Nº 20-24: Managing the Shortfall Risk of Target Date Funds by Overfunding

Is it possible to achieve almost riskless, non fluctuating investment payoffs in the long run, at a fraction of the traditional funding requirement, using equity investments? What is their shortfall risk? These questions are motivated by the need to increase yields, while limiting the variability of investment results. We show how to use contingent claims, denominated in units of a stock index, to achieve an almost riskless investment outcome.
To control the risk of the proposed hedge portfolios, we introduce an overfunded scheme and show its reliability using bootstrapping. Results show that a modest amount of overfunding is an effective risk-management approach that brings the probability of not achieving the target to less than 1%. Our results are demonstrated through the use of the minimal market model and a change of numeraire.