The Optimal Level of International Reserves for Emerging Market Countries; Formulas and Applications

We present a model of the optimal level of international reserves for a small open economy that is vulnerable to sudden stops in capital flows. Reserves allow the country to smooth domestic absorption in response to sudden stops, but yield a lower return than the interest rate on the country's long-term debt. We derive a formula for the optimal level of reserves, and show that plausible calibrations can explain reserves of the order of magnitude observed in many emerging market countries. However, the recent buildup of reserves in Asia seems in excess of what would be implied by an insurance motive against sudden stops.