Defensive online portfolio selection

The class of defensive online portfolio selection algorithms, designed for finite investment horizon, is introduced. The game constantly rebalanced portfolio and the worst case game constantly rebalanced portfolio, are presented and theoretically analysed. The analysis exploits the rich set of mathematical tools available by means of the connection between universal portfolios and the game-theoretic framework. The empirical performance of the worst case game constantly rebalanced portfolio algorithm is analysed through numerical experiments concerning the FTSE 100, Nikkei 225, Nasdaq 100 and S&P500 stock markets for the time interval, from January 2007 to December 2009, which includes the credit crunch crisis from September 2008 to March 2009. The results emphasise the relevance of the proposed online investment algorithm which significantly outperformed the market index and the minimum variance Sharpe-Markowitz’s portfolio.