Asset-based approaches – usually involving asset transfers and/or asset building – are increasingly central to thinking about poverty alleviation, social protection, graduation and livelihood resilience. Although the notion of assets is well established in the literature, the meanings of and relationships between asset(s), livelihood capital(s), risks(s), welfare and wellbeing, and graduation need further analysis. We examine issues arising from asset-based approaches to poverty reduction and introduce the idea of ‘asset-ness’ – the qualities and characteristics of different assets – which have received little attention from those promoting or designing asset-based social protection programmes. We argue that asset-ness provides a key to understanding differences in the impacts of asset-based social protection and associated processes and dynamics of graduation. As such the article aims to advance understanding of graduation theory. We develop this argument with reference to domestic livestock, which are commonly distributed to poor people as part of asset-based poverty alleviation and social protection programmes.