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This paper is part of an ongoing investigation of "pragmatic information",defined in Weinberger (2002) as "the amount of information actually used inmaking a decision". Because a study of information rates led to the Noiselessand Noisy Coding Theorems, two of the most important results of Shannon'stheory, we begin the paper by defining a pragmatic information rate, showingthat all of the relevant limits make sense, and interpreting them as theimprovement in compression obtained from using the correct distribution oftransmitted symbols.  The first of two applications of the theory extends the information theoreticanalysis of the Kelly Criterion, and its generalization, the horse race, to aseries of races where the stochastic process of winning horses, payoffs, andstrategies depend on some stationary process, including, but not limited to thehistory of previous races. If the bettor is receiving messages (sideinformation) about the probability distribution of winners, the doubling rateof the bettor's winnings is bounded by the pragmatic information of themessages.  A second application is to the question of market efficiency. An efficientmarket is, by definition, a market in which the pragmatic information of the"tradable past" with respect to current prices is zero. Under this definition,markets whose returns are characterized by a GARCH(1,1) process cannot beefficient.  Finally, a pragmatic informational analogue to Shannon's Noisy Coding Theoremsuggests that a cause of market inefficiency is that the underlyingfundamentals are changing so fast that the price discovery mechanism simplycannot keep up. This may happen most readily in the run-up to a financialbubble, where investors' willful ignorance degrade the information processingcapabilities of the market.

Pragmatic Information Rates, Generalizations of the Kelly Criterion, and Financial Market Efficiency