Definition of The Equity Premium Puzzle: Real returns to investors from the purchases of U.S. government bonds have been estimated at one percent per year, while real returns from stock ("equity") in U.S. companies have been estimated at seven percent per year (Kocherlakota, 1996). General utility-based theories of asset prices have difficulty explaining (or fitting, empirically) why the first rate is so low and the second rate so high, not only in the U.S. but in other countries too. The phrase equity premium puzzle comes from the framing of this problem (why is the difference so great?) and the attention focused on it by Mehra and Prescott (1985); sometimes the phrase risk free rate puzzle is used to describe the closely related question: why is the bonds rate so low? The problem can be inverted to ask: why do investors not reject the low-returning bonds in order to buy stocks, which would then raise the price of stocks and lower their subsequent returns?

The above is drawn from the excellent review by Kocherlakota (1996) which surveys the substantial literature on this subject. Abbreviating further from it: the theories against which the evidence constitute a "puzzle" (or paradox) tend to have these aspects in common:

1. Standard preferences described by standard utility functions
2. Contractually complete asset markets (against possible time- and state-of-the-world contingencies)
3. Costless asset trading (in terms of taxes, trading fees, and presumably information).