Measuring the Informativeness of Market Statistics

Market statistics can be viewed as noisy signals for true variables of interest. These signals are used by individual recipients of the statistics to imperfectly infer different variables of interest. This paper presents a framework under which the 'informativeness' of statistics is defined as their efficacy as the basis of such inference, and is quantified as expected distortion, a concept from information theory. The framework can be used to compare the informativeness of a set of statistics with that of another set or its theoretical limits. Also, the proposed informativeness measure can be computed as solutions to familiar problems under a range of assumptions. As an application, the measure is used to explain the difference in usage levels of temperature derivatives across different base weather stations. The informativeness measure is found to be at least as effective as city size measures in explaining the difference in usage levels