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Journal ArticleDOI: 10.1080/14697688.2020.1781237

A cost-effective approach to portfolio construction with range-based risk measures

04 Mar 2021-Quantitative Finance (Routledge)-Vol. 21, Iss: 3, pp 431-447
Abstract: In this paper, we introduce a new class of risk measures and the corresponding risk minimizing portfolio optimization problem. Instead of measuring the expected deviation of a daily return from a s...

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Topics: Portfolio optimization (74%)
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Journal ArticleDOI: 10.2139/SSRN.2784244
Chi Seng Pun1, Hoi Ying Wong2Institutions (2)
Abstract: The Merton problem determines the optimal intertemporal portfolio choice by maximizing the expected utility, and is the basis of modern portfolio theory in continuous-time finance. However, its empirical performance is disappointing. The estimation errors of the expected rates of returns make the optimal policy degenerate, resulting in an extremely low (or unbounded) expected utility value for a high-dimensional portfolio. We further prove that the estimation error of the variance-covariance matrix leads to the degenerated policy of solely investing in the risk-free asset. This study proposes a constrained l1 - minimization approach to resolve the degeneracy. The proposed scheme can be implemented with simple linear programming and involves negligible additional computational time, compared to standard estimation. We prove the consistency of our framework that our estimate of the optimal control tends to be the true one. We also derive the rate of convergence. Simulation studies are provided to verify the finite-sample properties. An empirical study using S&P 500 component stock data demonstrates the superiority of the proposed approach.

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15 Citations


Journal ArticleDOI: 10.1016/J.CSDA.2020.107105
Abstract: A self-calibrated direct estimation algorithm based on l 1 -regularized quadratic programming is proposed. The self-calibration is achieved by an iterative algorithm for finding the regularization parameter simultaneously with the estimation target. The proposed algorithm is free of cross-validation. Two applications of this algorithm are proposed, namely precision matrix estimation and linear discriminant analysis. It is proven that the proposed estimators are consistent under different matrix norm errors and misclassification rate. Moreover, extensive simulation and empirical studies are conducted to evaluate the finite-sample performance and examine the support recovery ability of the proposed estimators. With the theoretical and empirical evidence, it is shown that the proposed estimator is better than its competitors in statistical accuracy and has clear computational advantages.

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Topics: Estimator (58%), Linear discriminant analysis (56%), Iterative method (52%) ... read more

6 Citations


Journal ArticleDOI: 10.2139/SSRN.3635361
Chi Seng Pun1, Zi Ye1Institutions (1)
Abstract: This paper studies mean-variance portfolio selection problem subject to proportional transaction costs and no-shorting constraint We do not impose any distributional assumptions on the asset returns By adopting dynamic programming, duality theory, and a comparison approach, we manage to derive a semi-closed form solution of the optimal dynamic investment policy with the boundaries of buying, no-transaction, selling, and liquidation regions Numerically, we illustrate the properties of the optimal policy by depicting the corresponding efficient frontiers under different rates of transaction costs and initial wealth allocations We nd that the efficient frontier is distorted due to the transaction cost incurred We also examine how the width of the no-transaction region varies with different transaction cost rates Empirically, we show that our transaction-cost-aware policy outperforms the transaction-cost-unaware policy in a realistic trading environment that incurs transaction costs

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Topics: Transaction cost (57%), Efficient frontier (56%), Portfolio (52%)

4 Citations


Journal ArticleDOI: 10.1137/19M1291674
Abstract: This paper proposes a self-calibrated sparse learning approach for estimating a sparse target vector, which is a product of a precision matrix and a vector, and investigates its application to fina...

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2 Citations


Journal ArticleDOI: 10.2139/SSRN.3867297
Abstract: This paper incorporates Bayesian estimation and optimization into portfolio selection framework, particularly for high-dimensional portfolio in which the number of assets is larger than the number of observations. We leverage a constrained 𝓁1 minimization approach, called linear programming optimal (LPO) portfolio, to directly estimate effective parameters appearing in the optimal portfolio. We propose two refinements for the LPO strategy. First, we explore improved Bayesian estimates, instead of sample estimates, of the covariance matrix of asset returns. Second, we introduce Bayesian optimization (BO) to replace traditional grid-search cross-validation (CV) in tuning hyperparameters of the LPO strategy. We further propose modifications in the BO algorithm by (1) taking into account time-dependent nature of financial problems and (2) extending commonly used expected improvement (EI) acquisition function to include a tunable trade-off with the improvement's variance (EIVar). Allowing a general case of noisy observations, we theoretically derive the sub-linear convergence rate of BO under the newly proposed EIVar and thus our algorithm has no regret. Our empirical studies confirm that the adjusted BO result in portfolios with higher out-of-sample Sharpe ratio, certainty equivalent, and lower turnover compared to those tuned with CV. This superior performance is achieved with significant reduction in time elapsed, thus also addressing time-consuming issues of CV. Furthermore, LPO with Bayesian estimates outperform original proposal of LPO, as well as the benchmark equally weighted and plug-in strategies.

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Topics: Bayesian optimization (58%), Bayes estimator (51%), Hyperparameter (51%) ... read more

1 Citations


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Open accessBook
Vladimir Vapnik1Institutions (1)
01 Jan 1995-
Abstract: Setting of the learning problem consistency of learning processes bounds on the rate of convergence of learning processes controlling the generalization ability of learning processes constructing learning algorithms what is important in learning theory?.

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38,164 Citations


Open accessBook
01 Jan 1995-

12,597 Citations


Open accessJournal ArticleDOI: 10.1023/B:STCO.0000035301.49549.88
Abstract: In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV machines, covering both the quadratic (or convex) programming part and advanced methods for dealing with large datasets. Finally, we mention some modifications and extensions that have been applied to the standard SV algorithm, and discuss the aspect of regularization from a SV perspective.

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9,105 Citations


Open accessProceedings Article
03 Dec 1996-
Abstract: A new regression technique based on Vapnik's concept of support vectors is introduced. We compare support vector regression (SVR) with a committee regression technique (bagging) based on regression trees and ridge regression done in feature space. On the basis of these experiments, it is expected that SVR will have advantages in high dimensionality space because SVR optimization does not depend on the dimensionality of the input space.

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3,498 Citations


Journal ArticleDOI: 10.1093/RFS/HHM075
Abstract: We evaluate the out-of-sample performance of the sample-based mean-variance model, and its extensions designed to reduce estimation error, relative to the naive 1-N portfolio. Of the 14 models we evaluate across seven empirical datasets, none is consistently better than the 1-N rule in terms of Sharpe ratio, certainty-equivalent return, or turnover, which indicates that, out of sample, the gain from optimal diversification is more than offset by estimation error. Based on parameters calibrated to the US equity market, our analytical results and simulations show that the estimation window needed for the sample-based mean-variance strategy and its extensions to outperform the 1-N benchmark is around 3000 months for a portfolio with 25 assets and about 6000 months for a portfolio with 50 assets. This suggests that there are still many "miles to go" before the gains promised by optimal portfolio choice can actually be realized out of sample. The Author 2007. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org, Oxford University Press.

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Topics: Portfolio optimization (67%), Rate of return on a portfolio (65%), Replicating portfolio (63%) ... read more

2,440 Citations


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