Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/244566 
Year of Publication: 
2020
Series/Report no.: 
Working Paper No. 8/2020
Publisher: 
Örebro University School of Business, Örebro
Abstract: 
In this paper, we consider the sample estimator of the tangency portfolio (TP) weights, where the inverse of the sample covariance matrix plays an important role. We assume that the number of observations is less than the number of assets in the portfolio, and the returns are independent and identically multivariate normally distributed. Under these assumptions, the sample covariance matrix follows a singular Wishart distribution and, therefore, the regular inverse cannot be taken. This paper delivers bounds and approximations for the rst two moments of the estimated TP weights, as well as exact results when the population covariance matrix is equal to the identity matrix, employing the Moore-Penrose inverse. Moreover, exact moments based on the re exive generalized inverse are provided. The properties of the bounds are investigated in a simulation study, where they are compared to the sample moments. The di erence between the moments based on the re exive generalized inverse and the sample moments based the Moore-Penrose inverse is also studied.
Subjects: 
Tangency portfolio
Singular inverse Wishart
Moore-Penrose inverse
Reexive generalized inverse
Estimator moments
JEL: 
C13
C58
Document Type: 
Working Paper

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