Estimation Risk in Portfolio Selection: The Mean Variance Model Versus the Mean Absolute Deviation Model

Konno and Yamazaki (Konno, H., K. Yamazaki. 1992. Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management Sci. 39 519–531.) propose the mean absolute deviation (MAD) model as an alternative to the mean variance (MV) model. They claim it retains all the positive features of the MV model, saves the investor computing time, and does not require the covariance matrix. This paper shows that ignoring the covariance matrix results in greater estimation risk that outweighs the benefits. In both models, estimation error is more severe in small samples (small observations relative to the number of assets) and for investors with high risk tolerance. The MV model's lower estimation risk is most striking in small samples and for investors with a low risk tolerance.