Godeliva Petrina Marisu

Bio: Godeliva Petrina Marisu is an academic researcher from Nanyang Technological University. The author has contributed to research in topics: Bayesian probability & Bayesian optimization. The author has an hindex of 1, co-authored 1 publications receiving 1 citations.

Bayesian Estimation and Optimization for Learning Sequential Regularized Portfolios

Abstract: This paper incorporates Bayesian estimation and optimization into portfolio selection framework, particularly for high-dimensional portfolio in which the number of assets is larger than the number of observations. We leverage a constrained 𝓁1 minimization approach, called linear programming optimal (LPO) portfolio, to directly estimate effective parameters appearing in the optimal portfolio. We propose two refinements for the LPO strategy. First, we explore improved Bayesian estimates, instead of sample estimates, of the covariance matrix of asset returns. Second, we introduce Bayesian optimization (BO) to replace traditional grid-search cross-validation (CV) in tuning hyperparameters of the LPO strategy. We further propose modifications in the BO algorithm by (1) taking into account time-dependent nature of financial problems and (2) extending commonly used expected improvement (EI) acquisition function to include a tunable trade-off with the improvement's variance (EIVar). Allowing a general case of noisy observations, we theoretically derive the sub-linear convergence rate of BO under the newly proposed EIVar and thus our algorithm has no regret. Our empirical studies confirm that the adjusted BO result in portfolios with higher out-of-sample Sharpe ratio, certainty equivalent, and lower turnover compared to those tuned with CV. This superior performance is achieved with significant reduction in time elapsed, thus also addressing time-consuming issues of CV. Furthermore, LPO with Bayesian estimates outperform original proposal of LPO, as well as the benchmark equally weighted and plug-in strategies.

Resolution of Degeneracy in Merton's Portfolio Problem

Abstract: The Merton problem determines the optimal intertemporal portfolio choice by maximizing the expected utility, and is the basis of modern portfolio theory in continuous-time finance. However, its empirical performance is disappointing. The estimation errors of the expected rates of returns make the optimal policy degenerate, resulting in an extremely low (or unbounded) expected utility value for a high-dimensional portfolio. We further prove that the estimation error of the variance-covariance matrix leads to the degenerated policy of solely investing in the risk-free asset. This study proposes a constrained l1 - minimization approach to resolve the degeneracy. The proposed scheme can be implemented with simple linear programming and involves negligible additional computational time, compared to standard estimation. We prove the consistency of our framework that our estimate of the optimal control tends to be the true one. We also derive the rate of convergence. Simulation studies are provided to verify the finite-sample properties. An empirical study using S&P 500 component stock data demonstrates the superiority of the proposed approach.

Integrating Different Informations for Portfolio Selection

Abstract: Following the idea of Bayesian learning via Gaussian mixture model, we organically combine the backward-looking information contained in the historical data and the forward-looking information implied by the market portfolio, which is affected by heterogeneous expectations and noisy trading behavior. The proposed combined estimation adaptively harmonizes these two types of information based on the degree of market efficiency and responds quickly at turning points of the market. Both simulation experiments and a global empirical test confirm that the approach is a flexible and robust forecasting tool and is applicable to various capital markets with different degrees of efficiency.