Universal portfolio selection strategy by aggregating online expert advice
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Universal portfolio selection strategy by aggregating online expert advice Jin’an He1,2 · Xingyu Yang1 Received: 5 January 2020 / Revised: 19 August 2020 / Accepted: 19 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper concerns online portfolio selection problem. In this problem, no statisti‑ cal assumptions are made about the future asset prices. Although existing universal portfolio strategies have been shown to achieve good performance, it is not easy, almost impossible, to determine upfront which strategy will achieve the maximum final cumulative wealth for online portfolio selection tasks. This paper proposes a novel online portfolio strategy by aggregating expert advice using the weak aggregating algorithm. We consider a pool of universal portfolio strategies as experts, and compute the portfolio by aggregating the portfolios suggested by these expert strategies according to their previous performance. Through our analysis, we estab‑ lish theoretical results and illustrate empirical performance. We theoretically prove that our strategy is universal, i.e., it asymptotically performs almost as well as the best constant rebalanced portfolio determined in hindsight. We also conduct exten‑ sive experiments to illustrate the effectiveness of the proposed strategy by using daily stock data collected from the American and Chinese stock markets. Numerical results show that the proposed strategy outperforms all expert strategies in the pool besides best expert strategy and performs almost as well as best expert strategy. Keywords Online portfolio selection · Universal portfolio · Online learning · Weak aggregating algorithm
* Xingyu Yang [email protected] Jin’an He [email protected] 1
School of Management, Guangdong University of Technology, Guangzhou 510520, Guangdong, People’s Republic of China
2
Sun Yat‑sen Business School, Sun Yat-sen University, Guangzhou 510275, Guangdong, People’s Republic of China
13
Vol.:(0123456789)
J. He, X. Yang
1 Introduction Portfolio selection deals with the problem how to allocate an investor’s wealth among a variety of assets and aims to help the investor reach his/her investment goals. Markowitz (1952) originally proposed the mean-variance (MV) model, which is the cornerstone for the modern portfolio selection theory. The MV model aims to strike a balance between return and risk, i.e. minimizing the risk for a given level of the expected return, or maximizing the expected return for a given level of the risk. After Markowitz’s framework, many scholars extended the classical MV model by using different approaches and proposed many portfolio models, such as Li and Ng (2000), Cui et al. (2012), Li and Xu (2013), Liu and Zhang (2015), Lotfi et al. (2017), Clempner and Poznyak (2018). In an uncertain financial environment, it is impossible to accurately predict the future returns and risks of the various assets. Based exclusively on historical asset data, Cover (1991) proposed online portfolio theory, which gets over the
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