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.
Since Harry Markowitz's seminal work in 1952, which initiated modern portfolio theory, 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 build portfolios. The purpose of this paper was to implement a new version of the Exponential Gradient algorithm in which important information about the risk of stocks are considered in the algorithm's projection step. The portfolios built were compared with the Dow Jones Industrial Average Index (DJIA) and Best Constant Rebalanced Portfolio (BCRP). We used DJIA data from January 2000 to December 2017 with daily observations. The EG beta algorithm outperformed the DJIA in all tests performed, and it was very close to BCRP in periods of market upturn and was able to outperform it in downturns.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.