This is a slightly more technical Version of the 2010 BT Lecture, Oxford University, July 14, 2010. This can also be used as a second technical companion to the essay On Robustness and Fragility in the second edition of The Black Swan (the first one being the Fourth Quadrant). I also introduce a simple practical method to measure (as an indicator of fragility) the sensitivity of a portfolio (or balance sheet) to model error.Background
The central idea in The Black Swan is about the limits in the knowledge about of small probabilities, both empirically (interpolation) and mathematically (extrapolation)1, and its consequence. This discussion starts from the basis of the isolation of the “Black Swan domain”, called the “Fourth Quadrant”2, a domain in which 1) there is dependence on small probability events, and 2) the incidence of these events is incomputable. The Fourth Quadrant paper cursorily mentioned that there were two types of exposures, convex and concave and that we need to “robustify”3 though convexification. This discusses revolves around convexity biases as explaining the one-way failure of quantitative methods in social science.