 Thanks. Thank you very much for the introduction and of course thanks to all of you for attending this session on this beautiful day and also thank you for the Swiss CFA for well having me here, let's say I Have been involved in scenario analysis basically since the early days of my professional life both on the work on the On the business side, but also on the academic side. This was already mentioned in the introduction That goes back almost 20 years since that time. I've been yeah spending most of my working life on scenario analysis So hopefully I can make it worth your while for this hour It's only an hour and There's many things to say about scenario analysis So I'm gonna try to give you the main the main story and hopefully you can have some some fruitful discussion about that The story or the presentation that I have I should warn you upfront I have been doing this kind of presentation as well for The Dutch counterpart of your organization. So you're probably gonna evaluate me afterwards on the content of the presentation I can also evaluate you a bit and compare you to your Dutch to your Dutch counterpart. So Okay, the story that I have prepared It has basically two blocks The first is the part on what our scenarios and what can you use them for? That's that's then and how do they fit in? An approach to risk management Exxon to forward-looking risk management and strategic decision-making That's the first block. The second block is then I'm gonna go into more depth into how can you? Generate scenarios for these purposes And indeed they're going to be with frequency domain types of techniques Which are not very familiar in finance and economics in general, but nevertheless, I think have some some appeal So that's the two to do big parts So and in the whole line we're going to start off quite broad and slowly we're going to move into More detail and be a bit more Specific so in the beginning if it's a bit general hang in there. We're going to get more specific so first of all this light the general formulation of Decision-making problem a financial decision-making problem Looking at the future What is there in general lines whether it's for a pension plan or insurance company or a sovereign wealth fund or Even an individual and there is some things to make a decision about simple example asset allocation How do you divide your money across different asset classes at the top? There are of course objectives And there's some reason why you invest There are objectives in the long run or in the short run which you want to meet If there would be a one-to-one correspondence, let's say between an asset allocation and how that would play out in the future Things would be easy and we wouldn't be sitting here together and the key thing is of course that in the middle There's a lot of uncertainty in the world that lies ahead of us How will financial markets evolve? How will economies evolve and how they will evolve will have an impact on how good or bad our decisions that we make over here Will play out in terms of our objectives? So the key thing is uncertainty that lies ahead of us. We are in an Area where we need to make decisions under a lot of uncertainty Which is ahead of us and scenario analysis basically is a approach for dealing with that uncertainty And so scenario analysis the approach is mainly about this middle this middle part a bit more formal What is a scenario if you look into the the literature the operations research? Type of literature. I always use these two type of definitions, which I think yeah Give a quite good picture of what it's all about the first one says a scenario is a possible evolution of the future Consistence with a clear set of assumptions And there are two things important in there the clear set of assumptions is the first one It's basically says okay if we're talking about the future nobody knows what will happen So first of all everybody in one way or other will be making assumptions about how the future can evolve And this just says if you're making these assumptions just make sure that they're clear and that you know what you're doing The second one consistent sounds a bit trivial if you formulated your assumptions yet just implement accordingly But in practice that can be still quite tedious, but in principle it just says do what you intend to do the second definition you can read it for yourself But it's emphasized is one important another important aspect of scenario analysis or scenario definitions the interdependency if you're thinking about a scenario it's not just about how GDP growth we go or how inflation will evolve or how equity markets will evolve It's about how they will evolve together and so what a scenario is a possible evolution of the future basically of all financial markets and all Economic variables together including correlation And so don't think in terms of one dimension, but in a multi-dimensional approach Well, how can scenario analysis help in Improving those decisions that we make those strategy decisions that we make and it can be illustrated according to this picture on the left-hand side you see an example of Scenarios in this case scenarios of some interest rates horizontal axis is the future in years going from One until five years and on the vertical axis you see the level the value of the yields or the interest rate a Blue line is one individual Scenarios or one possible evolution of the future only for the interest rate the yellow lines all together are a thousand other potential scenarios And the orange line in the middle is the expectation We typically do not use the word forecast It's the expectation because what's the difference between a forecast and scenarios a forecast would only show you the orange line And not to take into account the uncertainty that there is Around that central line. That's one of the key ideas of course of scenario analysis Well, we're going to be talking later on about how do you construct these scenarios for the moment? Just think they are there. What do you need more you need a model? You need a model which translates those scenarios into sorry given What's called here input, but it can be those decision variables So an asset allocation a potential asset allocation that you would want to hold or an investment strategy in a wider sense Including hedging and derivatives etc that you would like to follow and in that model what that does that translates That asset allocation. Let's use that for simplicity translate that into the consequences In terms of the objectives So if you're in an asset liability management framework with assets and liabilities and solvency Legerations and contributions etc. And this is a You could say a balance sheet and a profit and loss type of model And you can use that then to produce scenarios again But now not of financial markets and economic variables But now of variables that you are interested in to evaluate your potential decision on and so if For a pension plan for example, you could show here the funding ratio the ratio of the value of the assets over the liabilities same interpretation of the graph and A correspondence between the two and so the blue line over here is how the funding ratio would evolve if the interest rate Would follow that scenario and if some kind of strategy would be followed Then this would be the evolution of the funding ratio and all the individual scenarios. There are the same just repeating it over and over Again in a Monte Carlo type of way Are you then done? No, you're not done because what the idea is of course the objective is to arrive here at Scenarios which yeah meet the objectives and the constraints of the organization or all the stakeholders If it doesn't meet the objectives at a fun ratio would be too low or the risk is too high You typically leave the scenarios intact. You go back over here and you try another asset allocation rerun the calculations and see how that works out in terms of these objectives and the Conceptual ideas that you keep circling over here experimenting with different strategies until you find or identify strategies which yeah meet your objectives as best as possible That's the whole idea and so it's a kind of a Monte Carlo version of the world And use it as a kind of management flight simulator I just experiment with strategies and see how they work out under all kinds of of scenarios yeah, and Indeed questions fine at the end if they're burning questions in the middle, please do not hesitate to jump in That's one part of the story as so these are the do you could say the rudimentary Calculations that you do if you are really moving into a decision-making space and so really comparing different strategies It's not very convenient if you're looking at these kind of graphs all the time and comparing them with each other What you need are kind of summary statistics which summarize Expected returns and risk in a general sense So in terms of these not just in terms of expected return and volatility of return But it can also be downside solvency risk for example, and so risk and return measures Which are relevant in terms of the actual objectives and constraint that the institution or the individual has well, one of the nice things about scenario analysis is You basically can think of any risk and return measure and you can calculate it from the scenarios and so here's a list Which you can read yourself off of risk return measures you can use Why can you use basically any of them? Well because it's based on the scenarios and you can show that on an example a path probability and so what is the probability that somewhere in the coming 15 years, let's say these are years and the coming 15 years that you will ever Arrive at a funding ratio below a certain threshold below 100 or below a 50 or whatever suppose these are a number of scenarios and What you then do well, you just count or identify the number of scenarios which in that 15 years ever One period or more periods in a row ever fall below that threshold You just count the number of scenarios suppose. It's ten and you divide it over the total number of scenarios Which suppose it's a hundred well you have ten out of a hundred so you get a ten percent probability as a very simple Math given that you have the scenarios can calculate any kind of risk and return measures That's the basic idea and on these risk and return measures. You can then compare start comparing Strategies you can also use it for risk management Purposes, so I want to show you a few examples What that looks like And so we call that Integrated Exanta risk management and both strategy formulation portfolio construction also the risk management and monitoring Of your strategy and just a few examples on what that looks like Again assuming you have the scenarios already and I have not said anything yet about how these scenarios are generated the first thing The first ingredient of that example risk management is then this stochastic scenario analysis, which I basically already told you Given that you have a set of scenarios Given that you have for example your current portfolio composition So how is it divided across the asset classes the maturity distributions the rating distributions and a strategy for taking the portfolio forward Fixed allocation rebalancing rules overlays etc etc if you have all of that you can simulate under all these scenarios For example the value of your assets Same interpretation of the grub. This is the expected evolution of the expected evolution of the assets and the wide range of Scenarios around that that's the index and these are then just the returns Well, you may wonder have why at all you such a stochastic Monte Carlo type of approach and why not work for example with Analytical approaches and so write out an analytical mathematical formulation of your problem Work out the optimal solution and produce a report with the numbers. Why do you want to work with scenario analysis? well, one of the reasons or to make two main reasons why at least it always had made me enthusiastic is a first of all flexibility and So no matter how you could almost say no matter how complex your investment strategy is in terms of dynamic rebalancing rules and overlays and derivatives etc or You have very complex solvency regulation as an insurance company for example You have complex dynamics in your contribution policy as a pension plan And so all these kinds of complexities are typically not a limitation to be applied in scenario analysis While on the other hand if you use these analytical approaches Yeah, just take the typical academic publications. They just start with well We make these and these and these simplifying assumptions because then we can fit it in a formula well, I know if you have ever tried going to a Client and then telling you well you've simplified your situation in this and this way and given these simplifications We think this is the right thing for you to do That's problematic, of course You want to get as close as possible to the real world as you can of course it at the end of the day It's still a model and it's supporting decision-making, but you need to get as close as possible to the true problem to have Yeah, the The largest value in the in the results that you come up with so flexibility Flexibility other one other important reason or pro of scenario analysis You can already see it from these kind of graphs and also from the next type of graphs I'm going to show you it has a lot of graphical at ingredients And so a lot of complex calculations are underlying The approach, but if you're talking at a decision-making level an investment committee or a board of a plan you work with graphical representations and it's typically relatively easy for people to relate to that and also therefore Again understanding or why certain decisions are good or why certain decisions are not good So it has a very good Communication value, which is important at the end of the day if you want people to actually make a change And so to take a decision rather than getting a thick report Put it on the shelf and keep doing what what what they were doing already. And so Understanding communication is also an important pro of the scenario analysis approach. I already said Only looking at these rudimentary calculations It's typically not enough when you start really experimenting with alternative strategies. What you do then is then you make these risk and return calculations As I told you as so C bars or probabilities or expected returns For different strategies and then plot them against each other in a graph So here you see on the horizontal axis. It has something like the expected Cumulative real return on a ten-year horizon and on the vertical axis It's the 10% CVAR of the cumulative real return. So a case where there would be some inflation objective To compensate for purchasing power the pie charts represent them different asset allocations Where red could be equities and green could be fixed income a very simplistic way and you can then calculate these efficient frontiers Underlying each of these pie charts are These rudimentary scenario simulations The economic scenarios underlying them is the same That's if you want to compare them in the in the same Monte Carlo world But the difference is of course in terms of the strategies in terms of the other allocations That you run and what do you do then in this space? Of course, yeah looking for efficiency improvements So moving the efficient frontier out in terms of the objectives and the criteria that you have So you want to move to the top right corner highest expected return lowest risk because it's negative fantasy bars And if you have arrived there if you have identified your efficient frontier You need a kind of a risk budget and some some kind of a risk limit and if you have the risk limit You can actually identify your optimal Decision and your optimal optimal asset allocation and that makes it kind of full circle has so having this Very basic problem. You need to make some decisions under uncertainty Well, you've translated your objectives in terms of basically any risk and return criteria You have a model for your strategy. How that translates into these objectives. You have the scenarios And when you are in this space you start doing your analysis and actually end up with an optimal strategy for a certain time period in certain conditions Yeah, that's the The strategy application of of the scenarios. Well, what we have learned at least over the last couple of years of course in the same may hold for you just having a strategy a long-term strategy and then Implementing it and well go do something else and look later on whether you've succeeded or not is of course not the right way to do Of course, you need to carefully monitor your strategy as you go along to see whether your strategy is still in line with what you assumed originally and Need to update the situation on how financial markets have evolved Also, there the scenarios play a role then you typically do not start experimenting any more with strategies you take your current strategy And you just update it to the latest market conditions and the latest Portfolio conditions as this would be as an example from December 2010 This is The funding ratio of a pension plan which doesn't want to be below one so 100% funding ratio The blue lines are the 10 percent quantiles from the distribution which was projected from December 2010 and the red line Is then what actually happened subsequently until end of 2011 as an example and the idea is of course Then you start monitoring, you know How have the how has the realization fallen into the distribution that I assumed and of course if from here I'm looking forward again, you know, this is still the right strategy to follow so scenarios also play a role in the Risk management or the risk monitoring of your strategy same type of scenarios Well, the final example what you can do With the scenarios in this risk management the process make risk-decompositions And so there's a lot of financial market and economic variables underlying The results that you get and in learning about, you know, where does most of the risk in my portfolio come from? A useful tool is a risk-decomposition Also that again because of the flexibility of scenario analysis you can calculate it on any measure basically that you like this This is some surplus at risk measure where it would be the total risk and you see here How it is build up from different sources interest rates equities inflation and at the end is brought down by the Frustration element different Yeah, exactly that exactly of course different ways of doing a risk-decomposition This is a scenario-based version of a risk-decomposition. You basically just Label your risk drivers according to these categories and indeed you run the simulations with and without These risk drivers switched on you could say and then look at the different risk components And you have the total and the difference is just the diversification. Yes Applications. Well, I already said to you This this can be applied for both strategy work portfolio construction and risk monitoring work Old scenario based it is also a very much applicable to different Yeah types of organizations or different types of problems and both on the institutional side. It's being used for pensions It's used for insurance companies private wealth or sorry sovereign wealth and are also more and more getting interested in this approach and Other types of versions but same idea are also being applied in the private wealth space of course all in very different Versions let's say so the the communication to individual clients of course is something very different than to a professional Investor, but the core idea is still the same Okay, so you can imagine that having said this that What these scenarios look like? And how they behave what are their correlations? What are their volatilities? Will have an impact on all these type of results and therefore it will have an impact on actual decisions That people and organizations will make so it's very important to think carefully about how do you formulate these scenarios rather than Just simulating some random numbers and then go on with your detailed work. At least that's what I've learned a long time ago So you need to think very carefully about How do you generate these scenarios? What is the basis I'm gonna take this what's the basis then what's the potential basis for producing these scenarios? I Should say first of all if you know the world's not so the word scenario or Monte Carlo probably also from another area of Valuation and so fell evaluation of derivatives for example also there you encounter the word Monte Carlo or scenarios Those are risk neutral evaluation type of scenarios. I'm talking now about risk management real-world type of scenarios And those are quite different Flavors as a basis for building these real-world scenarios. What's the end? Objective that we have the end objective that we have of course that these scenarios Bear resemblance to what can actually happen in the world that lies ahead of us Because if they are not realistic after there no resemblance to what can actually happen in the world ahead of us Also our decisions, you know will not be in line with what can happen and therefore we will not have you know The best results that we set out to achieve Well, there are two basic Ways you could think about you know how you how you want to set up these scenarios One would be great if there would be theory which could help us if there would be one theory which says, you know How do financial markets? How do economies evolve over time? How do they correlate with each other? It has been validated against the data the academics agree well in economics and finance We're not there yet and for a very long time probably not Are we completely lost then as a basis for scenarios? No, we're not because if you look carefully in the data you look in the literature You look at the models what you see is a kind of a list of what we call stylized facts So things that most people agree upon and saying okay These are things which are really out there and if you think about you know, how financial markets and economies evolve These type of issues should be included in there and you see typically that these stylized facts They have their own line of literature. They have their own types of models so And that's a basis for producing scenarios. I'm going to take you through a few examples and then Summarize them and then we're going to move on to how you do the techniques They go a bit from long to short term The first one is the term structure of risk and return. That's the notion that risk can return properties Can be different depending on the investment horizon? The key example we always give is the correlation between equity returns and inflation Cumulative equity returns and cumulative inflation across the investment horizon. This is the horizon in years 20 years into the future and on vertical axis its correlation between equities and inflation Then you see different lines the solid blue line is very long-term historical US data based You see that this correlation havers around zero until seven or eight years So not very much correlation between equities and inflation, but for longer horizons you see it gradually moving up So there's a pattern in this correlation, which depends on the horizon on the term So there's a term structure in this correlation The other lines you see in here There's the thin red line is also for the US but now not calculated from historical data, but calculated from Scenarios which are simulated with the approach. I'm going to be telling you a bit about it's not exactly the same But the idea is that you see that this increasing pattern is Observed in the scenarios in a similar way as it has been observed in the data and The other lines you see in there are for other countries and regions and that's just to illustrate that something is not a stylized fact If it is just observed for some country or some time period it needs to be kind of a broader concept And also in the academic literature there and also some some review or overview papers now on This topic in general. What do we know about this term structure of risk and return? Campbell and Vichyra if you know that line of literature They were the first at least in the academic side to look at the consequences of these type of properties for optimal asset allocations Across the investment horizon and because obviously if you have some inflation target and Leaving all else unchanged if you have a correlation around zero of a correlation around point two or point three We'll have an impact on the optimal amount of equities in your allocation and so if you're thinking about scenarios for all these applications I talked about you need to deal with this Stylized fact one way or the other on the medium term a Second stylized fact that you need to include or need to think about carefully is business cycle behavior repression a recession depression recovery and all the The words are a crisis and all the words of course from the news of the last couple of years People have thought several times in the past that it doesn't exist anymore and that we would only have Stable growth and high stable growth with no no hiccups on the way every time of course. We're proven differently So what is it's about it's about Medium-term deviations from longer term structural growth paths. There's a lot known about that started also in the In the US with the NBR started collecting information about you know What do we know about business cycle behavior? What are the lead lag relations between variables? What are the type with what are the is the average length of the cycles etc. etc? Example of what type of information We are talking about here. You see from 1974 onwards the blue line is the OECD Composite leading indicator just taken from the OECD website, you know, how does the OECD try to? Pre-track basically, what's the state of the business cycle in general for all developed countries? The red line is a kind of a counterpart of that which just pops out quite naturally from the methodology We're going to be spending a bit of time on and so it's not exactly the same It was also not designed to mimic the OECD indicator or something But you see that it shows a similar a pattern and the idea now if you use the red Type of information for producing scenarios going forward You say can say well I have produced scenarios in which business cycle behavior is included in a similar way as an organization like the OECD measures the state of the business cycle For the careful observers You can also see that the red one tends to be a bit leading on the blue one Which may sound a bit strange and because the leading Indicator of the OECD is meant to lead on the business cycle and apparently the lead can be improved We know from correspondence that it's actually true so this is not some artifact or something and that is for two reasons one is OECD tries to keep their methodology relatively simple because others that people can replicate it or Check the calculations. So they've given in a bit on the on the on the leading quality The other difference is that in the red one. There's much more financial markets Information used than by the OECD. OECD is very macro Type a key message here is that you think if you're simulating scenarios for the medium term You need to think carefully about the business cycle and business cycle behavior. How do you get that into your scenarios? Well, then if you move to the shorter horizons You get the obvious or the usual suspects you could say from the risk management world Volatility for example, we know that volatility is not stable. It for rise over time. It's also not just in equities It's in all kinds of asset classes. It's correlated across variables It has certain dynamics over time type of models over here Of course arch and gauge models and the typical way of dealing with this This phenomenon which can get you the the noble price So if you're simulating scenarios typically for the rock shorter run for volatility and how it moves should be included Another one from that line is still risk the notion that When things are really becoming really bad if we're moving in the really the left tails of the distributions Correlations are typically much higher than in more stable times Of course, it has been learned again also during the crisis an example here This is are the quantiles of the distribution We're looking here at the correlation between US equity returns and European equity returns monthly returns and Point 10 that means the worst 10% returns and point 05 means the worst 5% returns and so forth So if you move to the left we move into the tail of the distribution Then the green line shows you a correlation a normal correlation if you ignore That that correlation can vary across the distribution you would find a correlation historically of some point 75 point 8 If you look more carefully in the data you get the blue line Where you see well here? It's similar, but if you move into the left tail of the distribution this correlation moves to one very close to one So there's much more Codependency between variables in the tail Then in a normal circumstance and the red line now is the counterpart of that But now not calculated from historical data, but from the scenarios Which shows you not exactly the same, but that the scenarios have indeed Captured this type of stylized fact in an adequate way Well if you sum that all together You get this kind of list of stylized facts that you would like to include in your Scenarios if you want them to be realistic or plausible Looking forward and term structure for risk and return business cycle behavior volatility and tail risk Well, we know a lot of things also about distributions and that they're not normal, but skewed and fat tails Term structures, we know about how yield curves move and we have parallel movements and tilt movements all these special Factor models available there for yield curves on the dotted line at this high level You could still say there's something like seasonal behavior and typical macro variables show seasonal patterns What could you say then if you want to simulate? Realistic or plausible scenarios going forward and you want to use that for decision-making purposes strategy formulation risk management purposes You want to include all of these things in that framework, so that's kind of the Objectives you could formulate for producing Yeah, good real-world Scenarios everybody with me still yeah, okay I'm notorious for having trouble with time, so That's why I check my my my my time schedule now and then okay now We've talked about what our scenarios what can you use them for and what is a kind of a basis? You can use to construct these scenarios and these stylized fact Key question then is of course, how do you do it? So how do you produce scenarios in which all of these things are represented in an adequate way? That's of course where where most of the work is and indeed as I was mentioned in the introduction at the approach or The approach that I want to be talking a bit about is indeed a frequency domain type of approach which helps you to Actually achieve this and so I must say this is an Approach of scenario analysis, which we as a company and also me as a person think is a good way to do it It's it's a way which which has proven that it can do these things we talked about does it mean? It's the only way you can do it. No, it's not the only way. Of course. There are more Possibilities, but I'm gonna telling you be telling you about this approach In general for the approaches you could say that there are two big lines one is time series modeling in general So classical time series modeling approaches for producing this scenario This one is is basically in that category you could say and also encompasses some of the more Classical ways of doing that. The other category is more Yes, to get stick different differential equation base. So risk neutral You know black-shells whole wide type of models Which are also being being used for these purposes and they all have their their pros and cons So this is an approach from the From the class from from the time series modeling where it's what is a bit specific is indeed that it use a frequency domain approach At the heart of that approach and it's the most important thing that I want to share with you Is a decomposition approach and it's a by orthogonal decomposition approach I didn't think of that name myself It was a very bright guy at a European insurance company when I talked to this about him He said ah, you're doing a bio orthogonal decomposition as a move But after that I understood what he meant so by orthogonal it means by had to so we're doing a decomposition across two dimensions and The word orthogonal which means zero correlation and so they are orthogonal to each other So it's two decompositions which are orthogonal the first of these decompositions is a decomposition across horizons and frequencies as An example here you see us equity data total return basis on a logarithmic scale from 1900s a very long-term data It has been decomposed That historical data into these three colored lines the red one the green one and the Purple one in such a way that if you just add up these colored lines you get the blue one So it's just an additive decomposition very simple at the end of the day. I Already told you is orthogonal if you put these things in a spreadsheet and you calculate the correlation You will find a correlation of zero between these components. So they're orthogonal What is special otherwise about it? And you can already see that graphically of course that the red one captures kind of the long-term trending type of behavior in the index the green one tries to Focus or emphasize the medium-term business cycle type of fluctuations in the index and the purple one is more the Intra-year erratic type of movements in the index. I mean it cannot show you that here But intuitive you can think that the red one is very much driving. Let's say the decade returns in the index The green one is very much driving the annual returns in the index and the purple one is very much driving the monthly returns in the index So that's how you can think of them Approximately I could show you but it's not included in or what can you do with this on the one hand you can use this to Analyze historical data and so separately look at the long-term correlations and the short-term correlations for example And by the way a decomposition approach is also not Unique or something as that's also very well known. It was already Tim better already said, you know if you think about financial markets and Economies, it's a trend. It's a cycle. It's a seasonal and it's an irregular. It's also already a decomposition idea business cycle indicator Literature is all about decomposition decomposing the trend from The cyclical deviation so that's not unique. It's just the way that you make the decomposition Well, you can use it to analyze these components separately, but most importantly what you can do with it You can also use that Those components to build scenario models dedicated scenario models for the long term for the medium term and for the short term So this is the counterpart looking forward of the same graph. So same setup. This is the total logarithmic US stock price index total return and these are the components So the trend the business cycle and the monthly component a thousand simulations from each component going forward So let's say 30 years on a monthly basis same interpretation as the graphs as I showed you in the beginning so blue is just one number 500 something and The yellow ones are the other thousand Monte Carlo simulations and the orange line is the expectation So separate models here have been constructed for simulating the long medium and the short term Focusing on that long-term return behavior the medium term return behavior and the short term return behavior But of course, we're not interested in these components as such what matters at the end of the day is this one And the total scenarios of the US stock price index. How can they evolve? It would give you something like this And then the key question which I haven't said anything yet about why do you need to do it in this way? And why not just take monthly returns build a model and simulate from that again? I'm not saying this is the only way to do it, but if you start Digging into the properties of these scenarios and start looking for example at this term structure of risk and return Now how is the correlation between equity inflation across the horizon then by doing it in this way? That's a robust way of getting the job done Robust I mean if you add a little data you re-estimate the models The structure of the model stays in place where classical models have the tendency to be very sensitive in terms of their estimation results projecting long-term correlations all of a sudden, you know completely upwards or completely downwards So it's a way of getting these stylized facts in there by zooming in on the different type of characteristics of the data Yeah This is the first decomposition the second decomposition What does that relate to that relates to the fact that what I just talked about is just you as equities and I said to you in the beginning already scenario analysis is about Many variables many financial markets many asset classes many economies at the same time So how do you deal with the interdependencies with the correlations between the variables? and That's where the other decomposition comes in What you can do there is work with factor models That's a typical way of dealing with these correlations Factor models and an example what I showed you here all these this is zooming in on the business cycle Part the business cycle component from 1974 again. You see all these colored lines one of them is you as equities so that was That one but then from 74 with us equities But now it's been complemented with 300 other business cycle components of other equities interest rates Volatilitys credits GDP CPI exchange rates across a wide range of countries Basically mostly developed countries over here producing around 300 of these business cycle components of a lot of financial market and economic variables In there together describing the overall business cycle behavior or business cycle dynamics Well to extract the most important information from that you can use principal component factors And the principal components factor is just a linear combination Of all these time series which captures the largest part of the joint behavior I see all you most of you nodding so you know PCA and here you see The weights from the first principal component factors So now this is not time But these are 300 variables and if you just multiply these weights with these 300 lines you get the red line And so the first PCA is the Linear combination of all this data Which extracts the largest portion of the joint behavior of all these 300 business cycle filter series producing you the red line and This is the line I showed you together with the OECD leading indicator. I was just taking a lot of financial market and economic data Isolating the business cycle part of the behavior and extracting the first principal components factor. That's all that it does Producing you this line with the familiar dating of the troughs. I've learned a long time ago to pronounce it in English And so the loaves in there I thought I thought it was troughs, but it's troughs The beginning of the 80s 90s 2000 or 8 and so the familiar dating just you know pops up basically This is just one factor and this is only just Within the business cycle component to capture Sufficiently let's say the joint behavior you you typically need more than one factor So you mean you use 10 factors for example To capture all the the joint behavior and the second thing is you can do the same trick in The other components and so I was talking about this business cycle part now You can do the same thing for the trend model and the same thing for the for the monthly Model and then this by orthogonal approach. This is what it boils down to you start off with a lot of data You take it apart with this decomposition approach in terms of frequencies and horizon Isolating long-term medium-term and short-term behavior Per component you then build a factor model. You could say a classical Dynamic factor model where the factors drive the joint behavior of them and then when you have the simulations of the factors Yeah, you can use them very easily to also actually Produce the scenarios for the equities in the GDPs and the exchange rates, etc. And that's of course what matters And you bring it all back together at the end and you have your scenarios For all your variables and all your time horizons That's the that's the The core idea of this this bi orthogonal approach which which helps you to capture Long medium and short-term behavior in your scenarios as you would like it to be according to these stylized facts This one I'm gonna skip and just a short version is you need more than this And so if you want to have stochastic volatility if you want to have tail risk if you want to have yield curves in there This is not enough. So you need kind of add-ons To get them in there, but they can be integrated in the same framework Two things I still want to do one is show you an example what type of output you can get from such an approach And focusing then for a moment on this business cycle area What you see here in this graph this runs until March of this year The lines you see over here is the first business cycle factor So again the one I showed you together with the OECD and so it kind of mimics the general state of the business cycle but the lines the colored lines plotted over each other are The assessment based on this framework based on data Well, the last one is until March until February until January until December until November So as more information becomes available How does this approach assess the overall state of the business cycle where the dotted line is today you could say one key difference with an OECD type of approach is that Once you have this business cycle data and you have your dynamic factor model on this business cycle data You can make scenario projections going forward of the business cycle So what's according to this methodology based on where do we stand today? And what's kind of the average historical business cycle dynamics? What's then the assessment according to this methodology of the world that lies ahead of us? So after the dotted lines it gives the expectation going forward. This is only the expectation Yeah, so you see you get this pattern over here, which basically says well You know, there's been a bit of a turnaround. We are very high There are at the top Basically, well, we may linger on still at a high level for quite some time But then there's a turnaround to come and you can think of this one. This is very much directly related to equity type of Equity credit type of asset classes and also GDP Related so you get an expectation of the state of the business cycle four years to come Important remark going back again to the beginning Scenario analysis is not forecasting And so if you tell a scenario person that they're forecasting they get kind of Uncomfortable the key thing is of course that you have an expectation But around that that's uncertainty and scenarios analysis especially about taking into account this uncertainty and that you can see in this graph Same idea and so this is the business cycle indicator going forward the expectation But now with these red lines in there They indicate the 10 percent quantiles of the distribution So underlying that you can think of scenarios and just putting them in portions of 10 percent Yes, and from this you can deduce. Well, this actually probability of an improvement Further on improvement still but there's also probability of a much faster Turnaround and what actually if you look over here, you know the values of a rate Of course, they have a low probability But they are in that range as well So you can make also probability based assessments about the state of the business cycle and recently We have been very recently we have been doing some very formal backtesting of a type of experiments There's also the question which obviously pops up if you look at this On this approach and especially in this business cycle area You can show that you can actually do better with these Factor models than with a random walk type of approach. We can actually show you can get a little bit better forecasting Yeah, if you look at purely from the forecasting perspective, so this actually gives you some Confidence, you know that there's relevance because if you feel there's relevance in this historical data in this business cycle behavior as a Stylized fact that it says something about the future. Yeah, then you should be able to show all so that it Has its value and and and that's actually a possible And a way of thinking about that Is Especially for this audience perhaps if you look at the financial analyst journals some time ago two years ago or so there was an Interview with Eugene Farmer one of the founders of the efficient market hypothesis of the capital asset pricing model And this is a really nice quote. He said in an interview With with Robert Litterman. He said in the beginning we thought price changes were Random that that was what efficient markets meant. So we don't know anything at all later on He says now we know better. We say he says market efficiency means that deviations From equilibrium expected returns are unpredictable. We do not know where we will fall into the distribution, of course But he says ex equilibrium expected returns Can vary over time in a predictable way? and As a result overall The returns have a little bit of predictability in there and so these variations in equilibrium expected in Equilibrium expected returns have to do of course with changing Risk preferences for example over time and the what I showed you with this business cycle indicator And here it is in terms of some other variables and so equities high yield spreads And exchange rates and you look at the direction of the distribution projected from a certain Date in the past and how the realization has fallen in yet where exactly in the realization You know the spreads have fallen if you don't know but the direction of the expected returns and how the realization has fall show a very interesting relation so this way of looking at Returns and distributions very much links to how someone like using pharma thinks about that Just one final remark. I'm not going to do this in total All this I talked about is Scenario analysis based on stylized facts which are derived from literature, but also a lot about historical data So it builds on the presumption that there's relevance in historical data for looking at the future Already since the very early days of scenarios people have realized that of course that in itself is not enough or May not be enough to get the best forward-looking scenarios. Why not there may be changes over time Which impact the future which were not in the historical data and so when we For example from a long time ago. It was the the European Central Bank introduced its inflation target But at the moment they introduced that if you look back at the historical data that information was not included so inflations were For Europe were much above two percent If you would then have to given that information Project your expected inflation rate going forward. Of course you want to take into account What the European Central Bank has said about its inflation target? So then you put in additional Forward-looking you could say view type of information into your historical base framework in today's situation It would of course be central bank intervention and the effect that has on interest rates Not included in in that extent in the historical data on which you built your models You can also have other examples here You can have an investment committee of a pension plan which has certain Views on the equity risk premium for example and you want to include them in your scenarios or you want to do sensitivity Analysis so I just want to make the remark that it's important in scenarios that you not only you know Do your best as possible to extract information from historical data and literature But also allow for taking into account additional forward-looking information for abuse for producing the best forward-looking scenarios Well, if you summarize that how we've talked about stochastic scenario analysis Which in our experience is a very powerful tool to support strategy decision-making and also risk management in an integral way The properties of the scenarios that you put in there Are very important because if they are different The results from the models will be different and the decisions that people make will be different and that will actually impact You know to what extent will you achieve your objectives or not? Well, what I haven't put too much emphasis on but it's also important if you think about these different applications That's our long-term strategy and short-term risk management and all these stylized facts Which you typically see that people have different models for different purposes a Separate model for the long run and another model, which is good at tail risk for example. Well, of course strategy Portfolio construction and risk management are Integrated with each other So if you go through that process and along the way you switch from the underlying scenario model You're in trouble with consistency because a strategy which may be Working well in scenario model a may no longer be the optimal strategy in scenario model B So it's important to think about also about consistency in your scenario framework Well, we looked at these stylized facts that they Are a valuable basis for producing scenarios also if people use different methodologies It's my experience at the end of the day most scenario builders will recognize the list of stylized facts We talked about as a basis for producing your scenarios and also evaluating whether you have Good scenarios Well, it's indispensable to allow for views for additional forward-looking information And I told you a bit about this frequency domain type of technique as one of the possibilities Forgetting these stylized facts into the scenarios that leaves us still a little bit of time for the Four according to my schedule are there any questions or remarks Yeah Yeah, and it's a That's a very good point From I can best tell it from from from our experience The level where we typically stop with the modeling at the moment is let's say Triple a credits us So benchmark and sub benchmark at a type of left For fixed income the modeling typically works by simulating yield curves and putting in, you know the actual maturity distribution and rating distribution of The client of the pension plan for example, so then you could say Yeah, you're you're close to you know security level but in an aggregated a way Equity type is there more on a on a benchmark and sub benchmark level in concept For this methodology, it's not a limitation to push that further Especially also for this frequency domain technique that the original idea My personal ambition at the end for a long run still is you know, you can simulate scenarios from let's say 30 years out Until for the coming 10 days So it just would just would mean in what I talked about We have these let's say decade returns annual returns monthly returns There would be an additional component simulating the daily returns Conceptually is possible in them, but then you get into the typical short-term classical risk management Models and it would be great. Of course, you could really integrate long-term strategy until really Short-term operational risk management But the typical applications of these approach typically stop at the what we call the risk management or the risk monitoring of the strategy itself And they're the simulation the shorter simulation horizontally of horizontal is typically one month Combined with yeah, this benchmark sub benchmark way of modeling the assets But conceptually no no limitations and the other can always mean two things so either everything was completely clear I Yes Yes No, no, no, sorry it's that was yeah, no it is actually The horizon the horizon looking from today into the future No based on historical data, so this would take this has taken data from let's say 1900 So more than a century of data and then based on the data You're gonna collect all one-year returns and all one-year inflations calculate the correlation that gives you this number You're gonna look at all two-year returns and two-year Inflations gives you this number Until well the numbers over here So here it is all the ten-year returns and all the ten-year inflations giving you this number No, not yet. No because yeah, then you would get an equity index and a price index Which is not a good basis to calculate your so it's cumulative returns for different investment horizons Based in this case on long-term data, so that holds for the blue line The other lines are forward-looking calculated from the scenarios So then just having all these scenario simulations you do the same But then across all the scenarios and calculate these correlations Yeah, as well as well as well. Yeah, yeah, but drift but that there's still let's say the There's still considerable volatility. Let's say in in 20-year returns, so but of course indeed if if if the The longer the horizon the drift becomes more and more important for sure. Yes. Yes