A New Theory of Information Acquisition and Recovery: Intrinsic Geometry Approach with Asset Pricing Applications

Abstract

We introduce a novel geometry-based method of modelling information that encompasses entropy-based approaches. A key contribution is that we explicitly construct the optimal path to acquire information. The economic driver of this geometry-based framework is knowledge state dependent marginal cost of information acquisition. The modelling benefits of our framework is exemplified by studying an extended myopic portfolio choice problem in asset pricing with information acquisition. We show using theory and empirical evidence that return and volatility curvatures, derived from the optimal information acquisition path, significantly explain equilibrium risky asset return level and volatility level. Another key contribution of our framework is information recovery. When an econometrician only observes the agent’s portfolio allocations, we provide geometric conditions for which the agent’s mean-variance information dynamics can be successfully recovered. Beyond asset pricing, our method of information acquisition and information recovery is applicable to general expected utility maximization problems within a general stochastic environment.