Abstract

There is 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, Severino, Tamoni and Tebaldi (2017). Hence, 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, by using a rebalancing interval of 2^J periods. It comes 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 assets when the investor’s relative risk aversion rises. Finally, portfolio reallocation every 2^J periods is consistent with rational inattention. Indeed, observing assets value is costly and transaction costs make occasional rebalancing optimal.