Assessing the effect of tail dependence in portfolio allocations

Portfolio selection requires an estimate of the degree of association between assets. The Pearson correlation coefficient ρ is the most common measure and estimates the linear correlation implied by the underlying bivariate distribution. Correlations typically rise during stressful times and this nonlinear dependence is measured by a nonzero tail dependence coefficient. We investigate the effect of tail dependence on the estimate of the correlation coefficient. Simulations show that extreme joint losses or gains cause overestimation of the linear correlation coefficient in the presence of tail dependence. The degree of association during the usual days may be smaller than that indicated by the sample correlation coefficient, impacting long-run investments. Simulations show that portfolios based either on the rank correlation or on a conditional version of the Pearson correlation outperform those obtained with classical inputs for moderate and weak strengths of tail dependence association computed from 5 or 10 years of daily data. However, the Pearson correlation coefficient is hard to beat for shorter time horizons and stronger strengths of tail dependence. We recommend estimating the copula pertaining to the data on the presence of tail dependence to select the most suitable correlation coefficient.