Contents :
This paper is motivated by recent findings that current modelsof stock returns and interest rates are incapable to capture the actualbehavior of those financial variables (like hyper volatility, the behavior ofhigher moments and leverage effect), particularly during rare events. The papersolves analytically for the optimal portfolio strategies of bonds, stocks andcash when the investment opportunity set is driven by a mixture of jumpdiffusion and non-affine stochastic processes of interest rates and stockreturns. Such structure should be able to capture the characteristics offinancial data during rare events as many recent articles indicate. Resultsshow that investors hold a linear combination of a speculative portfolio and ahedging portfolio, with weights related to the investor’s risk tolerance. Theinvestor increases (decreases) the speculative allocation in his portfolio ifhe expects upward (downward) jump. The amount of increase or decrease to thespeculative portfolio depends on the degree of risk aversion and the investmenthorizon. The hedging portfolio consists of additional bond portfolio to hedgeagainst interest rate changes and additional stock portfolio to hedge againststochastic volatility changes. Those additional hedging portfolios depend onthe duration of the bond and the correlation between stock returns andvolatility processes, beside their dependence on the risk tolerance andinvestment horizon. The non-affine specification seems to increase the demandfor hedging and captures the leverage effect. Calibration results show that thejoint inclusion of jumps and non-affine structure into the investmentopportunity set dynamics introduces a plausible simultaneous resolution forboth Samuelson puzzle and asset allocation puzzle.