Results: exponent ~1/2 across stocks and traders

1:44:33I'm going to treat that. Yeah. >> Right. As it's pretty good. >> That's really good. >> And so you get these effective trader [laughter] IDs. You get you get the trader desk. >> Yes. >> Right. In these like firms. Yes. >> Right. And this allows them to to analyze the behavior of all the active traders across all liquid stocks, all 2,000 stocks for nearly a decade. It's like a god view >> of the market. >> I love that. >> Of the Tokyo Stock Exchange, right? Yeah. Yeah. >> Very cool. >> That's and that's clever. And like it again it it doesn't take a large leap to get Yeah. that connection. >> Yeah. Yeah. Yeah. But they did the due diligence, right? And they actually did it. >> And so when they when they actually go

1:45:13through and do the math, >> they find that the mean exponent >> is about 0.489, very close to 0.5. >> The standard deviation is 0.071. And there on the left you can see all of the different stocks they use. Toyota, um, NT, I don't know that that stock, but it's all of them are >> the same line. >> Yes. >> And they're all centered at 0.5. And if you look across all 20,000 stocks, the spread is quite big. I'll I'll admit it's like from 0.4 all the way to 0.6. But the mean of that spread is very sharply at 0.5. >> Okay. >> Mhm. >> So from this data set, they can actually

1:45:53falsify some of the earlier models. There's this one model called the GG PS model which is the I don't know go bikes go Krishnan Pluro Stanley model from 2003. This is the model of the inventory risk. This is the one that's saying that like okay market makers they provide liquidity but they face the risk right because like if I if I'm a market maker mean meaning like I have like I'm the one if if you're trying to sell I'll buy from you and if you're trying to buy I'm going to >> I'll sell to you and I'm going to make money on the spread. But if the price like >> goes off, then I'm just left with >> the bag. >> The bag, right? And I that I didn't want or maybe I did want. Okay. So, they

1:46:34charge a premium and that price impact is going to compensate for that risk. >> Okay. So, what if what if this stuff and the scaling argument is the size of the trades follows a power law, but to limit their risk, >> they're going to adjust the price to balance the probability of large orders. >> Mhm. >> Okay. Mhm. >> And there there's another sort of numerical coefficient that comes in beta that you can figure out, which is sort of the the probability of these large orders. And they say that the alpha, which is the the exponent of my price impact, the 1/2 that we're talking about here, the square root, is related to this beta. >> So these guys plotted those two, and there's no correlation.

1:47:16>> It's flat. >> It's flat. [laughter] >> Okay. So this 2003 model, this GGPS model, completely wrong. >> Nonsense. Yeah. Okay. Like most things in economics, but okay. [laughter] >> Um, >> you know, >> there's something wrong with the mic. >> So, zero correlation there. There was also another um fair pricing efficiency model. >> Zero. That's crazy. >> Yeah. Yeah. Zero correlation, right? Yeah. So, there's this FGLW model, which is the farmer Garig Lelo Wan Broic model that also was falsified. I'm not going to get into that, but it's about market efficiency and fair pricing.