Hedging Extreme Co-movements *

Based on a recent theorem due to the authors, it is shown how the extreme tail dependence between an asset and a factor or index or between two assets can be easily calibrated. Portfolios constructed with stocks with minimal tail dependence with the market exhibit a remarkable degree of decorrelation with the market at no cost in terms of performance measured by the Sharpe ratio. Over a hundred years ago, Vilfred Pareto discovered a statistical relationship, now known as the 80-20 rule, which manifests itself over and over in large systems: " In any series of elements to be controlled, a selected small fraction, in terms of numbers of elements, always accounts for a large fraction in terms of effect. " The stock market is no exception: events occurring over a very small fraction of the total invested time may account for most of the gains and/or losses. Diversifying away such large risks requires novel approaches to portfolio management, which must take into account the non-Gaussian fat tail structure of distributions of returns and their dependence. Recent shocks and crashes have shown that standard portfolio diversification work well in normal times but may break down in stressful times, precisely when diversification is the most important: as a caricature, one could say that diversification works when one does not really need it and may fail severely when it is most needed. Technically, the question boils down to whether large price movements occur mainly in an isolated manner or in a coordinated way. This question is vital for fund managers who take advantage of the diversification to hedge their risks. Here, we introduce a new technique to quantify and empirically estimate the propensity for assets to exhibit extreme co-movements, through the use of the so-called coefficient of tail dependence. Using a factor model framework and tools from extreme value theory, we provide novel analytical formulas for the coefficient of tail dependence between arbitrary assets, which yields an efficient non-parametric esti-mator. We then construct portfolios of stocks with minimal tail dependence with the market represented by * We acknowledge helpful discussions and exchanges with J.P. Laurent. Donnell Foundation 21st century scientist award/studying complex system.