Thomas Cover's Universal Portfolio - Part II, Further Reading

In Part I, I briefly discussed Thomas Cover and the Universal Portfolio. There’s lots of detailed reading material on the Universal Portfolio Method, including in Cover’s publication list. Cover has a book on Information Theory that contains a chapter on Information Theory and the stock market (that chapter from the first edition appears to be online here). Ernest Chan provides an easy to read description. Further reading:

Universal Portfolios With and Without Transaction Costs (1997). For the universal algorithm of Cover (Cover, 1991), we provide a simple analysis which naturally extends to the case of a fixed percentage transaction cost (commission), answering a question raised in (Cover, 1991; Helmbold et al., 1996; Cover and Ordentlich, 1996a; Cover and Ordentlich, 1996b; Ordentlich and Cover, 1996; Cover, 1996). In addition, we present a simple randomized implementation that is significantly faster in practice.

Can we learn to Beat the Best Stock? (2003). A novel algorithm for actively trading stocks is presented. While traditional universal algorithms (and technical trading heuristics) attempt to predict winners or trends, our approach relies on predictable statistical relations between all pairs of stocks in the market. Our empirical results on historical markets provide strong evidence that this type of technical trading can “beat the market” and moreover, can beat the best stock in the market. In doing so we utilize a new idea for smoothing critical parameters in the context of expert learning.

Universal Portfolios and the Hindsight Bias Issue: A New Perspective? As this paper involves the application of the Universal Portfolio concepts of Cover ([1][2]) to the Hindsight Bias issue, we begin by introducing each of these individually, beginning with the latter. The Hindsight Bias problem, often also referred to as the ’Data Mining’ problem, occurs when first, many possible models to describe an aspect of the past are posited, and then the bestfitting of these is selected a posteriori (i.e., after the fact). When a model thus selected is then applied as a model for the future, the results tend to be disappointing…

Efficient Algorithms for Universal Portfolios (2002). There has been much work on Cover’s Universal algorithm, which is competitive with the best constant rebalanced portfolio de- termined in hindsight (Cover, 1991, Helmbold et al, 1998, Blum and Kalai, 1999, Foster and Vohra, 1999, Vovk, 1998, Cover and Ordentlich, 1996a, Cover, 1996c). While this algorithm has good performance guarantees, all known implementations are exponential in the number of stocks, restricting the number of stocks used in experiments (Helmbold et al, 1998, Cover and Ordentlich, 1996a, Ordentlich and Cover, 1996b, Cover, 1996c, Blum and Kalai, 1999). We present an effcient implementation of the Universal algorithm that is based on non-uniform random walks that are rapidly mixing (Applegate and Kannan, 1991, Lovasz and Simonovits, 1992, Frieze and Kannan, 1999). This same implementation also works for nonfinancial applications of the Universal algorithm, such as data compression (Cover, 1996c) and language modeling (Chen et al, 1999).

A statistical view of universal portfolios (2005) In this thesis, we provide a statistical view of universal portfolios in order to develop a clearer understanding of their performance on actual financial data sequences. By recasting the analysis of a universal portfolio in statistical terms;with a special emphasis on statistical estimation;we are able to resolve a long standing and false perception of a disconnect between information theory and empirical finance.

There’s even a method that claims to outperform the Universal Portfolio:

Switching Portfolios. Recently, there has been work on on-line portfolio selection algorithms which are competitive with the best constant rebalanced portfolio determined in hindsight [2, 6, 3]. By their nature, these algorithms employ the assumption that high yield returns can be achieved using a fixed asset allocation strategy. However, stock markets are far from being stationary and in many cases the return of a constant rebalanced portfolio is much smaller than the return of an ad-hoc investment strategy that adapts to changes in the market. In this paper we present an efficient portfolio selection algorithm that is able to track a changing market. We also describe a simple extension of the algorithm for the case of a general transaction cost, including a fixed percentage transaction cost which was recently investigated [1]. We provide a simple analysis of the competitiveness of the algorithm and check its performance on real stock data from the New York Stock Exchange accumulated during a 22-year period. On this data, our algorithm outperforms all other algorithms mentioned above both with and without transaction costs.

Nonparametric Kernel-Based Sequential Investment Strategies (2006). The purpose of this paper is to introduce sequential investment strategies that guarantee an optimal rate of growth of the capital, under minimal assumptions on the behavior of the market. The new strategies are analyzed both theoretically and empirically. The theoretical results show that the asymptotic rate of growth matches the optimal one that one could achieve with a full knowledge of the statistical properties of the underlying process generating the market, under the only assumption that the market is stationary and ergodic. The empirical results show that the performance of the proposed investment strategies measured on past NYSE and currency exchange data is solid, and sometimes even spectacular.

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