On-Line Portfolio Selection Using Multiplicative Updates

The European Journal of Finance, 2013

The purpose of this paper is to develop a stock selection algorithm with similar properties as Cover's Universal Portfolio[2], but providing superior early growth. Cover's Universal Portfolio generates a growth rate asymptotically equal to the best achievable growth rate over the set of constant rebalanced portfolios. However, Cover's Universal Portfolio is empirically seen to generate poor early growth. While much research has been conducted in relation to Cover's Universal Portfolio, much of this has focused on efficient implementation of the algorithm and considerations of market frictions. As such, there remains a significant research gap in addressing the issue of poor early growth generated by Cover's strategy. With this in mind we develop the Adaptive Universal Portfolio, a sequential portfolio selection algorithm with similar asymptotic properties as Cover's Universal Portfolio but providing greater early growth. In this paper we provide an analysis of the growth generated by the two algorithms. Furthermore we present empirical evidence of the superior early growth generated by the Adaptive Universal Portfolio. Finally we discuss possible criticisms of the Adaptive Universal Portfolio, including evidence of momentum following and vulnerability to individual stock risks, and provide an insight into possible future work in this area.

Quantitative Finance, 2007

In last years there has been much work to design and to analyze online investment strategies based on constant rebalanced portfolios. A constant rebalanced portfolio is a sequential investment strategy which keeps fixed through time, trading period by trading period, the wealth distribution among a set of assets. In this framework Cover proposed the universal portfolio that is competitive with the best constant rebalanced portfolio determined in hindsight, i.e. the constant rebalanced portfolio obtained by assuming perfect knowledge of future stocks prices. However, the constant rebalanced portfolio is designed to deal with the portfolio selection problem in the case when no additional information, about the stock market, is available. To overcome this limitation, Cover and Ordentlich proposed the state constant rebalanced portfolio which is capable to appropriately exploit the available side-information about the stock market. In this paper we study and analyze the topic introduced by Cover and Ordentlich and focus the attention to the interplay between constant rebalanced portfolios and side-information. We introduce a mathematical framework to deal with constant rebalanced portfolio in the case when sideinformation, about the stock market, is available. The mathematical framework defines and analyzes the mixture best constant rebalanced portfolio which is proposed as the investment benchmark to be considered in the case when side-information, about the stock market, is available. The mixture best constant rebalanced portfolio outperforms the best constant rebalanced portfolio by an exponential factor in terms of the achieved wealth and therefore offers an interesting opportunity for side-information specialized online investment algorithms. We describe a new online investment algorithm which exploits the definition of mixture best constant rebalanced portfolio and the available side-information. The performance of the proposed online investment algorithm is investigated through a set of numerical experiments concerning four major stock market datasets, namely DJIA, S&P500, TSE and NYSE. The results obtained emphasize the relevance of the proposed online investment strategy and underline the central role of the side-information quality to outperform the best constant rebalanced portfolio.

2013

A major challenge for stochastic optimization is the cost of updating model parameters especially when the number of parameters is large. Updating parameters frequently can prove to be computationally or monetarily expensive. In this paper, we introduce an efficient primal-dual based online algorithm that performs lazy updates to the parameter vector and show that its performance is competitive with reasonable strategies which have the benefit of hindsight. We demonstrate the effectiveness of our algorithm in the online portfolio selection domain where a trader has to pay proportional transaction costs every time his portfolio is updated. Our Online Lazy Updates (OLU) algorithm takes into account the transaction costs while computing an optimal portfolio which results in sparse updates to the portfolio vector. We successfully establish the robustness and scalability of our lazy portfolio selection algorithm with extensive theoretical and experimental results on two real-world datasets.

Proceedings of the 23rd international conference on Machine learning - ICML '06, 2006

We experimentally study on-line investment algorithms first proposed by Agarwal and Hazan and extended by Hazan et al. which achieve almost the same wealth as the best constant-rebalanced portfolio determined in hindsight. These algorithms are the first to combine optimal logarithmic regret bounds with efficient deterministic computability. They are based on the Newton method for offline optimization which, unlike previous approaches, exploits second order information. After analyzing the algorithm using the potential function introduced by Agarwal and Hazan, we present extensive experiments on actual financial data. These experiments confirm the theoretical advantage of our algorithms, which yield higher returns and run considerably faster than previous algorithms with optimal regret. Additionally, we perform financial analysis using mean-variance calculations and the Sharpe ratio.

Investment Analysts Journal, 2020

The artificial segmentation of an investment management process into a workflow with silos of offline human operators can restrict silos from collectively and adaptively pursuing a unified optimal investment goal. To meet the investor objectives, an online algorithm can provide an explicit incremental approach that makes sequential updates as data arrives at the process level. This is in stark contrast to offline (or batch) processes that are focused on making component level decisions prior to process level integration. Here we present and report results for an integrated, and online framework for algorithmic portfolio management. This article provides a workflow that can in-turn be embedded into a process-level learning framework. The workflow can be enhanced to refine signal generation and asset class evolution and definitions. Our results confirm that we can use our framework in conjunction with resampling methods to outperform naive market capitalisation benchmarks while making clear the extent of back-test over-fitting. We consider such an online update framework to be a crucial step towards developing intelligent portfolio selection algorithms that integrate financial theory, investor views, and data analysis with process level learning.

International Journal of Financial Markets and Derivatives, 2011

The class of defensive online portfolio selection algorithms, designed for finite investment horizon, is introduced. The Game Constantly Rebalanced Portfolio and the Worst Case Game Constantly Rebalanced Portfolio, are presented and theoretically analyzed. The analysis exploits the rich set of mathematical tools available by means of the connection between Universal Portfolios and the Game-Theoretic framework. The empirical performance of the Worst Case Game Constantly Rebalanced Portfolio algorithm is analyzed through numerical experiments concerning the FTSE 100, Nikkei 225, Nasdaq 100 and S&P500 stock markets for the time interval, . The results emphasize the relevance of the proposed online investment algorithm which significantly outperformed the market index and the minimum variance Sharpe-Markowitz's portfolio.

Journal of Banking & Finance, 1977

Stochastic dominance methods which have been developed in recent years are generally more valid than mean-variance (EV) and higher moment methods for selecting a portfolio from a given finite set of possible portfolios. One of the limitations of these methods is the lack of procedures for building portfolios from a given set of securities and the probability distribution of their returns. Markowitz has developed an algorithm based on the restriction method in linear programming to build undominated portfolios. In this paper a more efficient method based on the relaxation method of linear programming is developed and tested for efficiency. Computational results justify its use as a practical tool for portfolio building.

International Journal for Research in Applied Science and Engineering Technology

An investment portfolio management system is a highly sophisticated software application meticulously crafted to assist investors in the management of their investment portfolios. This innovative system provides investors with a centralized platform that empowers them to track their investments meticulously, closely monitor their performance, and judiciously make informed investment decisions. The system encompasses several advanced features such as portfolio analysis, risk management tools, asset allocation strategies, and performance reporting, that provide investors with a comprehensive overview of their portfolio's performance. Additionally, this cutting-edge platform offers investors the opportunity to diversify their portfolio by investing across multiple asset classes such as stocks, bonds, and mutual funds. This paper delves into the various techniques and methods employed to identify the optimal strategy to maximize gains from the investment. The fusion of algorithms and investments has revolutionized the investment landscape, enabling investors to obtain insightful data and make data-driven decisions. Several research studies have been conducted in the investment field, bolstered by machine learning models and algorithms, resulting in exceptional gains for investors.

Iie Transactions, 2007

We consider a single-period mean-safety portfolio selection problem with transaction costs and integer constraints on the quantities selected for the securities (rounds). We propose an exact approach based on the partition of the initial problem into two subproblems and the use of a simple local search heuristic to obtain an initial solution. To the best of our knowledge, no optimal algorithms have been proposed in the literature for this problem. The proposed approach is simple, general and easily adaptable to other problems. An extensive experimental analysis based on real data from the main international Stock Exchange Markets is performed. The results show, on average, an impressive improvement with respect to the computational time and space memory required by CPLEX 7.0. We also show that the solution of the first subproblem can be used on its own as an extremely effective heuristic.