David Equalizer

founder of finance academy ||| explaining complex finance world in simple terms

[Athenario @athenari0]

Every trader believes the chart has a trend to follow. An MIT professor proved the price has no slope at all - not for a single instant.

Choongbum Lee - MIT mathematician, teaching the calculus Wall Street prices options with.

"it's nowhere differentiable... the standard tools of calculus can't be used here."

a stock's path is Brownian motion - the limit of infinite coin flips. it never smooths into a line, so ordinary calculus breaks on it.

to price anything at all, the Street had to invent a new one - Itô calculus - on one rule: dB² = dt. randomness squared is time. a French student, Bachelier, used it for option prices in 1900 - five years before Einstein used it for atoms.

your edge works the same. the trend you think you are trading is a slope that was never there, and the desk charges you for the noise you mistook for it.

MIT filmed the whole course and left it free. an hour at a chalkboard, and almost nobody has used a line of it.

the edge was never the trend. it is knowing the price has no slope, and charging for the randomness instead. watch it, and don't forget this.

[David Equalizer @equalizer_dev]

In 1983, Steve Jobs stood in a tent and described WiFi, the App Store, and the web, years before any of them existed. Apple stock was 10 cents that morning. It's above $200 now.

[Lumen @lumenxbt]

https://t.co/3hWKMIBJcw

[Athenario @athenari0]

the most important bank in a network can have the fewest direct deals, a tool built for ranking web pages explains why.

joseph blitzstein, harvard, stat 110.

a markov chain on a network takes one random step to a neighbor, only the current position matters next.

then the impossible part: run that walk long enough and it settles into one fixed distribution no matter the start, one number per node.

then the collapse: google's pagerank is that distribution, importance set by the importance of whatever links to it, one calculation solves the circle.

then the transfer: the most important bank in a network isn't the one with the most deals, it's the one closest to the other important ones.

watch the moment he sets pagerank up as a markov chain and finds its stationary distribution.

importance in a network was never about how many ties he had, it was which mattered.

[David Equalizer @equalizer_dev]

the money you already spent has zero vote in what you do next.

jonathan gruber, mit, 14.01, principles of microeconomics.

sunk costs are costs no future decision can recover, the exact classroom definition.

then the impossible part: the same lecture states it as a rule, a sunk cost should not affect any future decision, full stop.

then the collapse: a firm that already spent $2,000,000 on equipment with zero resale value still loses $50,000 more by finishing a run that costs $300,000 and returns only $250,000, the $2,000,000 has no vote.

then the transfer: the same math runs on a losing trade, a bad renovation, a subscription he's not using, only the numbers still ahead belong in the decision.

watch the moment he states that a sunk cost should not affect any future decision.

money already spent was never part of the decision, it only ever felt like it was.

[Lumen @lumenxbt]

https://t.co/3hWKMIBJcw

[FINILLÍN @finillin_dev]

A man who escaped China with no money and no English went on to compound about 30 percent a year for two decades. In 2006 he sat down in a Columbia classroom and taught the entire method to a room of students.

His name is Li Lu. He fled after Tiananmen in 1989 and reached America with nothing, then wandered into a lecture that turned out to be Warren Buffett speaking to a value investing class. Years later Charlie Munger handed him about $88 million of his own family money, the only outside investor Munger ever trusted that way.

The lecture is not a formula or a screener. It is about why the market is built against the few people who treat a stock as a piece of a business. He walks Timberland live off a stock manual, bought near book value at about 5 times earnings, a stock that rose about 7 times in two years. Then he does the same with a forgotten Korean stock that was even cheaper.

The uncomfortable part is what he says about the crowd. By one estimate fewer than 5 percent of the money in the market belongs to value investors. The other 95 percent is built to trade, and it funds the whole game. Columbia charges tens of thousands a year to sit in that room. The man at the front gave the method away for nothing.

His thesis was blunt. The stock market was not created for value investors. The edge, he said, is not more data. It is the temperament to stand alone when everyone disagrees.

He says that same class made him more than $100,000 within the year, just by acting on what he heard. The recording has sat online for years. Almost nobody sits through an hour of it.

The man Charlie Munger trusted with his own money taught the whole thing to a room of students for free. The people charging you to manage your savings have known it for decades. They just never sent you the tape.

[Athenario @athenari0]

Wall Street pays quants $600K to find an edge. an MIT mathematician put the theorem on the board that says most strategies never had one.

Choongbum Lee - MIT mathematician, teaching the probability theory behind stock prices and random walks.

the tool is a martingale: a process where, given everything you know up to now, your expected next value is exactly where you stand. a fair game, a stock with no edge in it.

then the optional stopping theorem: if a game is a martingale, no stopping rule changes your expected result. quit at a peak, quit at a target, quit on a hunch - expectation stays flat.

"even if you try to invent something really, really genius, you should not be able to win. your expected value is just fixed."

the edge was never the exit rule. it is finding a game that was never a martingale in the first place. watch it, and don't forget this.

[lizard @0xlizzzard]

Goldman Sachs uses this exact formula to decide if a company is worth $14,000,000.

Most of their analysts learned it from one free MIT lecture.

A Goldman recruiter once told a candidate: "If you can't derive an annuity price in under two minutes, we don't continue the interview." Starting offer for those who could: $250,000.

The formula fits on one line. MIT teaches it in 80 minutes. For free.

This is MIT 6.042J. Mathematics for Computer Science. The lecture Wall Street forgot to take down.

The professor opens with a simple question: $50,000 a year for 20 years, or $1,000,000 today?

Most people pick the million. Most people are right.

Then he shows you exactly why - with math you can verify yourself in 30 seconds.

Then the formula.

Every annuity - student loans, home mortgages, lottery payouts - is secretly just a geometric series. One formula prices all of them. He derives it live on the board using nothing but algebra.

Then Wall Street.

He explains how slight differences in interest rate assumptions - the p in the formula - let banks make money off the same instrument. Two banks, same contract, different p. One wins. He explains how that confusion caused the 2008 subprime collapse. The entire global recession. Traced back to one variable.

Then the company valuation.

A company adding $50,000 more in profit every year forever - what do you pay for it today? He plugs into the formula. Answer: $14,700,000. That is how acquisitions get priced on Wall Street.

Watch the moment he describes how people made hundreds of billions during the financial crisis while everyone else lost - "money went from one place to another." He says it casually. The room goes quiet.

A quant analyst at Bridgewater told me this was the first lecture that made financial modeling feel like arithmetic. Starting salary: $350,000. Bonus year: $900,000.

MIT 6.042J Lecture 12 | Mathematics for Computer Science | Fall 2010

[David Equalizer @equalizer_dev]

It's Bill Benter. He figured horse racing was just another counting problem. Same math, more moving parts.

He and a partner showed up with $180k and a computer. Benter spent years teaching that computer to guess one thing, the real chance each horse had to win. If his number was better than the odds the bookies gave, he bet. If not, he skipped it.

That's the whole trick. Expected value.

EV = p · b - (1 - p)

Only bet when your win chance p, at odds b, is worth more than your chance of losing.

This recording was never meant to be some hidden gem. Nobody expected Professor Tsitsiklis to hand the whole foundation away in 45 minutes, but that's exactly what happens on the board. Students in that room pay over $80,000 a year to sit through it. It's free right here. It's free right here.

Every quant, every professional bettor, every hedge fund analyst started with this exact hour. Benter just watched it and actually did the homework.

Almost nobody knows this lecture even exists. Watch it before it gets taken down.

[Lumen @lumenxbt]

https://t.co/3hWKMIBJcw

[David Equalizer @equalizer_dev]

a school can admit men at a higher rate than women while every department favors neither.

joseph blitzstein teaches probability at harvard, stat 110, free on youtube.

berkeley's 1973 admissions: men in at 44% of 8,442 applicants, women in at 35% of 4,321, a 9 point gap that reads as bias.

then the impossible part: broken into departments, almost none show a real gap, the few that do mostly favor women, not men.

then the collapse: women leaned toward departments that reject almost everyone, men toward ones that admit almost everyone, the choice built the gap, not the committee.

then the transfer: any aggregate admission, approval or hiring rate he is shown needs the breakdown before he trusts which way it points.

watch the moment he splits the admissions number into its departments and the gap disappears.

a single number can hide the group sizes doing all the work underneath it.

[Tigerflow @tigerfl0w]

https://t.co/Ye9wCJ9Jiv

[David Equalizer @equalizer_dev]

the wage it takes to stop cheating can be double the going rate, or it can be zero, same job, same temptation.

ben polak teaches this at yale, econ 159, free on youtube.

polak's outsourcing example: with no future in the deal, stopping cheating on a $10 an hour job costs $20 an hour, a 100% premium.

then the impossible part: give that job a 50% chance of continuing and the premium needed falls from 100% to 50%, $15 instead of $20.

then the collapse: make tomorrow certain and the premium hits zero, $10, the going wage, trust reduces to one number, how likely tomorrow is.

then the transfer: any deal you run with no contract is only as cheap to trust as how likely it continues, and that has an exact price.

watch the moment he prices the same job three ways and only the odds of tomorrow move the number.

trust was never free, it was always priced by how likely tomorrow was.

[Lumen @lumenxbt]

https://t.co/3hWKMIBJcw

[David Equalizer @equalizer_dev]

Hiring Tony Robbins today costs 1 million dollars for just one day.

This is a 21-minute tape recorded in his own home more than 30 years ago. There, he explains exactly how to get anyone to say yes. The same material for which they now charge a fortune... completely free.

It's a rare, unfiltered recording from the time when he still didn't charge millionaires just for being in the same room.

When someone says no, they give two excuses: “I don’t have time” or “I don’t have money” Neither is true.

The real reason is that they still don’t believe it’s worth it. It’s not a money problem. It’s a state problem.

Tony teaches something he calls “attack and confess” Instead of arguing the objection, you confess your own:

“I had the chance to go six months ago and I didn’t until two months ago. I can’t even imagine the time I wasted”

The room goes silent. No one argues.

Then he gets the person on the “yes train” Each little yes adds to the next. Until saying no at the end feels harder than saying yes.

When it’s time to sign, the person has already said yes five times without realizing it.

Just 21 minutes. There you learn the two only moves that people pay 1 million a day for: how to read anyone’s state… and how to shift it.

Most people spend years guessing in sales. He wrote it on a flipchart in his living room in less than half an hour.

A seat in that room cost $125 dollars. Today it costs $1 million dollars a day to sit in front of him.

[Tigerflow @tigerfl0w]

https://t.co/Ye9wCJ9Jiv

[David Equalizer @equalizer_dev]

A dead MIT professor accidentally destroyed the $20 billion executive coaching industry with one hour of lecture, and ten million people have already watched him do it.

He filmed it once in January 2018 and died eighteen months later.

Executive coaches charge fifteen thousand dollars a session to teach a third of what he covered in that one hour for free.

His name was Patrick Winston. He ran the MIT Artificial Intelligence Laboratory from 1972 to 1997 and wrote the AI textbook every computer science major in the world read for thirty years.

Every January for four decades, he gave a lecture called "How to Speak."

His entire framework fits on a napkin.

Do not read. Be in the image. Keep images simple. Eliminate clutter. Start with an empathetic connection. End with a punch line the audience can repeat over dinner. Never open with a joke. Never end with "thank you."

That last rule alone has probably cost the executive coaching industry a hundred million dollars.

"Your success in life will be determined largely by your ability to speak, your ability to write, and the quality of your ideas. In that order."

That is the actual opening line of the lecture. Winston believed it strongly enough to spend fifty years teaching computer scientists how to talk.

Founders spend $80,000 on an MBA and then hire a communications coach to teach them the same material Winston filmed once for free. Engineers write brilliant code and lose promotions to teammates who watched this lecture on the train.

The lecture is free on MIT OpenCourseWare. The textbook is free on his page.

Winston died in 2019. Almost none of the ten million viewers have actually implemented the four rules on the napkin.

The napkin is free. The willingness to actually use it in your next meeting is the entire edge.

[Lumen @lumenxbt]

https://t.co/3hWKMIBJcw

[David Equalizer @equalizer_dev]

you can play the same two cards perfectly twice and be wrong both times, your stack decided the answer.

kevin desmond teaches this at mit sloan, course 15.s50, free on mit ocw.

the m-ratio is your stack divided by one round of blinds and antes, a chip count turned into a countdown of rounds you can survive.

then the impossible part: above an m of 20 you play any style, below 10 hands you'd normally fold become forced all-ins, the correct play flips, cards unchanged.

then the collapse: below an m of 1, harrington calls it dead, the blinds already decided for you, the move is shove.

then the transfer: whatever stack he's sitting on puts him in one of these zones, and the zone decides which hands are worth playing before his cards.

watch the moment he shows the same cards, a fold in one zone, a shove in another.

after this, a stack size is a countdown, not a number on the screen.

[Lupen @0xLupenn]

https://t.co/87P80B6arY

[David Equalizer @equalizer_dev]

The week Lehman Brothers collapsed, an MIT professor walked into class and put its 2007 annual report on the screen.

$19 billion in revenue. $4 billion in profit. $145 billion in capital. 28,500 employees.

Nine months later, it was gone.

His explanation didn't start with Wall Street. It started with his own house.

In 1988 he bought his first home with just 5% down, which is 20-to-1 leverage. "I beat Lehman Brothers." (Lehman ran at about 16 to 1.)

Here's the math that sinks them both:
- Put 20% down and prices fall 10%: half your money is gone
- Put 5% down and prices fall 10%: all of it is gone, and you still owe more
Leverage isn't dangerous on its own. It becomes dangerous when prices stop moving smoothly. For years housing only went up, so nobody felt the risk. Then volatility arrived.
The lesson: before you borrow, don't ask how much prices usually move. Ask how much they could.

[Lupen @0xLupenn]

https://t.co/87P80B6arY

[David Equalizer @equalizer_dev]

A $100 bet on red in American roulette has an expected value of -$5.26. Bet it every night for a year and your expected loss is about $1,920. Yet the casino has almost zero chance of losing. Here's the math that makes gambling a business and not a game

An American wheel has 38 pockets: 18 red, 18 black, 2 green.

Bet $100 on red:
- Win $100 with probability 18/38 (47.4%)
- Lose $100 with probability 20/38 (52.6%)
Expected value = (18/38 x $100) - (20/38 x $100) = -$5.26 per spin.
Those two green pockets are the entire business model.

Now look at it from both sides of the table.

You, one spin a night for a year (365 spins):
Expected loss: $1,920
Typical swing: about +-$1,900
So you still have about a 1 in 6 chance of finishing the year ahead. Your luck is still bigger than the edge against you.

The casino, 1 million spins a year:
Expected profit: $5.26 million
Typical swing: about +-$100,000
The edge is 50 times bigger than the noise, so the casino's chance of a losing year is effectively zero.

Same bet, same odds. The difference is volume.
That's the law of large numbers: randomness averages out, and the edge doesn't. The more times you repeat a bet, the more the result converges to its expected value.
The lesson isn't "never gamble." It's this:
Always ask which side of the edge you're on.
If the edge is against you, repetition guarantees you lose.
If the edge is for you, like owning a diversified slice of the economy for decades, repetition makes you the casino.

This MIT lecture covers the math behind it: random variables, distributions, and the Central Limit Theorem 🎥

[Lupen @0xLupenn]

https://t.co/87P80B6arY

[David Equalizer @equalizer_dev]

A stock that goes up 50% then down 50% leaves you with 75 dollars out of every 100. The average return is 0%. You lost 25%.

This isn't a trick. It's how compounding works, and it quietly eats returns in every portfolio.

Gains and losses don't cancel out, because each one is applied to a different starting amount. The 50% gain is on 100 dollars. The 50% loss is on 150 dollars.

That's why losses need bigger gains to recover:
- Lose 20%, you need +25% to get back
- Lose 33%, you need +50%
- Lose 50%, you need +100%

Now take two portfolios, both averaging 10% a year:

A gains 10% every year. After 10 years, 100 dollars becomes 259.

B alternates +30% and -10%. Same 10% average. After 10 years, 100 dollars becomes 219.

Same average, 40 dollars less. B's real compounded return is about 8.2% a year, not 10%.

There's a simple rule of thumb for the gap:

compounded return ≈ average return − (volatility² ÷ 2)

B swings 20% around its average. 20% squared is 4%, half of that is 2%. So 10% becomes roughly 8%. The math checks out.

The average return tells you what a typical year looks like. The compounded return tells you how much money you actually end up with. Most return charts show you the first one.

This is also why leveraged ETFs bleed in choppy markets. If an index goes +10% then -10%, it's down 1%. A 3x fund goes +30% then -30% and is down 9%.

The takeaway: two investments with the same average return are not the same investment. Lower the swings without lowering the average, and you end up with more money. That's the whole case for diversification.

[Lupen @0xLupenn]

https://t.co/87P80B6arY

[David Equalizer @equalizer_dev]

A 2 dollar lottery ticket with a 1 in 300 million chance of a 500 million dollar payout has an expected value of negative 33 cents. A 30 thousand dollar car insured against theft in a neighborhood where 1 in 200 cars is stolen a year is worth positive 150 dollars in expected value.

The math to compute either one takes 4 seconds. Almost no one runs it.

Andrew Lo has been teaching Session 1 of MIT 15.401 since 2003. The Fall 2008 recording sits free on MIT OpenCourseWare. Every decision his students will ever make, from a stock trade to a job offer to which route to drive home, reduces to the same 4-second calculation. Expected value equals probability times payoff.

Institutional desks run it before every trade. Retail investors run it before none. The gap between them has a name and it is not luck.

The math is free. The willingness to run it before you sign is the entire fortune.

[Lupen @0xLupenn]

https://t.co/87P80B6arY

[David Equalizer @equalizer_dev]

Claude Shannon ran his personal stock account at 28% a year for 30 years. He's also the man who mathematically proved the ceiling above every filter the thread above is selling.

Both facts have been sitting in the same library since 1948.

Shannon didn't beat the market with a smarter moving average. He didn't beat it with a swarm, a neural net, or the sharpest filter of his generation, and he could have built any of them in an afternoon. He beat it because he understood the one thing the industry has been quietly ignoring for 78 years: no filter, no matter how clever, can pull more signal from a channel than the channel actually holds.

The market channel is almost pure noise by design. Every real edge gets arbitraged toward zero the moment enough people find it. A better filter doesn't create signal that wasn't there - it rounds noise into a shape that fools you into betting on it.

Shannon compounded like that because he was ruthless about which channels still had signal left, and disciplined about how much to bet when they did. The filter came last. It always comes last.

Build the filter. It's a fine tool. Just remember there's a ceiling above it no engineering can lift, and the part that finds signal before it decays - that part, you still have to bring yourself.

Shannon wrote it down in 1948. It's still free. The lesson has been sitting there for 78 years.

[Rossst.03 @Rossst_03]

https://t.co/OMkJ18IBwJ

[David Equalizer @equalizer_dev]

Harvard needs 8% return every year just to keep the lights on. 5% spending plus 3% inflation. Miss that number and buildings stop, professors leave, research dies. 40% of the operating budget comes from one portfolio.

Not tuition.Not grants. One fund. Jake Xia manages that fund's public markets. He also teaches the math behind it at MIT for free.

One of the top five most-watched courses on OpenCourseWare. Millions of views. Almost nobody changed how they invest. Every year he hands students a blank page. Build a portfolio.

No rules.Someone writes 100% Apple. Someone writes rare coins. Confident picks. Same blind spot, every time. Not one student asks the only question that matters: how much goes in each position.

They all pick what to buy. Nobody sizes it. Sizing is the entire job. The answer won the Nobel Prize. It's called the efficient frontier. Xia draws it on the board in under a minute.

Five equations sit underneath it. Compound growth. Present value. The geometric mean. The Rule of 72. Real return. All older than any bank on earth. All fit on a napkin. None behind a paywall.

A "guaranteed 5% bond" during 4% inflation is a 1% return. The industry doesn't hide this. It just hopes you never run the equation yourself. The lecture is free. The napkin is free.

The only thing that costs anything is not knowing The answer is in this video.

[Tigerflow @tigerfl0w]

https://t.co/Ye9wCJ9Jiv

[David Equalizer @equalizer_dev]

This man teaches at a community college in California.

His salary: around $800,000 a year.

The engineers who passed calculus because of him: $1,800,000 to start.

He has more calculus students than Harvard, MIT, and Stanford combined.

This is Professor Leonard's Calculus 2, Lecture 6.2. Free on YouTube.

Professor Leonard has taught calculus on YouTube for over a decade. His channel has millions of subscribers across 150 countries. Every major university has students who watch him the night before their exam.

Then the concept.

An inverse function is a machine that undoes another machine. If a function takes 2 and gives you 8, the inverse takes 8 and gives you back 2. Finding an inverse means switching every x and y in the equation and solving for y again. The graph flips across the line y = x like a mirror.

Then the problem.

Sometimes it is easy to find the inverse. Sometimes it is impossible to write it explicitly. A function like 3π sin x + sin x cannot be solved for x with algebra. You have to think. What angle makes the whole thing equal to 1? You work backwards through the unit circle until the answer appears.

Then the shortcut.

If you want the derivative of an inverse at a point, you do not need the inverse itself. You only need the derivative of the original function. The formula: the derivative of the inverse at a point equals 1 divided by the derivative of the original function evaluated at the switched point. The inverse flips the coordinates, so you flip where you plug in.

Watch the moment he shows why G prime of 8 equals 1/12 without ever writing the inverse function.

Every engineering student memorizes the derivative rules. Professor Leonard's lecture is the one that shows why the inverse derivative formula is just those same rules run backwards.

A software engineer at a semiconductor company in Austin said Professor Leonard's channel is the reason she passed Calculus 2 on her second attempt. She graduated, joined the company, and now makes $165,000 a year.

Bookmark this and watch later - after this lecture every inverse problem on your exam will feel like a question you already answered.

[Lupen @0xLupenn]

https://t.co/87P80B6arY