Robustness for asset-liability management of pension funds

Pension funds face both risk and uncertainty during their everyday operation.

Pension funds (and investors in general) face both risk and uncertainty during their everyday operation. The importance of distinguishing between risk and uncertainty was first emphasized in the seminal work of Knight, and it has been an achive research topic in the finance literature ever since. Risk means that the investor does not know what future returns will be, but she does know the probability distribution of the returns.

On the other hand, uncertainty means that the investor does not know precisely the probability distribution that the returns follow. As a simple example, let us assume that the one-year return of a particular stock follows a normal distribution with 9% expected value and 20% standard deviation. A pension fund who knows that the return of the stock follows this particular distribution, faces risk, but it does not face uncertainty. Another pension fund only knows that the return of this stock follows a normal distribution, that its expected value lies between 8% and 12%, and that its standard deviation is 20%. This pension fund faces not only risk, but also uncertainty: not only does it not know the exact return in one year, it also does not know the precise probability distribution that the return follows.

A risk-averse investor is averse of the risk with known distribution, while an uncertainty-averse investor is averse of uncertainty. Decisions which take into account the fact that the investor faces uncertainty, are called robust decisions. These decisions are robust to uncertainty because they protect the investor against uncertain outcomes (“bad events”).

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