Simulating Pension's Assets and Liabilities in a Regime Switching Framework

Abstract

In this paper we build a simple ALM model where future scenarios are generated assuming a Markov regime switching framework. Using the Shiller database of monthly equity returns and interest rate data since 1870, two regimes are revealed by the data that clearly correspond to a "normal regime" where returns behave like expected from economic theory, and a "high volatility" regime we may also refer to as a "crisis regime". Given the evidence of the non-stationarity of economic variables, we investigate the added value of reducing risk in the portfolio when the model indicates a high probability of a regime shift. The persistence of each of the regimes is high. This framework gives, each month and for each scenario, the probability of being in one of the two regimes, and hence the multivariate distribution of the simulated variables that pertains to the relevant regime. These variables are 1) equity returns, 2) long term (10-year) interest rates, 3) realized inflation, and 4) short term (6-month) interest rates. We then investigate a number of relevant statistics of the terminal wealth achieved after a 20-year period for two typical portfolios: a long-only portfolio well-diversified over stocks and bonds where the relevant metric is the portfolio’s value (for instance, an endowment fund), and a pension fund’s coverage ratio where the fund’s liabilities are valued by a market interest rate curve. We show that both types of investors greatly benefit from adjusting their exposure to equities and interest rates conditionally on the expected risk regime. Finally, we show the consequence when both the endowment fund manager and the pension fund board members optimize their own reward/risk ratio from their job. We argue that in such a case they seek to minimize the probability of large losses (either in absolute terms or relative to the pension fund’s liabilities), while maximizing the minimum level of wealth (or coverage ratio for the pension fund) achieved with a given (say 95%) confidence level. We quantify the added value of the risk-regime depending allocations for such managers.