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Singular inverse Wi...
Singular inverse Wishart distribution and its application to portfolio theory
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- Bodnar, Taras (författare)
- Stockholms universitet,Matematiska institutionen,Department of Mathematics, Stockholm University, Stockholm, Sweden
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- Mazur, Stepan, 1988- (författare)
- Lund University,Lunds universitet,Statistiska institutionen,Ekonomihögskolan,Department of Statistics,Lund University School of Economics and Management, LUSEM
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- Podgorski, Krzysztof (författare)
- Lund University,Lunds universitet,Statistiska institutionen,Ekonomihögskolan,Department of Statistics,Lund University School of Economics and Management, LUSEM
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(creator_code:org_t)
- Elsevier BV, 2016
- 2016
- Engelska.
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Ingår i: Journal of Multivariate Analysis. - : Elsevier BV. - 0047-259X .- 1095-7243. ; 143, s. 314-326
- Relaterad länk:
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Abstract
Ämnesord
Stäng
- The inverse of the standard estimate of covariance matrix is frequently used in the portfolio theory to estimate the optimal portfolio weights. For this problem, the distribution of the linear transformation of the inverse is needed. We obtain this distribution in the case when the sample size is smaller than the dimension, the underlying covariance matrix is singular, and the vectors of returns are independent and normally distributed. For the result, the distribution of the inverse of covariance estimate is needed and it is derived and referred to as the singular inverse Wishart distribution. We use these results to provide an explicit stochastic representation of an estimate of the mean-variance portfolio weights as well as to derive its characteristic function and the moments of higher order. The results are illustrated using actual stock returns and a discussion of practical relevance of the model is presented.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Nyckelord
- Singular Wishart distribution
- Mean-variance portfolio
- Sample estimate of precision matrix
- Moore-Penrose inverse
- Mathematical Statistics
- matematisk statistik
- Mathematics
- Mean–variance portfolio
- Singular Wishart distribution
- Sample estimate of precision matrix
- Moore–Penrose inverse
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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