Johnson–Omega for Pension Recovery

Underfunding due to either stock market weakness or, until recently, low discount rates remains an issue in pension fund management. This article presents a comprehensive, rigorous approach to portfolio construction, which is designed to recover a poor funding ratio within a desired recovery time. The method provided is applicable to marginally or severely underfunded pension schemes, where investing in the risk-free asset is not an efficient option for bringing assets and liabilities back in balance. The method complements constant proportion portfolio insurance–type pension strategies, where equity risk increases with adequacy. The Omega performance measure is a natural tool to use in recovering underfunded pension schemes, as the target rate of return to achieve a balance between assets and liabilities is, by design, the Omega-specific hurdle. The Johnson–Omega version applied in this article accounts for economically meaningful mean, variance, skewness, and kurtosis characteristics (and the co-moments between portfolio constituents). It is insensitive to (implicit) estimates of potentially noisy moments of higher order. The smooth Johnson distribution is convenient and robust for optimizations and flexible enough to adapt to tail asymmetries and fatness in return distributions. This article is based on US Thrift Savings Plan (TSP) constituents and illustrates that TSP Individual and Lifecycle Funds can be significantly outperformed, both in absolute and risk-adjusted terms, by applying a Johnson–Omega optimization. Speed and likelihood of recovery are significantly higher, and the probability of experiencing shortfalls the funding ratio is substantially lower. The method can be easily implemented by pension schemes, which only need to provide the current funding ratio and desired recovery time.