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

Bell, Peter Newton (2014): Design of Financial Derivatives: Statistical Power does not Ensure Risk Management Power.

Abstract

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Production, uncertainty, financial derivative, index number, statistical power, risk management
• Subjects: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C43 - Index Numbers and Aggregation; D - Microeconomics > D2 - Production and Organizations > D29 - Other; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty; G - Financial Economics > G2 - Financial Institutions and Services > G23 - Non-bank Financial Institutions ; Financial Instruments ; Institutional Investors; G - Financial Economics > G3 - Corporate Finance and Governance > G32 - Financing Policy ; Financial Risk and Risk Management ; Capital and Ownership Structure ; Value of Firms ; Goodwill; M - Business Administration and Business Economics ; Marketing ; Accounting ; Personnel Economics > M1 - Business Administration > M11 - Production Management

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