Strategic Asset Allocation and the Total Portfolio Approach differ in one thing: the tracking error the board grants the chief investment officer. The board's first decision should be the drawdown it can tolerate; the benchmark and tracking error budget follow. The value comes from spending that budget dynamically, adding active risk when the reward is high and shedding it as the fund nears its limit. Managed this way, a fund would have compounded about two percentage points a year faster at the same drawdown, with no security selection. What matters is dynamic versus static tracking error, not the label.
We study a series of static and dynamic portfolios of VIX futures and their effectiveness to track the VIX index. We derive each portfolio using optimization methods, and evaluate its tracking performance from both empirical and theoretical perspectives. Among our results, we show that static portfolios of different VIX futures fail to track VIX closely. VIX futures simply do not react quickly enough to movements in the spot VIX. In a discrete-time model, we design and implement a dynamic trading strategy that adjusts daily to optimally track VIX. The model is calibrated to historical data and…
Portfolio management problems are often divided into two types: active and passive, where the objective is to outperform and track a preselected benchmark, respectively. Here, we formulate and solve a dynamic asset allocation problem that combines these two objectives in a unified framework. We look to maximize the expected growth rate differential between the wealth of the investor's portfolio and that of a performance benchmark while penalizing risk-weighted deviations from a given tracking portfolio. Using stochastic control techniques, we provide explicit closed-form expressions for the op…
We develop a methodology for index tracking and risk exposure control using financial derivatives. Under a continuous-time diffusion framework for price evolution, we present a pathwise approach to construct dynamic portfolios of derivatives in order to gain exposure to an index and/or market factors that may be not directly tradable. Among our results, we establish a general tracking condition that relates the portfolio drift to the desired exposure coefficients under any given model. We also derive a slippage process that reveals how the portfolio return deviates from the targeted return. In…
Among professionals and academics alike, it is well known that active portfolio management is unable to provide additional risk-adjusted returns relative to their benchmarks. For this reason, passive wealth management has emerged in recent decades to offer returns close to benchmarks at a lower cost. In this article, we first refine the existing results on the theoretical properties of oblique Brownian motion. Then, assuming that the returns follow skew geometric Brownian motions and that they are correlated, we describe some statistical properties for the \emph{ex-post}, the \emph{ex-ante} tr…
We propose a long term portfolio management method which takes into account a liability. Our approach is based on the LQG (Linear, Quadratic cost, Gaussian) control problem framework and then the optimal portfolio strategy hedges the liability by directly tracking a benchmark process which represents the liability. Two numerical results using empirical data published by Japanese organizations are served: simulations tracking an artificial liability and an estimated liability of Japanese organization. The latter one demonstrates that our optimal portfolio strategy can hedge his or her liability…
In this work, we demonstrate how to apply non-linear cardinality constraints, important for real-world asset management, to quantum portfolio optimization. This enables us to tackle non-convex portfolio optimization problems using quantum annealing that would otherwise be challenging for classical algorithms. Being able to use cardinality constraints for portfolio optimization opens the doors to new applications for creating innovative portfolios and exchange-traded-funds (ETFs). We apply the methodology to the practical problem of enhanced index tracking and are able to construct smaller port…
This paper studies the finite horizon portfolio management by optimally tracking a ratcheting capital benchmark process. It is assumed that the fund manager can dynamically inject capital into the portfolio account such that the total capital dominates a non-decreasing benchmark floor process at each intermediate time. The tracking problem is formulated to minimize the cost of accumulated capital injection. We first transform the original problem with floor constraints into an unconstrained control problem, however, under a running maximum cost. By identifying a controlled state process with r…
An actively managed portfolio almost never beats the market in the long term. Thus, many investors often resort to passively managed portfolios whose aim is to follow a certain financial index. The task of building such passive portfolios aiming also to minimize the transaction costs is called Index Tracking (IT), where the goal is to track the index by holding only a small subset of assets in the index. As such, it is an NP-hard problem and becomes unfeasible to solve exactly for indices with more than 100 assets. In this work, we present a novel hybrid simulated annealing method that can eff…
Non-Convex Portfolio Optimization via Energy-Based Models: A Comparative Analysis Using the Thermodynamic HypergRaphical Model Library (THRML) for Index Tracking
In this work, we consider the optimal portfolio selection problem under hard constraints on trading amounts, transaction costs and different rates for borrowing and lending when the risky asset returns are serially correlated. No assumptions about the correlation structure between different time points or about the distribution of the asset returns are needed. The problem is stated as a dynamic tracking problem of a reference portfolio with desired return. Our approach is tested on a set of a real data from Russian Stock Exchange MICEX.
We address the problem of partial index tracking, replicating a benchmark index using a small number of assets. Accurate tracking with a sparse portfolio is extensively studied as a classic finance problem. However in practice, a tracking portfolio must also be diverse in order to minimise risk -- a requirement which has only been dealt with by ad-hoc methods before. We introduce the first index tracking method that explicitly optimises both diversity and sparsity in a single joint framework. Diversity is realised by a regulariser based on pairwise similarity of assets, and we demonstrate that…
Partial (replication) index tracking is a popular passive investment strategy. It aims to replicate the performance of a given index by constructing a tracking portfolio which contains some constituents of the index. The tracking error optimisation is quadratic and NP-hard when taking the L0 constraint into account so it is usually solved by heuristic methods such as evolutionary algorithms. This paper introduces a simple, efficient and scalable connectionist model as an alternative. We propose a novel reparametrisation method and then solve the optimisation problem with stochastic neural netw…
In this work, we consider the optimal portfolio selection problem under hard constraints on trading volume amounts when the dynamics of the risky asset returns are governed by a discrete-time approximation of the Markov-modulated geometric Brownian motion. The states of Markov chain are interpreted as the states of an economy. The problem is stated as a dynamic tracking problem of a reference portfolio with desired return. We propose to use the model predictive control (MPC) methodology in order to obtain feedback trading strategies. Our approach is tested on a set of a real data from the radi…
Index tracking is a popular form of asset management. Typically, a quadratic function is used to define the tracking error of a portfolio and the look back approach is applied to solve the index tracking problem. We argue that a forward looking approach is more suitable, whereby the tracking error is expressed as expectation of a function of the difference between the returns of the index and of the portfolio. We also assume that there is an uncertainty in the distribution of the assets, hence a robust version of the optimization problem needs to be adopted. We use Bregman divergence in descri…
Markowitz (1952, 1959) laid down the ground-breaking work on the mean-variance analysis. Under his framework, the theoretical optimal allocation vector can be very different from the estimated one for large portfolios due to the intrinsic difficulty of estimating a vast covariance matrix and return vector. This can result in adverse performance in portfolio selected based on empirical data due to the accumulation of estimation errors. We address this problem by introducing the gross-exposure constrained mean-variance portfolio selection. We show that with gross-exposure constraint the theoreti…
This article deals with the problem of optimal allocation of capital to corporate bonds in fixed income portfolios when there is the possibility of correlated defaults. Under fairly general assumptions for the distribution of the total net assets of a set of firms we show that retaining the first few moments of the portfolio default loss distribution gives an extremely good approximation to the full solution of the asset allocation problem. We provide detailed results on the convergence of the moment expansion. We also provide explicit results for the inverse problem, i.e. for a given allocati…
Mirae Asset Global Investments Co.,Ltd.（未来资产环球投资有限公司）
Index funds are substantially preferred by investors nowadays, and market sensitivities are instrumental in managing index funds. An index fund is a mutual fund aiming to track the returns of a predefined market index (e.g., the S&P 500). A basic strategy to manage an index fund is replicating the index's constituents and weights identically, which is, however, cost-ineffective and impractical. To address this issue, it is required to replicate the index partially with accurately predicted market sensitivities. Accordingly, we propose a novel partial-replication method via learning to predict …
Pohang University of Science and Technology（浦项科技大学）；Seoul National University of Science and Technology（首尔国立科技大学）
Portfolio traders strive to identify dynamic portfolio allocation schemes so that their total budgets are efficiently allocated through the investment horizon. This study proposes a novel portfolio trading strategy in which an intelligent agent is trained to identify an optimal trading action by using deep Q-learning. We formulate a Markov decision process model for the portfolio trading process, and the model adopts a discrete combinatorial action space, determining the trading direction at prespecified trading size for each asset, to ensure practical applicability. Our novel portfolio tradin…
We extend the Annually Recalculated Virtual Annuity (ARVA) spending rule for retirement savings decumulation to include a cap and a floor on withdrawals. With a minimum withdrawal constraint, the ARVA strategy runs the risk of depleting the investment portfolio. We determine the dynamic asset allocation strategy which maximizes a weighted combination of expected total withdrawals (EW) and expected shortfall (ES), defined as the average of the worst five per cent of the outcomes of real terminal wealth. We compare the performance of our dynamic strategy to simpler alternatives which maintain co…
Reinforcement Learning for Financial Index Tracking
HSBC Business School, Peking University（北京大学汇丰商学院）；Sargent Institute of Quantitative Economics and Finance, HSBC Business School, Peking University（北京大学汇丰商学院萨金特数量经济与金融研究所）；Business School, Hong Kong University of Science and Technology（香港科技大学商学院）；Department of System Engineering and Engineering Management, The Chinese University of Hong Kong（香港中文大学系统工程与工程管理学系）
