Going for Broke
TBL returns from hiatus.
TBL is back, baby.
Many thanks to all of you who reached out during my hiatus. Yes, I’m fine. I hurt my Achilles playing pickle ball but, really, I’m fine. However, a lot has gone on since we were last together.
My lovely bride and I packed up our home of 28 years and moved 2636 miles to where we bought and moved into a new house. We drove across the country (much slower than last time). We spent wonderful time with our grandchildren (at the place you may have read about here).
The biggest thing, though, was that my much-better-half retired. She didn’t want to, but she was no longer willing to have to fly across the country to see our grandchildren. All three of our children, their spouses, and all nine grandchildren now live within a half-mile of us. That she loved her work and that she made a real difference in kids’ lives is illustrated by the video below.
Our house was about 500 yards from the elementary school where she taught (all three of our kids attended there, too). As you will see, to honor her retirement, students and former students lined the entire route from her classroom to our house to applaud her. I thought it was amazing, and a wonderful surprise.
As Auggie says in Wonder, everybody deserves a standing ovation.
I’m pleased to be back.
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Going for Broke
Tom Stoppard’s Rosencrantz and Guildenstern are Dead presents Shakespeare’s Hamlet from the bewildered viewpoint of two of the Bard’s bit players, the comically indistinguishable nobodies who become headliners in Stoppard’s play. It opens before our heroes have even joined the action in Shakespeare’s epic. They have been “sent for” and are marking time by flipping coins. Guildenstern keeps tossing coins and Rosencrantz keeps pocketing them as they keep coming up heads each time. Significantly, Guildenstern is less concerned with his losses than in puzzling out what the defiance of the odds says about chance and fate.
“A weaker man might be moved to re-examine his faith, if in nothing else at least in the law of probability.”
This coin-tossing streak provides us with a chance to consider just that. Guildenstern offers, among other explanations, the one mathematicians and investors should favor.
“…a spectacular vindication of the principle that each individual coin spun individually is as likely to come down heads as tails and therefore should cause no surprise each individual time it does.”
In other words, past performance is not indicative of future results.
Even so, how unlikely is a streak of this length?
The probability that a fair coin, when flipped, will turn up heads is 50 percent (the probability of any two independent sequential events both happening is the product of the probability of both). Thus, the odds of it turning up twice in a row is 25 percent (½ x ½), the odds of it turning up three times in a row is 12.5 percent (½ x ½ x ½), and so on. Accordingly, if we flip a coin 10 times (one “set” of ten), we should only expect to have a set end up with 10 heads in a row once every 1024 sets [(½)10 = 1/1024].
Rosencrantz and Guildenstern got heads roughly 100 consecutive times. The chances of that happening are: (½)100 = 1/7.9 x 1031. In words, we should expect it to happen once in 79 million million million million million (that’s 79 with 30 zeros after it) sets.
By comparison, the universe is about 13.9 billion years old, in which time “only” about 1017 seconds (1 with 17 zeros after it) have elapsed.
Looked at another way, if every person who ever lived (around 110 billion of us) had flipped a 100-coin set simultaneously every second since the beginning of the universe, we should expect each of the 100 coins in a set to have come up heads two times.
If anything like that had happened to you (especially on a bet), you’d agree with Nassim Taleb that the probabilities favor a loaded coin.
But, then again, while 100 straight heads is less probable than 99, which is less probable than 98, and so on, any exact order of tosses is as likely (actually, unlikely) as 100 heads in a row: (½)100. We notice the unlikelihood of 100 heads in a row because of the pattern and we are pattern-seeking creatures, through-and-through. More “normal” combinations look random and thus expected. We don’t see them as noteworthy.
If there will be one “winner” selected from a stadium of 100,000 people, each person has a 1 in 100,000 chance of winning. But we aren’t at all surprised when someone does win, even though the individual winner is shocked at his or her good fortune.
Here’s an obvious conclusion: The highly improbable happens all the time.
In fact, much of what happens is highly improbable. This math explains why we shouldn’t be surprised when the market remains “irrational” far longer than seems possible.
But we are.
The world is far more random than we’d like to think. Indeed, the world is far more random than we can imagine.
Even worse, our economic and market models typically assume a “mild randomness” of market fluctuations. Instead, what visionary mathematician Benoît Mandelbrot called “wild randomness” prevails. Risk is concentrated in a few rare, hard (perhaps impossible) to predict, extreme, market events. The fractal mathematics that he invented allow us a glimpse at the hidden sources of apparent disorder, the order behind monstrous chaos. However, as Mandelbrot is careful to emphasize, it is empty hubris to think that we can somehow master market volatility. When one looks closely at financial-market data, seemingly unexplained accidents routinely appear.
The financial markets are inherently dangerous places to be, Mandelbrot stresses.
“By drawing your attention to the dangers, I will not make you rich, but I could help you avoid bankruptcy. I am a doomsday prophet — I promise more blood and tears than windfall profits.”
Despite those warnings, we continue to search (largely in vain) for methods to the madness. Perhaps worse, even if we had an essentially foolproof way to avoid ruin and get rich, there is an astonishing likelihood that we’d screw that up, too.
As I am wont to say, information is cheap while meaning is expensive.
A few years ago, 61 students of finance and recent finance graduates turned up for what they thought was going to be a talk by a hedge fund manager who had been a partner at Long-Term Capital Management, the famous hedge fund of Nobel laureates and Salomon Brothers prop desk alumni that, after a few of years of incredible results, spectacularly imploded almost thirty years ago now (you can read about it here).1
Full Disclosure: I was at an early LTCM pitch meeting (paraphrasing, but not much: We’re going to make a boat-load of money).
Instead, the subjects were offered a stake of $25 to bet on coin flips for thirty minutes (about 300 tosses) with the knowledge that the (computerized) coin was biased to come up heads with a 60 percent probability. The contestants could bet as much of their pot as they’d like on heads or tails on each flip and would receive whatever winnings they had accrued at the end of the half-hour, up to a maximum of $250.
Those are, of course, exceptionally good odds. The expected value of this game, uncapped, is about $3 million.
The optimal betting strategy can be derived from the “Kelly criterion,” a formula for maximizing the rate of growth of wealth in games with favorable odds. Optimization is important, especially with time limits, in that betting too much risks busting due to a bad run of luck, despite favorable odds, while betting too little risks leaving lots of money on the table when time runs out.
Using the Kelly criterion, a player should bet 20 percent of his or her account on heads on each flip. So, the first bet would be $5 (20% of $25) on heads, and if s/he won, then s/he’d bet $6 on heads (20% of $30), but if s/he lost, s/he’d bet $4 on heads (20% of $20), and so on. That said, a simple constant percentage betting strategy of anywhere from 10 to 20 percent would have offered a 95 percent likelihood of a player reaching the $250 maximum payout. Going bust would be highly unlikely.
Here’s the TL;DR: The test subjects – all students of finance or finance professionals, remember – overall...
…chose poorly.2
They exhibited a poo-poo platter of widely documented behavioral biases such as loss aversion, illusion of control, anchoring, over-betting, sunk-cost bias, and the gambler’s fallacy. And, like employees failing to take an employer’s 401(k) match, few seemed to appreciate the opportunity they had received for free money. And, sometimes, they were just plain stupid.
Only about one-in-five players reached the $250 maximum. One-third of participants ended up with less money than they started with and 28 percent somehow, with the odds highly in their favor, managed to lose everything. Despite 60:40 odds and about 300 rolls, the average ending bankroll of those who did not reach the maximum and who also did not go bust – about half the sample – was a mere $75. The average payout across all subjects was only $91.
A list of the coin-flippers’ mistakes reads like a how-to-go-broke manual. Rather than deciding on a strategy and sticking to it, the test subjects bet erratically. There was no indication whatsoever that the participants were, in any way, individually or collectively, converging toward optimal play over time, as evidenced by suboptimal betting of similar magnitude throughout the game. Nobody learned from his or her mistakes and adjusted their approach accordingly.
Many doubled down on losses, even though doing so is a reliable way of turning mild losses into catastrophic ones. Others made small bets in fixed dollar amounts, avoiding ruin but also giving up the lion’s share of their potential returns. Very few even seemed to consider the optimal strategy of betting a constant fraction of their wealth on an attractive opportunity.
If a high proportion of quantitatively sophisticated, financially trained individuals have so much difficulty playing a simple game biased in their favor, it’s little wonder the general population has difficulty investing their savings in stocks.
Shockingly, nearly a third wagered their entire pot on a single flip and, incredibly, some did so on the wrong side of the probability scale. They bet tails!
Indeed, fully two-thirds of participants bet on tails at some point during the experiment, about half of them bet on tails more than 5 times during the game, and more than 20 percent of them bet on tails more than a quarter of the time. They were more likely to bet tails after a string of heads.
Even after 100 heads in a row, the odds of the next toss being heads (with a fair coin) remain one-in-two or, in the experimental example, three-in-five (the “gambler’s fallacy” is committed when one assumes that a departure from what occurs on average or in the long-term will be corrected in the short-term). Still, we look for patterns (“shiny objects”) to convince ourselves that we have found a “secret sauce” that justifies our making big bets on less likely outcomes. In this regard, we are dumber than rats – literally.
In numerous experimental studies, as reported by Philip Tetlock in Expert Political Judgment (see here), the stated task was predicting which side of a “T-maze” held food for the subject rat. Unbeknownst both to observers and the rat, the maze was rigged such that the food was randomly placed (without a pattern), but 60 percent of the time on one side and 40 percent of the time on the other. The rat quickly “got it” and waited at the “60 percent side” every time and was thus correct 60 percent of the time.
You will recall that human subjects who knew about the “60 percent dice” couldn’t do that.
The human observers in the rat studies kept looking for patterns and chose sides in rough proportion to recent results (recency bias). Thus, the humans were right only 52 percent of the time – they were (as we are, in this respect at least) dumber than rats, demonstrating (yet again), as Blaise Pascal proclaimed in his Pensées, a claim with solid empirical support: “All of humanity’s problems stem from man’s inability to sit quietly in a room alone.”
Overall, we insist on rejecting probabilistic strategies that accept the inevitability of randomness and error.
Thus (because it’s October), I always have to re-convince myself that if the games are 50-50, then the probability that the World Series goes exactly six games is the same as the probability it goes seven.
The other lessons for investors from the dice experiment should be obvious. Because human nature tends toward too much (or wrongly proportioned) risk and/or too much spending, we should devise careful rules for spending, saving, and allocating investments, expressed as fractions of total wealth. Then we must stick to them, avoiding the temptation to chase hot assets or spend too much in the face of losses.
Another lesson is that position-sizing is much more important than commonly recognized. The more sophisticated may use “Merton shares,”3 a rule of thumb for determining asset allocation, which holds that allocations should rise in proportion to expected returns, fall in proportion to the investor’s risk aversion, and fall a lot in proportion to volatility (specifically, to its square).
Whatever else may be true, this experiment should highlight the risks of following our intuitions with respect to investing. Our conclusions need to be consistent with and supported by the data, no matter how bizarre the numbers or how long the streak.
Even if we got 100 heads (or tails) in a row.
Totally Worth It
Congress has kept the government open, at least for now, which means the National Park Service’s annual Fat Bear Week contest is still on.
Feel free to contact me via rpseawright [at] gmail [dot] com or on Twitter (@rpseawright) and let me know what you like, what you don’t like, what you’d like to see changed, and what you’d add. Praise, condemnation, and feedback are always welcome.
This interview with Rolling Stone co-founder Jann Wenner is fascinating on multiple levels. It also reinforces the argument I made here.
Of course, the easiest way to share TBL is simply to forward it to a few dozen of your closest friends.
This is the best thing I saw this week. The sweetest. The most important. Also really important. Life in Iran. Common sense on “book banning.” Signage. Don’t be fooled. Octobear. Baseball and AI. Sunken treasure … in New York City? School of Rock is 20. The backstory of Casablanca. What is the most successful movie of all-time? The British Empire peaked 100 years ago. This back-and-forth is remarkable. Common sense. College. Gen Z falls for online scams more than their boomer grandparents do. Do you play Wordle? Seems legit. Seems a bit much.
You may hit some paywalls herein; many can be overcome here.
Check out some friends’ music.
The following video is terrific. Full stop. But watch ‘til the end for a great (and very funny) illustration of confirmation bias.
Please send me your nominations for this space to rpseawright [at] gmail [dot] com or via Twitter (@rpseawright).
In 2015, residents in Woodland, N.C. expressed concern that a proposed solar farm would consume too much sunlight. One resident told the town council that the farm would steal sunlight that plants need, while another warned that it might “suck up all the energy from the sun.”
The TBL Spotify playlist, made up of the songs featured here, now includes over 260 songs and about 19 hours of great music. I urge you to listen in, sing along, and turn up the volume.
My ongoing thread/music and meaning project: #SongsThatMove
Benediction
This week’s benediction is offered by the incomparable Alison Krauss, she of 27 (!!!) Grammy awards.
As Anne Lamott says, grace gives help, says ‘buckle up,” and always bats last.
To those of us prone to wander, to those who are broken, to those who flee and fight in fear – which is every last lost one of us – there is a faith that offers hope. And may love have the last word. Now and forever.
Amen.
Thanks for reading.
Issue 155 (October 6, 2023)
For a real-life example, note that when it comes to the seemingly simple decision of when to start taking Social Security benefits, a recent study found that Americans are leaving more than a trillion dollars on the table by making suboptimal decisions, primarily by taking the benefits sooner than they should. The median loss in the present value of household lifetime discretionary spending for those aged 45-62 is $182,370. There is also good evidence that many spend too much on certain kinds of insurance, from protection on their kitchen appliances to comprehensive car insurance, while spending too little on other types of insurance products, such as annuities.
So great to have you back Bob. I missed your wisdom & worldview.
I missed you, Bob!