This paper examines the incentives offered by frictionless markets to innovate asset‐backed securities by owners who maximize the assets' values. Assuming identical preferences across investors with heterogeneous risk‐sharing needs, we characterize economies in which competition provides insufficient incentives to innovate so that, in equilibrium, financial markets are incomplete in all (pure strategy) equilibria, even when innovation is essentially costless. Thus, value maximization does not generally result in complete markets.