Prices as Factors: Approximate Aggregation with Incomplete Markets

Recent developments in intertemporal asset pricing theory focus on two sets of fundamental determinants of asset returns. Models with complete markets emphasize aggregate variables such as per capita consumption. Such models have not performed well empirically. Models with incomplete markets emphasize disaggregate variables such as the distribution of wealth. These models have shown empirical promise, but their lack of parsimony has led many to question their usefulness. Indeed, most empirical applications, as well as the best practice in the financial industry, ignore much of what theory has to say altogether. Practitioners favor factor models and, in particular, models in which asset returns serve as factors that explain other asset returns. This paper attempts to rationalize these very different approaches. We show that in an incomplete-markets economy—an economy in which the true pricing kernel is high dimensional and difficult to measure—a low-dimensional pricing kernel that depends on returns, as in the CAPM or the APT, can accurately price assets. In this sense, theory based on fundamentals admits an approximate aggregation that is consistent with practical application. Theory and practice, therefore, may not be as disparate as they might seem.