The risk-sharing role of redundant assets is not yet fully understood in constrained asset markets. For example, the well-known notions of arbitrage may fail to explain the viability property of asset prices when redundant assets are involved in generating a nontrivial linear structure of free portfolios in equilibrium in constrained asset markets. This paper establishes the existence of equilibrium in two-period asset markets which are subject to portfolio constraints. First, we provide a full analysis of complicated equilibrium behavior of constrained portfolios with redundant assets by adopting a new notion of arbitrage. To do this, a technique of portfolio decomposition is developed to identify the linear structure of free portfolios embedded in the aggregate set of constrained portfolios. Second, we present a new condition on the aggregate set of portfolios which is indispensable for the existence of equilibrium in constrained asset markets. The literature assumes that the individual portfolio constraint set or the individual marketed set of income transfers is closed to study the presence of optimal portfolios or viability of asset prices in a partial equilibrium framework. As illustrated later, however, this condition alone fails to be sufficient for the existence of equilibrium.