Online Portfolio Optimization with Risk Control

Portfolio selection is undoubtedly one of the most challenging topics in the area of finance. Since Markowitz's initial contribution in 1952, portfolio allocation strategies have been intensely discussed in the literature. With the development of online optimization techniques, dynamic learning...

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Bibliographic Details
Published in:	Trends in Computational and Applied Mathematics Vol. 22; no. 3; pp. 475 - 493
Main Authors:	Yamim, João Daniel Madureira, Borges, Carlos Cristiano Hasenclever, Neto, Raul Fonseca
Format:	Journal Article
Language:	English
Published:	Sociedade Brasileira de Matemática Aplicada e Computacional - SBMAC 01-09-2021 Sociedade Brasileira de Matemática Aplicada e Computacional
Subjects:	MATHEMATICS MATHEMATICS, APPLIED Online gradient descent portfolio optimization time varying CAPM online gradient descent portfolio optimization time varying CAPM
Online Access:	Get full text
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Summary:	Portfolio selection is undoubtedly one of the most challenging topics in the area of finance. Since Markowitz's initial contribution in 1952, portfolio allocation strategies have been intensely discussed in the literature. With the development of online optimization techniques, dynamic learning algorithms have proven to be an effective approach to building portfolios, although they do not assess the risk related to each investment decision.In this work, we compared the performance of the Online Gradient Descent (OGD) algorithm and a modification of the method, that takes into account risk metrics controlling for the Beta of the portfolio. In order to control for the Beta, each asset was modeled using the CAPM model and a time-varying Beta that follows a random walk. We compared both the traditional OGD algorithm and the OGD with Beta constraints with the Uniform Constant Rebalanced Portfolio and two different indexes for the Brazilian market, composed of small caps and the assets that belong to the Ibovespa index. Controlling the Beta proved to be an efficient strategy when the investor chooses an appropriate interval for the beta during bull markets or bear markets. Moreover, the time-varying beta was an efficient metric to force the desired correlation with the market and also to reduce the volatility of the portfolio during bear markets.
ISSN:	2676-0029 2676-0029
DOI:	10.5540/tcam.2021.022.03.00475