Mean-variance Portfolio Selection Research Articles

Time-Varying Mean-Variance Portfolio Selection under Transaction Costs and Cardinality Constraint Problem via Beetle Antennae Search Algorithm (BAS)

The Markowitz mean-variance portfolio selection is widely acclaimed as a very important investment strategy. A popular option to solve the static mean-variance portfolio selection (MVPS) problem is based on the use of quadratic programming (QP) methods. On the other hand, the static portfolio selection under transaction costs (PSTC) problem is usually approached with nonlinear programming (NLP) methods. In this article, we define and study the time-varying mean-variance portfolio selection under transaction costs and cardinality constraint (TV-MVPSTC-CC) problem as a time-varying nonlinear programming (TVNLP) problem. The TV-MVPSTC-CC also comprises the properties of a moving average. These properties make the TV-MVPSTC-CC an even greater analysis tool suitable to evaluate investments and identify trading opportunities across a continuous-time period. Using the Beetle Antennae Search (BAS) algorithm, we also provide an online solution to the static NLP problem. To the best of our knowledge, this is an innovative approach that incorporates modern meta-heuristic optimization techniques to provide an online, thus more realistic, solution to the TV-MVPSTC-CC problem. In this way, we present an online solution to a time-varying financial problem while eliminating the restrictions of static methods. Our approach is also verified by numerical experiments and computer simulations as an excellent alternative to traditional approaches.

Dynamic Optimal Mean-Variance Portfolio Selection with a 3/2 Stochastic Volatility

This paper considers a mean-variance portfolio selection problem when the stock price has a 3/2 stochastic volatility in a complete market. Specifically, we assume that the stock price and the volatility are perfectly negative correlated. By applying a backward stochastic differential equation (BSDE) approach, closed-form expressions for the statically optimal (time-inconsistent) strategy and the value function are derived. Due to time-inconsistency of mean variance criterion, a dynamic formulation of the problem is presented. We obtain the dynamically optimal (time-consistent) strategy explicitly, which is shown to keep the wealth process strictly below the target (expected terminal wealth) before the terminal time. Finally, we provide numerical studies to show the impact of main model parameters on the efficient frontier and illustrate the differences between the two optimal wealth processes.

Bayesian Filtering for Multi-period Mean–Variance Portfolio Selection

For a long investment time horizon, it is preferable to rebalance the portfolio weights at intermediate times. This necessitates a multi-period market model. Usually, dynamic programming techniques are applied to optimize the portfolio for the multi-period model. However, this assumes a known distribution for the parameters of the financial time series. We consider the situation where the distribution of parameters is unknown and is estimated directly from the dynamically arriving data. We implement the Bayesian filtering method through dynamic linear models to sequentially update the parameters. We also acknowledge the uncertain investment lifetime to make the model more adaptive to the market conditions. These updated parameters are put into the dynamic mean–variance problem to arrive at optimal efficient portfolios. Implementing this model to the S&P500 illustrates that the data strongly favor the Bayesian updating and is practically implementable.

Cardinality-constrained programs with nonnegative variables and an SCA method

We study a cardinality-constrained optimisation problem with nonnegative variables in this paper. This problem is often encountered in practice. Firstly, we study some properties on the optimal solutions of this optimisation problem under some conditions. An equivalent reformulation of the problem under consideration is proposed. Based on the reformulation, we present a successive convex approximation method for the cardinality constrained optimisation problem. We prove that the method converges to a KKT point of the reformulation problem. Under some conditions, the KKT points of the reformulation problem are local optimisers of the original problem. Our numerical results on a limited diversified mean–variance portfolio selection problem demonstrate some promising results.

TIME-INCONSISTENT MARKOVIAN CONTROL PROBLEMS UNDER MODEL UNCERTAINTY WITH APPLICATION TO THE MEAN-VARIANCE PORTFOLIO SELECTION

In this paper, we study a class of time-inconsistent terminal Markovian control problems in discrete time subject to model uncertainty. We combine the concept of the sub-game perfect strategies with the adaptive robust stochastic control method to tackle the theoretical aspects of the considered stochastic control problem. Consequently, as an important application of the theoretical results and by applying a machine learning algorithm we solve numerically the mean-variance portfolio selection problem under the model uncertainty.

A General Stochastic Maximum Principle for Mean-Field Controls with Regime Switching

Focusing on regime-switching diffusions with mean-fields interactions, this paper is devoted to obtaining a general maximum principle. A main feature is that conditional mean-field is used in the controlled dynamic systems and the optimization process. Analysis of variational and adjoint equations using forward and backward stochastic differential equations with regime-switching and conditional mean-field is carried out. Necessary conditions for optimality are obtained without assuming the convexity of the control space. An example on conditional mean-variance portfolio selection with regime switching is given to illustrate the sufficient conditions for optimality.

Continuous-time mean-variance portfolio selection with regime-switching financial market: Time-consistent solution

Abstract This paper studies optimal time-consistent strategies for the mean-variance portfolio selection problem. Especially, we assume that the price processes of risky stocks are described by regime-switching SDEs. We consider a Markov-modulated state-dependent risk aversion and we formulate the problem in the game theoretic framework. Then, by solving a flow of forward-backward stochastic differential equations, an explicit representation as well as uniqueness results of an equilibrium solution are obtained.

Justifying Mean-Variance Portfolio Selection when Asset Returns Are Skewed

We show that, in the presence of a risk-free asset, the return distribution of every portfolio is determined by its mean and variance if and only if asset returns follow a specific skew-elliptical distribution. Thus, contrary to common belief among academics and practitioners, skewed returns do not allow a rejection of mean-variance analysis. Our work differs from Chamberlain's [Chamberlain G (1983) A characterization of the distributions that imply mean-variance utility functions. J. Econom. Theory 29(1):185–201.] by focusing on the returns of portfolios, where the weights over the risk-free asset and the risky assets sum to unity. Furthermore, it extends Meyer's [Meyer J, Rasche RH (1992) Sufficient conditions for expected utility to imply mean-standard deviation rankings: Empirical evidence concerning the location and scale condition. Econom. J. (London) 102(410):91–106.] by introducing elliptical noise into their generalized location-scale framework. To emphasize the relevance of our skew-elliptical model, we additionally provide empirical evidence that it cannot be rejected for the returns of typical portfolios of common stocks or popular alternative investments.This paper was accepted by Kay Giesecke, finance.

Some new efficient mean–variance portfolio selection models

AbstractThe poor out‐of‐sample performance of mean–variance portfolio model is mainly caused by estimation errors in the covariance matrix and the mean return, especially the mean return vector. Meanwhile, in financial practice, what most investors actually like is to hold a few stocks in their portfolio. The goal of this paper is to propose some new efficient mean–variance portfolio selection models by considering the following aspects: (i) use the L1‐regularization in objective function to obtain sparse portfolio; (ii) use the shrinkage method of Ledoit and Wolf, Journal of Economics Financial, 2003, 10, 603–621 to estimate the covariance matrix; (iii) use the robust optimization method to mitigate the estimation errors of the expected return. Finally, empirical analysis demonstrates that the proposed strategies have better out‐of‐sample performance.

Time-Inconsistency with Rough Volatility

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 14 September 2020Accepted: 05 October 2021Published online: 21 December 2021Keywordstime-inconsistency, rough volatility, functional Itô calculus, mean-variance portfolio selection, Volterra Heston modelAMS Subject Headings91G80, 91A80, 60G22, 60H20Publication DataISSN (online): 1945-497XPublisher: Society for Industrial and Applied MathematicsCODEN: sjfmbj

A Subgame Perfect Equilibrium Reinforcement Learning Approach to Time-inconsistent Problems

In this paper, we establish a subgame perfect equilibrium reinforcement learning (SPERL) framework for time-inconsistent (TIC) problems. In the context of RL, TIC problems are known to face two main challenges: the non-existence of natural recursive relationships between value functions at different time points and the violation of Bellman's principle of optimality that raises questions on the applicability of standard policy iteration algorithms for unprovable policy improvement theorems. We adapt an extended dynamic programming theory and propose a new class of algorithms, called backward policy iteration (BPI), that solves SPERL and addresses both challenges. To demonstrate the practical usage of BPI as a training framework, we adapt standard RL simulation methods and derive two BPI-based training algorithms. We examine our derived training frameworks on a mean-variance portfolio selection problem and evaluate some performance metrics including convergence and model identifiability.

Multi-period mean-variance portfolio selection in a regime-switching market with a bankruptcy state and a state-dependent uncertain exit-time

Multi-period mean-variance portfolio selection in a regime-switching market with a bankruptcy state and a state-dependent uncertain exit-time

OPTIMAL MEAN–VARIANCE PORTFOLIO SELECTION WITH NO-SHORT-SELLING CONSTRAINT

In this paper, the objective is to study the continuous mean–variance portfolio selection with a no-short-selling constraint and obtain a time-consistent solution. We assume that there is a self-financing portfolio with wealth process [Formula: see text], in which [Formula: see text] represents the fraction of wealth invested in the risk asset under the short selling prohibition. We investigate the mean–variance optimal constrained problem defined by obtaining the supremum over all admissible controls of the difference between the expectation of the value process at some designated terminal time [Formula: see text] and a positive constant times the variance of [Formula: see text]. To envisage the quadratic nonlinearity introduced by the variance, the method of Lagrangian multipliers reduces the nonlinear problem into a set of linear problems which can be solved by applying the Hamilton–Jacobi–Bellman equation and change of variables formula with local time on curves. Solving the HJB system provides the time-inconsistent solution and from there, we derive the time-consistent optimal control.

A Hilbert transform approach for controlled jump-diffusions with financial applications

We propose a new computational method for a class of controlled jump-diffusions for financial applications. In the first step of our method, we apply piecewise constant policy approximation where we partition the time horizon into small time intervals and the control is constant on each interval. In the second step, we develop a Hilbert transform approach to solve a discrete time dynamic programming problem. We provide rigorous error bounds for the piecewise constant policy approximation for controlled jump-diffusions, generalizing previous results for diffusions. We also apply our method to solve two classical types of financial problems: option pricing under uncertain volatility and/or correlation models and optimal investment, including utility maximization and mean-variance portfolio selection. Through various numerical examples, we demonstrate the properties of our method and show that it is a computationally efficient choice for low-dimensional problems. Our method also compares favorably with some popular approaches.

Improving DEA cross-efficiency optimization in portfolio selection

This paper deals with the role of alternative optimal solutions existing in the data envelopment analysis (DEA) models for cross-efficiency evaluation in portfolio selection. The paper shows that incorporating alternative optimal solutions for constructing cross-efficiency matrix improves the result of the mean-variance portfolio selection method. This improvement means that building portfolios with lower risk and higher expected return is possible when alternative optimal solutions are considered. The proposed method in this paper is applied to stock portfolio selection in the Tehran stock market.

Mean-Variance Portfolio Selection with Tracking Error Penalization

This paper studies a variation of the continuous-time mean-variance portfolio selection where a tracking-error penalization is added to the mean-variance criterion. The tracking error term penalizes the distance between the allocation controls and a reference portfolio with same wealth and fixed weights. Such consideration is motivated as follows: (i) On the one hand, it is a way to robustify the mean-variance allocation in the case of misspecified parameters, by “fitting" it to a reference portfolio that can be agnostic to market parameters; (ii) On the other hand, it is a procedure to track a benchmark and improve the Sharpe ratio of the resulting portfolio by considering a mean-variance criterion in the objective function. This problem is formulated as a McKean–Vlasov control problem. We provide explicit solutions for the optimal portfolio strategy and asymptotic expansions of the portfolio strategy and efficient frontier for small values of the tracking error parameter. Finally, we compare the Sharpe ratios obtained by the standard mean-variance allocation and the penalized one for four different reference portfolios: equal-weights, minimum-variance, equal risk contributions and shrinking portfolio. This comparison is done on a simulated misspecified model, and on a backtest performed with historical data. Our results show that in most cases, the penalized portfolio outperforms in terms of Sharpe ratio both the standard mean-variance and the reference portfolio.

Indefinite mean-field type linear–quadratic stochastic optimal control problems

This paper focuses on indefinite stochastic mean-field linear–quadratic (MF-LQ, for short) optimal control problems, which allow the weighting matrices for state and control in the cost functional to be indefinite. The solvability of stochastic Hamiltonian system and Riccati equations is presented under indefinite case. The optimal controls in open-loop form and closed-loop form are derived, respectively. In particular, dynamic mean–variance portfolio selection problem can be formulated as an indefinite MF-LQ problem to tackle directly. Another example also sheds light on the theoretical results established.

Robust Mean-Variance Portfolio Selection with Ward and Complete Linkage Clustering Algorithm

Robust Mean-Variance Portfolio Selection with Ward and Complete Linkage Clustering Algorithm

A Dual Characterisation of Regulatory Arbitrage for Coherent Risk Measures

We revisit mean-risk portfolio selection in a one-period financial market where risk is quantified by a positively homogeneous risk measure ρ. We first show that under mild assumptions, the set of optimal portfolios for a fixed return is nonempty and compact. However, unlike in classical mean-variance portfolio selection, it can happen that no efficient portfolios exist. We call this situation ρ-arbitrage, and prove that it cannot be excluded -- unless ρ is as conservative as the worst-case risk measure. After providing a primal characterisation of ρ-arbitrage, we focus our attention on coherent risk measures that admit a dual representation and give a necessary and sufficient dual characterisation of ρ-arbitrage. We show that the absence of ρ-arbitrage is intimately linked to the interplay between the set of equivalent martingale measures (EMMs) for the discounted risky assets and the set of absolutely continuous measures in the dual representation of ρ. A special case of our result shows that the market does not admit ρ-arbitrage for Expected Shortfall at level α if and only if there exists an EMM Q ≈ P such that ll dQ/dP ll∞ < 1/α.

Portfolio selection with parameter uncertainty under [formula omitted] maxmin mean–variance criterion

We consider a mean–variance portfolio selection problem with uncertain model parameters. We formulate the mean–variance problem under the α maxmin criterion, in which the investor has mixed ambiguity aversion and ambiguity seeking attitudes and solves a convex combination of max–min and max–max optimization problems. By the Lagrangian method, we obtain the efficient portfolio and quasi-efficient frontier in closed form. We provide comparative statics of the quasi-efficient frontier to various parameters.