The demand for index bonds by households is studied in an inter-temporal optimization model in which households can choose a portfolio consisting of equity, nominal bonds, and index bonds. The rate of inflation is uncertain. In a setting where all income is from capital gains, it is shown that index bonds command a premium over nominal bonds only if equity is not a hedge against inflation; it is also shown that, if there are homogeneous expectations and no outside bonds, all lending and borrowing will be through index bonds with no nominal bonds existing. These conclusions are modified when individuals have income from human capital. The very stringent conditions under which a single index bond provides the household with the same utility as a full set of futures markets are examined in a model with many consumption goods.