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MARKET MAKING AND REVERSAL ON THE STOCK EXCHANGE

Victor Niedbrhoffer University of Chicago and M. F. M. Osborne Washington, D.C.

The accurate record of stock market ticker prices displays striking properties of dependence. We find for example that after a decline of} of a point between transactions, an advance on the next transaction is three times as likely as a decline. Further examinations disclose that after two price changes in the same direction, the odds in favor of a continuation in that direction are almost twice as great as after two changes in opposite directions.

The dealer (specialist) in a stock typically quotes the market by announcing the highest buy order and lowest sell order carried on his book. But these orders tend to be concentrated at integers (26, 43), halves (26J, 435), quarters and odd eighths in descending preference. This non-uniform distribution of orders produces some non-random effects in stock price motion. These properties of the stock market are typical of markets in many second-hand goods.

introduction

Our objective in this report is to find laws of price fluctuation in the stock market. We shall examine the most elementary data discernible, the record of successive transactions on the ticker tape. This record, which is published in usable form by Francis Emory Fitch, Inc., provides precise and abundant information.

It is convenient at the outset to compare the movements of successive trans ­actions with those predicted by a random walk model, the epitome of un ­relieved bedlam. The proponents of the random walk state that changes in the price of consecutive transactions are distributed independently of each other. The assumption of independence means that the change in price following the current transaction will not be influenced by the sequence of preceding price changes. That is:

and РЈ, is the price at which the rth transaction occurred.1 Although the prob ­ability of an advance in the future can be estimated from the relative frequenc}' of advances in the past, this probability does not change from transaction to transaction.

Godfrey, Granger, and Morgenstein [o] have argued that model (1) pro ­vides a reasonably accurate description of market behavior. Other writers have stated that model (1) fits when Yt represents the price at time t rather than the price at the fth transaction (cf. the articles in [2]). Finally, some scholars de ­fine a series as independent unless an investor can use the observed dependence to increase his expected profits [4].

In section 2, however, an analysis of a sample of Dow Jones Industrial Stocks shows considerable dependence between transactions. The results in ­dicate that after a price rise the odds are approximately 3 to 1 that the next non-zero change will be a decline, but after a decline the odds are about 3 to 1 in favor of a rise. Therefore, another model may be more appropriate for the explanation of these changes. In section 3, we analyze the process of change in ticker prices by employing statistical techniques developed and recommended by Goodman [l, 6]. We find, for example, that after two changes in the same direction the odds in favor of a continuation in the direction of a particular price move arc almost twice as great as after two changes in alternate direc ­tions.

With this empirical evidence on non-randomness in mind, we consider the structure of developed trading markets with particular applications to the stock market in section 4. This leads to definite predictions about the proper ­ties of stock prices. These predictions are tested in section 5 by a second sample of data taken from all the listed stocks. The predictions are in the main con ­firmed. They are natural consequences of the market making process.