Neighbor

Probability over prediction. Quant finance, statistics, risk management & market psychology

[Neighbor @Neighboritto]

A Nobel laureate mathematically proved how to build the perfect portfolio. He didn't use his own formula for his own money.

In 1952, a 25-year-old graduate student at the University of Chicago wrote an 11-page paper that would, decades later, earn him a Nobel Prize and completely upend how the world invests. His name was Harry Markowitz.

Before him, the logic of investing was simple: find the companies with the best prospects and put your money there. Markowitz asked a different question — what if a collection of the "best" individual assets isn't actually the best portfolio at all?

His key insight: an asset's risk shouldn't be judged in isolation. What matters is how it moves relative to the rest of the portfolio. Two assets that are each merely average performers on their own, but don't move in sync, can together form a portfolio that's safer — and more rewarding per unit of risk — than either one alone.

That's how Modern Portfolio Theory was born. For any given level of risk, there's a maximum possible expected return; the curve connecting all such optimal combinations is called the "efficient frontier." Anything below that curve is suboptimal. Diversification stopped being just the old saying "don't put all your eggs in one basket" — it became a solvable mathematical problem.

Markowitz defended this work as his dissertation, and Milton Friedman sat on his examination committee. By Markowitz's own account, Friedman half-jokingly questioned whether this was economics at all rather than pure mathematics — and whether it deserved an economics degree. He got the degree, of course. Then in 1990, nearly 40 years after the paper, once the influence of his ideas on trillions of dollars of institutional capital had become impossible to ignore, Markowitz received the Nobel Prize in Economics — together with William Sharpe (the same Sharpe who lent his name to the Sharpe ratio and built CAPM on this foundation) and Merton Miller.

Now for the most interesting twist in this story. When Markowitz, already elderly, was asked how he'd allocated his own retirement savings, he answered honestly: he hadn't run any optimization at all. He simply split the money in half — half in stocks, half in bonds. By his own account, what guided him wasn't a desire to mathematically maximize expected returns, but a desire to minimize future regret: he imagined how he'd feel if the stock market soared and he wasn't fully in it, or if it crashed and he was fully in it. The man who formalized optimal investing chose, for himself, not the optimum — but peace of mind.

This story isn't just a curiosity — it's practically a preview of an entire field of science: behavioral economics (Kahneman, Thaler), which is precisely about this — why even experts systematically deviate from mathematically optimal decisions out of fear of loss and regret.

There's also more serious criticism of the theory itself. Markowitz's model relies on the assumption that returns are normally distributed and that correlations between assets are stable. In real crises (1987, 2008), that assumption breaks down exactly when diversification is needed most: correlations across asset classes spike, and "different" instruments crash together. It's the same trap that ultimately brought down LTCM, as covered in the previous post — statistics built on historical data stay silent about what happens when history suddenly repeats itself differently.

What to take from this in practice: — diversification only works when assets are genuinely weakly correlated, not just differently named; — historical correlations are an estimate, not a law of nature — build in a margin for the case where they break down all at once; — a theoretically optimal portfolio you can't hold onto psychologically during a drawdown is worse than a less optimal one you'll actually stick with; — today's index funds, target-date retirement funds, and risk-parity strategies are, at their core, Markowitz's idea running at industrial scale on autopilot.
The main lesson here isn't really about the efficient frontier. It's that even the person who mathematically proved what an optimal portfolio should look like chose, for himself, not the formula but a good night's sleep. Sometimes the best portfolio is the one you won't sell in a panic.

[Rossst.03 @Rossst_03]

https://t.co/eMlCMF7liL

[Neighbor @Neighboritto]

@isssa0x it's easier for the crowd to believe that markets are always rational

[Neighbor @Neighboritto]

@lilch1ks_ I'm going to the gym tomorrow toooo

[Neighbor @Neighboritto]

@BuildWithYar we need to search old archives and study valuable information that will help in our time

[Neighbor @Neighboritto]

@semichenkko his looks like a literal galaxy!!!

[Neighbor @Neighboritto]

There's an equation on Wall Street almost nobody uses — even though it's been public since 1956.

Imagine a trader who calls the market's direction right 6 times out of 10. Not bad, right? Now imagine that same trader still goes broke by year's end. The problem isn't the calls. The problem is how much he bets on each one.

The formal answer to that question came from John L. Kelly Jr. — a physicist and colleague of Claude Shannon at Bell Labs. In 1956 he showed that the problem of a gambler with an edge is mathematically identical to the problem of sending a signal through a noisy communication channel — the same problem Shannon solved in information theory. That's how the Kelly criterion was born.

The formula for an even-money bet is almost embarrassingly simple: f = 2p − 1, where p is your probability of winning and f is the fraction of your bankroll to risk. A coin with a 55% edge on heads? f = 2×0.55 − 1 = 0.10 — that's 10% of your bankroll, not more.
In general form, for any odds b to 1: f = (bp − q) / b.
In plain terms: edge divided by odds. That's the whole secret.

The formula sat gathering dust in academic journals for years until a mathematician named Edward Thorp picked it up. He counted cards at blackjack, proved casinos could be beaten mathematically, and wrote it all up in the bestseller "Beat the Dealer" (1962) — after which Las Vegas changed its rules. Together with Shannon, he even built a wearable computer for roulette, hidden in a shoe.
Then Thorp did the thing that mattered: he pointed the same logic at the stock market. In 1969 he founded Princeton-Newport Partners — arguably the first quantitative hedge fund in history. Nearly 19 years without a single losing year, roughly 20% annual returns after fees. Not predicting the future — a small, measurable edge, sized correctly and repeated thousands of times.

Bill Gross, who went on to run the world's largest bond fund (PIMCO), counted cards in Vegas as a student and took his risk-sizing lessons straight from there. Charlie Munger has spent decades preaching essentially the same idea: bet rarely, but when the edge is truly on your side, bet big.

The clearest example is Jim Simons's Medallion fund (Renaissance Technologies). According to "The Man Who Solved the Market," the fund's own people admitted individual trades were correct only about 50.75% of the time — barely better than a coin flip. But sized correctly and repeated across millions of trades, that tiny edge turned into over $100 billion in profit across three decades, averaging roughly 66% a year before fees.

So why does nobody talk about the formula? Because "full" Kelly is emotionally brutal. It routinely produces 40–50% drawdowns that no investor — and no fund manager answering to investors — can stomach psychologically. That's why professionals almost always play a fraction of Kelly: half or a quarter. A little less growth in exchange for a much bigger margin of safety against bad estimates.

And this isn't a theoretical scare story. Long-Term Capital Management had Nobel laureates Myron Scholes and Robert Merton on its team, plus legendary trader John Meriwether. They genuinely had an edge. But they leveraged it 25-to-1 and beyond — exactly the signal Kelly's formula flags as "you're betting many times over the maximum." Russia's 1998 default wiped out roughly $4.6 billion in weeks and nearly took down the global financial system; the Fed had to organize a rescue. LTCM didn't die from a bad call. It died from being right — and betting too much.

The formula itself has been free and public since 1956. The scarce resource is an honest estimate of your real edge (most people overstate theirs) and the discipline to bet small even when your gut is screaming to go all in.

What to actually do with this: — Spend as much attention on position size as on picking the idea itself. — Estimate your win probability conservatively, not optimistically. — Play a fraction of Kelly (½ or ¼), not the full calculation. — Spread capital across several independent edges instead of concentrating it in one.

The same logic works today even on prediction markets like Polymarket or Kalshi: if a contract trades at 40 cents and you believe the true probability is 50%, you have a 10-point edge. The Kelly criterion tells you exactly how much to stake on that — not your emotions.

[Rossst.03 @Rossst_03]

https://t.co/eMlCMF7liL

[Neighbor @Neighboritto]

@KyleDeWriter if it really competes with HFT bots that’s massivvvv

[Neighbor @Neighboritto]

@xJellybon why do you think LTCM is the ultimate cautionary tale compared to 2008?

[Neighbor @Neighboritto]

Benoit Mandelbrot, mathematician, IBM Fellow, father of fractal geometry: "Markets often leap, don't glide."

That's the whole complaint, and it took him forty years of data to prove it. Every VaR model, every Black-Scholes greek, every "six-sigma event" headline assumes price changes behave like a bell curve — independent, well-behaved, thin-tailed. The paper underneath this is free too: "The Variation of Certain Speculative Prices," 1963, sitting in any library search bar.

At the board it's simple. Standard finance calls this "mild" randomness — like a casino, where outcomes vary but average out predictably. Mandelbrot's data, starting with a century of cotton prices, showed something else: the sequence of price changes was random and unpredictable, but independent of scale — daily and monthly curves matched. Strip the axis labels off a chart of daily returns and one of monthly returns and you can't tell them apart. Wall Street's core models have no room for that property.

Here's the number that should have ended the argument. If daily Dow Jones moves from 1916 to 2003 really followed a bell curve, you'd expect 58 days where the index moved more than 3.4%. There were 1,001. You'd expect 6 days beyond 4.5%. There were 366. Moves beyond 7% were supposed to happen once every 300,000 years — the 20th century alone produced 48 of them.

That's not a paradox. That's the gap between the model everyone was trained on and the market everyone actually trades in.

Which is exactly why treating a fat-tailed market as Gaussian manufactures false confidence, not safety. Long-Term Capital Management ran two Nobel laureates and still blew up in 1998 pricing risk this way — a "once in a millennium" move showed up and took the fund with it. Get the tails wrong and you're certain to be blindsided by something the model told you was impossible. Get it right, and you size and hedge assuming the rare event, the way people who actually survived 1987 and 2008 did — not the way a model built on 100-year-old physics says to.

The math is free and public. What nobody can sell you is the judgment to look at a calm market and remember it's one fat-tailed draw away from wild. That judgment is the edge, and it takes years to build.

[Rossst.03 @Rossst_03]

https://t.co/iZLuBLz082

[Neighbor @Neighboritto]

@xwhynoted the math is broken, incredible story

[Neighbor @Neighboritto]

@Amir_Radarit people buy a familiar face, even if it's digital. why not?

[Neighbor @Neighboritto]

@xJellybon damodaran’s logic is undefeated ...

[Neighbor @Neighboritto]

@gaboweb3 selling the outcome
not the tech

[Neighbor @Neighboritto]

@DenlitL Hot water is probably in the tub

[Neighbor @Neighboritto]

@fort1kkk If a token ever comes the people using Base naturally will probably be in a better position than those who arrive after the announcementt

[Neighbor @Neighboritto]

@twelvepills12 bigger win is optimizing context

[Neighbor @Neighboritto]

@XXIfomo Engelbart built the future we just pay rent for it 🫡🫡

[Neighbor @Neighboritto]

@vladoqp the greatest and wisest people in the world

[Neighbor @Neighboritto]

@Zeras_24 look for the builders lock in and just be patient😅

[Neighbor @Neighboritto]

@KyleDeWriter can they sustain this volume post-election?