The Effect of Introducing a Non-Redundant Derivative on the Volatility of Stock-Market Returns

We study the effect of introducing a non-redundant derivative on the volatilities of the stock-market return and the locally risk-free interest rate. Our analysis uses a standard, frictionless, full-information, dynamic, continuous-time, general-equilibrium, Lucas endowment economy in which there are two classes of agents who have time-additive power utility functions and differ only in their risk aversion. We solve for equilibrium in two versions of this economy. In the first version, risk-sharing opportunities are limited because investors can trade in only the market portfolio, which is a claim on the aggregate endowment. In the second version, agents can trade in both the market portfolio and a non-redundant zero-net-supply derivative. Our main result is to show analytically that, if the intensity of the precautionary demand for savings is not too high, then the introduction of a non-redundant derivative increases the volatility of stock-market returns. Furthermore, in the economy with the derivative, the volatility of stock-market returns can be substantially greater than that of aggregate dividend growth (fundamental volatility). We show also that the volatility of the locally risk-free interest rate increases with the introduction of the derivative