Ortec Finance Scenario approach

Transcription

1 Ortec Finance Scenario approach Ortec Finance Scenario Department May 2016 Hens Steehouwer

2 Contents 1. Executive summary Introduction The bottom line Historical perspective The early days ( ) Econometric rigor ( ) Yield curves (1996) Corporate credits (2002, 2011 and 2015) Short term scenarios (2005) Dynamic Scenario Generator (2009) Integration of short term scenarios (2011) The truly long term (2012) Ortec Finance Scenarioset (2016) Methodological foundations Stylized facts Term structure of risk and return Business cycles Time-varying volatility Tail risk Non-Normal distributions Yield curves Out-of-sample testing Views and expert opinion Practical scenario construction Factor models and other models Short term volatility Scenarios for valuation References...50 Disclaimer Ortec Finance bv 2 / 54

3 1. Executive summary The mission of Ortec Finance is to improve investment decision making, and economic scenarios play an important role in that effort. In a separate paper, Steehouwer (2016), we described why it is important to think very carefully about the construction and application of economic scenarios. The aim of the present paper is to describe the latest version of the Ortec Finance approach to constructing economic scenarios. These scenarios are available as of July 2016 (end of June 2016 scenarios). What does the Ortec Finance Scenarioset do? What does the Ortec Finance Scenarioset (OFS) provide to people and organizations? OFS bundles the results from continuous innovations, based on 30 years of experience in building and applying scenarios for clients around the globe. These innovations have consistently expanded and improved OFS, which means that old versions of the methodology can always be considered as a special case of the latest methodology. OFS can be used for both investment decision making and risk management, both in the institutional as well as in the private wealth markets, and thereby ensures consistency. OFS is always the most realistic reflection that Ortec Finance can produce of how economies and financial markets might (rather than will) evolve in the future. The methodology used is unique in its sort, the odd one out in the world of scenario models. Not because we want to be different, but because we think this methodology is in the best interest of our clients. The realism of the OFS scenarios are continuously being tested and, if needed, improved upon based on these tests. Currently, the forecasts from OFS are 10% better in line with reality than those from simple benchmark models. We are fully transparent about the construction of each version of OFS. OFS comes with extensive economic and financial market guidance and model documentation. OFS allows clients to make changes to the scenarios in a consistent way. In the future, we will make it possible to evaluate if such changes add to making the scenarios more realistic or not. OFS is available for the end of every month, for horizons from one month to decades, and with a worldwide coverage of more than 600 economic and financial market variables (benchmarks). Ortec Finance bv 3 / 54

4 The relevance of scenario models At Ortec Finance, we believe that models in general, and the latest version of our scenario models in particular, enable people to manage the complexity of investment decision making. Moreover, we believe that proper models, when properly used, are in fact the best tool for this, because they are consistent, objective and transparent. In this context, the use of scenarios with the aforementioned features can lead to better investment decisions, and can make people and organizations more successful in achieving their objectives. In the past 30 years, the historical evolution of our scenarios has reached many milestones. We continue to improve our scenario models. These innovations come in many small, and sometimes bigger steps. Without these innovations, we would not be able to meet today s requirements, and our scenarios would provide a much less realistic basis for investment decision making. Research and experience All these changes are the result of a way of working that in all these years has not changed: one of continuously improving and expanding our scenarios, based on a mixture of the latest research, the experience of applying the scenarios in practice and the growing and changing demands put on the scenarios. This has always been, and will remain, a consistent and stable innovation process in which new versions of our scenario methodology always encompass earlier versions, rather than one in which we start off in a completely new direction every now and then. The importance of dynamic scenarios The development of OFS was propelled forward by two underlying trends. The first started with the financial crisis in It has grown even stronger since then, because of events like the euro crisis and the subsequent unprecedented monetary interventions worldwide. This has raised attention to the way realistic financial models, and scenario models in particular, describe the world we live in. The second trend is the increased attention to short term risk management, in response to the crises of the past decade. Nowadays, only a few investors are willing and able to act as purely long-term investors. This has put more emphasis on the short term properties of scenarios. It has become increasingly important that scenarios are realistic in the light of the actual economic and financial market circumstances, and take into account how these circumstances change over time. In short, these two trends require the scenarios to become more dynamic by taking into account the actual economic and financial market circumstances, including the effects of interventions by the central banks. Dynamics are not wanted for their own sake, but because they make scenarios more realistic. And more realistic scenarios can lead to better investment decisions, helping people and organizations to become more successful in achieving their objectives. Ortec Finance bv 4 / 54

5 With the introduction of OFS, a question that has always been asked regarding scenarios has finally been answered: how to deal with the dynamics in expected returns in a unified and consistent way. Back in the 90 s, short to medium term expected returns that changed over time were seen as an undesirable side effect. At the introduction of our Dynamic Scenario Generator (DSG) in 2009, and its update in 2011, the same theme emerged. This led us to introduce two versions of the DSG scenarios: the so-called Equilibrium (EQ) and the Disequilibrium (DIS) scenarios. In 2013, we decided that having these two versions of the scenarios was undesirable. Instead, to enforce consistency, we wanted to present one version of the Ortec Finance scenarios. This version would represent our most realistic scenarios on both the short and long term, and would have to be able to be used for all applications in all markets, ranging from long term investment decision making to short term risk management. The result of this endeavor is OFS. The foundations of OFS What are the methodological foundations, the essential ideas underlying the scenarios of OFS? Or, if we use the scenario definition of Bunn and Salo (1993), which states that a scenario is a possible evolution of the future consistent with a clear set of assumptions, what exactly is that clear set of assumptions? The methodology is built on three components: stylized facts, out-of-sample testing and views and expert opinion. Stylized facts OFS is founded on the belief that a number of robust stylized facts of the evolution of economies and financial markets over time need to be reflected in the behavior of scenarios, in order for them to provide realistic descriptions of the future. These stylized facts concern the term structure of risk and return, business cycles, time-varying volatility, tail-risk, non-normal distributions and yield curves. Stylized facts are derived from studying economic and financial market data, not just by us, but by many academics, economists and investors around the world. All stylized facts are replicated together in a single version of OFS and are united in the DSG, the model which is used to generate the scenarios of OFS. Some models are good at describing business cycle behavior, other models are good at describing time-varying or stochastic volatility, and yet other models are good at describing yield curve dynamics. What is unique about the DSG model and OFS is that they are able to deal with all of these stylized facts at the same time. This brings a much needed consistency to the investment decision making and risk management process, by avoiding the use of different models for different purposes. Ortec Finance bv 5 / 54

6 Out-of-sample testing We use out-of-sample testing to be able to make a choice between different and competing calibrations of the DSG that replicate the stylized facts equally well, but may nevertheless exhibit very different short to medium term risk and return behavior. On the basis of outof-sample testing, we select the most realistic calibration. We do this by continuously exposing our scenarios to the toughest possible tests that we can design. It is import to perform such tests on an out-of-sample basis. This means that in calibrating and estimating models, it is prohibited to use data of the future that are also used to evaluate the quality of the short to medium term risk and return of the scenarios. It is easy to get a great in-sample model performance, but this is likely to perform very poorly on an out-ofsample basis, which is of course the only thing that matters in reality. The resulting risk and return, as described by OFS, is not fixed, but varies over time and is therefore dynamic. Building a model in which risk varies over time is not very special in itself. What is special is that the way in which risk varies is in line with the course of historical events, and our recollection of how risk evolved during this historical period. So, the dynamic risk of OFS responds in a realistic way to changes in economic and financial market circumstances. Views and expert opinion We use views and expert opinion to deal with the fact that one cannot rely on historical data and models alone. Information can also be available which is not, or not sufficiently, contained in the historical data on which the scenario models are calibrated, but which is very relevant for the scenarios of the future. We refer to such information as views. One obvious example in today s environment is the unprecedented monetary stimulus that is provided by central banks around the world, in their attempt to stimulate economic growth and increase inflation. Another example concerns the consequences of the recent decision of the British people to leave the European Union. We should also not shy away from intervening if we deem the scenarios of certain economic variables or asset classes not realistic enough. We refer to such interventions as expert opinion : improving the properties of the scenarios based on other information than the models provide, for example from modeling experts, asset class experts or regional experts. It is important to incorporate both views and expert opinion in the scenarios as consistently as possible, and to provide full transparency. Ortec Finance bv 6 / 54

7 Building consistent scenarios On the practical side of things, how are the scenarios actually constructed? In terms of the scenario definition of Bunn and Salo (1993), how do we manage to come up with scenarios that are consistent with our clear set of assumptions? Four key elements are involved in the practical construction of the scenarios. The scenarios start from the current market situation, which not only gives the latest values of economic and financial market variables to start the simulations from, but also describes the economic and financial market situation in a wider sense. What has been the direction of the developments in the recent past? What types of interventions by central banks are going on and what is the latest forward guidance that they have given? If we simulate for a horizon that is long enough, the scenarios will ultimately converge towards long-term steady state values. Stylized facts and views drive the transition of the scenarios from the current market situation towards the long-term steady state. This holds both in terms of expectations and in terms of uncertainty or risk. These four elements are not strictly divided, but fluently merge into one another. The current market situation is partly a consequence of the stylized facts, just as the views are also determined by the current market situation, and just as the long-term steady state values can be considered to be views. Factor based scenarios The scenarios of OFS are not constructed by simply extrapolating historical time series of individual variables. If we would use this approach, it would be impossible to replicate all the stylized facts in the scenarios and to obtain a realistic (out-of-sample) dynamic risk and return behavior. Instead, the scenarios of over 600 economic and financial market variables covered by OFS, from one month up to decades into the future, are generated by a small number of underlying factors. There are three dedicated factors for the long term, nine dedicated factors for the medium term, and ten dedicated factors for the short term. These factors are constructed from hundreds of input series. The dynamics of these factors drive the expectations and uncertainty of all variables, which ensures the consistency that is so important to generating realistic scenarios. We start by decomposing all input time series into a trend, business cycle and monthly component. Then we calibrate dedicated factor models for each of the components, which produce scenarios for the corresponding components for all variables. Finally, the scenarios of the components of variables are recombined into the scenarios of the total variables. An important example of these factors is the Ortec Finance Business Cycle Indicator (OF BCI). Unlike more conventional leading indicators, for example the OECD Composite Leading Indicator (CLI), OFS does not stop at producing (leading) historical data. It also provides realistic scenarios of the OF BCI for the future, and these are important drivers of the medium term scenarios for growth, equity returns, credit spreads, real estate, and so forth. Ortec Finance bv 7 / 54

8 Other important features A number of other modeling approaches are integrated into the DSG, so that it can reproduce all other stylized facts in the scenarios, and can incorporate views in a consistent way: high-dimensional stochastic volatility modeling, high-dimensional tail risk modeling, Nelson-Siegel based term structure or yield curve modeling, and various ways of imposing views on the scenarios. Short term volatility To facilitate a consistent application of OFS in both investment decision making and risk management, OFS corrects for the smaller short to medium term uncertainty that is caused by its forecastability. Expected returns and the dynamics of volatilities are unaffected, but short-term volatilities increase. OFS will continuously be tested and monitored to show how realistic the scenarios are in terms of their short-term uncertainty, and will be further improved based on the results of these tests. Furthermore, OFS allows clients to change scenarios in a consistent way, also in terms of the short-term uncertainty. Scenarios for valuation OFS provides realistic real world scenarios for investment decision making and risk management. However, these scenarios easily get mixed up with scenarios or Monte Carlo simulations that are used for valuation purposes. It is important to realize that these actually serve very different purposes. Valuation scenarios have to be highly accurate for the current market conditions, but they lack the ability to describe how these conditions might evolve over time. Real-world scenarios aim to describe the future, and not just the present. Besides OFS for realistic real world scenarios, Ortec Finance also provides riskneutral scenarios for valuation purposes, generated using different models than those of the DSG. We use the best models to generate our real-world scenarios, and we use the best (but different) models to generate our risk-neutral scenarios in a realistic and consistent way. Ortec Finance bv 8 / 54

9 2. Introduction The mission of Ortec Finance is to improve investment decision making, and economic scenarios play an important role in that effort. In a separate paper we described why it is important to think very carefully about how to construct and apply economic scenarios. See Steehouwer (2016). Scenarios and scenario models are used to take into account the uncertainty about the future of economies and financial markets in investment decision making. Investment decisions are made in the real world for real world future objectives of real people and real organizations. So what matters is to construct scenarios that as realistically as possible describe what might happen to economies and financial markets in the future, starting from the moment at which the investment decisions have to be made. But this still leaves unanswered the questions of how to construct such scenarios. The aim of the present paper is therefore to describe the latest version of the Ortec Finance approach to constructing economic scenarios. These scenarios are available as of the scenarios for June 2016 and onwards. Ortec Finance has 30 years of experience in building and applying scenario models. Because of the relevance for our clients achieving their objectives, we continuously innovate on our scenario models. These innovations come in small steps but sometimes also in bigger steps. An unpleasant aspect of innovations is that they bring changes: changes to how the models work, changes to the scenarios they produce and changes to the results from applications that use the scenarios. However, without innovations and changes we would of course still be working with the very same scenario models as 30 years ago. These would not be able to meet today s requirements by far and, on top of that, would also be a much less realistic basis for investment decision making. The latest version of our approach to constructing economic scenarios is based on 3 years of research and development, internal discussions and testing. So, the step we make with the scenarios for June 2016 clearly falls in the category of the bigger innovations. With this background, it is not hard to imagine that there are many things to say about how we construct the latest version of our scenarios exactly. In this paper, we aim to provide our description at an intermediate level in order to make it accessible to a larger, nonspecialized, audience while at the same time being sufficiently specific on how we actually construct the scenarios. Several more specialized papers are available, some of which we will refer to throughout the paper. To avoid losing track, we start with the end result, the bottom line. When all is said and done, what is it that the Ortec Finance Scenarioset (OFS) provide to people and organizations? After that, we sketch the historical context in which to place the latest version of our scenario methodology. Then we move on to describing the foundations of our methodology. This can be seen as the clear set of assumptions underlying our scenarios from the definition by Bunn and Salo (1993) who state that A scenario is a possible evolution of the future consistent with a clear set of assumptions. In the last section we discuss how we turn these methodological foundations into a more practical way of constructing the actual scenarios. How do we arrive at scenarios that are actually consistent with our assumptions? Ortec Finance bv 9 / 54

10 3. The bottom line If one cannot or does not want to delve deeper into the underlying ideas and models, what should one then at least need to know about the Ortec Finance Scenarios (OFS)? What do they provide to people and organizations and why is this relevant? OFS bundles the results from continuous innovations, based on 30 years of experience in building and applying scenarios for clients around the globe. These innovations have consistently expanded and improved OFS, which means that old versions of the methodology can always be considered as a special case of the latest methodology. OFS can be used for both investment decision making and risk management, both in the institutional as well as in the private wealth markets, and thereby ensures consistency. OFS is always the most realistic reflection that Ortec Finance can produce of how economies and financial markets might (rather than will) evolve in the future. The methodology used is unique in its sort, the odd one out in the world of scenario models. Not because we want to be different, but because we think this methodology is in the best interest of our clients. The realism of the OFS scenarios are continuously being tested and, if needed, improved upon based on these tests. Currently, the forecasts from OFS are 10% better in line with reality than those from simple benchmark models 1. We are fully transparent about the construction of each version of OFS. OFS comes with extensive economic and financial market guidance and model documentation. OFS allows clients to make changes to the scenarios in a consistent way. In the future, we will make it possible to evaluate if such changes add to making the scenarios more realistic or not. OFS is available for the end of every month, for horizons from one month to decades, and with a worldwide coverage of more than 600 economic and financial market variables (benchmarks). At Ortec Finance, we believe that models in general, and the latest version of our scenario models in particular, enable people to manage the complexity of investment decision making. Moreover, we believe that proper models, when properly used, are in fact the best tool for this, because they are consistent, objective and transparent. In this context, the use of scenarios with the aforementioned features can lead to better investment decisions, and can make people and organizations more successful in achieving their objectives. For more information on the relevance of realistic scenario models we refer to Steehouwer (2016). 1 10% may not seem much, but forecasting economies and financial markets is notoriously difficult. Achieving a 10% better forecasting performance across multiple horizons and a wide range of economic and financial market variables is a daunting task. For some, a 10% improvement may even be hard to believe. Ortec Finance bv 10 / 54

11 4. Historical perspective In this section we describe the milestones in the historical evolution of the scenarios of Ortec Finance and the reasons why, starting from the very first versions of 30 years ago until the most recent version that is available as of the scenarios for June 2016 and onwards. The difference between the first versions of the scenarios and the most recent ones is of course immense. In the past, the scenarios covered only a few economic variables and asset classes on an annual simulation basis while nowadays this has grown to more than 600 economic and financial market variables (benchmarks) on a monthly simulation basis. In the past, the scenarios were calibrated at most once a year, by one or at most two persons, and based on data collected manually from hardcopy reports while nowadays, a team of 10 to 15 specialists produces the scenarios in the first two weeks of every month, based on a multiple of automated data sources and delivered together with extensive documentation. In the past, simple Vector Auto Regressive models were used while nowadays, the models include complex things as filtering techniques, Dynamic Factor Models, stochastic volatility and so forth. In the past, there was one piece of programming code that simulated the scenarios based on flat text file input while nowadays, the software runs on a database, has an interactive interface and uses parallel computing. However, all these changes are the result of a way of working that in all these years has not changed: one of continuously improving and expanding the scenarios based on a mixture of the latest research, the experience of applying the scenarios in practice and the growing and changing demands put on the scenarios. This always has been, and always will be, a consistent and stable innovation process in which new versions of our scenario methodology always encompass earlier versions, rather than one in which we start off in a completely new direction every now and then 2. 2 This is quite striking because of course during those 30 years of innovation various generations have been working on the Ortec Finance scenario methodology. Each of them has (implicitly) passed on this way of working to the next generation and the original direction chosen has (apparently) stood the test of time. In chronological order, we mention Guus Boender( ), Jan van Mierlo, Lucas Vermeulen, the author, Henk Hoek and Alex Boer, of course without implying that there have been and are not many others making important contributions. Ortec Finance bv 11 / 54

12 4.1 The early days ( ) ORTEC, the parent company of Ortec Finance, was founded in 1981 and originated from the Erasmus University of Rotterdam. The core purpose of the company was to apply models and techniques from Operations Research for practical purposes. The financial applications of the models lifted off in 1985 with the development of an actuarial and Asset Liability Management (ALM) model for the pension plan of a large Dutch bank. Inspired by the following quote from Kingsland (1982), a simulation based approach was adopted for this model. The dynamic behavior of a pension plan is clearly dominated by rules and methodology which are discontinuous and non-linear function of its financial condition. The task of developing a closedform solution to evaluate the potential state of a pension plan following a series of stochastic investment and inflation experiences would be extremely difficult, if not impossible. To date, the only approach that has proven feasible is the application of Monte Carlo Simulation, wherein an investment and inflation scenario is generated by random draws based on the expected probability distribution of year to year investment and inflation behavior. In order to develop an accurate assessment of the range of potential uncertainties, it is necessary to repeat this simulation process by generating dozens or hundreds possible scenarios, consistent with statistical expectations. For the expected probability distribution of year to year investment and inflation behavior a simple Vector Auto Regressive (VAR) model was used to simulate long term scenarios on an annual basis for a small number of variables: inflation, interest rates and asset class returns. The parameters of the VAR model were calibrated with a method described by Boender and Romeijn (1991). This method made it possible to directly set the long term expectations, volatilities and correlations and (1 year) dynamics of the scenarios. During the years that followed, the approach for generating the scenario was slowly refined and the coverage of variables expanded. For example, exchange rate scenarios were added because of the needs of the first international clients starting to adopt the ALM approach. However, the focus in these years was more on developing the scenario approach to ALM as a whole than on the economic scenarios themselves. Ortec Finance bv 12 / 54

13 4.2 Econometric rigor ( ) As ALM and scenario analysis became more established, it became possible to look deeper into how the scenarios of economic and financial market variables were generated. One important step was to abandon the method of Boender and Romeijn (1991) and switch to the econometrically more rigorous method of Ordinary Least Squares (OLS) for estimating the parameters of the VAR model. This offered more flexibility in the model specifications which was important because the number of variables in the model kept growing. In particular, it was now possible to put (zero) restrictions on the parameters of the model to avoid having to estimate too many parameters based on limited data. Although this certainly makes sense and works well from an econometric perspective, we also learned that this does not necessarily mean that in practice it also results in scenarios with the desired properties. And therefore, next to the econometric rigor, also some more pragmatic approaches were introduced. A first example is that it was found that the volatilities and correlations as present in a limited set of, say 500, scenarios were different from those implied by the parameters of the model: sampling uncertainty as we call this nowadays. Due to computational constraints, it was not easy to simply increase the number of scenarios to reduce this sampling uncertainty. Therefore a solution was found by running a numerical procedure on the scenarios that made their expectations, volatilities and correlations match exactly with those of the model. A second example concerned the short to medium term expectations of the scenarios. Expected returns from a VAR (or any other dynamic) model vary with the investment horizon and with changes in the starting conditions (last year returns, interest rates, inflations, etc.). This was then seen as an undesirable side effect and required a solution. This solution was found by again running a numerical procedure on the scenarios which simply changed the means (or expectations) of the scenarios of each of the variables for each consecutive year to stable, user specified, values. This was a pragmatic approach because it was not consistent with the parameters of the VAR model and thereby also not with the dynamics of the underlying economic and financial market data on which the model was estimated 3. A third and final example of a more pragmatic than econometrically rigorous approach, was to resort to expert opinion to arrive at a parameter structure that resulted in scenarios with the desired properties. This is where estimating turned more into calibrating the VAR model. This became more and more necessary as the number of variables in the model kept growing. In the latest stages of this version of the scenarios it could take up to 2 months to arrive at an acceptable calibration of the model. This struggle also led to a revival of the method of Boender and Romeijn (1991) but under a different name. As described in section 3.1 of Steehouwer (2005), it turned out that they had actually reinvented the Yule-Walker equations which date back to the 1930 s. Steehouwer (2005) shows that the Yule-Walker approach can lead to better estimates of the parameters of a 3 Occasionally, forecasts from the VAR model without the stabilized means (or expectations) were compared with what had subsequently happened to for example the equity markets. It was then found that the forecasts had often been not that bad. This was a very first version of back-testing the scenarios to which we turn later. Ortec Finance bv 13 / 54

14 VAR model than the OLS approach in situations where there is relatively little data available compared to the number of parameters, which was precisely the case. In these years, a great deal was learned about the desired properties of the scenarios and about how VAR models can be used to produce these properties. This knowledge was obtained from the practical applications of the scenarios as well as from the more fundamental research described in Steehouwer (2005). One especially relevant property of the long term scenarios as used for ALM, based on annual economic and asset class return data, is that of the term structure of risk and return. This notion tells us that risk and return vary with the investment horizon. For example, the correlation between equity returns and inflation is found to be low for short to medium term horizons but higher for longer horizons. This effect, which was coined in the literature by Campbell and Viceira (2002), was the prime reason why it became more and more difficult to calibrate the VAR models in the appropriate way. An overview of how to apply VAR models in practice, as learned in these years, is given by Steehouwer (2006). Ortec Finance bv 14 / 54

15 4.3 Yield curves (1996) During the nineties, the scenario approach to ALM gained more and more traction and was applied on a large scale especially by and for pension plans. As a logical consequence, thinking started to see if the approach could also be applied for other institutions than pension plans, for example for real estate managers, insurance companies or banks. For pension plans, it was in those days sufficient to work with relative simple interest rate scenarios. On the balance sheet of a typically (Dutch) pension plan, fixed income assets were valued at nominal value and liabilities where valued based on a fixed discount rate of 4%. Therefore, the interest scenarios consisted of only a long term government bond yield which was considered to hold for all maturities, essentially a flat yield curve. When this approach was considered for use in an ALM model that was being developed for a Dutch bank, it soon became apparent that this was not realistic enough. The shape of the yield curve and how it changes over time is the central driver of the balance sheet and profit and loss account of a bank. What happened then was exemplary for the approach that has been followed with every improvement and expansion of the scenarios ever since. This approach starts with making more explicit what is meant exactly with the desired properties of the scenarios and results in a list of so called stylized facts, in this case of how yield curves behave in reality. The next step is then to develop a model which is able to replicate these stylized facts as best as possible. Or, as Diebold and Li (2006) put it: A good model of yield curve dynamics should be able to reproduce the historical stylized facts concerning the average shape of the yield curve, the variety of shapes assumed at different times, the strong persistence of yields and weak persistence of spreads, and so on. It is not easy for a parsimonious model to accord with all such facts. Apart from finding the best way of replicating the stylized facts, it is also important to maintain or improve the properties of the existing scenario model. This gives a clear objective to the model development and stimulates an open mind in thinking about which type of model to use. Inspired by Damm (1995), this led to extending the existing VAR model with Nelson-Siegel functions for yield curves. Nelson and Siegel (1987) introduced what is essentially a static and parsimonious function (i.e. a function with only a few parameters) that describes the yield as a function of the maturity at a specific point in time. Other models as those of Vasicek (1977) or Hull and White (1990) where less suitable because these are dynamic models that not only describe the shape of the yield curve at a specific point in time but also, in a very specific way, how the yield curve changes over time. This did not match well with the VAR model that governed the dynamics of the scenarios of exiting variables. Ortec Finance bv 15 / 54

16 The original results and approach to modeling yield curve scenarios are described in Steehouwer (1996) (in Dutch) and the Nelson-Siegel approach is nowadays used in the scenarios of Ortec Finance for basically any variable that has a maturity dimension such as government bond yields, break even inflations, swap spreads, credit spreads, all across countries. As said, the approach was originally developed for a bank ALM model, but it gained much wider use with the introduction of mark-to-market and economic valuation of assets and liabilities of pension plans and insurance companies. The Nelson-Siegel function as such also gained wider use, for example at central banks following Svensson (1995). And the combination with VAR models found a solid academic foundation following Diebold and Li (2006) and Diebold, Li, and Yue (2008). Ortec Finance bv 16 / 54

17 4.4 Corporate credits (2002, 2011 and 2015) Stimulated by the demand for more detail in the scenario modeling of asset returns, the fixed income scenarios were extended from government bonds towards corporate credits. In the historical developments of these corporate credit scenarios, three milestones can be distinguished. In 2002 corporate credits where introduced in the scenarios, based on the approach described in Londen (2002). This was a rating transition based approach in which the probabilities of rating transitions where linked to the economic conditions, for example in terms of GDP growth, which worked together with the existing risk free government bond yield curve scenarios. This approach has great intuitive appeal but it is difficult to calibrate this model in such a way that it produces the required stylized facts of the return scenarios. For example, after all the estimations had been done in an econometrically rigorous manner, it turned out that the correlations in the scenarios between the returns on equities and the returns on High Yield (HY) corporate credits where much lower than observed in reality, so additional measures where needed. Fortunately, the scenarios had an annual simulation basis and the model was calibrated only once per year, such that there was ample time to come up with corporate credit scenarios adequately replicating the relevant stylized facts. As we shall see in Section 4.7, in 2011 the simulation basis of the scenarios increased from annual to monthly. In the meantime also the required coverage of the asset returns had increased further in terms of asset class and regions. Specifically for corporate credits, also the returns for more detailed rating classes where requested (e.g. BB, B and CCC rather than just HY). More detailed stylized facts had to be represented in the scenarios in terms of for example business cycle dynamics, time varying volatility and tail correlations. And to complicate matters further, scenarios where now required for every month end for risk monitoring purposes rather than just one a year. Combining all these requirements with the existing rating transition based approach, simply became impossible, also because of data limitations. Therefore, in 2011 the rating transition based approach was replaced by an approach that modeled credits spreads and excess returns on top of the risk free government bond yields and returns. This approach is described by Boer (2013). One could argue that this was one of the very few cases in which an existing scenario modeling approach was discontinued in the evolution of the scenario of Ortec Finance. In terms of the modeling approach this is true but much less so in terms of the stylized facts that where modelled in the corporate credit return scenarios. For example, the spread and excess return based approach allowed for a much better replication of the equity HY return correlation in the scenarios. And one could say that the rating transitions are still implicitly present in the scenarios, but now dictated by how the credit spread scenarios evolve 4. 4 This also requires assuming a valuation model of corporate credits that is based on rating transitions. Ortec Finance bv 17 / 54

18 The spread based approach to corporate credits was also used by Steehouwer (2013) for extending the scenarios with sovereign spreads for European countries, using the German government bond yield curve as the reference curve with the highest credit quality. This was based on the experience of the Euro crisis which revealed that country specific risks within Europe where actually much larger than was suggested by the (relatively small) differences between the government bond yields for individual Euro countries in the years leading up to the crisis. Government bonds where not as risk free as one thought. The third and latest milestone in the modeling of corporate credit scenarios was in 2015, when, based on practical experience over the years and ongoing research, the approach introduced in 2011 was refined and expanded. In short, the corporate credit scenarios were made even more realistic and consistent. The spread component was removed from the excess returns, spreads and excess returns where made maturity dependent (with the help of the Nelson-Siegel approach) and a consistent framework was developed for deriving the long term steady state values across countries and ratings. This approach is described by Hennink (2015a,b). Ortec Finance bv 18 / 54

19 4.5 Short term scenarios (2005) The burst of the dot-com bubble in 2000 led to different responses. A first response was that Liability Driven Investment (LDI) strategies became popular because of their objective to mitigate the short term risk of assets against liabilities. But LDI was also learned to be potentially expensive on longer horizons as risk premiums could no longer be harvested. Another response was to develop Dynamic Asset Allocation (DAA) strategies, as a way of balancing between long term objectives and short term risks. This led to new requirements for the scenarios. The objective was to fill the gap between the long horizon scenarios for ALM purposes and the scenarios from the traditional short term risk management systems. For these purposes, a horizon of several decades on an annual simulation basis for asset classes at a high level of aggregations was too crude. On the other hand, a horizon of 10 days at the level of individual securities was too detailed and static in terms of asset allocation. Therefore, Ortec Finance developed the PRISMA (acronym for pension risk management) model with a horizon of one year, a monthly simulation basis and modeling of portfolios based on return based style analysis. The first version of the PRIMA model was available in The stylized facts that needed (and need) to be replicated in these kind of scenarios focused on the shape of the return distributions (fat tails) and the correlation structures, in particular the increasing correlations in the tails of the distributions (tail risk). A further challenge was that it was (and is) necessary to be able to simulate scenarios for very larger numbers of variables, without running into statistical troubles. The VAR approach that was in use for the long term scenarios was not up to this job and therefore a historical simulation based approach was developed. Such an approach performs well on the aforementioned requirements but is ill suited for, in this case month on month, dynamics such as momentum and return reversal effects. But because the horizon of one year was relatively short, the dynamics of the scenarios, and the corresponding stylized facts, were of less importance. However, effectively there now were two scenario models in use: the VAR model approach for the long run and the historical simulation based approach for the short run. This created the following problems. First, both scenario models provided scenarios for the one year horizon. This leads to the obvious question of which scenarios are the best? And second, the two scenario models were used in different phases of one and the same investment decision and risk management process, aimed at helping investors to achieve their objectives. Switching the underlying scenario model during this process clearly leads to problems with consistency. As Varnell (2009) puts it, in the context of Solvency II, [ ] it is useful to have a common set of real world [ ] scenarios used throughout the enterprise, against which all decisions would be based. This can put a lot of demand on the [ ] model to capture many features [...] and If the [ ] model cannot capture enough of the features of the economy [...] this would [...] increases the risk of inconsistent decisions being taken [...]. This problem would be lurking around to be solved only in 2011, see Section 4.7. Ortec Finance bv 19 / 54

20 4.6 Dynamic Scenario Generator (2009) The VAR model and historical simulation based approaches can be considered as the first generation of scenario models used by Ortec Finance. Over the years, these had been extended and improved along the lines described above. But the further this process continued and the requirements kept growing, the more likely it became that the boundaries of the approaches got into sight. To prepare for the second generation of scenario models, the years between 1997 and 2005 were therefore spent on the academic research described by Steehouwer (2005). The objectives of this research were twofold. The first objective was to expand and formalize the basis of stylized facts that the scenarios should be able to replicate, in order to obtain realistic scenarios with the desired properties : Which to scenario analysis and ALM relevant stochastic structures and relations have characterized the macroeconomic process of developed countries in the past, with respect to the real and financial sectors of the economy and their interaction, the properties at different frequencies (ranging from the very long run to shorter term business cycles) and possible changes of these structures over time? The second objective was to evaluate the existing scenario models against these stylized facts and, if necessary, find ways to improve the scenario models in terms of their replication of the stylized facts: Do VAR models and, more important, the way they are applied in both academic and practical ALM, indeed lead to scenarios that are consistent with the empirical knowledge obtained from the first research question and, if this is not the case, what modifications can be made to resolve the shortcomings of the current applications? The research resulted in some useful payoffs along the way, such as the reinstatement of the Yule-Walker estimation approach as described in Section 4.2. But it was also able to successfully pick up on fundamental issues that emerged over time, especially the problem of the inconsistent long and short term scenarios as described in Section 4.5. The results of the research indicated that there were indeed important directions to improve the scenarios. The use of frequency domain techniques was promoted for dealing with the long and short term, or low and high frequency, issue. These techniques are common to the natural sciences, but much less so to economics and finance. This is not because they lack intuitive appeal. On the contrary, if there is one thing we know about how economies and financial markets evolve, then it is they are never stable and move up and down all the time. And what is then more natural then to analyze how they move up and down? This is exactly what frequency domain techniques aim to do. The problem with these techniques for applications in economics and finance is that their traditional versions require a lot of data, something that we typically do not have in economics and finance. The benefits of a Ortec Finance bv 20 / 54

21 frequency domain approach and ways for dealing with this data problem are described in Steehouwer (2010). The choice for this less less traditional approach started from the objectives that were formulated and then searching with an open mind for the best approaches to achieve these objectives. The years between 2005 and 2007 were spent on developing the new methodology further, thereby bridging the gap between the academic results and suggested improvements on the on hand and being able to generate scenarios in a business environment on the other hand. This was the time when for example also the dimensionality problem was solved (how to model large numbers of variables without running into statistical troubles) by integrating Dynamic Factor Modeling (DFM) into the frequency domain approach. See for example Steehouwer (2011). In 2007, this resulted in a prototype which produced results that proved that the approach was viable for large scale business applications. The years between 2007 and 2009 were then spent on building and testing the professional software tool to be able to calibrate, generate and analyze scenarios according to the new methodology. This finally, in 2009, after almost 15 years of R&D, led to the official introduction of the Dynamic Scenario Generator (DSG) 5. The DSG can be considered as the second generation of scenario models as used by Ortec Finance. But it clearly builds on the first generation of models in a consistent way: the DSG can be set up and calibrated in such a way that one obtains the very same VAR model based scenarios as those from the early days. 5 The first name of the model was the Holistic Scenario Model (HSM). The name DSG is a variation on the more common ESG (Economic Scenario Generator) that is used for these types of models. Ortec Finance bv 21 / 54

22 4.7 Integration of short term scenarios (2011) With its introduction in 2009, the DSG opened up the road again for further expansion and improvement. The first version of the DSG still produced scenarios on an annual simulation basis, based on a dedicated long term trend model and a dedicated medium term business cycle model. But the DSG approach made it also possible to add to this an intra-year or monthly model and thereby making the step from an annual to a monthly simulation basis, while leaving the long and medium term properties of the scenarios intact. To be able to make this step however, additional modeling needed to be integrated into the DSG to be able to replicate additional important stylized facts specific to the monthly (or higher) frequency. This was the main research area between 2009 and The first of these stylized facts is that of time-varying or stochastic volatility: volatility in financial markets is not fixed but varies over time. The corresponding stylized facts are typically modelled by means of (G)ARCH 6 models, for which Robert Engle received the Nobel Prize in Despite that this may seem the apparent choice, (G)ARCH models were not selected for use in the DSG. The first and most important reason was that for risk monitoring purposes, as described in Section 4.5, the DSG had to be able to generate scenarios for large numbers (hundreds) of variables. Estimating (G)ARCH models of such dimensions was (at least in those days) very difficult, if not impossible, especially since the scenarios had to be produced in an operational business environment with a monthly cycle. The second reason was that (G)ARCH models to some extent combine the finding and formulation of stylized facts about volatility with the modeling of volatility. This was not in line with the OF scenario modeling approach that had become customary: first collecting stylized facts based on empirical research and then, with an open mind, finding the best models to replicate these stylized facts in the scenarios. So, if the (G)ARCH modeling approach was not selected, what approach was then used for modeling time-varying volatility in the scenarios? Inspiration was found in the presentation of Diebold (2008) who spoke of (G)ARCH as the first generation of volatility models and Realized Volatility (RV) 8 as the second generation models. With the RV approach there were no issues with the dimension of the models, at least no different from the problems that had already been tackled with the help of the factor modeling approach. And it offered great opportunities for analyzing how volatility behaved empirically and to derive corresponding stylized facts. What resulted was a realistic high dimensional stochastic volatility scenario modeling for equities, indirect real estate, commodities, credit spreads and excess returns, short and long interest rates across countries, based on some 170 RV series and integrated into the decomposition and factor approach. The stylized facts and RV based scenario modeling approach to volatility are described in Steehouwer (2011) while Lee (2012) describes how scenarios for option Implied Volatilities (IV) can be obtained. 6 (G)ARCH stands for (Generalized) Autoregressive Conditional Heteroscedasticity. 7 Engle received the Nobel Prize in economics together with Clive Granger, in his case for methods of analyzing economic time series with common trends (cointegration). 8 Realized Volatility comes down to estimating volatility by summing intra-period squared returns. For example, the volatility during a day can be estimated by summing the squared tick-by-tick returns during that day. As the return period gets small enough, this estimate can show to converge to the true underlying volatility. Ortec Finance bv 22 / 54

23 The second important stylized facts specific to the monthly (or higher) frequency is that of tail risk: correlations between asset returns typically increase in bad economic and financial market conditions, in times of stress in the markets. This is a very relevant stylized fact because it means that the benefits of diversification obtained from spreading investments across asset classes and regions are actually not there (or at least to a lesser extent) when they are needed the most. For the modeling of tail risk in the scenarios, a similar story holds as for volatility. The apparent modeling choice in this case is to use so called Copulas 9. But also here, a Copulabased approach was not selected for use in the DSG because, as Werker (2008) puts it, also Copulas suffer from the curse of dimensionality : the more variables need to be modelled, the harder it gets to estimate or calibrate the models, especially in an operational business environment. Fortunately, it turned out that by working with non-normal (or non-gaussian) distributions for the factors that drive the scenarios, very similar dependency structures, with increasing correlation in the tails of the distributions, can be obtained as by working with Copula models but without running into trouble with the dimensions of the model. What resulted was a realistic high dimensional tail risk scenario modeling for all (financial market) variables to the extent that this kind of return behavior was dictated by the data (rather than enforcing it to hold for all asset classes and all holding period returns). Only after the modeling had been completed, attention was drawn to the work by Oh and Patton (2005a,b) which might bring the DSG tail risk modeling approach back into the womb of Copula models after all. Based on the research into volatility and tail risk modeling as performed between 2009 and 2011, in 2011 the DSG scenarios, that until that point had known an annual simulation basis, were extended with a monthly intra-year model, thereby increasing the simulation basis to the monthly frequency. As of that moment the scenarios were updated to the latest economic and financial market conditions for the end of every month, resulting in scenarios per the end of Dec 2011, Jan 2012, Feb 2012 and so on. This also meant that finally the problem of inconsistent scenarios for long term investment decision making and short term risk monitoring, which, as described in Section 4.5, had been lurking around since 2005, had been solved. Realistic and consistent scenarios were now available for use in the different phases of one and the same investment decision and risk management process, aimed at helping investors to achieve their objectives. The historical simulation based approach scenarios of PRISMA had thereby became obsolete. 9 In Copula-based modeling, the univariate distributions of variables are separated from the dependency structure between variables which describes in which way variables tend to move together (or not). Ortec Finance bv 23 / 54

24 4.8 The truly long term (2012) The methodology for generating the scenarios was improved and expanded over time. But throughout the past 30 years, the stylized facts and the calibration of the scenario models has always been based quite directly on historical data that was deemed representative. However, the long term steady state expectations (or long term means, or equilibrium values as these are also called) have always been based on a separate approach, quite detached from the methodology for generating the scenarios as such. Without going into details, for various reasons, the link between (recent) historical data and realistic forward looking long term expectations should not be that strong. Instead, the long term expectations are based on a building block approach. In a building block approach one thinks about expectations in terms of components as growth, inflation, real interest rates, term spreads, inflation risk premiums and asset class risk premiums. This structures the approach because if forces one to think carefully about all forces that might affect the long term expectations. And it ensures consistency, for example by using the same approach for determining the risk premiums across asset classes. Over time, two issues emerged with the building block approach. The first was that the coverage of variables kept expanding which led to the question of how to extend the approach in a consistent way to incorporate the additional asset classes and countries. The second issue was that the DSG, with its frequency domain approach for integrating short and long term scenarios, brought up the question of which horizon the expectations actually corresponded to. The risk was that changes in short to medium term circumstances were getting mixed up with truly long term expectations. In times that markets were getting inflated, this created pressure to lower the long term expectations. Or, the other way around, if the markets had just crashed, this created pressure to increase the long term expectations. But, truly long term expectation of course should not change because of just short to medium terms event, but remain quite stable over time instead. In this way, the DSG sharpened the thinking about short, medium and long term expectations. Against this background, during 2011 and 2012, a large scale research project was performed into the framework for constructing the truly long term expectations and implementing this new framework. The long term expectations were positioned to hold on a 30 year horizon or more and also the uncertainty in the resulting long term expectations was taken into account. The latter can be seen as a form of the parameter uncertainty as discussed in Section 8 of Steehouwer (2016). The results of this research are described by Kramer (2014). The approach is used to date in the scenarios and updated only every few years, as one would expect to be the case for truly long term expectations. Ortec Finance bv 24 / 54

25 4.9 Ortec Finance Scenarioset (2016) Since the stepwise introduction of the DSG in 2009 and 2011, the world did not stand still of course. And these changes once again led to changing and expanding requirements for the scenarios. To keep up with these changes, in July 2016, as of the scenarios for June 2016 and onwards, another big step is taken by introducing the Ortec Finance Scenarioset (OFS). There are two underlying trends that stimulated the development of OFS. The first trend started with the financial crisis in 08 and since then has strengthened further based on events as the Euro crisis and the subsequent unprecedented worldwide monetary interventions. This has led to increased attention for how realistic financial models, and scenario model in particular, describe the world that we live in. This as such has not changed the way in which we generate scenarios. Our aim has always been to generate scenarios that are as realistic as possible. But the course of events in the years before the crisis, during the crisis and after the crisis has emphasized that risk and return are not static but dynamic as they change over time. As an example, recall the years 05, 06 and 07 leading up to the crisis. These were years of very low volatility and strong financial market performance. Then the crisis came in 08 with high volatilities and financial markets crashing. With exception of the Euro crisis in 2011, the period until 14 was then again one of low volatilities and strong financial market performance. In recent years volatility has been increasing again and financial market performance has started to falter as uncertainty about world economic growth, China, Emerging Markets and low inflation kicked in 10. The second trend that stimulated the development of OFS is the increased attention for short term risk management, of course also in response to the crisis periods of the past decade. Nowadays, only few investors want and can act as a pure long term investor. This has put more emphasis on the short term properties of scenarios and how realistic these are in the light of the actual economic and financial market circumstances and how these circumstances change over time. In short, these two trends require the scenarios to become more dynamic by taking the actual economic and financial market circumstances into account, including the effects of interventions as those by the central banks. Not dynamics for the sake of dynamics, but because dynamics make the scenarios more realistic. And more realistic scenarios can lead to better investment decisions and thereby to people and organizations becoming more successful in achieving their objectives. 10 This is also illustrated by Figure 8. Ortec Finance bv 25 / 54

26 Some may object that introducing more dynamics into the scenarios, and thereby timevariation in risk and return, is at odds with the Efficient Market Hypothesis (EMH). Without going into the details of the EMH, it says something like: at an aggregate level all available information is always fully incorporated in market prices and thereby the future is unpredictable. The EMH is agreed by most academics and investors to be at least partly true. But that does not need to mean that markets at an aggregate level are fully unpredictable. In Fama and Litterman (2012), the founder of the EMH, Eugene Fama, describes elegantly how this can work: [ ] price changes were random, which [ ] was what people thought an efficient market meant. We know now it doesn t. Market efficiency means that deviations from equilibrium expected returns are unpredictable based on currently available information. But equilibrium expected returns can vary through time in a predictable way, which means price changes need not be entirely random. With the introduction of OFS, an ancient scenario theme comes to a close: how to deal in a unified and consistent way with the dynamics in expected returns? In Section 4.2 we saw that already back in the 90 s, short to medium term expected returns that changed over time were seen as an undesirable side effect that was solved by pragmatically changing the expectations of each of the variables for each consecutive year to stable, user specified, values. With the introduction of the DSG in 2009 and 2011 the same theme emerged. This led to introducing actually two versions of the DSG scenarios: the Equilibrium (EQ) and the Disequilibrium (DIS) scenarios. The essential difference between the EQ and DIS scenarios is shown in Figure 1. The initial market values, for example todays interest rates, as well as the long term expectations, based on the building block approach from Section 4.8, are identical. The difference lies in the expected transition between the initial values and the long term expectations. In the EQ scenarios, this is a smooth transition for variables that are known to be sticky, variables like interest rates and inflation, and an instantaneous transition for variables without memory, variables like equity and exchange rate returns. This is very similar in spirit as the approach of the 90 s but now integrated in a consistent way within the frequency domain framework of the DSG. In the DIS scenarios, the expected transition includes cyclicality which follows from the dynamics of the stylized facts (e.g. business cycle dynamics, momentum, return reversal) as captured by the factor models of the DSG and applied on the initial economic and financial market conditions. In short, one could say that the expected returns in the EQ scenarios are in the spirit of the strict form of the EMH (fully unpredictable) while the expected returns in the DIS scenarios are in the spirit of the EMH from Fama and Litterman (2012) as quoted above (some predictability). Ortec Finance bv 26 / 54

27 Disequilibrium Equilibrium Ortec Finance scenario set Yield/Return Long term value Yield/Return Long term value Yield/Return Long term value Time Time Time Figure 1: Ortec Finance Scenarioset in a nutshell. In 2013 we decided that having these two versions of the scenarios was undesirable. Instead, we wanted to move to one most realistic version of the Ortec Finance scenarios, both on the short term and the long term, to be used for all applications in all markets, ranging from long term investment decision making to short term risk management, to enforce consistency. That was the start of an R&D project that lasted more than two years, which included a horse race between the EQ and DIS approach for producing the most realistic scenarios, methodological improvements, testing of the proposed approach, developing documentation and so forth. The result is the Ortec Finance scenarioset (OFS) as introduced in July In a nutshell, the relation of OFS to the EQ and DIS scenarios is shown in Figure 1. OFS includes cyclicality in its expected returns, and thereby similar signals as the DIS scenarios, but in a dampened way. And this dampening brings it closer to the EQ scenarios. So in that sense one could say that OFS brings together the best of the EQ and DIS scenarios. The remainder of this paper is dedicated to describing OFS in more detail but it is good to end this historical perspective by repeating a few things. The first is that OFS makes the scenarios more dynamic. Not dynamics for the sake of dynamics, but because dynamics make the scenarios more realistic in responding to changes in economic and financial market conditions. And more realistic scenarios can lead to better investment decisions and thereby to people and organizations becoming more successful in achieving their objectives. The second thing to repeat is that as Ortec Finance we believe that using models is a good thing, see Steehouwer (2016). Therefore, the dynamics in risk and return of OFS are primarily based on a model based approach and not on a big team of economists and analysts providing their forecasts for different countries and asset classes. And finally, we emphasize that what follows in this paper on OFS is not radically different from the earlier versions of our scenarios. Instead, OFS carries in it the results from experiences and innovations of the past 30 years and is thereby a step in which we again improve and expand the Ortec Finance scenario approach in order to keep up with the requirements. Ortec Finance bv 27 / 54

28 5. Methodological foundations Now that we have described the historical evolution of the scenarios leading up to the introduction of OFS, we are ready to discuss the methodological foundations of OFS. What are the essential ideas underlying the scenarios of OFS? Or, as in the scenario definition of Bunn and Salo (1993), what is its clear set of assumptions? This is summarized and can be described based on the pyramid as shown in Figure 2. In the following sections we describe each of the three levels of this pyramid and how these relate to each other, starting from the lowest and broadest level, that of the stylized facts. The three levels of the pyramid are united in the DSG, the model which is used to generate the scenarios of OFS. Views and expert opinion Out-of-sample testing of risk and return Dynamic Scenario Generator Dynamic Scenario Generator Realistic scenarios based on robust stylized facts Figure 2: Methodological foundations of Ortec Finance Scenarioset 5.1 Stylized facts We start with the lowest and broadest level of Figure 2, that of the stylized facts, on which the rest of the framework is built. Stylized facts, as a basis for generating scenarios, are not new for OFS but very fundamental to the scenarios of Ortec Finance. Our objective is to generate scenarios that as realistic as possible describe what might happen in the future. We translate realistic into requiring that the scenarios behave in line with a list of robust stylized facts. If one studies economic and financial data, the economic and financial literature and the available models and if one follows the economic and financial news, what emerges is a number of stylized features of how economies and financial markets evolve over time. As an example consider tail risk as described in Section 4.7 and below in Section This type of asset return behavior is observed over and over again in times of crisis and financial stress, it is observed across asset classes and countries and Copula models are typically used for modeling this behavior (but not by Ortec Finance as explained in Section 4.7). This is what makes tail risk a robust stylized fact that needs to be reflected in the behavior of scenarios in order for them to be realistic. Ortec Finance bv 28 / 54

29 In the following sections we describe the full list of stylized facts that the DSG models were designed to replicate in the scenarios of OFS. It is important to emphasize that this list is complete but that it is a rather high level formulation. Each of these stylized facts can be substantiated further by means of more detailed stylized facts. For example, business cycle fluctuations are mentioned below as one of the stylized facts while Section 17.2 of Steehouwer (2005) documents more than 30 stylized facts on business cycles. Furthermore we repeat that all the following stylized facts are replicated together in a single version of OFS. Some models are good at describing business cycle behavior, other models are good at describing time-varying or stochastic volatility and again other models are good at describing yield curve dynamics. What is unique about the DSG models is that they are able to deal with all of these stylized facts at the same time. This brings important consistency to the investment decision making and risk management process by avoiding the use of different models for different purposes Term structure of risk and return The first important stylized fact is that of the term structure of risk and return which is about the notion that risk and return in terms of volatilities, correlations and distributions can be different depending on the investment horizon. For example, volatilities increase with the horizon, but typically not following the (square root) pattern that is implied by the simple random walk model. Instead, some variables show lower volatility due to mean reversion while others show higher volatility due to trending behavior. Another example, as illustrated in Figure 3, is that the correlation between equity returns and inflation is found to be low for short to medium term horizons but higher for longer horizons. For any investor with some kind of purchasing power objective, this correlation pattern can have important consequences for the optimal amount of equities in the asset allocation. The general awareness of the term structure of risk and return, and its potential consequences for optimal asset allocations depending on the investment horizon, was created by Campbell and Viceira (2002). Figure 3: Example of the term structure of risk and return. Correlation between cumulative equity returns and cumulative inflations for different horizons, both historical as well as based on scenarios. Ortec Finance bv 29 / 54

30 5.1.2 Business cycles The second stylized fact, business cycles, concerns medium term fluctuations around underlying long term more structural trends in economies and financial markets. In their famous work, Burns and Mitchell (1946), define business cycles as a type of fluctuations found in the aggregate economic activity of nations that organize their work mainly in business enterprise. But business cycles are also very much alive today. For example, the Organization of Economic Cooperation and Development (the OECD) maintains a comprehensive system of (leading) business cycle indicators, see Gyomai and Guidetti (2012) 11. The OECD describes business cycles as recurrent sequences of alternating phases of expansion and contraction in economic activity. And also in the everyday news about the state of the economy we are confronted with what is essentially the business cycle. Much is known about the behavior of business cycles, especially about how variables typically relate to each other over the course of a business cycle. For example, stock prices tend to go down before GDP (growth) goes down and thereby stock prices tend to lead on the real economy. When there are signs of recovery in GDP (growth), unemployment will still be increasing for some time, meaning that unemployment typically lags the economy due to the rigidity in labor contracts. From a wider perspective, Lucas (1977) finds that Though there is absolutely no theoretical reason to anticipate it, one is led by the facts to conclude that, with respect to the qualitative behavior of co-movements among series, business cycles are all alike. Sections and of Steehouwer (2005) contain a literature overview on the different types of (alleged) cycles and their behavior while the OECD even publishes a journal dedicated fully to business cycle research and models: the Journal of Business Cycle Measurement and Analysis. Several times in the past people have thought that the business cycle was dead, that we were finally able to control these fluctuations in economic activity that are so characteristic to capitalistic societies. For example during the years leading up to the bust of the dot com bubble, there was this idea of a new economy which assumed that from that time on, driven by all the great things of the ICT revolution, economic growth would be stable (and high) forever. But every time people were proven wrong, most of the times in a pretty harsh way. All of the above on business cycles is to indicate that business cycle fluctuations are a stylized fact in the true sense of the word and therefore should be taken seriously when generating realistic scenarios for medium term horizons Of course also other organizations as statistical offices, central banks, economic bureaus and asset managers collect information on the state of the business cycle. 12 On a personal note: when submerged in literature research a long time ago, the author was literally stunned that until that time he had not once encountered the word business cycle in the context of scenario models. Ortec Finance bv 30 / 54

31 Figure 4: Example of business cycle dynamics. Composite Leading Indicator for all OECD countries ( together with the Ortec Finance Business Cycle indicator. As an illustration of business cycles in the context of OFS, consider Figure 4. This shows the OECD Composite Leading Indicator (CLI) for all OECD countries together with its natural counterpart from OFS: the Ortec Finance Business Cycle Indicator (OF BCI). Lee and Steehouwer (2012) describe the methodology underlying the construction of the OF BCI. From the same methodology, also dedicated business cycle indicators are available which focus on interest rates and inflation on the hand and on Asian markets on the other hand. The values of both series shown in Figure 4 are normalized to a standard deviation of 1. Values above 0 mean that economic activity (growth, equity returns, etc.) are above their underlying trend, values below 0 mean that economic activity is below trend. More specifically, four consecutive phases can be distinguished: (i) the expansion phase - above trend and increasing, (ii) the slowdown phase - above trend and decreasing, (iii) the contraction phase - below trend and decreasing, and finally (iv) the recovery phase - below trend and increasing. The OF BCI was not designed to mimic the OECD CLI but of course they measure similar things, which is why in broad lines they show the same patterns. If we look more carefully we see that the OF BCI is actually leading a few months on the OECD CLI. The reason for this is probably that the OF BCI includes much more financial market data than the OECD CLI, which focuses on economic data. Financial markets can respond almost instantaneously on new information while it takes time for this new information to feed through in macroeconomic data. As we shall see in Section 6, the OF BCI data is not used only to measure the current state of the business cycle but, more importantly, also to generate business cycle scenarios for the future. The scenarios of the OF BCI are important drivers of medium term economic growth, equity returns and credit spread. Ortec Finance bv 31 / 54

32 5.1.3 Time-varying volatility The third stylized fact is time-varying volatility which we already encountered in Section 4.7. Whereas the terms structure of risk and return and business cycles are important stylized facts for the long and medium term, time-varying volatility, together with tail risk from the next section, is especially relevant for generating realistic short term scenarios that are used for risk management purposes. As an example consider Figure 5. Here we see two measures of the volatility of US equity returns on a monthly basis: the (annualized) Realized Volatility (RV) and the option Implied Volatility (IV). This clearly shows that assuming a constant volatility for US equities of say 18% is not realistic. Instead volatility varies between spikes of more than 70% and values as low as 5%. The difference between these two volatility measures is called the volatility (or variance) risk premium. Investors that sell options want to be compensated for the fact that volatility itself, which drives the option price, is also uncertain. Bollerslev et al. (2009) demonstrate that this volatility risk premium (but not volatility itself) has predictive power for future equity returns. This is an interesting example of the complex dynamics of risk and return that OFS aims to capture in the scenarios. In Section 5.2 we will demonstrate how volatility and downside risk relate to the general economic and financial (business cycle) conditions. Figure 5: Example of time varying volatility. Monthly Realized Volatility of US equities based on daily returns together with 1 year at the money option Implied Volatility. The difference between these series is a measure of the volatility (or variance) risk premium. But not only the volatility of equities varies over time, the same holds for the volatility of interest rates, exchange rates, commodity prices, etc. And volatility across asset classes and countries is correlated. High volatility in itself need not be bad as long as the returns are positive. But unfortunately we typically see that high volatility comes with poor returns, and that volatility and returns are negatively correlated. The corresponding stylized facts are typically modelled by means of (G)ARCH 13 models, for which Robert Engle received the Nobel Prize in So, time-varying volatility is clearly a stylized fact that has to be included in short term scenarios and any model with constant financial market volatility is unrealistic. 13 (G)ARCH stands for (Generalized) Autoregressive Conditional Heteroscedasticity. Ortec Finance bv 32 / 54

33 5.1.4 Tail risk The fourth stylized fact, which is also of particular importance for generating realistic short term scenarios that are used for risk management purposes, is tail risk which we already encountered in Section 4.7. Correlations between asset returns typically increase in bad economic and financial market conditions, in times of stress in the markets. This means that the benefits of diversification obtained from spreading investments across asset classes and regions are actually not there (or at least to a lesser extent) when they are needed the most. As an example, consider Figure 6. Here we see the correlation between monthly returns on European and US equities and how this varies across the lower part of the return distribution. A value of 0.10 on the x-axis means that we are considering the worst 10% of the returns and the y-axis then shows that in that case the correlation is around 0.90 while in more normal circumstances, around the middle of the return distribution, the correlation is around The further we move into the left tail of the return distribution, the further the correlation increases and it even seems to converge to a value of one (a near perfect correlation). This important feature cannot be replicated by a Normal distribution with a fixed correlation. The apparent modeling choice in this case is to use so called Copulas 14. Figure 6: Example of tail risk. Tail Dependence Coefficient (TDC) translated into Normal correlations in the left tail of the joint distribution of monthly US and European equity returns, both historical as well as based on scenarios. 14 In Copula-based modeling, the univariate distributions of variables are separated from the dependency structure between variables which describes in which way variables tend to move together (or not). Ortec Finance bv 33 / 54

34 5.1.5 Non-Normal distributions The nice symmetrical and bell shaped Normal distribution is often applied and is convenient to work with for sure. Unfortunately it is not very realistic. Instead, in reality we encounter distributions that are not symmetrical as the Normal distribution but skewed, for example return distributions that are skewed to the left or interest and inflation distributions that are skewed to the right. We also see return distributions on short horizons with fat tails, in which very high and very low returns occur more often than indicated by the Normal distribution. Also in terms of the correlation structure, the Normal distribution is not realistic as we have seen in our discussion of tail risk. So, realistic scenarios must incorporate non-normal distributions Yield curves The last but not least stylized fact to discuss is that of yield curves or term structures: all variables that have a maturity dimension, such as government bond yields, break even inflations, credit spreads, swap spreads, etc. Generating realistic scenarios for such variables is more complicated than for regular variables as GDP growth or equity returns because there processes are effectively three dimensional: (i) time, (ii) value and (iii) maturity. To see this, consider Figure 7 which shows the historical evolution of the US Treasury yield curve between June 2013 and March Form this we can already see that the yields across maturities at a specific point in time relate to each other in particular ways. The typical shapes of yield curves encountered are (i) normal (increasing), (ii) inverted (downward sloping), (iii) flat or (iv) humped. Yield curves also move over time in particular ways. The typical dynamics of yield curves include (i) parallel shifts, (ii) tilts and (iii) flex movements. For a good overview of yield curve stylized facts see Section 2.3 of Diebold and Li (2006). Figure 7: US Treasury zero coupon yields from June 2013 until March Ortec Finance bv 34 / 54

35 There are many types of yield curve models available, that all try to describe the stylized facts of yield curves as best as possible. A search on Google for the phrase yield curve modeling results in thirteen million hits. Modeling yield curves is challenging to say the least, especially when it is considered across asset classes (government bonds, inflation linkers, corporate bonds, swaps and corporate credits) and across countries as required in OFS. Diebold and Li (2006) frame this nicely as: A good model of yield curve dynamics should be able to reproduce the historical stylized facts concerning the average shape of the yield curve, the variety of shapes assumed at different times, the strong persistence of yields and weak persistence of spreads, and so on. It is not easy for a parsimonious model to accord with all such facts Ortec Finance bv 35 / 54

36 5.2 Out-of-sample testing Then we move on to the second level of Figure 2, that of out-of-sample testing. In the past, the DSG has been designed in such a way that it is capable of replicating all the required stylized facts in the scenarios. However, it is very well possible to come up with different calibrations of the DSG models that replicate the stylized facts equally well but nevertheless exhibit very different short to medium term risk and return behavior. And thereby also very different dynamics of risk and return over time, an element crucial to OFS as described in Section 4.9. So, to be able to make a choice between these different competing calibrations of the DSG and to select the most realistic one, additional criteria are needed. We do this by continuously exposing our model calibrations to the toughest possible tests that we can design. It is import to perform such tests on an out-of-sample basis. This means that in calibrating and estimating models, it is prohibited not use data of the future that is also used to evaluate the quality of the short to medium term risk and return of the scenarios. It is easy to get a great in-sample model performance but this is likely to perform very poorly on an out-of-sample basis. And of course the latter is what matters in reality 15. Such testing is of course not new to Ortec Finance but setting up a large scale back-testing framework has been a crucial element of the development of OFS during 2014 and A great deal was learned from this research, especially on how to make the dynamics of the risk and return as described by the scenarios more realistic true-out-of-sample in the strictest sense can only be obtained by calibrating a model on all available data, producing scenarios and then letting time pass to collect new data that can be used to evaluate the quality of the scenarios. This obviously takes too much time in a process of calibrating models but is something that needs to be done anyways, building a live track-record. When calibrating models, one can in practice not do better than pseudo-out-of-sample. This means that consecutive model parameters are estimated without forward looking data but that it is unavoidable that one also learns about how the model performs on the full data sample. Calibrating a model in 2016 and testing how it would have performed back in 2006 and in the following years, will simply not produce the same model for 2006 as the model that would actually have been calibrated 10 years ago. 16 This was achieved especially by making the models more parsimonious. This means that the models are calibrated based on fewer parameters. The intuition is that if one has relatively little data available to estimate the model parameters on, as is typically the case in economics and finance, then these parameter estimates are uncertain. In an out-of-sample setting one is punished for wrong parameter estimates and working with fewer parameters leads to more precise and stable parameter estimates. Ortec Finance bv 36 / 54

37 Here we will not go into the details of the back-testing framework and the research results. These will be documented in a separate paper. Instead, based on Figure 8, we will give an impression of what the resulting dynamics of risk and return look like. This is not an easy graph so we will first go through it step by step to clarify what it shows. The topic of the graph is the downside risk of European equities. This downside risk is defined as the probability that the return in the next year will be lower than -15%, or the probability of a loss in the next year of more than 15%, i.e. a large drawdown. This 1 year probability is calculated on an out-of-sample basis, based on dynamic scenarios of OFS for every quarter from December 1998 until June 2015 and for every month from July 2015 until April 2016, in total for 77 sets of scenarios. This downside risk is shown by the dark blue line and should be read on the left y-axis. The horizontal grey line is the same downside risk but now not based on the dynamic scenarios of OFS but on a static risk and return model 17. Finally, to be read on the right hand y-axis, the orange line shows the historical development of the European equity total rate of return index (i.e. the value of the index including reinvested dividends). Probability 1 year ahead drawdown > 15% Dot com bubble Credit crisis Euro crisis? TRR index value Figure 8: Realistic dynamics of risk and return. Probability of a loss on European equities in the coming year of more than 15% (left hand scale), based on consecutive quarterly and monthly versions of the Ortec Finance Scenarioset. Together with historical development of European total rate of return equity index (right hand scale). For the static risk and return model, we (obviously) see that the downside risk is always the same, no matter how different the economic and financial market circumstances might be. In the years around the financial crisis the drawdown probability is around 12% (and not higher) while in the years of recovery and monetary stimulus after the crisis, the drawdown probability is also around 12% (and not lower). For the dynamic risk and return as described by OFS however, the downside risk is clearly not fixed, but varies over time. 17 This is an equilibrium (EQ) or random walk type of risk model. For a Normally distributed return with a fixed expectation of 8% and a volatility of 20%, the probability of a return below -15% is approximately 12%. Ortec Finance bv 37 / 54

38 Building a model in which downside risk varies over time is not very special in itself. What is special is that the way in which this downside risk varies is in line with the course of historical events and our recollection of how risk evolved during this historical period. As explained also in Section 6 of Steehouwer (2016), replicating history as such is not our aim. But history is and remains very relevant because we can learn from history what the future might bring. Past behavior is highly persistent and therefore we want to be able to replicate what we have seen in terms of the stylized facts. So, the dynamic downside risk of OFS responds in a realistic way to changes in economic and financial market circumstances. To illustrate this important point, let s follow the historical course of events. Mid 1999, downside risk was similar to that of the static model. But from September 1999 until March 2001, downside risk was elevated while the bust of the dot com bubble caused the total return index to lose almost 50% of its value between December 1999 and March During the following years, the years leading up to the collapse of Lehman Brother in 2008 which sparked the financial crisis, downside risk was relatively low. This was a period of good equity market performance, recovering from the bust of the dot com bubble. It was also a period of low volatility as illustrated by the first few years of US equity market volatility shown in Figure 5. But from December 2005 onwards, downside risk started to increase again and remained elevated until June Between June 2007 and March 2009, in the midst of the financial crisis, the total return index again lost almost 50% of its value. During most of 2009 and 2010, downside risk was very low again but not until another (more modest) peak emerged between September 2010 and June 2011, leading up to the height of the Euro crisis during the rest of Between December 2010 and September 2011, the total return index lost 15% (and not 50%) of its value. Central banks fought (and fight) the consequences of the financial crisis and the Euro crisis by first cutting short rates to values close to 0% or even below, also see Figure 9, and later on by government bond repurchase programs (Quantitative Easing). As a result of these measures, during the three years between September 2011 and September 2014, downside risk was again extremely low, equity market performance was strong and volatility was low. Between September 2011 and March 2016 the total return index climbed by as much as 80%. Mid 2014, the OF Business Cycle indicator reached its most recent peak and started to decline until its most recent values close to trend, see Figure 4 and Figure 13. This decline was (and is) fueled by concerns about the state of the Chinese economy, Emerging Market and commodity exporting countries, world economic growth, low inflation or even deflation, the effectiveness of the unprecedented monetary stimulus measures and the lack of structural reforms in Europe. Since the end of 2014 downside risk is on the rise again and equity market performance has started to falter. A deeper analysis based our DSG models, has shown that the low interest rates are the key reason why downside risk remains relatively suppressed. If interest rates would not be so low, downside risk would be much higher, perhaps more in the area of the values of previous crisis periods. Ortec Finance bv 38 / 54

39 5.3 Views and expert opinion Finally we then arrive at the top of the pyramid of Figure 2, views and expert opinion. That this is the smallest part of the pyramid does not mean that it is unimportant. But it is quite different than the first two layers of stylized facts and out-of-sample testing. These are based on the assumption that historical data contains information that is relevant for generating realistic scenarios for the future and that the models used are able to adequately capture this information. But the top of the pyramid acknowledges two important things. The first is that, for good reasons, in the first two layers we use a model based approach. But, no matter how realistic we manage to make these models, we should not forget that that they remain models. Any model is by definition a simplification of reality and we should therefore never see them as the truth but instead constantly be critical in our evaluation of how realistic the scenarios that they produce are. Seen from this perspective, we should not shy away from intervening if we deem the scenarios or certain economic variables of asset classes not realistic enough. And this is exactly what we mean with expert opinion : improving the properties of the scenarios based on other information than from the models, for example from modeling experts, asset class experts or regional experts. It would be troublesome if such expert opinion would be required for 90% of the variables covered in the scenarios but this is of course not the case. Expert opinion is applied on only a small part of the variables, typically the difficult ones for which relevant historical data to base the scenarios on is scarce. Ortec Finance bv 39 / 54

40 The second important thing that is acknowledged by the top of the pyramid in Figure 2 is that information can be available which is not, or not sufficiently, contained in the historical data on which the scenario models are calibrated, but which is very relevant for the scenarios of the future. Such information is what we mean with views. One very obvious example in today s economic and financial market environment is the unprecedented monetary stimulus as provided by central banks around the world in their attempt to stimulate economic growth and increase inflation. Though direct control of short term interest rates and bond repurchase programs (Quantitative Easing), they have pushed interest rates down to all-time lows and even into negative territory, see Figure 9. And they indicate to keep doing this still for quite some time into the future, or at least to go very slow in unwinding these interventions. On the one hand, such effects are not well represented in the historical data, so how could any model appropriately take this into account when being calibrated on such data? But on the other hand, these have a very large impact on at least expected interest rates going forward, and perhaps also on expected economic growth and expected returns on financial assets. Another example of views concerns the consequences of the recent decision of the British people to leave the European Union. It is crucial that such view information is incorporated in the scenarios and that this is done as consistently as possible. The DSG includes various ways of imposing views on the scenarios, the most advanced of which is described by Schans and Steehouwer (2014). Figure 9: Impact of monetary stimulus by central banks on short term interest rates since the financial crisis. Ortec Finance bv 40 / 54

41 6. Practical scenario construction Now that we have described the methodological foundations of OFS we can move our attention to the practical side of things. How are the scenarios actually constructed? Of, as in the scenario definition of Bunn and Salo (1993), how do we manage to come up with scenarios that are consistent with our clear set of assumptions? This is summarized and can be described based on Figure 10. Stylized Facts Current Market situation Dynamic Scenario Generator Long term steady state Views Figure 10: Four elements that work together in the actual construction of the scenarios of OFS. The first message of Figure 10 is that there are four key elements working together in the practical construction of the scenarios. On the left had side, the scenarios start from (i) the current market situation which not only gives the latest values of economic and financial market variables to start the simulations from, but also describes the economic and financial market situation in a wider sense. What has been the direction of the developments in the recent past? What types of interventions by central banks are going on and what is the latest forward guidance that they have given? On the right hand side, if we simulate for a horizon that is long enough, the scenarios will ultimately converge towards (ii) the long term steady state values from Section 4.8. And finally, shown at the top and bottom of the figure, (iii) the stylized facts and (iv) the views indicate that the transition of the scenarios from the current market situation towards the long term steady state is driven by the combination of stylized facts and views. This holds both in terms of expectations and in terms of uncertainty or risk. For example, applying average historical business cycle dynamics (stylized facts) on the current state of the business cycle will drive the medium term business cycle expectation as well as its uncertainty and even its distributional shape. Or, central banks continuing or even expanding their QE operations will cause expected interest rates in the scenarios to remain low for a prolonged period of time. Ortec Finance bv 41 / 54

42 The second message of Figure 10, in terms of the colored fan-like figure, is that the four elements are not strictly divided but fluently merge into one another. For example, the current market situation is partly the consequence of the stylized facts, the views are also determined by the current market situation, the long term steady state values can also be considered to be views and so forth. So it is the mixture of the four elements that determines what the scenarios look like but with a clear direction: stylized facts and views driving the scenarios from the current market situation on the left towards the long term steady state values on the right. And finally, all of this is implemented in the DSG as the model used to produce OFS. As an illustration of how the four key elements from Figure 10 work together in constructing the scenarios, consider Figure 11. We also use this figure to bring forward the important decomposition approach that the DSG uses to bring together long, medium and short term scenarios in a consistent way. Figure 11 shows 10 years of history (from Mach 2006 until March 2016) together with scenarios for 15 years into the future (from March 2016 until March 2031) for the 10 year interest rate on German Government bonds. Figure 11: Example of the elements from Figure 10 working together to generate scenarios for the 10 year interest rate on German Government bonds for the end of March The shaded areas are the 50%, 90% and 100% confidence bands of the scenarios. The dark blue line is the expectation. The grey, light blue and green lines are the trend, business cycle and monthly or intra-year components of the scenarios. The current market situation (i) is in this case the situation at the end of March One can simply consider the value of the interest rate at that point in time, which is only 0.15%, an all-time low. However, with the help of the techniques from the DSG, we can also look deeper than just the current value, by dissecting or decomposing this low interest rate level into a long term trend component (grey line), a medium term business cycle component (light blue) and a short term monthly or intra-year component (green) which captures the fickle short term market movements. This decomposition is such that is if one simply adds up the grey, light blue and green lines, one obtains again the original historical interest rate values (dark blue) This decomposition is performed with a frequency domain filter. The fact that the DSG model uses a decomposition approach is in itself not very special. For example business cycle indicators and structural time series models also build on a decomposition approach and it was Tinbergen how already thought about economic developments as the sum of a trend, a Ortec Finance bv 42 / 54

43 What do we learn from looking at the current interest rate level from such a long, medium and short term perspective? We learn that the low interest rate level is part of a wider underlying long term trend. Since the middle of the 1970 s, this trend has been decreasing and its current level of around 1.5% is an all-time low (going as far back as 1900). Trends move slowly by definition and thereby this low trend level puts downward pressure on the interest rate expectations in the scenarios for the future. Furthermore, we learn that also from a business cycle perspective the level of the interest rate is low, in the range of the 10 to 20% lowest values since This makes a lot of sense in the current environment where demand and inflation remain low and the ECB is pushing rates down with its QE operations. This low business cycle component puts (additional) downward pressure on the medium term interest expectations in the scenarios for the future. The DSG generates separate scenarios for each of the trend, business cycle and monthly components, both in terms of expectation and in terms of uncertainty. In the end, the decomposition which was applied on the historical data is reversed, by adding the scenarios of the trend, business cycle and monthly components back together again, giving us the realistic scenarios of the 10 year interest rate on German Government bonds. As for the other elements from Figure 10, the long terms steady state (ii) plays its role by being the point of convergence for the expectation of the interest rate scenarios (dark blue) if the horizon would be much longer than the 15 years displayed here. After 15 years, the expected interest rate level in the scenarios is around 3% and still increasing slowly. Because of the low current trend level, and the fact that trends change only slowly, 3% is still a long way from the assumed steady state value of 4.25%. The stylized facts (iii) and the views (iv) drive the expectations and uncertainty from the current values towards the long term steady state, along the lines of the trend, business cycle and monthly components which describe the long, medium and short term dynamics of the interest rate. In particular, the expectation of the medium term business cycle component (light blue) remains low for a prolonged period of time because a view has been imposed to reflect the latest forward guidance by the ECB. cyclical, a seasonal and an irregular component. But the use of the frequency domain filter described by Lee and Steehouwer (2012) and advocated in Steehouwer (2010) is far less common. It allows us to define exactly what we mean by trend, business cycle and monthly components (fluctuations with a period length of respectively between infinity and 16 years, 16 years and 2 years and 2 years and 2 months). Furthermore, the correlations between all resulting components are zero which is convenient in the scenario modeling process. As for the borders of the pass-bands : 16 years is a wide upper bound on what is considered as business cycle behavior ( in duration business cycles vary from more than one year to ten or twelve years in the words of Burns and Mitchell (1946)) while 2 years is the natural bound between fluctuations that can be observed in annual and in monthly data. Ortec Finance bv 43 / 54

44 6.1 Factor models and other models Figure 11 may seem to suggest that the scenarios are constructed by simply extrapolating historical components of time series of individual variables. But this is far from the case in the DSG model and would certainly not be the way in which it would be possible to replicate all the stylized facts from Section 5.1 in the scenarios and to obtain the (out-ofsample) dynamic risk and return behavior as described in Section 5.2. Instead, the scenarios of all more than 600 economic and financial market variables covered by OFS, from 1 month until several decades into the future, are generated by a small number of underlying factors. There are (three) dedicated factors for the long term, (nine) dedicated factors for the medium term and (ten) dedicated factors for the short term. These factors are constructed from hundreds of input series. The dynamics of these factors drive both the expectations and uncertainty of all variables which ensures the consistency that is so important to generating realistic scenarios. The interplay between the decomposition and the factor modeling approach is summarized in Figure 12. We start by decomposing all input time series into a trend, business cycle and monthly component. Then we calibrate a dedicated Dynamic Factor Model (DFM) for each of the components which produce scenarios for the corresponding components for all variables. And finally, the scenarios of the components of variables are recombined into the scenarios of the total variables. Figure 12: The bi-orthogonal decomposition approach as applied in the DSG. A decomposition into long term trend, medium term business cycle and short term monthly or intra-year components is combined with a Dynamic Factor Model (DFM) per component. bi-orthogonal indicates that both the components and the factors in principle have zero correlations, and are therefore orthogonal. Ortec Finance bv 44 / 54

45 Two aspects of this approach to factor modeling in the DSG deserve particular attention. The first is the factor model for the long term trend component. Due to the special nature of truly long term data (e.g. from 1900 until present), we have built more structure into the trend model in the way as described by Boer et al. (2016). This structure enhances the interpretation of the long term aspects of the scenarios, it enforce more consistency and offers more flexibility to impose views or expert opinion consistently. The second aspect to mention is the Ortec Finance Business Cycle Indicator (OF BCI) which we already described in Section It is produced with the general approach to the factor modeling as described by Lee and Steehouwer (2012) and applied to the medium term business cycle and short term monthly factor models. An example of the resulting factor scenarios for the OF BCI is shown in Figure 13. The OF BCI is just the first (out of nine) business cycle factors which captures the largest common part of the business cycle components of hundreds of input series. But unlike Figure 4, the DSG approach does not stop with producing (leading) historical data alone. The (nine dimensional) business cycle DFM is used to also produce scenarios of the OF BCI (and the other eight factors) going forward, in this case from the end of March These OF BCI scenarios are important drivers of the medium term scenarios for growth, equity returns, credit spreads, real estate, etc. June 2014 Figure 13: Example per March 2016 of the Ortec Finance Business Cycle indicator, the 1 st factor from the business cycle factor model, both historically and scenarios for the future. The shaded areas are the 50%, 90% and 100% confidence bands of the scenarios. The dark blue line is the expectation. For comparison, the light blue line depicts the Composite Leading Indicator for all OECD countries ( Ortec Finance bv 45 / 54