Design of Financial Derivatives: Statistical Power does not Ensure Risk Management Power

This paper presents a modelling framework for analysis of financial derivatives. The framework analyzes the derivative from the perspective of a producer who has uncertain quantity of production. Quantity has a statistical relationship to an index number, or risk factor, and the producer can buy a derivative on the index number, which provides the producer with an indirect hedge against low quantity. A practical concern is how to create such an index number: one approach is to define the index as an estimated regression equation with maximal explanatory power across some set of possible equations. I use my framework to conduct a simulation experiment that shows picking an index with maximal explanatory power can lead to a financial derivative with suboptimal efficiency. In other words, I show that it is possible for one index to have lower statistical power than another but higher risk management power. This result is due to the fact that statistical power is measured over all values of quantity, whereas losses only occur for low quantity and it is sufficient (in some cases) for the index to have strong explanatory power for low values of quantity to serve as an effective risk management tool.