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

Ämnesord

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

SAMHÄLLSVETENSKAP  -- Ekonomi och näringsliv (hsv//swe)

SOCIAL SCIENCES  -- Economics and Business (hsv//eng)

SAMHÄLLSVETENSKAP  -- Ekonomi och näringsliv -- Nationalekonomi (hsv//swe)

SOCIAL SCIENCES  -- Economics and Business -- Economics (hsv//eng)

NATURVETENSKAP  -- Annan naturvetenskap (hsv//swe)

NATURAL SCIENCES  -- Other Natural Sciences (hsv//eng)

Nyckelord

Tangency portfolio

singular inverse Wishart

Moore-Penrose inverse

reflexive generalized inverse

estimator moments

Statistics/Econometrics

Statistik

matematisk statistik

Publikations- och innehållstyp

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