We exhibit an algorithm for portfolio selection that asymptotically outperforms the best stock in the market. Let x<sub>i</sub>= (x<sub>i</sub>, x<sub>i2</sub>,…, x<sub>im</sub>)-super-t denote the performance of the stock market on day i, where x<sub>ii</sub> is the factor by which the jth stock increases on day i. Let b<sub>i</sub>= (<sub>bi1</sub> b<sub>i2</sub>, b<sub>im</sub>)-super-t, b;<sub>ij</sub>> 0, b<sub>ij</sub>= 1, denote the proportion b<sub>ij</sub> of wealth invested in the "j" th stock on day i. Then S<sub>n</sub>= II<sub>i</sub>-super-n= bi-super-tx<sub>i</sub> is the factor by which wealth is increased in "n" trading days. Consider as a goal the wealth S<sub>n</sub>*= max<sub>b</sub> II<sub>i</sub>-super-n=<sub>1</sub> b-super-tx<sub>i</sub> that can be achieved by the best constant rebalanced portfolio chosen after the stock outcomes are revealed. It can be shown that Sn * exceeds the best stock, the Dow Jones average, and the value line index at time "n." In fact, S<sub>n</sub>* usually exceeds these quantities by an exponential factor. Let x<sub>1</sub>, x<sub>2</sub>, be an arbitrary sequence of market vectors. It will be shown that the nonanticipating sequence of portfolios <formula format="inline"><file name="mafi_1_mu1.gif" type="gif" /></formula> db yields wealth <formula format="inline"><file name="mafi_1_mu2.gif" type="gif" /></formula> such that <formula format="inline"><file name="mafi_1_mu3.gif" type="gif" /></formula>, for every bounded sequence x<sub>1</sub>, x<sub>2</sub>…, and, under mild conditions, achieve Copyright 1991 Blackwell Publishers.
