Is Information Uncertainty Diversifiable? A Short Bayesian Answer

The properties of information, including "information uncertainty", can be understood only Bayesianly. Common formulations that define information uncertainty in terms of just statistical "precision" (i.e. sampling variance), or any one estimator characteristic (e.g. bias), are inadequate for generalized Bayesian analysis. Methods that deny information a Bayesian characterization are bound to yield Bayesianly incorrect generalizations. In the Bayesian way of thinking, information risk impacts the likelihood function f(x|φ,⋅), which captures the subjective strengths and weaknesses of signal x with respect to unknown φ. By affecting f(x|φ,⋅), information uncertainty alters posterior beliefs f(φ|x,⋅), and therefore also asset prices and expected rates of return. Less obviously, formal Bayesian allowance for information uncertainty can lead to unexpected reinterpretations of information, which can reduce (or increase) the cost of capital. A striking example is shown based on Simpson's paradox