The paper by Harry M. Kat, titled "The Dangers of Using Correlation to Measure Dependence," discusses the limitations of using correlation as a measure of dependence in financial asset returns. While correlation is widely used in modern portfolio theory to assess diversification potential, it is not always a reliable indicator, especially when dealing with non-elliptical distributions that exhibit skewness and kurtosis. The author highlights that correlation can be misleading, as it does not capture the full dependence structure, particularly in non-elliptical distributions. Examples are provided to illustrate how conditional correlations, which split data based on variable sizes or volatilities, can lead to incorrect conclusions about dependence. The paper concludes that low or high correlations do not necessarily imply low or high dependence, and alternative methods are needed to accurately measure dependence in complex real-life distributions.The paper by Harry M. Kat, titled "The Dangers of Using Correlation to Measure Dependence," discusses the limitations of using correlation as a measure of dependence in financial asset returns. While correlation is widely used in modern portfolio theory to assess diversification potential, it is not always a reliable indicator, especially when dealing with non-elliptical distributions that exhibit skewness and kurtosis. The author highlights that correlation can be misleading, as it does not capture the full dependence structure, particularly in non-elliptical distributions. Examples are provided to illustrate how conditional correlations, which split data based on variable sizes or volatilities, can lead to incorrect conclusions about dependence. The paper concludes that low or high correlations do not necessarily imply low or high dependence, and alternative methods are needed to accurately measure dependence in complex real-life distributions.