Liability-driven investment for pension funds: stochastic optimization with real assets

Using a multi-stage stochastic programming method, we suggest an optimal liability-driven investment (LDI) strategy for a closed defined-benefit pension fund including real assets. The objective is to jointly optimize contribution, funding ratio, and buyout cost, subject to a constraint on downside risk in terms of expected shortfall of assets relative to liabilities. Over a 10-year planning horizon, the optimal LDI strategy with a key-rate duration-matching bond portfolio outperforms the corresponding strategy with a duration-convexity matching bond portfolio as well as a strategy with an aggregate bond index-tracking portfolio. When real assets are introduced, the optimal LDI strategy includes significant investment in infrastructure and real estate, illiquidity notwithstanding. Nevertheless, delays in sales of real assets induced by illiquidity can increase downside risk.