Online Algorithms to Determine Large Portfolios

technique for portfolio selection monitoring reward and risk.
In a seminal paper Cover (1991) proposed a different understanding
of portfolio risk by measuring it wrt a reference portfolio.
His online trading strategy results in a portfolio P which has
asymptotically the same exponential growth rate as the reference
portfolio. The offline reference portfolio is chosen as the optimal
portfolio with a fixed distribution determined ex poste,
ie with full knowledge of the stock rates within the considered
time period. The log-optimal portfolio P is called universal
as no statistical assumptions on market parameters are made.

Requiring extensive computation this strategy has been limited
to universal portfolios containing up to three assets. By using new
approaches this strategy in extended to universal portfolios of
arbitrary size.

Results on the German stock market (1987-1997, daily basis) confirm
that the universal portfolio outperforms the value-line-index
and show its compatibility with the DAX-30.