  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.
