标题： 带负参数的多样性加权投资组合 显示英文标题

标题： Diversity-Weighted Portfolios with Negative Parameter

摘要： 我们分析了Fernholz、Karatzas和Kardaras（Finance Stoch 9(1):1-27, 2005）研究的多样性加权投资组合的一个负参数变体，该策略将财富的反比例分配给每家公司，与公司的市场权重成反比（其市值与整个市场市值的比率）。 我们在对波动率结构的非退化假设以及市场权重具有正下界假设下，证明了这种策略在概率上优于市场。 提出了几种对该投资组合的修改方案，在较弱的“无失败”条件下仍能优于市场，其中一种是基于排名的策略。 实证研究表明，如本文所研究的这些策略确实具有超越市场的潜力，并且在现实的按比例交易成本下，可能成为更有吸引力的投资机会。 显示英文摘要

摘要： We analyze a negative-parameter variant of the diversity-weighted portfolio studied by Fernholz, Karatzas, and Kardaras (Finance Stoch 9(1):1-27, 2005), which invests in each company a fraction of wealth inversely proportional to the company's market weight (the ratio of its capitalization to that of the entire market). We show that this strategy outperforms the market with probability one, under a non-degeneracy assumption on the volatility structure and the assumption that the market weights admit a positive lower bound. Several modifications of this portfolio, which outperform the market under milder versions of this "no-failure" condition, are put forward, one of which is rank-based. An empirical study suggests that such strategies as studied here have indeed the potential to outperform the market and to be preferable investment opportunities, even under realistic proportional transaction costs.