Security markets in major industrial countries have frequently been referred to as close to perfect markets. Probably the highest quality market for a class of securities is the United States government bill market; however, it is also frequently inferred that the United States listed equity market is also a near perfect market. In a perfect market, no opportunities for profit based upon past price movements or any other past data should exist; stocks in a perfect market are always at their proper price except for purely random fluctuations.

The basic idea behind the random walk hypothesis is that in a free competitive market the price currently quoted for a particular good or service should reflect all of the information available to participants in the market that influence its present price. To the extent that future conditions of the demand or supply are currently known, their effect on the current price should be properly taken into account.

In recent years, there has been considerable interest in the random walk theory of stock price behavior. This theory, as applied to the stock market, implies that past stock-price movements cannot be used to predict future market prices in such a way as to “profit” from the predictions. By not “profiting,” we mean that a trader using the past history of stock prices cannot apply mechanical decision rules that result in a consistently better performance than a simple buy and hold strategy. If stock price movements were to become systematic so that a “profit” were possible, proponents of the random walk theory argue that a sufficient number of market participants would quickly recognize the recurring pattern and exploit it. In exploiting it, they would drive out the opportunity for “profit,” causing the price series to approximate a random walk.

Many Wall Street financial analysts believe that a positive relationship exists between the level of short interest in equities and subsequent movements in the prices of these equities. This view is apparently grounded in the belief that short traders will push prices up in the future as they attempt to cover their short positions.

Perhaps one of the most time-honored of technical market indicators is the Advance-Decline Line. Its predictive powers as a leading indicator of the general market have been written about, and historical data on this index are published in Barron's. However, the validity of this series as a leading indicator has not been subjected to rigorous statistical analysis.

Analysts and investment advisors have long searched for investment tools that would either furnish predictive probabilities for future security price movements, or would aid in minimizing losses. One such tool, often recommended by market practitioners, is the Moving Average. This article describes a series of experiments that were performed upon actual market data, using Moving Averages of different lengths and weights, and presents results of the experiments. Conclusions derived from these experiments are suggested.

Recent literature has witnessed the emergence of an impressive body of empirical evidence relating to the relationship which exists between successive security price changes. The great majority of this evidence has tended to support what has come to be known as the theory of random walks in security prices—that is, the theory that successive security price changes behave as independent random variables, which implies that knowledge of “the past history of a series of price changes cannot be used to predict future changes in any ‘meaningful’ way.”

We shall investigate the problem of optimal exercising strategy for option holders for the case in which option holders are averse to risk. A model of stock price changes incorporating the Lognormal random walk assumption will be combined with a class of utility functions containing diminishing marginal utility of money. In general, the strategy of waiting until the last possible day to exercise an option, which maximizes expected value, will not maximize expected utility. The strategy which maximizes expected utility is obtained by a dynamic programming formulation of the decision problem. At each day (or decision stage), the option holder may choose to act (exercise) or wait until the next day. Working backwards from the last day, a series of critical prices are obtained, with the optimal strategy being as follows: act if the stock price on any day is greater than the critical price for that day; otherwise, wait. Using the concept of proportional risk aversion developed by Pratt, we will demonstrate that, under certain conditions, a utility function which exhibits increasing proportional risk aversion is sufficient to create a series of finite critical prices. Moreover, once an option is exercised, the option holder continually faces a tactical decision to hold the stock and wait for capital gains or sell and take profits as ordinary income, thereby avoiding further risk. This decision may also be optimized by a dynamic programming scheme similar to the approach used above.