On the product of a singular Wishart matrix and a singular Gaussian vector in high dimension

Bodnar, Taras; Mazur, Stepan; Muhinyuza, Stanislas; Parolya, Nestor

doi:10.1090/tpms/1078

Cited by 9 publications

(6 citation statements)

References 22 publications

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“…In this section, we present the auxiliary results, which are used in proving our main results of Section 2 and can be applied in the discriminant analysis (see [ 9 ]). Let us note that our findings are complementing the existing results obtained in [ 8 , 10–12 , 16 , 34 ].…”

Section: Auxiliary Resultssupporting

confidence: 90%

Higher order moments of the estimated tangency portfolio weights

Javed

Mazur

Ngailo

2020

Journal of Applied Statistics

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In this paper, we consider the estimated weights of the tangency portfolio. We derive analytical expressions for the higher order noncentral and central moments of these weights when the returns are assumed to be independently and multivariate normally distributed. Moreover, the expressions for mean, variance, skewness and kurtosis of the estimated weights are obtained in closed forms. Later, we complement our results with a simulation study where data from the multivariate normal and t-distributions are simulated, and the first four moments of estimated weights are computed by using the Monte Carlo experiment. It is noteworthy to mention that the distributional assumption of returns is found to be important, especially for the first two moments. Finally, through an empirical illustration utilizing returns of four financial indices listed in NASDAQ stock exchange, we observe the presence of time dynamics in higher moments.

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Section: Auxiliary Resultssupporting

confidence: 90%

Higher order moments of the estimated tangency portfolio weights

Javed

Mazur

Ngailo

2020

Journal of Applied Statistics

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“…Consequently, the posterior distribution of w TP can be expressed as the product of the (singular) Wishart matrix and a normal vector. The distributional properties of this product are well studied by Bodnar et al [32][33][34][35].…”

Section: Remark 22mentioning

confidence: 98%

Statistical inference for the tangency portfolio in high dimension

2021

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In this paper, we study the distributional properties of the tangency portfolio (TP) weights assuming a normal distribution of the logarithmic returns. We derive a stochastic representation of the TP weights that fully describes their distribution. Under a highdimensional asymptotic regime, i.e., the dimension of the portfolio, k, and the sample size, n, approach infinity such that k/n → c ∈ (0, 1), we deliver the asymptotic distribution of the TP weights. Moreover, we consider tests about the elements of the TP and derive the asymptotic distribution of the test statistic under the null and alternative hypotheses. In a simulation study, we compare the asymptotic distribution of the TP weights with the exact finite sample density. We also compare the high-dimensional asymptotic test with an exact small sample test. We document a good performance of the asymptotic approximations except for small sample sizes combined with c close to one. In an empirical study, we analyse the TP weights in portfolios containing stocks from the S&P 500 index.

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“…To tackle this problem, several transformation methods with practical applications to portfolio theory haven been proposed (c.f. Pappas and Kaimakamis 2010;Bodnar et al 2016Bodnar et al , 2017Bodnar et al , 2018Bodnar et al , 2019, among others for a more detailed discussion on different transformation methods and their practical relevance).…”

Section: Correlation Matrixmentioning

confidence: 99%

Portfolio Correlations in the Bank-Firm Credit Market of Japan

Luu¹

2021

Comput Econ

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The recent global financial crisis has shown portfolio correlations between agents as one of the major channels of risk contagion and amplification. In this work, we analyse the structure and dynamics of the cross-correlation matrix of banks’ loan portfolios in the yearly bank-firm credit network of Japan during the period from 1980 to 2012. Using the methods of Random Matrix Theory (RMT), Principal Component Analysis and complex networks, we aim to detect non-random patterns in the empirical cross-correlations as well as to identify different states of such correlations over time. Our findings suggest that although a majority of portfolio correlations between banks in lending relations to firms are contributed by noise, the top largest eigenvalues always deviate from the random bulk explained by RMT, indicating the presence of non-random patterns governing the correlation dynamics. In particular, we show that this dynamics is mainly driven by a global common factor and a couple of “groups” factors. Furthermore, different states in the credit market can be identified based on the evolution of eigenvalues and associated eigenvectors. For example, during the asset price bubble period in Japan from 1986 to 1991, we find that banks’ loan portfolios tend to be more correlated, showing a significant increase in the level of systemic risk in the credit market. In addition, building Planar Maximally Filtered Graphs from the correlations of different eigenmodes, notably, we observe that the local interaction structure between banks changes in different periods. Typically, when the dominance of a group of banks in one period gradually vanishes, the credit market starts to build-up a different structure in the next period in which another group of banks will become the main actors in the backbone of the cross-correlations.

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On the product of a singular Wishart matrix and a singular Gaussian vector in high dimension

Cited by 9 publications

References 22 publications

Higher order moments of the estimated tangency portfolio weights

Higher order moments of the estimated tangency portfolio weights

Statistical inference for the tangency portfolio in high dimension

Portfolio Correlations in the Bank-Firm Credit Market of Japan

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