Before revision:  In 1956 Kelly used this technique to propose an intuitive interpretation of relative entropy 1 . He considered a growth-optimizing investor in a game with mutually exclusive outcomes (a "horse race") and showed that the rate of return expected by such an investor is equal to the relative entropy which measures disagreement between the investor's believed probabilities and the official odds. Effectively, Kelly showed that a growth-optimizing investor would expect on average to convert 1 bit of additional information into a 100\% return on investment. Notwithstanding the mathematics, this interpretation has been vigorously criticized by Samuelson as dangerous on the grounds that most people are not growth-optimizing 2,3 . Here we show that a deeper connection between information and expected returns is in fact true.
After revision:  In 1956 Kelly used this technique to propose an intuitive interpretation of relative entropy 1 2,3 . Here we show that a deeper connection between information and expected returns is in fact true.