Asset-Liability Management in a Regime Switching Framework by Q.M.S Advisors

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Advisors

Asset-Liability Management in a Regime Switching Framework

Introduction: The enactment of the Pension Protection Act of 2006 (PPA) and the issuance of the Financial Accounting Standards Board Statement (FASB) No. 158 are imposing changes in funding and accounting procedures for plan sponsors. More stringent rules designed to improve the funding of America’s private pension plans, in conjunction with more transparent accounting rules for pensions’ assets and liabilities will significantly affect sponsor firms’ cash-flows and balance sheet volatility. In this context, sound asset-liability management practices can help financial sponsors achieve a competitive advantage, and even insure their survival during challenging market conditions. Past economic downturns have shown that pension plans’ funded ratios are highly sensitive to economic and financial cycles. Optimal investment strategies for long-term investors in the presence of liability constraints therefore calls for the use of modern financial engineering tools and advanced modeling techniques that incorporate the cyclical and non-normal nature of financial variables. Sensible strategic asset allocation solutions that integrate the impact of economic and financial cycles, in conjunction with the use of direct and integrated risk management tools can help mitigate the risks associated with pension plans’ cyclical funding ratios. In this paper, we introduce a general framework that addresses the well researched shortcomings of traditional Asset Liability Management approaches; taking into consideration the dynamics of pension plans’ liabilities and their associated volatility and correlation with asset returns.

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Advisors Rationale: Usual tools available to investors such as the standard CAPM model _which assumes mean-variance preferences over a time-invariant distribution of asset classes_ cannot be utilized when solving asset allocation problems with nonnormal underlying asset classes, as it fails to capture the basic characteristics of the asset classes introduced in the optimization and forces the model to be severely misspecified. To address this shortcoming, we introduce advanced modeling techniques that define optimal long-term asset allocation solutions that account for asset classes’ non-normal return distributions and solutions that correspond to institutional clients’ asymmetric risk preferences. Our approach offers an answer to the two most preponderant shortcomings of the classical mean-variance optimization framework: 1. The empirical evidence that markets display time-variations in investment opportunities -or cyclicality- and therefore exhibit non-normal return probability distribution functions and non-stable co-dependence parameters. Our approach addresses this inadequacy by appropriately capturing assets and liabilities’ non-normal return probability distribution functions and asymmetrical correlation structures, while also capturing volatility clustering phenomena. 2. The fact that institutional clients display asymmetric risk preferences. Our framework answers this limitation by incorporating pension plan managers’ specific objectives and asymmetric risk preferences; where higher moments of assets’ probability distribution functions and assets and liabilities cyclical nature are integrated in the strategic asset allocation decision process. Exhibit 1: Asset classes display non-normal individual and combined statistical features:

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Advisors The Regime switching Framework: Defined Benefit plans are characterized by guaranteed long-term obligations that are to be met whether by the contributions of the sponsoring firm or by the returns generated on the pension plan’s assets. Pension plan managers therefore primarily rely on a minimum rate of return on the plan’s assets to insure the sustainable funding of the plan’s financial obligations. The stochastic nature of Defined Benefit plans’ assets and liabilities advocates for the use of advanced financial engineering techniques and for the explicit modeling of the related dynamics of plans’ assets and liabilities. Our approach integrates the interrelated dynamics of both assets and liabilities in a regime switching framework which, as suggested by empirical evidence, provides more realistic results and risk estimate than the standard MeanVariance framework. Our model provides an accurate approximation of the distribution of returns of most asset-classes and captures the stylized fact that large declines occur simultaneously across markets. Additional stylized facts such as negative skewness, high kurtosis, volatility clustering, and asset classes’ asymmetric interdependence dynamics (the tendency of correlations to converge to one across asset classes in periods of market corrections and the simultaneous occurrence of outliers) are also accurately represented. Hence, efficient asset allocations and the associated risk estimates at the total pension plan level obtained via our approach are more realistic. Generating Pension Fund Liabilities and Asset Returns across regimes: Our dynamic asset allocation model is embedded in a stochastic multi-stage program (Monte Carlo simulation framework), where switches across economic regimes follow a Markov process. Defined Benefit pension plans’ liabilities and asset returns are generated concurrently at each step, conditionally of the simulated economic regime. We rely on detailed estimates of the plan’s liability structure to predict the fund’s outstanding liability exposure through time. Our multi-period model is determined by two main factors, the number of employees covered by the plan and the likely growth of pensioners’ benefits. PBO estimates are then derived concurrently with all other financial variables, so as to generate scenarios that are congruent with the simulated state of the economy at each time step. This approach preserves the volatility levels and dependence structures across simulated variables. In past analyzes, we identified two regimes: A low mean return with high volatility state and a high mean returns and low volatility state. This dual-state approach implies that conditional on knowing the state of the economy, the

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Advisors distribution of each asset returns is Gaussian. However, since the future states of the economy are not known in advance, the return distribution of each asset class is represented by a mixture of normal distributions, with weights reflecting the current and state transition probabilities. Such mixtures of normals provide a flexible representation that can be used to approximate many probability distribution functions. Additionally, our regime switching framework allows return correlations across financial variables to vary with the underlying regime, which is consistent with the empirical evidence of asymmetric correlations. Additionally, the approach accounts for autocorrelation in returns -a common feature of Alternative Investments- and for volatility clustering since our approach lets the financial variables’ first and second moments vary as a function of the underlying state probabilities. In essence, a regime switching framework offers a better representation of Defined Benefit plans’ assets and liabilities dynamics by incorporating the following well-researched empirical evidence: § Correlations among financial variables converge to one during market corrections, § Outliers tend to occur simultaneously across markets, § Asset return distributions display significant skewness and kurtosis. Strategic Asset Allocation: The pension plan manager’s objective is central to deriving optimal strategic asset weights. Regardless of the plan manager’s objective (minimize the fund’s expected shortfall risks, maximize funded status, minimize surplus volatility, minimize required contributions, or minimize pension expense volatility) our approach allows for the integration of all the non-Gaussian features of all financial variables considered in the analysis, and the incorporation of higher moments to the asset allocation decision. When compared to the standard Mean-Variance approach to obtaining optimal portfolio weights, our methodology is less dependent to the initial inputs of the optimization and particularly less sensitive to managers’ expected return estimates. Conclusion: As illustrated by the pronounced cyclicality of Defined Benefit plans funded ratios over the past decade, identifying and mitigating the uncertainties originating from managing a pension plan’s assets and servicing its liabilities involves modeling the non-linear features of assets and liabilities’ dynamics. Employing sophisticated optimization models in a multi-period setting helps provide an intellectual framework to manage financial risks and devise efficient strategic asset allocations. Our group offers a tractable approach that accurately represents those aforementioned stylized facts and can help devise more robust asset allocation decisions.

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Advisors Appendix: Exhibit 2: Asset classes’ display significantly different moments across economic regimes:

U.S. Inflation U.S. 30 Day TBill U.S. 1 Yr Treasury Const Mat U.S. IT Gvt U.S. LT Gvt U.S. LT Corp Domestic Hi-Yld Corp S&P 500 MSCI EAFE MSCI World MSCI Pacific MSCI Pacific ex Japan Fama-French Large Growth Fama-French Large Value Fama-French Small Growth Fama-French Small Value FTSE NAREIT All REITs

Expansion State

Recession State

Expansion State

Recession State

Expansion State

Recession State

Expansion State

Recession State

Returns (in % p.a.)

Volatility (in % p.a.)

Skewness

Kurtosis

4.3% 5.6% 6.4% 6.9% 7.7% 7.7% 9.2% 12.3% 14.2% 12.7% 14.1% 16.5% 10.9% 14.3% 9.5% 16.7% 11.5%

7.1% 8.5% 9.8% 15.0% 15.1% 15.4% 9.9% 4.8% -3.6% 0.1% -7.4% -12.9% 4.7% 8.4% 5.4% 17.4% 5.7%

1.1% 0.8% 0.8% 4.8% 9.5% 8.0% 6.5% 14.0% 15.2% 13.0% 19.5% 21.8% 15.4% 14.8% 22.8% 17.9% 13.0%

1.6% 1.0% 1.1% 9.3% 14.7% 14.6% 16.4% 20.9% 23.5% 20.3% 26.0% 32.5% 23.8% 20.8% 31.7% 28.0% 27.0%

0.47 0.81 0.64 -0.26 -0.10 -0.46 -0.58 -0.62 -0.33 -0.58 0.05 -1.01 -0.56 -0.38 -0.52 -0.29 -0.57

0.00 0.46 0.24 1.09 1.00 0.78 -0.01 0.34 0.48 0.14 0.54 0.39 0.40 0.52 0.06 0.43 0.62

1.69 1.63 0.89 0.68 1.09 1.81 3.56 3.04 0.77 2.21 0.57 8.26 2.66 2.40 3.01 6.09 2.57

-0.90 -0.44 -0.89 4.68 2.27 0.97 0.02 0.03 0.28 -0.42 0.31 1.19 0.27 1.50 -0.46 2.06 3.17

Exhibit 3: Asset classes’ Co-movement across regimes display significant differences:

U.S. Inflati on

U.S. Inflation U.S. 30 Day TBill U.S. 1 Yr Treasury Const Mat U.S. IT Gvt U.S. LT Gvt U.S. LT Corp Domestic Hi-Yld Corp S&P 500 MSCI EAFE MSCI World Fama-French Large Growth Fama-French Large Value Fama-French Small Growth Fama-French Small Value FTSE NAREIT All REITs

0 0.00 -0.11 0.01 0.02 -0.04 -0.19 -0.28 -0.11 -0.20 -0.30 -0.29 -0.37 -0.37 -0.26

U.S. 30 Day TBill

0 -0.04 0.22 0.19 0.16 0.06 -0.24 -0.01 -0.13 -0.25 -0.18 -0.31 -0.26 -0.11

U.S. 1 Yr Treas ury Const Mat

0 0.28 0.29 0.27 0.16 -0.10 -0.01 -0.05 -0.11 -0.06 -0.19 -0.15 -0.01

U.S. IT Gvt

U.S. LT Gvt

U.S. LT Corp

0 -0.01 -0.03 0.16 0.06 0.13 0.11 0.10 0.06 0.14 0.10 0.09

0 -0.01 0.18 0.16 0.24 0.24 0.17 0.13 0.23 0.20 0.18

0 0.18 0.26 0.31 0.33 0.29 0.20 0.32 0.27 0.27

Dome stic HiYld Corp

0 0.13 0.15 0.14 0.15 0.09 0.13 0.02 -0.01

S&P 500

MSCI EAFE

MSCI World

0 0.07 0.03 0.02 0.05 0.15 0.06 0.21

0 0.01 0.09 0.20 0.18 0.17 0.20

0 0.05 0.14 0.16 0.12 0.22

Fama Frenc h Large Growt h

0 0.09 0.08 0.08 0.25

Fama Frenc h Large Value

0 0.25 0.05 0.23

Fama Frenc h Small Growt h

0 0.14 0.29

Fama Frenc h Small Value

FTSE NAR EIT All REIT s

0 0.17