Statistical Inference for the Expected Utility Portfolio in High Dimensions

Bodnar, Taras; Dmytriv, Solomiia; Okhrin, Yarema; Parolya, Nestor; Schmid, Wolfgang

doi:10.1109/tsp.2020.3037369

Cited by 19 publications

(15 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…All portfolios are hit quite heavily by COVID in the early 2020, which is indicated by a This results are in line with the previous empirical findings of Bodnar et al (2021b) who document that the equally weighted portfolio performs well in the stable period on the capital market, but its performance is very bad during the turbulent periods. Finally, a notable feature of Strategy 5 is that it does not vary that much when COVID hits.…”

Section: 6497supporting

confidence: 89%

“…Recently, this procedure has also been applied in the construction of the improved estimators of the high-dimensional mean vector (cf, Chételat and Wells (2012), Wang et al (2014), Bodnar et al (2019b)), covariance matrix (see, e.g., Ledoit and Wolf (2004), Ledoit and Wolf (2012), Bodnar et al (2014)), inverse of the covariance matrix (see, e.g., Wang et al (2015), Bodnar et al (2016)), as well as of the optimal portfolio weights (see, Golosnoy and Okhrin (2007), Frahm and Memmel (2010), Ledoit and Wolf (2017), Bodnar et al (2018), Bodnar et al (2021c)). Interval shrinkage estimators of optimal portfolio weights have recently been derived by Bodnar et al (2019a), Bodnar et al (2021b).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Bodnar¹,

Parolya²,

Thorsén³

2021

Preprint

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 spectrum 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

Section: 6497supporting

confidence: 89%

Section: Introductionmentioning

confidence: 99%

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

Bodnar¹,

Parolya²,

Thorsén³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the latter case, the only optimal portfolio is the GMV portfolio (1.4), a special case of the EU portfolio (1.2) with γ = ∞, and its shrinkage estimators have already been developed in Frahm and Memmel (2010) and Bodnar, Parolya, and Schmid (2018). The assumption (A3) can be tested in practice by using Theorem 1 of Bodnar et al (2021c).…”

Section: Optimal Shrinkage Estimator Of Mean-variance Portfoliomentioning

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

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

“…Moreover, both the asymptotic and finite-sample distributions of the estimated efficient frontier, the set of all mean-variance optimal portfolios, were obtained by Jobson [45], Bodnar and Schmid [21], Kan and Smith [47], and Bodnar and Schmid [22], among others, while Siegel and Woodgate [60] and Bodnar and Bodnar [8] presented its improved estimators and proposed a test of its existence. Some of these results were later extended to the high-dimensional setting in Frahm and Memmel [37], Glombeck [39], Bodnar et al [19], Bodnar et al [18], whereas several limiting results related to the estimation of optimal portfolios under high-dimensional settings are present in Ao et al [5], Kan et al [48], Cai et al [28], Ding et al [33], Bodnar et al [10], among others.…”

Section: Introductionmentioning

confidence: 99%

Sampling distributions of optimal portfolio weights and characteristics in small and large dimensions

Bodnar

Dette

Parolya

et al. 2021

Random Matrices: Theory Appl.

Self Cite

View full text Add to dashboard Cite

Optimal portfolio selection problems are determined by the (unknown) parameters of the data generating process. If an investor wants to realize the position suggested by the optimal portfolios, he/she needs to estimate the unknown parameters and to account for the parameter uncertainty in the decision process. Most often, the parameters of interest are the population mean vector and the population covariance matrix of the asset return distribution. In this paper, we characterize the exact sampling distribution of the estimated optimal portfolio weights and their characteristics. This is done by deriving their sampling distribution by its stochastic representation. This approach possesses several advantages, e.g. (i) it determines the sampling distribution of the estimated optimal portfolio weights by expressions, which could be used to draw samples from this distribution efficiently; (ii) the application of the derived stochastic representation provides an easy way to obtain the asymptotic approximation of the sampling distribution. The later property is used to show that the high-dimensional asymptotic distribution of optimal portfolio weights is a multivariate normal and to determine its parameters. Moreover, a consistent estimator of optimal portfolio weights and their characteristics is derived under the high-dimensional settings. Via an extensive simulation study, we investigate the finite-sample performance of the derived asymptotic approximation and study its robustness to the violation of the model assumptions used in the derivation of the theoretical results.

show abstract

Statistical Inference for the Expected Utility Portfolio in High Dimensions

Cited by 19 publications

References 48 publications

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

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

Optimal Shrinkage-Based Portfolio Selection in High Dimensions

Sampling distributions of optimal portfolio weights and characteristics in small and large dimensions

Contact Info

Product

Resources

About