10 research outputs found
RM-CVaR: Regularized Multiple -CVaR Portfolio
The problem of finding the optimal portfolio for investors is called the
portfolio optimization problem. Such problem mainly concerns the expectation
and variability of return (i.e., mean and variance). Although the variance
would be the most fundamental risk measure to be minimized, it has several
drawbacks. Conditional Value-at-Risk (CVaR) is a relatively new risk measure
that addresses some of the shortcomings of well-known variance-related risk
measures, and because of its computational efficiencies, it has gained
popularity. CVaR is defined as the expected value of the loss that occurs
beyond a certain probability level (). However, portfolio optimization
problems that use CVaR as a risk measure are formulated with a single
and may output significantly different portfolios depending on how the
is selected. We confirm even small changes in can result in huge
changes in the whole portfolio structure. In order to improve this problem, we
propose RM-CVaR: Regularized Multiple -CVaR Portfolio. We perform
experiments on well-known benchmarks to evaluate the proposed portfolio.
Compared with various portfolios, RM-CVaR demonstrates a superior performance
of having both higher risk-adjusted returns and lower maximum drawdown.Comment: accepted by the IJCAI-PRICAI 2020 Special Track AI in FinTec
Machine Learning and Portfolio Optimization
The portfolio optimization model has limited impact in practice due to estimation issues when applied with real data. To address this, we adapt two machine learning methods, regularization and cross-validation, for portfolio optimization. First, we introduce performance-based regularization (PBR), where the idea is to constrain the sample variances of the estimated portfolio risk and return, which steers the solution towards one associated with less estimation error in the performance. We consider PBR for both mean-variance and mean-CVaR problems. For the mean-variance problem, PBR introduces a quartic polynomial constraint, for which we make two convex approximations: one based on rank-1 approximation and another based on a convex quadratic approximation. The rank-1 approximation PBR adds a bias to the optimal allocation, and the convex quadratic approximation PBR shrinks the sample covariance matrix. For the mean-CVaR problem, the PBR model is a combinatorial optimization problem, but we prove its convex relaxation, a QCQP, is essentially tight. We show that the PBR models can be cast as robust optimization problems with novel uncertainty sets and establish asymptotic optimality of both Sample Average Approximation (SAA) and PBR solutions and the corresponding efficient frontiers. To calibrate the right hand sides of the PBR constraints, we develop new, performance-based k-fold cross-validation algorithms. Using these algorithms, we carry out an extensive empirical investigation of PBR against SAA, as well as L1 and L2 regularizations and the equally-weighted portfolio. We find that PBR dominates all other benchmarks for two out of three of Fama-French data sets
Uncertainty Propagation and Dynamic Robust Risk Measures
We introduce a framework for quantifying propagation of uncertainty arising
in a dynamic setting. Specifically, we define dynamic uncertainty sets designed
explicitly for discrete stochastic processes over a finite time horizon. These
dynamic uncertainty sets capture the uncertainty surrounding stochastic
processes and models, accounting for factors such as distributional ambiguity.
Examples of uncertainty sets include those induced by the Wasserstein distance
and -divergences.
We further define dynamic robust risk measures as the supremum of all
candidates' risks within the uncertainty set. In an axiomatic way, we discuss
conditions on the uncertainty sets that lead to well-known properties of
dynamic robust risk measures, such as convexity and coherence. Furthermore, we
discuss the necessary and sufficient properties of dynamic uncertainty sets
that lead to time-consistencies of robust dynamic risk measures. We find that
uncertainty sets stemming from -divergences lead to strong time-consistency
while the Wasserstein distance results in a new notion of non-normalised
time-consistency. Moreover, we show that a dynamic robust risk measure is
strong or non-normalised time-consistent if and only if it admits a recursive
representation of one-step conditional robust risk measures arising from static
uncertainty sets
Technical note: a robust perspective on transaction costs in portfolio optimization
We prove that the portfolio problem with transaction costs is equivalent to three different problems designed to alleviate the impact of estimation error: a robust portfolio optimization problem, a regularized regression problem, and a Bayesian portfolio problem. Motivated by these results, we propose a data-driven approach to portfolio optimization that tackles transaction costs and estimation error simultaneously by treating the transaction costs as a regularization term to be calibrated. Our empirical results demonstrate that the data-driven portfolios perform favorably because they strike an optimal trade-off between rebalancing the portfolio to capture the information in recent historical return data, and avoiding the large transaction costs
and impact of estimation error associated with excessive trading
Mean-Covariance Robust Risk Measurement
We introduce a universal framework for mean-covariance robust risk
measurement and portfolio optimization. We model uncertainty in terms of the
Gelbrich distance on the mean-covariance space, along with prior structural
information about the population distribution. Our approach is related to the
theory of optimal transport and exhibits superior statistical and computational
properties than existing models. We find that, for a large class of risk
measures, mean-covariance robust portfolio optimization boils down to the
Markowitz model, subject to a regularization term given in closed form. This
includes the finance standards, value-at-risk and conditional value-at-risk,
and can be solved highly efficiently