Nonstationary Optimization Approach for Finding Universal Portfolios

The definition of universal portfolio was introduced in the nancial literature in order to describe the class of portfolios which are constructed directly from the available observations of the stocks behavior without any assumptions about their statistical properties. Cover has shown that one can construct such portfolio using only observations of the past stock prices which generates the same asymptotic wealth growth as the best constant rebalanced portfolio which is constructed with the full knowledge of the future stock market behavior. In this paper we construct universal portfolios using totally different set of ideas drawn from nonstationary stochastic optimization. Also our portfolios yield the same asymptotic growth of wealth as the best constant rebalanced portfolio constructed with the perfect knowledge of the future, but they are less demanding computationally. Besides theoretical study, we present computational evidence using data from New York Stock Exchange which shows, among other things, superior performance of portfolios which explicitly take into account possible nonstationary market behavior.