Story 4 begins — econophysics and market impact

1:34:18physics. >> That's right. >> As you can see, we are dawned in our finance bro garb. >> Yeah. >> Um >> I got my Jackson Hole. [laughter] You know, bunch of finance bros there. Let me tell you, last time I went, >> and I have no idea where this is going to go. I was when I saw this I was um I was I was pleasantly surprised and it caught my eye because this was a paper in PRL physical review letters. This is the story journal that has published, you know, superc conductivity, the black hole papers, Einstein, Wheeler, um, cosmic microwave background, and then a universal law about stock prices

1:35:02and the impact that orders have on the price of an asset. And I was like, what is this doing in a physics journal? >> Mhm. >> Okay. >> Mhm. >> So, here's the central question. Okay. Um you know when when you trade stocks stons >> stons >> yeah when you trade stocks right um the the trade itself affects the price of the asset. >> Mhm. [clears throat] >> Okay. The question is how does that price change? Okay, there's something called the square root law which says that if if I if I put in an order for a certain amount, the amount that the

1:35:43price is going to change as a response to that order is proportional to the square root of the size of my order. >> Okay. And it's sort of just been observed, but this was a paper that was trying to figure out is it a square root? Meaning, is the exponent a 1/2 or is it 1/4 or is it like 04? Is it 6? What is it? Okay. And the the the field of econo physics is actually quite old. Okay. All the way back in 1900, there was this guy Luis Bashellier. He wrote he wrote his senior thesis his PhD thesis la speculation. [laughter] That's my French. >> I was gonna say

1:36:25>> but but it's it's a it's a physics thesis about speculation in the markets. >> He actually predated Brownian motion. Like this is 1900. So this is before Einstein's 1905 paper on Brownian motion. Um derived the diffusion equation. It's a precursor to Brownian motion. all of this stuff just to get rich off speculation, right? Um, >> we love it. >> And and that was sort of the birth of like trying to use statistical mechanics and insight from physics to try and talk about agents in a stock market in a in a market with, >> you know, people that are trying to buy and sell stuff. >> Yes. >> Okay. >> Um, in the 1990s, there was a guy,

1:37:06Eugene Stanley. He he actually figured out something called the inverse cubic law of price returns which means if you if you plot the returns that you get and the probability distribution of the returns based on like all of the assets everywhere, right? It's it goes down like returns to the -3 power. >> Okay. >> Okay. Meaning like if you if you want 10 times the returns, the probability of getting 10 times the returns is 1 divided by 10 the 3 compared to just getting the same return. >> Mhm. >> Does that make sense? >> Yes, it does. It does. >> Okay. So, and it's it's the same for like whether you wait one day, whether

1:37:48you wait 2 days, whether you wait 3 days. It's kind of weird. >> That is a little weird >> that like the probability distribution remains the same. >> Yeah, I don't like that. >> Okay. Um, another one was the probability density of transaction sizes. If you look at all of the transactions in the New York Stock Exchange, in the Paris exchange, in the London Stock Exchange, and you plot the trade size on the x-axis, and like how many trades happen at a certain size, at another certain size, then the exponent is -2.5.