A Note on Life-cycle Funds

Life-cycle or target-date funds have been gaining tremendous market share and were recently set as default choice of asset allocation in numerous defined contribution schemes or related old age provision products in many countries. Hence, an appropriate assessment of life-cycle funds’ risk-return profiles – i.e. the probability distribution of returns – is essential for sustainable financial planning concerning a large group of investors. The core idea of lifecycle funds is to decrease the fund’s equity exposure and conversely increase its bond exposure towards the fund’s target date. This paper studies the risk-return profile of life-cycle funds in particular compared to standard balanced or lifestyle funds that apply a constant equity portion throughout the fund’s term instead. Assuming a Black-Scholes model, we derive balanced funds that reproduce the risk-return profile of an arbitrary life-cycle fund considering single and regular contributions. We then investigate our results’ accuracy applying more sophisticated asset models including stochastic interest rates, stochastic equity volatility and jumps. We further compare our methodology to approximations used so far only taking into account the life-cycle funds’ average equity portion throughout the funds’ term and conclude that this approximation fails in approximating the life-cycle funds’ risk-return profile properly. Our results on the one side facilitate sustainable financial planning and on the other side challenge the very existence of life-cycle funds since appropriately calibrated balanced funds can offer a similar risk-return profile. A NOTE ON L IFE-CYCLE FUNDS 1