Optimal Portfolio Choice with Fat Tails

Kent Smetters

NBER Retirement Research Center Paper No. NB 09-16
Issued in September 2009

The recent financial crisis has highlighted the importance of modeling and managing extreme risk, especially retirement savings. Virtually all standard optimal stock-bond portfolio allocation models, however, assume that risk is normally distributed (bell shape). In reality, stock market risk exhibits “fat tails." Allowing for “fat tails” can add considerable computational complexity to standard optimization framework, which is already quite complicated. This paper demonstrates how to model fat tails using a g-and-h distribution that allows for skewness and kurtosis of arbitrary degree. Unlike alternative extreme value and other coupla approaches, the g-and-h distribution has a well defined pdf, is smooth and satisfies certain regularity conditions that allow for tractable integration. It also appears to fit the data the best. We hope that our modeling approach will open the door for more realistic modeling of retirement income risk in the future. Our own SSA grant proposal for next year will extend the current research by adding a greater degree of fiscal policy institutions that materially can affect saving for retirement.

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