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This paper contributes to the theory of optimal international reserves by extending the Jeanne-Rancière (Econ J 121:905-930, 2011) endowment small open economy (SOE) model to a SOE with production that accounts for the main sources of economic growth. We, first, derive a richer analytical version of the optimal reserves formula in our set-up, essentially driven by labour-augmenting productivity and the saving rate. Then, under a plausible calibration based on 1975-2020 data averages for typical emerging market countries facing the risk of sudden stops in capital inflows, we find that the optimal reserves-to-output ratio is 7.5%, i.e., the mid-point in the range between that in Jeanne and Rancière (Econ J 121:905-930, 2011), of 9.1%, calibrated to the same sample of 34 middle-income countries, and that in Bianchi et al. (Am Econ Rev 108(9):2629-2670, 2018), of 6.0%, obtained in a different, sovereign debt model without capital and production. We explain the lower optimal reserves-to-output ratio relative to the endowment SOE by the role of capital accumulation as precautionary saving: the accumulated capital stock can potentially be used as a pledge to external creditors in obtaining borrowing, thereby insuring better a SOE against sudden stops. As the countries in our sample appear quite heterogeneous, we also compute the optimal reserves-to-output ratio by region. It turns out that our extended to production insurance SOE model matches well the average reserves-to-output ratio in the data for Latin America, represented by nearly half of our sample, 16 countries, at just above 10%. Yet, for Asia, Africa and Europe our regional model-based ratios understate considerably the respective data averages, suggesting the need to explore alternative modelling approaches. [ABSTRACT FROM AUTHOR]