This paper uses six waves of the Bank of Italy Survey of Households Income and Wealth to explore the dynamics of asset portfolio ownership. The household asset portfolio decision is a choice among discrete alternatives, and I model the problem in a multinomial framework. I focus on a particularly important feature of household portfolio behavior: the infrequency of portfolio allocation changes. I find evidence of strong unobserved heterogeneity through time-varying error components, which I interpret as taste persistence in both the risky and safe asset participation decisions. I estimate the model using the method of maximum smoothly simulated likelihood.