Portfolio Inefficiency and the Cross-Section of Expected Returns
Shmuel Kandel, Robert F. Stambaugh
NBER Working Paper No. 4702
A plot of expected returns versus betas obeys virtually no relation to an inefficient index portfolio's mean-variance location. If the index portfolio is inefficient, then the coefficients and R- squared from an ordinary-least-squares regression of expected returns on betas can equal essentially any desired values. The mean-variance location of the index does determine the properties of a cross- sectional mean-beta relation fitted by generalized least squares (GLS). As the index portfolio moves closer to exact efficiency, the GLS mean-beta relation moves closer to the exact linear relation corresponding to an efficient portfolio with the same variance. The goodness-of-fit for the GLS regression is the index portfolio's squared relative efficiency, which measures closeness to efficiency in mean-variance space.
Published: Journal of Finance 50(1995):157-184.