Dynamic Asset Allocation: a Portfolio Decomposition Formula and Applications

This paper establishes a new decomposition of the optimal portfolio policy in dynamic asset allocation models with arbitrary vNM preferences and Ito prices. The formula rests on a change of num'{e}raire which consists in taking pure discount bonds as units of account. When expressed in this new num'{e}raire the dynamic hedging demand is shown to have two components. If the individual cares solely about terminal wealth, the first hedge insures against fluctuations in a long term bond with maturity date matching the investor's horizon and face value determined by bequest preferences. The second hedge immunizes against fluctuations in future bond return
volatilities and market prices of risk. When the individual also cares about intermediate consumption the first hedging component becomes a coupon-paying bond with coupon payments tailored to the consumption needs. The decomposition formula is used to examine the existence of preferred habitats, the investment behavior of extremely risk averse individuals, the demand for long term bonds, the optimal international asset allocation rule, the preference for I-bonds in inflationary environments and the integration of fixed income management and asset allocation.