Estimating the risk-return trade-off with overlapping data inference

Investigations of the basic risk-return trade-off for the market return typically use maximum likelihood estimation (MLE) with a monthly or quarterly horizon and data sampled to match the horizon even though daily data are available. We develop an overlapping data inference methodology for such models that uses all of the data while maintaining the monthly or quarterly forecasting period. Our approach recognizes that the first order conditions of MLE can be used as orthogonality conditions of the generalized method of moments (GMM). While parameter estimates from the different non-overlapping monthly samples that start on different days vary substantively, a formal test does not reject parameter equality and constrained estimation of the risk-return trade-off produces a statistically significant value of 3.35 in post-1955 data.