Misc,
Optimization of relative arbitrage
(2014)cite arxiv:1407.8300Comment: 32 pages, 5 figures, 2 tables.
Abstract
In stochastic portfolio theory, a relative arbitrage is an equity portfolio
which outperforms a benchmark portfolio over a specified horizon. When the
market is diverse and sufficiently volatile, and the benchmark is the market or
a buy-and-hold portfolio, functionally generated portfolios provide a
systematic way of constructing relative arbitrages. In this paper we show that
if the market portfolio is replaced by the equal or entropy weighted portfolio
among many others, no relative arbitrages can be constructed using functionally
generated portfolios. We also introduce and study a shaped-constrained
optimization problem for functionally generated portfolios in the spirit of
maximum likelihood estimation of a log-concave density.
