High-Frequency Trading and the Design of Financial Markets with Eric Budish | a16z crypto research

Transcript

all right welcome everyone let's go ahead and get started to today's uh a16z crypto research seminar very happy to introduce Eric boodish who's a professor in the business school booth at University of Chicago um Eric's a super well-known Market designer he's worked in a lot of different application domains and matching markets financial markets which is what I'll talk to some about today although even though it's motivated by traditional financial markets I think we'll see some ideas that are also useful in sort of a decentralized finance context I'm also for sort of the web 3 crowd he wrote a paper the first version I think in 2018 around the economics of security of the Bitcoin protocol and protocol also an important paper but I'll leave it to him to now start talk about high frequency trading all right thanks Tim it's great great to

be with you for the week I really appreciate it so I'm going to talk about a series of papers that I've worked on over the past uh decade or more we were joking at the break about how we're now the old guys but um on high frequency trading and the design uh the design of financial markets um let me start with probably the most famous idea in finance certainly the first first idea you you get exposed to as a graduate student in the subject which is the efficient markets hypothesis my distinguished colleague Gene Fama famously defined the efficient markets hypothesis as a market in which prices quote fully reflect uh all available information and he was wise

enough to note that it's kind of a comically extreme hypothesis if you take it if you take it literally and he distinguished several different versions of the efficient market hypothesis in his words to pinpoint the level at which it it breaks down the weak semi-strong and strong depending on whether you can beat the market based just on the basis of past prices as your information set beat the market based on past prices and other forms of public information as your information set like earnings reports and so forth or company forecasts or the strong form in which the market you can't beat the market on the basis of either public or private information and what he concluded at the

time this is in the sick work in the 60s and 70s is that the fishing markets hypothesis held up very well in the weak and semi-strung form but that there was already a lot of evidence against the strong form of a hypothesis the translation is to beat the market you have to have private information you have to know something that the rest of the market does not know uh there have been um Decades of research on efficient markets Theory sense and the modern professional consensus um is that there is some predictability in financial markets that asset prices have some predictability over longer time Horizons for example using whether the price earnings ratio in the market is is high or lower Dividends are higher

low that kind of thing the debate is over the interpretation of this predictability of asset prices is it is it rational variation the price of risk is it more behavioral there's also debate about the magnitudes and some exploiting inefficiencies in financial markets is hard but the consensus in the profession has been that in the short Horizon in the short run efficient markets Theory works very well there's a hundred percent agreement with a a statement about short-run efficient markets and an IGM experts panel which I'm involved in um and then here's a quote from the 2013 Nobel citation to Fama and Schiller Shore is famous for this predictability

over the long run by the way so if it's possible to predict with a high degree of certainty you know short-term asset pricing fluctuations there's money to be made such a situation reflect a rather basic malfunctioning of the market mechanism so this intellectual and con context in mind I was genuinely perplexed as a really new assistant professor at the time as 2010 I still kind of remember starkly when I first read about first read about this when I started reading about the arms Reyes for trading speed among high frequency trading firms in a famous early Salvo in the race for trading speed was spread networks they invested 300 million dollars to dig a fiber optic cable connecting financial

markets in Chicago to financial markets in New York this cable shaved round trip data transmission time from 16 milliseconds to 13 milliseconds so my three thousandths of a second it's about a hundredth of the time it takes to Blink your eye industry observers describe three milliseconds as an eternity they joked at the time that someone's going to go through the Earth with a tunnel rather than around the earth with fiber optic cable to save even more time and this joke actually sorted it came true no one actually did the tunnel but microwaves are faster than fiber optic cable because of the physics of how light travels through glass versus through um through air so the Cable became

obsolete within a year and the arms race for Speed is continued it's now commonly measured in millions and even billionths of seconds so microseconds and nanoseconds and as you'll see I'll do some of the quantification later in this talk it's on the order of tens of billions of dollars of expenditure per year there's Hardware software these communications links like spread networks but a lot of high quality human capital devoted to shaving tiny amounts of time off of trading speeds so the question I was flummoxed by was how could such tiny speed advantages be worth investing so much money you see if you see an arms race for trading speed you assume it's a rational a rational response to an opportunity to make money but I was

trying to figure out what was that that source of economic profit of economic rent because three milliseconds is too short to be about fundamentals right so fundamentals think of quarterly earnings or you know five-year forecasts of of a company's profitability quarterly earnings are released once per 8 billion milliseconds so three milliseconds isn't about that um and the opposite of fundamental information is what's called technical information and economists have long been very skeptical about trading based on technical information so when you see on CNBC a a chartist talking about a head and shoulders pattern or a 200-day

moving average economists kind of laugh at that stuff they think it's not uh not serious usually amusing often comforting but of no uh no real value and that the answer though my collaborators and I came up with uh was again over a series of work that I'll tell you about over the last 10 plus years is that the arms race for trading speed is a response to an underlying structural flaw in the design of modern Financial exchanges um the most commonly used Financial exchange designer around the world is globally and across asset classes is something called The Continuous limit order book and the flaw is that it both treats time

is continuous so chime is infinitely divisible and processes requests to trade serially so one at a time in order of receipt and what I'll show is that the combination of continuous time and serial processing creates riskless Arbitrage profits from symmetric public information so information that in principle at least is disseminated to the homework at simultaneously and symmetrically in a public way nevertheless creates an Arbitrage rat so this is a violation of efficient markets Theory built straight into the market design the violation in even the weakest form of efficient markets uh Theory and these riskless Arbitrage profits they're kind of not supposed to exist

and I'll show you that they they harm liquidity they're like a tax uh on liquidity we're talking about Mev at uh at lunch which is also kind of like a tax on using ethereum for example um and these rents induce a never-ending uh arms race for trading speeds never-ending arms race to be ever so slightly faster than the next guy again now commonly measured in nanoseconds it's kind of like it's ridiculous but it's also really wasteful the market design solution that I'll talk about is uh what I call frequent batch auction so put time into units the time unit could be quite small but a long time for a computer so I think like a millisecond or maybe up to a second and then process TR requests to trade in

a batch process using an auction so really going from continuous serial to discrete batch that's the the core of the ID I'll talk to you about for the next hour so I'll talk to you about this over the over a series of papers Al Roth my mentor and advisor likes to talk about Market design research occurring over a long series of papers this is no uh no exception I'll talk about the first paper published in 2015 that really kind of developed uh data empirical facts about high frequency uh trading that hadn't really been understood before and then this theoretical understanding of the market design as the kind of underlying root root cause of the issue

and then batch auctions as the market design response and I'll talk about a more recent more recent work published in 2022 and the paper that's forthcoming that are about two of the most common questions that came up in response to the first paper one just how big a deal is this how do we quantify the arms race for trading speed that's that's this paper that I'll talk to you about that was joined with um researchers at the UK financial markets regulator and then the other question that came up over and over again is is this is a solution going to come from private private sector forces or for some from some kind of regulatory response so will the market fix the market I'll talk to you about the economics of financial exchanges and

their how that shapes their incentives to innovate on their Market design and then last I'll talk about my most recent research on the topic called flow trading with um uh Crampton Kyle Lee and Malik um that takes the batch auctions idea to the trade of multiple assets at a time so it's more of like a combinatorial market design for for finance I'll talk to you about that at the end of middle I'm going to mostly talk about quote unquote Trad fire which I I use non-ironically and traditional Finance is very important um and towards the very end I'll draw some connections between uh between This research on on high frequency trading and the design of financial exchanges

and traditional finance and uh connect and issues that arise in crypto markets and Mev is an important one there's a lot of sniping and crypto markets I'll talk about uh I'll cover up a bunch of connections towards the end and try to draw parallels as I go as well um okay so let me talk about this 2015 paper please chime in with questions as we go or at the end however you like is fine all right so I'm going to start with some empirical facts about how financial markets behave at very high frequency time Horizons this is data from the two financial instruments the two two most commonly traded financial instruments that track the S P 500 and as you'll see if you

look at the axis this is from quite some time ago this is data from 2011. um and what what this is showing is the price of these two instruments one is a Futures Contract that trades in Chicago one is an ETF that trades on the various equities exchanges really in New Jersey in various server forms there and this is this is prices over the course of the trading day where what we're doing actually got a kind of data that researchers hadn't studied previously called direct feed data from exchanges and we're it's the kind of best quality data you can get we're just plotting the the midpoint price over the course of the trading day for these two financial

instruments and as you'll see they're different instruments Futures and ETFs are a little bit different but there's a there's a pretty tight Arbitrage relationship between between the two of them they both tracked the S P 500 and as you'll see their their price is moving basically perfect lock step over the course of the trading day even this is quite a volatile trading day here's an hour of trading data uh a minute of trading data and then this is about the amount of time it takes to Blink your eye this is 250 milliseconds of trading data and what you see is is prices that it at a daily basis look like they're moving in perfect lockstep as you'd expect given the Arbitrage relationship at high frequency you're moving a much choppier a much choppier

Manner and there's lots of Arbitrage opportunities so at this moment in particular as an example the price in Chicago jumps up the price in New York hasn't responded yet there's an Arbitrage by the cheap one sell the expensive one and they're different moments where the uh the reverse is true so the next thing we did is we um we just count up all the arbitrages we asked how long do they how long do they last how much money is at stake um and so forth so first of all how long they last comes way down over time over the time period of this data set which was from 2005 to 2000 uh 2012.

how much money the arbitragers are worth this is per per share traded it's actually pretty flat over the course of the uh over the course of the data set and then the frequency of the arbitrages varies quite a lot over the course of the data set in 2005 2012 or so um but the variations based on whether the market happens to be volatile that day not not a Time Trend it's and which makes sense like if the Market's really volatile there'll be lots of opportunities to take advantage of slightly steel uh steel prices this is probably my favorite chart from the paper this is the correlation of these two assets at different time Horizons from a millisecond up to 100

milliseconds these are two assets that at a daily basis have a correlation of basically one you know 0.99 something they're they're really the same economic exposure and what you can see is at 100 milliseconds the correlations getting higher and higher in each year of our data it's nowhere near one but it's getting higher and higher in each year of our data so this is information getting from Chicago prices into New York prices and vice versa faster and faster each year but at high enough frequency the correlation is is basically zero if you think about it structurally there's just nothing in the financial Market architecture that could allow these two assets prices to jump at exactly the same time they're trading in two separate continuous limit order books

how on Earth are they going to move uh move simultaneously so the correlation completely breaks down at high frequency Eric can I just ask you yeah is it is it true that that that that that breakdown at high frequency is really not predictive at all of a change in the underlying slightly longer time time Horizon correlation between the two that is it really is just you see what I'm asking yeah the way I think about it is there's some and this will come through in the model there's some fundamental not super well understood process that drives just the daily fluctuation and say the S P 500 but then the very micro structure

Arbitrage relationship between these two ways of trading the S P 500 I see as almost like a form of just noise and rent extraction and and and the market design I'll show you over the next bunch of slides is going to help us understand why why the you know usually if there's an Arbitrage let me just kind of I should have emphasized this point a slide or two ago usually if there's an Arbitrage opportunity in a financial Market it gets competed away once it's obviously understood by once it's understood by a wide variety of people what I'm showing you here is that the Arbitrage opportunity it gets competed down in time but it doesn't actually disappear in in dollars and that's and and that will become clear once I go

through the kind of conceptual model for why this Arbitrage is an intrinsic feature of continuous Trading usually arbitrages get competed away but this one this one's sort of structural it says lots of Trades just like this one where you have highly correlated highly liquid assets where you can Arbitrage one off the other so here's just for funds a bunch of pictures uh treasury bonds I got a few different kinds of equity indices uh currencies uh gold and silver and other Commodities you could do oil natural gas I put coffee up here I think for fun here's just a long left one of my collaborators John shims in a in his a prior life was

a jump trading a big high frequency trading firm and he came up with this list in like 30 minutes it just like it's very uh insiders know just how much Arbor you know how many how many good Arbitrage uh peers there are in financial markets then there are other sources of of um of rents in the race for trading speed the second one's probably the most relevant for thinking about crypto markets actually which is in in in the stock market you can take a stock it trades on you know 15-ish different exchanges and you can Arbitrage if prices vary from One exchange to the next and there's stock market regulations that prevent different exchanges prices for the same asset from getting two out of whack with

each other I'll come back to that later in the talk um but in crypto markets you know the price of Bitcoin could trade at very different prices across across different exchanges I think that's how SPF got you know got off the ground right so there's a lot a lot of Arbitrage of that form in some other other markets there's some in traditional finances by a ton in crypto um there's a race to respond to public news so the consumer confidence number comes out of the University of Michigan or the FED announces an interest rate shift that creates an arms race for Speed there's races to the What's called the top of the book there's a lot of races everywhere once you start looking for them all right the next thing I want to talk about is this this relates the question that just came up is the theoretical

root cause of of these arbitrary arbitrages from uh from public information from kind of obvious pricing patterns the Arbitrage I just showed you like my grandma could spot that right she's almost 100. the the hard part is not spotting the the relationship between prices the hard part is ex is physically exploiting them not not understanding the mispricing so the model is a descendant of a famous model by Glaston and Milgram picture of security and I'll go through it at a some I'm not going to give the full mathematical details but I'll give you the the key mathematical intuition of the model there's a security that trades on a

continuous order book Market there's a publicly observable signal of the value of this security and I'm going to assume that the signal just jumps around in a poisson process and I want to make the perfect purposefully strong assumption that the asset is just worth the price of the the is worth this public signal so if the signal jumps up all Market participants agree this is the new value of the asset of the asset so I'm trying to create a a quote best case scenario for Price Discovery and liquidity provision in a continuous submit order book by assuming away asymmetric information for example the players are going to be investors and trading firms investors arrive to Market wanting to

buy or sell one unit they're not informed and then there's trading firms that are always present in the market they want to make a market they want to make a market with bids less than offers for example so given the model set up and this is purposeful you might conjecture that providing liquidity from it to investors so from Trading firms to investors has zero cost that and that Bertrand economic competition would compete the cost of liquidity down to to zero so effectively being able to buy an arbitrarily large quantity of this asset X at the price of this public signal Y at a zero bitesque spread why would you predict that all of the usual sources of

costly liquidity and finance I've assumed away so inventory costs assumed away risk aversion have assumed away um asymmetric information and adverse selection I've assumed away and so forth we call sniping or latency Arbitrage and it's a phenomenon that's that's special to The Continuous the mid order book Market design so here's the visual that will help you understand the idea of sniping so suppose a bunch of trading firms here's the current level of the signal why and I'm making a market with bids and asks around that uh around that Current public signal and suppose that single jumps there's a change you can think of

this as a change in the price in Chicago that affects where the market should be in New York or you could think of this as a change in the price of coinbase that affects where the price should be on uniswap or cow swap or others um so a trading firm that's providing liquidity in New York is going to send a message to cancel their orders that are now that are now stale and replace those orders with uh with new quotes that reflect the new uh the new public information at the same time other trading firms observing this symmetric public information will send a message to The Exchange seeking to snipe to pick off

the uh the steel quote and because the market design is processing this burst of activity uh in a continuous time serial process it's kind of a quintos who gets there first so even though it's public and symmetric there's some large probability that as a liquidity provider I'm going to get I'm going to get picked off that's n minus 1 over n on the model so what this visual shows us is that in in a continuous order book even symmetric public information creates Arbitrage runs so these mechanical orbs like I showed you in the S P 500 Arbitrage case are kind of built

into the market design again it's not supposed to happen in an efficient market we're all used to the idea that you can get paid if you know something the rest of the market does not know but what this analysis shows us is that in the continuous limit order book Market you can get paid knowing something the rest of the market does know um and in equilibrium these Arbitrage rents are ultimately paid by investors as I'll show you in the next next couple of slides and that Nobel citation I showed you earlier it's wrong asset prices the Nobel said asset prices are predictable in the long run but quote next to impossible to predict in the short short run that's wrong because that's the prices are actually extremely easy to predict in the extremely short runs at the millisecond level there's a

lot of predictability again all right so the the I'm not I'm not going through the full mathematical details of the model but I want to give you a couple of equations that give the key kind of the key mathematical intuition for equilibrium so in equilibrium there's a bid ask spread that's going to be the left hand side of this equation that reflects there's some poisson arrival rate of investors Lambda invest if I'm making a market I get I what I the way I make money is an ordinary investor comes to Market and buys from me at the ask or sells to me at the bid this is how much money I make from from ordinary investors showing up to Market and the way I lose money is on the right

hand side it's when there's a jump in the public information which happens with arrival rate Lambda jump if that jump is bigs if that jump is bigger than my half spread so here's my bid and ask the jump is up to here I'm going to get picked off with high probability how much am I going to get picked off that much the difference between the jump size and half of my bid ask spread so that's that's this amount here that I'm going to get picked off so in equilibrium my revenue from playing from making a market to investors is going to get offset by my costs of getting uh of getting sniped and that's going to uniquely pin down the equilibrium uh bid ask spread then yes Tim is this for large and they might

as well a brand has gone away right there's a subtlety in this equation which um which is that if I'm the guy making the market I get picked off n minus 1 over n of the time and then in equilibrium because I could also I have an opportunity cost of making a market and not being a sniper and that's the last one over n so if you take so if I'm a fast guy making a market I get picked off n minus 1 over n of the time and then one over n of the time yeah one over another time I get out of the way but that's that's my rent that's that's the way I get paid you get paid by being a successful sniper one over end of the time and then I get that last little bit if I'm a slow guy making

the market then I get picked off 100 of the time and that actually happens a lot in our data which I'll get to in the next there's kind of a blend of both cases in the in the data um if you then add an add endogenous entry so now you can invest in a costly speed technology you get one more equation where the left hand side is again this revenue from liquidity provision and then the right hand side is how much entry is there how much investment is there uh in trading speed the economic interpretation of this equation is that the investment in trading speed dissipates the pile of rent created by sniping which in turn gets passed on to investors as a larger than zero bid ask

spread and again in this model the spread should be zero in a richer model which I'll I do I work on in some subsequent work you you can have both sources of bid ask spread private information and public information but this model is trying to strip out the in the non-essential ingredients so you get this equivalence again the arms race prize the expenditures and speed and the the cost to investors so profits in an arms race have to come from somewhere there's profits in in the Mev game have to come from somewhere the kind of attacks on users of ethereum so one of the predictions that comes out of this model is that the arms race for Speed is never ending so let me just show you some fun data on that so here's um the first microwave link between Chicago and

New York you'll see in zigzags a little bit it's not a very straight line um but microwaves are faster enough than fiber optic cable that that it was still faster than the spread networks cable this microwave link from Chicago to New York next time you're in downtown Chicago visit Millennium Park here's the bean and then here's the top of the Aeon Center which is um when we're one of the microwave hopses so next time you're there take a look um and then here's the microwave Network filling out over a six or seven year period this is using FCC microwave license applications I have good use of RA time right it's a um so you can see and you can see the the line getting straighter and

straighter in each year of our data you can also see down here that Washington DC is in a very straight line link to Chicago and and New Jersey it's because a lot of symmetric public information gets released from Washington DC so fed announcements uh the jobs number and that creates sniping races okay so the last thing I want to do in for this paper and then I'll go through some of the the the newer work is how to fix how to fix the sniping problem with the idea of frequent batch auctions so at a high level frequent batch auctions take the current market design and make just two key changes so time is

treated as a discrete variable not a continuous variable and requests to trade or processed and batch not uh not serially a little bit more fully take the trading day divide it into equal length batch intervals I'll use Tau as the notation think of Tau practically for for Equity markets it might be a millisecond um for the for the float trading idea that I'll talk about towards the end where you're trading portfolios of assets that might be appropriate to use a slightly longer interval for computational reasons so maybe a second be a pretty still pretty fast but a lot slower than nanoseconds during the interval you can submit bids and all and asks just like with the

current language can freely modify bids and orders at any moment in time orders that aren't executed just stay outstanding and the market all kind of just like standard limit orders at the end of each interval The Exchange Aggregates all supply and demand if you will all outstanding orders there's two cases either supply and demand Cross or they don't I guess go ahead yeah for um in the actual batch during that time period the information being released back to Traders wait till the bottom of this slide so um if supply and demand intersect then uh then they clear at a you know the market clears a uniform price

um priority is still priced on time but treating uh time is a discrete variable so if my orders have been hanging on the market for many batches and yours are new this batch I have time priority over you but if we've both arrived in this batch we're treated as exactly the same and then information policy to your to your question the same information policy is in the continuous Market where in the continuous Market I send an order to The Exchange The Exchange economically processes the order and then I get an update of what happened like oh a new order got or added to the book or there was a trade at such and such a price same thing in the discrete time batch Market where I send the order the exchange The Exchange economically

processes the order and then I get an up and then the market gets an update the difference is the economic processing is happening in discrete time what's a big difference versus crypto markets in crypto markets you send the order to The Exchange think of it as sending an order to the mempool it's then like public and visible for all to see before it gets economically acted upon and that gives rise to lots of rent extraction um so it's a it's a bad design from the perspective of financial exchange design I mean it doesn't make any sense um okay so after each each interval report all the trades report all outstanding order is just like I was talking about I find it helpful to think about the FBA

proposals through the lens of three cases I found this to be a helpful way to explain it the first case is in a particular batch interval it's a picture a millisecond nothing happens so then what happened what's going on there's a lot of orders to sell and a lot of orders to buy and they're just kind of flashing to the market once per millisecond if you will just hanging out making you know providing liquidity just like in a limit order book there's an outstanding bid an offer that's the analog in a in a batch auction Market in periods of calm where not much is happening a second case is that there's a small amount of trade so the Market's kind of hovering you know bid 10 ask 12. someone shows up and wants to buy 100 shares at

12. that's also a very common that would also a very very common case and that executes very analogously to us in a limit order book Market the third case is though if there's a burst of activity in the interval so if there's some information Innovation that causes a lot of algorithms to respond then using the auctions very different from using the limit order book that's kind of the whole point of using the auction is to to manage that burst of activity using an auction with price competition as opposed to on the serial process which is speed competition so the auction has I think quite intuitively reduces the economic relevance of tiny speed advantages most public information arrives at a time

where all Market participants can see it in time for the next batch right so most information will have arrived from the previous batch and you have a whole batch to think about and decide what to do for the next batch information that comes externally could arrive anywhere in this window and there'll be a tiny interval towards the end where if you're a little bit faster than me if information arrives at that critical window you see it and I don't so speed is not zero relevance but it's a lot less economically relevant whereas in the continuous Market if you're a billionth of a second faster than me that's relevant always like any any piece of new information a tiny speed Advantage is always is always relevant

the second value of auctions which is more subtle is that auctions change the nature of competition from competition on speed to competition on price so imagine that information arrives in that critical window where if you're faster than me you see it and I don't but now imagine that there's two of you in only one of me and I'm vulnerable to getting picked off but the two of you now have to compete in an auction so you have incentive to pass through to me a better price that reflects the public information even even though you're faster than me so in a Bertrand Nash kind of equilibrium you'll pass through the whole the whole game you'll perfectly pass through the The Innovation and the public signal and in

different auction games that might be more partial um but you get competition on price because of because of the auction there's a conceptual point that I like to make about the company purely computational benefits of discrete time I think this is a good topic at the intersection of computer science and economics so I want to briefly advertise it here which is continuous time markets at some computational level make no sense it's as if they're assuming that computers are infinitely fast and we all know computers are very fast but they're not infinitely fast and some of the the Chicago New York stuff is like quite literally relativity differences between geographies it takes time time for light to get from one geography to another and

a lot of that the computational and speed of light constraints go away if you have discrete time not continuous time so you get a much cleaner Financial system if you go from continuous to discrete get a cleaner regulatory paper trail for example which you don't have to adjust for relativity anymore so I think is a good topic all right next paper I want to talk about um is about quantifying the sniping problem a lot more widely and broadly than we're able to do in the previous paper using a really cool new type of data that I was able to get by working with Regulators who who used regulatory muscle to get a kind of data no one had gotten before I see a hand up yeah go ahead yeah I just on the the second last point I guess

about the the lower powered but arms race incentives still exists it seems like this the magnitude of those incentives is decreasing in the time interval yeah the the key ratio in the paper is Delta over Tau where Delta is the speed difference between you and me and tau is the time interval so what's the cost side of making Tau bigger I so that's a hard question um my honest answer is in the paper I act as if going from Tau of continuous to tell a very fast discrete doesn't cost anybody anything I mean as a mathematical matter that we're just we're we're pointing out that there's a discontin discontinuity in the in the

efficiency of the market as you go from continuous to very fast discrete a hard question is what happens as you further lengthen Tau from say a millisecond it's hard to take seriously that there's costs of waiting a millisecond to trade it's not hard to take seriously that there's cost of waiting a day to trade and what those costs are is not very fully modeled it's something I'm thinking about have been thinking about for a while but this paper this whole agenda really is about going from zero to something very fast with an open-mindedness about further benefits and costs of going to something slower and making Tau a random variable doesn't do it you're just going to integrate across that and it's not going to change the power of the incentives in this

model it just confu it kind of doesn't accomplish anything and it makes the market kind of more confusing um but they're they're I I have a I have a lot of thoughts on the randomization so some Mark there's Europe Europe is now about five percent frequent batch auctions in European Equity Market most in European Equity markets mostly using randomized batch auctions but we kind of a different information policy they're more like dark pools than exchange there's a lot of kind of weeds in that discussion that I would be very glad to talk about offline in this model randomization doesn't accomplish anything yeah Joe so I mean is there a risk if the Tau gets really long that like people won't want

to submit trades early in the time period because they might be sort of stale by the time the the batch auction actually yeah you're allowed and this I think is kind of an important practical detail you're allowed to freely cancel your order whenever you like so if you want to if you want to submit an order let's say the the batch interval is one second which is you know eternity um and you submit an order and then 990 milliseconds into the second some news comes along it makes you change your mind what price you want to offer at you can adjust your quote um freely cancel freely modified any moment in time you can't you can't confuse the market by sending a message canceling it sending it canceling it and

having that all get disseminated publicly so that's part of why information gets disseminated in discrete time is to not open up scope for gaming with non-actionable orders that if because if I if I release an order to buy a lot and then cancel it at the last second and send it in order to sell a lot that's just trying to that's like manipulation that doesn't accomplish it so when you say you can't is that kind of from a tradify like it's a legal standpoint well in this in this design they're just information doesn't gets disseminated in discrete time so if I submitted that order and then cancel that you wouldn't see that I'd done those things they weren't at any point to and also yeah it is illegal to to purposely try to manipulate the market and I think

there's good reasons that we have those laws but that's another longer conversation um I think a lot of a lot of Trad Phi rules and regulations were just discovered in for good reasons and crypto is discovering those rediscovering some of those principles um slowly like a big issue in these like freaking batch auctions like because like you have to random if every all the bids that come in during the same time block you have to you're randomizing prices it's like randomizing not randomizing which of those get filled yeah but keep in mind that in most milliseconds very there's not going to be a burst of activity in most milliseconds or most seconds even

um but yeah you if if there were if there was a need to break ties you could break ties Pro rata you just wouldn't break ties based on time priority so I think you're absolutely right I don't think of it as a big issue but you're absolutely right that there might be a need for tie breaking let me talk to you about the quantification paper and I'll try to go a little bit more quickly through the I have fewer slides for each of the other papers when I go through them a little bit more quickly all right so this paper this is Joint with researchers who at the time were at the UK Financial conduct Authority Mateo aquilina and Peter O'Neill and it uses a new kind of data you know to measure latency Arbitrage in a way that hadn't previously been doable before it's called message data

it's a limit order book data like we used in the previous study and that's widely used in financial research provides a complete play-by-play of the limit order book it's great for lots of studies but what it doesn't have is if Tim and I are racing to pick off a steel quote and Tim wins and I'm a little bit too late it doesn't have the fact that I tried to get that trade and just missed because I'll get bounced back with an essentially an error message or if I was trying to get out of the way of Tim Tim picked me off and I just missed canceling limit order book data won't have that I just missed because I'll get i'll get bounced back with kind of an error message you're too late to cancel um so the simple Insight of this paper is

that these failure messages these attempts to trade that fail are really good empirical signature of the fact that there was a race going on because races have winners and losers limit order book data you see that someone traded at 12 but you don't see the three other people tried to trade at 12 and just missed but there are computers keeping track of this stuff so we we kind of subpoenaed and it's the wrong word but we use regulatory muscle to get get this full back and forth message traffic between Market participants and in this case the London Stock Exchange but only the regulator has that data like the the Traders themselves besides their own rejections the Traders themselves would see their own rejections The Exchange keeps it but more in an audit Trail

like they keep it to audit in case something is disputed but they did not keep they weren't keeping it in a user-friendly format and I don't think that was to make our lives difficult as researchers I think this data just isn't studied very much unless there's a a need to audit it but it's really great for studying high frequency trading so that's so we we were the first to to my knowledge first ever to really study it um so we we got message data from the London Stock Exchange um under a formal request uh nine weeks of message data for the whole UK stock market from fall 2015. uh with millionth of a second level uh accuracy this data allows us to directly quantify a lot of stuff I was super interested in quantifying for a

long time how often are there races how long do they take how many participants are there is the are the winners and losers pretty concentrated how much is it worth overall um so here's a visual of how a a stock exchange architecture is fairly typical of how how it works a Trader would send a message to The Exchange so I want to buy 100 shares at 12. it passes through one of a bunch of gateways on its way to what you think of as the exchange itself which is a sometimes called the matching engine the matching engine would do something like add this order to the book or execute this order against the resting order and then send messages back to that

participant saying like oh you just added an order to buy 100 shares to the book at 12. and it would also send messages back to public data fields like there's a new order to buy 100 shares at at 12. and we grabbed all of the message data just outside of the boundary of the exchanges uh exchanges systems on the way in and on the way out so we could see for example if T1 T2 and T3 were all trying to trade the same hundred shares of 12 at very close to the same time we'd be able to see that in this data the way we Define a race is we we look for cases where there are multiple participants same symbol same price and same side of the market so you know buy it 12 or or cancel my offer at 12 where

there's either a mix of offers to buy and attempts to cancel or just a lot of offers to buy where some succeed and some fail all at quote the same time and of these the first three are kind of empirically trivial to Define we do some sensitivities around each one the same time is harder to define empirically because you know the theory model there's such a thing as the same time you make time to screen you analyze what happens at the same time in data no two things happen at exactly the same time so the main approach we look we look at what I'll show you results from is two events are said to be two messages are said to be at the same time if they're sufficiently close together in time that the second couldn't possibly be a

response to the first just because the first didn't have enough time to kind of make the round trip and that that that's about 200 millionths of a second um as you'll see the modal race is really five to ten millionths of a second so the modal race is much faster than even that so here's the main results of the paper first of all Races are very frequent for large cap UK stocks about a race per minute they're fast the modal race lasts between 5 and 10 millionths of a second so that's a what is a you blink your eye it takes 300 000 millionths of a second it's really really fast um this was kind of astonishing to me so over 20 percent of the UK stock market this is back in 2015 was high frequency

trading races so that just kind of pause for a moment on that a huge fraction of the mark of Market volume is trading races race participation is very concentrated the top six firms uh win over 80 percent of Races they also lose over 80 percent of races which makes sense given the Mile right we're kind of racing I win sometimes you you win sometimes the top firms are also disproportionately aggressive so they're disproportionately taking steel quotes and this relates to Tim's question earlier it's actually fairly frequent that the guy being sniped isn't as fast as the guy's doing the sniping I don't see identities just to be clear but we can track if it's the same firm over time all anonymized races are small per

race so the average about a couple bucks half a tick but because it's 20 percent of volume it adds up so there's a couple different ways to quantify what it adds up to um one is to use um and for those of you interested in this area I really point you to this part of the paper is to use empirical Market microstructure decompositions of the cost of liquidity in financial markets we augment those to add sniping and sniping is about a third of the of the of the decomposition of of the sources of the cost of liquidity um in and this is in traditional financial markets so if you uh and I can if those of you who are interested I can point to the relevant references and

relevant part of the paper afterwards but sniping's about a third of the of the source of the bidesque spread uh in in this market you can also do some kind of theory based in Purex and ask well if you used a different Market design that didn't have sniping so specifically if you use frequent batch auctions how much lower would the Market's cost of liquidity be and you have to take into account that as you narrow the Market's cost of liquidity that's a good thing but that also is going to increase adverse selection as kind of an endogenous response and that's a 17 reduction uh in the markets uh cost of liquidity and then it adds up to a lot of money

it's about a half basis point tax on on trading volume which adds up to about five billion dollars a year in in stock markets alone so if you extrapolate to bonds far you know Foreign Exchange futures markets options like you get five billion is already real money as they say and you get to significant dollars per year after extrapolate the bonds don't trade in continuous order books normally right some do some don't um so you mean treasury Bonds in the US do some other bonds don't it's it there's a lot of there's a wide variety of of Market designs um so I I want to talk about the magnitudes

in this study for just one slide which is there's a sense in which there the magnitudes are huge and then there's a sense in which the magnitudes are tiny I think both are sort of true um the cost per transaction is actually pretty small like a half basis point tax on trading is not exactly a five alarm uh fire but the sums as a whole are large like a third of the cost of liquidity is kind of massive five billion dollars per year just the stock market not even counting all the other asset classes that trade this way I mean take an npv of 5 billion a year you can get the big I mean that's that's a lot of money you kind of have a concentrated dispersed Dynamic I've been reading a lot of political political science and political economy lately where you have

this small group of participants that make a lot of money from this issue this issue is existential to those participants and the issues sort of at the expense of a larger number of Market participants who don't care about it so much so it's kind of the dispersed in the language of mancer Olsen when we talk about the question of Will the Market fix the market and I'm going to do this paper very quickly and then talk about is papers now coming on the Journal of political economy and they'll talk about the flow trading paper and then I will wrap so Market design research usually focuses on designing the best possible Market mechanism for a given problem and what we're going to study in this paper is a different kind of complementary question I suppose you actually have a good Market design for a given problem you know researchers

have already done that part of their job will it actually get adopted by the private private sector what are the private incentives for stock exchanges to adopt in this case frequent batch auctions do this is an innovation Innovation and Technology adoption question do the private incentives uh Financial exchanges align with what's socially best for the market Will the Market if you will fix the market uh the way we study this this question is we with a model it's it's very closely tailored to the institutional details of of modern electronic Financial exchanges so the the players are your exchanges trading firms and form Traders and uninformed investors

exchanges choose their Market design and then set prices for trading and also prices for accessing their exchange quickly so for what we call speed technology the trading firms decide whether to buy this speed technology and then all Market participants play a a trading game kind of like in the in the previous paper and we take the regulatory details of of modern Financial exchanges quite seriously in this paper in particular stocks are fungible across exchanges that's an idea called unlisted trading privileges and then the frictionless search and information provisions in regulation National Market System in the U.S stock market the first thing we do is we study what we call we think of as the status quo

the game in which all exchanges use the continuous submit order book design in equilibrium of that game trading fees are perfectly competitive where exchanges are able to make some economic profit is from selling speed technology and the intuition there is that if I charge a high trading fee and you don't that an investor choosing where to trade can just go to the market without the fee so if Uber charges a much higher price than Lyft you can go to Lyft um but now if there's a speed sensitive trading opportunity on NASDAQ NASDAQ kind of has a monopoly over selling fast access to that opportunity so it can charge a price for that that does not get competed away in equilibrium and this aligns very closely with facts that

we document in this paper SO trading fees in the U.S stock market are very competitive they're as close to Bertrand competition as I've ever seen about .01 cents per share per side traded so at 100 stock one percent would be a buck a basis point whether it be a penny it's a hundredth of that so trading fees are really small in the U.S stock market but the speed technology fees are pretty significant they're over a billion dollars a year and they've been growing uh pretty quickly we then study sub games in which there's some adoption in which one or more exchanges adopts the frequent batch auction design the first result is because of the frictionless search if there's one adapter it actually wins a

lot of share when in any equilibrium it wins share and earns profits because if I make a better market like let's say I launch a let's say Lyft has better prices than Uber and you're regulatorily required to check both which in the U.S stock market you kind of are then lyft's going to get a lot of share from Uber um so it's not a chicken and egg problem but then the second result is that if there are multiple adopters of this better Market design then the the design kind of wins but the exchanges are back to brutal Birch Run competition but now they've blown up their ones one good business which is selling Fast Access because the market is less less speed less speed sensitive and then

so a third result is that there exists an equilibrium in which the incumbents stay at the status quo Market design just keep the market continuous keep earning the billion dollar billion plus dollars a year of a speed technology right it's kind of like a cooperation in the repeated prisoners dilemma this analysis then has a lot of policy implications which in the interest of time and just given the crowd I'm going to skip just to get to the next uh to the next uh next paper there's actually been a lot of positive policy progress in this on this topic recently uh the Securities and Exchange Commission for those of you interested is proposed to have auctions be a large part of the way retail investors in the United States uh trade uh trade stocks I wrote a detailed

letter about that it's on my website if you're if you're interested all right last thing I'll talk about in the last five minutes or so is um the idea of flow trading with uh this is with Pete Kyle and Peter Crampton Mina Lee and David Malek so we figured out a way to take the batch auctions idea to the trade of um arbitrary portfolios of assets where what we mean by a portfolio is an arbitrary linear combination real valued positive or negative weights on assets this allows you to encode compliments across assets substitutes across assets and it allows you to encode portfolios it allows you to encode Arbitrage I want to buy acell B if their prices get out of line portfolios and Arbitrage are at

the heart of finance and we we're excited because we figured out a way to trade trade portfolios directly and engage in Arbitrage strategies directly this in particular one thing I'm excited about is it builds a solution to the correlation breakdown problem directly into the market design because rather than waiting for X and Y to diverge and then having a batch auction to compete y back to X or vice versa you can just submit an order to The Exchange I want to buy xly whenever their prices diverge and that's like a string that ties their prices together prevents them from diverging into the first place and to accomplish this we had to marry the F the frequent batch action design to Prior work by Pete and Mina that

proposed the idea of smooth trading they figured out a way to using downward sloping demand curves to express requests to trade as a flow over time so instead of I want to buy 100 shares of apple I want to buy one share of app up to one share of Apple per second and at most 100 shares total and if you think about the way large institutional investors trade they trade gradually over time using sophisticated trading algorithms this builds in what they want to do already directly into the uh into the market designs you could for example get the tiwap the time time weighted average price like quite uh quite directly with our with our design uh this is some of the mathematics and

in the paper I'm going to go through the I'm kind of I'm running very low on time so let me just kind of go through this go through the highlights of this very quickly a portfolio is a just a vector of portfolio weights that lives in RN where n is the number of assets where each way could be just a real valued positive or negative number um you can make a market by with two portfolio orders one uh that are that are the positive and negative of each other and the way you would Express demand is with two limits we call lower limit and an upper limit where the economic interpretation is if the price is the lower limit or better trade at my full rate so if I want to buy say two portfolio units per second trade all two of them if the price is at my upper

limit or Worse trade zero and then linear interpret interpolation in between those two uh those two limits and there's a maximum execution rate and a cumulative uh quantity to be executed um this is the math of one one portfolio order um Eric yes should I think of this as kind of your shooting for a maximum expressivity subject to computational tractability or yeah what we get in this paper is we get we get something pretty expressive they think is expressive in a way that's quite useful for finance right you can express portfolios Arbitrage you could do customized ETFs your ETFs are a huge fraction of the U.S stock market and they they're expensive they cost

investors on the average 20 basis points and you could build your own ETF directly with our language it could be a long short ETF built directly with our language so it's very expressive not arbitrarily expressive and that's going to help us get existence theorems and then computational results so we think of it as a sweet spot it's a pretty good language that has existence results and computational performance and I there's no theorem I can say that it's the best such language but I really like it so it's that's that's short of a theorem but it's a genuine it's a genuine I guess biased economic view but that's the way we're thinking about the paper is that expressiveness existence computation so hopefully a sweet spot among those three

um this is what I just told you about in the previous slide just in math let me skip it in the interest of time the market clears um jointly across all and assets so we all submit our orders to to trade individual stocks or portfolios or long short arbitrages or whatever um at any moment at any moment in times like let's say the Market's clearing once per second the market has to find prices for all say 500 Assets in the market and this is the math that expresses that idea where the markets if there's a demand an excess demand Vector over all the assets in the market the goal is to find prices such as the excess demand Vector zeros out

um so you know D of pi equals zero this is n equations and where the ends number of assets and unknowns were able to prove that prices exist that clear the market and then we're able to find them so this is the just a kind of the existence theorems you know the con formulate the problem as a because the demands are linear you can think of it as a quadratic objective function that then has a derivative that's linear and that lets us use ideas from quadratic programming to to State and and prove existence theorems that for the Existence and uniqueness of optimal quantities in the existence of Market querying prices and the proofs are actually relatively straightforward they use math I I didn't previously know

math and quadratic programming and convex optimization but it's it's math you can learn from textbooks and we're able to have and in the end like pretty succinct uh pretty succinct proofs second theorem one and two basically convex Duality or yeah yeah it's very much um yeah Primal it's it's Duality for a quadratic program that's right um and why did why did this work and I think if you think in terms of quadratic programming like yeah it kind of works but the reason why I was so surprised that it worked is that there's so many negative results for existence of prices if you have complements and this language lets you have compliments because you could say I want to buy I want to buy a and b together as a portfolio that's like a form of

complementarity uh and GE Theory and in the division indivisible Goods literature complements make existence and computation really hard think of all the work Paul milgram's been doing over the last several decades um the existence proof here is pretty simple why is that if you go through the proof we're taking advantage of a bunch of features that are not present in other Market design problems with complementarities the goods are infinitely divisible we're treating Goods as infinitely divisible you could take a share of stock and you know cut it into divisible slices the portfolio demand schedules are restricted to be downward slopings or piecewise linear demands the utility for each order is only

defined on the line segment corresponding to that specific portfolios it's not really your utilities zero off diagonal it's not defined off the diagonal all the quantities are bounded and then the the key limitation of the language to Tim's question is I can't link what happens in this order to my preferences in that order so I can't for example say buy whichever of Apple or Google has a better price than the next batch you know relative to my value I could say I want to buy a portfolio of half an apple and half a Google um I only want to buy it if the portfolio is this price or lower but I can't say buy me whichever of these two is more attractive given my preferences so there's some there are limits on what I can express with this language and as

you think about like okay there's some real things you can't express and then there's some limits um so we think of this as hopefully a sweet spot this is the conversation Tim and I were having a few moments ago we can compute prices quickly um using what are called interior Point methods let me skip the details just I'm already over time let me let me pose a couple open topics that I think connect this this whole agenda to some topics in crypto put those up and then I'm happy to chat as long as as long as you have questions or over coffee about about anything you like so here are a couple a couple of research topics I'd love to see in crypto markets that relate to this agenda and financial exchange design and high frequency trading so first of all quantification so someone should do the

study we did with the uh with the UK data for crypto markets and I I bet you you'd find that sniping is a massive percentage of volume and a massive tax on trading we're talking at lunch about how there is um Mev that relates to the reordering of transactions within a batch which is kind of crazy that you can do that in a financial market like just well I'm going to rearrange your orders to extract extract value from the Traders like that that's that's Whoever thought of that's kind of it's kind of an evil genius very clever um and then you also can quantify it as a percentage tax uh tax on trading um and I bet you that would be large too

we found half a basis point I bet it's much larger uh in crypto markets and I should have said there's the reordering and then there's also just the price on coinbase changes and that leads to sniping on uniswap maybe that's massive too so a lot of information design questions and exchange information policy of exchanges that I think would be very interesting to study as I alluded to Reg nms in the U.S stock market Engineers this very brutal price competitions very efficient for the market it limits the magnitude of within stock Arbitrage crypto markets don't have these limits that might be a good way to study these these matters of information policy um so I think that would be a great a

great study to do and that as a result also I bet there's lots of within symbol Arbitrage and then the last the last couple of studies I'll I'd point to so what one is implementing frequent batch auctions in crypto markets I've been a technical advisor to cow swap um and they're doing a multi-asset um a multi-asset back Junction exchange it's kind of inspired by the flow trading paper a difficulty they face and I think crypto markets face more generally is a kind of philosophical one of a lot of auction design takes advantage of quasi-linear preferences over stuff and money money is a numerator good like a US dollar but crypto markets are hesitant to declare a

new Marie or good because I'm not going to get into the philosophical debates but it makes the math a lot harder and then they have this kind of decentralized solver competition which is kind of creative I think that's interesting to Think Through the economics for a centralized exchange adopting fbas and whether they face these kind of Will the Market fix the market perverse incentives and then there's a lot of uh research around minor extractable value that I think is very interesting to study very similar to the the data and co-location economics we study in the Wilder Market uh fix the market paper there's the quantification of the of the dollars in the tax um there's the question around exchange design to counter Mev

um so fbas would would certainly do it I wonder if there are other complementary ideas and I think a really interesting open question is protocol design uh to counter Mev and the fact that you can rearrange transactions and time to to steal or extract money from the transactions is sort of crazy it'd be really interesting to think about a protocol a more abstract level than just finance that solves the Mev problem um let me stop there thank you for your time and attention glad to glad to chat further take any questions you have thank you for the flow trading you have to eventually approximate prices down to like a penny right does that lead to like does that approximation of the optimum lead to

issues so you said like a penny as if a penny is small in financial markets a penny is large and we can get we can get prices down to on the order of millions of pennies and so then economically it's not very important and then computationally um no computate it's not it's not a hard computational issue either but it is important just to I went through this very quickly right it is important in the if you think about how stock markets work my critique is of the time being continuous and I want time to be to screen instead another critique and this is more impedance Mina's prior work is that another issue is that prices are very

discreet prices come for example in the U.S stock market in pennies and it would solve a lot of issues if it would it would simplify simplify a lot of complexities if prices were more continuous um so in the flow trading idea is kind of flipping the sign on both of those instead of make instead of time discrete so instead of time continuous price is discrete we have time discrete and prices continuous also quantity is continuous and practically you could I mean it would take some regulatory action but practically you could easily trade millions of shares and really and in in millions of pennies well would that mean like the banks would have to settle trades at like it's like millions of pennies millions of pennies of the

yeah that's not that's as a that's just not hard that's a but yes and because you banks are really good at multiplying numbers together and and then rounding if you're at the end of the day if you round to the nearest Penny been and then no one's doing the Superman scam that's uh we're I think we're that's gonna be fine um yes so on the first point I forget the details of everything about how cow swap works but um look at this you mentioned two things already that are important one is using a different mechanism by using this sort of batch clearing another is the competition which I assume is important but then also this kind of isn't there

like a different isn't there information hiding right isn't stuff like not going through the public Med pool instead this kind of you know being hidden from other people to see so I was curious like what do you think is driving which of these is the most important do you think uh it's a great great question um yeah so Cal swap I mean again I I've been I've been a technical advisor to them yeah they try to again if you put orders in the mempool that's very snipeable they're trying to avoid that thank you for for bringing that up um the the reason so they have them this like multi-asset batch auction design which I think is pretty clever the solver competition idea is because

it's it's kind of it's part philosophical and it's part practical um which is that the the philosophicals well we don't want to you know we you don't want to have a centralized Authority saying what the prices are which to me like I you know I I have a philosophy major from undergraduate I philosophically disagree with that but that's okay we're good um I have nothing against exchanges saying what the price is as a function of clear rules but the more practical difficulty is that a lot of the pricing data is external to cow swap because it's you know pretty small so a lot of batches are found by taking some orders that come into Cal Swap and combining them with with orders or

liquidity on other on other exchanges and kind of doing a like a grand batch if you will between cow Swap and you know uniswap Sushi Swap all the other different places all the other swaps out there um where you can all wear all of those so the solver competition is a way of of taking inside information and external information where like computationally it'd be hard to design The Exchange that takes in all of the external information without like a reg and a mess that says what the external information has to report to you so the solver competition is a way of dealing with that um with that incompleteness so you can imagine castlev saying here's the best

exchange only trade and if you could do better than that bringing in external liquidity um that's the solver competition that's an effect what they're doing with some like we call them Envy freeness constraints um it's it's been it's a pretty neat a pretty neat design I like no I don't I don't want to get into a plug of I want to plug my own research not it's not it doesn't feel appropriate for me to plug Castle but I really like what they're doing um all right thank you [Applause]