  A constant rebalanced portfolio is an asset allocation algorithm which keeps
the same distribution of wealth among a set of assets along a period of time.
Recently, there has been work on on-line portfolio selection algorithms which
are competitive with the best constant rebalanced portfolio determined in
hindsight. By their nature, these algorithms employ the assumption that high
returns can be achieved using a fixed asset allocation strategy. However, stock
markets are far from being stationary and in many cases the wealth achieved by
a constant rebalanced portfolio is much smaller than the wealth achieved by an
ad-hoc investment strategy that adapts to changes in the market. In this paper
we present an efficient Bayesian portfolio selection algorithm that is able to
track a changing market. We also describe a simple extension of the algorithm
for the case of a general transaction cost, including the transactions cost
models recently investigated by Blum and kalai. We provide a simple analysis of
the competitiveness of the algorithm and check its performance on real stock
data from the New York Stock Exchange accumulated during a 22-year period.
