Will Kinlaw : All right, So Megan and I are going to talk about two different papers that we released this year. The first one is going to be about what is driving inflation, putting it in historical perspective. The second one is going to look at price stats data and give some insights into how that data can help predict inflation and hedge inflation. So I'm going to start by telling you a little bit about this first paper. And to do that, I'd like to give you some backstory. Marc Kritzman and David Turkington and I in 2019 wrote a paper called A New Index of the Business Cycle. And in that paper what we were trying to do is come up with a model to forecast the likelihood of recession. And it looked at four variables the stock market, the yield curve, nonfarm payrolls and industrial production. And the goal was to use the Mahalanobis distance, which Mark and Dave spoke about yesterday at length, to compare those variables at a given point in time to the way they behaved during past recessions using that multivariate distance. And believe it or not, in late 2019, the probability of recession from that model was 72% in November, which was way above consensus at the time. And of course, in early 2020, we did see a recession. Now, this is not to say that this predicted the COVID 19 pandemic. That would have been impossible just with economic data. But what it did show was that there was some underlying vulnerability in the economy that many didn't recognize and didn't see. And interestingly, we've continued to update that model. It's available on insights right now. It's showing about and this is as of earlier this month, there'll be a new one early next month. It's showing about a 22% chance of recession. But if you take out nonfarm payrolls from the model, it jumps to 65%. And I expect that that will go even higher when it gets released this month because of some of the changes in the yield curve. And as we heard yesterday from Kristin Forbes and others, payrolls remains one of these rare areas in the economy that look strong. So in any event, Michael Metcalfe, our chief strategist, was, I think it's fair to say, a fan of the paper he's in the team have used it quite a bit in their strategy work. And earlier this year, Michael called us up and said, what if we use this same methodology to try to analyze inflation and understand understand the drivers of inflation? And that's what we've done in this research. Now, our goal is a little bit different in this research. We're not seeking to forecast inflation. Megan's going to introduce some great tools for forecasting inflation here. We're just going to try to put it in context and understand what its drivers are. So let's start by looking at the nature of the problem. I won't spend too much time on this because Kristen and others spent spend some time on it yesterday.

Will Kinlaw : This just shows the year over year change in CPI going back to 1960. And you might think that most of this is due to food and energy prices. Obviously, we're at a very elevated level level we haven't seen since the 1970s and early 1980s. But even if you adjust for food and energy, so here we're showing in light blue the core inflation and we're showing in gray the headline inflation. It's still at a very elevated level relative to where it was historically. So the question is, what's driving this? And there's been a lot of ideas put forward by politicians, by economists and the media of what could be driving inflation. And what we're doing in this work is introducing a model to try to understand statistically in a factual way based on data what could be driving inflation. So using it, this model to connect inflation data to inflation narratives. Here are some narratives. I was going to have a poll, but but the polling technology, as you probably noticed, isn't working very well. Some potential narratives that could be explaining inflation. So is it supply shortages? Is it low interest rates and expansion of the money supply? Is it federal spending? This is the question that we're going to try to answer. So here's how we're going to do that. We're going to start by identifying different inflation regimes through history. Talk about how we do that.

Will Kinlaw : And then we're going to identify a set of economic variables that could explain inflation and look at how they behave in each of those regimes. And then through time, we're going to introduce a time varying way of decomposing. Which of those variables are most important in determining the current inflation regime? So that's the overall approach. Let's let's unpack that a little bit. Now, our first step is to define inflation regimes. And in order to do that, we need a good inflation measure. Now, Alberto yesterday showed you how he used this kind of complex regression tool to look for changes and trends. So look at changes in the slope line of inflation. That's very much akin to what we're doing here. But we're using a much simpler approach. We're just taking the recent one year inflation rate minus the annualized rate over the last three years. So how is the rate of inflation changing last year versus the three years before? And then we're going to do is we're going to take this and separate it, going back to 1960 into different regimes, High, low disinflation. Right. And I'll show you exactly what those are. But that's a challenging thing to do. You might think it's easy. Just pick a level. If this is over two, that's high inflation. If it's below two, it's low inflation. The problem with a simple threshold is that volatility also changes during inflation, regime changes. Right? So if you look at the 1970s, this was a very high inflation regime, period.

Will Kinlaw : But you also see some of the largest declines in inflation happened during that period. Another way to think about this, think about looking at the S&P 500. Some of the biggest one day gains in the S&P 500 happened during the financial crisis. Right. Because you also have a lot of volatility there during these regimes. So you need a tool that's going to account not only for the levels changing in the regimes, but also the volatility changing. And to do that, we use a hidden Markov model. And this actually came up yesterday during one of the questions I'm not sure who asked it, a question about how hidden Markov models might relate to the work that Marc and Dave presented. Let me give you an analogy to explain what a hidden Markov model is, and then I'll show you how we actually apply it. Imagine that I am shuttered in a room by myself with the door closed and no one can see in the room. And the only access you have to the room is a heart monitor. It's connected to me. And at one minute intervals, it gives you my heart rate. And your goal is to forecast at any point in time whether I'm awake or asleep based on that heart rate. So think about this problem. When I'm asleep, my heart rate is going to be lower on average. When I'm awake, it's going to be higher.

Will Kinlaw : But when I'm awake, it's also going to be much more volatile. I could be watching television, I could be exercising right. The rate will be different. So there's a difference in the regime, not only in the mean, but also in the volatility. Now, there's also a degree of persistence in these regimes. Right? If I'm awake one minute, it's more likely than not. I'm probably going to be awake the next one, same if I'm asleep. Right. So we need to model that persistence as well. And that's exactly what a hidden Markov model does. If you gave it this time series of my heart rate, it would give you back and you asked it to give you two regimes. It would give you back a mean and standard deviation for one regime and a mean and standard deviation for the other. And it would give you the persistence or the transition matrix between the two regimes. Most people have reasonable persistence and being awake or asleep. My my nine year old is an exception to this. He sleeps any time except his bedtime. But he's a he's a special case of the model. So in our case, what we're going to do is we're going to apply this to that inflation shift that I just showed you, and we're going to use it to come up with four different regimes that describe inflation historically. One way to think about this is it's almost like the opposite of Monte Carlo simulation.

Will Kinlaw : Monte Carlo simulation. You give the model some assumptions about the distribution. It gives you fake data. Here we're giving the model data and it's giving us the regimes, the distributions and the transition matrix that best fit that data. So here are the regimes going back to 1960 that we observe. Now, of course, the model doesn't name the regimes, we name the regimes, but it does pick four very intuitive regimes for inflation based on this time period. And I want to emphasize here, this is a very parsimonious model, right? We're really just basically giving it the number four and it's converting it into these regimes. There is some calibration that goes on. I'm happy to get that in the Q&A, but it's quite robust. And what you see here is that you've got a steady regime where inflation is pretty low and stable. You've got a rising, stable regime where it's a little higher but not too volatile. You've got a rising, volatile regime where it's rising and very volatile. Spoiler alert, that's where we are right now. You also have a disinflation regime where it's falling. So it's a very nice way of segmenting the historical data into these different environments and allowing us to analyze how economic variables behave during those environments. So here on the top chart, you can see those regime likelihoods going back through time. So you observe an orange there we were in a very high rising volatile inflation regime for much of the 1970s, early 1980s.

Will Kinlaw : That's again back where we are today. You can see in blue the disinflation regimes. These are usually associated with periods of economic recession. When you see consumer prices declining, you can see the COVID recession, you can see the global financial crisis, the dot com recession and back to the early nineties. So there's a lot of good intuition behind these numbers. You can also see the transition matrix. You can see the probability if you move down the diagonals of that matrix at the bottom of remaining in one of those regimes, if that's where we are today. And unfortunately the rising volatile regime is the most persistent of the four regimes, although they're all reasonably persistent. So what we're going to do now is come up with some economic variables that might be good proxies for what's driving inflation. And we're going to look at how they behave in those regimes. So here are our variables. I'm not going to spend a ton of time on this slide. There are eight of them. We've tried to categorize them a bit. So we look at cost push, we look at producer prices, we look at some demand variables, we look at inflation expectations, we look at a couple of monetary policy variables and one fiscal policy variable, which is changes in government spending. And we're focused here on changes in these variables year over year or in the case of the slower moving variables, a five year average.

Will Kinlaw : So what we're going to do is we're now going to use the Mahalanobis distance again. Dave and Mark mentioned this at length yesterday to look at how these eight variables are behaving at each point in time through history and figure out which of these four regimes using those eight variables we are closest to in that multivariate distance at each point in history. So this is a very simplified example, right? Imagine there's only two variables. Imagine we're just looking at, say, wages and pi and one imagine each of these circles is a overlapping scatterplot. So one dimension is changes in wages. The other dimension is changes in pi. And each of these four circles is a regime, a distribution of those two variables. So if we're now where that blue diamond is, we can measure how far are we in a multivariate space accounting for correlation effects from the center of each of those four regime distributions. And that's going to allow us to do a couple of things. Most interestingly, it's going to allow us to measure a sensitivity. So a change in which variable pi or wages is going to move that blue diamond the most what seems to be driving the regime that we're in today, what's the most sensitivity that we see now in practice? Of course, we're doing this across eight variables, so there's eight dimensions, which is very, very hard for most of us to visualize. But the math remains exactly the same.

Will Kinlaw : Here are the equations. I'm not going to spend too much time on these, but the quick guided tour is that it all starts with the Mahalanobis distance. You convert that into a regime likelihood so you can calculate the likelihood that we're in any of the four regimes, and from that we can derive a sensitivity measure. And what we look at is an average sensitivity of a shift in the variable and how that will change the likelihood that we're in a given regime and we average that across the four regime. So this gives us a sense of importance. What changes and what variable are most going to change that regime choice? Now here are the likelihoods going back through time. So this is again, this is using those eight variables. How close are they to the regime in question? So at the top, how close are the eight variables through time to their averages during the study regime using that multivariate distance, you can see rising, stable, rising, volatile, disinflation. And what this shows is the eight variables do a really nice job of recapturing the behavior in those regimes. So they're clearly behaving very differently in these four inflation environments. It's not as if they're always the same. These regimes matter for these variables. All right. And this is where it gets interesting. So what we can then do is measure this sensitivity. So what variables, if they change, will most change the regime definition that we're in now.

Will Kinlaw : And I'm going to start by talking a little bit about the 1970s, because it's a really interesting case study and probably in recent history, the only comparison that we really have to what's going on now. And then we'll talk about the COVID crisis in the current inflation regime. So if you look at the 1970s, this has been studied, studied ad nauseam about by hundreds of economists, and which interesting is most of them agree on what caused inflation to start during that period. It was low interest rates and loose monetary policy expansion of the money supply. They disagree on what caused it to last so long. But if you look at what happens in the beginning of the late 1960s, there in dark blue, you can see the money supply is the most important variable. Now, as you get into the mid to late 1960s, Lyndon Johnson is president. He's implementing his Great Society program, which has a huge amount of federal spending associated with it. He's also ramping up spending on the Vietnam War. You can see federal spending becomes very important and describing the regime definition, if you move forward a little bit further and you get into the early 1970s, in 1971, there was a lot of pressure on the gold standard. There's a lot of other nations were redeeming dollars for gold. President Nixon, under that pressure, exited the Bretton Woods system. Right. And ended the ability to exchange dollars for gold.

Will Kinlaw : And what happened over the next several years was that the dollar depreciated and inflation expectations started to go up. And you can see that there and yellow in the early 1970s. So it didn't solve the problem. And what Nixon then did was implement wage and price controls from 1971 to 1974, started implementing these wage and price controls. And that didn't work either. And you can see again, you can see during that period, you can see the wages and consumption variables rising in importance. And then after the failure of those policies, you can see inflation expectations rising again in importance. And it was only in 1979, August of 1979, when Paul Volcker was appointed to be the chair of the Federal Reserve and started aggressively raising interest rates, that inflation expectations started to subside. And you can then see in green and blue there you can see the monetary policy variables, the yield curve, money supply becoming more important. So it offers this very intuitive view of what variables seem to be driving inflation throughout the 1970s. The other conclusion you can take away from this is seven years were just an awful decade. I mean, the music was bad, the fashion was bad, the economy was a dumpster fire. I'm really delighted that it's not a decade I had to experience, and I'm sympathetic to those who did. But let's look at the more recent episode of inflation associated with the COVID pandemic. You actually see some similarities.

Will Kinlaw : So you can see in the beginning of the pandemic going into 2019, before it started, you can see monetary policy, you can see the changes in the money supply being very important and describing inflation as we get into the pandemic and we start seeing job losses, you can see wages and salaries and personal consumption becoming more important. And as we get further into 2021, you see federal spending spike quite a bit as the stimulus programs start to pick up. And one of the key conclusions of our paper is that federal spending was a very, very important variable in driving inflation during this period. The way the New York Times put it was in 2020 and then again in some of the programs in 2021, the federal government unleashed the largest flood of federal money on the US economy in recorded history. And you can clearly see the impact of that here. And of course, it has now led to an increase in inflation expectations and recently an increase in the importance of wages. And I think that pattern that you see there echoes some of the points that Christine made yesterday about the way that federal stimulus can move through into impacting inflation expectations and wages. So I'm going to conclude just with a chart of where we stand now in terms of the importance of these various variables. Again, federal spending and wages seem to be most important and describing the inflation regime right now. And then I'm going to turn it over to Megan.

Megan Czasonis: Great. Thank you all. So now that we've contextualized the current inflation environment, let's take a look at how we can use price stats to anticipate and hedge the future short term trends in inflation. And so as we'll introduce earlier, this is based on another recent paper that was co-authored between Will and myself, as well as Dave Turkington and Alberto Cavallo. So let's start with just a really brief look at what the existing literature says about inflation hedging. And it's actually a somewhat disappointing takeaway, which is that there is no asset class that reliably hedges inflation, at least not in a static portfolio. So even in this small collection of related papers that are listed here, you'll see that there are differing and. Even conflicting conclusions as to which asset classes reliably and effectively hedge inflation. So this certainly creates a challenge for investors because it suggests that there is no buy and hold solution. So there's no obvious asset that you can just throw into your portfolio and you're suddenly hedged against inflation. Now, that doesn't mean that you can't hedge inflation, but what it means is that you probably need to take a more dynamic approach in order to do that. And so that's exactly what we look at in this paper. So the basic idea here is that inflation linked securities or tips in the US, they're a fantastic candidate for hedging inflation, right? Their return is explicitly linked to inflation. Their drawback, their key drawback is that they are not a great buy and hold investment, and that's because their yields are lower than nominal yields when inflation is low. And that's going to be most environments. So ideally as an investor, what you would like to do is you'd like to hold nominal treasuries when inflation is low, you know, harness or harvest their nice yield and then rotate into tips as inflation expectations begin to rise. So only hold that inflation hedge when you think you're going to need it the most. Now, of course, the caveat to doing this is that you need to be able to then anticipate inflation expectations. And that's certainly not an easy thing to do. But as we'll show, price stats can help you do just that. So I think many of you are familiar with price stats, so I won't really belabor the introduction here. We heard from Alberto Carvalho yesterday. He's a co-founder of Price Stats partner at State Street Associates. But the key thing to keep in mind here is that they produce daily inflation series and they're building those from online data. And the point that I want to emphasize here is that we find that in the long run, trends in online prices tend to align with trends in offline prices or in store prices. But more importantly, perhaps at least for our purposes, is that in the short run trends in official excuse me, in online inflation tend to anticipate trends in offline inflation. This is just one anecdotal example of that, where we're zooming into the US series around the first year or so of the COVID pandemic. And what you'll see is that in early 2020, the US Price Stat series fell ahead of CPI inflation as consumer demand was dropping due to lockdowns. And then that trend reversed and we saw that price that started to accelerate in mid 2020 ahead of official inflation and again earlier in 2021. So again, this is just one very anecdotal example of this anticipation, but we've looked at this more rigorously, both US State Street associates as well as people at price stats. And an important point to note here is that this anticipation tends to extend beyond the timing advantage of priced out. So presets is available with a three day lag, which is obviously or certainly much more timely than official inflation, which is usually about a two week lag. But the anticipation that we see goes beyond that. So it's not just that price data is available sooner, it's that online prices are actually moving ahead of in-store prices. And there's a couple of reasons why this might be. For one, it could be that online prices are easier and cheaper to change, so retailers may adjust those ahead of their in-store prices. Another reason could just be to to due to the nature of how the statistical offices construct their inflation series. So if there's missing items they might use hedonic adjustments, they might use steel prices, they may also collect some prices less frequently than others.

Megan Czasonis: So these are all reasons why we might expect to see or why we do see that online prices tend to move ahead of in-store prices or at least price stats is capturing those changes ahead of the official series. So here's a look at how we have tested this predictive relationship statistically. So what we do is we take 21 countries and we pool together all of their monthly CPI inflation rates since 2009. And then what we do is we run a single panel regression on this data to estimate the predictive relationship between a countries priced at inflation for a given month and their CPI inflation over the the following month. Now we know that there are certain effects in inflation, so we need to control and include controls properly to do this. So we actually include six predictor variables in our regression. Three of those are country specific. The first is designed to capture seasonality in official inflation. The second is designed to capture any sort of autocorrelation in official inflation in a particular country. And then the third variable that's country specific is the one that we're most interested in, and that is a country's lagged price stats, inflation. So it's their inflation price stats, inflation rate for the month prior to their CPI inflation rate. And so that's going to tell us if there's a predictive relationship there. And then we also include three global variables which are meant to control for global trends and inflation, which may be influencing all countries at a given point in time.

Megan Czasonis: So here's a look at the results. These are the statistics for the six predictor variables that I just described. The first takeaway is that seasonality of these variables we looked at, seasonality is the most significant variable in terms of explaining month to month variation in CPI and inflation. And I don't think that's particularly surprising. We're all aware that that inflation is quite seasonal, It has a lot of seasonal patterns. But what's most interesting for our purposes, if you look at that third bar, which I've labeled country online, so this is the T statistic for lagged price stats inflation, and you'll see that it's highly significant as a T statistic of 17. So this suggests that statistically there's quite a predictive relationship between price stocks, inflation for a given month and CPI inflation over the following month. So this is a really great result. It establishes that price stats can anticipate realized inflation. But if our goal is to then time tips versus nominal, as we have to do a little better than that, we have to also be able to anticipate changes in inflation expectations. Otherwise we'd be rotating between tips and animals after prices have already adjusted against us. So with that in mind, what we do next as we look at whether or not price sets can anticipate changes in breakeven inflation, and many of you again are probably familiar with breakeven inflation, but it is the future inflation rate at which an investor who has long tips and short nominal treasuries would break even on that trade.

Megan Czasonis: So it's the market's aggregate expectation and view on future inflation. It's the inflation that's priced into tips. So in order to test whether price stats can anticipate changes in those expectations, we're going to focus on the returns of the break even trade. So that's a strategy that is simultaneously long tips and short nominal treasuries, and those are duration matched positions so that you neutralize any impact of real interest rates. So it's really meant to capture the the influence of of inflation. So the return of the strategy will be positive over a given period if realized inflation exceeds expectations, if expectations rise or if to a lesser extent if the premium that's demanded for holding inflation risk falls. And I've bolded the first two conditions here, because they're going to be the most important determinants of this strategy's return. And it's also reasonable to hypothesize or conjecture that price stocks can anticipate these environments. So that's what we'll look at next. So we return to our regression framework that I described earlier, and now we're just focusing on the US because now we're going to look at whether we can predict monthly returns of the US breakeven strategy. We're going to use our same six variables from before, but we're now going to include two additional variables.

Megan Czasonis: So we include a lagged returns of the breakeven strategy. And again, this is just a control for any sort of autocorrelation month to month. And then most importantly, we also include a price stats trend signal. So this is defined as the one year percentile rank of rolling 60 day median inflation. And so this signal is designed to capture inflection points in recent inflation. And importantly, we actually designed this signal ten years ago. So I think we actually first introduced it back in 2012 at our research conferences. So keep in mind, as you see these results, that the last ten years of the signal are truly out of sample, which is, I think, quite. Impressive. So here's a look at the results from the regression. Again, these are the statistics. You'll notice that seasonality is no longer statistically significant. And again, that makes sense. The market does a pretty good job of anticipating and pricing and these recurring patterns and inflation. But if you look all the way to the right, you'll notice that the US price signal is the most statistically significant variable here and it has a T stat of four. So this suggests that price states can anticipate effectively anticipate the relative return returns of tips versus nominal treasuries. So based on that, let's look at just a very simple way that we could use this for dynamic inflation hedging. So we're going to follow and monitor that price signal that I just described. And we backed us a very simple rule here where if that signals above 80%, then we will take a long positions in the breakeven strategy. So again, that means we're long tips, we're short nominal. If that signals below 20%, then we will take a short position. So we'll go long, nominal and short tips. And then if the signal is between 20 and 80, we don't have a real view on which direction inflation might be heading. So we just remain neutral. Here's a look at the performance of this rule since 2009. We back to the two versions of that breakeven strategy, one with a five year, one with a ten year maturity for each. We show the performance of a static position in that breakeven strategy, as well as the performance of the dynamic strategy. Using the signal. I described one thing to note I don't think the static strategy here is actually your benchmark. In the long run, you would actually expect the break even strategy to probably deliver about a zero return. So I would actually kind of benchmark this to to just an absolute benchmark of zero. But in any case, you'll see that information ratios of the dynamic, dynamic strategy close to one drawdowns are a lot smaller than the strategy that we're actually timing. And the turnover is pretty reasonable. It's about five times a year. And here is now a look at the cumulative performance of those two strategies. The shading is showing you what positions the strategy are in in terms of their positions for the the break even index.

Megan Czasonis: The shading is the same because, again, we're using that same single signal for two different versions of breakeven. And you'll just see that the lines, the cumulative performance is upward trending for most of this sample. In particular in the beginning part of the sample, the earlier part of the sample and more recently. And that's just because we've seen more short term volatility in breakeven inflation in those periods. And so there's a greater opportunity set to time that. But by and large, I just think this shows that it's worked very effectively and again, out of sample for the last ten years. So I think that's pretty impressive. So with that, I guess, oh oh, we do have a summary side. I guess we'll just summarize. So we'll show that he introduced a new way of, of understanding the drivers of inflation in a way that's just purely statistical, very objective. And I think it's really interesting that the conclusions that have come out of that, which again are purely objective, do align with a lot of the comments that we've heard throughout the course of of the retreat. And then as I showed that in terms of inflation hedging, there really is no a buy and hold solution. But if you take a more dynamic approach, price charts can help you do that. So with that, I'm happy to answer questions.

Lee Ferridge: Thank you, Will and Megan. I've been very remiss this morning. I haven't been given you a chance in the audience to ask questions. So if anyone has got a question, please raise your hand. Yes. Behind in the middle here, we've got a mic. Perfect. In fact. Sorry, just in the middle of that. If we raise your hand again. Yeah. Perfect. Thank you.

Audience: Yeah, I guess. Happy to see that you guys have addressed the marker today. So my co-star is. Just just for the benefit of audience, is it possible to explain, like how something like a hidden Markov chain right model is used to measure a continuous measure? Because whenever you say Markov chain, right, you use it for unsupervised learning. So now we are using it in a supervised learning context to measure continuous. So can you explain how you are doing that? And also, is it possible to share an example of the metrics of observations you are using for Hidden Markov model?

Will Kinlaw : Yeah. So we we use the bound well algorithm and we give all those details in our paper. But basically when you fit that model, you have to give it some initial guesses. We use guesses of equal probability for each regime and 80% for persistence of each regime, and then for the guesses around the mean and standard deviation of the inflation and the different regimes. We use the full sample average, but we have to introduce some noise and then we run it 50 times and basically pick the the one that fits best. But it's very robust to those assumptions. It doesn't matter a tremendous amount. It seems like there's enough difference in those four inflation regimes that the model is able to distinguish. So the smooth probabilities we show are kind of the standard smoothed forward, backward probabilities that come out of a hidden markup process. So I'm not sure exactly if that answers your question, but perhaps we can we can chat after and we can share the paper. It has all those all those details.

Lee Ferridge: So I think we've got time for one more question, Max.

Audience: Thank you. Thank you very much, Megan and Will. We are transitioning to a higher inflation environment and all these tools are going to be extremely useful, certainly going forward. My question maybe is going to bring together some of the other stuff that was discussed in this conference. And the the the problem with the iob market is that it's not very developed in every single market. Certainly we have a liquid TIPS market, but not a lot of other countries in that in that list. And from a practitioner's point of view, you know, working with inflation expectations embedded in the job market is always a little bit tricky because there are structural elements and regulatory elements and so on. But one aspect that was discussed in other sessions is is currency and the interplay between inflation and currency. And there are two big things that you've highlighted is one is the application of price stats for PPTP. And so there's direct connection between currencies and prices stack that way. And the other one, of course, is the indirect linkage through central bank response function to changes in inflation expectations and inflation shocks. So have you seen in the literature or considered extending this work to a hedging strategy deployed in currency space in parallel, or maybe as a substitute to using index linked bonds? Yeah.

Megan Czasonis: You wanna start? Yeah, I can start actually way, way back when, probably not quite ten years ago, we actually did have a timing strategy based on differentials in price inflation, and it worked quite well. It's been a while since I've looked at that, but we actually have looked at that. I that was before the Price starts Up series. So I think if you want to use the price stats inflation as a way of timing or anticipating movements in currencies, I would direct you towards the PGP series. Again, that didn't exist when we were there, but I think I think that makes a lot of sense. Again, we did do some preliminary work on that a long time ago. I don't have anything updated to show, but I would probably guide people towards the PGP series as as an effective way of doing that.

Will Kinlaw : Yeah, totally agree. And maybe just to add to that, Maxime, I think I think you're absolutely right that there are a lot of ways this could be extended. I think of it as there's an inflation factor and it's embedded in assets. And if you want the purest possible play, this is probably the way to do it in the US. But we, for example, Alex and Team have created a in the equity space. We have an inflation style factor that ranked sort stocks on inflation exposure and looks at looks at flows based on that factor. So I think there are a number of interesting ways you could think about timing that factor in other areas. But when you get out of this pure play like into currencies, I don't have to tell you that there are many other factors affecting currencies than inflation, whereas breakeven only has a few and arguably inflation is the biggest one. So that's that's why we started here.

Lee Ferridge: Okay. Unfortunately, we are out of time. William, Megan, thank you very much.

Will Kinlaw: Thank you.