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A Stochastic Investment Model for Asset and Liability Management

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Upgrading the standard actuarial valuation into a stochastic risk assessment is the way of the future, and the TY Model was built with this objective in mind. We therefore believe that this model will be a valuable tool for the UK actuarial profession. The publication of stochastic investment models is to be encouraged so that their features can be compared and actuaries can have a greater choice of investment models. Our contribution to this process is presenting a model with the following qualities: ã Clarity of Design ã Synthesis of the Economic Framework, Investment Practice, and Historic Data ã Unique Approach to Equity Risk ã Grounded in Reality
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  The TY Model   A Stochastic Investment Model for Asset and Liability Management Y. H. Yakoubov, M. H. Teeger and D. B. Duval  Foreword  A)   The TY Model We presented the following paper in August 1999 to the AFIR and ASTIN colloquia inTokyo. The paper describes a robust stochastic investment model that has a clear design andis easy to communicate.Building on some of the concepts of the Wilkie model developed in 1984, the TY Modelfeatures a fundamentally different and unique approach to modelling equities. The modelwas designed using modern statistical techniques as well as a wider data set.Upgrading the standard actuarial valuation into a stochastic risk assessment is the way of thefuture, and the TY Model was built with this objective in mind. The TY Model has alreadybeen successfully used for UK pension fund applications. Actuaries advising life insurancecompanies, general insurance companies and other funds with long term liabilities will findthe TY Model to be a valuable tool. Whatever the area of application, using the model willassist the understanding of the source and nature of the financial and economic risks to whicha fund is exposed, enabling more informed decisions and a better management of risk.We believe that the TY Model has the following qualities: ã   Clarity of Design.  The TY Model’s clear structure incorporates understandable inputswith a direct economic meaning. The model output is easy to communicate to clients andinterpretable by the actuary responsible for modelling. ã   Synthesis of the Economic Framework, Investment Practice, and Historic Data . Byusing these three fundamental inputs we gain a better understanding of the complexbehaviour and interaction between the assets modelled. The use of all relevant availableinformation is in line with the theory of statistical reasoning as proposed by ProfessorAkaike [“On the strategy for efficient realisation of statistical reasoning”, ASTINKeynote Lecture 1999]. ã   Unique Approach to Equity Risk.  An explicit market sentiment component is introducedto describe the changing nature of equity volatility over the short and long term. Meanreverting equity yields are no longer necessary with this approach.  - 2 - ã   Grounded in Reality.  The TY Model produces a sufficient range of realistic outputscenarios, reflecting the complexity of the economy and investment markets. It capturesthe fundamental features of individual asset classes and focuses on the major linksbetween assets and economic variables (eg the sensitivity of equity prices to movementsin bond yields). The model structure is designed to give credible investment behaviour inthe medium term over which actuarial risks are monitored and decisions taken. B)   Inputs to the TY Model It is important to use all relevant information available to assess the best model design.Hence the use of the three fundamental inputs: economic framework; investment practice;and historic data. When combining these inputs we focused on the areas of greatestuncertainty whilst reducing the emphasis on less significant areas. a)   Economic Framework We have taken a practical approach to incorporate a visible economic structure that buildson actuarial knowledge, recognising the importance of certain economic relationships.One such relationship suggests that price inflation tends to feed into salary inflation, butwith some time lag. Another suggests that very high inflation scenarios are unlikely to besustained as the economy will either move into hyper-inflation (which itself isunsustainable) or the government will act to bring down inflation. b)   Investment Practice Investment market behaviour varies around the world. Some variations are due toexternal factors such as taxation and accounting rules, while others are cultural andhistoric. Actuarial and economic theory suggest that a fixed interest yield can be derivedfrom a real yield such as an index linked bond yield. However, the TY Model followspractical investment experience, which indicates that the market actually works the otherway round, primarily because the index linked market is so much smaller and less liquidthan the fixed interest market. c)   Data For mature markets like the UK there is a substantial amount of historic data availablefrom which to build an asset model. The problem is the extent to which the past is aguide to the future. There have been important changes in capital markets, namely therelaxation of government controls, and the improvement of market information. The TYModel is structured to deal with aspects of the data that conflict with economic theory andinvestment practice.  - 3 - C)   The Features of the TY Model a)   ‘Change in Equity Rating’ or Sentiment The model contains an explicit market sentiment component since the ‘change in equityrating’ (represented by a ‘change in equity yield’) is by far the most volatile component inthe short term. Focusing attention on the most uncertain component results in a betterrisk analysis tool. Recognising the unpredictability in the level of the dividend/earningsyield, the TY Model allows for a range of stable yield levels.Although the sentiment component dominates in the short term, over longer periodsgrowth and income elements provide the majority of the total equity return. The explicitmarket sentiment component therefore demonstrates the time varying risk profile of theequity return (section 9.3.3). b)   Use of Corporate Earnings We derived the equity price return from the PE ratio and corporate earnings growth. ThePE ratio is widely accepted as a better indicator of equity valuation than the dividendyield. Earnings growth is more reactive to economic change compared to dividendgrowth. By modelling a ‘change in earnings yield’, changes in accounting practice areremoved to a great extent. The model is therefore more robust in that a one off shock willaffect only one year’s data rather than biasing all future years. c)   Forces of Return The use of a log transformation leads to linear relationships between the modelledvariables that are more suited to time series modelling tools. A further advantage is thatonly by using a force of return can the return on equities be separated into threecomponents (section 9.2): dividend income; earnings growth; and a ‘change in PE ratio’(the equity sentiment component). d)   Resultant Links Asset and liability modelling output is sensitive to the links between economic variablesand asset classes. We modelled the short term links based on ‘changes in yields’ that arerelevant to short term solvency as well as the long term links that affect strategic financialplanning.  - 4 - D)   Comparison with the Wilkie Model It is natural to draw comparisons between the Wilkie model and the TY Model (section 3.5).The major differences between the two models are: ã   The different approach to UK equity modelling including the three component structureand the explicit link from the ‘change in gilt yield’ into the ‘change in equity yield’. ã   The use of earnings growth rather than dividend growth, with a link from salary ratherthan price inflation. ã   The development of a new index linked gilt model based on a wider data set. The link from price inflation models a rising demand for index linked gilts as inflation rises. ã   A jump in price inflation produces a smaller jump in salary inflation (in line with Smith“Salary Related Cash Flows”, IMA 1998). E)   Summary Upgrading the standard actuarial valuation into a stochastic risk assessment is the way of thefuture, and the TY Model was built with this objective in mind. We therefore believe thatthis model will be a valuable tool for the UK actuarial profession. The publication of stochastic investment models is to be encouraged so that their features can be compared andactuaries can have a greater choice of investment models. Our contribution to this process ispresenting a model with the following qualities: ã   Clarity of Design ã   Synthesis of the Economic Framework, Investment Practice, and Historic Data ã   Unique Approach to Equity Risk ã   Grounded in Reality It is only by sharing research that actuaries will become familiar with a range of investmentmodels, thereby strengthening the position of the actuarial profession when competing withother professions involved in the long or short term management of risk.
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