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«Essays on Robust Portfolio Selection and Pension Finance Thesis submitted in partial fulfilment of the requirements for the degree of Doctor of ...»

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The main objective of Chapter 2 is to introduce the reader to the basic aspects of portfolio theory, asset liability management (ALM) modeling and pension scheme design – the key elements of Chapters 3, 4 and 5. In particular, the fundamental Markowitz (1952) portfolio theory (mean-variance portfolio optimization), the most important criticisms of the mean-variance portfolio optimization framework, the latest developments in portfolio techniques that deal with estimation errors in the input data as well as alternative metrics used for portfolio evaluation are discussed.

Second, Chapter 2 describes the benefits of the asset-liability management (ALM) models for long-term institutional investors such as insurance companies, pension and endowment funds, instead of ignoring the corresponding liabilities and using asset-only portfolio strategies. In addition, Chapter 2 describes the close relation between Operations Research (OR) and ALM modelling, provides a review of the most important techniques used in the computation of optimal ALM strategies (e.g.

stochastic programming, portfolio theory, stochastic simulation, dynamic programming and stochastic control) as well as the most popular methods for generating scenarios, and explains the issue of the computational intractability of scenario-based ALM methods in solving realistic asset-liability management problems. Third, Chapter 2 provides a detailed description of the two dominant types of pension schemes (defined benefit and defined contribution) in the UK and US, and gives a comprehensive review of the relevant pension studies that compute the intergenerational redistributive effects between the stakeholders of a pension scheme, which occur after various pension rule changes.

In Chapter 3, a novel numerical portfolio optimization technique – robust (worstcase) optimization – is used to formulate and solve the asset-liability management (ALM) problem for a real-world pension scheme (USS). Robust optimization is particularly well suited to solving the ALM problem since it assumes that the uncertain input data are not known with certainty, but they lie within uncertainty sets. Hence, it adopts a maximin approach by solving the ‘worst-case’ optimization problem under the assumption that the stochastic input parameters used in the optimization problem take the worst-case values within the uncertainty structures defined by the modeler. As a result, robust optimization deals with estimation risk by ruling out possible optimal solutions that promise superior performance due to statistical misspecifications in the input data. Furthermore, the robust formulated ALM model presented in Chapter 3 incorporates additional important characteristics of the pension asset-liability management model such as upper and lower bounds for each asset class, prohibits borrowing and short sales and imposes a non-negative constraint on the expected value of the asset-liability portfolio return. Problems formulated with robust optimization techniques are easily solved and can handle problems with large data requirements in a more computationally tractable manner than scenario based approaches (e.g. stochastic programming and stochastic simulation), and often requires the estimation of fewer stochastic parameters and reduces estimation risk.

This is the first application of a computationally tractable (easily solved) assetliability management model based on robust optimization techniques to a real-world pension scheme (the Universities Superannuation Scheme, USS), and the first pension asset-liability management model that maximizes the Sharpe ratio. Also, the pension liabilities in Chapter 3 are split into three categories – active members, deferred members and pensioners, and the optimal asset allocation is transformed into the overall contribution rate. In addition, the proposed pension asset-liability management framework is benchmarked against various important benchmarks such as the actual USS performance computed by using the actual USS asset allocation decisions as well as the Sharpe and Tint, Bayes-Stein, and Black-Litterman models. The empirical results reveal that robust (worst-case) optimization has a clearly superior out-of-sample performance than the four benchmarks across 20

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characteristics such as risk, risk-adjusted performance, second-order stochastic dominance, diversification, stability, contribution rate, funding ratio and cumulative wealth amongst others. Finally, the conclusions remain unchanged by various robustness checks such as by testing different estimation and investment periods, relaxing the constraints on asset weights, and by using an alternative set of asset classes and different uncertainty sets with a smaller size.

Chapter 4 investigates whether the selection of the portfolio optimization strategy matters in the SRI industry and provides some answers to the question of which portfolio approaches tend to create SRI portfolios with better out-of-sample performance, given certain socially responsible investment criteria. This issue is of great importance for institutional investors since it is well known that long-term institutional investors such as pension funds, life insurance firms and endowment funds are committed to corporate social performance (CSP) and socially responsible investment (SRI). Although the size of the SRI literature is very broad, the number of studies that have investigated different ways of optimal SRI portfolio construction is very limited. Most importantly, these studies are very limited as the portfolio methods used are very heavily based on the Markowitz (1952) portfolio theory (mean-variance portfolio framework), and hence ignore the negative effects of estimation risk and parameter uncertainty in the corresponding input data. Such studies simply use the mean-variance portfolio framework by adding additional constraints with SRI preferences or incorporate these preferences by altering the objective function of the optimization process. Although the large majority of modern portfolio optimization techniques are heavily based on Markowitz (1952) portfolio theory, their optimal portfolio solutions are highly sensitive to perturbations in the input parameters, see for instance Green and Hollofield (1992), and often lead to portfolios that are poorly diversified, unstable and with a weak out-of-sample performance.





To construct socially responsible investment (SRI) portfolios with only US companies in Chapter 4, this study uses corporate social performance (CSP) metrics based on the MSCI ESG STATS (MSCI KLD) database. It is well known that this database is the most popular in the relevant research, and according to Sharfman (1996) it is described as a reliable and consistent database that contains about 3,000 US firms over a time horizon of over 20 years. This study attempts to contribute to the existing literature by employing three different optimal portfolio diversification methods (Markowitz, norm-constrained and Black-Litterman portfolios) and three more simplistic asset allocation techniques (equally weighted, risk-parity and reward-to-risk timing portfolios) to the same SRI-screened universe. Out-of-sample performance comparisons are made between these six different portfolio construction methods, and 14 different performance measures are used to capture several important characteristics such as risk and risk-adjusted performance, diversification and stability, amongst others. The empirical results show that more ‘formal’ portfolio optimization methods (Markowitz, Black-Litterman and normconstrained portfolios) tend to construct less risky Socially Responsible investing (SRI) portfolios with superior risk-returns trade-offs and a significantly smaller number of ‘active’ assets than more simplistic asset allocation techniques (1/N, risk parity and reward-to-risk). The Black-Litterman portfolio approach often comes first, while naïve diversification (1/N) usually has the worst performance on these criteria.

Finally, the main conclusions are robust to a variety of additional tests that include stricter screening criteria for the construction of socially responsible investment portfolios, the use of estimation windows with a different length than the base case as well as different ways of evaluating the out-of-sample portfolio performance.

Chapter 5 deals with the short, medium and long term performance of a real world pension scheme (the Universities Superannuation Scheme, USS) before and after the rule changes that took place in October 2011, as well as the wealth redistribution between various age cohorts of the future and active members, pensioners, and the sponsor that occur as a result of the pension scheme rule changes. Specifically, in October 2011 USS closed the final salary (FS) scheme to the new members, where the sponsor bears all the risks such as investment, longevity, interest rate, inflation, salary growth and regulatory risk, and forced new members to join the newly established career average revalued earnings (CARE) scheme, while USS also introduced a ‘cap and share’ rule for setting contribution rates.

The study presented in Chapter 5 also includes many important aspects that have not previously been incorporated in pension studies such as lump sum payments, deferred members (members that have left the scheme and are not currently paying contributions), spouses’ pensions, both final salary (FS) and career average revalued earnings (CRB) sections and a dynamic retirement age. Furthermore, the framework that simulates the pension scheme in Chapter 5 is modeled for a period longer than the working life. It also employs three different asset allocation strategies; the fixedmix, risk-shifting and risk management approach, with the last two strategies responding to the funding ratio each time the portfolio is rebalanced. A stable over time vector auto-regressive (VAR) model with 13 variables is used to generate future asset returns, inflation rates and the factors of the Nelson-Siegel yield curve, while the population of active and deferred members of the pension scheme each year follows a stochastic process. Although this study mainly focuses on a particular pension fund (USS), the general methodology presented in Chapter 5 could also be applied by other schemes in countries such as the UK and USA that have changed their rules.

The empirical results presented in Chapter 5 reveal that the post-October 2011 USS scheme (the pension scheme after the rule changes in October 2011) is sustainable in the long run with some problems in the mid-term, in contrast to the pre-October 2011 scheme that is non-viable in the long run. Also, the fixed-mix and risk-shifting asset allocation strategies are more favorable than the risk-management approach for both the pre and post 2011 schemes. The quantification of the redistributive effects due to the pension rule changes in October 2011 shows that future members lose about the 65% of their pension wealth (or an 11% reduction in their overall compensation) with an increase in the risk of their pension wealth by about a third, in contrast to the older age-cohorts where the corresponding losses are insignificant and the risk of their pension wealth is almost the same after the rule changes. The sponsor’s pension costs decrease by about 26%. Finally, the main conclusions remain unchanged by trying various robustness checks such as the replacement of the stochastic discount factors (SDFs) with the riskless discount rates for the computation of the NPVs and the use of different upper bounds on the total contribution rate.

Finally, Chapter 6 summarizes the main ideas, scientific contributions and the corresponding outputs of each chapter separately, and provides some possible directions that could be investigated and explored for future research.

Chapter 2

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2.1 Introduction The main purpose of this chapter is to familiarize the reader with the literature in portfolio theory, asset liability management (ALM) modelling and pension schemes design. In the following section (2.2), the fundamental Markowitz portfolio theory is discussed, while section 2.3 describes the criticisms of modern portfolio theory, which have been discussed in the literature the recent years, such as its high sensitivity to estimation risk and parameter uncertainty. Section 2.4 provides a comprehensive review of portfolio techniques dealing with estimation risk, while section 2.5 discusses alternative performance measures used for portfolio evaluations, such as measures based on lower partial moments, drawdown and value-at-risk. Section 2.6 gives the motivation behind the use of ALM techniques by long-term institutional investors (e.g. pension funds) instead of just using asset-only approaches. Section 2.7 explains how Operations Research (OR) is involved in the process of deriving optimal ALM strategies, describes the main methods used in ALM modelling and explains the disadvantages in applying scenario-based techniques to solve realistic ALM problems. Section 2.8 provides a review of techniques for generating scenarios. In addition, section 2.9 describes the two main types of pension schemes (defined benefit and defined contribution) that are dominant in the UK and US and provides a review of studies that deal with the intergenerational redistributive effects after pension scheme rule changes. Finally, a conclusion is provided in section 2.10.



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