We provide a theoretical framework to uncover in a model‐free way the relationships among international stochastic discount factors (SDFs), stochastic wedges, and financial market structures. Exchange rates are in general different from the ratio of international SDFs in incomplete markets, as captured by a stochastic wedge. We show theoretically that this wedge can be zero in incomplete and integrated markets. Market segmentation breaks the strong link between exchange rates and international SDFs, which helps address salient features of international asset returns while keeping the volatility and cross‐country correlation of SDFs at moderate levels.

Under mild assumptions, we recover the model‐free conditional minimum variance projection of the pricing kernel on various tradeable realized moments of market returns. Recovered conditional moments predict future realizations and give insight into the cyclicality of equity premia, variance risk premia, and the highest attainable Sharpe ratios under the minimum variance probability. The pricing kernel projections are often U ‐shaped and give rise to optimal conditional portfolio strategies with plausible market timing properties, moderate countercyclical exposures to higher realized moments, and favorable out‐of‐sample Sharpe ratios.

We provide novel evidence for an equilibrium link between investors' disagreement, the market price of volatility and correlation, and the differential pricing of index and individual equity options. We show that belief disagreement is positively related to (i) the wedge between index and individual volatility risk premia, (ii) the different slope of the smile of index and individual options, and (iii) the correlation risk premium. Priced disagreement risk also explains returns of option volatility and correlation trading strategies in a way that is robust to the inclusion of other risk factors and different market conditions.

We develop a new framework for multivariate intertemporal portfolio choice that allows us to derive optimal portfolio implications for economies in which the degree of correlation across industries, countries, or asset classes is stochastic. Optimal portfolios include distinct hedging components against both stochastic volatility and correlation risk. We find that the hedging demand is typically larger than in univariate models, and it includes an economically significant covariance hedging component, which tends to increase with the persistence of variance–covariance shocks, the strength of leverage effects, the dimension of the investment opportunity set, and the presence of portfolio constraints.