set is divided in days during which long and short positions are held. They show that the short positions initiated are disastrous for the investor. But even if positions were only held at buy signals, the buy-and-hold strategy cannot consistently be outperformed. Until the 1990s Fama and Blume (1966) remained the best known and most influential paper on mechanical trading rules. The results caused academic skepticism concerning the usefulness of technical analysis.
Return and risk
Diversification of wealth over multiple securities reduces the risk of investing. The phrase ``don't put all your eggs in one basket'' is already well known for a long time. Markowitz (1952) argued that every rule that does not imply the superiority of diversification must be rejected both as hypothesis to explain and as a principle to guide investment behavior. Therefore Markowitz (1952, 1959) published a formal model of portfolio selection embodying diversification principles, called the expected returns-variance of returns rule (E-V-rule). The model determines for any given level of anticipated return the portfolio with the lowest risk and for any given levels of risk the portfolio with the highest expected return. This optimization procedure leads to the well-known efficient frontier of risky assets. Markowitz (1952, 1959) argues that portfolios found on the efficient frontier consist of firms operating in different industries, because firms in industries with different economic characteristics have lower covariance than firms within an industry. Further it was shown how by maximizing a capital allocation line (CAL) on the efficient frontier the optimal risky portfolio could be determined. Finally, by maximizing a personal utility function on the CAL, a personal asset allocation between a risk-free asset and the optimal risky portfolio can be derived.An expected positive price change can be the reward needed to attract investors to hold a risky asset and bear the corresponding risk. Then prices need not be perfectly random, even if markets are operating efficiently and rationally. With his work Markowitz (1952, 1959) laid the foundation of the capital asset pricing model (CAPM) developed by Sharpe (1964) and Lintner (1965). They show that under the assumptions that investors have homogeneous expectations and optimally hold mean-variance efficient portfolios, and in the absence of market frictions, a broad-weighted market portfolio will itself be a mean-variance efficient portfolio. This market portfolio is the tangency portfolio of the CAL with the efficient frontier. The great merit of the CAPM was, despite its strict and unrealistic assumptions, that it showed the relationship between the risk of an asset and its expected return. The notion of trade-off between risk and rewards also triggered the