To find the general solution to the wave equation, we first prove an important lemma which has many useful applications in the theory of waves, the principle of superposition. Much like the principle of superposition which you learned in your introductory course on E&M, this principle allows us to quickly solve complex problems by breaking them into smaller parts for which we know the solutions. Thus, according to the EMH, no investor has an advantage in predicting a return on a stock price because no one has access to information not already available to everyone else. In efficient markets, prices become not predictable but random, so no investment pattern can be discerned. A planned approach to investment, therefore, cannot be successful. This "random walk" of prices, commonly spoken about in the EMH school of thought, results in the failure of any investment strategy that aims to beat the market consistently. In fact, the EMH suggests that given the transaction costs involved in portfolio management, it would be more profitable for an investor to put his or her money into an index fund.