Essay: Why Inversion Is Indispensable for Long-Term Success

How to Succeed Phenomenally by Not Failing Catastrophically

Man muss immer umkehren. (“One must always invert.”) —German mathematician Carl Gustav Jacob Jacobi

The concept of inversion has been a highly effective problem-solving tool across disciplines. By thinking about a challenge in reverse, we can identify what not to do, getting us closer to answering the question of what to do. Carl Gustav Jacobi famously applied this concept to solving difficult mathematical problems, and Charlie Munger has spoken of inversion as one of his core philosophical principles. According to Munger, “[Jacobi] knew that it is in the nature of things that many hard problems are best solved when they are addressed backward.”¹ Munger attributed much of the investment success of Berkshire Hathaway to his and Warren Buffett’s application of the principle of inversion: “It is remarkable how much long-term advantage people like us have gotten by trying to be consistently not stupid, instead of trying to be very intelligent.”²

Over long periods of time, being “not stupid” tends to converge with “being smart”. This is particularly true in the field of investing, where an investor’s long-term return is a multiplicative series of short-term returns. In other words, final wealth = starting wealth times (1 + sub-period return) times (1 + sub-period return), and so forth for all the sub-periods involved. This simple formula shows that any sub-period return of -1, or -100%, results in ending wealth of zero, or a cumulative total-period return of -100%. So, being “not stupid” in all the sub-periods is far more beneficial to an investor than “being a genius” in all the sub-periods except for a single period in which the investor turns out to have been stupid. Notice my wording here — “turns out”. The genius investor does not even need to lose his marbles in the disastrous sub-period. It is sufficient that Mr. Market lose his marbles to such a degree that the “genius” investor suffers a single-period wipeout. The phrase “the market can stay irrational longer than you can stay solvent”³ applies here. The lesson: No investor should make his survival dependent on the actions of others, as herd mentality runs rampant in markets.

The historical stock price volatility of GameStop serves as an instructive example. GameStop became a prominent “meme stock” when its market quotation rose from less than $1 per share in January 2020 to a high of $125 per share in January 2021, a month during which the stock price increased 30-fold. Investors who had shorted the shares due to overvaluation concerns found themselves in a crowded trade as short interest reached 140% of the public float. The result was a massive short-squeeze that pushed prominent investment fund Melvin Capital to the edge of ruin.⁴

The power of inversion is evident all around us. Hence Charlie Munger’s advice: “Just constantly invert. You don’t think about what you want. You think about what you want to avoid. When you think about what you want to avoid, you also think about what you want. You just go back and forth all the time.”⁵

For instance, if you wish to stay healthy long into advanced age, identify the major killer diseases and avoid their causes. This is the premise of Peter Attia’s eye-opening book, Outlive: The Science and Art of Longevity.⁶ Attia identifies four major slow-onset killers: heart disease, diabetes, cancer, and Alzheimer’s. As a key to avoiding these diseases, Attia cites a focus on exercise, nutrition, and sleep. Unsurprisingly, adopting beneficial behaviors in these three areas not only prevents or delays the onset of the four core ailments, but improves health across the board — enhanced metabolism, greater energy, higher mobility, improved digestion, and better mental health. By doing what it takes to avoid the four major diseases of old age, we simultaneously create bliss in the body.

Munger shares a personal anecdote from an unrelated field: “When I was a meteorologist in World War II, they told me how to draw weather maps and predict the weather. But what we were doing was to clear pilots to take flights. I just reversed the problem. I inverted it. I said, ‘Suppose I wanted to kill a lot of pilots, what would be the easy way to do it?’ I soon concluded the only easy way to do it would be to get the planes into icing the planes couldn’t handle. Or, you could get the pilot to a place where he’d run out of fuel before he could safely land. I made up my mind: I would stay miles away from killing pilots by either icing or getting them into conditions when they couldn’t land. That helped me be a better meteorologist in World War II. I just reversed the problem.”⁷

Mohnish Pabrai applied inversion to figure out how the Dakshana Foundation could maximize its philanthropic impact: “Because it’s hard to measure outcomes in the non-profit world, I decided to look only at endeavors where outcome measurement is easy. I inverted the problem and said we’d only look at those things where we get the same feedback loop as in a capitalist society. What Dakshana does is help kids in India get into elite colleges, like IITs (Indian Institutes of Technology) or AIIMS (All India Institute of Medical Sciences). Getting into those schools is tough, and in effect, we get an independent grade on how we are performing based on the number of kids that get accepted.”⁸

Venture capitalist Josh Wolfe, founder of Lux Capital, applies inversion to the process of building companies: “If you look at the foundations of a company, it comes down to team, technology, and market. In each of those, you assess everything that can go wrong, which is a favorite lens through which I like to look at how you can create value. In my framework, it is by eliminating risks, which means you have to identify them. Thus, everybody at Lux has been indoctrinated with the quote that ‘failure comes from a failure to imagine failure’. This leads you to the positive, constructive things you can do to eliminate what could go wrong.”⁹

Amazon’s Jeff Bezos has his own inversion paradigm — distinguishing between reversible and irreversible decisions. The latter can be debilitating or even fatal, while the former can be undone fairly easily. Avoid or thoroughly scrutinize irreversible decisions — that is Bezos’ recipe for compounding long-term success. Writes Bezos, “Some decisions are consequential and irreversible or nearly irreversible — one-way doors — and these decisions must be made methodically, carefully, slowly, with great deliberation and consultation. If you walk through and don’t like what you see on the other side, you can’t get back to where you were before. We can call these Type 1 decisions. But most decisions aren’t like that — they are changeable, reversible — they’re two-way doors. If you’ve made a suboptimal Type 2 decision, you don’t have to live with the consequences for that long. You can reopen the door and go back through. Type 2 decisions can and should be made quickly by high judgment individuals or small groups.”¹⁰

Following the Crowd Does Not Lead to Superior Outcomes

If you have been investing for any length of time, you will know how seductive it can be to follow the crowd. Even if you consider yourself an independent-minded investor, you will have experienced this feeling. Maybe you are not susceptible to a stock tip shared by your Uber driver — after all, the average retail investor is part of the “hottest-stock-at-the-moment” crowd, while you consider yourself a member of the much more rarified intelligent investing crowd. Still, when a seductive story about a particular company circulates among the group of investors you value and respect, it is difficult not to get swayed.

It may not be detrimental to consider an idea that is “trending” within your chosen investment tribe. The smaller the tribe, the greater the likelihood that the investment thesis in question does not reflect the market consensus, potentially offering a favorable risk-reward tradeoff. The greater the crowd endorsing an idea, however, the greater the likelihood that the relevant company is already fully valued or even overvalued, implying subpar returns going forward.

William Green, author of The Great Minds of Investing and Richer, Wiser, Happier, puts it this way: “…you need to be willing to diverge from the crowd if you’re going to succeed. You have this extraordinary default option. If you don’t want to diverge from the crowd, you can simply buy an index fund. We know you’ll do great over many years, and you may even do better with this option. But if you want to outperform, you have to be willing to go against the crowd. […] Think about what the crowd does and all of the stupidity of the crowd, all of the folly of the way most people invest, and then invert it. When it comes to investing, we know the crowd is emotionally very reactive. It makes very short-term decisions, trades too much, and gets carried away by fads. It listens to market predictions a great deal, and as Marty Whitman wonderfully put it, market prediction is the last refuge of the incompetent. We know market prediction doesn’t work, and you won’t be able to figure out when the market and interest rates are going up. Yet so many people spend their time being yanked around emotionally and intellectually by watching the latest news on CNBC and the like.”¹¹

An Illustrative Stock Price Chart

Source: Barchart.

Consider the stock price chart above. The company in question is irrelevant. The thought experiment is simply to try to imagine consensus investor expectations near the stock price highs as compared to the stock price lows. Similarly, ask yourself how it would have felt to be a buyer near the lows and a seller near the highs. The vast majority of investors would have disagreed or even ridiculed you. The crowd can have high conviction and be wrong at the same time, particularly at times of maximum optimism or pessimism. It is therefore imperative to think independently and ask, “What does today’s low (high) price tell us about investor expectations, and how realistic are those expectations?”

According to investor Phil Ordway, Michael Mauboussin’s classic Expectations Investing is fundamentally a book on inversion: “The core principle in the book is that you should take the price and work backwards — invert. What expectations are baked into the price? What assumptions do you have to believe to be true to justify this price today or think there is an attractive investment opportunity there?”¹²

In a fireside chat with Ordway at MOI Global’s Latticework 2023 conference, Mauboussin put it this way: “…the thrust of expectations investing is [your] first question, which I also think people don’t do — invert. The only thing I know for sure is the stock price. The question is, ‘What do I have to believe about the financial performance of this business to justify today’s stock price?’ It’s a very simple question. There are consensus numbers for growth, margins, and so on. It’s plenty of art, with some science. You can construct a scenario and say, ‘This is what I have to believe.’ Then you do your strategic and financial analysis to see if it’s going to be better or worse.” Adds Mauboussin: “If the consensus growth rate is 8%, you fully acknowledge… it could be better or worse than that, and that’s what the base rate stuff tells us.”¹³

The argument for the use of base rates, according to Mauboussin, is that “instead of looking at every company uniquely (as if you are the only person ever having done the work before), rather say, ‘Let’s think about this company as an instance of a reference class. Can we select an appropriate reference class and understand how things have unfolded for that reference class? Does that inform how we should think about the prospects for this particular company?’ When you explain the idea, everybody gets it, but most investors and most analysts operate as if they are unique in some way and their analysis is everything, versus understanding the sweep of corporate performance which can be informative for understanding prospects.”¹⁴

Domino’s Pizza serves as a case study: “If the company nails it, everything goes great. It’s firing on all cylinders. How good could revenue growth be? If all these initiatives don’t work out or the company does as badly as in the past, how bad could it be? The key is to think about operating leverage. People have missed the operating leverage component, which is if sales come in better, what does that mean for operating margin delta? If sales come in worse, what does it mean for operating margin delta? Analysts are horrible at that. Companies are bad at it, too.”¹⁵

Probabilistic thinking goes hand-in-hand with base rate-aware analysis: “You assign the probabilities. Base rates are always going to be super helpful… you’re working off expected values. […] If you are a gambler, this is how you do things. This is how you operate, so it shouldn’t be that alien to people who are in that mode of thinking.”¹⁶

In a fireside chat with Saurabh Madaan, managing member of Manveen Asset Management, at Latticework 2021, Mauboussin cited fitness equipment maker Peloton as an example. “In September 2020, an analyst forecasted — and I don’t mean to pick on this specific analyst because I think this was the consensus at the time — that Peloton would grow something like 30 percent for a decade. They are at $1.8 billion in revenue… The question to ask is, ‘How many companies with $1.8 billion in revenue have ever grown 30 percent a year for ten years?’ The answer is that it does happen — about one or two percent manage it — but if it’s a two-percent probability, do you make that your base case? Probably not. You would be much more moderate. You might say, ‘I’m really bullish. I think it’s a 20-percent scenario.’”¹⁷

Forget Momentum

Avoid hot stocks in hot industries. —Peter Lynch

Just like in Lake Wobegon all the parents consider their kids to be above-average, in the stock market all investors consider themselves to be mostly rational. It is almost always other market participants who are prone to cognitive biases. In the rare case when an investor is aware of the psychological factors impacting his judgment, the belief is that by being aware of the existing biases, the investor can effectively mitigate or even eliminate them.

Unfortunately, the typical investor cannot help but get swayed by the prevailing market sentiment. He feels better on a day when the ticker tape is flashing green. He experiences a magnetic pull toward the market’s favorite story stocks. As indices hit new highs, he asks, “How high can we go?” As indices hit new lows, he worries, “How low can we go?”

A rational investor would take these two questions in reverse. At the COVID-induced market lows of March 2020, few investors wondered, “How high can we go?” Yet, the S&P 500 Index rose from a low of 2,237 in March 2020 to 4,800 in early January 2022, a gain of 115%. The Nasdaq 100 Index rose from 6,771 in March 2020 to 16,760 in late 2021, a gain of 148%.¹⁸

Of course, there is nothing wrong with asking both questions at the same time, but if an investor is to prioritize one question over the other, the more rewarding question will typically be the one that goes against the prevailing market sentiment, especially when such sentiment is at or near an extreme. Warren Buffett once famously stated, “I will tell you how to become rich. Close the doors. Be fearful when others are greedy. Be greedy when others are fearful.”¹⁹ The first step to succeeding at this simple but psychologically difficult task is asking the right questions at the right time.

The artificial intelligence boom ushered in by the launch of ChatGPT in late 2022 saw many investors embrace AI-related story stocks, with little regard for the lofty expectations imputed into their market quotations. While valuation considerations took a backseat for many investors, those same investors also failed to assess the long-term competitiveness, staying power, and business economics of so-called AI plays. This is of little surprise considering that even the smartest market participants could not predict with any confidence how AI would evolve, who the winners would be, and which companies would be able to sustain their momentary advantage over the long term.

The inability to predict the future did not stop scores of investors from embracing the market’s favorite AI stocks. Investors who might consider themselves rational allocators of capital became “momentum investors”, piling into stocks with the strongest upward price movement. Investors in effect outsourced their analysis of the underlying business fundamentals to other market participants and the ticker tape. “The tape tells a story” is a favorite saying of those who embrace momentum and/or technical analysis. You will not find many such market participants on a Forbes rich list.

The market’s love affair with AI chip designer NVIDIA provides an illustrative example. The company’s products experienced an explosion in demand following the launch of ChatGPT, causing NVIDIA’s sales and profits to rise exponentially. Investors viewed NVIDIA as synonymous with AI, making it a “must own” stock for many. As valuation considerations took a back seat and investors ignored the fact that no one could predict how the competitive landscape for AI chips would evolve, NVIDIA’s market capitalization reached $3.5 trillion in October 2024. Sales, while growing quickly, had amounted to a mere $0.1 trillion in the previous twelve months. Investors were paying a significant premium for what they considered to be the dominant player in AI. Venture capitalist and entrepreneur Peter Thiel summed it up in his characteristically pithy way, “in AI it’s basically one company — NVIDIA — making over 100 percent of the profits. Everybody else is collectively losing money.”²⁰

The company’s outsized market capitalization, its enviable growth profile, and eyepopping margins, placed a large bullseye on NVIDIA. Greater competition was not a matter of if but when. Even customers were scrambling to lessen their dependence on NVIDIA. Companies like Tesla and OpenAI were actively exploring alternatives. A parallel might be Amazon some years ago, seeking — and ultimately finding — alternatives to its reliance on shipping providers like FedEx.

While NVIDIA had a strong competitive advantage, the ultimate sustainability of that advantage was an open question. Even if NVIDIA maintained leadership for a long time, the mere existence of viable alternatives would keep the company honest in terms of pricing, thereby affecting margins. A factor that was downplayed by many investors but could ultimately affect NVIDIA’s moat was the company’s status as a “fabless” semiconductor firm. NVIDIA was a chip designer, but it relied on third-party foundries, like Taiwan Semiconductor Manufacturing Company and Samsung Electronics for actual production. Competing AI chip designers as well as the likes of Tesla and OpenAI could call on those same foundries for state-of-the-art production of competing chip designs.

Undisputed was the fact that the enthusiastic uptake of AI by consumers and businesses caused venture funding for AI-related startups, including next-generation AI chip designers, to skyrocket. Venture capitalists, while willing to make risky bets and take losses, expect their venture portfolios to include some big winners, more than offsetting the losers. Companies targeting the bullseye placed on NVIDIA were literally in the pipeline.

Thiel draws a parallel to 1999, when the market quotations of internet stocks rose along a similarly torrid trajectory. He makes two excellent points. First, a bubble can bring clarity in terms of the significance of a new technology. It seems undeniable that AI will have major implications for consumers, businesses, and investors. The impact of AI may well exceed the impact of the internet. According to Thiel, “The peak of the [internet] bubble was also in a sense the peak of clarity. People realized the new economy was going to replace the old economy. The internet was going to be the most important thing in the 21^st century, and people were right about that.”²¹

Yet, even if an investor agrees that AI may rival or surpass the internet, it does not automatically follow that specific AI stocks, or even AI stocks as a group, will turn out to be rewarding investments. Buffett put it succinctly while referring to the invention of human flight: “If a capitalist had been present at Kitty Hawk back in the early 1900s, he should have shot Orville Wright; he would have saved his progeny money.”²²

The invention of flight changed the world forever by making travel faster and cheaper, but this did not automatically mean riches for investors deploying capital to the airline industry. Similarly, the invention of the automobile changed society, but picking among the winners and losers in the automotive sector would have been a herculean task. Thiel’s second point echoes the experience of the airline and automotive sectors while referring to the early days of the consumer internet: “The specific investments were hard to make… The no-brainer investment would have been Amazon stock… it peaked in December 1999 at $113 per share. It was $5.50 in October 2001, twenty-two months later. You then had to wait until the end of 2009 to get back to the ‘99 highs, and then if you waited until today, you would have made twenty-five times your money… Even the no-brainer investment from ‘99 was wickedly tricky to pull off in retrospect.”²³

A Better Way: Align Yourself with Where the World Is Going, But Insist on Value

Let’s say we accept and embrace the enormous potential of AI to bring about unprecedented change for the benefit of consumers. Demand for AI-related products and services is likely to skyrocket, creating winners and losers across many categories. While a company like NVIDIA has been one of the winners and is likely to remain a beneficiary of AI adoption, it is unclear whether NVIDIA will offer an attractive return to investors buying the shares at a lofty market quotation.

As Howard Marks points out in a 2015 memo, “First-level thinking says, ‘It’s a good company, let’s buy the stock.’ Second-level thinking says, ‘It’s a good company, but everyone thinks it’s a great company, and it’s not. So the stock’s overrated and overpriced; let’s sell.’”²⁴ While not referring to a specific company, Marks argues that investors should consider market-implied expectations when deciding whether a good company is likely to make a good investment. This echoes Mauboussin’s emphasis on base rates and expectations-aware investing.

When applying second-level thinking to AI-related investments, we might ask ourselves what sectors or companies are likely to benefit from AI adoption but are valued as if they will see few or no benefits. Electricity generation and transmission come to mind. AI data centers consume unusually large amounts of power, and the growing need for data center capacity suggests exponentially greater power demand. Commodities such as uranium and copper are needed for generation and transmission of electricity. An investor evaluating public companies owning uranium or copper assets may have found quite a few lowly valued companies at the same time as AI darlings were trading at sky-high valuations. While first-level thinking led most investors to the latter, second-level thinkers might have preferred the former.

If You Don’t Blow Up, the Upside Will Take Care of Itself

Investor Christian Billinger of Billinger Förvaltning considers the question “how do I lose money” as core to his security selection process. According to Billinger, once the prospect of a losing outcome is raised, “We can then figure out ways of hopefully avoiding such losses. The idea here is that not losing money is the best way of making money. For instance, if I think up a business that would be likely to result in losses over the long term, I would probably imagine a business with no moat or real competitive advantage (e.g. selling a commodity product), highly cyclical revenues, a significant fixed cost base (which in combination with volatile revenues will result in periodic losses), high financial gearing (which together with the above increases the likelihood that we will end up in financial distress), lack of liquidity in the shares (so that we are unable to exit the position without incurring significant losses), etc.”²⁵

Billinger uses inversion to create a list of the likely characteristics of robust businesses:²⁶

- Revenue (“diversified revenue streams, recurring revenues, limited cyclicality, low exposure to potential technology disruption”)

- Cost structure (“limited operating leverage”)

- Balance sheet (“strong balance sheets, limited complexity in terms of the capital structure”)

- Governance (“long-term owners… tend to focus on the survival of the business”)

Another important factor for Billinger is longevity: “…we want the companies we invest in to be time-tested, with long track records across different types of environments, etc. The reason for this is that regardless of the amount of work and analysis we perform on a business, time is a much better arbiter of its ultimate durability, often through filters that are not visible to us as investors.”²⁷

When investor Nils Herzing of Shareholder Value Beteiligungen AG sought to deepen his understanding of the energy sector, he applied inversion: “I spoke with 140 different industry participants in 2020 and asked them, ‘How do I lose money investing in oil and gas?’ They said, ‘Invest all your money into only one E&P company…’”²⁸ The answer applies across sector and asset classes: If you deploy your entire portfolio into a single investment — and do so repeatedly — it is only a matter of time until you go broke.

Investing, Fast and Slow

Nobel laureate Daniel Kahneman is one of the great thinkers of the past century, and his 2011 book Thinking, Fast and Slow is a masterpiece. The topic is judgment and decision making from a psychological perspective. Kahneman’s premise is that the human brain operates in two modes: System 1, which is an automatic and subconscious state similar to auto-pilot; and System 2, which is a slow and more deliberate way of thinking. System 1 is fast, automatic, subconscious and prone to stereotyping, whereas System 2 is slow, effortful, logical and calculating. System 1 is constantly feeding System 2 ideas, impressions and feelings, and it’s up to System 2 to validate or refute them.

The catch is that System 2 has to be actively engaged. Business as usual occurs in System 1, and that is when bad habits or subconscious biases can do significant damage. Letting System 1 run unchecked can lead to the belief that “what you see is all there is,” which runs counter to the well-established investment practice of seeking disconfirming evidence. System 1 is also “radically insensitive to both the quantity and the quality of information that gives rise to impressions and intuitions,” which should sound familiar to anyone who has watched CNBC, read sell-side research or sat in front of a Bloomberg. The power for investors lies in engaging System 2 to avoid mistakes and to take advantage of opportunities created by the “fast”-thinking mistakes of others.

Eliminating mistakes, not hitting home runs, may be the “holy grail” of investing. Avoiding permanent capital loss and outperforming during market declines is the surest way to generate superior returns over time. But the evaluation of a choice or opportunity under System 1 is usually done relative to a reference point, and in financial markets that reference is usually the recent market price, not a more stable and concrete measure of value. Along those lines, many System 1 mistakes are the product of lazy, formulaic thinking — “it’s Aaa-rated, so it must be safe” or “home prices have never declined on a national basis” — and they are often obvious in hindsight. “What was I thinking?!” is a common complaint, but it is largely avoidable when the original process is sound and based in these principles. Kahneman explains that the way to block errors stemming from System 1 is to recognize the signs of danger, slow down, and ask for help from System 2.

In that regard, a simple checklist is a practical and powerful tool. Think of it as an external and pre-ordained System 2. As Kahneman, Atul Gawande and others have explained, checklists are extremely effective at initiating the deliberate thinking that will override many System 1 mistakes, particularly when emotions or chaotic conditions might otherwise wreak havoc. Thinking, Fast and Slow details all of the major concepts from behavioral psychology; it’s useful to go through it systematically and make a list of the common biases and heuristics (with a particular emphasis on personal vulnerabilities). Loss aversion, overconfidence and overoptimism, anchoring, availability, base rates, sunk costs, the planning fallacy, and framing effects, among others, should all be part of an investor’s working vocabulary. Effective checklists should be simple, easy to use, and instructive, without being formulaic. An investment checklist should also be continuously refined and updated for newly learned lessons.

Some of the most successful investors also perform a “pre-mortem” as part of their security selection process. Investor Phil Ordway explains it well: “Imagine a time in the future after the decision at hand has played itself out. The investment has turned out to be a total disaster, and your job is to write its obituary. What went wrong? What assumptions were faulty? What mistakes were made and could have been avoided? Imagining the potential causes of failure will forestall many common [Kahneman] ‘System 1’ mistakes and biases. This also follows the Jacobi/Munger mandate to invert the problem or issue at hand. It is often more useful to start by asking how an investment will lose money rather than focusing on the potential gains.”

Investors can also directly benefit from the System 1 opportunities in the market created by others. Distressed companies and spin-offs are two particularly favorable niches that are prone to System 1 mistakes. In both cases, investors are often presented with a characteristic or event that is tailor-made for System 1 thinking, leading to a sell decision without regard to investment merits or rationality. Bankruptcies and financial distress often cause many investors to dump their debt and equity holdings for regulatory, institutional or psychological reasons that are unrelated to — or at least disproportionate to — the economic reality. Similarly, spinoffs can be sold indiscriminately by investors who suddenly find themselves holding securities in two different companies that may differ dramatically in size, liquidity, industry, credit rating, dividend yield or other characteristics that aren’t necessarily related to a rational valuation of each security on its own merits.

Ergodicity: How to Play and Win Infinite Games

The principle of inversion ties in with the somewhat obscure but highly instructive concept of ergodicity. According to fund manager Christopher Tsai, president and chief investment officer of Tsai Capital Corporation, “a basic mathematical concept elucidates the importance of capital preservation: while a 50 percent loss reduces $1 of capital to 50 cents, a 100 percent gain is now needed to recover back to the initial $1 of capital. This phenomenon grows in a non-linear fashion as demonstrated by the following: a 400 percent gain is required to offset an 80 percent loss. Indeed, Carl Jacobi’s quip ‘invert, always invert’ may aptly apply to investing, for the best way to make money is first not to lose it.”²⁹

In an interview with MOI Global, author Luca Dellanna illuminates the idea of ergodicity with an example: “It’s a story of my cousin, who was a great skier. He made it to the World Championship in his age bracket when he was very young, but with one leg injury after another, he sadly had to quit professional skiing very early. From him, I learned the lesson that it is not the fastest skier who wins the race but the fastest one amongst those who make it to the finish line.”³⁰

Dellanna uses a numerical example to show that not only does survival matter, but that over long timeframes it matters more than performance: “Imagine a ski championship consisting of ten races. My cousin is a great skier, so he has a 20% chance of winning each race. However, because he takes a lot of risks, he also has a 20% chance of breaking his leg in each race. The question is how many races he is expected to win in a championship of ten races.”

“The naive answer is two races because we think, ‘There are ten races and a 20% chance of winning each; ten times 20% makes two.’ However, the real number is only 0.71, because if my cousin breaks his leg during the first race, not only does he lose that race, but he also loses the possibility of participating in future races. He only has an 80% chance of participating in the second race, a 64% chance of participating in the third race, and so on.”

“In a world where irreversible losses do not have long-term consequences, my cousin wins two races. In the real world, where irreversible losses absorb future gains, my cousin only wins 0.71 races. This difference caused by irreversibility is what ergodicity is about. A situation is ergodic if irreversible losses do not have long-term consequences and you can rely on averages. The real world is non-ergodic, which means that 1) irreversible losses absorb future gains, and 2) because of that, you cannot rely on averages.” Dellanna sums it up in his book on the subject: “A system is ergodic if, for all its components, the lifetime outcome corresponds to the population outcome. Otherwise, it is non-ergodic.”³¹

The Spear of Lugh blog illustrates the idea of ergodicity with an example proposed by author Nassim Taleb: “Imagine a hundred players going to the casino. You know that among them one is going to be bankrupt. You can compute the expectancy of return by computing the average return (the total wealth of the players out of the casino minus the money they brought in the casino) which is not 0. But if you take a single player P going to the casino 100 times, you know for a fact that P will be bankrupt, because in one instance P will lose everything. P’s average return is 0. In this case the ergodic hypothesis is not verified.”³²

Ergodicity and Long-Term Investment Success

Investors who embrace and internalize the concept of ergodicity enhance their chances of long-term success by constructing portfolios that can survive external shocks as well as security selection mistakes. According to Dellanna, survival is a prerequisite for longevity: “If you go bankrupt, are forced to liquidate an investment at an awful price or have so many losses that your investors decide to cash out, this basically brings you to a zero, a failure point (the technical term is ‘absorption barrier’). The other phenomenon is multiplicative risk: if you go up 50% and then go down 40%, you have actually lost money. You are not up 10% but below where you were at the beginning… if you invest $1,000 and then lose 50% of your investment, you did not just lose $500 but also the future profits those $500 might have generated.”³³

The idea of risk-adjusted returns is well-established in the institutional investment world. Capital allocators grade the quality of an investor’s past returns by considering the risk involved in generating such returns. Measures such as the Sharpe ratio and the Sortino ratio come to mind. The fundamental challenge owners of capital face when allocating capital to an investment manager is that the core product — future returns on assets under management — is unknown. This is quite unique to the investment industry; in almost all other industries, the customer knows the product or service being bought. Due to the fundamental mystery of an investment product, owners of capital go to great lengths to determine to what extent past returns are an indicator of future returns. Unfortunately, longevity remains the single most reliable input into a reality-based measure of risk-adjusted returns.

According to Dellanna, “The longer your returns are sustained, the more likely it is that your strategy will produce future returns. Nassim Taleb calls it the Lindy Effect in his book Antifragile. It is the idea that the longer something has been around, the longer it is expected to survive, but it does not apply to things that have a limit to how long they can survive, such as humans. If you survive 90 years, you are maybe expected to survive another five years, but there is a hard limit. For things that do not have this natural bound — such as ideas, investments, and technologies — what you observe is that the longer they have been around, the longer they are expected to be around in the future.”³⁴ Dellanna continues: “For example, for Warren Buffett, who sustained returns for many decades, we can be rather confident that his hazard rate is low, whereas if you pick a random investor who has very high returns but has been in the game for only the last two years, we do not know the hazard rate.”