Problem: It was stated that under Weak-Form EMH you cannot design an investment strategy which "beats the market" (gives you higher return than average market return, given the riskiness), if such a strategy is based only on analyzing past price movements. Is it possible to design an investment strategy, based on past price movements, which systematically underperforms? By underperforms it is meant that its expected return is lower than average market return on portfolios with the same variance.
Please illustrate mathematical proof if possible.