Portfolio Optimization with Robust Covariance and Conditional Value-at-Risk Constraints

• URL: http://arxiv.org/abs/2406.00610v1
• Date: Sun, 2 Jun 2024 03:50:20 GMT
• Title: Portfolio Optimization with Robust Covariance and Conditional Value-at-Risk Constraints
• Authors: Qiqin Zhou,
• Abstract summary: We evaluated the performance of large-cap portfolio using various forms of Ledoit Shrinkage Covariance and Robust Gerber Covariance matrix. robustness estimators can outperform the market capitalization-weighted benchmark portfolio, particularly during bull markets. We incorporated unsupervised clustering algorithm K-means to the optimization algorithm.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The measure of portfolio risk is an important input of the Markowitz framework. In this study, we explored various methods to obtain a robust covariance estimators that are less susceptible to financial data noise. We evaluated the performance of large-cap portfolio using various forms of Ledoit Shrinkage Covariance and Robust Gerber Covariance matrix during the period of 2012 to 2022. Out-of-sample performance indicates that robust covariance estimators can outperform the market capitalization-weighted benchmark portfolio, particularly during bull markets. The Gerber covariance with Mean-Absolute-Deviation (MAD) emerged as the top performer. However, robust estimators do not manage tail risk well under extreme market conditions, for example, Covid-19 period. When we aim to control for tail risk, we should add constraint on Conditional Value-at-Risk (CVaR) to make more conservative decision on risk exposure. Additionally, we incorporated unsupervised clustering algorithm K-means to the optimization algorithm (i.e. Nested Clustering Optimization, NCO). It not only helps mitigate numerical instability of the optimization algorithm, but also contributes to lower drawdown as well.

Related papers

• ODAR: Principled Adaptive Routing for LLM Reasoning via Active Inference [60.958331943869126]
  ODAR-Expert is an adaptive routing framework that optimize the accuracy-efficiency trade-off via principled resource allocation.<n>We show strong and consistent gains, including 98.2% accuracy on MATH and 54.8% on Humanity's Last Exam.
  arXiv  Detail & Related papers  (2026-02-27T05:22:01Z)
• Conformal Thinking: Risk Control for Reasoning on a Compute Budget [60.65072883773352]
  Reasoning Large Language Models (LLMs) enable test-time scaling, with dataset-level accuracy improving as the token budget increases.<n>We re-frame the budget setting problem as risk control, limiting the error rate while minimizing compute.<n>Our framework introduces an upper threshold that stops reasoning when the model is confident and a novel lower threshold that preemptively stops unsolvable instances.
  arXiv  Detail & Related papers  (2026-02-03T18:17:22Z)
• A Novel approach to portfolio construction [0.0]
  This paper proposes a machine learning-based framework for asset selection and portfolio construction.<n>It is called the Best-Path Algorithm Sparse Graphical Model (BPASGM)<n>Monte Carlo simulations show BPASGM-based portfolios achieve more stable risk-return profiles, lower realized volatility, and superior risk-adjusted performance.
  arXiv  Detail & Related papers  (2026-02-03T09:52:06Z)
• Bulk-Calibrated Credal Ambiguity Sets: Fast, Tractable Decision Making under Out-of-Sample Contamination [8.826173150779145]
  Distributionally robust optimisation (DRO) minimises the worst-case expected loss over an ambiguity set.<n>We show how IP credal sets translate into DRO objectives with interpretable tolerance levels.
  arXiv  Detail & Related papers  (2026-01-29T06:37:36Z)
• Covariance-Aware Simplex Projection for Cardinality-Constrained Portfolio Optimization [0.0]
  Covariance-Aware Simplex Projection (CASP) is a two-stage repair operator that selects a target number of assets using volatility-normalized scores.<n>On S&P 500 data (2020-2024), CASP-Basic delivers materially lower portfolio variance than standard Euclidean repair.
  arXiv  Detail & Related papers  (2025-12-23T02:22:53Z)
• Distributionally Robust Optimization with Adversarial Data Contamination [49.89480853499918]
  We focus on optimizing Wasserstein-1 DRO objectives for generalized linear models with convex Lipschitz loss functions.<n>Our primary contribution lies in a novel modeling framework that integrates robustness against training data contamination with robustness against distributional shifts.<n>This work establishes the first rigorous guarantees, supported by efficient computation, for learning under the dual challenges of data contamination and distributional shifts.
  arXiv  Detail & Related papers  (2025-07-14T18:34:10Z)
• End-to-End Large Portfolio Optimization for Variance Minimization with Neural Networks through Covariance Cleaning [0.0]
  We develop a rotation-invariant neural network that provides the global minimum-variance portfolio.<n>This explicit mathematical mapping offers clear interpretability of each module's role.<n>A single model can be calibrated on panels of a few hundred stocks and applied, without retraining, to one thousand US equities.
  arXiv  Detail & Related papers  (2025-07-02T17:27:29Z)
• Asymptotically Optimal Linear Best Feasible Arm Identification with Fixed Budget [55.938644481736446]
  We introduce a novel algorithm for best feasible arm identification that guarantees an exponential decay in the error probability.<n>We validate our algorithm through comprehensive empirical evaluations across various problem instances with different levels of complexity.
  arXiv  Detail & Related papers  (2025-06-03T02:56:26Z)
• Provable Robust Overfitting Mitigation in Wasserstein Distributionally Robust Optimization [23.17991102874279]
  We propose a novel robust optimization framework under a new uncertainty set for adversarial noise via Wasserstein distance and statistical error. We demonstrate that our method significantly mitigates robust overfitting and enhances robustness within the framework of WDRO.
  arXiv  Detail & Related papers  (2025-03-06T10:58:35Z)
• Joint Estimation of Conditional Mean and Covariance for Unbalanced Panels [0.0]
  We propose a nonparametric, kernel-based joint estimator for conditional mean and covariance matrices in large unbalanced panels. Our estimator is applied to a comprehensive panel of monthly US stock excess returns from 1962 to 2021, conditioned on macroeconomic and firm-specific co variables. In asset pricing, it generates conditional mean-variance efficient portfolios with out-of-sample Sharpe ratios that substantially exceed those of equal-weighted benchmarks.
  arXiv  Detail & Related papers  (2024-10-29T08:42:22Z)
• Model-Based Epistemic Variance of Values for Risk-Aware Policy Optimization [59.758009422067]
  We consider the problem of quantifying uncertainty over expected cumulative rewards in model-based reinforcement learning. We propose a new uncertainty Bellman equation (UBE) whose solution converges to the true posterior variance over values. We introduce a general-purpose policy optimization algorithm, Q-Uncertainty Soft Actor-Critic (QU-SAC) that can be applied for either risk-seeking or risk-averse policy optimization.
  arXiv  Detail & Related papers  (2023-12-07T15:55:58Z)
• Robustifying Markowitz [3.154269505086154]
  The heavy-tail characteristics of financial time series are in fact the cause for these erratic fluctuations of weights. We present a toolbox for stabilizing costs and weights for global minimum Markowitz portfolios. We demonstrate that robustified portfolios reach the lowest turnover compared to shrinkage-based and constrained portfolios.
  arXiv  Detail & Related papers  (2022-12-28T18:09:14Z)
• Probable Domain Generalization via Quantile Risk Minimization [90.15831047587302]
  Domain generalization seeks predictors which perform well on unseen test distributions. We propose a new probabilistic framework for DG where the goal is to learn predictors that perform well with high probability.
  arXiv  Detail & Related papers  (2022-07-20T14:41:09Z)
• LoCoV: low dimension covariance voting algorithm for portfolio optimization [0.0]
  We analyze the random matrix aspects of portfolio optimization and identify the order of errors in sample optimal portfolio weight. We also provide LoCoV (low dimension covariance voting) algorithm to reduce error inherited from random samples.
  arXiv  Detail & Related papers  (2022-04-01T04:42:56Z)
• Safe Online Bid Optimization with Return-On-Investment and Budget Constraints subject to Uncertainty [87.81197574939355]
  We study the nature of both the optimization and learning problems. We provide an algorithm, namely GCB, guaranteeing sublinear regret at the cost of a potentially linear number of constraints violations. More interestingly, we provide an algorithm, namely GCB_safe(psi,phi), guaranteeing both sublinear pseudo-regret and safety w.h.p. at the cost of accepting tolerances psi and phi.
  arXiv  Detail & Related papers  (2022-01-18T17:24:20Z)
• Risk Minimization from Adaptively Collected Data: Guarantees for Supervised and Policy Learning [57.88785630755165]
  Empirical risk minimization (ERM) is the workhorse of machine learning, but its model-agnostic guarantees can fail when we use adaptively collected data. We study a generic importance sampling weighted ERM algorithm for using adaptively collected data to minimize the average of a loss function over a hypothesis class. For policy learning, we provide rate-optimal regret guarantees that close an open gap in the existing literature whenever exploration decays to zero.
  arXiv  Detail & Related papers  (2021-06-03T09:50:13Z)
• Large-Scale Methods for Distributionally Robust Optimization [53.98643772533416]
  We prove that our algorithms require a number of evaluations gradient independent of training set size and number of parameters. Experiments on MNIST and ImageNet confirm the theoretical scaling of our algorithms, which are 9--36 times more efficient than full-batch methods.
  arXiv  Detail & Related papers  (2020-10-12T17:41:44Z)
• Least Squares Regression with Markovian Data: Fundamental Limits and Algorithms [69.45237691598774]
  We study the problem of least squares linear regression where the data-points are dependent and are sampled from a Markov chain. We establish sharp information theoretic minimax lower bounds for this problem in terms of $tau_mathsfmix$. We propose an algorithm based on experience replay--a popular reinforcement learning technique--that achieves a significantly better error rate.
  arXiv  Detail & Related papers  (2020-06-16T04:26:50Z)
• Distributional Robustness and Regularization in Reinforcement Learning [62.23012916708608]
  We introduce a new regularizer for empirical value functions and show that it lower bounds the Wasserstein distributionally robust value function. It suggests using regularization as a practical tool for dealing with $textitexternal uncertainty$ in reinforcement learning.
  arXiv  Detail & Related papers  (2020-03-05T19:56:23Z)
• Detecting Changes in Asset Co-Movement Using the Autoencoder Reconstruction Ratio [5.5616364225463055]
  We propose a real-time indicator to detect temporary increases in asset co-movements. The Autoencoder Reconstruction Ratio measures how well a basket of asset returns can be modelled using a lower-dimensional set of latent variables.
  arXiv  Detail & Related papers  (2020-01-23T22:33:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.