Index Investing and Asset Pricing under Information Asymmetry and Ambiguity Aversion

In a setting with a tradable value-weighted market index, ambiguity-averse investors do not trade, and the index is not mean–variance efficient. But when a passive fund offers the risk-adjusted market portfolio (RAMP), whose weights depend on information precision as well as market values, investors share risk via index investing and effectively hold the same portfolios as in the economy without model uncertainty. This follows from a new Information Separation Theorem: equilibrium portfolios are the sum of RAMP, which is the optimal portfolio conditional on public information, and their optimal private-information-based portfolios. RAMP is in equilibrium mean–variance efficient.