Minimax regret portfolios for restricted stock sequences

A stock market game where one player (the investor) plays against another (the market) with payoff given by the ratio of the investor´s wealth (at time n) to the market wealth given by the performance of the best constant rebalanced portfolio in hindsight on the market sequence is analysed. This paper consider markets in which no stock underperforms the average by a given amount, and consider portfolio strategies that allow both short selling and margin. The possibility of universal portfolios in the market which do as well against any specific stock sequence. Putting a constraint α on stock performance creates the opportunity for short selling and margin. This increases the relative performance of the universal portfolio.