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.

The Effects of Quantitative Easing on Interest Rates: Channels and Implications for Policy

This 2011 Brookings Papers on Economic Activity paper by Arvind Krishnamurthy and Annette Vissing-Jorgensen evaluates the effect of the Federal Reserve’s large-scale purchases of long-term Treasuries and other long-term bonds – QE1 in 2008-09 and QE2 in 2010-11 – on interest rates, and argues that quantitative easing works through several distinct channels that affect different assets differently, so it is inappropriate to focus only on Treasury rates as a policy target and effects depend critically on which assets are purchased. The authors decompose the yield on a long-term risky, illiquid asset into the expected safe short rate, expected inflation, and premia for duration risk, illiquidity, lack of safety, default risk, and prepayment risk, and identify seven candidate channels (signaling, duration risk, liquidity, safety, prepayment risk, default risk, and inflation), each tied to instruments that should load on it (federal funds futures for signaling, CDS for default risk, inflation swaps/TIPS/swaption volatility for inflation). Identification comes from an event study around the QE1 announcement dates (Nov 25, Dec 1, Dec 16, 2008; Jan 28, Mar 18, 2009) and the QE2 announcement dates (Aug 10, Sep 21, Nov 3, 2010), combined with difference-in-differences comparisons across pairs of assets that share most characteristics but differ in one dimension (e.g., agency versus Treasury bonds isolating liquidity), and a 2SLS regression of the Baa-Treasury and Baa-Aaa spreads on the log ratio of ten-year-equivalent long-term Treasury supply to GDP using 1949-2008 annual data. For QE1, summed two-day yield changes around the five event dates were sizable and pervasive: Treasury yields fell 73 bp (30-year), 107 bp (10-year), 74 bp (5-year); Fannie Mae agency yields fell 144-200 bp across maturities; agency MBS yields fell 88-107 bp; the signaling channel alone (a roughly 6.3-month delay in anticipated rate hikes, a 40 bp drop in 24-month fed funds futures) is estimated to account for about 20-40 bp of the declines out to ten years, while duration effects only partly explain the pattern (they cannot account for agency bonds falling the most or for the absence of a within-rating maturity effect in corporates), and safety, MBS prepayment, default, and inflation channels are all found to be operative, with MBS purchases described as crucial to the fall in MBS yields and corporate credit risk. For QE2, which purchased only Treasuries, the results look different: signaling lowered 5-year yields by 11-16 bp and 10-year yields by 7-11 bp, safety lowered 10-year low-default-risk yields by a further 6-11 bp, and inflation expectations rose (implied 10-year inflation expectations up 14-16 bp), but the authors find no evidence of duration, liquidity, prepayment, or default channels for QE2, and conclude that its effect on the mortgage and lower-grade corporate rates most relevant to households worked mainly through signaling and inflation rather than a portfolio-balance effect. The safety-channel regression estimates an elasticity of -0.83 (Baa-Treasury) and -0.32 (Baa-Aaa) on log relative Treasury supply, implying safety effects of roughly 4-11 bp for QE1 and 8-20 bp for QE2 under “normal” demand conditions – substantially smaller than the safety effect the event study attributes to QE1, which the authors suggest reflects unusually elevated crisis-period demand for safety rather than an average relationship. The paper’s central mechanism claim is that the portfolio-balance channel operating in both QE1 and QE2 works through a preferred-habitat safety channel – a clientele demand for long-term assets with little or no default risk – rather than through the duration-risk channel emphasized in some contemporaneous work, a conclusion the authors state directly: they “do not find support for the operation of the duration risk channel.”

Arvind Krishnamurthy | Macro Paper Warehouse

A Model of Safe Asset Determination

The Effects of Quantitative Easing on Interest Rates: Channels and Implications for Policy