Capital asset pricing model using copula based SUR for interval-valued energy index

The objective of this paper is to analyze risk, return and dependency of energy index based in CAPM with copula based Seemingly Unrelated Regression (SUR) model and convex combination interval-valued data. The data are daily maximum and minimum of MSCI US, UK and EU energy index start from Feb 12, 2001 to Dec 22, 2017 for a total of 4,404 observations. The results show that Gaussian is the most appropriate copula family for data with proper distribution of each CAPM equation is student-t. The copula dependency between EU-UK is positive and high value (0.7392) while EU- US and UK-US are positive and low value (0.0803 and 0.036, respectively). The beta risk of EU and UK is high 0.8 while of US is 1.05.