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Wall Street doesn't predict prices - it prices the randomness in them. That is where the billions are, and it runs on one equation. The model trading desks actually use is Geometric Brownian Motion: dS = μS·dt + σS·dW μ (drift) is the slow expected trend. σ·dW is the...

251,980 views • 3 days ago •via X (Twitter)

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same crash, same window: this strategy ended at $117, buy-and-hold at $67 the difference is one operation in the formula on screen M_t = ( Σ r_{t-i} ) / ( σ_t · √N ) the top is momentum: just the sum of recent returns. net directional drift the bottom is the part retail never adds: divide by volatility that denominator is the whole edge raw momentum has a fatal flaw. a 2% move in a calm market and a 2% move in a panic look identical to it but they are not the same signal. one is information, the other is noise wearing a big number dividing by σ_t rescales every signal into the same risk units now a move only counts as momentum if it's large relative to how much the asset is currently shaking strong drift in a quiet tape scores high. the same drift inside chaos scores near zero this is why the strategy survived the drawdown that ate buy-and-hold when volatility exploded, the denominator exploded with it, the signal shrank toward zero, and the position sized itself down automatically no rule that said "reduce risk in a crash." the math did it because σ_t was in the denominator this is called time-series momentum, and it's one of the most documented effects in finance moskowitz, ooi and pedersen, AQR, 2012: it worked across 58 markets, every asset class, back to 1900 the reason it keeps working is structural, not a pattern trends persist because information diffuses slowly and institutions can't enter all at once. a pension fund moving billions takes weeks, and that slow entry is the drift the signal captures retail buys the move and gets bigger as it accelerates, which means biggest right before the reversal a desk scales inversely to volatility, which means it's largest when the trend is clean and smallest when it's about to snap the paper is free. the whole thing is a rolling sum divided by a rolling standard deviation ten lines of python, twenty years of data that never cost anything the momentum was never the edge. everyone can see a trend the edge was dividing it by the one number that tells you whether to believe it full breakdown in the article below

delost

32,624 views • 1 month ago

Persi Diaconis, Stanford mathematician and former professional magician: "I spent fifty years proving one thing: almost nothing is as random as it looks. The 50.75% that built Renaissance wasn't luck. It was a tiny crack in the randomness, found and repeated a million times." this free lecture holds the exact idea the thread above is built on. and the man giving it isn't a trader. he's a stanford professor and former professional magician who spent his career on one question: where does real randomness end, and where does a hidden edge begin. here is his life's finding. a coin, a shuffle, a market, all look random, yet each hides a faint, measurable bias. on its own that bias is nothing, indistinguishable from luck. repeat it enough times and it stops being luck and becomes a law. that faint crack, found and repeated, is the whole distance between a 50.75% win rate and a hundred billion dollars. none of this is new or hidden. diaconis has taught it for decades, the math runs back to 1713, and the lecture is free. i mapped the full system in my article, expected value, kelly, and this. same point the thread makes: the edge was sitting in plain sight. here is the part the gurus skip. a faint edge only pays if you survive long enough to reach it, and that takes correct sizing and the patience to trust it through thousands of losing-looking trades. most quit while it still looks like randomness. the math is free. the nerve to hold it is the edge.

Rossst.03

230,779 views • 1 month ago

Harry Markowitz, the Nobel laureate who invented modern portfolio theory: "Every fund from Bridgewater to Citadel runs on one equation I wrote as a 25-year-old grad student. Wall Street pays quants $500K to use it. It's free." the thread above teaches you to build a portfolio the real way, with the mathematics of capital allocation. every line of it traces back to one paper markowitz wrote in 1952. before him, "don't put all your eggs in one basket" was folklore. he turned it into algebra. he proved a portfolio's risk isn't the average of its parts, it's driven by how the parts move together, the covariance. combine assets that don't move in lockstep and you cut risk without giving up return. that is the closest thing to a free lunch in all of finance, and he wrote the exact equation for how much of it you get. that single insight, mean-variance optimization, is the engine under every serious fund on earth. renaissance, bridgewater, citadel, your pension, all of them size risk with markowitz's math. he published it in 1952, won the nobel in 1990, and it sits in every textbook and this free lecture. same story i keep telling: the math that runs the trillion-dollar machine has been public and free for seventy years. here is the part markowitz himself warned about. the equation is only as good as the numbers you feed it, your estimates of return and covariance. feed it garbage and the "optimal" portfolio it hands back is confidently, precisely wrong, and it detonates in the exact crisis it was built to survive. the optimizer is free. estimating the future honestly, and knowing when to distrust your own inputs, is the entire job.

Rossst.03

44,259 views • 1 month ago

Elon Musk said the most important thing anyone has said this century. Musk: “I think we need to assume that life and consciousness is extremely rare, and it might only be us.” 13.8 billion years. Trillions of galaxies. Billions of trillions of stars. Not one signal from any of them. That silence is the loudest data point in human history. Musk: “The image in my mind is of a tiny candle in a vast darkness. A tiny candle of consciousness that could easily go out.” That is not poetry. That is a threat assessment from the only person on Earth building the response. Stars don’t know they burn. Black holes don’t know they consume. The universe has been running for 13.8 billion years with no awareness of itself. We are the only known point in all of that time and all of that space where matter woke up and understood what it was looking at. Every law of nature ran in complete silence for billions of years. Gravity pulled. Light traveled. Elements fused. None of it meant anything. Because meaning requires a mind. And there might only be one. Musk is not building rockets because he likes engineering. He is building an escape route for the only thing in the universe that knows the universe exists. If consciousness disappears, the stars keep burning. The physics keeps running. But the universe is no longer a universe. It is just matter moving through space with nothing to call it that. The most profound thing Musk said is not that the candle is small. It is that without the candle, there is no such thing as light or darkness. Just physics performing to an empty room for the rest of eternity. One man looked at that and said no.

Dustin

61,244 views • 1 month ago

Flip a coin. Heads, your account goes up 50 percent. Tails, it goes down 40 percent. Expected value is plus 5 percent a flip, so you take the bet a hundred times. Expected value says your $10,000 becomes $1.3 million. The most likely path leaves you with $52. An MIT professor explains the entire gap in one sentence, in a free undergraduate lecture, then moves on like it was nothing. His name is John Tsitsiklis. He teaches undergraduate probability at MIT. He also proved in 1994 that Q-learning converges, the result that says the algorithm under modern reinforcement learning does not merely happen to work, it has to. INFORMS gave him the von Neumann Theory Prize for that line of work in 2018. He runs the lecture on the students for an hour. First he takes the average apart. A random variable is not a number, it is a function. A bar graph of probabilities is a PMF. Expectation is the center of gravity of that bar graph, the single point where you slide a pen underneath and the thing balances. He is slow and patient about it. By minute 35 you trust the average completely. Then he stops and says he wants to give "one general word of caution." "The average of a function of a random variable, in general, is not the same as the function of the average... in general, you can not reason on the average." Everything before that sentence was the trap. Go back to the coin. Compounding is not addition. Up 50 then down 40 is not plus 10. It is 1.5 times 0.6, which is 0.9. You are down 10 percent. Do that 50 times each way and you have 0.9 to the fiftieth power. Fifty-two dollars. So where did the $1.3 million go? It is real. It is parked at the very top of the distribution. Run the hundred flips and only about one path in seven finishes above where you started. Only about one in a hundred ever reaches that $1.3 million. Those few runs are gigantic, and they carry the average for everybody else. You will not be in them. In February 2018 that trade had a ticker. XIV, short volatility, $1.9 billion in it. It had paid on the average day for seven years. On February 5 the VIX rose 115.6 percent, the biggest one-day jump ever recorded. XIV went from $115.55 to $4.22 overnight. Credit Suisse shut the note two weeks later. Nobody in it was wrong about the average. They were wrong about which path they were standing on. The usable version: your compound return is your average return minus roughly half your variance. A system averaging 20 percent a year at 40 percent vol does not compound at 20. It compounds at 12. That missing 8 is not fees or slippage. Tsitsiklis delivers the most expensive sentence in finance, finishes the variance section, and ends with "see you on Wednesday." The lecture is free. The average is free. Knowing which path you are standing on is the trade.

Veles

628,984 views • 25 days ago