Comment On “Capm Risk Adjustment For Exact Aggregation Over Financial Assets,” By Barnett, Liu, And Jensen

The Divisia monetary index weights each monetary asset by its expenditure share, evaluated at its user cost. See Barnett et al. [1997, equations (5) and (6)]. In a world of perfect certainty, the user costs can be computed directly from asset return data, and so, the index is model-free. In the presence of uncertainty, however, the true user cost of a monetary asset depends on the covariance of the asset's return with the marginal utility of wealth. Intuitively, an asset's value depends both on its expected payoff and on the asset's ability to hedge wealth fluctuations. As a result, the true user cost cannot be computed without an explicit model of preferences. It follows that the exact Divisia monetary index in a stochastic economy is not model-free, but depends on the underlying preference assumptions.