Bayesian forecasting and scalable multivariate volatility analysis using simultaneous graphical dynamic models

The recently introduced class of simultaneous graphical dynamic linear models (SGDLMs) defines an ability to scale on-line Bayesian analysis and forecasting to higher-dimensional time series. This paper advances the methodology of SGDLMs, developing and embedding a novel, adaptive method of simultaneous predictor selection in forward filtering for on-line learning and forecasting. The advances include developments in Bayesian computation for scalability, and a case study in exploring the resulting potential for improved short-term forecasting of large-scale volatility matrices. A case study concerns financial forecasting and portfolio optimization with a 400-dimensional series of daily stock prices. Analysis shows that the SGDLM forecasts volatilities and co-volatilities well, making it ideally suited to contributing to quantitative investment strategies to improve portfolio returns. We also identify performance metrics linked to the sequential Bayesian filtering analysis that turn out to define a leading indicator of increased financial market stresses, comparable to but leading the standard St. Louis Fed Financial Stress Index (STLFSI) measure. Parallel computation using GPU implementations substantially advance the ability to fit and use these models.Comment: 28 pages, 9 figures, 7 table

Beating the index with deep learning:a method for passive investing and systematic active investing

Abstract. In index tracking, while the full replication requires holding all the asset constituents of the index in the tracking portfolio, the sampling approach attempts to construct a tracking portfolio with a subset of assets. Thus, sampling seems to be the approach of choice when considering the flexibility and transaction costs. Two problems that need to be solved to implement the sampling approach are asset selection and asset weighting. This study proposes a framework implemented in two stages: first selecting the assets and then determining asset components’ weights. This study uses a deep autoencoder model for stock selection. The study then applies the L2 regularization technique to set up a quadratic programming problem to determine investment weights of stock components. Since the tracking portfolio tends to underperform the market index after taking management costs into accounts, the portfolio that can generate the excess returns over the index (index beating) brings more competitive advantages to passive fund managers. Thus, the proposed framework attempts to construct a portfolio with a small number of stocks that can both follow the market trends and generate excess returns over the market index. The framework successfully constructed a portfolio with ten stocks beating the S&P 500 index in any given 1-year period with a justifiable risk level

A Generalized Description Length Approach for Sparse and Robust Index Tracking

We develop a new minimum description length criterion for index tracking, which deals with two main issues affecting portfolio weights: estimation errors and model misspecification. The criterion minimizes the uncertainty related to data distribution and model parameters by means of a generalized q-entropy measure, and performs model selection and estimation in a single step, by assuming a prior distribution on portfolio weights. The new approach results in sparse and robust portfolios in presence of outliers and high correlation, by penalizing observations and parameters that highly diverge from the assumed data model and prior distribution. The Monte Carlo simulations and the empirical study on financial data confirm the properties and the advantages of the proposed approach compared to state-of-art methods

Statistical inference for the EU portfolio in high dimensions

In this paper, using the shrinkage-based approach for portfolio weights and modern results from random matrix theory we construct an effective procedure for testing the efficiency of the expected utility (EU) portfolio and discuss the asymptotic behavior of the proposed test statistic under the high-dimensional asymptotic regime, namely when the number of assets $p$ increases at the same rate as the sample size $n$ such that their ratio $p/n$ approaches a positive constant $c\in(0,1)$ as $n\to\infty$. We provide an extensive simulation study where the power function and receiver operating characteristic curves of the test are analyzed. In the empirical study, the methodology is applied to the returns of S\&P 500 constituents.Comment: 27 pages, 5 figures, 2 table

Sparse Index Tracking: Simultaneous Asset Selection and Capital Allocation via ℓ0\ell_0-Constrained Portfolio

Sparse index tracking is one of the prominent passive portfolio management strategies that construct a sparse portfolio to track a financial index. A sparse portfolio is desirable over a full portfolio in terms of transaction cost reduction and avoiding illiquid assets. To enforce the sparsity of the portfolio, conventional studies have proposed formulations based on $\ell_p$-norm regularizations as a continuous surrogate of the $\ell_0$-norm regularization. Although such formulations can be used to construct sparse portfolios, they are not easy to use in actual investments because parameter tuning to specify the exact upper bound on the number of assets in the portfolio is delicate and time-consuming. In this paper, we propose a new problem formulation of sparse index tracking using an $\ell_0$-norm constraint that enables easy control of the upper bound on the number of assets in the portfolio. In addition, our formulation allows the choice between portfolio sparsity and turnover sparsity constraints, which also reduces transaction costs by limiting the number of assets that are updated at each rebalancing. Furthermore, we develop an efficient algorithm for solving this problem based on a primal-dual splitting method. Finally, we illustrate the effectiveness of the proposed method through experiments on the S\&P500 and NASDAQ100 index datasets.Comment: Submitted to IEEE Open Journal of Signal Processin