Market Making from First Principles: Order Books, Spreads, and Risk

The wonderful part about marketmaking is that people are trading for their own economic incentive, their own profit. Because even though they're completely self-s serving, they serve this purpose of the exchange in that they warehouse risk. If a buyer and a seller arrive to the exchange, the same point in space, but at different points in time. By allowing these people to trade against other people, what happens is we allow the market to determine a fair price. This is really important because what this illustrates is how important free frictionless markets are to a capitalist economy. Hi everyone, my name is Anan. Um I used to be a high frequency trader at Flow Traders and then Tower Research Capital and now I'm founder and CEO of QEX, the first 24/7 perpetual futures exchange just for equities, commodities, FX. And today I'm going to be teaching you how marketmaking works. Okay. So um when we talk about market making we take a step back and really think about the context that we're working in right so people often confuse the terms high frequency trading market making quantitative trading algorithmic trading what does a quant do what does a trader do what a developer do so we'll just spend a few minutes going into this world and I'm going to give the overall

world the name systematic trading so systematic trading covers two axes. There is the capital side and the speed side.

Now, on the speed side, you basically have a range of strategies that go from what's called high frequency trading to mid-frequency trading and slower. And on the capital side there are two types of firms. So there are the proprietary firms which called prop for short and then there are the firms that take other people's money. So the definition of a hedge fund is just some kind of trading outfit that takes other people's money. It's called hedge fund. So within this space you can have non-sistatic trading as well. That's called discretionary. We're not going to cover that today. We're going to talk about systematic trading which is also sometimes called quantitative trading. So the idea is we make trading strategies based on rules and statistical patterns that we've observed in the past and we use them to make money. And if we focus on this side, the difference between a proprietary trading firm and a hedge fund is that proprietary trading firms tend to um have only their own partners' money. So they tend to be less well capitalized.

So they need to achieve a good return on capital, a lot of margin in order to make money. and they tend to run strategies that you can't necessarily put a lot of money behind but you can make a lot of return from them. So returns on proprietary trading firms can be upwards of 50 even 100% a year. I think you'll struggle to find a hedge fund achieving those kinds of returns but the point with a hedge fund is they take in a lot of capital and therefore even if they achieve a modest return on that capital they still make a lot of money. The difference between the types of strategies they run is um also colored by the fact that hedge funds ultimately are dealing with clients money. They have to act within risk constraints that their clients put on them. Those are subject to negotiation between the fund and the client. There needs to be a sales process to get the capital in and there also needs to be a process with how to return the capital, how to release the capital, what happens if the fund loses money and so on. With proprietary trading firms, none of those regulatory considerations really apply because ultimately you're trading with your own money. It's kind of like um uh

trading a stock portfolio with your own money. Um the regulators are much less concerned with what happens with the money and what are the circumstances with which you take it and give it back. Then we go on to the speed side. So we have high frequency trading and we have mid-frequency trading and sometimes you know called low frequency trading. Um but in the systematic world we tend to work within these two. So the difference between high frequency and frequency trading is um high frequency trading typically you try and predict prices and you try and um trade in a way that you don't take risk for more than a few seconds um seconds to a minutes I would say. So in high frequency trading that tends to sit very well within the proprietary trading world and I'll give you a quick intuition as to why proprietary trading needs to attain a high return on capital and therefore it needs to basically be able to take capital and not wait too long for it to start making returns on itself. If you do high frequency trading, you are trading constantly in and out of positions and that means you don't end up in a very large position. Okay? So, if I am running a strategy that is

trading, let's say S&P futures and I buy and then my signal says I have to sell because I'm only trying to predict a few seconds ahead or I'm only trying to aim for that time horizon of a few seconds or maybe up to a minute, then I will never end up in a very big position because I'm constantly buying and selling and buying and selling and buying and selling. I won't end up in a position of hundreds of millions or billions of dollars and I don't need a lot of capital to outlay and basically furnish the risk on that position. So proprietary trading firms who don't have a lot of capital need to achieve a very high return on capital tend to do high frequency trading because they never end up in big positions. By contrast, hedge funds tend to end up more in mid-frequency trading because they're not interested in small gains or losses that you can realize on each trade from high frequency trading. In HFT, if I'm trying to predict a few seconds ahead, I'm only holding risk for a few seconds.

Ultimately, the market won't move that much and allow me to capitalize much spread after fees when I do those trades. Therefore, if I'm aiming to if I if I have the ability to basically put a lot of capital behind my trades and I have the ability to take large positions, then I have the privilege of being able to predict much longer in the horizon, potentially being able to make much more return, allowing whatever stock or future or option I'm trading to move a lot more and achieve an outside return because I can do that because I have more capital to put behind the trade. I can take a bigger position and a bigger size. So in that region where we're trying to predict more like hours, days, maybe even weeks um out into the future and hold positions for a longer term, um I need to take on bigger positions overall to to make it worth my while and therefore I need more capital and you know I'll probably achieve a lower um return on investment because I can put more money behind the strategy.

Um it'll end up for me better in the the the long run. I'll be able to make more dollars even if I don't make as much percentage return. Odds on Open is

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So the different types of model and the way that you would create these strategies and the rules you would create around these strategies and the way you would control risk around these strategies really vary um in this grid you know proprietary HFT hedge fund mid-frequency um it really depends on what the relationship is with the capital holders whether internal or external and depends what um size positions you're taking um you know in high frequency trading because you're not ending up in big positions if the strategy isn't doing well, you can always just turn off the strategy and um sell all your positions very quickly. That's very cheap and very easy to do. In mid-frequency, you could have positions running into the hundreds of millions or billions of dollars. If you want to liquidate those positions, like we saw Leopold Ashar liquidate his positions in his portfolio to Ken Griffin, that could be a very expensive trade. So, you have to be really careful that your model is working correctly because once it's started and if you figure out there's a bug, it might be too late to stop it. So, all of these quadrants kind of think differently about trading and risk. And today we're going to talk about a specific type of trading called market making.

And market making sits within this part of the quadrant. So it is high frequency trading and it's typically done with proprietary money because it's um very high sharp. That means it has very good risk adjusted returns. It has very high return on capital and typically you don't need a lot of cash. You don't need to raise external cash to do it. Um so let's talk about market making. So market making is one very particular kind of strategy that we can run um in the context of proprietary high frequency trading. So uh we'll do a quick recap of what a market is and then figure out why we need market makers and what's the purpose market makers are doing and I'll try and illuminate it in a way that it's kind of aimatic and it kind of um unveils the reason that market makers should exist and the economic uh service that they're delivering for the fees and the profit and loss that they're making. So within markets, markets um in the financial context um are also called commodity markets. Um and what that means is that in financial markets, all of the goods that we're trading are fungeible in some sense. Basically, if I buy one share of Tesla and Ethan sells me one share of

Tesla, then those shares of Tesla are the same as all the other shares of Tesla of that class that exist out there in the world. I don't have to be worried that Ethan's giving me a bad share of Tesla or I'm getting a particularly good share of Tesla or whatever. It's the same with um oil futures. The kind of underlying delivery of the oil is made so that it's completely standardized. You don't have to check the oil yourself. It's the same with grain futures. Um it's the same with options contracts. um they have very specific uh well-defined specifications that we can use to have trust that if I am buying one unit of this thing um and I'm selling one unit of those things, those two things are completely um fungeible, which is to say that they're completely identical for the purposes of trading.

So in funible markets, the way trading occurs is you need buyers to find sellers. You need buyers and sellers to meet each other. And this is kind of a difficult problem because buyers and sellers may not know where each other are. So one way you can solve this problem, not the only way, but one way is to have something called an exchange. An exchange simply acts to be a physical place in space where buyers and sellers can find each other. Right now exchanges in the olden days were pits of traders that would stand around and shout orders at each other. And it was literally that. It was a physical space in place. The New York Stock Exchange was famously on Wall Street um still is there. London Stock Exchange in the city of London here in London. And it would be a place where people would go and they would know that if they were a seller, they could find a buyer there. And if they were a buyer, they could find a seller there. And they could meet each other at the same point in space, which is really cool. And now exchanges tend to be a little bit more formalized. They tend to be electronic. People tend to submit their orders electronically. And the way

exchanges work is they use something called a central limit order book model which is called a clo. What a central limit order book is is I'm going to explain it using um a very common diagram that some of you may have seen before. It's called a ladder. What a central limit order book is is a single accounting ledger where everyone can submit their orders and those orders go into this accounting book. And what happens is the job of the exchange is to basically figure out who is able to agree on a price to buy and sell to transact their economic commodity, their futures, their gold, their um FX pair, their their shares. So let's talk about shares just to keep things simple for now. So say you have a share and somebody wants to buy this share for a price of $100. Okay? So what I'm going to do is I'm going to put a h 100red in the middle here. And say this person wants to buy 10 shares. I'm going to put 10 over here. And I'm going to give these two sides some special names. I'm going to call these bids.

And I'm going to call these offers. And they're also called asks by some people. So my order to buy up to 10 shares at a price of 100, okay, is called a bid. And a bid just means an order to buy. Equally, if I wanted to sell these shares, I could put it on this side and it would be called an offer to sell 10 shares at a price of 100. These orders are also called bids. So these are orders to buy. And equally, if I wanted to sell, that would be called an offer. And I would just put the 10 over there in this diagram that I'm representing. So these are bids. These are offers. Offers to orders to buy and to sell. And they're also called limit orders because when I specify a price, what I'm really saying is this is the worst price I'm willing to trade at. Okay? So if I put in a bid to buy 10 at 100, I'm saying the worst price that I'm willing to trade at, which for a bid is the highest price because you always want to buy as low as possible. You want to buy as cheap as possible is 100. But I'd actually be happy trading for 99, 98, 97, 97.5 if the exchange allowed.5s.

Um, and likewise on the other side for offers, uh, because you want to sell as high as possible. If I put in a limit offer to buy 10, well, that means is 100 is the lowest price I'm willing to go down to. I'm willing to sell at 100. I'm willing to start at 101. I'm willing to sell at 102. That's not a problem. The job of an exchange is basically to take in all these orders and try and match them up and basically figure out who is willing to agree on a price to transact at and then make that transaction happen. It's very simple. So, um, if I came in and I was willing to offer to buy 10 shares at 102, the exchange would say, "Oh, well, there's no one agreeing on a price in this current order book.

So, I am just going to put your order in here and I'm going to let other people see it and potentially trade against it and know that they can trade against it." Equivalently, if I said I was willing to buy, sorry, willing to offer 10 shares at 100. The exchange would say, well, this guy's willing to bid 10 shares at 100. So, this is a buy and this is a sell. These people are willing to match and trade at the price of 100 10 shares. We run through some more scenarios. Say I was only willing to offer five shares at 100. Well, then the exchange would say, well, this person's willing to bid up to 10, so he's probably willing to do he or she's probably willing to do up to five. In fact, they definitely are willing to do up to five because they want to do the full 10. So I can do five against this person. This person can then stay but only bidding five. And the person who just wanted to offer or to sell five shares at 100 would then execute against this person, trade against this person and then their order would be executed.

Would need to lessen the book. The final case we'll cover. What if I'm willing to sell um five shares at 90? Well, now the exchange had a decision to make. It can do those shares at 90 because I'm willing to sell to 90 and this person's willing to buy at up to 100, which means they're definitely willing to buy at 90. It can do those trades at 100 because this person's willing to pay up to 100 and I'm willing to sell down to 90. So, I'm definitely willing to sell at 100. It's a better price for me. And generally, the way most exchange do it, not all, but the way most exchanges do it is whoever had the order first gets the worst price. And that's called take a price priority. So um generally whoever is trading um and matching against someone who already has their order in the book, their bid or their offer gets the wor the better price and the person who already is in the book gets the worst price. Um and there's no averaging between them. That's how most exchanges work. Okay. So now that we know what a central order book is, we know why they exist, we know why markets exist, they exist to serve the function of a capitalist economy. We are now in

this position where we have a centralized ledger where people can put their orders and they either trade immediately or they don't trade at all and they land in the book for someone else to trade against. All right. So in this context we're going to go a bit deeper into understanding how can we make money from this. Okay. And what kind of trading strategies could exist?

If you look at an order book, this is a very simple order book. The way most order books work is um firstly they have some kind of well- definfined minimum jump that you can have in price. So for this order book we're going to say it's $1. So going to put in these prices $99.98. I'm going to put in these prices. 101 sorry 103. Uh I had a master degree I can't count up. Let's put in 97 here as well. Why not? So the way most order books will work is they'll actually have a bunch of different orders at all the different prices that exist because generally there'll be a lot of people who are willing to buy into sell at prices they can't agree on right now. So there's 99, we could have someone who wants to buy 30 and we could have someone who wants to buy another 70. So it's a separate order. Okay. So the total size on this level is 100. You can sell 100 shares for $99.

We could have someone who also wants to do 10 here and someone who wants to do 36. Okay. We could have a single order on this level who wants to do 121 shares. And on the 103, we could have a single person who wants to do five shares, a single person who wants to do 12 shares, single person who wants to do 20 shares. And on 104, we could have someone who wants to do, let's say, 90 shares. So, I've just made all these numbers up obviously, but um this is kind of giving you a better idea of what a typical order book and a typical, let's say, US stock would look like, right? So, there's lots of different people willing to buy different prices. Let's take a step back and look at what does this order book actually mean. Okay? Now, some of you are probably familiar with the idea of no free lunch. So in economics um or in marketplace economics in particular there's a equivalent version of no free lunch uh philosophy which is called um the rational arbitrage pricing philosophy or um uh you can also call it arbitrage free pricing and what that means is if there is any risk-free or close to risk-free money that you can make from a

particular market then someone rational would go out there and make that money and that opportunity would not exist there for you basically. you trade against. So what does that mean in the context of central limit order book right? So in the context of this order book what that means is if I look at it most of the time okay I say most of the time there could be the odd time when there is an opportunity to make money but most of the time what this book order book is telling me is that if the fair price or the price at which you can make easy money or risk-free money of this market say this stock or whatever is correlated to something else or there's a derivative on the stock or there's some way basically to say I can make free money by selling this order, this bid at 100 or selling this uh these bids at 99 or selling these bids at 98.

Somebody would have done it already and basically those bids would disappear, say 100, you can make risk-free money trading against that order. And because that bid has disappeared, now the market is kind of fair and efficient again. And same on the office side. So if the fair price of the stock or the risk-free price of the stock that I can make risk-free money on was at 102 or above, then I could trade against 102, I could trade against 103. I can basically make some risk-free money trading against these people. And what that seeks to do is we can say, well, actually, hold on a second. This 10 does exist. Okay, so this 10 does exist and this 102 uh the 10 for the 102 offer does exist. So what that means is no one thinks there's any risk-free money to be made by trading this market. So the fair price of this stock, the price at which you can say I'm not going to make any risk-free money trading at that price, okay, is somewhere between 100 and 102, right?

Because if it wasn't between 100 and 102, somebody would go out there and trade and make risk free money and there's no free lunches in the market. And by that mechanism, what happens is you get some notion of a fair price, which um a lot of trading firms call a theoretical price or a theo for short. It's kind of like a Chicago Amsterdam lingo um in the trading world. And a good approximation for the fair price or the the price is the price between 100 and 102 the mid price. So in this case it's 101. I'm going to put this in a square box and say square box let's put it down here equals fair price. Okay. So why is 101 a fair price? Well I'm saying no one in this market thinks they can make free money trading at 100 102. So it must be between 100 and 102.

And therefore I've just decided that it's going to be 101 because that's the best estimate that I have um of the fair price. It's somewhere between 100 and 102. So we'll call it 101. This is really important because what this illustrates is how important free frictionless markets are to a capitalist economy. What this allows us to do is say by virtue of having a central limit order book this wonderful construction over here where people can submit orders and trade against each other if they want to buy or sell or in particular people who want to make risk-free money arbitrageers as they're called I'll use that phrase the first time arbitrageers are people who trade in markets for the goal of making risk-free money by allowing these people to trade against other people what happens is we allow the market to determine a fair price by simple virtue of the fact that if If the fair price wasn't between the highest bid, which I'm going to call the best bid, and the lowest ask, which I'm call the best ask, okay? Then the arbitrageers would have traded against it and made some other price the midpoint between the best bit and the best ask. So by doing this what we can do is we can go to any central limit

order book in the world whether it's for oil whether it's for gold whether it's for stocks whether it's for an option or any of those and say the fair price of this commodity equity FX pair index option instrument is approximately the number between the best bid and the best ask most of the time and that's really useful because in modern market economies this allows us concretely to figure out the supply demand imbalance between two instruments right we can basically figure figure out what the relative supply and demand um equilibrium is and therefore the fair price of a product because if somebody wants to buy a lot of this instrument, you know, they would have to buy from this person who's offering 10 at 102, this person who's offering five at 103, this person is offering 12 at 103 and so on and then the midpoint between the best bid and the best ask would move up and therefore because there's more demand the price would move up. So this is a very concrete manifestation of the fair market um supply demand imbalance price as well as a manifestation of the no arbitrage condition the rational pricing condition price of an economic instrument. So that's basically how we figure out what a fair price of instrument is. Now let's go on to market

making finally right we we've spoken for long enough about all the other things.

Let's really talk about how do we make money in the context of the central limit order book. And to start with that, I'm going to give you a hint, which is that these orders here, the 10, the 70, the 30, the 36, the 10, 121, the 10, the 5, the 12, the 20, the 90. There's very very very few cases where these orders are actually put in place by individual retail investors, people who generally want to buy and sell this product because they need the product or they want to speculate on the product or because um you know they have a business reason to be to to buy or sell this product, right? Most of these orders are placed by professional highfrequency trading proprietary trading firms. So we're going back to the first slide proprietary high frequency trading top left quadrant firms called market makers and the job of a market maker now that we have all the machinery developed for understanding markets is really really simple it's basically the fair price of this product is about 101. So if I bid below 101 or I offer above 102 on average I am selling above and buying below the fair price and on average I expect to make money from that. Okay.

And we can see it really concretely with say we got lucky and we put in this 10 at 100 and we put in this 10 offer at 102. If somebody bought from us on this 10 and somebody sold to us at this 100, right, in quick succession, we would guarantee $2 profit times 10 shares $20 in profit before fees. This is a concrete manifestation of, hey guys, if I put in 100 and I put in 102, I will make money. Okay, very very concrete. I will make money doing this. and therefore I can kind of do it full-time professionally and this is a professional way of making money, right? And not only that, but if you recall the way markets work is in order for me to basically trade in a market and in order for me to have someone to trade against, you know, if if if I'm if I'm an investor, let's say, and I am bullish on this stock and Ethan is an investor on the other side and he already has the stock and he's bearish on he doesn't want to hold it anymore. we need to go and find each other. The job of an exchange is they put one place in space where Ethan and I can go find each

other. And if I go to this exchange, I hope Ethan's there and I he can take the other side of the trade as me. For every trade, there needs to be another player in the transaction. Now, the exchange part only solves the physical point in space part of that equation. You also need to arrive at the same time. Okay? So, there's space and time. Exchange is one place in space where I can go and find sellers if I'm a buyer. if I can go buy find buyers if I'm a seller, but there's no guarantee that the genuine buyers and sellers are going to arrive at the same time. So, what the market maker does as a service, if you want to think about it from an uh kind of an economic need perspective, is if I'm a seller, I can go buy at the price of 100 for 10 shares and I can warehouse that risk. Okay? So, I now long 10 shares at price of 100. I've now held this risk and the price might move down and then I could lose money. It might move up and I might make money. But basically, I now hold this risk until Ethan comes, right?

And he buys from me and I sell those shares to him and hopefully I realize a profit. Hopefully the price hasn't moved in a bad direction for me and hopefully I can sell above the place where I buy. On average, I am expecting to sell above the price that I buy because my fair estimate for this price is 101. And in the future, at least in the short term, this price shouldn't move up or down. this price is going to be a brownie in motion. Okay, so that is the economic purpose of market makers. And you'll notice that in order to be a market maker, you don't have to wake up in the day and think that, you know, I never woke up in the day when I was running marketmaking strategies and think how can I best service the exchange. The wonderful part about marketmaking is that people are trading for their own economic incentive, their own profit. We discovered this strategy just from understanding how an order book works.

But these guys are crucial for exchanges because even though they're completely self- serving, they serve this purpose of the exchange in that they warehouse risk. If a buyer and a seller arrive to the exchange, the same point in space but at different points in time and by then they time spread risk. There's a great um thinker and ex-trader at Jane Street called Augustine Lebron um who describes market make exactly as this. It's just time spreading risk. Um, if two people want to buy and sell a product, but they're not completely aligned on the exact time that they want to do it, you can help them discover each other by warehousing the risk in the middle. So, that's market making.

Let's go a bit deeper into how we might actually do market making then. All right. So, let's talk about how we might actually do market. [snorts] So, um, a very common and simple way of doing a market making strategy is just to do exactly what I said before. So, basically figure out a fair price. In this very crude estimate, our fair price is just going to be the midpoint between the best bid, that's the highest bid, and the best ask or the best offer, which is the lowest offer. So, our midpoint is just going to be 100.5. The calculation in my head is basically every time I trade, I'm going to mark that trade against 100.5. And the amount of money I make in expectation is 100.5 minus the amount of dollars that I've traded at credit. So, um, if if it's a buy, then um 100.5 minus the buy price times the number of shares I do. If it's a sell, it's the sell price minus 100.5 because selling above is better times the quantity that I do. And that's the amount of money I'm expecting to make an expectation. So, that number for bids 100 um 100.5 minus the bid price. And for asks, the ask price minus 100.5 is called the edge. So, um, edge is

basically how many dollars per share that I trade or per contract that I trade or per uh troy ounce that I trade am I expecting to make, um, uh, in in dollars. Um, so if I want to market make on this exchange, this order book, and say, well, my fair price is 100.5. So, my options are I can add in um an order here, right? And then every time I trade, I expect to make about 50 cents on every share that I do. I can add in an order here. expect to make 50 cents on every share I do. I definitely don't want to add a bid here because then I lose 50 cents for every share that I do and I similarly I don't want to add an ask over here because then I lose 50 cents for every share that I do. Um, my other options are, you know, I could add an order here, then I make $150.

But the problem here is that there are these people, you know, this person's bidding 30 shares, this person bidding 70 shares, that could be a problem because most exchanges actually say whoever put their order on that price level first gets to do the trade first. So, if somebody comes to sell or to buy, they definitely will get the trade first. And therefore, I probably will trade. it'll take me longer to basically get my trades and I could have made more money by just trading here. Um, even though I was making less per per share that I was trading, I will probably do more more shares overall. These are the kind of questions you have to start thinking about as as a market maker. Um, the bonus question, why do you think an exchange would have a rule that the first person on the level uh on on a particular price level gets the the the trade first? Give you a second to think about it.

Okay. So, it's basically to incentivize people. If you think about it, this market over here, I'm not super incentivized to place a trade over here because I'm not making a lot of money per share that I trade. And the problem with market making is there's a concept called adverse selection, which basically says you're way more likely to trade when your estimate of the fair value is wrong because you're more likely to give an arbitrageer some free money. And those people are more likely to trade against you than um the so-called random trader or just an investor who just wants to buy and sell in the market who's kind of equally likely to trade at all times. So if I think the fair price 100.5 it's actually 99.9 right then this market still kind of exists there's still no free money in this market but as soon as I put a bid over here um then I am on average losing 10 cents for every share that I do and due to this concept called adverse selection I'm way more likely to trade when this market occurs when I have a bid at 100 uh just because arbitrageers are generally smart and they'll trade very quickly um if they think your pricing is wrong. So in order to

incentivize people to be the first people to place, you know, if I place an order here and nobody trades against me, then the rest of the world is pretty sure that the fair price is above 100, they're willing to join behind me. And to give me that extra little incentive to place my orders on a price level where no one else has placed any orders yet, the exchange gives priority to the first people who who place that price level. So that's why that would occur. So those are choice I can make as a market maker. I can join behind these people and make $150 per trade. I can join here. I make 50 cents per trade. Um, I could add some really wide orders here. If a huge seller comes in and they want to buy, they want to sell, let's say, 500 shares. Well, you know, they can pick up 30 shares from this person, 70 shares from this person, 30 from this, 36 from this, 121 from this. In order to get 500 shares at once, they would have to trade against me. And here, I make a lot of money. I make $350 per per share. So, that's pretty good, but I'm just less likely to trade.

So, those are kind of the things obviously symmetric for asks. Those are kind of things you have to think about as a market maker. Other things you have to think about, if I trade at the 100 price level, okay, I am now long, say I put 10 shares over here, I am now long 10 shares of this product, right? I'm now long 10 shares. The thing that could happen is some news could come out or this person could continue selling and they could continue to trade against these people and then the fair price of this product which is the mid between the best bid and the best ask would go down and I might not be able say I also put this 10 over here. I might not be able to get filled which means basically to to trade um at the 102 level. So, I may have bought for 100, but the market could move down a bunch because the person who sold to me here also sold to all these people and moved the fair price down. And then I might then have to get out of my long 10 position by basically putting in a bid, an offer here or even an offer here at 100 or 99.

And then obviously if I put an offer at 100, I don't make any money. If I put an offer at 99, I lose $1 per per share that I do. So that's that's a risk that I'm taking on. Basically, market making is inherently a competitive game. you're competing to offer liquidity. That's liquidity means the ability to trade um at any instantaneous given time to people who want to transact in the market and are willing to pay a spread or give up some edge against the fair price of this product in order to get liquidity. So, you're selling liquidity. You're basically people are demanding liquidity, you're selling it. That's the way to view it economically. It's a competitive game. If I decided, as I did before, to place a bid at 10 of 10 at a price of 100, right? Another market maker could go in and say, "Hey, actually, I think the fair price is 101.5.

So, I'm going to also bid 10 at 101." And now what's happened is I tried to improve the market, but somebody improved me. And overall, the effect is I now will no longer be the first priority to get trades from any seller. This person will. And even if I do, I get them at a worse price than if I just placed over here at 99, right? I could also place this 10 and then this person and this person could say, "Well, we're no longer the best in the market for getting these orders, so why on earth should I continue to bid at 99? Um, I would rather get rid of these orders and also improve this person." And now I could say, well, I don't want to improve this person any further. Why am I bidding at 10 at 100? I could just bid at 99, right? Because then I'm the same priority in the queue to get trades from all the other people, but I can make an extra dollar of edge no matter what the fair price is because I'm just buying for a dollar less than I did before. So now maybe I get rid of this and I put this here. And now these guys are like, well, why the hell are we

bidding at 101? There's no one at 100. We could all just move to 100 and make one extra dollar per share. So then they will move down here. And you see how this goes. It becomes a race and a competitive condition. So the ultimate aim of this race and again one of the wonderful things about the free market is that this race tends to compress what we call the bid offer spread. Okay? And the bid offer spread is basically there's many ways to look at it but the easiest way to look at it is how much edge is the taker giving up against the fair value in order to transact in this market. Okay. So basically here the bid offer spread is $1, which is the minimum possible bid offer spread that can exist in this market given the tick size given the minimum price increment of prices.

And what that means is if I am a trader and I sell and then nothing happens and I buy I only lose $1. Okay? Or in other words uh the fair price of this is 101.5 because 101 102 the best the best offer. So every time I trade I lose 50 cents for every share that I trade. If none of these prices existed and the best bid was 99, the best offer is 102. Now the fair price is 10.5. But every time I want to trade, I either want to sell at 99 or buy at 102. I'm going to lose $150 at every share that I trade. And that if you think of that as a transaction cost for demanding liquidity, the price of liquidity, that transaction cost is much higher than in this competitive game where people were trying to improve each other and ultimately compress the bid offer spread. So that's another way that competition breeds lower transaction costs. Again, a great feature of the markets. Um, all these people are self-interested. They're all just trying to make as much money as possible and by virtue of their competitive behaviors or so often happens in economics. The overall competition in the market and therefore the uh experience and the costs for people who are aiming to

transact in this market and demand by the liquidity which is what this market's offering decreases uh as competition happens. All right. So um so far we've covered um why markets exist, the structure of markets, um how people place orders in markets, how that naturally leads something called the central limit order book, how that leads to price discovery, which is basically the ability of a market to signal what the fair price of an asset is most most times of the of the day if you just kind of froze the market. And we've also covered how this natural structure of the market leads way to a trading opportunity, a type of trading opportunity called market making. uh why that's good for markets, what economic uh service the market makers are producing in order to justify that the costs that they're making and how it's different to every other kind of business where competition amongst market makers ultimately leads to lower costs and better outcomes for the um users and purveyors of that market. So

I'm just going to drill this home by talking a little bit more about how marketmaking is done like a modern context and um the difference between different but we're going to do that by comparing the difference between two types of markets. Okay. So in a modern context, we have our order book which I'm going to draw again. This time I'm going to draw two types of order books. So this one I'm going to call the thick book. Okay. And the thick book is going to have um we're just going to do total quantities now. So not individual orders, but it's going to have like a th00and here. It's going to have 2,500 here. 99 98's going to have 7,000. And at 101, these are the bids. These are the offers. It's going to have 4,000.

102, it's going to have 5,000. And 103, it's going to have 7,000 as well. Now, the way modern market, we we're talking about this world of quant, right? And nothing I've said to you so far really is about mathematical models, quantitative trading, um, algorithmic trading. You'll be unsurprised to know the way this happens in modern markets uh for most instruments at least is that people basically figure out their own model for what the fair value should be. So I said the fair value is 100.5 because it's just between 100 and 101 and most of the time the fair value is not going to cross the current market because if it did there would be some easy money to be made but people figure out their own version of fair value and it can be anywhere between 100 101 but it can it can even cross 100 and 101 sometimes a little bit that's due to frictions in the market. It may you know there may be a transaction fee or cost element associated with doing arbitrage.

If your fair value creeps up above 101 or below 100 that means it's not actually profitable to do that arbitrage and therefore um because it's not a frictionless market the market may remain inefficient for some time. That's also basic economic theory. There may also be um other products that kind of trade in line with this which have moved and this product hasn't moved. That might lead to some trading opportunities. But the key thing to remember is that what quant firms do is they produce a really good fair value model over here. And then they basically weight that fair value model by asking how much evidence is there for that fair value to occur. Now in this book, I'm going to tell you this book trades $10 billion of notional volume every single day. Okay, $10 billion is a lot, right?

And this book also has a relatively high amount of liquidity. What that means is I can go and buy a lot of shares or I can sell a lot of shares without impacting the price that much. My transaction cost will be very low. If I compare this to something called a thin book. I'm going to do a sidebyside comparison here. Okay. in this thin book. Let's say um there's 10 quantity here, there's 25 quantity here, and there's 70 quantity here, and there's three here, and there's 21 shares here. Okay? If I compare, and this book trades $1 million a day. Now, I can compare these two books against each other. If I had an estimation for the fair value, I would be much more confident in my estimation in this book because so many people have traded in this and because so many people are willing, so many market makers are willing to offer me so much quantity to trade in this. They must be supremely confident in their estimate of the fair value. Right? What this book is telling me is all the market makers are willing to bet a lot of money. The fair values collectively is between 100 and 101. Here the market makers don't even know if it's above 101. No one is willing to bid on 101. So

people have a very broad estimate, a very broad estimate of where the fair value may be. This market doesn't trade that much. Okay? Remember, it's trades that tell us price discovery. Trades that tell us somebody's willing to buy, somebody's willing to sell. This is what the fair price must be. This person disagrees with me that this is the fair price, that's why they're willing to buy from me, that's why they're willing to sell to me. This is therefore the fair price must be around this. This market overall, I would be much more confident to predict what the fair price of this market is versus this market. even though they could be the same stock just two different scenarios. And this is precisely how quantitative algorithmic market works. Okay. So what we do is we produce a fair value the stock and we add in orders into the book that allow us to trade around that fair value and we size our orders and we size how much order size we put in based on how confident we are in our fair value. Okay. Okay. So here if I'm very confident I can put in a lot of size a very big bid and a very big offer. Here I might be much more hesitant to put in a big bid and a bid

offer. This book is called thin. The consequence of thin books is that transaction costs are high. Here if I want to buy and sell a share in quick succession I would lose $2. Here I would lose $1. The transaction cost is double. If I want to do a big quantity if I want to buy a 100 shares okay in this market I would have to go well beyond my average price to sell 100 shares. Okay. in this market would be 10 * 100 + 23 * 99 + 70 * 98 plus whatever remaining quantity oh no uh uh 67 * 98 right uh divide by 100 so basically it's just above 98 that's fair price over here so if I want to sell 100 shares I would get 98 point something it's about2 roughly not doing the math in my head and here if I want to sell 100 shares I can sell them for a price of So on average, I have got $1.8 better execution in this market than this market for 100 shares. Okay, that's pretty good. That's $180 that I've saved in transaction costs for trading here.

And ultimately, this is how market this is this is a healthy book or a thick book. This is one where there's a lot of competition between market makers. Frictions are low. You can trade for very low um transaction costs. This is a thin book where the fair value price is uncertain. Because the fair value price is uncertain, people are willing to offer less liquidity. Because people are willing to offer less liquidity, the volumes traded lower. Because the volumes traded lower, market makers don't feel the need to offer as much liquidity because it's just needless risk on a market where they don't even know the fair price and therefore people don't trade as much. It just ends up in a vicious loop. So this is the gold standard of uh what market making looks like. This is what the books look like in any kind of large cap US stock, US equity. And the way market makers go trade this book is they have a fair value and they place orders around those fair values and hope for people to trade against them and they manage their risk by ensuring that they or trying as much as they can to sell any position they go long or buy back any position where they go short and maintain a neutral

portfolio just helping buyers and sellers find each other who arrive at different points in time. So when I started my last job, we were trading over $10 billion a day in volume. That's why I picked this number. And that goes to show that if you do market making well and you have all the edge cases worked out, you can trade a lot of volume without having to manage your orders manually. You can let algorithms do it. And that's how top trading firms uh that's one of the strategies that top trading firms have for making money. And it's one of the oldest strategies and that's how many people in quant finance start their career. That's how marketmaking firms and high frequency trading firms make