Since 2008, eurozone sovereign yields have diverged sharply, and so have the corresponding credit default swap (CDS) premia. At the same time, banks' sovereign debt portfolios have featured an increasing home bias. In this paper, we investigate the relationship between these two facts, and its rationale. First, we inquire to what extent the dynamics of sovereign yield differentials relative to the swap rate and CDS premia reflect changes in perceived sovereign solvency risk or rather different responses to systemic risk due to the possible collapse of the euro. We do so by decomposing yield differentials and CDS spreads in a country‐specific and a common risk component via a dynamic factor model. We then investigate how the home bias of banks' sovereign portfolios responds to yield differentials and to their two components, by estimating a vector error‐correction model on 2007–13 monthly data. We find that in most countries of the eurozone, and especially in its periphery, banks' sovereign exposures respond positively to increases in yields. When bank exposures are related to the country and common risk components of yields, it turns out that (1) in the periphery, banks increase their domestic exposure in response to increases in country risk, while in core countries they do not; (2) in most eurozone countries banks respond to an increase in the common risk factor by raising their domestic exposures. Finding (1) suggests distorted incentives in periphery banks' response to changes in their own sovereign's risk. Finding (2) indicates that, when systemic risk increases, all banks tend to increase the home bias of their portfolios, making the eurozone sovereign market more segmented. — Niccolò Battistini, Marco Pagano and Saverio Simonelli