Linear Correlation Estimation
by Filip Lindskog of ETH-Zentrum
December 11, 2000
Abstract: Most financial models for modelling dependent risks are based on the assumption of multivariate normality and linear correlation is used a a measure of dependence. However, observed financial data are rarely normally distributed and tend to have marginal distributions with heavier tails. Furthermore, the observed synchronized extreme falls in financial markets can not be modelled by multivariate normal distributions. However, there are other elliptical distributions with these properties and the assumption of multivariate normality can often be replaced by the assumption of ellipticality. A useful property of elliptical distributions is that these distributions support the standard approaches of risk management. Value-at-Risk fulfills the desired properties of a risk measure and the mean-variance (Markowitz) approach can be u ed for portfolio optimization.
between Kendall's tau and the linear correlation coefficient r is shown to hold for (essentially) all elliptical distributions and the estimator of linear correlation provided by this relation is studied. This non-parametric estimator inherit the robustness properties of the Kendall's tau estimator and is an efficient (low variance) estimator for all elliptical distributions.