This paper shows that the behavior of entrepreneurs facing incomplete financial markets and risky investment can explain why growth accelerations in developing countries tend to be associated with current account improvements. The uninsurable risk of losing invested capital forces entrepreneurs to rely on self-financing, so that when business opportunities open up entrepreneurs increase saving to finance the investment that produces growth. The key insight is that saving has to rise more than investment to allow also for the accumulation of precautionary assets. Plausibly calibrated simulations show that this net saving increase can sustain large and persistent net capital outflows.