What Market Information Should I Pay Attention To?
Mathematically speaking, the amount of information contained in a message is proportional to the amount of novelty, or, put another way, the amount of uncertainty. Seems counter intuitive doesn't it? Uncertainty seems to be the antithesis of information. However, real information should tell us something that we don't already know. It should be unpredictable. But most messages we encounter everyday are, in fact, predictable. Usually we sort of know what the guy on CNBC is going to say next. This is because most messages contain a lot of noise—that is, words or phases that we could likely predict.
From this insight, we realize that only the messages we couldn't predict are useful, put another way, contain Information... or have a low probability. If you can predict what someone is going to say then it’s not information... it’s worthless... same goes with models. With pure information, we are in a state of pure uncertainty. The models we build takes what we know nothing about (e.g. when prices are going), and reduces the unpredictability by generating real information.
This is how models should be assessed for validity. If you can’t clearly define a models output a the information value in its purest form, then it’s not a model for a practicing riskmatician.