A portion of the global wealth portfolio is directed towards a safe and liquid reserve asset, which recently has been the US Treasury bond. Our model links the determination of reserve asset status to relative fundamentals and relative debt sizes, by modeling two countries that issue sovereign bonds to satisfy investors’ reserve asset demands. A sovereign’s debt is more likely to be the reserve asset if its fundamentals are strong relative to other possible reserve assets, but not necessarily strong on an absolute basis. Debt size can enhance or detract from reserve asset status. If global demand for the reserve asset is high, a large-debt sovereign which offers a savings vehicle with better liquidity is more likely to be the reserve asset. If demand for the reserve asset is low, then large debt size is a negative as it carries more rollover risk, leading to a riskier vehicle for saving. When global demand is high, countries may make fiscal/debtstructuring decisions to enhance their reserve asset status. These actions have a tournament feature, and are self-defeating: countries may over-expand debt size to win the reserve asset tournament. Coordination can generate benefits. We use our model to study the benefits of “Eurobonds” – i.e. a coordinated common Europe-wide sovereign bond design. Eurobonds deliver welfare benefits only when they make up a sufficiently large fraction of countries’ debts. Small steps towards Eurobonds may hurt countries and not deliver welfare benefits.