Do Financial Planners Take Financial Crashes into their Advice : Dynamic Asset Allocation Under Thick Tails and Fast Volatility Updating

This paper is motivated by recent findings that current models of stock returns and interest rates are incapable to capture the actual behavior of those financial variables (like hyper volatility, the behavior of higher moments and leverage effect), particularly during rare events. The paper solves analytically for the optimal portfolio strategies of bonds, stocks and cash when the investment opportunity set is driven by a mixture of jump diffusion and non-affine stochastic processes of interest rates and stock returns. Such structure should be able to capture the characteristics of financial data during rare events as many recent articles indicate. Results show that investors hold a linear combination of a speculative portfolio and a hedging portfolio, with weights related to the investor's risk tolerance. The investor increases (decreases) the speculative allocation in his portfolio if he expects upward (downward) jump. The amount of increase or decrease to the speculative portfolio depends on the degree of risk aversion and the investment horizon. The hedging portfolio consists of additional 100% bond portfolio to hedge against interest rate changes and a 100% stock portfolio to hedge against stochastic volatility changes. Those additional hedging portfolios depend on the duration of the bond and the correlation between stock returns and volatility processes, beside their dependence on the risk tolerance and investment horizon. The non-affine specification seems to increase the demand for hedging and captures the leverage effect. Calibration results show that the joint inclusion of jumps and non-affine structure into the investment opportunity set dynamics introduces a plausible simultaneous resolution for both Samuelson puzzle and asset allocation puzzle