Using stochastic frontier analysis instead of data envelopment analysis in modelling investment performance

We introduce methods to apply stochastic frontier analysis (SFA) to financial assets as an alternative to data envelopment analysis, because SFA allows us to fit a frontier with noisy data. In contrast to conventional SFA, we wish to deal with estimation risk, heteroscedasticity in noise and inefficiency terms. We investigate measurement error in the risk and return measures using a simulation-extrapolation method and develop residual plots to test model fit. We find that shrinkage estimators for estimation risk makes a striking difference to model fit, dealing with measurement error only improves confidence in the model, and the residual plots are vital for establishing model fit. The methods are important because they allow us to fit a frontier under the assumption that the risks and returns are not known exactly.