A Study of Future Markets and Stock Price Volatility Using Shannon's Separation Theorem

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Information relevant to market transactions is usually generated exogenously and at random times. A given sample of these market "fundamentals" must be reliably transmitted to prices before the next sample occurs if the market is to be efficient. Markets clear sequentially at a frequency which is typically far in excess of the average frequency of fundamentals. This time-base relation between fundamentals and market clearing prices is shared by communications channels which transmit individual information source samples using multiple transmissions on the channel. But the market-channel analog is incomplete because market agents are motivated by profits while channel users pursue reliable communication. This proposal suggests these sometimes conflicting goals can be resolved. The embodiment of the suggestion is a demonstration that a popular futures market model is identical to a model of bandwidth expansion over a channel with noiseless feedback when market agents tradeoff profits against reliable communication. Empirical tests of this tradeoff are proposed for a grain futures market. The demonstration also suggests that sequential auction models act as estimators of information sources and therefore are relevant to the controversy surrounding price volatility in stock valuation models. The research estimates information rates for recognized stock market fundamentals and establishes volatility standards by comparing source information rates with the stock valuation model capacity. The market models considered assume source information is generated in randomly timed bursts. Consequently, the multiple- trader futures model is a study in multiple-access channel source coding. In an efficient market with optimal profit-taking and information transfer, both testable hypotheses, agent trading behavior should solve a multiple-access coding problem. Tat solutions of pen problems in market theory can contribute to open problems in communication theory is further evidenced by showing that the determination of the proportion of informed market participants solves a challenging problem of finding the capacity of an arbitrarily varying channel. The significance of the study lies in the recognition that there are no known tests yielding a standard measure of the ultimate reliability with which market prices can reflect fundamental information. Successful empirical studies will establish such a standard. In addition, treating markets as a symbiont of communication theory offers the prospect that actual markets can serve as experimental resources for solving significant problems in communication theory.