Information Geometry of Risks and Returns

We reveal a geometric structure underlying both hedging and investment products. The structure follows from a simple formula expressing investment risks in terms of returns. This informs optimal product designs. Optimal pure hedging is considered (including cost-optimal products) as well as hybrid hedging where a partial hedge is built into an optimal investment product. Duality between hedging and investment is demonstrated with applications to optimal risk recycling. Geometric interpretation of rationality is presented.