Bounds on the Risk-Free Interest Rate in Incomplete Markets With and Without Utility Functions Exhibiting Constant Absolute Risk Aversion

In a model of a two-period exchange economy under uncertainty, we find an upper bound for the equilibrium risk-free interest rate when the expected aggregate endowment in the second period is no greater than the first-period aggregate endowment. We also find a lower bound when the agents' utility functions exhibit constant absolute risk aversion and the expected aggregate endowment in the second period is no smaller than the first-period counterpart. These bounds are independent of the degree of market incompleteness, and so these results show to what extent market incompleteness can explain the risk-free rate puzzle in this class of general equilibrium models with heterogeneous agents. A general method of finding lower bounds is also presented.