A reader asks: I'm a paying subscriber. How about some bonus content?

A reader asks: I’m a paying subscriber. How about some bonus content?

Archer replies: We at Ask Archer are all about giving. In response to reader demand, we are offering the bonus content below, excerpted from my book, Radical Problems, Simple Solutions: How Markets can Help Fix the Retirement Crisis and Solve Wealth Inequality, available for purchase here.

It’s about probability, and risk, and is particularly relevant giving the current state of the markets (and the world). It goes like this …

In his podcast, How to Tickle Yourself, the writer Duff McDonald advances the viewpoint of the Boddhisatva: the future doesn’t exist, probability is an illusion and figuring the odds is a waste of time.

Others differ on this. In his book, A Drunkard’s Walk, Leonard Mlodinow writes about the history of probability and how, in his words, it “rules our lives.” His point, simply put, is that we make certain assumptions based on our experiences. Many of these assumptions are wrong. We see patterns where none exist and fail to correctly calculate the likelihood of any particular outcome. Things we think are wildly improbable happen with some regularity, and vice versa. Luck, defined as the favorable intersection of random events, is a bigger factor in our lives than many of us care to admit.

Not surprisingly, many probability pioneers were also gamblers. Having money at stake is always clarifying, and there are those whose lives, and livelihoods, depend on the correct calculation of the odds. Casinos, for one, run on probability. In “Starting from Scratch,” a 2020 episode of the radio show, This American Life, producer Mary Beth Kirchner follows the fortunes of a part-time Las Vegas limo driver named Joe (“please don’t use my last name”). Joe’s goal is to end up every day with more money than he began with. “One time I started out with $32 and ended up with $84,000,” he tells Kirchner. He does this not by driving the limo, but by periodic forays into the casinos to play blackjack.

A professional acquaintance of Joe offers this insight. “He is by no means dishonest. He’s an opportunist. He’s the kind of guy that if there’s a dollar to be made, he’ll make ten.” This view is confirmed by, among others, Joe’s daughter (“please don’t use my first or last name”), whom Joe raised as a single parent. “We would walk in (to the casinos) and everyone would know him,” she says. She remembers both the good times and the not so good. “Sometimes we had to search for quarters on the floor,” she says.

George, a Las Vegas casino pit boss (“please don’t mention my full name or where I work”), adds, “I see the numbers. There’s not a player in this place or any casino I’ve ever been who made more than they lost.” Possibly George’s experience proves nothing, possibly his experience is itself random, but it is seconded by the fact of Las Vegas itself.

In a different book about a more singular set of variables, A Random Walk Down Wall Street, Princeton economics professor Burton Malkiel also grapples with uncertainty, in his case the behavior of markets.

Investors, like punters, have contrived all manner of systems to game the world in which they operate. In markets, these systems and their practitioners can be identified variously as chartists (those who create graphs of stock prices or other factors and look for recurring patterns over time), momentum players (buying shares of stock that are going up on the theory that they will keep going up), fundamentalists (valuations based on discounted cash flows), Smart Beta, and Risk Parity, among others.

There is a colorful agglomeration of theories: Elliott Wave, Dow, Relative Strength, Efficient Market, Modern Portfolio. There is the academically blessed study of Behavioral Economics and its corollary, Behavioral Finance, for which lead acolyte Richard Thaler won the Nobel Prize in 2017.

Malkiel runs through them all, concluding that they are essentially worthless for the simple reason that “past movements in stock prices cannot be used reliably to foretell future movements.” Score one for Duff.

The distribution of health and sickness may not be entirely random but, like markets, it’s impossible to predict. Knowing that a healthy 65-year-old-male has a 80%+ chance of living to 80 is good, but it doesn’t say anything about you. As Duff might say, possibly the entire concept of probability is an illusion, a mathematical construct.

As a spiritual matter, that may be correct; as a guide for monastery living it is doubtless a useful insight. As a framework for retirement planning it’s not especially helpful. We have to make certain assumptions about longevity and the performance of markets. “I long ago came to the conclusion that all life is 6 to 5 against,” says a Damon Runyon character in the story, “A Nice Price,” and, for planning purposes, that seems about right.

There are areas where everyone can agree. In a discussion of dice-throwing, Mlodinow asks, “What does it mean, from a practical point of view, when we say the chances are 1 in 6 a die will land on two? If it doesn‘t mean that in any series of tosses the die will land exactly on the two exactly one time in six, then on what do we base our belief that the chances of throwing a two are really one in six?”

Good question.

A pivotal moment in Mlodinow’s book is his discussion of Jakob Bernoulli and the “Law of Large Numbers.” Developed in the early 18th century, this idea is formally stated as follows: “as the number of identically distributed, randomly generated variables increases, their sample averages approach their theoretical average.” In other words, with enough repetitions the odds, whatever they may be, will assert themselves. That is the essence of probability, and of Las Vegas.

Because our own sample set will always be limited, most of us prefer to operate on a more intuitive principle: the Law of Small Numbers. This, however, is almost certain to lead to many wrong turns in life, and in the markets.

Health is random. Wealth, in its inherited form, is, too. Markets, as Malkiel has noted, behave unpredictably over the short term. Fads come and go. Does value outperform growth? Sometimes. Will small cap beat large? Depends on what period you measure. Can chartists predict the future? Sure, if it looks more or less like the recent past.

Throw the bones.

What’s to be made of all this? Mlodinow’s most helpful insight may come from a Venn-diagram-like musing on the practical applications of theory. “Successful people in every field are almost universally members of a certain set – the set of people who don’t give up,” he writes.

Work hard enough, long enough, and something will happen. You just don’t know what or when. It might or might not be good. Getting to the most probable outcome is a law of large numbers problem; getting any old outcome is just flipping a coin. The best way to improve the chances of getting the outcome you want is to flip a lot of coins.

For investors, this is useful in a very specific way. The likelihood of getting a positive return on your investment goes up the longer you invest. From 1926 to the present – not quite Bernoulli’s Infinite Series but the best we’ve got – stocks have had a positive return in every rolling 15-year period. This includes those periods spanning the Great Depression, Black Monday, the Dot Com bust, the Financial Crisis, and the Great Cessation. The investing equivalent of flipping a lot of coins is holding a diversified portfolio over time.

We’re all on a random walk. For Mlodinow, that journey is defined by the laws of probability. For Duff, who declines to acknowledge the existence of time, this calculated approach is meaningless. For Malkiel, markets hold a certain truth but we have to be patient to uncover it.

Woof!