Thanks, Michael. Nice to see everybody. Another title that we debated for this paper is the Triumph of market Efficiency. And I'm going to start with a poll for you. And the poll question is, when you think of the enormous impact of growing assets in passive indices, what do you think is the impact of that on the market? And we've heard all sorts of things from passive, from active managers complaining that they're destroying the opportunity set. We're thinking about the informational efficiency. What do you think of as the primary efforts? And I'll give you while you're filling this out, I'm going to give you some statistics about this. People say and there are a variety of different estimates that the dollars in passive indices can be as much as 30 to 50% of the equity markets. And big numbers in the fixed income markets as well. Okay, Concentration, crowding, everything goes up. Cost saving. Yeah, it's good for certainly good for investors concentration. Very good. Now, academics actually like to study the indices and in particular, they like to study index inclusions for a very particular reason because it's a place where you can see investor flows. And in fact, State Street's been tracking flows and presenting flow data to you for the past 20 years. And it's a great laboratory for thinking about what's the impact of flows on prices. So, for example, is that going to have a large impact on prices or a small impact on on prices? You can see here huge amount of different themes here.
And I kind of I sort of agree with almost all of them. I'm going to jump into. Um, what we're going to look at in this, in this paper, which is this well known phenomenon that when a stock gets added to an index, not just a stock, frankly, bond index as well, when a security gets added to an index, the price goes up. Right. Probably many of you have seen this. Those of you who track indices usually find this to be a bit of a nuisance and view it as actually one of the big costs of being an index investor or an index linked investor. And in fact, if you look at the data for the equity index, I started my career when I was writing papers on this type of thing 20 years ago, the effects were actually pretty enormous. In fact, in the 1990s, stocks that went into the S&P 500 went up an average of 7%. And today those numbers are under half a percent. And if you're going to I'm going to show you some evidence that shows that on average, it's about zero. And the reason that we writing this paper is that for the past 30 years, it's very surprising. The dollar's tracking indices have only gone up and up and up. And so you would think, if anything, that you'd get the opposite effect.
You'd think that, geez, if it's 7% in the 1990s, maybe the impact of going into the index today would be 30% or 40%. And that's why I said an alternate title for this paper was the Triumph of market efficiency. So this paper is really about trying to understand why, and this is a simple schematic for organizing the thoughts here, which is really that the price impact is really this multiplier. Let's call this M I'm going to be focused on and D is how many dollars are the flow, How much is going to go in when a stock goes in or is dropped out of the index? So why do we care? Well, actually, when people first started studying this in the 70s and 80s, people had this basic efficient markets perspective and that was demand curves for securities are flat, meaning information or flows that are not really related to information about those securities shouldn't change the price. Now, that was disproven. People started looking at this in the 1980s and then in the in the 90s and people said, you know what? Demand changes prices. You should look at flows. This is very important for thinking about what happens. And then now we're looking at the evidence again and things have changed kind of back to to where they are and where they were earlier in the data.
And so we're trying to understand why. So what's my plan? First, let me just document the basic facts and I'm going to focus on the S&P 500. But we've actually done this for a bunch of different indices. If we have the time, I will show you some results for the Russell and some other indices and show you essentially the time series decline of announcement and effective date returns. I'm going to explain what those things are, of course, when I get to the data that's happening with a backdrop of the rise of index tracking. And I'm going to show you some numbers that suggest that those are at least 8% for the S&P 500. Maybe there's as high as 13%. Okay. In fact, if you look at trading on the date that a stock goes into the S&P 500 index, on average today, you have 30% volume on the close. I mean, literally on the closing day, on the on the closing auction, 30% of the market cap trades. So moving around into and out of an index is a big deal. We're going to consider four types of explanations. The first one is really maybe the stocks that are going in and out today are different. Okay. Maybe there are larger stocks today. Maybe there are smaller stocks today. Maybe they're more liquid. That kind of a thing. Maybe that explains what's happening. Second type of explanation that I'll consider is offsetting demand shocks.
And that's this idea that actually the world is becoming so indexed that when you're moving into one index, you're actually probably moving out of another. And in fact, there are dollars tracking that other thing. And so maybe you just kind of want to be very careful about how you net stuff. Okay. With respect to the S&P 500, it's actually pretty simple. A lot of stocks are coming out of the S&P 400, the mid cap index, and they're going into the S&P 500. That could be a force as well. Number three, maybe things are just more predictable today. And there are all these smart people tracking and trying to figure out what's going to happen with these indices and maybe and there's all sorts of sell side reports about what's happening. Maybe that's what's driving it. And really what's happening is that the price impact is happening earlier as people have figured this out. And then the last, last one here is this market efficiency explanation, which is really that there's better event arbitrage and better liquidity for these events. In other words, markets have adapted over the past two decades to provide liquidity for these enormous shocks. In other words, the price impact of flows has come down. Okay. So this is going to be like a mystery novel. Let's see if we've got evidence for any one of these things. But first, let me show you some of the facts.
Okay? So first, we got to collect some data on index changes. We're going to look at a comprehensive list of that we got from Sybliss research from 1990 through 2020. And we supplemented this with some data that we put together on index changes from the 1980s. And we're excluding here a small handful of stocks that list delist or are acquired within 100 days of the index change. Sometimes when stocks come in and out, it's because of some weird reason like, you know, gets divested or something like that. So we exclude those and we're also going to exclude it if we can't match the stock to some of the ownership data or we have missing returns around index changes, none of these little changes matter, but I mentioned them in the interest of completeness. So what are we going to look at? We're going to look at the market adjusted return When you go into the index beginning from the moment it's announced, typically these are announced on on a Friday and to the moment of implementation. Kind of fun, fun little trivia here is this gap between announcement and implementation has moved over time. So it used to be very, very quick. And nowadays most indices give you a big window in order for people to essentially rebalance. And we're going to look at the return over the entire period.
So not just the announcement, not just the implementation, but that entire period. Okay, here are those answers. Here's what it looks like. These are the averages by year. The additions are those on the left. The deletions are on the right. And. Actually, I'm going to give a little pull on the fly poll question for the audience. You'll notice there's one big outlier on the very right of the editions in 2000, near 2020. Anybody know that's driven actually by one stock. Anybody remember what that stock is? Went into the S&P and a really popped. Pardon? Tesla. Yeah. So in fact was one big outlier and the additions is Tesla. But overall, what do you see here? You see that essentially there was during the late 1990s and early 2000s, the impact of going into the index was actually pretty substantial, averaged about 7 or 8% and has come down to roughly zero. Okay. In the deletions it's actually even more extreme. So in the late 1990s getting kicked out of the index caused a return of around minus ten, -11% and that number is right around zero today. So you're really seeing parallel effects both in the additions and the deletions. Okay. As I said, this is the Tesla for you. Okay, Here are the actual numbers. These are abnormal returns. So I'm subtracting the market from the return that's happening over this this interval. So you're really focusing on what's happening in that stock.
Okay. And these are averages over each decade. So just to give you an example, 1990 through 1999, you can see here the total return net of the market for the additions is just over 7%. That drops to about 5% in the first decade of the 2000, and then in the 20 tens is essentially zero. Okay. I've broken this out into announcement and effective date. I'm not going to go through those details here. But in the paper, of course, we try to disentangle those two things. Okay. All right. So deletions, let me show you those numbers here even more extreme. So in the late 1990s or in the 1990s, the average effect was -16%. I misspoke earlier. Actually, it was bigger than than I had said in the early 2000s, -12%. And then in the most recent decade, those numbers are just like the additions, essentially zero. Okay. Okay. Just circle some of those numbers. The little stars here are telling you statistically, how is that number different from zero? Okay. Now, this is happening in a backdrop where more and more money is piling into the index. That's why this is surprising. Okay. So let me just show you some of what we've done here. First step is to figure out, okay, when a stock goes into an index, how much is actually trading? Like who's buying and selling? So we got a bunch of data from this is on mutual fund owners.
And actually we have some we're interested in extending this using some State Street data. And essentially we're trying what we do is identify funds that tend to buy additions or sell deletions around the time of an S&P 500 index change. So essentially what we're doing is looking for every single owner in the market. If you're somebody who tends to buy when a stock goes into the index, we're going to call you an index tracker. Okay? Or if you tend to sell when a stock comes out of the index, we're going to call you an index tracker. Okay. Now, there's a bunch of details about how we do this, but because sometimes there are splits and so on. But that's essentially what we do. And then these are the averages. So we're looking here at the net trading by all of these index trackers over time. Okay. And this looks pretty different from that earlier picture that I showed you. Right? What do you see for the additions? You just get more and more people buying. And for the deletions, you get more and more people selling when there's an index change. Okay, This is the actual underlying data. So I just showed you the averages by year, but these are literally every single one of those stocks that goes into or out of the index. And you can see that it's telling exactly the same same picture here.
And the unit, as I said, the unit of observation here is a is a single change. The units here just to give, just to to fix things. This is as a percent of market cap. So you can see they're capping out at about 8% of market cap. Again, these are just the people we have data on and that's why we think the numbers are actually probably even higher than that are reasonable estimate is instead of being 8%, this would probably be around 12 or 13%. Okay. Now here's an interesting and surprising exercise. We're just plotting the return on the left axis on the amount of buying or selling on the right axis. And we're doing that on the left for the additions and on the right we're doing it for the deletions. What do you see? I kind of see a whole bunch of nothing. Right. It's pretty surprising. You would have thought that more buying, more price impact, more selling, more price impact. And in fact, it's we really see very little of that in the data. And to us, that was the puzzle that kind of got us started on this paper and on this project and is trying to understand why why that was happening. All right. So let me get into it. So the first story is, you know, maybe the securities we're looking at just have changed enough over time.
So one example, one one story you might have is, geez, the stocks that are going into the index today, they're smaller relative to total S&P cap or maybe they're bigger relative to S&P cap, but maybe there's some changes that we just need to be aware of. So this is looking at the percentage of S&P total cap of an addition or deletion the day before it's announced, and it's looking at it over time. You could see here Tesla, I'm pointing out, because, of course, when Tesla went into the S&P, it was a big chunk of the S&P. Right. But what do you see over here? Again, not really much of a change in anything. These stocks that are going into and out are really looking pretty similar over time. Okay. Maybe there maybe there are other parts of composition that we should pay attention to. You know, maybe they're more liquid today. Maybe there's more analysts covering in addition, today when it goes in, maybe there are other things that we haven't measured. So we try to look at this in a regression framework. Essentially we're going to do is run a regression of the returns for each one of these ins and outs on as many of these characteristics as we can collect, and then also have dummy variables for the decades to see, well, geez, those dummy, those effects for the decades, do they persist even after we control for what we have seen.
Okay. Characteristics that we look for size, trading, volume, turnover, arbitrage risk. I won't get into what that is but analyst coverage and we're going to try to see what what what comes next. Okay. So here's a table, a lot of numbers and let me explain what's happening. Again, the dependent variable here is the return that we're trying to explain. The characteristics that we're controlling for here are listed. Those are the first few lines turnover, size, risk and analyst coverage. And really what we're trying to see is do we still this dummy variables, these average effects by decade, do they remain after we control for these characteristics? And the shorter answer is essentially yes. Okay. The numbers change a little bit. But essentially, if you're trying to look at the difference between the 20 tens and, say, the 1990s, that difference still persists even after you control for these characteristics. So at a minimum and at a minimum, we have to be looking elsewhere if we want to have the whole explanation. Okay. Same story, by the way, with the deletions. Okay. Second explanation that we considered is this idea of a migration or an offsetting demand shock. As I said today, if you're not in one index, you're probably in another. And so when you're moving back and forth, maybe we've got to pay attention to where you're coming out of and so on.
Okay. Let me give you an example of a direct addition to the S&P 500. This is PGA replacing Citrix Systems. This is in last year. This is Pag. Pga is coming out is coming into the S&P from essentially nowhere. Okay. Migration, on the other hand here is an example is we have tiger resources which is coming out of the S&P midcap index, the S&P 400, and it's going into the S&P 500. Okay. Now, you might say, geez, if you're coming out of the S&P 400, there are people who track the midcap index. And so maybe the price impact of moving from there to the S&P 500 will be more muted, maybe. Okay. So it's a reasonable hypothesis to have. If you're just looking at the S&P 500, the percent of the mid-cap that is tracked, we estimate using the exact same methodology is about 7%. So it's kind of almost like what we see for the S&P 500. And you might think it's like kind of a wash. Okay. So it turns out if you look at the additions from the cap, it's certainly true that they have experienced declining returns. So here there are four pictures. Again, it's a lot to take in. In a quick presentation here, the top two pictures are the drops or the deletions from outside versus the migrations. Here are additions from the outside versus additions from the mid-cap, the migrations.
And what you can see here is that the returns associated with the migrations, those are the ones where it's really, really coming down more. So certainly this has got to be part of the story is that just the netting out of demand shocks is an important thing to be aware of. Okay. That said, the effect. What we have found and again, I will skip some of the math behind this, but essentially this can't be the whole story. Again, this can be a small part of the story because quantitatively it just doesn't account for fully what what is going on. The only thing I would add additionally here is that migrations are a larger share of additions and deletions today. Again, this is this idea that it's more likely today that you're coming into the index from already being in another index than coming from coming out of nowhere. Okay. As I said, mid cap migrations are not the whole story. What we do here is an exercise where, as I said, kind of a simple empirical framework is that the price impact should be the the flow. This D how much is moving times a multiplier? M And think of that price impact term as that. M And we could estimate that. M term. Well, you could do that kind of not taking into account the migrations. And you'll see here that that multiplier is essentially falling from six to about 0.1 over this long period of time.
Now, if you now take into account the migrations, which is to say that it's not when a stock comes in a migration, it's not that 8% of the market cap moves. It's more like 3 or 4% of the market cap moves. Okay. In that case, you see that this estimated multiplier, instead of going from 6 to 0.15, goes from about 6 to 0.4. Okay. So in other words, they help you understand what's going on, but they can't possibly account for the full effect of what we see in the data. Okay. And so I think this sort of leaves this question of, well, the migrations, they can't be the whole story, but they're part of it. And in fact, one of the theories that we have is that the reason there are more migrations today is in fact that the index doesn't like having lots of price impact because it's bad for their investors. And so they prefer to have stocks coming out of mid-cap index or they prefer to essentially do things to mitigate the price impact. Third explanation that we consider is that. The market is smarter today so that these changes in the market are actually more predictable to everyone. And I think about this as when Tesla went into the S&P 500. Just to give you an example, we were kind of all expecting it.
We knew it had to happen eventually. Tesla hadn't been eligible because they hadn't had enough consecutive quarters of profits. And once they had enough consecutive quarters of profits, we knew it was only a matter of time before one Friday, the S&P would announce that they would go in. Okay. And so if you look at the proprietary trading desks at Goldman Sachs, Susquehanna, Citadel and many others, they have entire operations of people where they're trying to figure out how the indexes are going to change. Essentially, think of them as trying to forecast flows in the market. And many fortunes have been made among Wall Street traders, by the way. Many also have been lost because if you bet the wrong way doesn't work out so well. And sell side desks also are putting out lists of potential changes. This is all pretty new, right? This wasn't really happening in the 1980s, wasn't even happening in full force in the 1990s. And there's almost an entire industry around this today. Now, if you thought this was what was explaining what happens. Then what would you expect to see in the data? Well, I think what you'd see is that when a stock goes into the index, it's not that you see that price impact then, but you actually see it before because people would be anticipating this and bidding it up already in the weeks and months before. Okay. Now, it's very hard to actually evaluate that explanation.
Why? Because the big confound, which is that stocks that are going up before are also more likely to get added to the index in the first place. So you have to be a little bit careful in evaluating the evidence. All of that said, let me just show you what we've looked at. Okay. So first I would point out that a larger share of the total return occurs pre-announcement for for additions. So this is showing you here on the top line the return from -20 days before to ten days after. So it's a very long horizon return. And these are abnormal returns. You can see in the 1990s, those numbers are about 8% in the 2000, about 5%. And then here you're seeing -20 to -1. That is the 20 day window before anything is even announced. Okay. And what are you seeing? Well, a bigger share of that is coming in that minus that pre period now than it was in the past. But you can also see here, this can't possibly be the full explanation why these numbers on the bottom, they're really between 1 and 2%. And we know that the index effect back in the day was around 5 or 7%. So it can't possibly be the full thing that's going on. Okay. Same basic story for the deletions. This is the long horizon return on the top and then the pre return on the bottom panel here.
This -20 to -1 here. I think it's a bit more of a nuanced picture. Maybe deletions are a little bit more forecastable. This is a cool picture. We still don't really know what to make of it, but I think everybody likes to see this picture. This is the 100 day returns before the announcement of an index change. And so I'll just point you to look at why don't you start with a red line so you can see this is really the story of the 1980s of the 1990s, which is that stocks were going up and then you announced that it was moving into an index and it really popped when it went in. And now this. The yellow line there is what happens today. You can see that it's rising, rising, rising and is basically, on average, nothing that happens when it goes in. One of the things we looked at here was actually trying to build our own predictive model. So can we forecast which stocks are going in and out? And we used a really simple the simplest model would be to say, geez, what are the largest stocks in the in the mid cap that haven't gone in yet? That's like a totally naive model. You don't need no machine learning here. You're just saying if you're big and and you're not in yet, you're probably next.
Okay. It turns out that that does okay. There's a little it's a little bit narrower today in terms of in the past, they used to admit sometimes a very large stocks and sometimes a very small stock. And today they're more likely to select those stocks. But it's still not a great predictive model. In fact, if you did that, you still basically have like a 1 in 20 chance of getting it right on any given day. That's a pretty risky strategy. Okay. So it's not that easy to pick what's happening next. Okay. So I've gone through three explanations. I think they're all reasonable and they all explain a little bit of what's going on, but they don't explain all of it. So what's left? Well, the only thing that could be left is that the market has just gotten more efficient and that the market is better at accommodating these changes. And here everything that I'm going to show you is indirect, okay? Because at some level, by definition, this is the explanation. When you can't when the other explanations are not working. So it has to be that the market has gotten more efficient at accommodating these flows. So as I said, I showed you these numbers before. The real question is what could explain this multiplier, this price multipliers decline and really think of two types of enhanced liquidity in the market, two types of enhanced market efficiency.
Okay? One is just to say the overall market has become much more liquid over the past 30 years. You know, if you trade anything, you're going to impact the price less today than you were 30 years ago. Okay. That's part of it. Another one that's more subtle, I think, is that it's not just that the market has gotten lower transaction costs overall, but that the event specific liquidity is enhanced. Now, what does that mean? It means that when something happens over and over again, the market adapts to provide liquidity in these settings. And part of our research was actually having lots of calls with people who had some a couple of calls with State Street folks on the on the buy side, a couple of calls with a bunch of the large players in the index world to try to understand how is it actually that you navigate these changes in the market. And it turns out that the infrastructure has simply changed. So now for an addition to give you an example, it's much more likely that the prime brokers will assemble liquidity very quickly by calling the people who are net long by rearranging portfolios. So there's just a lot more effort at creating liquidity in the market. And that's why I said again, alternate way to think about this is there's a triumph here of market efficiency. To me, it's still stunning that it took 30 years to get there.
So it's I don't know if you call that glass half full or glass half empty, but it is it does say something about the adaptability of the market mechanism. Okay. I'm about to finish here. We have a bunch of investigations in the paper to try to understand exactly how how much of this was really the market overall becoming more efficient versus the event specific. That's not really an answerable question, but I would say that's something that we've spent a lot of time thinking about. As I said, there was just lots of infrastructure to provide liquidity. Let me say one more thing, which is people ask me about an explanation that we actually looked at and we didn't find any evidence for. But people are very excited about this potential story, which is people say, geez, when stocks go into the index today, the companies are more sophisticated and so they issue stock into those index changes. Right. They essentially provide their own liquidity. And it's funny because that does happen, but it's still very, very rare. So it's not really explaining what we see in the data, but it does explain a couple of the examples. So Google, for example, when they learned they were going into the S&P 500, they issued and there are few other examples of that and that did mitigate the price impact, but it was just one of a few.
Events. Okay. A couple more pictures here. This one is this is one of my favorites. This is from my co-author Marco, actually on another project. But this is the share of volume each day in a 22 day window around an index change. And you can see the enormous impact of index changes. That's literally on the implementation day. That's the zero and that's in the last decade. You can see that 30% of cap moves in the market. Okay. As I said, we did look at some other indices, dollars tracking other indices has increased as well. And we looked at Russell Editions. These are the same numbers for average returns for the Russell Editions on the left, deletions on the right. Actually, surprisingly, you get the same basic picture here. We looked at also the Nasdaq 100 and some other indices as well. And I won't say that every index looked the same, but you see common elements of what we've done for the S&P 500 in other settings. So just to wrap up first the facts. Addition deletion returns have moved closer to zero in spite of the S&P dollars tracking indices having gone way up. We considered for explanations characteristics doesn't really explain very much offsetting demand shocks. That explains a piece of it more predictable events that explains a piece of it, but not very much. And then lastly, we were left with this explanation that really the market has gotten more efficient at accommodating all of these changes. And I will stop there.
Speaker2: So so we have a little bit of time for questions so you know the drill now. So we'll take them through Slido. But again, happy to take any in the room if there are any. Okay, so we do have one on Slido. So S&P 500 is a high discretion index. How does the observed index effect differ in more mechanistic indices or this is a good little twist in this or in country indexes like MSCI Em Equity benchmark?
Robin Greenwood: So the Russell is a fairly mechanistic index. They have a rule that drives things. And in fact, if you look at the migrations in the Russell, they are relatively efficient because of that. Yeah, that's one of the reasons we focused here on not the migrations because this is the moving from the Russell two to the Russell one. Yeah, but we focused on the direct editions, which are harder to forecast, but even those are somewhat forecastable. In fact, that's one of the reasons we like the S&P is it's a closer to perfect kind of unexpected demand shock, Right. Right now for the MSCI. It's kind of it's a little bit in between. We haven't we haven't done the MSCI analysis. Many years ago, I assembled the MSCI data, but that data is a pain, as you might imagine. It's lots of different countries. And, you know, those of you who trade in international markets, you know, this but it's but it's it's a tougher bear. We might get to that at some point.
Speaker2: So just how good a question was when I first saw the paper, that was the exact email that I sent you, wasn't it? Are we in the.
Robin Greenwood: And I would say, honestly, I hope that somebody else writes that paper. I hope personally not to have to write it because it's a real hassle to work with that data.
Speaker2: Okay. Okay. I think there was a question over there. Thanks, Dave. You got. Oh, sorry. Thanks.
Speaker3: Thanks, Dave. Yeah, thanks for the for the presentation. So I recall you mentioned about the bond maybe in and out out of the index as well and whether we have seen the same thing for the bond index because naturally some bond securities, they are just, you know, less liquid if the liquidity is the answer to the disappearing effect. Thank you.
Robin Greenwood: It's a great question. I haven't looked at, for example, the ag indices and the changes. I would say one thing so I don't have I don't have an empirical answer to your question. I would say one thing that is quite different about the bond indices relative to the stock indices is that the securities going in and out have much better substitutes. And so what do people who track the index, what are they worried about? They're worried about tracking error. This is why when Tesla goes into the S&P 500, you have to buy it, right? Because if you don't own Tesla, you're going to incur significant tracking error relative to the index. It's different for a bond because most bonds are fairly substitutable for one another, especially the high grade low credit risk bonds. And so that limits the actual amount of price impact because if it starts to go up too much in price, you just buy another one. So but anyway, it's a great empirical exercise. We haven't looked at it. I did look at bond indices in general in some earlier work myself, and I've done some work on price impact in bonds. But this substitutes point, it turns out to be really important for understanding the price flow action there.
Speaker2: Is there another one on that side? Uh, no. Okay. I have another one. I have another one here. Has the effect of additions and deletions moved away from large cap stocks into growth stocks like the ones found in the Nasdaq. So I guess, is there any any factor analysis that we could throw into this?
Robin Greenwood: It's definitely true that the more volatile stocks, they go up more. Right. So when conditional on a stock going into an index, the more volatile it is coming in, the more likely it is to to go up in price. More in fact, kind of great examples of this. Tesla was an example. Tesla had other things going on. But if you remember during the 1990s, late 1990s, there was a wave of index additions from the.com Yahoo! Went in when Yahoo went into the S&P 500. I think I'm going to get the number wrong, but something like 20% or 25%, it went up. And I think there are two phenomena for the growth stocks. Number one, super volatile. And number two, they often have lower float, which also constrains their liquidity. So they have inside ownership. There are some other things that affect the the overall liquidity of those securities.
Speaker2: Terrific. Yep. Over here. And it's probably the last one.
Speaker4: Yeah, sorry. I'm going to geek out and ask a technical question. Why did you decide on the decade as a way to check for in your test? Yeah. What was the reason for making the decision for the decade period and not break it down for maybe, I don't know, business cycles or something like that.
Robin Greenwood: I The reason we looked at decades is because the main trend over the past 30 years has been just a consistent increase over time in indexation. That hasn't really had a business cycle component. Remember that early picture that I showed you? It's just going up and up and up. And so decades is arbitrary. In fact, the first draft of the paper, we did it in five year periods. You don't want to look too narrowly because there any individual event is a bit noisy, but five year periods would be fine. It turned out. I kind of think for this presentation I probably already had too many numbers. Imagine I would have twice as many numbers if I did that in five year blocks rather than ten year blocks. So that was why we focused on that instead of the business cycle variation.
Speaker2: Perfect. Brilliant. Well, I think we're done on questions. So, Robert, thank you. Thank you. Great to be here.
Robin Greenwood: Thank you.
