A growing literature has sought to quantify the impacts of natural disasters on economic growth, but has found seemingly contradictory results, ranging from positive to very large negative effects. This paper brings a novel macroeconomic model-based perspective to the data. We present a stochastic endogenous growth model where individual regions face uninsurable cyclone risks to human and entrepreneurial capital, building on the tools developed in the incomplete markets macroeconomics literature (Krebs, 2003, Angeletos, 2007). Our model can reconcile key divergent results from prior empirical studies, as they measure different elements of the overall impact of disasters on growth: (1) Higher disaster risk can increase growth by increasing (precautionary) savings, whereas disaster strikes induce (potentially persistent) output losses, in line with the empirical evidence of positive growth effects in cross-sectional analyses (e.g., Skidmore and Toya, 2002) but negative impacts in panel studies (e.g., Hsiang and Jina, 2015a). We explore a combined two-step estimation to assess the overall impact of cyclones on growth, which - on average - appears to lie in between. (2) Competing measures of cyclone risk - average capital destruction, fatalities, or storm intensity - can be related to growth in opposite ways, again in line with the literature (e.g., Hsiang and Jina, 2015b vs. Skidmore and Toya, 2002). Intuitively, long-run growth depends on the level and composition of investments across different assets, which, in turn, depend differentially on the vector of expected damages to all capital goods. (3) Finally, we show that disaster risk can have opposite effects on growth and welfare.