Unconventional wisdom: How to generate returns out of thin air
Shannon’s Demon is a thought experiment which carries important lessons for investors.
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: How to generate returns out of thin air
“Gambling is a tax on ignorance. People often gamble because they think they can win, they’re lucky, they have hunches, that sort of thing, whereas in fact, they’re going to be remorselessly ground down over time.”
- Ed Thorp
What if I told you I could make returns appear out of thin air? Through financial alchemy money would materialise where common sense suggests no profit is possible.
To perform this magic trick I need two things – an asset that is extremely volatile and has a long-term expected return of zero and an asset that has no volatility and a long-term expected return of zero.
For long-time readers of this column it is obvious that I’m not a proponent of investing magic tricks. But I think exploring this particular case can teach investors some important lessons.
An unknown great investor
Bell Labs was started by Alexandar Graham Bell and became one of the premier research organisations in the world. The premise was simple – hire brilliant people and let them study what they want. The results would change the world with countless inventions.
One of the brilliant people was Claude Shannon. He joined Bell Labs in 1941 and took to entertaining his colleagues by riding a unicycle around the laboratory while juggling.
Shannon’s talents extended beyond providing slapdash entertainment for his colleagues. He is widely considered a genius. So much so that his flying instructor wrote a letter to the president of MIT saying Shannon shouldn’t fly because of the risk to humanity if he died in a crash.
Early in his tenure at Bell Labs Shannon was tasked with developing encryption systems as part of the war effort. He was part of the joint British / American team along with Alan Turing that developed the first encrypted phone line allowing Roosevelt and Churchill to evade German eavesdropping.
Shannon went on to invent binary coding which converts information to 0s and 1s and forms the basis of computer language. Then he came up with information theory which is the foundation of the digital age. Shannon was an academic superstar at 32 years old.
Even one of the most influential scientists of the 20th century needs to do something outside of work. In Shannon’s case he used his spare time to become one of the best investors ever.
Shannon’s Demon
After his stint at Bell Labs, Shannon was hired as a professor at MIT. In addition to his research and regular teaching duties in electrical engineering he occasionally gave investing lectures. In one of those lectures he introduced Shannon’s Demon.
Shannon’s Demon was a simulated coin flip game with a 50% return on your money if the coin lands on heads and a 33.33% loss if the coin lands on tails. The expected long-term return of the game is zero. To understand why involves some maths.
Shannon’s Demon highlights the differences between arithmetic returns and geometric returns. An arithmetic return is simply the average return. If a share goes up 10% in the first year and goes down 10% the next year the arithmetic return is 0%.
This tends to be how many people think about returns. Using the logic of an arithmetic return would cause many people to believe a $100 position would be worth $100 after a 10% rise is followed by a 10% fall.
The geometric return shows how the value of a position or portfolio actually changes. If a $100 investment went up 10% it would grow to $110. A 10% loss in the subsequent period would bring the position value down to $99. In this example the difference between the arithmetic return and the geometric return is $1 which is known as volatility drag.
If there is more volatility the difference between the arithmetic and geometric return increases. A 20% gain followed by a 20% loss means a $100 position would be worth $96. Increasing volatility means the volatility drag is now four times as high.
One of the reasons that many people naturally default to arithmetic returns is because we are conditioned to think in an absolute sense. If you have $100 and somebody gives you $20 and then takes away $20 you are left with $100. Thinking in relative terms means considering both the magnitude of a percentage return and the figure the percentage is applied to.
Geometric returns explain why the expected return in Shannon’s Demon is zero. If a $100 bet was made after a coin landed on heads you would have $150. If the next flip landed on tails and you lose 33.33% of your money bringing you back to $100. The following chart illustrates how this works.
Your immediate reaction to this chart might be to question the pattern of alternating results between heads and tails. Over the long-run half of all flips will land on tails and half on heads. That doesn’t mean there won’t be streaks of consecutive heads or tails.
The following chart shows what happens if the coin comes up tails 10 times in a row. This is very unlikely as the probability is 1 in 1024 but it does show that even with a long-term expected return of zero you can lose most of your money. This is illustrative of Keynes’ quote “The market can stay irrational longer than you can stay solvent.”
The insight that Shannon gave his students was that he could transform this scenario with a zero expected return into a profit through rebalancing. If 50% of the money was bet on the coin flip and 50% rebalanced into cash after each flip the expected return is now positive. The following chart illustrates this approach.
This works in any scenario of coin flip results. The rebalancing means the coin flipper will stay solvent long-enough for the long-term expected outcome of 50 / 50 heads and tails results to play out.
Rebalancing reduces volatility which in turn lowers volatility drag. The process of rebalancing is sizing the bet or position sizing in investment speak. Along with demonstrating volatility drag the point of Shannon’s lecture was to show the impact of position sizing.
Shannon borrowed from the work of a colleague from Bell Labs. This was former Navy fighter pilot turned scientist John Larry Kelly Jr. who came up with the Kelly Criterion for determining how much wealth to risk on a single bet based on the probability of being correct.
The Kelly Criterion is a rabbit hole that involves Claude Shannon and mathematician / Hedge Fund Manager Ed Thorp in Vegas with the first wearable computer trying to win at roulette. There are some important lessons for investors which I will cover in an upcoming article – for now I want to concentrate on the lessons from Shannon’s Demon.
What can we learn from Shannon’s Demon
Shannon’s Demon is clearly a hypothetical exercise that ignores the realities of investing – transaction costs, buy / sell spreads, taxes, the existence of assets with zero expected returns and no correlation, etc. That doesn’t mean there aren’t lessons.
Lesson one: Consider trade-offs of returns and volatility
The immediate lesson might be that less volatility is better. In theory this is true but the important caveat is that picking an asset with lower volatility is only beneficial if the expected returns are the same or higher than an asset with higher volatility. Investing theory tells us this shouldn’t happen as we exchange volatility for higher returns.
Too many investors focus on avoiding volatility and instead sacrifice the returns needed to achieve their goals. An investor focused on risk capacity – the returned needed to achieve your goal – will design a portfolio with an appropriate expected return. This is not some academic theory. Just set a goal and figure out the return you need considering how much you can save, your timeline and how much you currently have. I’ve covered it in this article.
Conversely, during long bull markets investors often take on too much volatility to try and get rich quick. Now might be one of those times. Excessive volatility and the potential for large drawdowns increases volatility drag. This can happen with highly speculative shares or with increased leverage as my colleague Sim discussed in her article on geared ETFs.
There are two Buffett quotes which perfectly encapsulate the mistakes investors often make on opposite sides of the volatility spectrum.
For those that overly fear volatility remember that “someone is sitting in the shade today because someone planted a tree a long time ago.” Figure out where you want to be and come up with a plan to get there.
For those that want to get there tomorrow there is wisdom in Buffett’s maxim “the stock market is a device for transferring money from the impatient to the patient.” Slow and steady wins the race because avoiding permanent loss capital can crush long-term returns. Buffett’s quote also applies to the next lesson from Shannon’s Demon.
Lesson two: The value of rebalancing
There are investors who intentionally or ignorantly pile into speculative bets to get rich quick. Then there are investors who do everything right initially but drift into a position where there portfolio no longer aligns with their goals.
Rebalancing is the mechanism for ensuring your portfolio continues to align with the appropriate return / volatility trade-off for what you want to achieve. In times when markets are surging you can take on too much risk which increases volatility drag when the inevitable downturn occurs.
In Shannon’s Demon the rebalancing occurred after each coin flip. In real life there are downsides to rebalancing like taxes and transaction costs. Set a reasonable band for your portfolio to drift from your target and only rebalance periodically when necessary - just don’t ignore rebalancing completely.
Final thoughts
In a future article I will cover Shannon’s antics with Ed Thorp and his evolution from a mathematician fascinated with beating the casinos to an investor who achieved a return of 28% annually from the late 1950s to 1986.
However, a brief overview of Shannon’s approach offers another important lesson. Shannon took a page from Michelangelo’s notion that a beautiful sculpture is within each marble block and is unveiled simply by getting rid of the superfluous material.
Shannon used his famously analytical mind to uncover the core of successful investing by getting rid of all the stuff that doesn’t matter. As a mathematician and electrical engineer you might think he came up with an algorithm or complicated technical technique to pick shares. He didn’t.
When asked if math could be used to predict fluctuations in the market Shannon answered, “I think it is easier to predict which of the companies are going to succeed than to predict short-term fluctuations, things lasting only weeks or months, which they worry about on Wall Street Week. There is a lot more randomness in that un-predictable things happen that cause selling or buying pressure. If you get into the short-term thing, you keep paying short-term capital gains. With a long-term thing, you may never pay taxes because you keep it forever.”
His study of the share market led him to the conclusion that all that matters is finding sound companies with great products and strong leadership. After that avoid all the superfluous day to day noise. Claude Shannon was simply a fundamental buy and hold investor.
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What I’ve been eating
Jacks is a dive bar in the Bang Rak section of Bangkok. Being perched precariously on the banks of the Chao Phraya River has some plusses and minuses. The bar is a great vantage point to watch the frenetic river traffic as giant tourist laden party boats weave between barges, long-tails and all manner of hotel shuttles. The bar also tends to flood at high tide. The Chao Phraya may be the river of kings but that doesn’t mean you want to come in contact with the filthy water.
The food at Jacks is simple, cheap and delicious. Pictured is a green curry and pad see ew from the penultimate night of a short getaway to Bangkok last week.
