Lifetime Ruin Minimization: Should Retirees Hedge Inflation or Just Worry About it?

Abstract

Inflation for retirees is different from, and mostly higher than, the macroeconomic (average) inflation rate for the entire population. In the U.S. for example, the Consumer Price Index for the Urban population (CPI-U) calculated and reported by the Bureau of Labor Statistics (BLS) has a lesser known cousin called the CPI-E (for the elderly) in which the sub-component weights are based on the consumption patterns of Americans above the age of 62. This suggests that Inflation Linked Bond Funds (ILBFs) - whose individual component bond adjustments are based on broad population (CPI-U) inflation - might not be the best hedge for individual retirees’ cost of living. But then again, broad shocks to inflation are likely to impact both indices. So, motivated by the question, Is it good enough? The current paper uses lifetime ruin minimization (LRM) techniques to investigate the optimal allocation between an ILBF and a nominal investment fund for a retiree facing an exogenous liability. Our model trades-off the benefit of an imperfect hedge against the cost of lower investment growth. Alas, our numerical results suggest that although ILBFs can be a large part of the optimal retirement portfolio, it should treated as just another asset class in the broad optimization problem as opposed to a special or unique category.