We characterize dependence in corporate credit and equity returns for 215 firms using a new class of large-scale dynamic copula models. Copula dependence and especially tail dependence are highly variable and persistent, increase significantly in the financial crisis, and have remained high since. The most drastic increases in credit dependence occur in July/August of 2007 and in August of 2011 and the decrease in diversification potential caused by the increases in dependence and tail dependence is large. Credit default swap correlation dynamics are important determinants of credit spreads.

The 4 equity market factors from Fama and French (1993) and Carhart (1997) are pervasive in academia and practice. However, not much is known about their joint distribution and dynamics. We find striking evidence of asymmetric tail dependence across the factors. While the linear factor correlations are small and even negative, the extreme correlations are large and positive, so that the linear correlations drastically overstate the benefits of diversification across the factors. We model the nonlinear factor dependence dynamics and explore their economic importance in a portfolio allocation experiment showing that significant economic value is earned when acknowledging nonlinear dependence.

A method is provided for tuning (i.e. modifying, changing) the impedance of semiconductor components or devices using a focused heating source. The method may be exploited for finely tuning the impedance of semiconductor components or devices, by modifying the dopant profile of a region of low dopant concentration (i.e. increasing the dopant concentration) by diffusion of dopants from adjacent regions of higher dopant concentration through the melting action of a focused heating source, for example a laser. The present invention is in particular directed to the use of lasers in relation to circuits for the creation of conductive links and pathways where none existed before. The present invention more particularly relates to a means wherein impedance modification (i.e. trimming or tuning) may advantageously be carried out as a function of the location of one or more conductive bridge(s) along the length of a gap region.