Article Detail

Simulation and Performance Evaluation of Liability Driven Investment (LDI)

Journal 32: Applied Finance

Katharina Schwaiger, Gautam Mitra

In contrast to decision models which use in-sample scenarios we use out-of-sample scenarios to conduct simulation and decision evaluation including backtesting. We propose two simulation methodologies and describe six decision evaluation techniques that can be applied to test the performance of liability-driven investment (LDI) models. A good practice of evaluating the performance of funds is to apply risk-adjusted performance measures; we have chosen two widely applied ratios: the Sortino ratio and the funding ratio. We perform statistical tests and establish the quality of the portfolios. We report our empirical findings by testing an asset and liability management model for pension funds where we propose one deterministic linear programing and three stochastic programming models.

The decisions suggested by the generic models proposed in Schwaiger et al. (2010) are examined and evaluated in detail through simulation studies. Two simulation methodologies and six evaluation techniques are introduced and statistical methods and performance measures are used to interpret these solutions. We start with a brief literature review of simulation and evaluation methods applied to asset and liability management (ALM) so far. The simulation and decision evaluation framework proposed is generic and can also be applied to areas other than ALM.

We review briefly simulation methodologies used in portfolio planning and ALM applied to pension funds, banks, and insurance companies. A bank ALM model is introduced by Kusy and Ziemba (1986), where the aim is to find the optimal trade off between risk, return, and liquidity of the bank. A multiperiod stochastic linear programming model is introduced and then compared with the Bradley-Crane stochastic decision tree (SDT) model. The simulation study determines which model of the two gives better first-period results by testing two hypotheses: whether or not the ALM initial period profit is superior to the SDT and whether the mean profit of the ALM is superior to the SDT. Oguzsoy and Güven (1997) tested their bank ALM model in different ways. Firstly, they relaxed their management policy constraints and compared its results with the results of the fully included management policy constraints to show their importance in avoiding risk. This also allows the determination of the most important policy constraints. Secondly, they conducted sensitivity analysis on the rate of loans becoming irregular, different inflation effects, and on the rate of short term loans returning before maturity. And finally they analyzed the occurrence probabilities of possible outstanding deposit values. Zenios et al. (1998) developed a multi-stage stochastic programing model with recourse for fixed-income portfolio management under uncertainty. They show that their stochastic programing models perform well using both market data (historical backtesting) and simulated data (using Monte Carlo simulation procedures) compared to portfolio immunization models and single period models. They conclude that that these results show robustness with respect to changes in the input data. Mulvey et al. (2000) use stress testing in their pension plan and insurance ALM model for Towers Perrin-Tillinghast with generated “devastating” cases such as dropping equity markets and falling interest rates simultaneously. Once the desired scenario characteristic is set, the CAP:Link system (scenario generator) filters the desired scenarios. Their stochastic planning approach was compared to the current equity/bond mix of the company, an equity hedged mix, and a long-bond strategy. Kouwenberg (2001) developed a multi-stage stochastic programing ALM model for a Dutch pension fund. The model is tested using rolling horizon simulations and compared to a fixed mix model. The objective of the SP model is to minimize the average contribution rate and penalizing any deficits in the funding ratio. The rolling horizon simulations are conducted for a period of five years, where the model is resolved using the optimal decisions after each year. Then the average contribution rate and the information about underfunding is saved after each year and compared to the solution of the fixed mix model. The multistage simulation method in our present paper is comparable to this method and explained in more detail below. Their findings are that the SP model dominates the fixed mix model and that the trade off between risk and costs are better in the SP model than in the fixed mix model. Fleten et al. (2002) compare the performance of a multistage stochastic programming insurance ALM model and a static fixed mix insurance ALM model through in-sample and outof-sample testing. The stochastic programing model dominates the fixed mix model, but the degree of domination decreases in the out-of-sample testing. Only the first stage solutions are used to test the quality of the models. The models are solved, the first stage decisions are fixed, and at the next time period the models are solved again and the new first stage decisions are used. Our multistage simulation methodology also draws upon the algorithm described in their paper. More papers on decision models and simulations for asset liability management can be found in Mitra and Schwaiger (2011).

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