Two-year bond yields in six European countries recently turned negative. The decline in bond yields has prompted a growing number of commentators to say that bonds are overvalued.
In this column, we present a framework that can rationalise and explain current bond prices. The framework also sheds light on other trends in bond markets. It builds on the rare-disaster framework of Reitz (1988), Barro (2006), Barro et al. (2010), Barro and Ursύa (2008) and Gabaix (2012). This class of models was originally proposed to explain the equity premium puzzle by introducing the possibility of large and negative shocks to GDP or consumption, i.e. disasters.
Disaster risk can explain low bond yields
For asset prices, it is investors’ perceptions of risks that matter. There is good reason to believe investors might be more alert to the threats of disaster after many decades in which such risk appeared to decline. Iceland and Ireland have already suffered peak-to-trough declines in GDP of more than 10%, in line with the definition of a disaster according to Barro and Ursύa (2008). In contrast, only two OECD countries experienced disasters in the whole of the second half of the 20th century. A number of other countries teeter close to disaster-level contractions, which has resulted in a clear upward shift in the left tail of GDP growth distribution for developed countries. The potential consequences of the problems in the Eurozone are one reason boosting disaster risk. One set of forecasts produced by ING (Der Spiegel 2012) estimates that every Eurozone country would suffer a GDP decline in excess of 10% within two years of a total break-up of the euro, suggesting that disaster risks are unlikely to disappear soon. The upward revision in disaster risk is consistent with the learning model of Wieland and Koulovatianos (2011).
This has implications for asset prices. In our framework, disasters hit not only income or consumption but also equities and bonds. Equities do badly because the decline in GDP affects earnings. Bonds suffer because a disaster raises the probability of government default. However, provided this probability remains low, investors will still find bonds attractive as they provide stable and largely safe returns when consumption is low. In other words, when investors fear a disaster, they will be willing to pay a premium to hold bonds because they still view them as safe havens despite the increase in default risk. It is this insurance property that makes bonds attractive when disaster risk is high. Therefore, bonds become riskier but their relative riskiness goes down.
The question remains whether an increase in the likelihood of disasters can explain the exceptionally low bond yields in Germany, the US and elsewhere. Our calculations show that it can, and with modest increases in disaster risk.
Standard bond valuation frameworks – which do not take disaster risk explicitly into account—suggest that 10-year German bond yields are around 0.5% below ‘fair value’. This discrepancy can be explained by an increase in disaster risk from 2% to merely 2.8% (which is still lower than the long-run historical frequency of 3.7%). This increase in disaster risk is sufficient even if we assume that German default risk has risen from 2% to 10%, mirroring the behaviour of the German credit default swap (CDS) spreads. Similarly, the gap between US 10-year bond yields and their fair value, estimated be around 1%, can be explained by a rise of just 20% in disaster risk from its historical mean.
Variable default risk
The rare-disaster framework helps explain the very low bond yields for safe havens. The standard approach has not, though, considered the importance of changing default risk. As we show in Brookes and Daoud (2012), this provides other interesting implications.
In practice, default risk is likely to vary with changes in disaster risk. And, with variable default risk, the behaviour of bonds spans a whole spectrum. At one end of this spectrum, default probability is low and bonds behave like safe havens when disaster risk rises. In this case, the rational flight to safety increases the price of bonds and lowers yields. Equities, on the other hand, provide a poor hedge against disasters and their price falls. In this case, bonds and equities are negatively correlated.
With low default risk, the framework explains how rising default risk (and CDS spread) can co-exist with falling bond yields. This has been observed at several points in time in Germany as Chart 1 below shows. This may seem puzzling at first, but it is entirely consistent with the process we described for bonds that are considered largely safe despite the increase in their default risk. Their relative safety pushes yields down even though the absolute riskiness has increased.
Figure 1. Negative correlation between five year German bond yields and CDS spreads
At the other extreme, if default probability is high, bonds become as risky as equities in a disaster-struck world. As with equities, investors will then demand a high rate of return on risky bonds if they fear disasters because the assets will no longer offer protection against a fall in investors’ income. Bonds must fall and yields increase to provide this return. In this case, bonds and equities become positively correlated.
Somewhere between these two extremes, there is a change in default probability at which bonds switch from being safe havens in a world threatened by disaster to equity-like risky assets that require a high rate of return for investors to hold them.
How high must default risk be for investors to start perceiving sovereign bonds as risky assets causing their correlation with equities to switch from negative to positive?
Theory does not provide an answer, but there appears to be an empirical regularity. For each of Greece, Spain, Italy and France the correlation switched as the annual default probability (measured from CDS spreads) rose above 3%. This corresponds to around 200bps for a five year CDS. Consistent with our theory, as markets’ perception of the credit worthiness of Greece, Spain and Italy continued to worsen, their bond-equity correlations remained positive. There has been no shift in correlation in Germany because the default probability is still below the 3% threshold.
Figure 2: Correlation between Spanish bonds and equities switched to positive in 2010 when annual default probability crossed 3%
Figure 3. Correlation between Italian bonds and equities switched to positive in 2010 when annual default probability crossed 3%
This column has outlined a simple framework for bond yields building on the rare disasters framework. It can help explain low bond yields despite abstracting from a host of factors such as quantitative easing, a possible shortage of safe assets, household deleveraging and increased risk aversion, each of which is sometimes used to justify low yields. The insight from our model is that a simple framework in which there is a greater chance of extreme economic events can help explain a number of patterns in bond markets, including abnormally low yields, rising credit risk alongside falling yields, and changing correlations between bonds and equities as the former become more ‘equity like’.
Barro, Robert (2006), “Rare Disasters and Asset Markets in the Twentieth Century”, Quarterly Journal of Economics, 121:823-866.
Barro, Robert, Emi Nakamura, Jón Steinsson and Jose Ursύa (2010), “Disasters, Recoveries, and the Equity Premium”, VoxEU.org, 8 July.
Barro, Robert and Jose Ursύa (2008), “Macroeconomic Crises since 1870,” Brookings Papers on Economic Activity, 2008:255-335.
Brookes, Martin and Ziad Daoud (2012), “Disastrous Bond Yields”, Fulcrum Asset Management Research Paper.
Der Speigel (2012), “The Disastrous Consequences of a Euro Crash”, available at http://www.spiegel.de/international/europe/fears-grow-of-consequences-of....
Gabaix, Xavier (2012), “Variable Rare Disasters: An Exactly Solved Framework for Ten Puzzles in Macro-Finance”, Quarterly Journal of Economics, 127:645-700.
Reitz, Thomas (1988), “The Equity Premium: A Solution”, Journal of Monetary Economics, 22:117-131.
Wieland, Volker and Christos Koulovatianos (2011), “Rational Learning about Rare-Disaster Frequencies: A Persistent Source of Asset-Price Overreaction”, VoxEU.org, 1 November.