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The purpose of the paper is two-fold. First, we demonstrate that arbitrage pricing rules can be linear in a limited manner under heterogeneous portfolio constraints. One novelty is that asset pricing information is encoded in the value of zero-income portfolios. Arbitrage pricing rules are linear to the extent that the set of free zero-income portfolios is large. This result amounts to a generalization of the law of one price. Second, the existence of equi-librium is established by analyzing exhaustively the risk-sharing role of redundant assets under portfolio constraints. This problem is addressed in the literature but as remarked in Cass et al. (2001), they make assumptions which seriously restrict the income-spanning role of redundant assets. Both lines of research are taken together here because the de-coding process for asset pricing information is a key step to understanding the effect of frictions on optimal portfolios