In the presence of a large number of stocks, we examine the problem of computation 
of a constant rebalanced portfolio that would have made the most wealth on a given 
sequence of stock returns.  A greedy algorithm is presented in which at each step 
either a new stock is added to the portfolio or the relative weight given to an 
already included stock is adjusted.  We prove that the algorithm computes a portfolio 
that approaches the maximum wealth portfolio, with drop from the maximal exponent bounded 
by v/k where v is an empirical volatility and k is the number of steps of the algorithm.
Empirically we find that out of thousands of available stocks, only a handful are needed 
to come close to the maximum wealth constant rebalanced portfolio of all publicly available 
stocks.  

This theory provides the basis for a universal portfolio strategy that mixes across 
subsets of stocks.  It provides a sequence of portfolios that evolve in time, and for any 
T time periods acheives a wealth exponent that drops from the maximum by not more than
the square root of V(log M)/T.  The relationship of this to past work by Cover and 
Ordentlick and by Hembolt and Warmuth is discussed.