Sovereign wealth funds (SWFs) have been increasingly active over the past decade, with governments raising concern regarding their actual motives and the potential for cross-border interest in national strategic sectors. The aim of this paper is to contribute to the existing literature by improving our understanding of the decisions being taken by this new class of investors. The decision-making process informing such investments is complex in the sense that it involves several levels of decision that may potentially interact. In this study, we investigate the determinants of SWFs’ foreign investments, while considering in a single model the sequence of choices involved in their decisions, specifically (i) the decision to invest abroad or not, (ii) the decision to invest in a listed versus unlisted firm, and (iii) the decision to take large versus small stakes. Using a nested logit approach on one of the largest SWFs, the Singaporean fund Temasek, over the period 1990–2010, we provide clear evidence of dependence in the three levels of decision making considered. In addition, we show that the probability of Temasek's cross-border investment increases with the excess of foreign exchange (FX) reserves, that the SWF tends to target unlisted firms when asymmetry of information is low between the target company and its home country, and that its involvement in large stakes depends on a firm's financial characteristics.