Subjective discounting in an exchange economy

This paper describes the equilibrium of a discrete-time exchange economy in which consumers with arbitrary subjective discount factors and homothetic period utility functions follow linear Markov consumption and portfolio strategies. Explicit expressions are given for state prices and consumption-wealth ratios. We provide an analytically convenient continuous-time approximation and show how subjective rates of time preference affect risk-free rates but not instantaneous risk-return trade-offs. Hyperbolic discount factors can be a source of return volatility, but they cannot be used to address asset pricing puzzles related to high-frequency Sharpe ratios.