Robust Reversion Strategy For On-Line Portfolio Selection

Portfolio selection based on Markowitz mean-variance theory and Kelly capital growth theory is one of the core issues in the field of financial economics in recent decades. It aims to achieve the largest cumulative return or risk-adjusted return in the long by allocating wealth among available assets. In particular, with the development of artificial intelligence and machine learning, on-line portfolio selection based on Kelly growth theory and on-line learning has become an important research topic in recent decades, it aims to sequentially construct portfolio by designing on-line learning algorithms. On the other hand, the stock price reversion is a very common and important phenomenon in securities markets. Based on this phenomenon, many researchers have designed a series of interesting online portfolio selection strategy in recent years for analysis of the microstructure of the stock market and actual investment operations. In this series of portfolio strategy, the most important type of strategy is the mean reversion strategies, such strategies generally through the use of the mean-value of stock historic price as the next input to approximate the stock price vector, then through some statistics and online learning algorithm to determine the final portfolio vector. Although in all major global stock price index data sets, such as the NYSE, DJA, etc., the performance of such online portfolio strategy is acceptable, because these strategies often fail to fully consider the noisy data and outliers, which often causing the underlying estimation error of the stock price and therefore produce non-optimal portfolio, thus affecting the actual performance of the strategies.To address these shortcomings, in this thesis we will investigate the reversion strategies of stock price by statistically robust estimation and online learning theory. We propose a new multi-period online portfolio strategy, i.e., robust median reversion strategy to describe the stock price reversion phenomenon. To achieve this strategy, we first introduce a very important robust estimators in statistics, i.e., L1-median estimator to estimate the underlying stock price vector, and then to construct the final portfolio vector by using the passive aggressive learning algorithm in online learning theory. We have designed three algorithms to accomplish this estimate and construction, and we also implement our algorithm on multiple real data sets, such as the NYSE, DJA and MSCI and so on, to demonstrate the accumulated wealth, the annual yield, volatility, Sharpe ratio and maximum retracement and other financial indicators. The experimental results show that our strategy is better than the previous ones which success in overcoming the drawback of outliers and noisy data and the assumption of single-period. What’s more, our strategy is robust for parameters and has a linear time complexity, which can be applied to large-scale transactions. Finally, we also extend the L1-median estimate in our reversion strategy by replacing the Euclidean norm of L1-median with Huber loss function. We re-estimate the underlying stock price vector and obtain the similar results with L1-median by experiments. Research of this thesis has some theoretical significance to describe stock price reversion phenomenon in the financial and securities markets. It also plays an important role in guiding the actual portfolio selection in the financial industry.