Optimal Asset Allocation with Heterogeneous Persistent Shocks and Myopic and Intertemporal Hedging Demand

There is a wide evidence that financial time series are the outcome of the superposition of processes with heterogeneous frequencies. This is true, in particular, for market return. Indeed, log market return can be decomposed into uncorrelated components that explain the reaction to shocks with different persistence. The instrument that allows us to do so is the Extended Wold Decomposition of Ortu et al. (2017). In this chapter, we construct portfolios of these components in order to maximize the utility of an agent with a fixed investment horizon. In particular, we build upon Campbell and Viceira (1999) solution of the optimal consumption-investment problem with Epstein–Zin utility, using a rebalancing interval of 2J periods. It turns out that the optimal asset allocation involves all the persistent components of market log return up to scale J. Such components play a fundamental role in characterizing both the myopic and the intertemporal hedging demand. Moreover, the optimal policy prescribes an increasing allocation on more persistent securities when the investor’s relative risk aversion rises. Finally, portfolio reallocation every 2J periods is consistent with rational inattention. Indeed, observing assets value is costly and transaction costs make occasional rebalancing optimal.