Lehman Brothers collapsed in 2008 after a bank run. The loophole was that, legally, it was not a bank.
Robert Shiller explains what that meant in a Yale lecture on investment banking. By 2008, Lehman had to refinance roughly $100 billion every day. It did not rely on ordinary deposits from households. It relied on the repo market.
A repo is a short-term loan backed by securities. Lehman handed a lender collateral, took cash, and promised to buy the collateral back soon after. Then it did the same thing again the next day.
It looked safe because the loans were collateralized. But every lender had one option: refuse to renew.
That is what made Lehman a bank in everything but legal status. Its lenders were not people standing outside a branch with savings accounts. They were institutions moving billions through overnight loans. But when they all wanted their money back at once, the mechanics were identical.
Lehman had piled into mortgage-related securities. Housing prices fell, the value of the collateral became uncertain, and lenders stopped rolling the repos. A firm that needed roughly $100 billion in fresh financing every day suddenly had no way to fund itself.
Lehman filed for bankruptcy on September 15, 2008. Its collapse helped turn a housing crisis into a global financial panic.
The story of 2008 is usually told as a story about bad mortgages.
Shiller’s point is darker: the biggest bank run of the crisis happened at an institution that was not legally a bank.
Yale, 2011: two years before winning the Nobel Prize, Robert Shiller used a $1 bank deposit to explain why $10,000 at 10% becomes $452,593.
Most people stare at the final number.
The number that matters is $67,275.
Someone with a $100,000 portfolio paying a 1% advisory fee gives up $1,000 every year to have retirement decisions modelled around this math. The 75-minute Yale lecture has been free on YouTube for fourteen years. Shiller gives away the mechanism, then derives it with one dollar.
Put $1 in a bank at rate r. After one year, the balance is 1 + r. After the second year, the bank is no longer calculating interest on the dollar you deposited. It is calculating interest on 1 + r. The balance becomes (1 + r)².
Now run the same equation on $10,000. At a fixed 10% annual return, it becomes $25,937 after 10 years, $67,275 after 20, $174,494 after 30, and $452,593 after 40.
That $67,275 is the answer. The first 20 years add $57,275. The next 20 add $385,318.
No new money entered. The return stayed at 10%. The only thing that changed was the base the 10% was being calculated on.
This is where most people misread compounding. The first 20 years look slow enough to make the result feel linear. They are not. Every year's gain becomes capital for the next year's calculation.
Shiller was teaching debt and interest-rate theory. But the part worth keeping is simpler: people spend their time searching for a better rate while underestimating what the same rate does after the base has had time to grow.
The equation is one line: (1 + r)ᵀ.
The hard variable is T.
Black-Scholes is wrong.
Not useless. Not outdated.
Just wrong about one thing that happens constantly in real markets.
An MIT professor puts real option prices on the board and compares them with what the famous model says they should be.
The model expects something simple:
Options on the same stock should imply roughly the same volatility.
The market says otherwise.
Change only the strike price, and the implied volatility changes.
Plot it.
You get a smile.
The volatility smile.
This is one of the most important things you can learn about financial models:
A model can be mathematically elegant, widely used, and still fail to describe what actually happens.
That doesn't make the model worthless.
It tells you where the real world starts.
Black-Scholes gave finance a way to put a number on uncertainty.
The market then showed everyone how much uncertainty the equation was missing.
In 1973, three mathematicians found a way to put a price on something that didn't exist yet. Their equation would become one of the foundations of modern finance.
The problem sounds simple. A stock is trading at $100, and someone gives you the right to buy it for $100 six months from now. What is that right worth today? $5? $10? $20? There is no obvious answer. If the stock reaches $150, the option becomes extremely valuable. If it falls to $50, it expires worthless.
Fischer Black, Myron Scholes and Robert Merton approached the problem differently. Instead of trying to guess where the stock would be six months from now, they asked what could actually be measured today: the current price, the strike price, the time remaining, the interest rate and the expected volatility.
Put those variables into the model and you get a theoretical price for the option.
But there was something even more interesting behind it.
Imagine you sell that option. Every time the stock moves, the risk of your position changes. If the stock goes up, you adjust your position. If it goes down, you adjust again. You keep doing this as the market moves, using the underlying stock to offset the changing risk.
You don't need to know where the stock will end up.
You only need to keep adjusting.
That idea became known as dynamic hedging, and it was one of the key ideas behind the Black-Scholes model.
The mathematics behind it is not simple. The model brings together probability, calculus, volatility and the mathematics of continuous price movements to answer a surprisingly practical question:
How much should uncertainty cost?
Black and Scholes published their paper in 1973, and Robert Merton later extended the theory. Their work became one of the foundations of modern quantitative finance, and Scholes and Merton eventually received the Nobel Prize in Economics in 1997.
But the part I find most interesting isn't the equation itself.
It's the idea behind it.
You don't always need to predict what will happen.
Sometimes, you can build a mathematical system that allows you to deal with the fact that you don't know.
Black-Scholes didn't make the future predictable.
It made uncertainty measurable.
@andreysuperior The deeper you get into Black-Scholes, the more you realize it was never really about predicting the market — it was about learning how to price uncertainty.
A test that's 99% accurate for a disease. You take it. It comes back positive. Most people assume they almost certainly have the disease.
They're almost certainly wrong.
John Tsitsiklis teaches why at MIT — same course, same classroom where the lecture on the gambler's fallacy came from.
Say the disease affects 1 in 1,000 people. The test catches it correctly 99% of the time, and gives a false alarm only 1% of the time. Sounds airtight.
Run the actual numbers. Out of 1,000 people, one person actually has the disease, and the test almost certainly catches them. But of the 999 healthy people, 1% — about 10 people — get a false positive anyway.
So eleven people test positive. Only one of them is actually sick.
Your real odds, after a positive result, aren't 99%. They're closer to 9%.
The test isn't broken. The math is doing exactly what it's supposed to do. The problem is that "how accurate is the test" and "how likely am I to have this, given a positive result" are two completely different questions — and almost everyone answers the second one using the number for the first.
This isn't just a classroom trick. It's the same reasoning behind airport security flags, spam filters, and drug tests. Any time you're screening for something rare, the false positives start outnumbering the real ones — no matter how "accurate" the test claims to be.
Tsitsiklis puts the whole thing on the board in about ten minutes. Most people go their whole lives making the opposite mistake, for free.
Two brain systems fight over every decision you make about your time, and one of them is rigged to win the argument tonight, every single time.
Frank Schilbach teaches this at MIT. The study behind it comes from a Science paper by McClure, Laibson, Loewenstein, and Cohen.
They gave people a choice. Juice now, or twice as much juice in five minutes. 60% took it now.
Then they moved the whole choice twenty minutes into the future. Juice in twenty minutes, or twice as much in twenty-five. Same five-minute wait, just relocated. This time only 30% chose the smaller, earlier option.
Nothing about the math changed. Only how far away "now" was.
Economists call it hyperbolic discounting. Not a smooth curve, like a bank compounding interest. A cliff. Your brain slashes the value of anything inside the next few minutes almost in half, then barely discounts anything past that.
This is the same mechanism sitting underneath every "just one more hour of work" that beats "go home to your kid." Tonight sits on the cliff. Missing it doesn't feel like losing anything — the cost is twenty years away, flattened out where the brain can't price it.
Laibson has a line about this in his own research: self-control isn't a personality trait, it's a technology problem, solved by people who bind their future selves before temptation arrives.
Nobody who ends up with the empty auditorium seats made one bad call. They made the same three-minute miscalculation, thousands of times, each one too small on its own to notice.
By the time you're standing in the doorway deciding whether to go in, the math was rigged twenty years earlier.
this is insane. i genuinely don't understand why every ambitious person isn't shown this lecture before work starts consuming their entire life.
clayton christensen dedicated his career to studying why successful companies collapse. in his final class, he turned that theory on his students: if you keep allocating your time the same way, what life will you eventually build?
he had already seen the answer in his own harvard mba class.
at the fifth reunion, almost everyone looked successful. by the 10th, 15th, 20th, and 25th, some had stopped coming.
behind the empty seats were divorces, broken families, children living across the country, and people who had become wealthy but deeply unhappy.
none of them had planned that life.
work shows progress today. finish the presentation, ship the product, close the sale, get promoted, watch the number move.
an evening with your child may give you nothing you can show the next morning. it may take 20 years before you understand what all those evenings built.
so the next free hour goes back into work. the decision feels responsible, and tomorrow it feels responsible again.
this is how a life moves in the wrong direction without a single obviously wrong decision. every hour made sense on its own.
money, titles, and headcount fit neatly into a spreadsheet. christensen proposed another measure: how many lives became better because you were there?
he died in 2020.
open your calendar and look at where your time went over the last year. does it match what you say matters?
the full 70-minute lecture is in the video below.
Warren Buffett once collected $4 billion in cash and didn't have to put up a single dollar as collateral.
Yi Tang teaches why at MIT — the final lecture of a Morgan Stanley-taught course on the math banks use to survive their own trading desks.
Here's the trade. Berkshire Hathaway sold long-dated put options on four major stock indexes — the S&P 500, the FTSE 100, the Euro Stoxx 50, the Nikkei 225. Betting, in effect, that those markets wouldn't collapse before the contracts expired decades later.
In exchange, whoever bought those puts paid Berkshire roughly $4 billion, upfront, in cash. Day one.
Normally, a trade like this requires collateral — money set aside in case you're wrong and can't pay. Berkshire posted none.
Every major bank on the other side of that trade had to ask the question Tang spends the whole lecture teaching how to answer: what happens if Buffett is wrong, and Berkshire can't pay decades from now?
That risk has a name. Counterparty credit risk. It's the same risk that took down Lehman Brothers and forced the government to bail out AIG in 2008 — AIG had sold protection it couldn't actually pay out on when the bill came due.
Banks build entire pricing models just to answer one question before they'll do a trade like this: how much do we charge, in advance, for the chance you can't pay us back later?
They call it a credit valuation adjustment. It's a price tag on trust itself, calculated to the decimal point.
Buffett got his $4 billion partly because Berkshire's promise to pay was worth more, to the banks doing the math, than almost anyone else's.
Every contract on earth has two prices. What it's worth if everyone pays. And what it's actually worth once you price in the chance that someone won't.
A psychologist watched couples argue for fifteen minutes and claimed he could predict divorce with 94% accuracy. For years, almost nobody checked the math.
John Gottman built something he called the Love Lab at the University of Washington. Wired couples up to heart monitors. Filmed them fighting about nothing — dishes, money, who forgot to call whose mother.
He found four behaviors that showed up again and again in couples who eventually split. Criticism. Contempt. Defensiveness. Stonewalling. He called them the Four Horsemen.
Contempt was the worst one. Not yelling. Not even the fighting itself. Just one partner talking down to the other like they're something less.
The number that made Gottman famous: 94% accuracy, predicting divorce from a single conversation.
Here's what almost never makes it into the articles.
That number came from fitting a model to couples whose outcomes he already knew. When other researchers took the same method and tested it on new couples — actually predicting instead of explaining — the accuracy collapsed. One re-analysis found the real predictive power was closer to 21%.
Not 94%. Barely better than a coin flip with a slight edge.
So which part is still true?
The Four Horsemen themselves hold up. Contempt really does corrode relationships. Couples really do fall into these patterns before things end.
What doesn't hold up is the fortune-telling. Nobody can watch you argue for fifteen minutes and know your future.
The four warning signs are real. The crystal ball was never real to begin with.
@rendeeex the 1913 story is real, by the way — that's literally where the term comes from. Monte Carlo casino, black hit 26 times straight, people lost fortunes assuming red was "due." the fallacy is named after that exact night.
Oil crashed 42% in 2008. Everyone who traded it lost money that year.
Except one company. They had their best year in history.
They didn't short it. They didn't predict the crash. They didn't trade oil at all, really.
On January 15, 2009, a barrel of oil for February delivery cost $35. The exact same barrel, for delivery 13 months later, cost $60. Storing it for that year costs $3.50 in interest.
Buy now, store it, sell it later. $25 gap, minus $3.50 in storage.
$21.50 a barrel. Locked in the moment you sign, whether oil crashes further or doubles.
Alexander Eydeland teaches this at MIT — runs commodity modeling at Morgan Stanley by day, guest lectures the math by night. The company from the Bloomberg headline was Trafigura, one of the largest oil traders on earth. Their edge wasn't forecasting anything. It was owning empty steel tanks in the right places at the right time.
Then Eydeland's lecture goes one step further. What if you don't own the tank — you just have the right to lease it? He prices that right too. One tank, one year: the lease itself is worth $4.47 a barrel to whoever holds it. Not a guess. The exact number where the deal breaks even no matter which way oil moves.
Storage doesn't look like a financial asset. It's steel and empty space. Priced correctly, it behaves exactly like an option — one that pays out regardless of which direction the market panics.
Most traders spend entire careers guessing which way prices go next.
The ones who get rich figured out how to stop needing to guess.