Underperforming Investment Strategy

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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 provide mathematical proof if possible

Solution:

The random walk theory asserts that price movements will not follow any patterns or trends and that past price movements cannot be used to predict future price movements.
The Weak Form EMH asserts that all past market prices and data are fully reflected in securities prices. In other words, technical ...