Following Hansen and Jagannathan, 1991, we use the observed data on asset returns to compute volatility bounds on the IMRS, expressed as mean-standard deviation pairs. This is given by the shaded area in Figure 4. For illustration, we also use quarterly data on aggregate total expenditure from the UK National Accounts to compute estimates of the IMRS. Assuming that within-period utility functions exhibit Constant Relative Risk Aversion, and maintaining the assumption of inter-temporal separability, the IMRS is given by:
where у is the coefficient of relative risk aversion and [3 the discount factor. Assuming different values of у (between 0.5 and 5) and a discount rate of 2 per cent we plot the mean and standard deviation pairs for the IMRS implied by the growth in aggregate consumption for the period 1978-95. These are shown by the ‘crosses’ in Figure 4. This figure shows clearly that the IMRS mean-standard deviation pairs implied by aggregate expenditure data (and plausible values for the coefficient of relative risk aversion9 and of the discount factor) lie well outside the region admissible by the asset return data. In the next two sections we explore the possibility that limited participation in asset markets, and the stock market in particular, may be able to resolve this puzzle.