THE EFFICIENCY OF INVESTMENT INFORMATION

We investigate how the description of a correlated information V impro ves the investment in the stock market X. The objective is to maximize the growth rate of wealth in repeated investments. We find a single-l etter characterization of the incremental growth rate Delta(R), the ma ximum increase in growth rate when V is described to the investor at r ate R. The incremental growth rate specialized to the horse race marke t is related to source coding with side information of Wyner and Ahlsw ede-Korner. We provide two horse race examples: jointly binary and joi ntly Gaussian. The initial efficiency Delta'(0) is the maximum possibl e increase in the growth rate per bit of description. We show that the initial efficiency is related to the dependency between V and the mar ket. In particular, for the horse race market, the initial efficiency is the square of the Hirschfeld-Gebelein-Renyi maximal correlation bet ween V and X. This provides a connection with the hypercontraction of the Markov operator of Ahlswede and Gacs. For the general market the i nitial efficiency is 1 when the side information V is equal to the sto ck market outcome X.