Tony: Thomas, we’re back, my friend! The Skinny on Options Math and Jacob in the house, and Jacob welcome back.
Tom S: I cannot believe how fast this show's going today, it's crazy. Jacob, What's up man?
Jacob: It's 9am, how fast do you think it's going?
Tom S: Oh my god, it's crazy …
Tony: Explain to him Jacob, that it doesn't go any faster than any other day.
Jacob: No time is relative, it can go at any speed he thinks it goes at.
Tony: Oh yeah I'm sorry.
Tom S: It feels like it sometimes …
Tony: There you go.
Tom S: I'll put a little context around this, sometimes 2 hours with Tony drags a little bit, I mean since 6:30 this morning it's been 2 and a half hours with Tony already, sometimes time drags a little bit. Sometimes, things go faster.
Jacob: But he's so charming!
Tom S: Oh, my god, yeah. He is charming … What?
Tony: You know he doesn't sign the paychecks.
Jacob: Yeah, I..
Tony: It's Kristy in there, and Kristy, me and her are like this.
Jacob: I called you charming, I don't understand where your offences are coming from.
Tom S: How's everything going?
Jacob: Things are good.
Tom S: Things are good?
Jacob: Yeah. I'm finishing up in Chicago for a couple of weeks.
Tom S: What does that mean?
Jacob: It's Burning Man, I'll be gone for the next three weeks.
Tom S: Did you approve this?
Tony: I know about it.
Tom S: It's Burning Man.
Jacob: It is Burning Man, or it will be shortly.
Tom S: Where is Burning Man again?
Jacob: In Nevada.
Tom S: In the desert, in Nevada right?
Jacob: Yeah.
Tom S: You're going there for 3 weeks?
Jacob: I'll be there for a little over 2 weeks.
Tom S: At Burning Man.
Jacob: Yeah.
Tom S: Where do you sleep?
Jacob: In a tent.
Tom S: In a tent. I do not like this whole situation.
Tony: Do we have anybody going with you for protection?
Jacob: No, not as far as I know, but might be behind my back.
Tom S: Can we send a film crew?
Jacob: I can't stop you from doing that.
Tony: What happens at Burning Man stays at Burning Man.
Tom S: I don't even know what happens at Burning Man, I have no idea, is it a little like Woodstock? What is it?
Jacob: It's a art and music festival in the desert.
Tom S: Yeah, there's a lot of music isn't there?
Jacob: There's a lot of music, there's a lot of large scale art pieces that get put up.
Tom S: Yeah.
Tony: Cool.
Jacob: I work on sort of …
Tony: Do you contribute something there?
Jacob: Mostly I do camp infrastructure, I build showers and …
Tony: Really?
Jacob: Shade structures and things.
Tom S: You don't give classes in option [Greeks 00:02:24]?
Jacob: Nah, I don't.
Tom S: Okay, All right.
Tony: Good for you man that's great!
Jacob: I could probably look at the list, there's usually some sort of goofy class, I could probably find some goofy class on finance and attend it.
Tom S: Can you bring us back a large statue for the office?
Jacob: No idea how I'd get it on the plane, I'm flying there and back.
Tony: You thought about it though which is nice.
Tom S: Yeah, okay… All right well this going to suck, we don't like this.
Jacob: You'll have to deal without me for 3 weeks, you'll be okay.
Tom S: You're going to leave us with TP.
Jacob: I'm going to leave you with TP? I'm filming a bunch of extra [Doe 00:02:52] segments today, so …
Tom S: You're filming stuff?
Jacob: Yeah.
Tom S: All right great. Let's do it, what are we covering today.
Jacob: Today I want to talk about co-integration. Which is something that a reader asked a question about they said, "What is this thing that's been proposed? Is it something I'm supposed to pay attention to?" But they had no idea what it was.
Tom S: Co-integration.
Jacob: Co-integration.
Tom S: Is co-integration as it relates to [Pairs 00:03:15] trading?
Jacob: The primary application of co-integration is going to be pairs, co-integration is a property of two time series, usually what you use it for prices with underlines, but you can use it for anything that, you have a series of data.
You have two such series of data and you want to know are they co-integrated, essentially with being co-integrated means, is that all of the …There's some random differences between the two, but all of the velocity, all of the trending in one, is explained away by the other. With some sort of proportional factor.
Tom S: This is just kind of classic, basis risk under a different kind of name.
Jacob: Right, this is a particular statistical measure you can use to try to figure out how a pair trade …
Tom S: It can't be exact.
Jacob: In the pure theory land, I can construct co-integrated pairs, but in reality we just have data and we have to guess. Are these two series of data actually co-integrated or not?
Tom S: So co-integration is a measurement of the relationship between two series of data, independent data right?
Jacob: Not necessarily.
Tom S: Oh, not necessarily?
Jacob: In fact if two things are independent they won't be co-integrated.
Tom S: Got it, okay. Such as the time series for prices of a pair of underlyings. While this full definition is un… What is that?
Jacob: Unwieldy?
Tom S: Unwieldy, yeah, unwieldy. It doesn't look right. Is unwieldy. What does unwieldy mean?
Jacob: Hard to hold.
Tom S: Unwieldy.
Jacob: Yeah if you wield something, you're …
Tom S: You're right.
Jacob: You're using it.
Tom S: Well the full definition is unwieldy, I've never seen that word, I'm not sure I've ever seen that word used before. The intuitive notion is that the two series are co-integrated if, despite having some additional noise in their values, the velocity of one completely determines the velocity of another. This can make trading with co-integrated pairs intentionally very useful and unintentionally very dangerous, hopefully you can give us some examples of this. Similarly but more predictably to working with correlated pairs.
Jacob: Right, it's one of those things we often want to worry about. When we were just trying to get our number of occurrences up what we want are these independent we want. Many independent things to be doing our trades on. Then we realize, okay we're not going to have perfect independence and we're going to be concerned about which things are heavily correlated.
Co-integration is similar to correlation in that it tells you that these two series are related to each other in a way that means they're not independent, but it's different in about how it means they relate to each other.
Tom S: In the case of let's look at bonds, and [SMP's 00:05:51].
Jacob: Yeah.
Tom S: Would that be a fair co-integration.
Jacob: Pair?
Tom S: The measurement of that pair, would that be fair co-integration discussion.
Jacob: Yeah it would be probably a legitimate thing to take your two series of data, take your two series of prices for that, stick it into our or some sort of statistical program, and ask it are these two things co-integrated? It will spit out two things for you. One of those is, we'll get to it in a second, a factor of co-integration and the other will give you some sort of confidence interval, because in reality you don't know …
Tom S: What is the technical definition?
Jacob: The technical definition of co-integration is that two series are co-integrated if there's some linear combination of them, which means you multiply one of them by a constant and you add it to the other, you're allowed to scale one of them to fix the scale. Other than that you just have to add them together, usually the scale is negative so you're subtracting them in most practices.
Tom S: This means then that there's some measure of normal.
Jacob: Right, the thing is that the co-integration of the linear combination is then what's called stationary. Or in more generality, of lower integration order, but usually order one is stationary.
Tom S: The play is too far away from the mean, and you're assuming some reversions, some means, some normal, something to normalize?
Jacob: It's not really a mean reversion property, what it means is that the difference between the two of them is what's called stable.
Tom S: Yeah.
Jacob: Stable distributions are almost an ideal thing you sort of want when you're trading …
Tom S: But you're looking for something that's not stable for an opportunity.
Jacob: A stable distribution doesn't mean constant, it means every time you look at it, it has the same distribution. No matter when you look at it.
Tom S: Okay, so …
Jacob: You can trade on it now and then you can trade on it next week, then you can trade on it two weeks later, and all of those times are going to give you very probabilistically similar behavior. It won't give you the same output every time, which isn't really what you want, that would just be the same thing every time, they will give you probabilistically the same thing, so let you make …
Tom S: So sort of …
Jacob: The same value trade over and over.
Tom S: The [Nob 00:07:47] spread, or the SMP's 500 versus the 100 or something like that would be the serious consistency here.
Jacob: Yeah those would be perfectly co-integrated …
Tom S: Yeah.
Jacob: To put in words, beyond stable it would be constant, or nearly constant, there are weaker co-integration where the constant is going to be a little less high than that.
Tom S: [crosstalk 00:08:04] Yeah a weaker co-integration would be SMP's versus bonds.
Jacob: Right.
Tom S: Stronger would be bonds versus notes.
Jacob: Right.
Tom S: I got it, so take us through this, this is the actual …
Jacob: [Crosstalk 00:08:12] This is the technical of the math, this is the technical definition. I'm just putting up the definition for first order co-integrated, there are higher orders, but let's not worry about it.
Two series are co-integrated if some linear combination of them is stationary, usually the linear combination lets you add them together with any constants on both, but you can divide through by one of them. If you can just add them together and you get some sort of stationary distribution, a stationary distribution is that UT which means that the distribution of UT doesn't depend on T.
If you look at it tomorrow, if you look at it in a week, if you look at it in a year, they're all going to have the same distribution, which means you can then start doing low duration plays, you no longer need long duration to start driving up your volatility between these things.
Tom S: Is there a distance between co-integrated and correlation? Is there a measure?
Jacob: They're both things that won't be the case for independent variables, amongst things that are dependent on each other, it's going to be hard to tell. Generally things that are co-integrated are also going to be highly correlated, things that are highly correlated may or may not be co-integrated, but that's sort of a …
Tom S: No set percentage or anything like that?
Jacob: No, there's not theoretical reason that one …
Tom S: [Crosstalk 00:09:23] Okay, what should I do if I have a co-integrated pair? Because that's a reasonable question, I actually have lots of co-integrated pairs right now, so what should I do?
Jacob: You've got a big pile of things to satisfy this property …
Tom S: That's right.
Jacob: What it means is that you then take that kappa, that factor that made them be stable, if you trade with both of them as a pair with that kappa scaling factor and usually it’s going to be negative, usually you're going to be buying one and selling the other. In theory it could also be positive ready it could be two things that are …
Tom S: [Crosstalk 00:09:50]
Jacob: You've got this trend list stationary distribution which means that you don't have to be relying on large time until expiration's to make your trades play out, you can be operating more quickly and get your number of occurrences up that way.
Tom S: Okay, so the co-integration piece it's almost about a portfolio of efficiency.
Jacob: Right. It's about finding good efficient pairs, that once they're out flipped against each other you have these nice stationary distributions, which are quantitatively a much better thing to be trading off of.
Tom S: Okay, so if you understand the co-integration part of your portfolio that would fit under the co-integration category, what you're saying is you can assess that you have enough risk in a certain direction and or with a certain property of underlyings, so that you can, as we said yesterday you can string more occurrences than by adding more independent..
Jacob: Right.
Tom S: More independent [Crosstalk 00:10:47].
Jacob: You can get more occurrences by going to shorter duration's.
Tom S: That's actually more useful than I thought of this one today. You're getting soft man, on your way to Burning Man getting this soft. How can I tell if two series are co-integrated? And how can I get K?
Jacob: Kappa.
Tom S: Kappa.
Jacob: Greek K, I only used kappa because of the standard letter to use for co-integrated pairs is beta, but we're already using beta for too many things. In practice you're going to want to use software to tell it to you, it's going to be done centrally by a regression model, the most common way to do it is that first you'll see which kappa gets you something that's the closest to stationary. When you do the combination, and then for that thing you'll do a statistical test for stationary, which there are numerous of them. The readers suggested that I probably should make sure to mention the Dickey-Fuller test, it's pretty funny sounding.
Tom S: Which one is the Dickey-Fuller test again?
Jacob: The Dickey-Fuller test, is a test for stationary, you give it a time series it randomly orders the time series, and then it starts trying to pick it and tries to see if there's a difference between the series randomly re-ordered and the series that you gave it originally, and if it can't then it's stationary. Because it couldn't tell what order you did the times in.
Tom S: Why is it the Dickey-Fuller?
Jacob: Because it was named by two guys, one named Dickey one named Fuller.
Tony: See, everybody has a sense of humor.
Tom S: Yeah, got it. There you go, there are various statistical tests for both stationarity and co-integration, Granger Dickey-Fuller etc.
Jacob: Engel-Granger test is this two-step process where you first get a kappa, and then you run one of the stationarity tests, Dickey-Fuller is one of the more popular stationarity tests.
Tom S: Wow, will these give an approximate and a confidence level that the two underlyings are really co-integrated, that is the best that can be done in the real world.
Jacob: Right.
Tom S: [Crosstalk 00:12:43]
Jacob: We're never going to know that we have a really for sure co-integrated, but we can get a good confidence, we can get a good 90% these two things seem very co-integrated and it will tell you a kappa, probably not the true perfect kappa even if they were co-integrated, but it will be pretty close to it, and when you start trading it against something at that scaling rate you will get something at least close to the behavior you wanted.
Tom S: It seems to me that this is something that will be used for people that are trying to … In the world of trading, and in the world just outside of trading it's an interesting model or way to judge your business against your space
Jacob: Yeah, it's a good way to compare a lot of things, one of the things that gets used …
Tom S: It's a pair model.
Jacob: One of the things it gets used for in the far from finance world, is when they're comparing traffic for road building, they'll see if the highway is co-integrated with taking the side streets, then maybe one's faster than the other but their traffic build up is roughly the same.
Tom S: Got it.
Tony: That was easy.
Tom S: No, nothings easy. With Jacob nothings easy, everything’s heavy, that's why we needed to throw you a break at Burning Man.
Tony: Don't worry about your well-being at Burning Man, I got [Jay Blaze 00:14:00] on the lookout for you.
Jacob: All right.
Tony: Don't worry he'll take good care of you.
Tom S: How many people go to this event?
Jacob: 50,000, 60,000.
Tom S: That's it?
Jacob: Yeah.
Tom S: Do a lot of people from University of Chicago go?
Jacob: Not a ton, but there certainly are others.
Tom S: You're traveling with other people.
Jacob: I'm traveling with people who I've known for longer, some of them are at Northwestern, some of them are from the East Coast … [Crosstalk 00:14:20] some from West Coast.
Tony: I'll make sure he makes it back.
Jacob: I've done it before I'll be okay.
Tony: Sounds good, let's take a quick break. When we come back we're going to have Bootstrapper next. Thank you, Jacob, and we'll see you in a couple of weeks. This is tastylive live.