Information Geometry of Risks and Returns

TL;DR

This paper uncovers a geometric framework linking risks and returns, guiding the design of optimal hedging and investment products through a duality principle and geometric interpretation.

Contribution

It introduces a novel geometric structure that unifies hedging and investment, providing new insights into optimal product design and risk management strategies.

Findings

Duality between hedging and investment demonstrated

Geometric interpretation of rationality provided

Optimal risk recycling strategies identified

Abstract

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.