Before revision:  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. Relative to the Kelly information benchmark, variation in people's risk aversion does indeed cause a drop in expected returns. However, the amount of the drop is also information-driven: it is proportional to the absolute difference between the relative entropy and its celebrated generalization -- the R\'enyi divergence 4 . Given the widespread use of the R\'enyi divergence in science and engineering, and because financial returns are much easier to imagine, we expect our intuition to be useful in a broad range of fields.
After revision:  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 Disagreement is an essential element of science and life in general. Currently, the amount of the drop is also information-driven: it is proportional to the absolute difference between the relative entropy and its celebrated generalization -- the R\'enyi divergence 4 . Given the widespread use of the R\'enyi divergence in science and engineering, and because financial returns are much easier to imagine, we expect our intuition to be useful in a broad range of fields.