This paper presents a portfolio construction process, including mainly two parts, Factors Selection and Weight Allocations. For the factors selection part, We have chosen 20 factors by considering three aspects, the global market, different assets class, and stock idiosyncratic characteristics. Each factor is proxied by a corresponding ETF. Then, we would apply several weight allocation methods to those factors, including two fixed weight allocation methods, three optimisation methods, and a Black-Litterman model. In addition, we would also fit a Deep Learning model for generating views periodically and incorporating views with the prior to achieve dynamically updated weights by using the Black-Litterman model. In the end, the robustness checking shows how weights change with respect to time evolving and variance increasing. Results using shrinkage variance are provided to alleviate the impacts of representativeness of historical data, but there sadly has little impact. Overall, the model by using the Deep Learning plus Black-Litterman model results outperform the portfolio by other weight allocation schemes, even though further improvement and robustness checking should be performed.
The Black-Litterman model extends the framework of the Markowitz Modern Portfolio Theory to incorporate investor views. We consider a case where multiple view estimates, including uncertainties, are given for the same underlying subset of assets at a point in time. This motivates our consideration of data fusion techniques for combining information from multiple sources. In particular, we consider consistency-based methods that yield fused view and uncertainty pairs; such methods are not common to the quantitative finance literature. We show a relevant, modern case of incorporating machine lea…
Elice AI Quant Lab, MODULABS Seoul Republic of Korea；Meritz Fire \& Marine Insurance AI Quant Lab, MODULABS Seoul Republic of Korea；Mirae Asset Global Investments AI Quant Lab, MODULABS Seoul Republic of Korea；Ulsan National Institute of Science；Elice AI Quant Lab, MODULABS；Meritz Fire \& Marine Insurance AI Quant Lab, MODULABS；Mirae Asset Global Investments AI Quant Lab, MODULABS
Latent Variable Estimation in Bayesian Black-Litterman Models
Department of Physics, National Taiwan University（国家台湾大学物理系）；Department of Computer Science, Northwestern University（西北大学计算机科学系）；Center for Foundation Models and Generative AI, Northwestern University（西北大学基础模型与生成人工智能中心）；D’Amore-McKim School of Business, Northeastern University（东北大学D’Amore-McKim商学院）；Whiting School of Engineering, Johns Hopkins University（约翰霍普金斯大学Whiting工程学院）；Gamma Paradigm Capital（Gamma Paradigm资本）
The Black-Litterman model combines investors' personal views with historical data and gives optimal portfolio weights. In this paper we will introduce the original Black-Litterman model (section 1), we will modify the model such that it fits in a Bayesian framework by considering the investors' personal views to be a direct prior on the means of the returns and by adding a typical Inverse Wishart prior on the covariance matrix of the returns (section 2). Lastly, we will use Leonard and Hsu's (1992) idea of adding a prior on the logarithm of the covariance matrix (section 3). Sensitivity simula…
We analyze a nonlinear equation proposed by F. Black (1968) for the optimal portfolio function in a log-normal model. We cast it in terms of the risk tolerance function and provide, for general utility functions, existence, uniqueness and regularity results, and we also examine various monotonicity, concavity/convexity and S-shape properties. Stronger results are derived for utilities whose inverse marginal belongs to a class of completely monotonic functions.
Hedge funds have long been viewed as a veritable "black box" of investing since outsiders may never view the exact composition of portfolio holdings. Therefore, the ability to estimate an informative set of asset weights is highly desirable for analysis. We present a compositional state space model for estimation of an investment portfolio's unobserved asset allocation weightings on a set of candidate assets when the only observed information is the time series of portfolio returns and the candidate asset returns. In this paper, we exhibit both sequential Monte Carlo numerical and conditionall…
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…
It is widely recognized that when classical optimal strategies are applied with parameters estimated from data, the resulting portfolio weights are remarkably volatile and unstable over time. The predominant explanation for this is the difficulty of estimating expected returns accurately. In this paper, we modify the $n$ stock Black--Scholes model by introducing a new parametrization of the drift rates. We solve Markowitz' continuous time portfolio problem in this framework. The optimal portfolio weights correspond to keeping $1/n$ of the wealth invested in stocks in each of the $n$ Brownian m…
Portfolio optimization has been a central problem in finance, often approached with two steps: calibrating the parameters and then solving an optimization problem. Yet, the two-step procedure sometimes encounter the "error maximization" problem where inaccuracy in parameter estimation translates to unwise allocation decisions. In this paper, we combine the prediction and optimization tasks in a single feed-forward neural network and implement an end-to-end approach, where we learn the portfolio allocation directly from the input features. Two end-to-end portfolio constructions are included: a …
Improving Bayesian Optimization for Portfolio Management with an Adaptive Scheduling
School of Computer Science University of Bristol Bristol, UK（计算机科学学院 伯明翰大学 伯明翰，英国）；Business School University of Birmingham Birmingham, UK（商学院 伯明翰大学 伯明翰，英国）；Stratiphy Limited London, UK（Stratiphy有限公司 伦敦，英国）；University of Bristol（伯明翰大学）；University of Birmingham（伯明翰大学）；Stratiphy Limited（Stratiphy有限公司）
In this paper we introduce a novel approach to risk estimation based on nonlinear factor models - the "StressVaR" (SVaR). Developed to evaluate the risk of hedge funds, the SVaR appears to be applicable to a wide range of investments. Its principle is to use the fairly short and sparse history of the hedge fund returns to identify relevant risk factors among a very broad set of possible risk sources. This risk profile is obtained by calibrating a collection of nonlinear single-factor models as opposed to a single multi-factor model. We then use the risk profile and the very long and rich histo…
I juxtapose Cover's vaunted universal portfolio selection algorithm (Cover 1991) with the modern representation (Qian 2016; Roncalli 2013) of a portfolio as a certain allocation of risk among the available assets, rather than a mere allocation of capital. Thus, I define a Universal Risk Budgeting scheme that weights each risk budget (instead of each capital budget) by its historical performance record (a la Cover). I prove that my scheme is mathematically equivalent to a novel type of Cover and Ordentlich 1996 universal portfolio that uses a new family of prior densities that have hitherto not…
