A portfolio frontier superior to the Markowitz one-period buy-and hold efficient frontier does exist. Such a superior frontier can be generated by pursuing a rebalancing policy, even under the conditions of random walk. By rebalancing we mean that an investor maintains a fixed but optimal set of weights among the securities in a portfolio throughout an investment period by buying and selling securities at the end of some predetermined intervals.

The advent of the computer has permitted financial theorists to collect and analyze large amounts of financial data. In the field of investments some of the most important work has focused on historical rates of return in investments in common stocks. The classical study in this area is the Fisher-Lorie study [8, 9] in which intern al rates of return were calculated for every security listed on the New York Stock Exchange from 1926–1965. Other studies related to the area have been complicated by Herzog [10], Fisher [6, 7], Latané and Young [11], Soldofsky and Biderman [12], and Evans [3, 4].