Asset/Liability Management for Pension Funds Using CVaR Constraints

Abstract

This article studies formal optimal decision approaches for a multi‐period asset/liability management model for a pension fund. The authors use Conditional Value‐at‐Risk (CVaR) as a risk measure, the weighted average of the Value‐at‐Risk (VaR) and those losses exceeding VaR. The model is based on sample‐path simulation of the liabilities and returns of financial instruments in the portfolio. The same optimal decisions are made for groups of sample‐paths, which exhibit similar performance characteristics. Since allocation proportions are time‐dependent, these techniques are more flexible than more standard allocation procedures, e.g. “constant proportions.” Optimization is conducted using linear programming. Compared with traditional stochastic programming algorithms (for which the problem dimension increases exponentially in the number of time stages), this approach exhibits a linear growth of the dimension. Therefore, this approach allows the solution of problems with very large numbers of instruments and scenarios.