We use a machine-learning algorithm, the LASSO, to study the cross-sectional dependence of sovereign credit default swap (CDS) spreads on real-time, country-specific macro indicators during the different phases of the eurozone sovereign debt crisis. In contrast with the existing literature, we find that macro fundamentals played an important, albeit time-varying, role in explaining the cross-section of sovereign CDS spreads, with an average R2 of 98.5%. Moreover, we show how the cross-sectional regression coefficients help predict the VSTOXX volatility index, out of sample.