Unconventional wisdom: What beating the casino teaches us about position sizing
The Kelly Criterion and the maths behind smarter investing.
Conventional wisdom is a byproduct of groupthink that presents solutions good enough for the average person while simultaneously not being right for any individual. You follow it at your peril. Each Monday I will challenge the investing norms that just may be holding you back from living the life you want.
Unconventional wisdom: What beating the casino teaches us about position sizing
“In the abstract, 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.”
- Ed Thorp
Two men enter a Las Vegas casino with their anxious wives in tow. Hidden in their shoes is a small device with a wire connecting to an earpiece. It is August 1961.
Each member of their small party had a specific role. Betty Shannon and Vivian Thorp were on the lookout for any suspicious casino staff.
Claude Shannon and Ed Thorp’s role was at the roulette wheel. As the wheel spun and their first bets were placed they set off on a journey that would make them both millions of dollars.
The men with the earpieces were both MIT professors who - without hyperbole - were two of the smartest men alive.
While not with them physically that day, a chain-smoking Texan physicist named John Larry Kelly, Jr was intellectually present. His work was critical to their mission with implications far beyond the casino floor.
Uneasy bedfellows: Gamblers and investors
There has always been an uneasy connection between gambling and investing. In both cases the key to success is similar:
- Find profitable opportunities
- Size the position / bet correctly
The challenge gamblers face is there are few profitable opportunities. Casinos make money because the rules for games of chance tilt the odds firmly in their favour.
We face another set of challenges as investors. We often struggle to assess the probability of different outcomes. We ping pong between over confidence and under confidence based on our emotional state. Ultimately, many investors self-sabotage away advantageous odds of success.
Claude Shannon and Ed Thorp knew the casino had all the advantages. Unlike most gamblers they found a way to put the casino on the back foot.
The device in their shoes was the first wearable computer. In an age when computers took up entire rooms, Shannon and Thorp invented a cigarette pack sized device which could roughly estimate where a roulette ball would land based on the speed of the wheel rotation and where the the ball is dropped.
They were exploiting a flaw at the casino. Bets could be placed after the ball was dropped. Using their toes as an input into the computer the odds were calculated and relayed to Shannon and Thorp through the earpiece.
This was not a fool proof system. The wearable computer indicated roughly where the ball would end up but not the exact slot. But precision wasn’t needed. Narrowing down the possible outcomes was enough to give them a higher probability of winning each spin.
Over time they were guaranteed to make money if the variance in outcomes didn’t cause their bankroll to run out prior to the long-run favourable odds taking effect.
The casino’s remaining advantage was a virtually unlimited bankroll. Shannon and Thorp had to size their bets correctly to not be foiled by their limited means.
A correctly sized bet or investment
Investors and gamblers are often told to wait for the right time to jump in. Taking advantage of opportunities is portrayed as the way to be successful.
Warren Buffett summed up this concept in his folksy manner by saying ‘be fearful when others are greedy, and greedy when others are fearful.’ In the gambling realm we have Kenny Roger’s advice to ‘know when to hold’em, know when to fold’em.’
Is being greedy pushing all your proverbial chips into the middle of the table or slightly raising your bet? Intuitively it makes sense that how much you bet or invest should be based on your probability of success.
Nothing is 100% certain. If too much capital is committed to even a high probability chance of success you can go bankrupt if you are unlucky. If too little is committed the winnings won’t overcome the inevitable failures.
This is the question John Larry Kelly, Jr. set out to answer. Kelly worked at Bell Labs, the preeminent research institute of the day. He was a contemporary of Claude Shannon who gained scientific fame with his groundbreaking Information Theory.
Information Theory governs how information is transmitted, processed, extracted, and used. Shannon’s theory led to the compact disc, mobile phones, the internet, AI and countless other advances.
Kelly built on Shannon’s theory to get better at betting on horses. What became known as the Kelly Criterion answers one question: what is the optimal amount to bet whenever you have an uncertain outcome. That should sound a bit like investing.
All you need to know is the probability of success and failure. This is why the Kelly Criterion worked so well for Shannon and Thorp in their casino schemes which later expanded to card counting. The formula is as follows:
f = (bp-q) / b
where:
Outcomes were set by the rules of the casino and Shannon and Thorp knew the exact probabilities of winning based on the card counting and roulette systems they developed.
It is more difficult to apply the Kelly Criterion to investing. Like any investing model the principle of garbage in, garbage out applies. A model is only as good as the inputs.
Yet the beauty of a mathematical formula is the clarity it brings to the directional relationships of variables and desired outcomes. Remember that perfect is the enemy of good.
In that spirit here are three ways to apply the Kelly Criterion to your own investment approach.
Focusing on the long-term increases your chances of success
Many investors likely believe the Kelly Criterion is irrelevant to their investing approach. If you are an ETF or fund investor who buys diversified investment products the notion of sizing individual positions may not be a consideration.
The Kelly Criterion may not influence the investments you pick but it should influence how you should invest.
The following chart shows the percent of time the S&P 500 generates a positive return over different periods. The data spans more than 90 years between the late 1920s and 2019.
The clear lesson is that your time frame matters. The Kelly Criterion demonstrates that the probability of success should be a key input into any investment decision.
If you are a day trader or investing for a month or even a year the probability of success is significantly less than if you hold for 10 years.
Not only does the time frame increase the probability of making money but the reward can be quite substantial. I’ve used the median or middle value of returns as it is less sensitive to outliers. The rewards of investing for the long-term are substantial and significantly exceed inflation.
If you constantly tinker with your portfolio and adjust your approach based on your perception of market conditions you are dampening the impacts of time on results. You are lowering your probability of success. This is just as true if you are buying and selling diversified funds and ETFs as individual shares.
Not only is the probability of success less across shorter time frames but the outcome achieved is generally lower.
There is a significant amount of data showing that when investors try and time the market by tinkering they lower returns. Taxes and transaction fees are also higher which puts most short-term investors in an insurmountable hole.
If you want to be successful the majority of your portfolio should be long-term buy and hold. Any tinkering should be on the edges and not involve wholesale changes.
Consistency and process matter more than an individual result
Shannon and Thorp spent two years getting ready to head to Vegas to take down roulette. They developed and tested their theory. They published academic papers and built the first wearable computer.
Arriving in Vegas they methodically executed their strategy of tilting the odds in their favour and sizing their bets based on their probability of success. This was not a get rich quick scheme and success came from slowly building their bank roll over time.
Shannon and Thorp’s system differed from the approach most gamblers take. One perennially popular approach is to have too many cocktails and place a large bet on a ‘lucky’ number. Most of the time the casino happily collects this tax on intoxication. But sometimes the drunken superstitious gamblers win – and win big.
As an investor it is discouraging to do everything right and have the outcome go against you. Especially when you periodically hear about somebody who did nothing right but happened to buy Nvidia five years ago on a whim.
I find this frustrating. But I also know the more I focus on what other people are doing the less likely I will achieve my goals. Luck and the unpredictability of the future will always play a role in outcomes.
During particularly frothy and speculative times like our current environment it is more tempting to abandon your process and take a punt. I try to remember that what the Kelly Criterion shows is how process and consistency matter far more than the results of individual actions.
Returns and risk
One approach to maximising wealth is to put 100% of your money into the investment you think will perform the best. To succeed you just need to be right. The problem with this approach is that it often leads to losing all your money.
The Kelly Criterion addresses the variance of possible outcomes and not just the expected outcome. Mathematically the Kelly Criterion punishes investments with the potential for large losses more than it rewards equal sized gains.
This makes sense from an investment standpoint. Investments that offer higher returns have higher variance. There are a greater range of outcomes and this isn’t just volatility which is a temporary change in value.
If you buy an individual share the company could go bankrupt or become a 100 bagger. An ETF that tracks an index with thousands of shares doesn’t have the return potential of the individual share but also won’t go to zero. Many investors put their entire portfolio in a single ETF. Few would do the same with a single share.
Consider how variances in outcomes impacts your ability to achieve your goal. In bull markets investors tend to normalise strategies with high variance of returns whether that is leveraged ETFs, options, overly concentrated portfolios or speculative shares.
Right now people mostly experiencing the good side of that variance. At some point the downside will become clear.
Final thoughts
John Larry Kelly, Jr died of a stroke at 41 years old on a Manhattan sidewalk in 1965. Claude Shannon continued as a professor at MIT and invested privately with his wife. He was very successful, and I covered his story in a previous article.
Ed Thorp invented card counting and turned his attention to tipping the odds in his favour at Blackjack. Eventually he quit gambling and started investing. His suspicion the mobsters running the casinos were trying to kill him encouraged this switch.
Thorp started trading options and designed an option pricing model as part of his efforts.
Thorp’s model was identical to the Black-Scholes option pricing model which was published in 1973. The Black-Scholes model eventually won professors Fischer Black and Myron Scholes the Nobel Price in Economics.
Thorp had created the model in 1967 but didn’t want the publicity like the professors. Instead he started a hedge fund to exploit his discorvery which helped him amass a fortune of $800 million.
Thorp used the principles of the Kelly Criterion when he gambled and when he invested. His success was grounded in his focus on the probability of success and sizing bets appropriately.
He always remembered that variance is a necessary component of high returns but must be managed. That is why Thorp knew something didn’t make sense when he was hired to review a fund manager by an investment committee.
The returns were high but they had little variance – they were just steadily good. Thorp’s advice was taken and the fund manager was dumped in 1991 - 17 years later the world found out why Bernie Madoff’s returns showed little variance.
Please share your thoughtsby emailing me at mark.lamonica1@morningstar.com.
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What I’ve been eating
The Italian word for clams - vongole – has origins in Neapolitan dialect. From Roman times clams from the Bay of Naples were prized. The most famous dish is spaghetti alle vongole but this version from Embla served the clams with butter beans, chicory and parsley.
Embla is the first reader recommended restaurant – and it was a good one. I was down in Melbourne for the tennis and had a lovely Friday night meal. Keep the recommendations coming!
