Why do many of us feel like we’re not doing so well financially — even in times of relative prosperity?
Perhaps there’s a fundamental error underlying current economic theory that accounts for this disconnect, as well as many other key challenges plaguing the field. That’s the gist of a provocative thesis outlined in a new paper in the journal Chaos.
Several years ago, Ole Peters of the London Mathematical Laboratory became intrigued by what’s known as the leverage problem in mathematical finance. The leverage problem asks how much of one’s bankroll one should risk when making an investment. “Here’s the key problem of the discipline of economics: how do you judge the desirability of an uncertain venture? The established answer is a fudge,” Peters told Gizmodo via email. “This must have consequences for the entire discipline. And then the financial system had just collapsed, apparently because risks had been misjudged.”
In 2010, he gave a talk on the subject at the Sante Fe Institute. The audience included Nobel prizewinning physicist Murray Gell-Mann, a distinguished fellow at the institute, and the two men formed what proved to be a fruitful collaboration.
The development of probability theory in the 17th century produced key concepts that inform much of current economic theory. Back then, questions of how much one should bet in a game of chance, or how much to pay for an insurance contract, were typically addressed by imagining that every possible outcome would happen in its own parallel world. One would then take an average across all those possible worlds. But physicists in the mid-19th century adopted a different method, asking how those probabilities played out in one world only — your world, a.k.a. reality — across time.
Peters and Gell-Mann found that this shift in perspective changes everything, particularly when it comes to risk management. “If you look at the organisational chart of an investment bank, you will find groups whose job it to make money (like trading desks), and individuals or groups whose job is to manage risks,” said Peters. “What our work says is that you can’t separate the two issues. Growth management and risk management are the same thing.”
Asking how fast your money will grow over time, in just one world line, will give you an optimal leverage. “The answer may be ‘keep 80 per cent of your money and invest 20 per cent,’” said Peters. “Under the parallel-worlds perspective, the answer is always invest as much as you can, either long or short — no optimum exists. More risk is always better.”
Take a simple case: toss a coin repeatedly, and whenever it comes up heads, add 50 per cent to your wealth. When it comes up tails, subtract 40 per cent of your wealth. If the sole criterion were expected value, you should play the game. In fact, you should borrow money and bet more than you have.
“If a small investment increases my expected wealth, then a large investment increases it even more,” said Peters of this faulty reasoning. “Result: it looks as if I should leverage as much as I can, borrow 100 times the money I have, (or even better 1000 or 1,000,000 times), and invest it all. This mathematically naive perspective would fool me, and I will be bankrupt pretty soon.”
The problem is that the expected value is typically averaged over parallel worlds. But you exist in just one of those worlds.
Plot this coin-flipping game out over 1000 or 1 million iterations using the parallel-worlds approach, and gradually the random fluctuations smooth out, showing a clear overall upward trajectory. Sounds great, right? But when Peters and Gell-Mann took just one world’s average over time, their models showed the opposite conclusion. Instead of ending up with a clear upward trajectory, they saw a pronounced downward trajectory in the resulting plot.
That’s the disconnect. Crunch the numbers in aggregate (the parallel worlds, or ensemble method) and we all collectively appear to win. Do the same with the trajectory of a single world line using the time-centric method, and we lose as individuals.
This happens because certain rare cases skew the aggregate results. For example, a nation’s GDP is calculated using an aggregate approach. But a sharp increase in wealth for its richest citizens can skew the average. The overall GDP may show an increase, but the majority of its citizens aren’t prospering.
The difference between how individual wealth behaves across parallel worlds, and how it behaves over time, also quantifies how wealth inequality changes, according to Peters. “The mathematical system where everyone’s wealth grows at a lower rate than the expectation value translates into an economic physical system where 99 per cent of the population is losing, while one per cent is making such big gains that the average looks good,” he said. “So we find that our work chimes with the disconnect that has been reported between the economic experience of the man on the street and the generally more positive economic figures that are quoted in the press.”
Back in 2011, Peters gave a TEDx talk about all of this at Goodenough College in London, England, concluding with a helpful takeaway message for the vast majority of us who don’t fall into that lucky one per cent. We have a warped perception of reality, according to Peters, in that we focus on the rare successful exceptions, like Bill Gates or Warren Buffet, rather than the people we interact with on a daily basis, like teachers, bus drivers, or salespeople. We focus on excellence and reward rare fluctuations. We shouldn’t, Peters advised, because if you combine that warped perspective with steep inequality, the result is higher levels of anxiety and depression in society at large.
So what should we do? Don’t compare yourself to absurd expectations. “On average, we are average, not excellent, and typically we are mediocre,” Peters concluded. Recognising this might just save us from financial ruin. We’ll also be happier. “Life is more fun if we feel free to do the things we’re bad at,” Peters clarified. “When is the last time you’ve sung in front of your friends?”
Top image: Still from Mississippi Grind (2015).