Two empirical questions concerning the equity and housing have been studied extensively: (1) Are the price and return serially correlated, and (2) What is the optimal weight of housing in the portfolio? The answer to the second question crucially depends on the cross-correlation of assets. This paper complements the literature by building a simple dynamic general equilibrium with fully rational agents, and obtain closed form solutions for the implied auto- and cross-correlations. The length of time horizon, as well as the persistence of economic shock matter. Implications and future research directions are then discussed.