The expected market return is a number frequently required for the solution of many investment and corporate finance problems, but by comparison with other financial variables, there has been little research on estimating this expected return. Current practice for estimating the expected market return adds the historical average realized excess market returns to the current observed interest rate. While this model explicitly reflects the dependence of the market return on the interest rate, it fails to account for the effect of changes in the level of market risk. Three models of equilibrium expected market returns which reflect this dependence are analyzed in this paper. Estimation procedures which incorporate the prior restriction that equilibrium expected excess returns on the market must be positive are derived and applied to return data for the period 1926–1978. The principal conclusions from this exploratory investigation are: (1) in estimating models of the expected market return, the non-negativity restriction of the expected excess return should be explicity included as part of the specification: (2) estimators which use realized returns should be adjusted for heteroscedasticity.