Introducing risk into a Tobin asset-allocation model

The Tobin asset-allocation model has become a standard component in stock-flow consistent (SFC) models. It relates asset returns to wealth allocation, and thereby to the value of assets as reflected in Tobin’s q. The model is flexible, parsimonious, and intuitively appealing, but it suffers from a large number of independent coefficients and depends only on returns for the allocation. A truism from financial theory and practice is that allocations depend on both risk and return. In this paper we introduce risk into a Tobin model. We propose that allocations are a compromise between competing goals of low turnover and high return, constrained by the degree of risk that investors are willing to tolerate. In our model, the Tobin coefficients depend on asset-specific risk and a small number of independent parameters. The model also yields an expression for the q values of different assets as a function of risk and parameters reflecting market sentiment.