On the Competitive Theory and Practice of Portfolio Selection
On the Competitive Theory and Practice of Portfolio Selection
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发表时间：
2002
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通讯作者：
A. Borodin;Ran El-Yaniv;Vincent Gogan
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作者：
A. Borodin;Ran El-Yaniv;Vincent Gogan
投资组合选择问题显然是计算金融领域最基本的问题之一。给定一组比如说 m 只股票（其中一个可能是“现金”），自然的在线问题是根据之前 i ? 1 个交易周期的价格序列（或等效的相对价格）确定第 i 个交易周期的投资组合。对于在线投资组合选择算法的竞争理论的价值，人们越来越感兴趣，也越来越怀疑。竞争分析是基于最坏情况的视角，而这种视角与更广泛接受的基于统计的分析和理论不一致。竞争框架确实（也许令人惊讶）允许相对于 CBAL-OPT 的相对性能存在不平凡的上限，CBAL-OPT 是一种最佳的恒定再平衡投资组合，也许更令人印象深刻的是一些初步实验结果，表明某些具有“可观”竞争（即最坏情况）性能的算法似乎在历史数据序列上也表现得相当好。这些算法和新兴的竞争理论与信息论和计算学习理论的研究直接相关，实际上其中一些算法已经在信息论和计算学习社区中首创。本文的一个目标是试图更好地理解竞争性投资组合算法确实“学习”的程度。在此过程中，我们讨论了一些可以适应数据序列的简单策略。我们提供了理论和实验结果的混合。我们还针对许多研究中引用的标准历史数据序列，对现有算法和新算法的性能进行了更具包容性的研究。此外，我们还提供了来自其他三个历史数据序列的实验。我们得出的结论是，投资组合选择算法具有巨大的潜力，这些算法既受到竞争性考虑的推动，又试图了解数据的统计特性。
The portfolio selection problem is clearly one of the most fundamental problems in the eld of computational nance. Given a set of say m stocks (one of which may be \cash"), the natural online problem is to determine a portfolio for the i th trading period based on the sequence of prices (or equivalently relative prices) for the preceding i ? 1 trading periods. There has been both a growing interest and a growing skepticism concerning the value of a competitive theory of online portfolio selection algorithms. Competitive analysis is based on a worst case perspective and such a perspective is inconsistent with the more widely accepted analyses and theories based on statistical assumptions. The competitive framework does (perhaps surprisingly) permit non trivial upper bounds on relative performance against CBAL-OPT, an optimal ooine constant rebalancing portfolio. Perhaps more impressive are some preliminary experimental results showing that certain algorithms that enjoy \respectable" competitive (i.e. worst case) performance also seem to perform quite well on historical sequences of data. These algorithms and the emerging competitive theory are directly related to studies in information theory and computational learning theory and indeed some of these algorithms have been pioneered within the information theory and computational learning communities. One goal of this paper is to try to better understand the extent to which competitive portfolio algorithms are indeed \learning". In doing so we discuss some simple strategies which can adapt to the data sequence. We present a mixture of both theoretical and experimental results. We also present a more inclusive study of the performance of existing and new algorithms with respect to a standard sequence of historical data cited in many studies. Furthermore, we present experiments from three other historical data sequences. We conclude that there is great potential for portfolio selection algorithms that are motivated by both competitive considerations as well as by an attempt to learn statistical properties of the data.