Episode #77 Robert Almgren – A Deep Dive into Optimal Trade Execution in Fixed Income and Futures Using Quantitative Methods

 

Robert Almgren is the Chief Scientist and co-founder of Quantitative Brokers. Rob was previously a professor of mathematics at the University of Chicago, the University of Toronto, and currently teaches High-Frequency Markets at Princeton University. Prior to QB, Robert was a Managing Director and Head of Quantitative Strategies in the Electronic Trading Services group at Bank of America until 2008. Robert Almgren completed a B.S. in physics and a B.S. in mathematics at MIT, then an M.S. in Applied Mathematics at Harvard University. He holds a Ph.D. in Applied and Computational Mathematics from Princeton University. 

In this episode we nerd out a bit: We get deep into the weeds of optimal trade execution, particularly in Fixed Income and Futures markets. We talk about the history, theory, and practice of minimizing trading costs by minimizing slippage in fixed income markets. We learn why trade execution is an important topic to think about, how to measure optimal trade execution and what research is done to further improve it. We dive into the ideas of the quantitative models and methods used and get some tips on where to learn more about the increasing quantification of financial markets. 

Links

https://www.linkedin.com/in/robert-almgren-31303147/

https://en.wikipedia.org/wiki/Robert_Almgren

https://quantitativebrokers.com/our-people-bios/robert-almgren

 

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EPISODE 75

[INTRODUCTION]

[00:00:04] ANNOUNCER: Welcome to The Wall Street Lab Podcast, where we interview top financial professionals and deconstruct their practices to give you an insider look into the world of finance. 

[00:00:23] AVH:

Hello and welcome to another episode of The Wall Street Lab podcast. With me today is Robert Almgren. Rob is the Chief Scientist and Co-founder of Qualitative Brokers. Rob was previously a professor of mathematics at the University of Chicago, the University of Toronto and currently teaches high frequency markets at Princeton University.

Prior to QB, Robert was a managing director and head of quantitative strategies in the Electronic Trading Services Group at Bank of America until 2008. Rob also completed a Bachelor’s in Physics, a Bachelor’s in Mathematics from MIT, and then a Master’s in Applied Mathematics at Harvard. And he also PhD in Applied Computational Mathematics from the University of Princeton.

So today, I’m really happy I get to put in my master’s work into practice, and really geek out with Rob about optimal trade execution. Rob was the offer of a fairly well cited and interesting paper called Optimal Execution of Portfolio Transactions, and we’re going to get into all of that a bit in the show.

[INTERVIEW]

[00:01:38] AVH: Rob, so cool to have you here. Welcome to the show.

[00:01:41] RA: Hi, good to talk to you. Thanks for having me.

[00:01:44] AVH: Let’s start a bit with QB. What’s Quantitative Brokers? Can you quickly talk about why you started the company? And what is it actually what you do?

[00:01:54] RA: Sure. So, the background of this was my partner, Christian and I were both, as you said, at Bank of America and electronic trading services, doing – well, Christian was doing derivatives. I was doing algorithmic execution for equities, which was a big thing back then. This was in – well, it was a long time ago, 2005 to beginning of 2008. What we realized was that, actually, I have a vivid memory, I went to see a client and the client said, “Why are you doing equities? Equities are a solved problem. I have no problem executing in equities. My problem is interest rate products, bonds. Can’t you do something for interest rates?”

So, we thought about it and realized, yeah, what the world needs is ways to execute efficiently and to measure transaction costs for interest rate products. So, we set out basically to do that. It turned out to be a difficult time to start a company, 2008. But we knew it was the right thing to do. So, we kept on with it and eventually became what we are today, which is pretty successful. Our mission is agency algorithmic execution in futures and interest rate products. We started out with futures on interest rates, that is CME, euro dollars, and treasuries. And then we expanded interest rates and other exchanges, euro expert, [inaudible 00:03:12], and then by customer demand, we expanded to all the futures products on the exchanges that we cover, and we also now do us cash treasury security, which is actually a much larger market than equities, but people don’t know about it.

The mission, as always, is to do optimal execution, algorithmic execution, and to give clients tools for measuring their execution cost models and knowing what constitutes a good trade. What we found was that at the time, in equity markets, people were used to thinking about slippage and transaction costs and the cost of portfolio rebalancing. But in fixed income, they just were not used to thinking about that at all. It’s just as important there as in equities, but people are not doing. Now, we help them to do it.

We’re now active on, I think, all the major futures exchanges around the world, North America, Europe and Asia. We have offices in New York, London, Chennai, India, Sydney, Australia, and even, I think, in Singapore. Yeah, we trade nearly 24 hours a day on all these products. We’re pretty proud of what we’ve been able to do in this space.

[00:04:24] AVH: If you think about our long market state, in 2008 there was still nobody focusing on trade execution for interest rate press. But let’s maybe start with what – if you just very easily could describe what makes trade execution? What is it? Because usually how, and I’m purposely oversimplify, you send it, try to exchange, you get your shares back, like you have to own the rights of the share, which is then with the custodian. Why is there a whole company focusing around execution of trade?

[00:05:03] RA: Sure. So that would be true for you as me as individuals. If we want to buy 200 shares of Tesla or something, sure, we’ve just hit a button that goes to the exchange or it goes to an internalized or something and we get a quick throw back at pretty good prices. But if you’re trading 200,000 shares, then there’s not going to be enough liquidity there. You’re going to have to wait, you’re going to have to space the trade out across some length of time. As you do that, people will guess what you’re doing, you’re going to consume liquidity, you will push the price. And consistently the price that you receive on your sale, or that you pay on your purchase will consistently be just a little bit worse than what you thought the market price was at the time you sent the trade.

And across a lot of trading, this adds up. So, we have a slogan, “A penny saved, and execution is a penny gained and alpha.” So, obviously it doesn’t replace doing the right decision. Whether buying Tesla is the right thing or wrong thing to do, we have no opinion about it. But if you could save a few pennies every time you do that transaction, it wouldn’t make material difference to your final investment, bottom line. Imagine that you’re an investment manager and we have examples. We did a study a couple years ago, where a fairly active futures manager just by switching from different execution venue to using QB, the difference in slippage cost was equivalent to 77 basis points in annual return. They were pretty high turnover fund.

[00:06:30] AVH: You said, pretty high turnover fund. Who are the people that usually really, really deeply think about the things like slippage costs, ultimate execution. I had a conversation with Dan Houlihan of Northern Trust Asset Management. He said, a lot of the asset managers, they outsource trading, because it’s not a core function anymore, because they focus on asset allocation on stock picking. I guess, you do exactly the opposite, right? You’re probably working with either the –

[00:07:02] RA: The outsources the dots. Yeah, that’s absolutely correct. So, the asset managers should be spending all their time thinking about asset allocation about what to buy, what to sell, making sure their portfolio is at every moment, the optimal by whatever criteria they have. They should not be thinking about how to execute.

So historically, what would happen is large buy side firms would have internal trading desks to a portfolio manager would sit and come up with his list of trades. He wants to buy this and sell that. He would send it to an internal desk that would work it through the market. So, those internal desks would interface maybe with the exchanges, maybe with external brokers. For example, Bank of America when I was there.

So, the argument now is they would outsource it to us, because this is all that we do. All that we do is take the trade work through the market, and we live and die by the slippage relative to whatever the benchmark is on that order. We’d like to say that our ratio of quants per product is higher than an internal buyside desk because we do nothing else and we aggregate flow. What I mean, is we don’t aggregate the flow in the sense of putting it together, but we offer our services to a large collection of bite sized firms. So, we’re in a position to really collect a lot of information about what works in the market and what can save cost for those clients.

[00:08:28] AVH: You do the actual trade execution. An asset manager sense this is the stocks, I want to sell the stocks. No, not stock. Sorry. This is the future that I want to buy or sell. And then you really go to the chair and like do the execution.

[00:08:44] RA: Exactly. So, we’re totally electronic, we’re zero touch. They don’t have to make a phone call. We’re integrated into their system. They send us an electronic fixed message, our algorithmic servers are proximity hosted at the exchanges, we have direct connections, or depending on the relationship, we’ll go through their clearing firm, but preferably a direct connection, and we just send the limit orders and market orders to the exchange on behalf of the client. We don’t clear, it’s not even a give up. I mean, we’ve never owned a trade, we act as though we are the client. And then as I say, we live or die by the quality. So, we provide very detailed statistics on what trades we did, what the slippage was, we’ll show them every single limit or market order that we sent to the market, and why we did what we did. Our slogan is, it’s a white box, not a black box.

[00:09:31] AVH: Interesting. I really want to dig into that. We show them what we did and how we did and all that. But before we do that, I’m curious on why did nobody think of that in fixed income, in futures, and why was this prevalent in equity? Because we all kind of know the income, the fixed income market is just so much better than equity markets, right? Why was there no history of doing trade execution for futures?

[00:10:02] AVH: So very rich and interesting question. Part of the answer is, there didn’t always used to be such a focus in equities. So, when I was beginning to learn about financial modeling and trading, the big name was ITG. So, this was in the 1990s. And they, in my mind, were the ones who really introduced sort of systematic execution, quantitative modeling of execution and equities. Before that, there were academic studies about cost of trading, but there wasn’t really an industrial way to do it.

So, it didn’t always exist in equities and there was this best execution mandate, that the SEC handed down that firms had to have some procedure to document how they executed and they weren’t too specific about what they should do. But there were they had to do something about best execution.

At one point, I looked back through the history of this, and you would find statements from the SEC saying, “Look, guys, when we said best execution for securities, securities doesn’t just mean stocks, it also means fixed income.” So, they’ve been pushing for that to happen for a long time. Another reason that it took off more quickly in equities than in other markets is, I mean, in my somewhat perhaps biased point of view, equities are pretty boring. Every stock is kind of the same thing as every other stock, it doesn’t have a term structure, it doesn’t have coupons, it’s not too closely related to anything else. So, problem is somewhat cleaner.

If somebody sends you an order for a stock, they know that the hit rate on investment decisions is pretty low, it’s pretty hard to eke out alpha. So, these little differences matter of odd and it’s pretty straightforward to focus on slippage in stocks, because the products are so simple. If you go to the bookstore, and you pull down a book on quantitative trading of fixed income products, what you’re going to find is a lot of discussion about coupons and day count conventions and yield curves and depending how sophisticated that book is, the stochastic dynamics of the yield curve, how many degrees of freedom that has. There’s a lot more things to worry about, and to some extent, not inappropriately, but people who are interested in those markets spend their time thinking about those issues, rather than the nuts and bolts of how they trade through the market.

But it’s just as true that a penny saved and slippage is a penny earned and alpha. So, assuming you’re on top of all the yield curve, and stochastic models and so on, you still would like to save some money when you actually go to the markets. But it’s less obvious because there are other things going on.

[00:12:41] AVH: And that gets also in futures, by definitely should not. In interest rate derivatives, you have a high over the counter part where the trading is actually happening, where trade execution in like, especially quantitative trade execution, is by definition can’t happen that well.

[00:13:03] RA: It depends which part of the fixed income market you’re talking about. So that certainly has traditionally been true for products like corporate bonds and muni securities, very much over the counter. So, we don’t target those as QB. We talk only about interest rate products, which is US Treasury securities, hopefully, at some point, European ones and futures on those products. So, futures are very electronic, very liquid. They’re not faded over the counter. I mean, there are block trades, but there are small and decreasing part of the market. If it’s an over the counter market, you can’t do algorithms and we also found some some great quotes. I found some quotes somebody said, “It’s like no, and fixed income markets, it’s really more about the quality of the execution and the actual price that the customer paid.” He used to read that stuff. “What is he talking about?”

People had different points of view. It’s a cultural difference between equity markets and fixed income markets. Customers didn’t have any alternative. So, they just had to go with that, so we wanted to offer them an alternative.

[00:14:08] AVH: I’ll be interested too, you mentioned slippage. And just to quickly define, please correct me if I mistakenly have that wrong, but slippage is basically the price you basically see, you think, you’re going to execute to the actual average price to get because you have such a large trade that you actually move the market. That’s slippage. What other factors are there? So, in the abstract of your paper, example, you talk about minimizing a combination of volatility risk and transaction costs, and what other factors constitute a bad execution from a good execution?

[00:14:46] RA: Your first sentence of what you just said exactly hit it on the head. So, slippage by definition is the difference between the actual realized price that you got on the trade when all is said and done. Compared to what you thought you were going to get on the trade, which usually the most popular benchmark is in an arrival price benchmark, which is the bid offer midpoint at the time you make the decision to trade or at the time you submit the order. Everything that happens between that and the final execution is slippage.

So, that may be for example, the fact that your trade is so harsh that it pushes the market. It may also be the fact that you were lucky or unlucky and news came out and move the market, in your direction or away from you. It also includes the fact that presumably, you are buying this asset because you believe it will go up. And when you buy it and it starts to go up, that will cause you to get a worse price because other people have the same idea.

All of those things go into slippage. The reason that I emphasize that is you can consider various other forms of it. So, I mean, at various times, I’ve explored things like you correct for the beta relative to the market. You say I’m buying a stock, but let me subtract beta times the motion of an index or something. I look at, you can also talk about slippage relative to whatsoever legitimate benchmark is VWAP or TWAP, which is the average price over an interval. So, you could talk about the execution price relative to that. I say that only to say that really, that numbers slippage is the be all in the end all of what you want to mock.

Now that said, what goes into that number. So, that number is you do a thousand trades, and you get a sample collection, and that has a sample mean and a sample variance. You may want to design your algorithm to reduce not only the mean, but also to have more consistent performance. So, it may be a tough sell to an asset manager, if you say, “Look, I saved you three basis points on average. But in exchange, you now have a percent and a half standard deviation around your result.” You may say, “Look, I can’t rely on that, because I understand what you’re saying across a year and a half of trading, I’ll save some money, but I want more. I want more productivity.”

So, it’s usually worth a little bit of cost and expected value to reduce the uncertainty. And certainly, you want to reduce outliers, you don’t want surprises to the downside. I say all of that just to say that in that single number slippage, it has a whole collection of statistical properties that you can tune. I also emphasize that number to say that, if for example, you send us an order to buy something, and the price moves up sharply between when you send it to us and when we complete the order, we would include that in our statistics. We’re not going to say, “Well, nobody could have anticipated that the price would move, therefore, we’re not going to count that one goes into the statistics, and we should have reduced the risk exposure.” What I mean, is all of those numbers go into average slippage and there’s no excuses, no things that you can exclude. We don’t apply correction terms. There’s some sort of abstract. It’s just what was the execution relative to the benchmark?

[00:18:07] AVH: Let’s try to pick this apart bit by bit, because I think like there were a lot of terms that for the average listener, and what insight, and you set push the market, for example. And please, again, correct me, push the market especially if you hit a bid or an ask, and then the first order is like 500 shares, a thousand. You move up and up and up and up and up, right? The order book, is that you’re pushing the market, because you’re like taking up the entire order book and then how would you define pushing the market?

[00:18:45] RA: So, that would be one form of pushing the market. That would be what’s called a sweep order. Certainly, if, as you said, I think you said there’s 500 on the inside quote, and then thousand on the next level quote, if you send a marketable order for 1,500 lots, you will take out the first level and second level. And then just as a mechanical fact, the midpoint price will have moved up by half of that amount. That’s unavoidable. But we would never send that kind of an order.

So, if there’s 500 lots on the inside, we would only take maybe 100 to 200 at a time. We will also be posting, so let’s say you’re a buyer. The whole game in trading is to try to conceal your intention. We may know that you’ve sent us the order, this order must complete within the next half hour or you get fired catastrophe. But what we want to do is it’s like the analogy is you go to the market in some casual market and there’s a piece of silver that you like. You don’t tell the guy, “Oh my God, that’s the most beautiful thing I’ve ever seen. I must have it.” You’d be like, “Yeah. We have much better stuff at home. I don’t really know. I don’t really feel like buying.” Even if you know you must have it, you want to pretend that you don’t really want to have it and that you could trade or not trade, even if you’re desperate to get your trade done in the next half hour, you’re going to post a limit order, because maybe there was somebody else who is more eager to sell than you are to buy. And maybe you can capture that spread.

So, you try to do that. Now, you can’t do too much. If there’s 500 each side and you post 2,000, you’re probably going to tip off the market that you have a big piece to buy. So, what you do is your post, maybe a few 100. And then if that gets taken, you’ll replenish it, but not too quickly. Because if you replenish it quickly, that will tip off people that somebody there is motivated to buy. The moment the market in general senses or guesses that you have an order that you’re trying to do, they will try to walk the price away from you.

So, you shouldn’t think about sending single orders that consume the book, what you should think about is little pieces that consume maybe a little bit of liquidity at a time, that post and try to get filled. But then what happens is there’s a very delicate statistical balance. If there’s a certain balance, maybe across 10 minutes, there are 5,000 lots bought, 5,000 lots sold, you come in with an additional 500. Well, in some sense, you’ve now shifted the balance. So, some of these sell orders that would have pushed the market down or not supported by your limit order so it doesn’t move down. Sometimes you cross the spread and take it out or push it up a little bit. So, there can be a very delicate, the fact that you’ve come to the market with a directional trade unbalances, the otherwise to you, what you assume is sort of random buy and sell, causes on average a measurable shift. But it’s not so simple as just taking out the bid. Taking out the offer. Let’s say you’re a buyer is not as simple as taking out the offers. This delicate sort of imbalance in the general flow.

[00:21:45] AVH: I spoke with some high frequency hedge funds and traders and they kind of described that they would be probably, some of them, or if you read books, like the Flash Boys from Michael Lewis, you get the idea, which is like waiting to pounce on your clients because they know, it’s like, “Okay, there’s this this pension fund or this asset management.” They’re trying to sell a big chunk of Tesla stock and like interest like gone – not not front run. Front run is the wrong word. But I’m going to try to like preset the trade in a way that I’m taking performance, I’m taking alpha off of you. So, you have to kind of look for those predators and try to conceal from those.

[00:22:32] RA: Yeah, so fascinating subject. A couple points there. First of all, nobody comes to the financial markets for the good of humanity. Everybody’s there to try to make some kind of money for themselves off of information that they have. So, there’s an anecdote, I might be misremembering it but where I remember, I think it’s in Flash Boys. There’s a guy who – this is my version of what I remember from Flash Boys. There’s a guy who’s watching Singapore TV, and he sees a notice on the TV that some company is going to get acquired. So, he quickly wants to go send a buy order for 5,000 lots. And as he does it, all the liquidity on his screens, he manages to fill, he’s looking at, say 2,000, on each of six exchanges. We think 12,000 should be able to fill 5,000. What happens is the moment he gets filled on one, all the other liquidity vanishes.

So, he’s like, “This is terrible. I thought I had liquidity, I can’t do my trade.” But look at that from the other point of view. The other side of that trade. The guy on the other side is offering liquidity, assuming that he’s not trading with an informed trader. So, this guy, because he’s watching Singapore TV has special information. He would like to profit from that the other guys are trying not to let a profit.

One time I remember I was on a panel, we were talking about sort of, you know, evil, high frequency predatory traders. I was like, right now, there’s probably a mirror panel, like it a different conference, where there’s a group of high frequency traders, talking about the evil informed traders who are trying to take their liquidity and cause them to lose money. It’s sort of like, I don’t know if you’ve ever watched The Twilight Zone, but you discover that sort of, maybe this American TV show in the 1860s, sort of strange plots. But you sort of discover that actually, you’re the monster in some sense.

Just to say that the high frequency traders are not necessarily evil, what they’re trying to do is offer liquidity. Look, I teach this in my course, it’s all about informed traders, uninformed traders. So, if everybody comes to the market, what you want to do is trade with people who don’t know anything, right? So, you can offer liquidity, you can buy at the bid, sell at the offer. The more you can do that, you make money and people get their trades done. But if somebody comes and has information that you don’t have, you need to protect yourself against that. Markets are also about information flow, just how information propagates.

So, somebody learns information by watching Singapore TV, or whatever, he or she tries to profit from that information in the marketplace. In the course of doing that, the information works its way through the markets because other people are saying, “Oh, somebody is creating that person may know more than I do. Let me try to guess what information they have by watching their order flow and then see if I can profit from that too.”

[00:25:18] AVH: It’s basically like in inside trader, mosaic theory, that you’re probably also aware of. I tried to fuse together, and then one piece in the mosaic is order flow, and then it might tip you off to something, it might be the missing piece that you were lacking. It’s like, I want to buy this company, it seems really good. I’m missing the last link, should I put in the buy order? And then you see somebody else like pushing the market, doing this. Alright, okay, I’m not the only one that seeing this kind of –

[00:25:56] RA: Yeah, I mean, to be clear, I’m not going to defend insider trading. I mean, insider trading is bad. Private information should stay private. But there’s another great anecdote, it’s this guy, Jesse Livermore, who wrote a book. He was a trader back in the 1910s, and ‘20s, in the US, and he wrote about his great experience. He made a fortune, I think, four times and then went bankrupt just as often. Every time he’s like, “I’ve learned my lesson. And now I’ll never do that again.” But there was one anecdote. He said – actually, this doesn’t quite speak to your point. But it’s a good anecdote.

He said, there was this stock and everybody’s an insurance company. And everybody was like, “You should buy this. It’s really undervalued, it’s going to be great. The future is great. You should buy it.” I don’t think so. I think I’m going to short it. And everybody’s like, “You’re crazy. What are you talking about? This is a great company.” He’s like, “Yeah, I just don’t like it, I’m going to short it.” And then that night, there was the San Francisco earthquake and the company had massive exposure and lost a lot of money, and went way down. He made a lot of money and his friends were like, “Wait a sec, you can’t tell us that you predicted the earthquake by looking at the tape of market data.” And he’s like, “No, but I could tell just the way it was trading, people didn’t want to own the stock, it could have reacted differently to the news, based on sort of the market flow.”

But what I’m saying is, so you can get a sense – I’m just talking about it. His thing was just observing the tapes. He said, by observing the tape, in those days, was a tape, literal tape. But you could get a sense of sort of what the sentiment was beyond what people were saying. And so, if you see price support, maybe people have information. I’m not even talking about extra market information, which is what you were talking about. I’m just talking about pure market information. So, basically, if you see a directional trader, you guess that somebody has information, maybe you should join, and you may have no idea what the information is. But you can get online quick.

[00:27:51] AVH: To circle back into optimal trade execution, we talked about all those ways, and like how people try to make use of your information or have a more dark theme of trying to take alpha away from you, or like, even protect themselves. But then, how do you protect yourself against it? You already mentioned, you’re like trying to pick up a bit here or there, and then you do an opposite off the actual trade you’re doing. Suddenly, you want to sell a stock, and suddenly, you start buying a little.

[00:28:26] RA: No, so we don’t do that, for two reasons. So, first of all, as a broker, we’re only executing for the client, so the client gives us symbol side size, we cannot do a trade of the opposite side. The clients buying, we can’t sell for that client. Even if we were trading for our own account, the regulator’s take a dim view of spoofing. I mean, it’s not perfectly well defined. But what you’re not allowed to do in the markets is try to project false information. So, they will come down to you. We don’t do that.

If you’re a buyer, you can’t pretend to be a seller to try to push the price down. But what you can do is if you’re a buyer is you can tread very lightly, and try to conceal the fact that you’re a buyer. So, we do things like put in small pieces with random time intervals at random depths in the book. What you don’t want to do is put your whole order into the limit book at once. because that’ll show up, and you put in little pieces at a time.

[00:29:25] AVH: I won’t even pretend to read the paper, but from what I read about your paper, there is kind of a duality to beat off execution, which has the floss of you make it more visible where you want to go. And then there’s a higher risk of people jumping ahead of you and like taking that there’s a higher risk of moving the market. And then the other hand is like, you’re moving slower, but you kind of obscure what you want to do, and you’ll probably get a better price. But then there’s a higher risk in moving slower. Because, as you said, there might be news, there might be an earthquake, there might be – somebody else might want to do the same trade, because then there’s the second person watching the Singapore news channel. And then she wants to have all those shares, right? Can you talk a bit about this duality?

[00:30:24] RA: So, you’re zooming in on something, which actually, I think I evolved toward that point of view after I wrote that paper. At the time we wrote the paper, you outlined very accurately the central sort of question or dichotomy or balance in trading. So, it’s why do you trade quickly? Why do you trade slowly? Let’s say, you come to me and you say, “I want to buy 10,000 shares of stock before the end of the day.” Do whatever you want. So, I have to decide should I do that all right now? I could set a market order. I could do it very quickly. Or I could space it out through the entire day. I could do a thousand shares an hour, whatever. Whatever the length of the day is.

So, I don’t have to have a precise solution. But I have to have some idea why would I do it quickly? Why would I do it slowly? So, as you very accurately said, the reason to do it slowly, is so that I don’t tip my hand, so that I don’t reveal that I have a large part to do. I want to do 10,000 lots, I don’t want the market to guess after 1,000 that I have a lot to do. But then the question is, why don’t I just take the whole day to do it? Why don’t I think a week? Why even one day? There’s got to be some effect that limits the length of time.

What we said in that paper is, what limited is pure volatility risk. We assumed that there’s no information, more precisely, which was more true, I think back then than it is today, you come to me with this order for a day, because you’ve done some fundamental research and your horizon is six months to a year, for your alpha. You’re doing it for fundamental reasons. So, you really don’t think there’s going to be much price motion through the course of the day. This company has good products, whatever.

So, we don’t have any urgency. But what happens is, there’s just going to be volatility, there’s going to be swap. If you send me the trade in the morning, and I wait till the afternoon, there’s always going to move even if there’s no directionality in the market, it’ll be up, it’ll be down, and you just don’t need that general and finance extra volatility is bad. You’ve already carefully tuned your portfolio to minimize volatility risk for a given level of expected alpha, you don’t want an additional source of volatility risk from the execution.

So, I’d rather do it earlier just for the sake of reducing the uncertainty relative to the benchmark. Now, I don’t want to pay too much for that. But if it doesn’t cost very much, I would rather do it earlier than later. But I think what’s become more and more true, as the markets become more efficient, is that, it’s what you said, is that the other people getting the same information. In the model, this would be alpha, so this would be drift. So, you’ve run your fundamental model, you’ve said I have a one-year horizon, I think this thing is going to go up. But what you may or may not be aware of is that there’s hundreds of other firms out there that have similar models. They’ve all read the same paper, they have similar factor models, they’ve processed the same information. They also have a one-year alpha target. But because everybody is doing that, that becomes a one-day target.

So, a lot of people will run similar models, and it will move in the direction that you’re trading. As you said, you want to get your trade done before other people do. Even if you think you have a completely uncorrelated source of information, you don’t necessarily. Yeah, so it’s alpha. The longer you wait, the worse the price will be.

[00:33:51] AVH: What are decision criteria of your clients or of you on how long to execute the trade? Are you looking at order size versus average market liquidity? Are you looking at importance? Are you looking at – what are some of the determines, when you say we want to execute this trade in 5 minutes or 30 seconds or over a week?

[00:34:12] AVH : So, I’ll give you first the mathematical modeling answer and then I’ll give you a sort of more pragmatic answer that we have have evolved in the direction of in our trading. The mathematical modeling answer would be you write down the properties of the thing you’re trading, stock or futures. So, in particular, you say, I have some estimate of liquidity, which is if I trade a certain amount, how much am I going to move the price? So, some market impact model and I have some estimate of the volatility, and I have some estimate of the expected drift. How much value, per hour, am I losing for every hour that I wait? And then I put in all those factors and I can use various mathematical techniques to compute an optimal trajectory.

So, if the stock is very liquid and very volatile, and you think a lot of people are going to be in on this trade, then you should trade it quickly. Because it’s liquid, there’ll be not too much extra cost and because it has high volatility and high expected drift, there’s a large benefit to trading quickly.

On the other hand, if a stock is fairly illiquid, so let’s say it doesn’t trade very much, so you expect the trading a small amount is going to move the price a lot, and you think, rightly or wrongly, that your trade is uncorrelated from what other people are doing. So, you have no reason to think it’s going to move one direction or the other hand, and is fairly low volatility, then you should wait a longer time. The cost of waiting is not very high, because you don’t think it’s going to move much and the benefit of waiting is high, because it’s fairly illiquid. So, if you have the inputs, you can put those in and make a mathematical model.

Now, that said, one point of view that I’ve sort of evolved towards, from years of being in the market is that, well, I like to put it this way to our team. The markets not in here, it’s then. I’m an applied mathematician by trade. I love math, I love applied mathematical market models, and differential equations, and nice coefficients and square root functions, and so on. But the market, I like to tell my students, the market is not these mathematical symbols you write on the board. I showed them a picture of like the Chicago pitch, where everybody’s yelling at each other, and they got hands. That’s what the market is like. It’s a bunch of guys, yeah, mostly guys, yelling at each other, and all trying to rip each other off.

You basically need to go in, so you can write your differential equations, that’s fine. But when you actually go to trade, you need to be much more opportunistic. So, the way this came up is, we looked at a lot of executions, and let’s say, you draw your schedule of how much you’d like to execute each hour through the day. Okay, that’s your mathematical optimum, and then in this second hour, the market offers you a chance to do a large amount of the trade. But let’s say there’s suddenly a lot of liquidity.

So, I would say you should take it. Why would you not take it? You’re not going to turn down the opportunity to get the trade done, because your schedule says, “No, you should only do this much each hour.” And then similarly, let’s say you have limit orders in the market, they’re not getting filled, but the price isn’t going anywhere. But you’ve determined to schedule that says you should have traded this much by the end of the second hour. Should you go ahead and do it. If the market has no particular signs of wanting to be with you, I would say no. I mean, some of the products, we trade from interest rate products, but some of them the price won’t move for hours at a time. You can just sit there on the bid or on the offer. Why would you cross the spread? You have no reason to think the price is going to move? Why would you go pay the spread? Why not just wait? I mean, there might be a sort of average optimal trajectory. But if the markets not cooperating, don’t do it.

[00:37:55] AVH: Do you sometimes go back to your clients and be like, “Well, the market does not cooperating, we don’t recommend you to do the trade right now?” Or is it that like, “Well, we kind of do this.”

[00:38:08] RA: So, once they give us the trade, this is part of the discussion. They give us a trade by a thousand lots in the next half hour. So normally, we will try to complete that. It’s a parameter that you can set, we call it, must complete. So, should be absolutely complete it even if you have not gotten a good opportunity. Sometimes they’ll want that, because it’s more hassle than the position open. They’re not happy at all. But sometimes they’ll say, “Yeah, don’t trade it if it doesn’t happen.” But I’m talking more about sort of scheduling. So, if you give me a thought, depending on the product, let’s say you give me thousand lots across four hours, I will be able to get that done. It’s just a question of do I do it in the first 10 minutes or 2 hours? I’d rather be able to wait and be opportunistic.

So, most of the orders that we do not completing is not a real risk, not really something to worry about, it’s just should you follow a schedule. So, we’ve become much more opportunistic. I mean, you can – of course, mathematics, defending mathematics, you can make models where I wrote a paper where you can say, “Okay, liquidity and volatility very randomly.” So, what’s my optimal strategy, which is dynamic programming, depending on the current state of the market. 

For example, let’s say the market is currently in illiquid state, but you have an hour to wait and you think it cycles, every 10 minutes or so, you’re very likely to get liquidity before the end. But let’s say you’re 10 minutes before the end, and typically, these states last half an hour, then you’re not likely to cycle back to a better state. So, you probably should go ahead and execute. You can make models that describe that. I mean, mathematics can do a lot of things. But if in practice, you’re dealing an order book, which is very complex and very discreet, so you need to be opportunistic.

The other thing that you did raise is clients do want advice on what will be the expected or the forecast cost of a trade. So, that goes into to their decision on whether to trade or how much to trade. If you’re a portfolio manager, you have to size your position, maybe you have a strategy that makes money on a small portfolio, but you scale it up by a factor of 10. Suddenly, it’s not making money. The reason is the slippage costs are killing you. So, it’s very important to have some sort of model for what would be the expected cost of a particular transaction.

In general, so you can do things like portfolio activities. You’re a portfolio manager, so you can buy contract A or contract B, they have similar, say return profiles, but one of them is much more liquid. You rather buy the more liquid one. So, you’ll pay less getting in and out.

But then the other thing we can do is we can identify market regimes. So, intraday, the market goes through various states of liquidity and volatility and we can provide that information. It can be real time, it’s a little tricky, because providing it at the time the order is submitted is not so useful, because the orders already submitted. Providing it a day before is not so useful, because it’s going to change. There’s some sort of – you have to figure out when you want to get the information, what’s the decision flow. But yeah, we do provide that information. If they send us the order, we won’t second guess it, but we’ll give them information to help them make that decision.

[00:41:16] AVH: Really interesting. I want to quickly go to your job as chief scientists and you said you love mathematics, applied mathematics, you’re teaching it. So, what is your role about? Are you all day long, trying to find a new model? I’m quoting this for the listeners that can’t see me, like air quoting. Are you trying to have a better model to try to predict which market regime you’re in, or how to even optimize the models? How are you going about this? Are you constantly trying new approaches?

I spoke of a high frequency trader, they use kind of AI to test different approaches, do different back tests. But the AI is not trading because it’s way too slow. But AI is super helpful in deciding which algorithm to use in which regime.

[00:42:09] RA: Yes, so I’m a co-founder. I was head of research for a while, which meant overseeing. We have about half a dozen, quants, master’s and PhDs. We have a whole lot of projects going on. I’ve stepped back from the day to day supervision of all the projects. So, as chief scientist, I oversee the sort of general intellectual approach, and I’m involved in all the – we produce a steady stream of white papers, and I’m working on bigger ones, which I think are sort of fundamental issues. We have a transaction cost model that I wrote that. I’ve been calibrating that. There are some things that go into the infrastructure of trading. We have a model for volume and volatility prediction based on historical profiles, including contributions of events.

So, for example, one difference between futures and equity markets is that equity markets are generally speaking, closed during the time of major economic releases. Things like changing non-farm payrolls. Most of those things come out before market open, equity market, but futures are open during that time. We have models that forecast the expected amount of additional volatility and changes in port sizes, and so on. So, those kinds of statistical models.

We have a whole signal framework with a consensus. So, we’ve tracked various kinds of momentum, and bubble and reversion signals and trade imbalance. We’re doing, if you’d like the evil thing, we also try to figure out what there is happening that we might not know about. We have some good stuff. We do use machine learning, I don’t know if I call it AI, but machine learning or modern statistical techniques to process, because market is a very high dimensional state. So, there are a lot of parameters that go into a model. You can’t really make an explicit statistical model. But we have various kinds of machine learning models. We’re getting some good results of sort of limit order replacement. We’re using reinforcement learning. This is still preliminary, designing some optimal strategies for worker placement. I oversee all of that and work on larger paper size things, where I think there’s a topic that really needs to be written up. 

I mean, one thing that’s fascinated me through my career is actually the reason I made the switch is the variety and the range and the amount of interesting problems that are available in the market. When I was an academic applied mathematician, somebody told me a piece of wisdom. You always want to be at a university as an engineering school. So, you can sort of walk over and you’ve got people looking at some experiment. I don’t know why it does that, but you want people that are doing real things. And it’s the same in markets. You have all this fascinating stuff happening, and just crying need for models to make some sense of it, even if they’re approximate and imperfect, just know how to think about things.

[00:44:53] AVH: It sounds so much like the sermons from Renaissance Technologies, where he basically like, yeah, I love math. But like the markets are like the real world to apply them. I feel like from what you talked about, the reason we could have like a whole other episode to like dig into, like probably each of your white paper, we could do a whole episode. So, for me I love to geek out a bit on those things. I hope we didn’t lose too many of the listeners of like, “What are they talking about? Applied mathematics?”

But maybe for people that are interested and that are still listening, how could people learn more about quantitative – to have this as a career option. I’m like, maybe not about optimal trade execution in detail, but what skills? If you could just get a bit into how could people acquire the skills needed to use applied mathematics? I know you have co-created a financial engineering program, what kind of resource skills would they use? What university should they look into? What courses? What books? Any resources.

[00:46:06] RA: So, you may be referring to the program in Chicago, which we co-created that back in the ‘90s. So, back in the late ‘90s, financial mathematics was all about derivatives, option pricing, and that’s not true anymore. Now it’s a lot of trading and markets and big data. So, what is true is that the, I guess the word of wisdom, I would say, when I was an applied mathematician, I remember somebody saying to me, when I was young, he’s like, “Look, people who can do mathematics, there’s a lot of those people. People that can write computer programs, there’s a lot of people that can make computer programs.” I’m not sure it’s so true, but it’s sort of true. But people that can conceive of mathematical models, and then implement them in computer programs correctly, that’s a hard skill.

So, you need to be able to know enough mathematics to be able to think about what’s going on, but not be so in love with your mathematics that you would rather have an elegant theoretical model over something that works on real data. You need to be able to deal with the data, you need to know – I mean, all the nuts and bolts and mechanics of programming and data handling, but then also be able to sort of conceptualize from the data. So, I laugh, sometimes people say, “Well, I’m going to look at the data and let the data tell me what the model should be.” And I’m like, “Well, you’re going to wait a long time, because you have to come with some sort of conceptual framework, and then test the calibrator on data. But the data itself is very messy, and large.” So, it’s that ability to sort of know some theoretical models and be able to make them work on real data. That’s really hard to do. It takes a lot of common sense. This stuff is not that difficult. I’m not talking differential equations. Mostly common sense and statistics.

[00:47:53] AVH: Awesome. Rob, this has been for me, a nice throwback to my university days and super interesting. I always like to dig into the whole quant stuff. So, this is really cool. Thank you so much for taking the time.

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