This paper introduces a new functional optimization approach to portfolio optimization problems by treating the unknown weight vector as a function of past values instead of treating them as fixed unknown coefficients in the majority of studies. We first show that the optimal solution, in general, is not a constant function. We give the optimal conditions for a vector function to be the solution, and hence give the conditions for a plug-in solution (replacing the unknown mean and variance by certain estimates based on past values) to be optimal. After showing that the plug-in solutions are sub-optimal in general, we propose gradient-ascent algorithms to solve the functional optimization for mean-variance portfolio management with theorems for convergence provided. Simulations and empirical studies show that our approach can perform significantly better than the plug-in approach.
In this paper, we present an extended exploratory continuous-time mean-variance framework for portfolio management. Our strategy involves a new clustering method based on simulated annealing, which allows for more practical asset selection. Additionally, we consider past wealth evolution when constructing the mean-variance portfolio. We found that our strategy effectively learns from the past and performs well in practice.
There is a great number of factors to take into account when building and managing an investment portfolio. It is widely believed that a proper set-up of the portfolio combined with a good, robust management strategy is the key to successful investment. In this paper, we aim at an analysis of two aspects that may have an impact on investment performance: diversity of assets and inclusion of cash in the portfolio. We also propose two new management strategies based on the MACD and RSI factors known from technical analysis. Monte Carlo simulations within the Heston model of a market are used to …
Value-at-Risk is one of the most popular risk management tools in the financial industry. Over the past 20 years several attempts to include VaR in the portfolio selection process have been proposed. However, using VaR as a risk measure in portfolio optimization models leads to problems that are computationally hard to solve. In view of this, few practical applications of VaR in portfolio selection have appeared in the literature up to now. In this paper, we propose to add the VaR criterion to the classical Mean-Variance approach in order to better address the typical regulatory constraints of…
We employ model predictive control for a multi-period portfolio optimization problem. In addition to the mean-variance objective, we construct a portfolio whose allocation is given by model predictive control with a risk-parity objective, and provide a successive convex program algorithm that provides 30 times faster and robust solutions in the experiments. Computational results on the multi-asset universe show that multi-period models perform better than their single period counterparts in out-of-sample period, 2006-2020. The out-of-sample risk-adjusted performance of both mean-variance and r…
Prediction models are traditionally optimized independently from their use in the asset allocation decision-making process. We address this shortcoming and present a framework for integrating regression prediction models in a mean-variance optimization (MVO) setting. Closed-form analytical solutions are provided for the unconstrained and equality constrained MVO case. For the general inequality constrained case, we make use of recent advances in neural-network architecture for efficient optimization of batch quadratic-programs. To our knowledge, this is the first rigorous study of integrating …
We consider a reference security, understood to be an attractive investment, with the caveat that an investor is not willing to directly invest in the security, for presence of constraints, either investor specific or pertaining to the security itself. The investor, however, is open to a portfolio constructed with an accepted set of securities, where returns could be considered similar to the reference security. We demonstrate, under a measure of similarity, such a portfolio could be selected with a mean-variance characterization, as defined by Markowitz. Furthermore, we consider the performan…
Under mean-variance-utility framework, we propose a new portfolio selection model, which allows wealth and time both have influences on risk aversion in the process of investment. We solved the model under a game theoretic framework and analytically derived the equilibrium investment (consumption) policy. The results conform with the facts that optimal investment strategy heavily depends on the investor's wealth and future income-consumption balance as well as the continuous optimally consumption process is highly dependent on the consumption preference of the investor.
With the improvement of computer performance and the development of GPU-accelerated technology, trading with machine learning algorithms has attracted the attention of many researchers and practitioners. In this research, we propose a novel portfolio management strategy based on the framework of Deep Deterministic Policy Gradient, a policy-based reinforcement learning framework, and compare its performance to that of other trading strategies. In our framework, two Long Short-Term Memory neural networks and two fully connected neural networks are constructed. We also investigate the performance…
One of the reasons that higher order moment portfolio optimization methods are not fully used by practitioners in investment decisions is the complexity that these higher moments create by making the optimization problem nonconvex. Many few methods and theoretical results exists in the literature, but the present paper uses the method of successive convex approximation for the mean-variance-skewness problem.
We propose a virtual bidding strategy by modeling the price differences between the day-ahead market and the real-time market as Brownian motion with drift, where the drift rate and volatility are functions of meteorological variables. We then transform the virtual bidding problem into a mean-variance portfolio management problem, where we approach the mean-variance portfolio management problem by using the exploratory mean-variance portfolio management framework
In this paper, we document a novel machine learning based bottom-up approach for static and dynamic portfolio optimization on, potentially, a large number of assets. The methodology applies to general constrained optimization problems and overcomes many major difficulties arising in current optimization schemes. Taking mean-variance optimization as an example, we no longer need to compute the covariance matrix and its inverse, therefore the method is immune from the estimation error on this quantity. Moreover, no explicit calls of optimization routines are needed. Applications to equity portfo…
This paper describes multi-portfolio `internal' rebalancing processes used in the finance industry. Instead of trading with the market to `externally' rebalance, these internal processes detail how portfolio managers buy and sell between their portfolios to rebalance. We give an overview of currently used internal rebalancing processes, including one known as the `banker' process and another known as the `linear' process. We prove the banker process disadvantages the nominated banker portfolio in volatile markets, while the linear process may advantage or disadvantage portfolios. We describe a…
Deep reinforcement learning (DRL) has been widely studied in the portfolio management task. However, it is challenging to understand a DRL-based trading strategy because of the black-box nature of deep neural networks. In this paper, we propose an empirical approach to explain the strategies of DRL agents for the portfolio management task. First, we use a linear model in hindsight as the reference model, which finds the best portfolio weights by assuming knowing actual stock returns in foresight. In particular, we use the coefficients of a linear model in hindsight as the reference feature wei…
On Reference-Regulated Multiperiod Mean-Variance Portfolio Optimization in High Dimensions
Faculty of Business and Economics, The University of Hong Kong（香港大学工商管理学院）；School of Information Management and Engineering, Shanghai University of Finance and Economics（上海财经大学信息管理与工程学院）
In this paper, we study closed-loop equilibrium strategies for mean-variance portfolio selection problem in a hidden Markov model with dynamic attention behavior. In addition to the investment strategy, the investor's attention to news is introduced as a control of the accuracy of the news signal process. The objective is to find equilibrium strategies by numerically solving an extended HJB equation by using Markov chain approximation method. An iterative algorithm is constructed and its convergence is established. Numerical examples are also provided to illustrate the results.
We introduce a $k$-fold boosted version of our Boostrapped Average Hierarchical Clustering cleaning procedure for correlation and covariance matrices. We then apply this method to global minimum variance portfolios for various values of $k$ and compare their performance with other state-of-the-art methods. Generally, we find that our method yields better Sharpe ratios after transaction costs than competing filtering methods, despite requiring a larger turnover.
