Long-Tail Distributions And Total Returns On Risk-Based Investment Products

Abstract

Use of target date funds (TDFs) in retirement plans increased in popularity following the 2007-2008 financial crisis. However, some argued that TDFs do not provide an acceptable level of protection against market downturns and long-tail events. This study assesses the ability of TDFs to deal with long-tail events. It builds a system of equations for seven asset classes that are used to build four hypothetical TDFs, and compares simulated total returns for four hypothetical TDFs over a 50-year horizon, where the stochastic terms for each of the underlying asset classes is based on the normal distribution and a long-tail distributions (the Laplace distribution). Simulations are repeated 2000 times. Total returns for four TDFs are calculated over non-overlapping 1-, 2- 3-, and 5-year horizons over the 50-year span for the 2000 simulations. Results show that about half the time the risk measure for the long-tail distribution are wider than the normal, and about half the time the opposite holds. It seems that the processes of asset diversification along with calculating returns over horizons of at least one year mitigates effects of long-tail characteristics. Even so, results do not bode well for those nearing retirement. Negative returns over 1- and 2-year investment horizons are possible 17% of the time for a conservative allocation over a 50-year period.