FX Hedge Ratios: Implications and Applications
Thank you, Michael, for that generous introduction. I wasn't really quite sure how to take it when I saw the wine being served before our talk, but hopefully that's not a message about the content that we're going to talk about today. It's been great working with Alex on this project and, as you'll see, it's really the beginning of a research programme. I'm also going to be speaking in Boston on a different topic Michael mentioned - 'Froth and the Equity Markets' - and so we're developing some interesting products and indicators around that and I hope to speak to many of you about that in the weeks to come. So people always tell me that when you do a presentation about something in economics, it's not like a mystery novel where you're waiting to get to the punchline. So we like to tell you exactly where we're headed. So, actually, this is a back-to-basics presentation today. As you know, State Street has developed over the years a number of different FX hedging and industrial behaviour metrics that are focused on the foreign exchange markets. What we're going to do today is really take a step back and try to actually establish some basic facts in this area that, surprisingly, actually, aren't that well-known. Some of them, you people have on the tip of their tongues and they think are true, and we're going to show exactly how FX hedging works, what types of hedge ratios investors adopt, and so on. So finance theory offers, actually, a lot of guidance about how investors should hedge their foreign exchange exposure. So, for example, a mean variance investor might do well to fully hedge if they were a bond investor; less so if they were an equity investor. As you know, many bond investors actually have almost 100 per cent hedging. Actually, FX hedging decisions are driven by a bunch of other factors as well: the cost of maintaining the hedge, so the carry; and then norms across asset classes - for example, yen hedges might be bigger than in other currencies, and so on. Actually, it turns out there's almost no evidence of how hedging is actually done. So this is a research effort where we're going to try to establish some basic facts about that and then think through some of the implications. So we're going to use a panel. This is incredible State Street data of equity and fixed income funds for which we have both their underlying asset positions and their FX positions, which are primarily in forwards; if they're not in forwards, we convert them to effective forwards. We're going to organise ourselves around the following questions. How common is the FX hedging for investors? How does that vary across fixed income versus equity investors? How much has that moved over time? I'll show you some cool pictures of that. So FX hedging overall has increased pretty substantially over the past 20 years among investors. Then we're going to try to understand dynamic hedging, which is to say let's say you're a US-domiciled investor and you have an Aussie equity position and that Aussie equity position goes up in value, how much do you typically adjust your hedge position? Do you do that one for one if you were a fully hedged investor, as we might think, or do you do something different? Then we're going to try to understand at the end what determines some of these hedge ratios that we find in the data. Okay, so hedging in theory, I don't want to spend too much time on this because Alex is actually going to go through the evidence, but why hedge? Mandates, for one, relative volatility - I'll show you some numbers on this in a moment - but volatility matters a huge amount, of course. Mark Kritzman pointed this out to me very early when I was talking to him about this work, that if you're a fixed income investor and you don't hedge the currency, well, it's going to give you a huge amount more risk in your portfolio than you might… Less so in the equities. When to hedge, cost of hedging, I already mentioned, and then what to hedge and how much. Okay, so let me just do some basics. Not everybody here lives and breathes this stuff, so I just want to be very clear about what we're doing. So what's the return an unhedged investor gets? So if you do it, for example, you're buying, for example, Japanese equities, okay, and let's say you're a US-domiciled investor. So you have to buy the yen first, right, then you use the yen to buy equities, and then you sell the equities later on if you were going to liquidate the portfolio. So what's your return? Your log US-dollar return is going to be the currency return, plus your log, plus your local return, right. Okay. What does a hedge investor do? You're basically eliminating or partially eliminating the currency return from the above; essentially, mixing out the currency return from that. Now, actually, you're not getting exactly this. I'm going to do a quiz later to tell me what term is missing here from this, the hedge log, but it's simplest to think about it this way - that your hedged return is, essentially, you're just getting the local return. Okay. So let me just show you this. I thought, to me, this was a pretty illuminating picture. This is actually the annualised risk during our dataset, which is from 1988 through 2022. We're going to be focused on these sets of currencies. Everything that we're looking at is from the perspective of a US-domiciled investor, so we're looking at always US dollar, Aussie dollar, US dollar, Swiss franc, and so on. So if you look at the dollar returns in equities, the volatility, you can see here is in the range of 16 to 20 per cent. The FX return - and I'm showing the local return, as well - you can see that hedging the returns in equities doesn't make nearly as much of a difference as it does in fixed income. In fact, if you're in the fixed income markets, which you see in those rows below, you're facing local returns with a pretty low vol, so basically between three and seven per cent. That's if you're hedged. So if you choose not to hedge the dollar return, you're actually putting a huge amount of additional currency volatility on your portfolio. So easy to understand why. Of course, the exact contribution to the total return depends on the correlation and then the mix of the volatilities. Okay. So let me give you a couple of definitions here. Matched funds, these are funds in our sample that have both foreign assets and trade FX, and then we're actually going to be able to match these, as I said, using their FX forwards to their underlying assets. I think that's really what's very unique about our data. To preserve confidentiality, all that we're going to be showing you is really distributions to give you a sense of what's happening, so nothing, of course, going on beyond those aggregates. I think even those aggregates are pretty illuminating. As I said, focusing on US-domiciled funds. Okay. So the first part of what we did is really the simplest, which is just to look at the static hedge ratio. What's a static hedge ratio? It's literally how much is the forward position relative to the value of the underlying. So, for example, this number if you were 50 per cent hedged would just be 0.5, okay. So it's the forward holdings divided by the value of the asset holdings, and we could do this for both an equity portfolio and a fixed income portfolio. Okay, so let me just show you what these numbers look like. So I'm going to focus your attention on the right-hand side of this table and then we're going to move our eyes to the left as we look through. So let's look at the very top line on the right. This is for Aussie dollar equity positions. Okay. So this tells us that 34 per cent of the funds that we've looked at… This in June of 2022, so this is our most recent snapshot of the data; our data is monthly. Thirty-four per cent of them are hedged, 54 per cent are unhedged and then there are 12 per cent in that set that actually don't have an underlying equity position but still have an FX position, just to give you a sense. Okay. Then the mean hedge ratio for the people who have a hedge on at all is only 15 per cent. This is in equities. Now, if you move your eyes to the left, you'll see that now I'm showing you the same set of numbers but averaged over the entire sample, so for the past 20 years. What do you see? You see those numbers generally are lower, so less hedgers and then lower hedge ratios, okay, but keeping in mind that these are low numbers to begin with, right. So in the equities, in general, as you go through this picture, the numbers tend to be low. So if you look on the right-hand column of the left panel, you'll see that median ratio of hedgers hovers between 20 and 70 per cent - that's over time. Then if you look again over on the very right, you see that number has come up. So that is to say both in a fraction of equity funds that hedge has gone up and the overall hedge ratio has gone up. You'll notice it's not one. So we really rarely see a hedge ratio of one among the equity investors. Okay. Fixed income looks pretty different, okay. So let's start again on the very right of the picture and you can see here the numbers, the typical hedge ratio that you see actually hovers around one today and about somewhere between 30 per cent and 70 per cent of funds in the fixed income space are hedged. This is based on the most recent data. Much like in the equities, however, those numbers have come up pretty considerably over time. That's you can see if you compare everything that's on the left to what we have on the right, those numbers have come up pretty significantly. I'll show you some individual pictures in a second. So here's a picture from the euro, for example. So this is, again, US-domiciled investors who have a euro, for example, equity position. So the top picture is showing you the per cent unhedged - that's the red. The blue is the per cent that's hedged. You can see that that has trended steadily up. Then you can see that median hedge ratio for euro equities as it has evolved over the years. Here's another picture, for example, now for fixed income investors. I'll focus now on the bottom picture to start and then we'll move back up to the top one. You'll see, incredibly, that median really hovers pretty steadily around one. So the typical hedge ratio is really moving very little. That said, the fraction of investors who choose to hedge at all, that has, for euros at least, actually, has been relatively steady although there have been some fluctuations that Alex will talk about exactly what those drivers are. So two more pictures that I want to show you before I turn it over to Alex, who's going to talk about dynamics of hedging. This is the histogram and an accumulated distribution, essentially, of those same pictures that I showed you before. The reason I show you this picture is to really focus on the bunching in two places, right. So where do you see the bunching in the picture? You see the bunching at around zero. This is for equity. Then you see the bunching around one. So you actually - basically, most people decide they're going to either hedge and they're going to hedge fully, or they're going to not do it at all and there's less weight in the middle. There is some weight in the middle, but… Now, for fixed income, it's pretty dramatically different, that distribution. You can see really the modal hedge ratio is one and, as Alex will tell you, people actually stick to that hedge ratio pretty religiously in that data. Thanks, Robin. So Robin's talked about the statics; I'm going to talk about the dynamics, how do hedge ratios evolve. So what do we mean when we say a dynamic hedge ratio? Well, what we're really referring to is how much investors are hedging on the margin when their underlying positions fluctuate. We're going to define this in the format of a regression. We're going to try to explain for a given amount a fluctuation in underlying asset positions. So, say, your Aussie equity goes up by one per cent, how much of that incremental variation are you going to hedge away? So the way the regression set-up is… On the left-hand side we have changes in the FX forward position. On the right-hand side we have changes in the underlying asset position - this would be a combination of local market return and flow driving this variation. The coefficient on this regression, the beta in this regression, is how we're going to define the dynamic hedge ratio. It tells you, basically, how much of the incremental position variation you're actually hedging away. Now, if you imagine a case where a fund is 50 per cent hedged in a given currency and wants to maintain that 50 per cent hedge, you would have to have a beta of minus 0.5. If you've got one dollar of return in local terms, you'd have to hedge 50 per cent of that away to stick to your 50 per cent hedge ratio. Both of these variables we're expressing as proportions of lagged underlying asset positions just so that the normalisation makes sense. This is a study that we can carry out at a number of different levels. We're going to look at this at the fund currency level in a very granular way and we're going to look at it in some more aggregated framings, as well. We're also going to study this over different timescales. On the one hand, we're going to look at a relatively swift adjustment period of one month and we're going to go all the way out to a 12-month horizon just to see if there's any variation in fast versus slow adjustment. So we're going to begin with more accumulative distribution functions. Now, a single dot in one of these CDF plots corresponds to one fund's coefficient in one currency. Now, here we're focusing on the distribution of positions across yen, so each one of these dots is a beta for the yen by some fund somewhere. On the top we're looking at equity portfolios. On the bottom we're looking at fixed income portfolios. Remember these are the beta coefficients. So what should we expect to see? Well, if these investors are hedging at the margin, all the distribution should be shifted over to the left, to the left of zero, in fact. They should skew negative. That is, in fact, what we see; all of these lines are shifted to the left, shifted away from zero into the negative domain. We also see that things don't change that much from left to right, from the one month to the one year horizon, so most investors are making their adjustments to their hedges relatively quickly, but, boy, do they change when you go from top to bottom. You can see the string does get plucked to the left, and why is that? That is because fixed income investors who Robin has shown you have higher static hedge ratios also have more aggressive dynamic hedge ratios because they are sticking to those hedges in aggregate it. They mean it; they want to maintain their hedge ratios. Now, this is just yen. We can do the same thing adding in all the other currencies. So now we have roughly nine times as many dots as we had before underlying the chart. Nothing really changes. You find the same facts across other currencies as we see in yen going down to that very granular fund currency level. Now, we can slice things a bit differently. Let's look at the cross-section, how different are things across the different currencies that we sample? Same set-up - the top set of charts is equities, the bottom set of charts is fixed income, left one month, right one year. We see that across all the different currencies - and in this case we're actually pooling all the funds together and running one regression per currency across all the funds - we still see negative coefficients for every single currency in every single set-up that we have here, although the equity coefficients are substantially smaller in absolute value than the fixed income coefficients. So across currencies investors are trying to stick to their hedges, but they care a lot more about their fixed income positions, consistent with what we saw at the granular level. So that's slicing across cross-sectional units. Now we can slide across time too to see how patterns of hedging had varied. Now, as Robin pointed out, and as you can see on our indicators today, hedging has generally increased over time. We do see that dynamic hedging has also increased over time. So to study this, we just running a rolling panel regression. Now, here we're lumping together all the funds, all the currencies, but we're shifting our window through time in a rolling 12-month window, looking at the coefficients that pop out. We do see that, generally speaking, the numbers have been negative both for equity and for fixed income, but, boy, have they gotten a lot more negative for equities, not just post GFC, but also post eurozone crisis. That equity hedge ratio, while still small relative to fixed income, has roughly doubled over the past decade or so. So investors, generally speaking, are dynamically hedging their equity. Their maintaining their larger hedge ratios in equities to a substantial degree. In fixed income, the dynamic hedge ratios are pretty high; they got pretty high pretty early and they've generally stayed there. Alright, so we've got our statics, we've got our dynamics. Do they talk to each other? Now, it's nice to have aggregate evidence of statis hedge ratios varying, it's nice to have aggregate evidence of dynamic hedge ratios varying. That does not prove that particular funds are maintaining their particular hedge ratios. It could still be the case that the variation we're seeing overall is driven by different funds shifting their behaviour around. Maybe fund A is swapping it's normal hedge ratio with fund B, and we still see an aggregate trend, but individual portfolios are not being persistent in their behaviour. The changes in the levels don't necessarily line up fund by fund even if they line up in aggregate. So we want to demonstrate or to test whether or not they do line up at a more granular level and we will, indeed, find that they do. Alright, so how are we going to do this? What we're looking at here are a set of scatter plots. Here's what we've done. Now, in this case we're looking at sterling - we'll look at other currencies in a bit, and sorry about sterling. What we're doing is we're first going fund by fund and trying to get a sense of what's a reasonable estimate for the target hedge ratio. Well, we're just going to say your historical average, how's that for a reasonable estimate of your target hedge ratio? So for each fund in each currency we're going to compute its historical average hedge ratio, then we're going to ask for the funds with a given range of target of average hedge ratios what's the typical dynamic coefficient that we estimated in our other regression. So what we're doing is, on the X axis, we're sorting out the various target hedge ratios, and then we're asking within those groups what's the average dynamic hedge ratio on the Y axis. When the bubbles get bigger, that means more funds live in a particular bubble. Now, if it's true that investors with high target hedge ratios are maintaining those aggressively, we would see for a large positive number in the hedge ratio a large negative number in the dynamic hedge ratio and we would see a negative slope to this graph or a negative correlation coefficient or whatever you like. We do, in fact, see this both in equity investors on the left and in fixed income investors on the right. So it really starts to take shape when there's actual hedging, when the hedge ratio is actually positive. Now, we can have cases with a negative hedge ratio; it's actually quite common in emerging markets, rare in DM, and that means investors are taking additional currency risk, they're not hedging it. So they don't follow this law, but the normal hedging law of investors does. So what we did before for sterling, we were able to observe the slope of this line. Here I'm just showing you that if you run the same experiment for all the other G9 currencies, you see similar very sharp negative slopes, near unity negative correlation coefficients across all currencies both in equities and in fixed income. So this demonstrates that investors truly are sticking to their hedge ratios at the micro level. That allows us to have a more rigorous foundation for saying that we understand their behaviour rather than guessing from aggregates. Alright, so what might drive the kinds of target hedge ratios that investors actually choose to abide by? What are the determinants of hedging? Well, we considered a number of natural macroeconomic variables. So one might be what's the short-term yield spread relative to one's base currency. So here that would be your local currency's three-month rate versus the three-month US Treasury rate. That's the cost of hedging. If you do a one-month rate, you would get a similar answer. So the cost of hedging. Another measure that one might use is a carry measure: what is the net yield I earn on a hedged ten-year bond position for a given foreign bond market; what does currency volatility look like? Here we're using aggregate volatility from the JPM index. Various measures of momentum. So momentum factors typically are - let's say a standard definition is the most recent year of return skipping the most recent month. We can look at this for both currency return momentum, and that means appreciation of the currency, the way that we've framed it. So a positive number for a given currency means it appreciated versus the dollar. We can look at the same thing in the local asset markets. So have the bonds done well, have the currencies done well, and for bonds and equities, this will both be in local terms, and what's the reversal factor, as well, just for completeness, that month momentum skips, we include those, as well. Finally, we actually look at patterns of correlation because, as Robin pointed out earlier, these can be quite interesting and important. So we're also controlling for a rolling five-year correlation between the local asset market and the currency itself. Now, what we're trying to predict is pretty simple: what are the levels of hedging using this vector of covariates in our X variable here? Now, we've done this study at a granular fund currency level, we've done it a number of different ways - with and without fixed effects, and such. Right now, what we're going to focus on is a much more aggregated quantity. We're going to be focusing on those median hedge ratios that Robin was plotting before, though, broadly speaking, the results are similar if you drill down to a more granular component. Alright, so what we're looking at here is a set of regression results. So on the rows we have our different regressors. In each case, we have a coefficient on the left, T stat on the right, the different columns tell us what the different regression specifications are. Most of the significant coefficients have been highlighted in yellow. Now, in all of these cases, we're including a time trend just to account for the fact that hedging has generally gone up. Here we're looking at fixed income portfolios; we'll look at equities next. Let's just go through covariate by covariate and get a sense of how these things look. Well, we actually get a positive loading on the short-term yield spread, which might be a little bit weird. That means that investors are hedging more when it's costlier to hedge. Now, I will note that if you look at this with currency fixed effects, which is equivalent to taking out a trend for Australia, a trend for Canada, etc., this actually flips around to a noisy negative coefficient. So this is really telling you that across currencies the higher yielders seem to be hedged a bit more than the lower yielders, at least in our sample. Okay, what about the FX volatility loading? Well, here we get a negative coefficient and that tells us that investors are actually hedging a bit less when vol is high. That, however, does fade away when we include all the other covariates. So this is true in a univariate setting, but there's nothing incremental here after we control for other factors. Then we have our two momentum factors, and this might look a little funny, as well. When FX momentum is positive, investors are hedging, hence shorting more. So that means investors are hedging more, on average, currencies that have depreciated. At the same time, we're getting a positive loading on fixed income momentum. So that means that investors are typically hedging more when yields have decreased or bond prices have gone up. Now, those may seem a little bit odd, especially when we consider that these two things are negatively correlated, at least in our sample. On average through time, we have seen that fixed income returns are typically negatively correlated with currency returns within developed markets, but if you look all the way over to the right… Let's see if this pointer works. There we go, over here. That's the column I showed you earlier, over there. Then we see that the coefficient on FX momentum flips to negative and the coefficient on fixed income momentum becomes more positive. Okay, fine, what does that mean? That means that we see more hedging in cases where bond yields are down and currencies have depreciated. That makes a bit more sense. It looks weird individually, it makes sense when you put it together. We also see higher - a positive coefficient on the net hedged yield, so the net hedged yield of a ten-year bond - when people can earn yield and hedge it, they're happy to do so - and a positive loading on correlation. So when correlations are higher than usual, there's a bit more hedging than usual, although the effect is relatively small. So in equities we have a pretty similar picture, so I'm not going to go through everything again. The main thing that changes is that in equities the FX momentum loading goes to a negative number, which is consistent with what we saw in fixed income after we controlled for fixed income momentum. So, basically, that means that equity investors are hedging a bit less when currencies have appreciated. Also, the equity momentum is a lot less important to determining hedging than fixed income momentum was. Alright, so what are the implications of some of this? Well, we've established a fairly rigorous foundation that investors do tend to stick to their hedges. So, fine, what does that mean? Well, that implies rebalancing demand. If your Aussie dollar assets go up one per cent, that means you're going to want to rebalance your hedge and that implies future selling of the Australian dollar just in the forward market. So there's a rebalancing demand that is induced by this observation about investor behaviour in currency hedging. Now, to fully understand the picture of currency demand even for this subset of international portfolios, we have to think about the spot or asset market as well. So there's an old theory called uncovered equity parity. This is focused on unhedged equity investors. There the idea is pretty simple; it's that investors rebalance. Well, what does that mean in an international context? Well, that means, again, if your Aussie equity goes up and you want to maintain a target weight of Australia in your global portfolio, you will sell down Australian assets. So there will be a rebalancing effect on the Aussie as well as on the ASX. So that's another headwind similar to the hedging headwind from the forward market, but there's also the phenomenon of country equity momentum. There is trend following across country equity markets, so that tends to be a positive for currency demand. As people follow the trend, they buy more of the country that's gone up, and if the country has gone up, the currency has typically gone up as well. So the next stage of all of this research is to put all of these things together. We're going to use these micro-estimated mean reversion parameters, if you will, around hedging demand and how investors have dynamically rebalanced their hedges, and we can put that together with the asset or the spot side of things to get a sense of what the net currency demand ought to be, which will eventually lead us to understanding returns. Just as 'Conan the Barbarian' had a sequel, excellent sequel, 'Conan the Destroyer', we too shall have a sequel to this bit of research. [Audience laughter] I'm just going to skip over the conclusions because I know we're a little bit full on time. Hopefully, this is all apparent to you, and, with that, I will open up the floor to questions and whatever the next stages are. [Applause] I feel like my first question should be for the audience as to who's actually seen 'Conan the Destroyer', but let's not go there. Okay. So I've got a couple of questions here just to kick us off, but, obviously, we'd love to take some questions from the room if there are any. First question - you probably know this one's coming… So you've done this for dollar-based investors. Any chance within our database that you could do it for other base currencies? We can definitely do it, we have the data. Whether or not we arrange it by a different study is something to determine just in terms of a write-up, just because there's so much one could write and one has to fit it into a coherent paper. If you go to our indicators today, you'll see that we have, basically, what we call domestic hedge ratios, so aggregate hedging by investors from a given base currency, basically, for euro investors for CAD investors, for Aussie investors and for sterling investors. That's the set of base currencies that we could reasonably explore with an analogous study to this, and, in fact, a lot of it's set up to be explored if we choose to. Great. Look, well, certainly as an active user of our FX fund, and I'm sure many of you in this room are similar, is the idea that the hedging related…? Let's say that someone just has a target of one per cent, sorry, 100 per cent, sorry, hedge ratio, are we trying to extract the passive hedging that is just occurring automatically, because is that where we're going with this? So, yes, so we're really trying to establish a research foundation for understanding things, but if you think about it in terms of a path to a product, long ago before we released our current set of FX indicators - you'll probably recall this conversation - this is similar to the ideas that we had around identifying active versus benchmark FX forward flow. So I do think that this may end up in that sort of place over time, because if you have a sense of what the typical - particularly for a particular portfolio in a particular set of conditions, what the typical hedging flow ought to be, deviation from that could be deemed active. Right. Yes, you need to basically establish first that if somebody looks like they're a hedger, that they're actually a hedger so that then you can add it up into something that tells you about what you think the flows might be, conditional on, say, a movement in the Aussie equity market or whatever the asset market is. It's fascinating how - and it came across very strongly in the presentation, how equity managers are hedging more. Look, obviously, you dug into that a little bit with the regression analysis, but what do you think are the main drivers of that in terms of the longer-term trend of them hedging more; any thoughts? Yes, there are a number of possibilities because the regime really shifted post GFC. So what else happened post GFC? Well, it got pretty cheap to hedge, didn't it, across currencies, so I actually think our current environment is a lovely natural experiment for this, because it ain't so cheap to hedge anymore or it's getting less cheap. So the short answer is I don't know, and just because, yes, we've got 20 years in the sample, but we have two regimes and a crisis in the middle. So I wonder if the cost of hedging is a factor there, I wonder if changes in correlations are a factor there, but there's also just the possibility that people - and this is more of an MKT MediaStats sort of thing - but as concepts become salient, people pay more attention to them, often rules change. Even if the underlying rationale was there for 20 years that maybe one ought to be optimising things by hedging a bit, once some set of people/portfolio managers started to hedge more, if there was more attention to the idea of the notion that one ought to equity hedge, that might itself create a sort of feedback loop where people hedge equity much more, because it's 'a thing', as the millennials say, which I'm an elder millennial, so I guess as I say. We probably have more to do in understanding the individual players and, for example, if across an organisation different funds tend to have the same kind of hedging behaviour, that's something interesting to explore. I just wanted to add to what Alex said there. Two dimensions in which this could lend itself to indicator-type insights. One is you've already nailed that, which is that if you think that the hedge ratio is one, then you can say something about what happens if the Aussie equity market goes up by ten per cent, you can infer what the hedging demand is. That's one. The other is on the last part of what Alex was talking about, which is if we understand over time what drives the hedge ratios, we can say things like, 'Well, if the central bank rate in Japan moves by this much, then we can forecast how much demand, essentially, that's going to stimulate in terms of changes in FX hedging behaviour.' So we're also going to try that direction. You can see from those regressions that there's less explanatory power relative to… The simplest thing to say is, 'It looks like Alex is hedging with a ratio of one, and he was doing that yesterday, and he's going to do that tomorrow.' It's harder to say, 'Jeez, Alex is going to go from a one to a 0.7 next year based on what's happening in the macroenvironment.' Got it, yes. Oh, Mark, I think. Oh, yes, one question here in the front. Great presentation, thank you very much. So it seems to me that the rational approach to currency risk is for it to be managed at the asset owner level, otherwise you have managers perhaps trading with each other at the asset owner's expense. I presume the results you're showing pertain only to asset managers and not asset owners. It implies what I would think of as a pretty significant inefficiency in the way these portfolios are managed. So, yes, I would say the data that we're using is account by account, so I think you're correct in that this does imply we're measuring at the asset manager level because we're measuring at the portfolio level. Yes, I think the returns to scale that you're talking about are valid; that's a valid concern. You can think of it as optimal execution often involves a bunch of trades generated by a bunch of quant models at a particular firm, but you don't execute all those trades and pay all those spreads; you figure out what the net flow is, you kick it out of your firm and then you allocate everything to your PMs. That does seem optimal and, luckily for me, people aren't doing that because, otherwise, our data would be a lot less rich a dataset. It's a great comment. If we were going to make a list of the inefficiencies between the asset allocators and the asset managers, this would be on it, but this probably wouldn't make my top ten list. I think about asset managers hedging the beta use inputs when the asset allocator wouldn't necessarily want to do that. There's lots of settings in which that's true. It's definitely something that we haven't spent a lot of time thinking about or exploring but something that we should look at. I guess the other thing to consider is that there might be - particularly fixed income investors, they think of themselves as macro specialists. So their current forecast could add a lot of value to their overall portfolio return. So there are cases where there's sufficient specialisation - maybe harder a case to make in equities - where you might actually - an individual PM might express their skill through a joint consideration of the short end of the curve through the currency forward and the longer end through the bond investment. So I'm sorry to say, as optimistic as Pippa was about the lack of nuclear conflict, we have a flashing red countdown on the front of the screen here. It is really off-putting, so I'm afraid that means that time's up, but I can assure you we're going to hear a lot more about the research you're doing. I know that for a fact. We can see where it's going and really looking forward to seeing it. So thank you, again. Thanks, Michael. [Applause]
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Robin Greenwood, George Gund Professor of Finance and Banking at Harvard Business School, and academic partner at State Street Associates, and Alex Cheema-Fox, head of flow and positioning research at State Street Associates, use the co-movement of FX and equity and bond positions to estimate target hedge ratios for investors. They then explore the determinants of these hedge ratios over time and over currencies, and how one can forecast FX demand by combining hedge ratios with other features of investors’ portfolios.