Portfolio Selection and Asset Pricing with Dynamically Incomplete Markets and Time-varying First and Second Moments

This paper simplifies Merton’s (1973) fund separation theorem by showing that investors will hold hedge funds in their optimal portfolio only to hedge against changes in the slope or position of the instantaneous capital market line. This result allows for incomplete markets and does not assume that the securities prices are Markovian. By aggregating, we derive a single factor capital asset pricing model (CAPM) with a constant capital market line, where the first and second moments of security returns may change over time and markets are potentially incomplete. This model is consistent with some autoregressive conditional heteroscedastic in mean (ARCH–M) and generalized ARCH–M (GARCH–M) specifications from the recent empirical literature. It differs from the consumption CAPM by allowing capital market incompleteness and by the fact that the single factor is the return to the market portfolio rather than aggregate consumption. The model resolves the paradox of Rosenberg and Ohlson (1976).