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 (including cost-optimal products) and hybrid hedging (where a partial hedge is built into an optimal investment product) are considered. Duality between hedging and investment is demonstrated with applications to optimal risk recycling. A geometric interpretation of rationality is presented.