A Model of Safe Asset Determination

This paper asks what makes a government bond a “safe asset” and answers that safety is to a large degree a coordination outcome rather than a property of the income stream standing behind the bond. In a two-period model, two countries – a large one whose debt is normalized to size one and a small one of size s in (0,1] – each auction zero-coupon bonds to a continuum of risk-neutral investors who have savings of 1+f to place and, in the baseline, nowhere else to put them. A country defaults precisely when its fiscal surplus plus its bond proceeds fall short of the debt coming due, so an investor’s payoff depends on how many other investors buy the same bond: below a participation threshold the bond is worthless, which makes investor actions strategic complements, and above it extra demand simply bids the fixed supply of bonds up and returns down, which makes them strategic substitutes. Using global-games techniques – a publicly observed world fundamental, an unobserved relative-strength variable, and private signals whose noise vanishes – the authors solve for a unique threshold in the monotone strategy space and obtain a closed form in which the large country’s advantage is a market-depth term scaled by aggregate funding conditions and its disadvantage is a rollover-risk term. Three implications follow. First, relative rather than absolute fundamentals determine safety, which is why US Treasuries and the German Bund can retain and even strengthen their safe-asset status while their own fiscal positions deteriorate, since everyone else’s deteriorated too. Second, debt size helps or hurts depending on the aggregate funding condition: when world savings are abundant a large float is the best parking spot and is safer, but when savings are scarce investors fear that the large issue will not attract enough demand and coordinate instead on the smaller issuer – possibly one with worse fundamentals. Third, once positive recovery in default is allowed, cash-in-the-market pricing makes the safe bond a negative-beta asset whose price rises as aggregate fundamentals worsen, and the beta becomes more negative the stronger the safe country’s relative position. The authors then use the model normatively. For Eurobonds, with a share alpha of debt issued as a common bond, welfare gains in the form of greater safety for both countries arrive only once alpha exceeds a threshold; below it, in the equilibrium where only one country is safe, raising alpha can make the small country less safe, because it captures proportionally little of the common-bond proceeds – so “small steps towards a fiscal union could be worse than no step.” Endogenizing debt size, the competition for safe-asset status has a tournament structure: when natural sizes are similar and aggregate funding is strong both countries expand beyond their natural sizes in a self-defeating rat race that the model links to the pre-crisis expansion of US agency debt and of euro-area sovereign debt, while sufficiently asymmetric sizes produce a “top dog” who contracts and a challenger who expands. The results are derived in a deliberately stylized setting – two periods, two countries, risk-neutral investors placing price-independent market orders, no alternative storage technology in the baseline, and the vanishing-noise limit – and the authors present their historical and crisis applications as interpretations the model can rationalize rather than as estimated effects.

Konstantin Milbradt | Macro Paper Warehouse

A Model of Safe Asset Determination