch between economists and popular financial advice - the James Choi paper illustrates this well. Although I do think the latter camp gives a lot of terrible advice, I place the blame on economists - they really need to up their game to communicate their ideas to end-users. This book has done a tremendous job at this task.
It did start to drag a bit (volatility drag lmao) and I did lose some focus towards the end, hence this 1 definitely warrants a re-read. Also lacks more direct, practical advice - most chapters imo stop short of merely illustrating the elegant economics of finance, and hence it reads yet again like another uni econ class, not practical financial advice.
Most financial advisors don't use EUT (nor do I think they've even heard of it tbh), and frankly there must be a reason for that. There is a large mismatch between economists and popular financial advice - the James Choi paper illustrates this well. Although I do think the latter camp gives a lot of terrible advice, I place the blame on economists - they really need to up their game to communicate their ideas to end-users. This book has done a tremendous job at this task.
It did start to drag a bit (volatility drag lmao) and I did lose some focus towards the end, hence this 1 definitely warrants a re-read. Also lacks more direct, practical advice - most chapters imo stop short of merely illustrating the elegant economics of finance, and hence it reads yet again like another uni econ class, not practical financial advice.
February 6, 2026
I found this extremely hard-going. Not really because of the (extremely limited) amount of math or the concepts: I went into it reasonably aware of the Kelly Criterion for bet sizing, Constant Relative Risk Aversion (CRRA), certainty equivalency, and the Merton Portfolio problem. I've even written a large-ish number of blog posts using CRRA and certainty equivalency in my own thinking about retirement planning.
Some of the hard-going is maybe unavoidable. The authors need to introduce concepts that most people (even those in finance!) have never heard of. They're trying to do it in a layman's kind of way. To help build up an intuition for the results rather than just "see, a lot of complicated math says this is right!". But much of the early part of the book is very, very, very far from any kind of real-world financial planning and there's a lot of "trust us, we'll eventually flesh out things that aren't just toy examples about flipping coins".
I also feel like a book maybe isn't the best way to try to get this information across: there are a fair number of charts and tables that, especially in an ebook, do little to clarify things. Some kind of interactive website is almost certainly a better way to express a lot of this information. But obviously the authors have a dilemma there because books simply have far more reach than some random website is likely to ever get.
Once the authors reveal their advice it feels somewhat underwhelming: use the Merton Portfolio Problem (which means constantly shifting your asset allocation), measure your wealth with a CRRA utility function, and learn to live with variable withdrawals in retirement. I actually don't massively disagree with any of those things -- though the each of them comes with criticisms and complaints that I don't feel like the authors fully grappled with -- but I felt like the book never really gave a compelling vision of what using their framework means for a typical real world retiree and instead spent a lot of time on less interesting tangents (like an endowment: how many readers will ever manage an endowment?).
To some extent they mostly say: Yes, we know most people don't actually do things this way but they should because it is better. And there is some truth in that. But there are also some pretty valid reasons for why most people don't that I don't feel like they really settled in their favour. For instance, many people don't like changing their asset allocation dramatically. There are perhaps not great behavioural reasons for that -- "I'm trailing an arbitrary benchmark!" -- but there are also very valid tax reasons for it. Tax efficiency gets a single dismissive paragraph:
That's a massive increase in complexity, virtually requiring an advisor to execute it for most people, in order to reach a wishy washy "more tax efficient than one might guess". How much money are we actually losing to tax inefficiency here? Why so coy when they present things down to the dollar in other simulations?
That ties into probably the biggest complaint: the vast majority of people can't do any of this on their own, the math is beyond them, especially once you start adding in tax overlays, handling bequests, monthly rebalancing, constantly updating estimates of expected returns and correlations, and other complicating factors.
Which leads to the biggest disappointment which is simply that the end result is a much more marginal improvement over less complicated solutions than the title might imply. In the section on endowments (a subject that the vast majority of people aren't going to care about) they tell us that:
So following a simple, easily understood policy that doesn't require an advisor to execute achieves something like 85% of the efficiency of a Merton-optimal-portfolio that has a lot going on under the hood.
To get to an Merton-optimal portfolio requires the estimation of a lot of parameters. Section III covers this to an extent. How sure are you that you've chosen the right coefficient for your CRRA? That you've estimated the joint distributions (and correlations) of all your investment options? Can you imagine doing that every month or every quarter? When you're 75? Again: this approach really requires an advisor...who is going to charge you some percentage which then undercuts the efficiency gains.
To get a better feel for how all of this might work in practice, there's an unrelated free planner that uses many of the same ideas called TPAW Planner. Take a look at it but also take a look at the hundreds upon hundreds of questions and doubts in the discussion threads about it on Bogleheads.
Some of the hard-going is maybe unavoidable. The authors need to introduce concepts that most people (even those in finance!) have never heard of. They're trying to do it in a layman's kind of way. To help build up an intuition for the results rather than just "see, a lot of complicated math says this is right!". But much of the early part of the book is very, very, very far from any kind of real-world financial planning and there's a lot of "trust us, we'll eventually flesh out things that aren't just toy examples about flipping coins".
I also feel like a book maybe isn't the best way to try to get this information across: there are a fair number of charts and tables that, especially in an ebook, do little to clarify things. Some kind of interactive website is almost certainly a better way to express a lot of this information. But obviously the authors have a dilemma there because books simply have far more reach than some random website is likely to ever get.
Once the authors reveal their advice it feels somewhat underwhelming: use the Merton Portfolio Problem (which means constantly shifting your asset allocation), measure your wealth with a CRRA utility function, and learn to live with variable withdrawals in retirement. I actually don't massively disagree with any of those things -- though the each of them comes with criticisms and complaints that I don't feel like the authors fully grappled with -- but I felt like the book never really gave a compelling vision of what using their framework means for a typical real world retiree and instead spent a lot of time on less interesting tangents (like an endowment: how many readers will ever manage an endowment?).
To some extent they mostly say: Yes, we know most people don't actually do things this way but they should because it is better. And there is some truth in that. But there are also some pretty valid reasons for why most people don't that I don't feel like they really settled in their favour. For instance, many people don't like changing their asset allocation dramatically. There are perhaps not great behavioural reasons for that -- "I'm trailing an arbitrary benchmark!" -- but there are also very valid tax reasons for it. Tax efficiency gets a single dismissive paragraph:
In the simulations we presented in Exhibits 5.4 and 5.6 with monthly rebalancing, the average turnover of the dynamic strategies were 30% and 65% per annum, respectively, versus 10% for the static weight strategy. The strategies can be much more tax efficient than one might guess based on these turnover figures. This is because the buying and selling is usually limited to the most recently traded segment of the portfolio. This allows long‐term tax deferral to build up in the oldest and lowest basis tax lot holdings. The strategies can be made even more tax efficient through a tax loss harvesting overlay and through rebalancing less frequently and less fully to targets.
That's a massive increase in complexity, virtually requiring an advisor to execute it for most people, in order to reach a wishy washy "more tax efficient than one might guess". How much money are we actually losing to tax inefficiency here? Why so coy when they present things down to the dollar in other simulations?
That ties into probably the biggest complaint: the vast majority of people can't do any of this on their own, the math is beyond them, especially once you start adding in tax overlays, handling bequests, monthly rebalancing, constantly updating estimates of expected returns and correlations, and other complicating factors.
Which leads to the biggest disappointment which is simply that the end result is a much more marginal improvement over less complicated solutions than the title might imply. In the section on endowments (a subject that the vast majority of people aren't going to care about) they tell us that:
An endowment following the sustainable spending policy 3 for 100 years, spending 4.1% per year, would need about 15% more in starting assets in order to deliver the same Expected Lifetime Utility as by following the Merton‐optimal rule
So following a simple, easily understood policy that doesn't require an advisor to execute achieves something like 85% of the efficiency of a Merton-optimal-portfolio that has a lot going on under the hood.
To get to an Merton-optimal portfolio requires the estimation of a lot of parameters. Section III covers this to an extent. How sure are you that you've chosen the right coefficient for your CRRA? That you've estimated the joint distributions (and correlations) of all your investment options? Can you imagine doing that every month or every quarter? When you're 75? Again: this approach really requires an advisor...who is going to charge you some percentage which then undercuts the efficiency gains.
To get a better feel for how all of this might work in practice, there's an unrelated free planner that uses many of the same ideas called TPAW Planner. Take a look at it but also take a look at the hundreds upon hundreds of questions and doubts in the discussion threads about it on Bogleheads.
July 19, 2025
I was recommended this book because one of the authors was hawking it to a colleague via LinkedIn, probably thinking he has enough money to park it in their wealth management business.
It turned out to be the best personal finance book I've read, and significantly impacted some of my thinking about savings and money. Although the premise is simple, the concrete examples and exercises to think through make expected utility maximization seem much more practically actionable for an individual than I previously realized.
It turned out to be the best personal finance book I've read, and significantly impacted some of my thinking about savings and money. Although the premise is simple, the concrete examples and exercises to think through make expected utility maximization seem much more practically actionable for an individual than I previously realized.
May 25, 2025
About maximizing expected utility rather than expected wealth. Has some chapters on bet sizing but the rest of it is on personal finance. Apparently Fortunes Formula is better for bet sizing knowledge.
January 17, 2025
Too theoretical. Read like an economics textbook. Lack of real world examples putting the theories to practice
January 22, 2026
Very thorough with lots of data
December 24, 2023
I expected this book to address the many ways that Uber wealthy families dissipate their fortunes. It doesn’t do that. Instead it is a fairly academic overview of asset allocation and market psychology. Anyone educated enough to understand their equations most likely already understands the nuances of various asset classes. So most of the book offers fairly straightforward advice.
That said, there are quite a few good nuggets here. Especially for young investors establishing their industry knowledge.
That said, there are quite a few good nuggets here. Especially for young investors establishing their industry knowledge.
November 18, 2025
https://elmwealth.com/MissingBilliona...
Wiki
https://en.wikipedia.org/wiki/The_Mis...
TEDx 2013 ‘Where are all the billionaires?’ Victor Haghani
https://youtu.be/1yJWABvUXiU?si=6ANyE...
Compare vs Endowus Core-Enhanced portfolio (incl. U Access (IRL) Campbell Absolute Return UCITS (20%), AQR Sustainable Delphi Long-Short Equity UCITS Fund (20%))
https://app.sg.endowus.com/add-goal/c...
https://endowus.com/newsroom/endowus-...
May 2025 Elm Webinar - Dynamic Index Investing
https://youtu.be/Bx6upApSbOc?si=M9Kmu...
Elm funds - Elm Market Navigator ETF
https://www.elmfunds.com/
'Investment longevity: the secret behind Warren Buffett’s success' -Leonardo Drago
https://www.businesstimes.com.sg/weal...
'Concentrated portfolio managers: Courageously losing your money' -Owen Lamont Mar 2025
https://www.acadian-asset.com/investm...
'As stocks gyrate, it's time to know your risk tolerance' -BT 16 Feb 2025
https://www.businesstimes.com.sg/weal...
'Now Is the Time to Ask: How Much Market Risk Can You Take?' -BT 18 Apr 2025
https://www.bloomberg.com/opinion/art...
What %portfolio to allocate to stocks?
Prior conception: 75% but dynamic depending on where I think we are in the mkt cycle.
Haghani: Dynamic asset allocation ranging from 0-100% (no leverage) depending on Mean/Variance. Expected return of CAPE earnings yield above TIPs. Outperforms static 65/35 and even 100% allocation with higher Sharpe Ratio (excess return above risk-free rate/std deviation).
Merton's share %investment = µ/(𝜸*𝝈^2)
Why 60/40 doesn’t work for Aswath Damodaran - the case for 0% allocation to bonds =>it all depends on your personal situation
https://youtu.be/fmlPJBxzpMo?si=uN-MR...
The hot new investment trend is the ‘Total Portfolio Approach’. Does it work? -FT 18 Nov 2025
https://www.ft.com/content/540b2f9a-9...
What %wealth to spend p.a.?
Prior conception: Mr $ Moustache 4% rule
Haghani: max(discounted value of lifetime utility of spending)
infinite horizon optimal spending C♾️ = Rra - (Rra - Rtp)/𝛾
Where:
Rra = risk adjusted return of optimal portfolio
Rtp = investor's rate of time preference
𝛾 = investor's level of constant relative risk‐aversion
But since we don't have infinite life span:
finite horizon optimal spending Ct = C♾️/[1-(1+C♾️)^(-t)]
'Riding the Wheel of Fortune: A Practical Guide to Lifetime Investing and Spending' -Elm 11 Sep 2025
https://elmwealth.com/lifetime-invest...
What is bet size as %portfolio?
Prior conception: scale in up to max(5%, Kelly criterion)
https://www.albionresearch.com/tools/...
Haghani: half Kelly or 1/risk aversion x Kelly
I. Investment Sizing
Concept of volatility drag =>larger the %bet size =>larger the volatility drag. 20% up & 20% down =>4% drag but 50% up & 50% down =>25% drag
Look beyond just E(Return), variance, Sharpe ratio. Need to consider skew as well.
Chpt 8 Case Study of Victor Haghani's personal portfolio exposure in LTCM
Book suggested 50% allocation to Victor's liquid assets as optimal utility maximising allocation without providing any reasoning.
Here's Grok's explanation:
https://x.com/i/grok/share/GmVVCwNc8d...
You want to decide how much money to put into a risky investment versus a safe one. The risky investment has a good chance of earning 20% per year, but there’s a tiny 0.5% chance it could lose 90% of its value. The safe investment earns 5% guaranteed. You’re cautious about risks (you don’t like big losses), and we’re trying to find the best mix to make you happiest with your money’s growth, using a method called "maximizing expected utility." This method balances how much you could earn with how much risk you’re willing to take.
Key Facts:
Risky investment: Usually earns 20%, but 0.5% chance of losing 90%.
Safe investment: Always earns 5%.
Your preference: You’re cautious (risk aversion = 2), so you really dislike big losses.
Goal: Find the percentage of your money to put in the risky investment to maximize your utility.
What We Did:
Instead of just looking at average returns like in the earlier calculation (which suggested putting over 300% in the risky investment by borrowing), we used a method that considers how happy or unhappy you’d be with different outcomes. Big losses make you very unhappy, so we need to be careful.
The risky investment’s average return, after accounting for the 0.5% chance of a 90% loss, is about 19.45%.
Because you hate big losses, we used a formula that values avoiding bad outcomes more than chasing high returns.
We tested different percentages in the risky investment (like 0%, 50%, 100%) in a Monte Carlo simulation to see which makes you happiest.
Simplified Result:
Putting too much in the risky investment (like 100% or more) is too dangerous because of that small chance of a huge loss, which would make you very unhappy. Putting too little (like 0%) misses out on the good returns. After testing, about 50% in the risky investment and 50% in the safe investment seems to balance your desire for growth with your fear of big losses.
Why 50%?
It gives you a good shot at earning more than the safe 5% (possibly around 12-13% on average).
It protects you from losing everything if the rare 90% drop happens.
It matches your cautious nature, avoiding extreme risks.
Final Answer:
Put 50% of your money in the risky investment and 50% in the safe one. This mix should keep you happy by balancing potential gains with safety.
II. Lifetime Spending & Investing
What is the optimal joint spending & investing rule to follow over the rest of your life?
max(discounted value of lifetime utility of spending)
III. Where the Rubber meets the Road
How does Elm choose what deserves a place in your portfolio? 6 criteria that every asset class must pass:
1/ Low cost
2/ E(risk premium) >0
3/ Ability to systematically estimate expected return
4/ Non-zero-sum
5/ Liquid
6/ Tax-efficient
https://elmwealth.com/asset-classes/?...
Major asset classes:
https://cdn.prod.website-files.com/67...
1 TIPS
2 Treasury bills/bonds
3 Listed equities
4 Corporate bonds & o/r risky lending - minefield for the missing billionaires (especially when combined w/ pte bank margin lending, structured notes & o/r derivatives etc)
5 Real estate
6 Actively managed mutual funds - why would they beat the mkt af fees?
7 Factor investing eg Dimensional
https://www.magicformulainvesting.com/
8 Arbitrage - need to think carefully abt tail risks. If something is “mispriced”, what stops it fr being >mispriced?
9 Alternatives eg HF/PE/VC - why would they beat the mkt af fees? Are you rewarded for illiquidity? =>-ve liquidity premium. Lack of exits (distributed to paid-in capital (DPI) is the new IRR). Correlation to equities; macro funds/managed futures funds may provide diversification benefits
Damodaran on Alternatives: 'The (Uncertain) Payoff from Alternative Investments: Many a slip between the cup and the lip?'
https://aswathdamodaran.blogspot.com/...
Private market funds lag US stocks over short and long term - https://on.ft.com/3FIhor5 via @FT
10 Collectibles, art, commodities, gold, crypto - tracks wealth of "collectors" eg btc correlation w/ NASDAQ/Silicon Valley crowd
IV. Puzzles
i/r <0 ?
Cheat Sheet
1/ Bet sizing >impt than picking the right invt. Almost impossible to go broke picking the bad invt if you get the sizing right but easy to go bust taking too much risk even if you choose great invt.
Merton's Share %p = E(ERP)/(CRRA*σ^2)
Where E(ERP) = expected excess return of risky asset above risk free rate
CRRA = coefficient of risk aversion. If CRRA = 1 then Merton's Share = Kelly formula
https://evergreensmallbusiness.com/me...
2/ Mkts are highly competitive: who's on the otherside of the trade? Steer clear of leverage, shorting, concentration & complexity. Overconfidence is costly
3/ Goal = Max(E(lifetime utility of spending)) ≠ Max(E(Wealth))
Don't just focus on most likely outcome. Need to consider cost on risk.
4/ Control what you can by being attentive to fees, taxes, and efficiency in expenditures
'Stay invested for the long run? Think again' -Christopher Tan, BT 21 Apr 2025
https://www.businesstimes.com.sg/weal...
"Living simply and spending below my means gave me peace. It freed me to make life and business decisions without being held hostage by money... Clarify what really matters. Stop buying things you do not need, with money you do not have, to impress people you do not even know or care about. In investing, do not chase after best returns; rather, use an approach that gives you the highest probability of success. Peace is not found in more – it is found in enough."
Endowus Wealth Insights 2025
https://cdn.endowus.com/static-files/...
How to invest your enormous inheritance
https://elmwealth.com/how-to-invest-y...
https://www.economist.com/finance-and...
Wiki
https://en.wikipedia.org/wiki/The_Mis...
TEDx 2013 ‘Where are all the billionaires?’ Victor Haghani
https://youtu.be/1yJWABvUXiU?si=6ANyE...
Compare vs Endowus Core-Enhanced portfolio (incl. U Access (IRL) Campbell Absolute Return UCITS (20%), AQR Sustainable Delphi Long-Short Equity UCITS Fund (20%))
https://app.sg.endowus.com/add-goal/c...
https://endowus.com/newsroom/endowus-...
May 2025 Elm Webinar - Dynamic Index Investing
https://youtu.be/Bx6upApSbOc?si=M9Kmu...
Elm funds - Elm Market Navigator ETF
https://www.elmfunds.com/
'Investment longevity: the secret behind Warren Buffett’s success' -Leonardo Drago
https://www.businesstimes.com.sg/weal...
'Concentrated portfolio managers: Courageously losing your money' -Owen Lamont Mar 2025
https://www.acadian-asset.com/investm...
'As stocks gyrate, it's time to know your risk tolerance' -BT 16 Feb 2025
https://www.businesstimes.com.sg/weal...
'Now Is the Time to Ask: How Much Market Risk Can You Take?' -BT 18 Apr 2025
https://www.bloomberg.com/opinion/art...
What %portfolio to allocate to stocks?
Prior conception: 75% but dynamic depending on where I think we are in the mkt cycle.
Haghani: Dynamic asset allocation ranging from 0-100% (no leverage) depending on Mean/Variance. Expected return of CAPE earnings yield above TIPs. Outperforms static 65/35 and even 100% allocation with higher Sharpe Ratio (excess return above risk-free rate/std deviation).
Merton's share %investment = µ/(𝜸*𝝈^2)
Why 60/40 doesn’t work for Aswath Damodaran - the case for 0% allocation to bonds =>it all depends on your personal situation
https://youtu.be/fmlPJBxzpMo?si=uN-MR...
The hot new investment trend is the ‘Total Portfolio Approach’. Does it work? -FT 18 Nov 2025
https://www.ft.com/content/540b2f9a-9...
What %wealth to spend p.a.?
Prior conception: Mr $ Moustache 4% rule
Haghani: max(discounted value of lifetime utility of spending)
infinite horizon optimal spending C♾️ = Rra - (Rra - Rtp)/𝛾
Where:
Rra = risk adjusted return of optimal portfolio
Rtp = investor's rate of time preference
𝛾 = investor's level of constant relative risk‐aversion
But since we don't have infinite life span:
finite horizon optimal spending Ct = C♾️/[1-(1+C♾️)^(-t)]
'Riding the Wheel of Fortune: A Practical Guide to Lifetime Investing and Spending' -Elm 11 Sep 2025
https://elmwealth.com/lifetime-invest...
What is bet size as %portfolio?
Prior conception: scale in up to max(5%, Kelly criterion)
https://www.albionresearch.com/tools/...
Haghani: half Kelly or 1/risk aversion x Kelly
I. Investment Sizing
Concept of volatility drag =>larger the %bet size =>larger the volatility drag. 20% up & 20% down =>4% drag but 50% up & 50% down =>25% drag
Look beyond just E(Return), variance, Sharpe ratio. Need to consider skew as well.
Chpt 8 Case Study of Victor Haghani's personal portfolio exposure in LTCM
Book suggested 50% allocation to Victor's liquid assets as optimal utility maximising allocation without providing any reasoning.
Here's Grok's explanation:
https://x.com/i/grok/share/GmVVCwNc8d...
You want to decide how much money to put into a risky investment versus a safe one. The risky investment has a good chance of earning 20% per year, but there’s a tiny 0.5% chance it could lose 90% of its value. The safe investment earns 5% guaranteed. You’re cautious about risks (you don’t like big losses), and we’re trying to find the best mix to make you happiest with your money’s growth, using a method called "maximizing expected utility." This method balances how much you could earn with how much risk you’re willing to take.
Key Facts:
Risky investment: Usually earns 20%, but 0.5% chance of losing 90%.
Safe investment: Always earns 5%.
Your preference: You’re cautious (risk aversion = 2), so you really dislike big losses.
Goal: Find the percentage of your money to put in the risky investment to maximize your utility.
What We Did:
Instead of just looking at average returns like in the earlier calculation (which suggested putting over 300% in the risky investment by borrowing), we used a method that considers how happy or unhappy you’d be with different outcomes. Big losses make you very unhappy, so we need to be careful.
The risky investment’s average return, after accounting for the 0.5% chance of a 90% loss, is about 19.45%.
Because you hate big losses, we used a formula that values avoiding bad outcomes more than chasing high returns.
We tested different percentages in the risky investment (like 0%, 50%, 100%) in a Monte Carlo simulation to see which makes you happiest.
Simplified Result:
Putting too much in the risky investment (like 100% or more) is too dangerous because of that small chance of a huge loss, which would make you very unhappy. Putting too little (like 0%) misses out on the good returns. After testing, about 50% in the risky investment and 50% in the safe investment seems to balance your desire for growth with your fear of big losses.
Why 50%?
It gives you a good shot at earning more than the safe 5% (possibly around 12-13% on average).
It protects you from losing everything if the rare 90% drop happens.
It matches your cautious nature, avoiding extreme risks.
Final Answer:
Put 50% of your money in the risky investment and 50% in the safe one. This mix should keep you happy by balancing potential gains with safety.
II. Lifetime Spending & Investing
What is the optimal joint spending & investing rule to follow over the rest of your life?
max(discounted value of lifetime utility of spending)
III. Where the Rubber meets the Road
How does Elm choose what deserves a place in your portfolio? 6 criteria that every asset class must pass:
1/ Low cost
2/ E(risk premium) >0
3/ Ability to systematically estimate expected return
4/ Non-zero-sum
5/ Liquid
6/ Tax-efficient
https://elmwealth.com/asset-classes/?...
Major asset classes:
https://cdn.prod.website-files.com/67...
1 TIPS
2 Treasury bills/bonds
3 Listed equities
4 Corporate bonds & o/r risky lending - minefield for the missing billionaires (especially when combined w/ pte bank margin lending, structured notes & o/r derivatives etc)
5 Real estate
6 Actively managed mutual funds - why would they beat the mkt af fees?
7 Factor investing eg Dimensional
https://www.magicformulainvesting.com/
8 Arbitrage - need to think carefully abt tail risks. If something is “mispriced”, what stops it fr being >mispriced?
9 Alternatives eg HF/PE/VC - why would they beat the mkt af fees? Are you rewarded for illiquidity? =>-ve liquidity premium. Lack of exits (distributed to paid-in capital (DPI) is the new IRR). Correlation to equities; macro funds/managed futures funds may provide diversification benefits
Damodaran on Alternatives: 'The (Uncertain) Payoff from Alternative Investments: Many a slip between the cup and the lip?'
https://aswathdamodaran.blogspot.com/...
Private market funds lag US stocks over short and long term - https://on.ft.com/3FIhor5 via @FT
10 Collectibles, art, commodities, gold, crypto - tracks wealth of "collectors" eg btc correlation w/ NASDAQ/Silicon Valley crowd
IV. Puzzles
i/r <0 ?
Cheat Sheet
1/ Bet sizing >impt than picking the right invt. Almost impossible to go broke picking the bad invt if you get the sizing right but easy to go bust taking too much risk even if you choose great invt.
Merton's Share %p = E(ERP)/(CRRA*σ^2)
Where E(ERP) = expected excess return of risky asset above risk free rate
CRRA = coefficient of risk aversion. If CRRA = 1 then Merton's Share = Kelly formula
https://evergreensmallbusiness.com/me...
2/ Mkts are highly competitive: who's on the otherside of the trade? Steer clear of leverage, shorting, concentration & complexity. Overconfidence is costly
3/ Goal = Max(E(lifetime utility of spending)) ≠ Max(E(Wealth))
Don't just focus on most likely outcome. Need to consider cost on risk.
4/ Control what you can by being attentive to fees, taxes, and efficiency in expenditures
'Stay invested for the long run? Think again' -Christopher Tan, BT 21 Apr 2025
https://www.businesstimes.com.sg/weal...
"Living simply and spending below my means gave me peace. It freed me to make life and business decisions without being held hostage by money... Clarify what really matters. Stop buying things you do not need, with money you do not have, to impress people you do not even know or care about. In investing, do not chase after best returns; rather, use an approach that gives you the highest probability of success. Peace is not found in more – it is found in enough."
Endowus Wealth Insights 2025
https://cdn.endowus.com/static-files/...
How to invest your enormous inheritance
https://elmwealth.com/how-to-invest-y...
https://www.economist.com/finance-and...
August 10, 2025
Let me admit upfront – When I picked Victor Haghani’s and James White’s highly recommended book “The Missing Billionaires – A Guide to Better Financial Decisions”, I was neither expecting extraordinary findings about financial planning nor encountering challenging quantitative investment puzzles (more on it later). As I started the book and finished chapters and sections, I was stunned by the quality of writing, depth of knowledge, breadth of ideas and soundness of empirical analyses presented in the book. That’s why despite its technical writing style (the reader should have good grasp of probability, statistics, economics and basic finance) and sometimes complex discussions about key decisions such as risk/return trade-offs, cost of risk, retirement planning, tax effects and risk vs uncertainty, I found myself buried in the book for most part of last week and couldn’t put it away. Don’t be misled by the title - the book is NOT about billionaires who have gone missing (for various reasons). It explains why some of the wealthy people couldn’t retain their wealth, and how their spending and investment decisions led to wealth destruction over time.
Victor and James have joined hands (and minds) in producing this smart and sophisticated text covering wealth management and financial planning using quantitative risk-management techniques and have reintroduced concepts which were developed decades ago but are not applied commonly. The book is insightful and informative, but not a light read. Understanding concepts such as Expected Utility, Volatility Drag, Relative Risk Aversion, Bet Size etc. require close attention and occasionally a notebook with a pen to derive formulas and validate results. The authors have mostly deployed clear language to explain complex concepts, with use of examples and stories, which makes the book engaging to readers with foundation level financial and economic knowledge.
The book has four sections – 1) Investment Sizing which is often an over-looked factor when making an investment decision and how it impacts risk-return trade-offs. The authors explain that “bet-sizing” is much more critical, even more than identifying the asset mix and specific asset to invest. The section covers the question of “How Much” and not just “What” and “Where”. They use a formula called “Merton Share” – named after the Nobel-winning economist Robert Merton, who was on the board of LTCM as well. Merton Share is a simple rule of thumb for determining the bet size, and link allocations to expected returns, investor’s risk aversion and asset volatility. The book gives the example of Victor himself, whose billions in losses at LTCM could have been avoided had he optimised his “Bet Size”. The authors also explain that “Maximization of Expected Utility” is a superior investment/spending criteria relative to wealth maximization, as sizing investments to maximise expected utility, rather than wealth, reduce the chances of heavy losses (including complete financial ruin) while optimizing risk and returns. In other words, going All-In into a top performing stock or a rising digital asset, despite the potential of X times upside is NOT the right investment decision.
2) In this section the authors cover lifetime spending and investing, talking about retirement, longevity, estate planning and inheritance.
3) Here the authors cover concepts such as Risk Aversion, Utility, characteristics of major asset classes and more importantly Human Capital. The inclusion of Human Capital in our financial decision making is an interesting and critical factor. The authors also explained whether stock options (very popular these days) really add to utility and have tackled the difference between risk and uncertainty very deftly.
4) The final section talks about various puzzles such as popularity of lottery tickets (buying a lottery never increases utility), equity risk premium (reality is different from models), perpetuities in a negative interest rate environment and how much to allocate to assets with almost unlimited upside and some probability to fall to zero. Expected Utility tells us that for such assets, allocate less as upside increases. In other words, “Curb Your Enthusiasm” as you get more bullish.
The book has a bonus chapter on Liar’s Poker – indeed a bonus. Those who have read Michael Lewis’s book Liar’s Poker will agree. This is a must read for professionals involved in managing money (whether personal or institutional), risk management, trading, financial advisory and wealth management. Keep your calculators and notebooks handy.
Victor and James have joined hands (and minds) in producing this smart and sophisticated text covering wealth management and financial planning using quantitative risk-management techniques and have reintroduced concepts which were developed decades ago but are not applied commonly. The book is insightful and informative, but not a light read. Understanding concepts such as Expected Utility, Volatility Drag, Relative Risk Aversion, Bet Size etc. require close attention and occasionally a notebook with a pen to derive formulas and validate results. The authors have mostly deployed clear language to explain complex concepts, with use of examples and stories, which makes the book engaging to readers with foundation level financial and economic knowledge.
The book has four sections – 1) Investment Sizing which is often an over-looked factor when making an investment decision and how it impacts risk-return trade-offs. The authors explain that “bet-sizing” is much more critical, even more than identifying the asset mix and specific asset to invest. The section covers the question of “How Much” and not just “What” and “Where”. They use a formula called “Merton Share” – named after the Nobel-winning economist Robert Merton, who was on the board of LTCM as well. Merton Share is a simple rule of thumb for determining the bet size, and link allocations to expected returns, investor’s risk aversion and asset volatility. The book gives the example of Victor himself, whose billions in losses at LTCM could have been avoided had he optimised his “Bet Size”. The authors also explain that “Maximization of Expected Utility” is a superior investment/spending criteria relative to wealth maximization, as sizing investments to maximise expected utility, rather than wealth, reduce the chances of heavy losses (including complete financial ruin) while optimizing risk and returns. In other words, going All-In into a top performing stock or a rising digital asset, despite the potential of X times upside is NOT the right investment decision.
2) In this section the authors cover lifetime spending and investing, talking about retirement, longevity, estate planning and inheritance.
3) Here the authors cover concepts such as Risk Aversion, Utility, characteristics of major asset classes and more importantly Human Capital. The inclusion of Human Capital in our financial decision making is an interesting and critical factor. The authors also explained whether stock options (very popular these days) really add to utility and have tackled the difference between risk and uncertainty very deftly.
4) The final section talks about various puzzles such as popularity of lottery tickets (buying a lottery never increases utility), equity risk premium (reality is different from models), perpetuities in a negative interest rate environment and how much to allocate to assets with almost unlimited upside and some probability to fall to zero. Expected Utility tells us that for such assets, allocate less as upside increases. In other words, “Curb Your Enthusiasm” as you get more bullish.
The book has a bonus chapter on Liar’s Poker – indeed a bonus. Those who have read Michael Lewis’s book Liar’s Poker will agree. This is a must read for professionals involved in managing money (whether personal or institutional), risk management, trading, financial advisory and wealth management. Keep your calculators and notebooks handy.
July 21, 2024
"The Missing Billionaires" attempts to apply rigorous mathematical principles to the complex world of financial markets and wealth management. The author's approach is reminiscent of solving a multi-body problem in physics but with a crucial difference: the underlying laws governing financial markets are not only unknown but also in constant flux.
The approach relies heavily on equations, probabilities, and theories that, while logically coherent, are fundamentally speculative. They are approximations of reality. While these models may appear sound, their ultimate effectiveness hinges on the outcomes they produce. These constructs are undoubtedly preferable to an utterly undisciplined approach, providing a semblance of order.
The authors present various examples, but they are primarily US-centric, limiting the generalizability of their conclusions. A more comprehensive analysis incorporating global market data would have strengthened the book's rigor and provided a deeper understanding of wealth preservation across different contexts. Chances are most laws deemed workable are not applicable with even a slight change of contexts within an era. As a result, their applicability at different times, even in the US or for the US, is not as given as presumed.
One of the book's key strengths is its in-depth exploration of utility theory in the context of personal finance. The framework attempts to quantify an individual's risk tolerance and financial goals, providing a practical tool for structuring one's thinking. The authors’ actionable investment strategies based on these principles have relatively sound conclusions, making the book a valuable resource for those seeking to understand and apply these concepts.
For example, the authors discuss the need for diversification and asset allocation as a result of their analysis. These concepts are unlikely to excite anyone who has read any portfolio theories even briefly (and those who have not should not pick this extreme jargon-heavy book).
While intriguing, the central question of the missing billionaires serves more as a narrative device than a core focus of the book. The authors' analysis of the mundane misses or understates the tail risk events for any lineages: even the wealthiest are susceptible to the vagaries of extraordinary events when the periods are in centuries. Catastrophic wealth-destroying events, such as wars, revolutions, and other natural, economic, or political upheavals, have occurred throughout history and across the globe.
Examples like the Russian Revolution of 1917, which wiped out the wealth of the country's aristocracy, or the hyperinflation in Weimar Germany in the 1920s, which decimated middle-class savings, would have provided valuable context to the author's arguments. By neglecting to incorporate global market examples, the authors miss an opportunity to highlight the universality of this phenomenon.
The mathematical complexity of the book may also be its Achilles' heel. The intricate equations and models presented are built on a foundation of assumptions that, when scrutinized, reveal a high and mounting degree of subjectivity. The assumptions regarding correlations, utility functions, and other variables are plentiful and can significantly influence the outcomes. Investors may find themselves tweaking these assumptions to achieve desired results. This raises questions about the practicality and real-world applicability of such elaborate frameworks. The critique leveled at the Black-Scholes option pricing model, which, while mathematically elegant, relies on assumptions that don't always hold in real-world markets, applies to all discussed in the book.
Overall, the book's emphasis on rigorous analysis and quantitative methods is a welcome departure. Its practical applicability is not as straightforward as the suggestions from the bestseller books in the field. The book is more of a thought-provoking exploration of quantitative methods in personal finance.
The approach relies heavily on equations, probabilities, and theories that, while logically coherent, are fundamentally speculative. They are approximations of reality. While these models may appear sound, their ultimate effectiveness hinges on the outcomes they produce. These constructs are undoubtedly preferable to an utterly undisciplined approach, providing a semblance of order.
The authors present various examples, but they are primarily US-centric, limiting the generalizability of their conclusions. A more comprehensive analysis incorporating global market data would have strengthened the book's rigor and provided a deeper understanding of wealth preservation across different contexts. Chances are most laws deemed workable are not applicable with even a slight change of contexts within an era. As a result, their applicability at different times, even in the US or for the US, is not as given as presumed.
One of the book's key strengths is its in-depth exploration of utility theory in the context of personal finance. The framework attempts to quantify an individual's risk tolerance and financial goals, providing a practical tool for structuring one's thinking. The authors’ actionable investment strategies based on these principles have relatively sound conclusions, making the book a valuable resource for those seeking to understand and apply these concepts.
For example, the authors discuss the need for diversification and asset allocation as a result of their analysis. These concepts are unlikely to excite anyone who has read any portfolio theories even briefly (and those who have not should not pick this extreme jargon-heavy book).
While intriguing, the central question of the missing billionaires serves more as a narrative device than a core focus of the book. The authors' analysis of the mundane misses or understates the tail risk events for any lineages: even the wealthiest are susceptible to the vagaries of extraordinary events when the periods are in centuries. Catastrophic wealth-destroying events, such as wars, revolutions, and other natural, economic, or political upheavals, have occurred throughout history and across the globe.
Examples like the Russian Revolution of 1917, which wiped out the wealth of the country's aristocracy, or the hyperinflation in Weimar Germany in the 1920s, which decimated middle-class savings, would have provided valuable context to the author's arguments. By neglecting to incorporate global market examples, the authors miss an opportunity to highlight the universality of this phenomenon.
The mathematical complexity of the book may also be its Achilles' heel. The intricate equations and models presented are built on a foundation of assumptions that, when scrutinized, reveal a high and mounting degree of subjectivity. The assumptions regarding correlations, utility functions, and other variables are plentiful and can significantly influence the outcomes. Investors may find themselves tweaking these assumptions to achieve desired results. This raises questions about the practicality and real-world applicability of such elaborate frameworks. The critique leveled at the Black-Scholes option pricing model, which, while mathematically elegant, relies on assumptions that don't always hold in real-world markets, applies to all discussed in the book.
Overall, the book's emphasis on rigorous analysis and quantitative methods is a welcome departure. Its practical applicability is not as straightforward as the suggestions from the bestseller books in the field. The book is more of a thought-provoking exploration of quantitative methods in personal finance.
January 2, 2025
Ok this one definitely merits me writing out some thoughts, and likely a reread a few years down the line.
To start off - the title is quite clickbaity. There is little historical evidence or even anecdata to justify the claim that poor investment sizing has led to wealthy families frittering away their inheritance.
Luckily, however, the meat of the content on investment sizing, asset allocation, and financial planning was pretty compelling and new to me.
Listing down concepts I found useful here:
- Related concepts of the Merton share (fraction of total wealth to invest in some risky asset) and Kelly criteria (bet size that maximises log-wealth). These are brought to life a very simple biased coin flip gain that gives some visceral feeling to these concepts.
- Using “Utility” as a concept that can be simply modeled as log-wealth, with increasing risk aversion modeled by increasing the concavity of the wealth-utility relationship.
- The Utility concept is useful because an individual should seek to maximize Expected Utility, and not Expected Wealth (the latter would result in being exposed to more risk than necessary)
- Thinking and accounting for “personal human capital” - whether it is stock-like (high risk-return) or bond-like (predictable and steady), and whether it is correlated to the individual’s investment returns, when deciding an optimal asset allocation on an investment portfolio.
The authors also bake in quite a bit of nuance to somewhat bridge the gap between abstraction and real life. Nuggets I especially liked were:
- Whether there really is a risk-free asset? (Spoiler - maybe not, but the abstraction can still work with multiple risky assets instead of one risky and one risk-less)
- Discussing the source of the equity risk premium (there seems to be more compensation for taking equity risk than is warranted based on historical performance)
- Discussing how much to spend as a fraction of wealth, including the case of treating the wealth as a forever ‘endowment’ and not burning it down
- Discussion of annuities as a vehicle for predictable cash flows
This read has made me realise that the state of ‘common knowledge’ around investment sizing and asset allocation is pretty suboptimal. The ideal standalone equity portfolio as a diversified low-cost index fund has gained wide acceptance. However the questions of “how much to invest” (e.g should I borrow to invest in the above fund), and how to weave in investment allocation with individual particularities and decisions of life (borrowing / spending on real estate, education, choice of career) are very much open-ended. This leads to a diversity of approaches taken by individuals, some of them possibly not thought through and mistaken.
The stance taken in the book is that although individual investors often do not exhibit the rational utility maximization, they would be better-served to do so. This is not too compelling in that if investors have no choice except to feel irrational emotions, acting in service of those emotions may be the best approach rather than trying to conform to some idealistic model. Loss aversion and regret minimization are particularly relevant here, and it might be interesting to consider modifications of the “utility curve” to reflect this. Even if it makes mathematical modeling tougher, it should still be amenable to simulations or other computational analysis. For example, some of the analysis around loss aversion introduced the concept of a ‘subsistence level’ of wealth below which the investor would be much more risk averse - but in reality with the hedonic treadmill and lifestyle inflation, it is likely that such an (emotional) 'subsistence level' tracks current wealth closely over time for most people.
That said, I’m very happy to have made time to read this and have gained some handholds over concepts that are much discussed but all too often in hand-wavy ways.
(Obligatory note that the above are my views and not my employers’)
To start off - the title is quite clickbaity. There is little historical evidence or even anecdata to justify the claim that poor investment sizing has led to wealthy families frittering away their inheritance.
Luckily, however, the meat of the content on investment sizing, asset allocation, and financial planning was pretty compelling and new to me.
Listing down concepts I found useful here:
- Related concepts of the Merton share (fraction of total wealth to invest in some risky asset) and Kelly criteria (bet size that maximises log-wealth). These are brought to life a very simple biased coin flip gain that gives some visceral feeling to these concepts.
- Using “Utility” as a concept that can be simply modeled as log-wealth, with increasing risk aversion modeled by increasing the concavity of the wealth-utility relationship.
- The Utility concept is useful because an individual should seek to maximize Expected Utility, and not Expected Wealth (the latter would result in being exposed to more risk than necessary)
- Thinking and accounting for “personal human capital” - whether it is stock-like (high risk-return) or bond-like (predictable and steady), and whether it is correlated to the individual’s investment returns, when deciding an optimal asset allocation on an investment portfolio.
The authors also bake in quite a bit of nuance to somewhat bridge the gap between abstraction and real life. Nuggets I especially liked were:
- Whether there really is a risk-free asset? (Spoiler - maybe not, but the abstraction can still work with multiple risky assets instead of one risky and one risk-less)
- Discussing the source of the equity risk premium (there seems to be more compensation for taking equity risk than is warranted based on historical performance)
- Discussing how much to spend as a fraction of wealth, including the case of treating the wealth as a forever ‘endowment’ and not burning it down
- Discussion of annuities as a vehicle for predictable cash flows
This read has made me realise that the state of ‘common knowledge’ around investment sizing and asset allocation is pretty suboptimal. The ideal standalone equity portfolio as a diversified low-cost index fund has gained wide acceptance. However the questions of “how much to invest” (e.g should I borrow to invest in the above fund), and how to weave in investment allocation with individual particularities and decisions of life (borrowing / spending on real estate, education, choice of career) are very much open-ended. This leads to a diversity of approaches taken by individuals, some of them possibly not thought through and mistaken.
The stance taken in the book is that although individual investors often do not exhibit the rational utility maximization, they would be better-served to do so. This is not too compelling in that if investors have no choice except to feel irrational emotions, acting in service of those emotions may be the best approach rather than trying to conform to some idealistic model. Loss aversion and regret minimization are particularly relevant here, and it might be interesting to consider modifications of the “utility curve” to reflect this. Even if it makes mathematical modeling tougher, it should still be amenable to simulations or other computational analysis. For example, some of the analysis around loss aversion introduced the concept of a ‘subsistence level’ of wealth below which the investor would be much more risk averse - but in reality with the hedonic treadmill and lifestyle inflation, it is likely that such an (emotional) 'subsistence level' tracks current wealth closely over time for most people.
That said, I’m very happy to have made time to read this and have gained some handholds over concepts that are much discussed but all too often in hand-wavy ways.
(Obligatory note that the above are my views and not my employers’)
November 23, 2024
While the pitch for this book is certainly appealing, in reality it is a fundamentally flawed merger between an introductory textbook and pop science book which ends up with the worst aspects of both. In particular, the core of the book is that it takes several economic models by Merton and introduces them to the reader, positing that following these models is a likely strategy for investing success. In practice, while there are vague gestures at the known limitations to said models, if anything the book feels set up to give you the false confidence that the simple models it explains would be enough to outperform as an investor. Indeed, when discussing endowments, it finds that Merton's models give a substantially different solution than actual practices, and (rather than thinking though if there are any real-life limitations for this to be true, which might justify why optimal models are not deployed, or if there are no limitations, and Merton's models are simply known not to actually apply correctly in that case) it simply insists that basically the entire world of endowment spending is doing things incorrectly---certainly a surprising conclusion for a brief off-the-cuff remark in a book mostly focused on personal finance, and one which reflects quite badly on this book's overall reliability.
Of course, to a target audience of a retail day-trading option buyer, or someone who blindly picks stocks by feeling or candlesticks, the much more systematic analysis the book brings might have value. However, in the modern day where it is easy and cheap to invest in equities through index funds, it seems to me that this book is more likely to provide noise than signal.
Of course, to a target audience of a retail day-trading option buyer, or someone who blindly picks stocks by feeling or candlesticks, the much more systematic analysis the book brings might have value. However, in the modern day where it is easy and cheap to invest in equities through index funds, it seems to me that this book is more likely to provide noise than signal.
March 29, 2025
This is a very academic book with some practical implications. I found it insightful enough to want to buy a second copy after losing the original on a flight. I think this book has a unique perspective on financial decision-making and, therefore, has earned a spot on the shelf of a finance junkie and/or practitioner.
I think the interplay between Merton's share calculations and utility functions is a useful framework for wealth management considerations. Yet I find some logical inconsistencies; the whole equity portfolio weighting formulation used in this work is adjusted +/- 30% pending the momentum indicator (if you look at the book's footnotes)—it seems like a plug to make retroactive portfolio returns fit to the best look. I do not want to discount the overall insights here, however, particularly the theoretical underpinnings that make intuitive sense, like, for example, the Shiller P/E being a material driver in determining the weight of equity allocation within a portfolio. And of course, stories about LTCM and Liar's Poker are worthy to ponder since they are coming from an insider's view and also utilize the framework introduced in this book.
This book will be of particular interest in guiding asset allocation for those later in life, especially, and help those on the younger side to avoid major pitfalls. Though tedious, repetitive, and dull at times, I am glad I have read it.
I think the interplay between Merton's share calculations and utility functions is a useful framework for wealth management considerations. Yet I find some logical inconsistencies; the whole equity portfolio weighting formulation used in this work is adjusted +/- 30% pending the momentum indicator (if you look at the book's footnotes)—it seems like a plug to make retroactive portfolio returns fit to the best look. I do not want to discount the overall insights here, however, particularly the theoretical underpinnings that make intuitive sense, like, for example, the Shiller P/E being a material driver in determining the weight of equity allocation within a portfolio. And of course, stories about LTCM and Liar's Poker are worthy to ponder since they are coming from an insider's view and also utilize the framework introduced in this book.
This book will be of particular interest in guiding asset allocation for those later in life, especially, and help those on the younger side to avoid major pitfalls. Though tedious, repetitive, and dull at times, I am glad I have read it.
August 31, 2025
The author posits that the "how much" is way more important to "what" when it comes to investing. In other words - sizing of the investments is the key aspect that explains the "missing" thousands of US billionaires in the last century.
The author used to be one of the young LTCM fund partners at the time and he personally lost 9-figures in the process, thus presumed experienced. He uses school-level math and financial theory to explain how to access those all-important sizing decisions: how much to buy of a good investment, how much to spend today and over time, how much tax to defer, how much to spend in insurance against low probability events.
Indeed, in practical investing, nearly all time and energy is devoted to finding the best/suitable investments, some effort spent on planning the risk management and nearly none - on figuring out the optimal size of such investment.
I personally am skeptical of over-simplifying the investing as a mathematically-modelled series of (uncorrelated) stochastic returns. Expected utility optimization was discovered in academia already 50 years ago and still is not widely used by practitioners - that's a revealing fact.
Despite that, this optimal betting / expected utility angle is definitely valuable, though not as entertaining or easy to read as, say, M. Housel's books.
A must read for investing professionals!
The author used to be one of the young LTCM fund partners at the time and he personally lost 9-figures in the process, thus presumed experienced. He uses school-level math and financial theory to explain how to access those all-important sizing decisions: how much to buy of a good investment, how much to spend today and over time, how much tax to defer, how much to spend in insurance against low probability events.
Indeed, in practical investing, nearly all time and energy is devoted to finding the best/suitable investments, some effort spent on planning the risk management and nearly none - on figuring out the optimal size of such investment.
I personally am skeptical of over-simplifying the investing as a mathematically-modelled series of (uncorrelated) stochastic returns. Expected utility optimization was discovered in academia already 50 years ago and still is not widely used by practitioners - that's a revealing fact.
Despite that, this optimal betting / expected utility angle is definitely valuable, though not as entertaining or easy to read as, say, M. Housel's books.
A must read for investing professionals!
January 31, 2024
If you're interested in a conceptual/theoretical overview of investing, featuring endless thought experiments about coin flipping and a lot of equations and graphs that remind you of your ancient economics course work, this might be just the book for you.
I don't care for that stuff at all. I took finance and statistics and speak that language, but when I read about investing, I am not interested in theory. I want practical advice, so that I may invest better.
When I am in the mood for thought experiments, I read philosophy or novels.
I had read a positive review of "The Missing Billionaires", which summarized the authors' key finding that the size of positions matters a lot. So I already knew their general conclusion, just by reading a review.
Then, I bought this book expecting to get specific, detailed advice on how position sizing should be applied to my own portfolio. I was confident that in a 333 page book, whose subtitle is, "A guide to better financial decisions", there would eventually be some specific advice on that topic that I could actually use.
There wasn't.
What a complete waste of time and money.
I don't care for that stuff at all. I took finance and statistics and speak that language, but when I read about investing, I am not interested in theory. I want practical advice, so that I may invest better.
When I am in the mood for thought experiments, I read philosophy or novels.
I had read a positive review of "The Missing Billionaires", which summarized the authors' key finding that the size of positions matters a lot. So I already knew their general conclusion, just by reading a review.
Then, I bought this book expecting to get specific, detailed advice on how position sizing should be applied to my own portfolio. I was confident that in a 333 page book, whose subtitle is, "A guide to better financial decisions", there would eventually be some specific advice on that topic that I could actually use.
There wasn't.
What a complete waste of time and money.
February 4, 2025
Looking at the title, I was thinking if this was book about billionaires going off-grid and not be seen anymore. Instead, it is to bring awareness of how poorly managed investment, spending and bad decisions, can change one person's future. The opening case study of how one, even from old money, that should last generations a life of financial freedom can disappear, makes me wonder, "how am I managing my money?" Naturally there are many other factors and consideration as well, which I felt the author was able to highlight perspectives that are important as well, such as "there is more to life than financial well-being" and as how he continues "but getting that right helps everything else". As Mae West says, "I have been rich and I have been poor. Rich is better". Less never forget, the thoughts and triggers linking with financial is high within us.
So, it is understand of several basic points that speaks to me in this book:
Understanding my perception and my relationship with risk;
Expenditure and other cost;
Consistency in decision making;
Alertness and flexibility to making changes
So, it is understand of several basic points that speaks to me in this book:
Understanding my perception and my relationship with risk;
Expenditure and other cost;
Consistency in decision making;
Alertness and flexibility to making changes
June 1, 2024
I got some useful ideas from this book. The biggest perspective shifting insight is that wealthy families in America are terrible at perpetuating themselves over a long time horizon. Almost none of the robber baron era fortunes survive today, even though market returns should have resulted in dozens of inherited billionaires today. Paging Pikkety, maybe r>g doesn't matter if nobody is actually capturing r!
The reasons why have to do with cognitive and behavioral biases we all have. The authors then explore optimal financial planning through the lens of expected utility.
The reason I'm giving three stars is that it was honestly a slog. They spent a lot of time talking about the implications of expected value for things like options trading that I think only a narrow audience would find interesting. Still I'm glad I read it and a few of the puzzles they give actually helped me see my own cognitive biases. It just felt like the parts I got value from only constituted ~25% of the book.
The reasons why have to do with cognitive and behavioral biases we all have. The authors then explore optimal financial planning through the lens of expected utility.
The reason I'm giving three stars is that it was honestly a slog. They spent a lot of time talking about the implications of expected value for things like options trading that I think only a narrow audience would find interesting. Still I'm glad I read it and a few of the puzzles they give actually helped me see my own cognitive biases. It just felt like the parts I got value from only constituted ~25% of the book.
May 7, 2025
The hook of "The Missing Billionaires" is simple - why do so many generationally wealthy families end up frittering their wealth away, despite the mathematical difficulties of doing so. The answer, sadly, is not much explored in the book. Instead, Haghani and White provide a theory-heavy look at how to maximise expected wealth (using a utility-focussed lens) and how to think about asset allocation. Several of the concepts are useful but it is densely written and the focus on financial theory and equations may be offputting to some.
The most interesting parts come when Haghani discusses his experiences at Salomon and then LTCM, providing a brutally vivid description of what it's like to lose 80% of your wealth.
Ultimately, whilst conceptually helpful, I think there are other books that present some of the arguments inset better, like "Fooled by Randomness" or "Ergodicity".
The most interesting parts come when Haghani discusses his experiences at Salomon and then LTCM, providing a brutally vivid description of what it's like to lose 80% of your wealth.
Ultimately, whilst conceptually helpful, I think there are other books that present some of the arguments inset better, like "Fooled by Randomness" or "Ergodicity".
May 17, 2025
A very smart duo writes an extremely well researched book about what wealthy people should do to stay wealthy. What can go wrong in this one? Well, a lot. The book is so technically inclined that I absolutely couldn’t follow more than a percent or two and this is when I might have read over a 100 investing books and have engineering training. The authors tried to write a masterpiece and have reviews from the high and mighty to boast but it’s time we call the king naked. The book adds not much value to any serious investor’s knowledge and on the flip side explains how the quants have over complicated the world of investing in their pursuit of greatness and fat fees.
The issue with books like this one is that people are scared to call them out for the fear of being labelled as dumb. Well, this is a seriously bad book and that’s pretty much it.
The issue with books like this one is that people are scared to call them out for the fear of being labelled as dumb. Well, this is a seriously bad book and that’s pretty much it.
August 21, 2025
Such a difficult read, even though he tried to dumb it down for us.
His statistical bend definitely shows the bias.
Main messages for me:
Position sizing matters in minimizing a wipeout or an erosion in wealth
Changing decisions at high and low risk points is important.
Most ex-billionaires lost out because of trying to maxmize wealth vs maximizing the utility of the wealth which would have been more important anyway.
Informative was Victor's letter:
That keeping a good chunk away so, even if all the risky wealth goes away - that was not a good idea in hindsight. Because the risky (concentrated) wealth going away did happen, and it was better to swallow ego, and be humble before the event.
His statistical bend definitely shows the bias.
Main messages for me:
Position sizing matters in minimizing a wipeout or an erosion in wealth
Changing decisions at high and low risk points is important.
Most ex-billionaires lost out because of trying to maxmize wealth vs maximizing the utility of the wealth which would have been more important anyway.
Informative was Victor's letter:
That keeping a good chunk away so, even if all the risky wealth goes away - that was not a good idea in hindsight. Because the risky (concentrated) wealth going away did happen, and it was better to swallow ego, and be humble before the event.
May 6, 2024
This was a bit of a frustrating read. The book offers many helpful and informative concepts and ideas, but it misses out on leaving an impression on the reader, because the book feels unstructured, often like a sequence of unordered essays of varying importance. The intro and the final checklist both offer a glimpse into the five-star potential that this book has, but the large majority of the book is unsatisfying, unconnected, and not intuitive. With a great editor, I think this has the potential to be a fantastic book, but I would not recommend the first edition to many people.
September 1, 2024
Interesting core concept: most finance professionals and people managing their wealth don’t spend enough time on sizing investments. The discussion of the Kelly criterion and Robert Merton’s theories were quite interesting and valuable.
But overall I found the book a bit too theoretical and academic, filled with formulas instead of real world examples. I left it scratching my head about how I would implement it (I think for me it would involve using the Shiller PE ratio to adjust my % public equity allocation over time?).
Maybe worth revisiting one day.
But overall I found the book a bit too theoretical and academic, filled with formulas instead of real world examples. I left it scratching my head about how I would implement it (I think for me it would involve using the Shiller PE ratio to adjust my % public equity allocation over time?).
Maybe worth revisiting one day.
September 8, 2024
Little dense and technical, but some important insights conveyed. Investments are all about getting the sizing right as a function of personal risk aversion. Maximize diversification across all asset classes, including international markets, steer clear of leverage, shorting, concentration and complexity. Suggestion is to invest in low-cost global equity index fund and ret in long-term TIPS. Invest and spend based on real, after tax income stream that your capital can generate. Be attentive to fees and taxes of financial products, try to keep to minimum.
September 21, 2024
A couple of useful ideas but is a total pain to read. Do not recommend at all.
Instead google: "log utility function", "Kelly criterion", and "ltcm downfall"
-1 star because it never mentions fundamentals. Apparently investing is all about stats on random variables.
-1 star because authors can't even explain games completely (had to google because their explanations don't make sense)
-1 star because they keep glossing over details while they mention how they do The Whole Thing™ with their very smart clients. Pathetic advertisement.
Instead google: "log utility function", "Kelly criterion", and "ltcm downfall"
-1 star because it never mentions fundamentals. Apparently investing is all about stats on random variables.
-1 star because authors can't even explain games completely (had to google because their explanations don't make sense)
-1 star because they keep glossing over details while they mention how they do The Whole Thing™ with their very smart clients. Pathetic advertisement.
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