On the mean and variance of the estimated tangency portfolio weights for small samples

In this paper, a sample estimator of the tangency portfolio (TP) weights is considered. The focus on situation where number observations smaller than assets in and returns are i.i.d. normally distributed. Under these assumptions, covariance matrix follows singular Wishart distribution and, therefore, regular inverse cannot be taken. bounds approximations for first two moments estimated TP derived, as well exact results obtained when population equal to identity matrix, employing Moore–Penrose inverse. Moreover, based reflexive generalized provided. properties investigated simulation study, they compared moments. difference between also studied.