| 1. |
- Bauder, David, et al.
(författare)
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Bayesian inference for the tangent portfolio
- 2018
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Ingår i: International Journal of Theoretical and Applied Finance. - : World Scientific Publishing Co. Pte. Ltd.. - 0219-0249. ; 21:8
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we consider the estimation of the weights of tangent portfolios from the Bayesian point of view assuming normal conditional distributions of the logarithmic returns. For diffuse and conjugate priors for the mean vector and the covariance matrix, we derive stochastic representations for the posterior distributions of the weights of tangent portfolio and their linear combinations. Separately we provide the mean and variance of the posterior distributions, which are of key importance for portfolio selection. The analytic results are evaluated within a simulation study, where the precision of coverage intervals is assessed.
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| 2. |
- Bodnar, Taras, et al.
(författare)
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A test for the global minimum variance portfolio for small sample and singular covariance
- 2017
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Ingår i: AStA Advances in Statistical Analysis. - : Springer. - 1863-8171 .- 1863-818X. ; 101:3, s. 253-265
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Tidskriftsartikel (refereegranskat)abstract
- Recently, a test dealing with the linear hypothesis for the global minimum variance portfolio weights was obtained under the assumption of non-singular covariance matrix. However, the problem of potential multicollinearity and correlations of assets constitutes a limitation of the classical portfolio theory. Therefore, there is an interest in developing theory in the presence of singularities in the covariance matrix. In this paper, we extend the test by analyzing the portfolio weights in the small sample case with a singular population covariance matrix. The results are illustrated using actual stock returns and a discussion of practical relevance of the model is presented.
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| 3. |
- Bodnar, Taras, et al.
(författare)
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Bayesian estimation of the global minimum variance portfolio
- 2017
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Ingår i: European Journal of Operational Research. - : Elsevier. - 0377-2217 .- 1872-6860. ; 256:1, s. 292-307
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we consider the estimation of the weights of optimal portfolios from the Bayesian point of view under the assumption that the conditional distributions of the logarithmic returns are normal. Using the standard priors for the mean vector and the covariance matrix, we derive the posterior distributions for the weights of the global minimum variance portfolio. Moreover, we reparameterize the model to allow informative and non-informative priors directly for the weights of the global minimum variance portfolio. The posterior distributions of the portfolio weights are derived in explicit form for almost all models. The models are compared by using the coverage probabilities of credible intervals. In an empirical study we analyze the posterior densities of the weights of an international portfolio.
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| 4. |
- Bodnar, Taras, et al.
(författare)
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Central limit theorems for functionals of large sample covariance matrix and mean vector in matrix-variate location mixture of normal distributions
- 2019
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Ingår i: Scandinavian Journal of Statistics. - : John Wiley & Sons. - 0303-6898 .- 1467-9469. ; 46:2, s. 636-660
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal distributions. The central limit theorem is derived for the product of the sample covariance matrix and the sample mean vector. Moreover, we consider the product of the inverse sample covariance matrix and the mean vector for which the central limit theorem is established as well. All results are obtained under the large-dimensional asymptotic regime where the dimension p and the sample size n approach to infinity such that p/n → c ∈ [0, +∞) when the sample covariance matrix does not need to be invertible and p/n → c ∈ [0, 1) otherwise.
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| 5. |
- Bodnar, Taras, et al.
(författare)
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On the product of a singular Wishart matrix and a singular Gaussian vector in high dimensions
- 2018
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Ingår i: Theory of Probability and Mathematical Statistics. - : American Mathematical Society (AMS). - 0094-9000 .- 1547-7363. ; 99, s. 37-50
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we consider the product of a singular Wishart random matrix and a singular normal random vector. A very useful stochastic representation is derived for this product, in using which the characteristic function of the product and its asymptotic distribution under the double asymptotic regime are established. The application of obtained stochastic representation speeds up the simulation studies where the product of a singular Wishart random matrix and a singular normal random vector is present. We further document a good performance of the derived asymptotic distribution within a numerical illustration. Finally, several important properties of the singular Wishart distribution are provided.
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| 6. |
- Bodnar, Taras, et al.
(författare)
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Singular inverse Wishart distribution and its application to portfolio theory
- 2016
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Ingår i: Journal of Multivariate Analysis. - : Elsevier BV. - 0047-259X .- 1095-7243. ; 143, s. 314-326
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 7. |
- Bodnar, Taras, et al.
(författare)
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Tangency portfolio weights for singular covariance matrix in small and large dimensions : estimation and test theory
- 2019
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Ingår i: Journal of Statistical Planning and Inference. - : Elsevier. - 0378-3758 .- 1873-1171. ; 201, s. 40-57
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we derive the finite-sample distribution of the estimated weights of the tangency portfolio when both the population and the sample covariance matrices are singular. These results are used in the derivation of a statistical test on the weights of the tangency portfolio where the distribution of the test statistic is obtained under both the null and the alternative hypotheses. Moreover, we establish the high-dimensional asymptotic distribution of the estimated weights of the tangency portfolio when both the portfolio dimension and the sample size increase to infinity. The theoretical findings are implemented in an empirical application dealing with the returns on the stocks included into the S&P 500 index.
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| 8. |
- Javed, Farrukh, 1984-, et al.
(författare)
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Higher moments of the estimated tangency portfolio weights
- 2017
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Konferensbidrag (refereegranskat)abstract
- In this paper we consider the estimated tangency portfolio weights. We derive analytical expressions for the higher central and non-central moments of these weights. Main focus has been given to skewness and kurtosis due to the importance of asymmetry and heavy tails of the data. We complement our results with an empirical study where we analyze an international diversified portfolio.
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| 9. |
- Karlsson, Sune, 1960-, et al.
(författare)
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Flexible Fat-tailed BVARs
- 2019
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Konferensbidrag (refereegranskat)abstract
- We propose a general class of fat-tailed distributions which includes the t,Cauchy, Laplace and slash distributions as well as the normal distribution as spe-cial cases. Full conditional posterior distributions for the Bayesian VAR-model arederived and used to construct a MCMC-sampler for the joint posterior distribution.The framework allows for selection of a specic special case as the distribution forthe error terms in the VAR if the evidence in the data is strong while at the sametime allowing for considerable exibility and more general distributions than oeredby any of the special cases.
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| 10. |
- Kotsiuba, Ihor, et al.
(författare)
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On the asymptotic and approximate distributions of the product of an inverse Wishart matrix and a Gaussian random vector
- 2015
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Ingår i: Theory of Probability and Mathematical Statistics. - Kyiv, Ukraine : Taras Shevchenko National University of Kyiv. - 0868-6904 .- 0094-9000 .- 1547-7363. ; 93, s. 95-104
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study the distribution of the product of an inverse Wishart random matrix and a Gaussian random vector. We derive its asymptotic distribution as well as its approximate density function formula which is based on the Gaussian integral and the third order Taylor expansion. Furthermore, we compare obtained asymptotic and approximate density functions with the exact density which is obtained by Bodnar and Okhrin (2011). A good performance of obtained results is documented in the numerical study.
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