Risk Allocation: The Double Face of Financial Derivatives

For the past two decades, derivatives provided the core financial innovation for risk- management and risk-sharing activities. However, in the aftermath of the 2007-2008 crisis, derivatives have started received, partly for good reason, an increasingly bad press. The main purpose of this paper is to lay the foundations for a theoretical frame-work in which systemic risk is centrally involved in the assessment of derivative usage. We begin by introducing a definition of systemic risk based on a Mixed Binomial model for the number of defaults. Then, we define an allocation to be efficient if it maximizes the Aggregate Sharpe ratio of the economy, i.e. if it allows to finance the maximum amount of productive investments while minimizing the overall systemic risk of the economy. We then say that a derivative is socially efficient or cooperative if it leads to an allocation having higher Aggregate Sharpe ratio. We illustrate the applicability of our model by means of a qualitative analysis of three types of derivatives, namely Plain vanilla, Asset backed securities and Credit default-swaps.