Before revision:  This result resolves the equity premium puzzle , informs interest rate setting , and constitutes a theory of noise in financial markets  .
After revision:  This result resolves the equity premium puzzle , informs interest rate setting to avoid leverage-driven price instabilities; and a method for detecting fraudulent investment schemes by exploiting differences between the stochastic properties of their prices and those of legitimately-traded assets. To submit the hypothesis to a rigorous test we choose price data from different assets: the S .