Individuals who are buffeted by stochastic shocks will wish to substitute consumption intertemporally. To effect this substitution they can enter into insurance contracts, or they can use money. This paper investigates the connection between optimum insurance and Friedman's  concept of the optimum quantity of money, using a simplified version of Lucas's  pure currency economy. Monetary efficiency and efficient insurance are equivalent here. An example is presented in which an efficient monetary equilibrium exists. Contrary to Bewley's  conjecture, in the example the efficient rate of return on real balances is less than the internal rate of discount.