RATE-DISTORTION THEORY AND THE VOLATILITY OF ASSET PRICES

A market with many traders clears at a single price. The intuition that such a market can be modeled as a multiple access channel with many source inputs and a single output is confirmed and supported by single stock trading data. If all stocks in an exchange with a price index are so traded, then the Capital Asset Pricing Model (CAPM) of the index should find the index a prediction of future returns to holding a portfolio of the indexed stocks. This inference is shown to be true by applying Shannon's rate distortion theorem to the CAPM, and thereby ending the decade-old controversy that the CAPM cannot explain stock and bond price volatility. Data from the NYSE are found to be compatible with the CAPM rate distortion function. In contrast to communication system channels, market channels cannot operate at channel capacity, but rather at a mutual information rate demanded by trader profit taking. This rate compared to the trader information source rate distortion function determines the minimum price distortion that can be expected of markets.