Liability Driven Investment with Downside Risk

Abstract

We develop a liability driven investment framework that incorporates downside risk penalties for not meeting liabilities. The shortfall between the asset and liabilities can be valued as an option which swaps the value of the endogenously determined optimal portfolio for the value of the liabilities. The optimal portfolio selection exhibits endogenous risk aversion and as the funding ratio deviates from the fully funded case in both directions, effective risk aversion decreases. When funding is low, the manager 'swings for the fences' to take on risk, betting on the chance that liabilities can be covered. Over-funded plans also can afford to take on more risk as liabilities are already well covered and so invest aggressively in risky securities.

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