Capital mobility may equalize investment opportunities across industries, and further, may cause the return-risk trade-offs of industry portfolios to converge. We show that over an extended period from 1926 to 2014, value-weighted industry portfolios based on Fama-French 5, 10, 12, 17, 30, and...

We identify decompositions of multi-period optimal portfolios, in which each subportfolio is dedicated to achieving a single investment target, in dynamic models with Von Neumann-Morgenstern preferences and diffusion asset returns (“Merton's problem”). These decompositions rest on...

Volatility models of the market portfolio's return are central to financial risk management. Within an equilibrium framework, we introduce an implementation method and study two families of such models. One is deterministic volatility, represented by current popular models. Another is in the...