Stochastic Nonstationary Optimization for Finding Universal Portfolios

We apply ideas from stochastic optimization for defining universal portfolios. Universal portfolios are that 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 a different set of ideas drawn from nonstationary stochastic optimization. Our portfolios yield the same asymptotic growth of wealth as the best constant rebalanced portfolio constructed with the perfect knowledge of the future and they are less demanding computationally compared to previously known universal portfolios. We also present computational evidence using New York Stock Exchange data which shows, among other things, superior performance of portfolios which explicitly take into account possible nonstationary market behavior.