THE DEMAND FOR RISKY ASSETS UNDER UNCERTAIN INFLATION

Abstract

IN SEVERAL RECENT PAPERS by a colleague and ourselves, we have derived and empirically tested utility functions for individual households which were then combined to construct an aggregate demand function for risky assets.' The main conclusions of this earlier work are: The assumption of constant proportional risk aversion for households is as a first approximation a fairly accurate description of the market place. Second, regardless of their wealth level, the coefficients of proportional risk aversion for households are on average well in excess of one and probably in excess of two, so that households are more risk averse than would be implied by a log utility function. Third, under the assumption of constant proportional risk aversion, a simple form of the aggregate equilibrium relationship between the relative demand for risky assets and the market price of risk (MPR) can be (and has been) developed. The determination in this earlier work of the aggregate relationship between the demand for risky assets and the MPR is based on a number of different models ranging from the simplest case where a risk-free asset in nominal terms exists, the separation theorem is valid, all assets are readily marketable, and there is no taxation to the more complex case where there is no risk-free asset, the separation theorem is not applicable, and both non-marketable assets and taxation exist. However, none of these models explicitly considers the effect of inflation on the demand for risky assets. The subsequent analysis, where the variables are defined in nominal terms, will use the analytical framework and results developed in our previous work to obtain new results on the effect of inflation on the MPR and on the pricing of individual risky assets (as specified by the familiar capital asset pricing model). To summarize our new results: (1) The traditional capital asset pricing model measured in nominal terms (CAPM) understates the MPR if an uncertain inflation is expected and if there is a positive covariance between the rate of return on the market and the rate of inflation. (The reverse is true if an uncertain deflation is expected or if there is a negative covariance between market return and inflation). (2) The CAPM overstates the risk of an asset under expectations of uncertain inflation if there is a positive covariance between the rate of return on the asset and the rate of inflation.