Spectral Analysis of Large Reflexive Generalized Inverse and Moore-Penrose Inverse Matrices

Bodnar, Taras; Parolya, Nestor

doi:10.1007/978-3-030-56773-6_1

Cited by 2 publications

(3 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For c > 2 the Moore-Penrose approximation is not reliable anymore. We observe a similar behavior for other structures of the covariance matric n and the mean vector μ n , which indicates that the results are robust and justifies the theoretical findings of Bodnar and Parolya (2020) for the optimal shrinkage intensity given in (2.32). Figure 2 provides further numerical results related to the comparison of the two optimal shrinkage intensities.…”

Section: Estimation Of Unknown Parameters Bona Fide Estimatorsupporting

confidence: 84%

“…Next, we investigate the quality of this approximation in general case without imposing restrictions on n . This issue was studied for other quantities involving S * n and S + n in detail by Bodnar and Parolya (2020), who compare the limiting spectral distributions of S * n and S + n by deriving the limits for their corresponding Stieltjes transforms. It is concluded that the two inverses behave completely different in general.…”

Section: Estimation Of Unknown Parameters Bona Fide Estimatormentioning

confidence: 99%

See 1 more Smart Citation

Optimal Shrinkage-Based Portfolio Selection in High Dimensions

Bodnar

Okhrin

Parolya

2021

Journal of Business & Economic Statistics

Self Cite

View full text Add to dashboard Cite

In this article, we estimate the mean-variance portfolio in the high-dimensional case using the recent results from the theory of random matrices. We construct a linear shrinkage estimator which is distributionfree and is optimal in the sense of maximizing with probability 1 the asymptotic out-of-sample expected utility, that is, mean-variance objective function for different values of risk aversion coefficient which in particular leads to the maximization of the out-of-sample expected utility and to the minimization of the out-of-sample variance. One of the main features of our estimator is the inclusion of the estimation risk related to the sample mean vector into the high-dimensional portfolio optimization. The asymptotic properties of the new estimator are investigated when the number of assets p and the sample size n tend simultaneously to infinity such that p/n → c ∈ (0, +∞). The results are obtained under weak assumptions imposed on the distribution of the asset returns, namely the existence of the 4 + ε moments is only required. Thereafter we perform numerical and empirical studies where the small-and large-sample behavior of the derived estimator is investigated. The suggested estimator shows significant improvements over the existent approaches including the nonlinear shrinkage estimator and the three-fund portfolio rule, especially when the portfolio dimension is larger than the sample size. Moreover, it is robust to deviations from normality.

show abstract

Section: Estimation Of Unknown Parameters Bona Fide Estimatorsupporting

confidence: 84%

Section: Estimation Of Unknown Parameters Bona Fide Estimatormentioning

confidence: 99%

Optimal Shrinkage-Based Portfolio Selection in High Dimensions

Bodnar

Okhrin

Parolya

2021

Journal of Business & Economic Statistics

Self Cite

View full text Add to dashboard Cite

show abstract

“…and The results of Theorem II.6 are derived by approximating the Moore-Penrose inverse with the reflexive inverse (see, e.g., Cook and Forzani [51]), which provides a good approximation of the Moore-Penrose inverse when c i ∈ (1, 2) (see, Bodnar and Parolya [52]). In this case, the dynamic shrinkage estimator of the GMV portfolio (II.32)-(II.34) is expected to perform good in practice, while for larger values of c i it should be used with caution.…”

Section: Dynamic Gmv Portfolio For Singular Sample Covariance Matrixmentioning

confidence: 99%

Dynamic Shrinkage Estimation of the High-Dimensional Minimum-Variance Portfolio

Bodnar

Parolya

Thorsén

2023

IEEE Trans. Signal Process.

Self Cite

View full text Add to dashboard Cite

In this paper, new results in random matrix theory are derived, which allow us to construct a shrinkage estimator of the global minimum variance (GMV) portfolio when the shrinkage target is a random object. More specifically, the shrinkage target is determined as the holding portfolio estimated from previous data. The theoretical findings are applied to develop theory for dynamic estimation of the GMV portfolio, where the new estimator of its weights is shrunk to the holding portfolio at each time of reconstruction. Both cases with and without overlapping samples are considered in the paper. The non-overlapping samples corresponds to the case when different data of the asset returns are used to construct the traditional estimator of the GMV portfolio weights and to determine the target portfolio, while the overlapping case allows intersections between the samples. The theoretical results are derived under weak assumptions imposed on the data-generating process. No specific distribution is assumed for the asset returns except from the assumption of finite 4 + ε, ε > 0, moments. Also, the population covariance matrix with unbounded largest eigenvalue can be considered. The performance of new trading strategies is investigated via an extensive simulation. Finally, the theoretical findings are implemented in an empirical illustration based on the returns on stocks included in the S&P 500 index.

show abstract

Spectral Analysis of Large Reflexive Generalized Inverse and Moore-Penrose Inverse Matrices

Cited by 2 publications

References 15 publications

Optimal Shrinkage-Based Portfolio Selection in High Dimensions

Optimal Shrinkage-Based Portfolio Selection in High Dimensions

Dynamic Shrinkage Estimation of the High-Dimensional Minimum-Variance Portfolio

Contact Info

Product

Resources

About