Calibration of risk aversion to real pension asset allocation

We introduce a method to infer an investor's risk aversion based on the observed asset allocation of their pension savings. By assuming the actual allocation is optimal under a constant relative risk aversion (CRRA) utility, we invert Merton's optimal investment formulas to estimate the risk aversion parameter. The approach incorporates the present value of future premiums, resulting in strategies that align with life-cycle pension products. To ensure stability, we develop a customized risky fund matched with the investor's allocation, enabling reliable calibration across various asset classes. A numerical study on a Danish pension portfolio demonstrates the practical use. The findings show realistic and stable risk aversion levels consistent with the CRRA assumption and offer a tool to better understand and benchmark the implicit preferences embedded in pension product design.