Verax

The quiet math behind every financial decision.

Math · Money · Old knowledge, resurfaced.

[Verax @veraxlab]

https://t.co/24vrVljftL

[Verax @veraxlab]

@Beaver_0x never thought about McDonald’s sizes this way lol

[Verax @veraxlab]

@commonsmade hey @commonsmade I vouch for @vexelxbt

[Verax @veraxlab]

@0_xSan wild that he figured it out in 1991 and people still ignored it for years

[Verax @veraxlab]

Check your portfolio every morning and you'll see red on 49 days out of every 100. Check it once a decade and you'll see red 13 times. Same portfolio.

The man who proved why was told his thesis wasn't good enough to get him a job.

In 1900 Louis Bachelier handed the Sorbonne a thesis called Théorie de la spéculation, the first serious attempt anyone had made to describe a market with mathematics. Poincaré wrote a favourable report on it. It was still graded honorable instead of très honorable, and that wasn't enough for a teaching post in France. He spent his career in provincial universities and died forgotten in 1946.

Five years later Einstein derived the same mathematics for particles jiggling in a liquid, and that's the version everyone remembers.

What Bachelier proved fits in one line. Price movement doesn't grow with time. It grows with the square root of time.

Double your horizon and risk rises by 41 percent, not by 100. Your expected return grows in a straight line. So the return slowly outruns the noise, and the only question is how often you interrupt it to look.

Ordinary portfolio, 7 percent expected, 20 percent volatility. How often you're in the green:

one day, 51 out of 100
one year, 64
ten years, 87
twenty years, 94

Nobody's investing changed between those lines. Only the length of the window they looked through.

This isn't a discipline problem. The signal and the noise grow at different speeds, and nobody says that out loud, so checking often feels like diligence when it's really just a high sampling rate.

Textbooks call it a random walk now. MIT filmed a full lecture on them and put it up for nothing. In fourteen years it has 20,000 views.

Bachelier put it in one sentence: "The mathematical expectation of a speculator is nil."

Underneath all of this sits a harder question, and it's about how many attempts you've actually had rather than how often you looked at them. Most people have never worked out their own number.

The mathematics has been free since 1900. What costs you is the frequency.

[Verax @veraxlab]

Check your portfolio every morning and you'll see red on 49 days out of every 100. Check it once a decade and you'll see red 13 times. Same portfolio.

The man who proved why was told his thesis wasn't good enough to get him a job.

In 1900 Louis Bachelier handed the Sorbonne a thesis called Théorie de la spéculation, the first serious attempt anyone had made to describe a market with mathematics. Poincaré wrote a favourable report on it. It was still graded honorable instead of très honorable, and that wasn't enough for a teaching post in France. He spent his career in provincial universities and died forgotten in 1946.

Five years later Einstein derived the same mathematics for particles jiggling in a liquid, and that's the version everyone remembers.

What Bachelier proved fits in one line. Price movement doesn't grow with time. It grows with the square root of time.

Double your horizon and risk rises by 41 percent, not by 100. Your expected return grows in a straight line. So the return slowly outruns the noise, and the only question is how often you interrupt it to look.

Ordinary portfolio, 7 percent expected, 20 percent volatility. How often you're in the green:

one day, 51 out of 100
one year, 64
ten years, 87
twenty years, 94

Nobody's investing changed between those lines. Only the length of the window they looked through.

This isn't a discipline problem. The signal and the noise grow at different speeds, and nobody says that out loud, so checking often feels like diligence when it's really just a high sampling rate.

Textbooks call it a random walk now. MIT filmed a full lecture on them and put it up for nothing. In fourteen years it has 20,000 views.

Bachelier put it in one sentence: "The mathematical expectation of a speculator is nil."

Underneath all of this sits a harder question, and it's about how many attempts you've actually had rather than how often you looked at them. Most people have never worked out their own number.

The mathematics has been free since 1900. What costs you is the frequency.

[Vexel @vexelxbt]

https://t.co/62wJFf5wYq

[Verax @veraxlab]

@Dipper_pol big bets make sense when you have actually done the work

[Verax @veraxlab]

@Mavrickoss simply idea, but a really good way to think about markets

[Verax @veraxlab]

@Allx032 This book is actually worth a read, great mix of math and real stories

[Verax @veraxlab]

@andreysuperior Gruber always has great lectures
Really good post, man

[Verax @veraxlab]

@Beaver_0x most people never get past the labor part

[Verax @veraxlab]

Up 30 percent, then down 30 percent. Your average return for those two years is exactly zero. Your money is not.

You're holding 91 cents on the dollar, and the man who proved why never held a university job.

Johan Jensen ran the technical department at the Copenhagen telephone company for thirty-four years and did his mathematics after hours. In 1906 he published the proof in French, in a Swedish journal. On a $100,000 account over thirty years, the same gap comes to $738,674.

Every projection you've ever been handed uses the number that doesn't happen.

Here's the one that does.

Take a stock fund averaging 10 percent a year and bouncing around by 20. Nothing dramatic. Half the funds you've ever been pitched look like that.

Ten percent on $100,000 for thirty years is $1,744,940. That's the figure that goes in the deck.

What your money actually grows at is nearer 8, and 8 percent leaves you $1,006,266.

The missing $738,674 isn't a fee. It isn't tax and it isn't a crash. Nobody took it, because it was never there. The average was describing a portfolio that doesn't exist.

You can do the correction on your phone. Take the volatility, square it, halve it, subtract. Twenty percent squared is 0.04, half of that is 2 percent a year, gone before anyone has touched your account.

Fifteen percent volatility costs you about 1.1 a year. Thirty percent costs about 4.5. Whatever average return you were promised, run it through that, and what's left is the part you can actually spend.

You're not bad at math. You were shown the one figure that doesn't survive contact with compounding, and it was the flattering one, which is why it was the one you were shown.

The rule has a name. Jensen's inequality: the average of the logs can never be bigger than the log of the average. Your compounding is the log. The average is the brochure.

MIT filmed Tsitsiklis proving it in a few minutes and gave the clip away, along with the rest of the course.

And that's only the first bill volatility sends you. The second one isn't about money at all. The same number, squared again, decides how many years have to pass before your own track record means anything. For a fund manager the answer is around fifty. Careers are shorter than that.

The math is free. The lecture is free. The only thing that costs anything is not knowing which of the two bills you're paying.

[Verax @veraxlab]

Up 30 percent, then down 30 percent. Your average return for those two years is exactly zero. Your money is not.

You're holding 91 cents on the dollar, and the man who proved why never held a university job.

Johan Jensen ran the technical department at the Copenhagen telephone company for thirty-four years and did his mathematics after hours. In 1906 he published the proof in French, in a Swedish journal. On a $100,000 account over thirty years, the same gap comes to $738,674.

Every projection you've ever been handed uses the number that doesn't happen.

Here's the one that does.

Take a stock fund averaging 10 percent a year and bouncing around by 20. Nothing dramatic. Half the funds you've ever been pitched look like that.

Ten percent on $100,000 for thirty years is $1,744,940. That's the figure that goes in the deck.

What your money actually grows at is nearer 8, and 8 percent leaves you $1,006,266.

The missing $738,674 isn't a fee. It isn't tax and it isn't a crash. Nobody took it, because it was never there. The average was describing a portfolio that doesn't exist.

You can do the correction on your phone. Take the volatility, square it, halve it, subtract. Twenty percent squared is 0.04, half of that is 2 percent a year, gone before anyone has touched your account.

Fifteen percent volatility costs you about 1.1 a year. Thirty percent costs about 4.5. Whatever average return you were promised, run it through that, and what's left is the part you can actually spend.

You're not bad at math. You were shown the one figure that doesn't survive contact with compounding, and it was the flattering one, which is why it was the one you were shown.

The rule has a name. Jensen's inequality: the average of the logs can never be bigger than the log of the average. Your compounding is the log. The average is the brochure.

MIT filmed Tsitsiklis proving it in a few minutes and gave the clip away, along with the rest of the course.

And that's only the first bill volatility sends you. The second one isn't about money at all. The same number, squared again, decides how many years have to pass before your own track record means anything. For a fund manager the answer is around fifty. Careers are shorter than that.

The math is free. The lecture is free. The only thing that costs anything is not knowing which of the two bills you're paying.

[Vexel @vexelxbt]

https://t.co/62wJFf5wYq

[Verax @veraxlab]

@vexelxbt Crazy that cutting variance in half can be mathematically as valuable as doubling your edge. Most people would probably spend years chasing the second and ignore the first.

[Verax @veraxlab]

In 2009, Eugene Fama and Kenneth French took 3,156 US equity funds and recreated their performance 10,000 times.

In every simulated world, they removed one thing: skill.

The winners still appeared.

So how much of a great track record is simply the result of having thousands of people trying?

Their dataset covered 273 months, from 1984 to 2006. For every fund, they estimated its return above a risk-adjusted benchmark, removed that alpha, then repeatedly reshuffled the historical months.

This created 10,000 versions of the fund industry in which every manager’s true alpha was zero. Any winner produced by those simulations was winning through noise alone.

Then they compared those imaginary winners with the real ones.

Around 30% of the actual funds had positive net alpha. That sounds like evidence of skill until you look at the control group: most of those winners were no better than the winners created in a world where nobody had skill.

Funds near the 90th percentile had beaten their benchmarks by more than 3.3% per year across their histories. They would be marketed as exceptional managers.

But roughly 90% of the zero-skill simulations produced a stronger 90th percentile.

Put 3,156 people in a room and let each flip a coin once a month for 23 years. Some charts will look smooth. Some will contain extraordinary winning streaks. A few will look like undeniable genius.

None of them had an edge.

That is the trap hidden inside every leaderboard: the more people who compete, the more convincing the luckiest winner becomes.

A 20% return tells you what happened. It does not tell you whether the person who produced it can do it again.

Never study the winner without studying how many chances the system had to create one.

Once you understand that, every performance chart looks different.

[Verax @veraxlab]

https://t.co/24vrVljftL

[Verax @veraxlab]

@Vektrix Wild story. One bad bet took down a 233 year old bank

[Verax @veraxlab]

@Vektrix Exactly. Same average return, completely different outcome depending on when the bad years hit.

[Verax @veraxlab]

William Sharpe walked onto a stage in Seattle in 2014 with a number most investors had never seen: 20 percent.

The Nobel Prize winner had calculated that two people could save the same amount, invest in similar assets and face the same market, yet one could sustain a standard of living in retirement more than 20 percent higher.

Where did the money disappear?

Sharpe won the Nobel Prize for explaining the relationship between risk and return. His name is now attached to the ratio used across finance to measure how much return an investor earns for the risk taken.

But a reported return is only the first line of the calculation.

A portfolio earns 7 percent. Inflation takes 3. Fees take 1. Taxes take another piece. Volatility lowers the compound return even when the average looks unchanged.

And if the worst years arrive at the wrong time, two investors with identical average returns can finish with completely different amounts.

A year after publishing his calculation, Sharpe sat down with Robert Litterman, the Goldman Sachs quant behind the Black-Litterman model, to discuss what he considered the hardest problem in finance: turning uncertain returns into reliable retirement income.

The man who gave finance its most famous measure of risk had reached a simpler conclusion.

The return on the screen matters less than how much of it remains yours.

[Superior @andreysuperior]

https://t.co/rUN1cPDY65

[Verax @veraxlab]

William Sharpe walked onto a stage in Seattle in 2014 with a number most investors had never seen: 20 percent.

The Nobel Prize winner had calculated that two people could save the same amount, invest in similar assets and face the same market, yet one could sustain a standard of living in retirement more than 20 percent higher.

Where did the money disappear?

Sharpe won the Nobel Prize for explaining the relationship between risk and return. His name is now attached to the ratio used across finance to measure how much return an investor earns for the risk taken.

But a reported return is only the first line of the calculation.

A portfolio earns 7 percent. Inflation takes 3. Fees take 1. Taxes take another piece. Volatility lowers the compound return even when the average looks unchanged.

And if the worst years arrive at the wrong time, two investors with identical average returns can finish with completely different amounts.

A year after publishing his calculation, Sharpe sat down with Robert Litterman, the Goldman Sachs quant behind the Black-Litterman model, to discuss what he considered the hardest problem in finance: turning uncertain returns into reliable retirement income.

The man who gave finance its most famous measure of risk had reached a simpler conclusion.

The return on the screen matters less than how much of it remains yours.

[Verax @veraxlab]

@vexelxbt Always interesting to read the stories you find, boss