A Man For All Markets — Edward Thorp on Blackjack, Investing and Life

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A Man for All Markets – Edward Thorp on Blackjack, Investing and Life

From Las Vegas to Wall Street with Edward Thorp

Today, I’d like to focus on Edward Thorp and his autobiography, A Man For All Markets. For the unfamiliar, Thorp was one very successful investor, blackjack player and mathematician. Not only did he devise a winning system for blackjack, he achieved an annual investment return of ~20 percent for nearly thirty years as a hedge fund manager.

You won’t find a secret formula to gambling or investing in his autobiography. What you’ll get is Thorp’s enduring philosophy to life, family, education, problem solving and investing; shaped in part by his youth during the Great Depression, and his less than stellar opportunities for education. This post will share the lessons that I took from Thorp’s work, focusing on his reflections on mental models, winning systems, business and investing.

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Thinking in models

“Some think in words, some use numbers, and still others work with visual images. I do all of these, but I also think using models… Physics, chemistry, astronomy and biology revealed wonders of the world, and showed me how to build models and theories to describe and predict. This paid off for me in both gambling and investing.”

Edward Thorp, A Man For All Markets, 2017

Thorp highlights the power of models for decision making and how we should discover the rules to models through experiment and observation. But we have to remember that models are only a “simplified version of reality”. Unlike the physical laws in science, theories that describe human behaviours are rarely unchanging. Here, we rely more on “limited concepts [that] tie things together and serve as shortcuts to understanding”. All of this is reminiscent of Charlie Munger’s philosophy on the pursuit of worldly wisdom, emphasising the cultivation of mental models in a latticework. Thorp himself describes it as the process of building a “multidisciplinary collection of insights”.

Learning and checking

“Learning is like adding programs, big and small, to this computer”

Edward Thorp, A Man For All Markets, 2017

Thorp, ever the scientist, loved to learn and experiment. Curiosity in his view can help with much in life. And like many other legendary investors, he was a voracious reader, describing how he once read 60 novels in a single summer.

As an independent learner and critical thinker, Thorp preferred to check things for himself – a recurring rule in his book. He approached life rationally and witheld judgement until the evidence arrived. He recalls how ‘experts’ would tell him about the futility of beating the house at blackjack. But Thorp checked the math himself and devised a winning system in turn. While this example speaks more to his genius, the practice of checking things for ourselves is a good one.

The gambler’s edge

“Gambling is investing simplified.”

Edward Thorp, A Man For All Markets, 2017

Thorp shares an obvious but sometimes forgotten rule: that we participate only in favourable gambles that we understand and have an edge. Others, like Warren Buffett, refer to it as their circle of competence. Thorp’s early success in blackjack for example was attributed to his superior system at a time when the market was relatively inefficient, ignorant and superstitious.

Implementing the winning system

But even if you have an edge or winning system, it doesn’t guarantee results. The challenge for blackjack players is in implementing a system that allows them to recognise and act on opportunities as the game unfolds. Such systems are often volatile in nature. And it assumes they have the bankroll and stomach to handle losing streaks.

There is also the learning curve that comes with playing a system well. Thorp himself began playing blackjack with small bets. He didn’t proceed onto larger stakes until he was emotionally comfortable and fluent with his process. He describes how early losses in gambling or investing aren’t all bad if it contributes to your long-term education in a meaningful way.

Hence, practice, patience and discipline is key. Thorp practiced card counting under simulated conditions, which included high speed dealing, cigarette smoked rooms, and casual conversations. He took it “one step at a time, adding a new difficulty only after [he] became comfortable and relaxed” with what he learned prior.

Fundamental Theorem of Card Counting

“Life is a mixture of chance and choice. Chance can be thought of as the cards you are dealt in life. Choice is how you play them”.

Edward Thorp, A Man For All Markets, 2017

Your odds in blackjack can improve or worsen as the game progresses. This depends on the cards left to play. But it’s this information, at least prior to the next shuffle, that allows you to make better decisions, and to bet boldly when the odds are favourable. Thorp and Bill Walden refer to this as the Fundamental Theorem of Card Counting. Our odds will improve if we can act correctly on the informational advantage that emerges from time to time. It also means that better situations tend to come towards the end of play. An interesting parallel for investing, learning and life I think.

Counter measures

It’s important to recognise the reflexivity inherent in systems like gambling and investing. When Thorp’s blackjack reputation gathered acclaim, he found casinos taking increasingly aggressive stances to limit his returns. This ranged from the reshuffling of cards after every hand to outright barring from play. Thorp responded with disguises and personas to allude them. But eagle-eyed management countered with even greater surveillance. Winning strategies attract mimicry and counter measures. Since much of it serves to drive excess returns away, continued innovation appears key.

A good secret

The reflexivity and mimicry in financial systems means that “if you have a good investment idea, you might want to keep it secret”. Thorp for example had developed a market beating formula and trading tool for valuing warrants in 1967. And given the rarity of market beating strategies, he kept the formulation secret, using it only for his own account and clients.

But not long after in 1972-73, Fischer Black and Myron Scholes had independently developed and published a formula identical to Thorp’s. While “their proof verified that the formula [Thorp] had discovered was correct; the bad news was that the formula was now public knowledge”.

Black and Scholes’ work helped to fuel the boom for derivatives securities, eliminating some of the excess returns that Thorp was able to enjoy. That formula turned out to be the now famous Black-Scholes Formula. And Myron Scholes would go on to receive the 1997 Noble Prize for his contributions. It’s an interesting case study on the diffusion and convergence of ideas.

Six degrees of separation

On innovation and diffusion, Thorp refers at length to the six degrees of separation. As social creatures, we live in an interconnected social network. The author describes the speed at which ideas can spread due to the low degree of separation between people. Malcolm Gladwell made a similar observation in The Tipping Point, paralleling the spread of ideas to models in epidemiology.

Thorp himself likens the diffusion of information to a food chain. Those at the front of the chain get to eat, and those at the end get eaten. The eventual popularity of Thorp’s blackjack system was case in point. His experience with the Black-Scholes Formula was another. So, an enduring competitive advantage requires sustained innovation and/or processes that are adaptive to changes in the environment.

Satificers and maximisers

Thorp makes an interesting distinction between two categories of people: maximisers and satisficers. Maximisers search for the best possible deal, while satisficers look for ‘good-enough’ results given their opportunity cost. In investing, the cost of search imposes tension between optimal and practical decision making. Should we buy the asset now? Or should we wait and search for something better? Thorp has a few thoughts on the matter.

The marriage problem

First, Thorp gives an example of the marriage problem in mathematics. It asks whether one should settle down today or continue to search in hope of a better partner tomorrow? Apparently, the optimal strategy to this search problem is to reject the first 37 percent of prospects before choosing the next prospect that is ‘better’ than the first 37 percent. If not, you go with the last person in the set. It’s an intuitively bizarre result, and a reminder about the complexities of search theory.

The marriage problem in investing is somewhat trickier. Small time investors for example don’t have the resources, information or time to maximise or optimise their search and evaluation function. It’s near impossible for the individual, with competing priorities in life, to compare even a moderate sample of stocks in proper detail. Even then, information is often ambiguous. Some risks and uncertainties are not definable, calculable and/or knowable.

Investors should seek a set of guiding policies that is fit for them and their constraints. It must be sufficiently simple and practiceable to allow for critical thinking and learning; And adaptive enough to thrive in many environments of different competing strategies. For example, a strategy to ‘buy high quality businesses at a price below intrinsic value‘ is useable when everyone else or no one else is using the same strategy.

The Kelly Criterion

Thorp talked about the utility of the Kelly criterion, a formula that John Kelly devised in 1956. For a favourable two outcome bet, the formula tells us the optimal fraction (K) of our bankroll to bet, given the net fractional odds (b) and probability of winning (p). Intuitively, the larger your edge, and/or smaller your risk, the larger the bet you should make. The Kelly Criterion also tries to avoid permanent total loss. As the rule implies, you shouldn’t bet the farm when there’s a non-zero likelihood of permanent capital loss.

K = [bp – (1 – p)] / b

While a powerful idea, the Kelly Criterion also presents a few limitations in practice. Firstly, the return trajectory of Kelly-type strategies are volatile. It’s unsuitable for those with short horizons or higher risk (volatility) aversion. Secondly, the formula above optimises for a simple two outcome bet. The optimal strategy grows in complexity as our opportunity set grows. It may lose its practicalities in more complex problems. Thirdly, you need to know the probabilities and payoffs of your bets. While possible in casino games, it’s more nebulous for stocks. But its ideas and intuition remain useful nonetheless.

Scalping and fat pitches

Thorp highlights the value in knowing when to and not to haggle. If the market prices a stock at $5 today, and you estimate its intrinsic value to be $10, will you wait for prices to fall further? While you have the opportunity to save a bit, you’re also risking the loss of $5. Knowing your odds and opportunity cost is vital. Serial scalping may not offset your losses from missed opportunities. As Phil Fisher’s wrote in Common Stocks for Uncommon Profits, “don’t quibble over eights and quarters”.

Good investors are patient, swinging only at the “fat pitches”. Thorp for example recalls turning down the opportunity to invest in Long Term Capital Management (LTCM) for three reasons. Firstly, LTCM’s founder, John Meriwether, had a reputation for risk taking at Salomon Brothers, which he didn’t like. Secondly, the Nobel laureates on LTCM’s ‘dream team’, Myron Scholes and Robert Merton, were theorists that lacked “street smarts and practical investment experience”. Finally, LTCM’s strategy relied on a dangerous amount of leverage (anywhere from 30:1 to 100:1!!). He didn’t think LTCM was a fat pitch.

From contagion to abyss

“The lesson of leverage is this: Assume that the worst imaginable outcome will occur and ask whether you can tolerate it. If the answer is no, then reduce your borrowing”.

Edward Thorp, A Man For All Markets, 2017

The troubles of excess and leverage was another recurring topic in A Man For All Markets. Those that lived through the hardships of the Great Depression took the risk of leverage more seriously. The experience made risk management a priority for Thorp. This reminded me of Dave Packard, co-founder of Hewlett Packard in 1939, who shared a similar sentiment in The HP Way. Packard too was reluctant to use long-term debt, and stressed the importance of working capital discipline. He, like Thorp, wanted to keep the risk of catastrophe as low as possible.

Repetition and rhymes

“Those who cannot remember the past are condemned to repeat it.”

George Santayana

Short memories, easy credit, enormous leverage, financial engineering and this-time-is-different syndrome are common tropes in financial history. “Easy money and leverage” for example was an important contributor to the Great Depression. The Black Monday Crash of 1987 came about as a result of feedback loops and unintended consequences in new futures markets. Then there was the collapse of LTCM, the result of extraordinary leverage and a ‘black swan’ event. We shouldn’t forget the 1980s S&L boom and bust, or the irrational exuberance of the 1990s Dot Com bubble. All of this culminated with the Global Financial Crisis of 2008-09.

Lunacy of lemmings

So, Thorp has a warning for those who believe fervently in perfectly efficient markets. History has shown how cognitive dissonance can fuel “the lunacy of lemmings”. Thorp for example recalls the narrative between “fraudster or investment genius” that surrounded Bernie Madoff, long before his collapse. While Thorp was suspicious of Madoff’s strategy and returns early on, other investors found it easy to believe the genius narrative while Madoff’s returns were other-worldly.

The question is not whether markets are efficient, but where and to what extent it is not. History provides us with a long list of counterfactuals to the Efficient Market Hypothesis (EMH). But that’s not to say that EMH itself is not a worthwhile idea. Thorp’s point is that we can learn from the consequences of models that do and do not describe our reality.

Under EMH, we expect investors to be rational, and for prices to incorporate new information immediately. Inverting this, we can see why markets are sometimes inefficient: (1) information can diffuse slowly, and sometimes to a small number of listeners; and (2) we’re not always rational, and don’t have the capacity to incorporate useful information in its entirety.

This also suggests several ways to beat the market: (1) get information of higher quality and/or timeliness; (2) be disciplined and rational; (3) develop or find a superior system for analysis; and (4) take advantage of mispricing before the crowd eliminates it. Each is easier said than done. 

Adapting to history

While an education in financial history is valuable, it’s not easy to profit from it. Like a Ponzi scheme, it’s difficult to know when a mania might end. As John Maynard Keynes remarked, “the market can remain irrational longer than you can remain solvent”.

It’s not easy to avoid losses during manias as well. While we can avoid investing in bad assets, disasters can bring about contagion and spillover. Thorp recalls that even Warren Buffett was “looking into the abyss” during the Great Financial Crisis, seeing how the situation threatened everything, including Berkshire Hathaway itself.  

Again, limiting the excesses of leverage may reduce the risk of catastrophe. And for the long-oriented value investor, purchasing high quality companies, run by competent and honest managers, at reasonable prices seems a time-tested approach. But for all the science and jargon we feed into investment thinking, much of it still rests on an underlying belief and optimism that the future is promising.

Further reading

There are plenty more ideas and lessons that I took from Thorp’s memoir, but I prefer to end the post here. If you haven’t yet read Thorp’s book and hold an interest in blackjack and/or investing, do check it out.

Thorp also referenced several books in his autobiography. I highlight the few that caught my eye: Birkhoff and Maclane’s A Survey of Modern Algebra; MacDougall’s Danger in the Cards; Reid and Demaris’ The Green Felt Jungle; Poundstone’s Fortune’s Formula; and Munger’s Poor Charlie’s Almanack.

References

Edward Thorp, (2017), A Man For All Markets : From Las Vegas to Wall Street, How I Beat The Dealer And The Market. More books and articles are available at < http://www.edwardothorp.com/ >