Why Are State-Contingent Bonds Priced so Unfavorably?

In a recent IMF working paper, we propose a framework to rationalize the observed unfavorable prices of state-contingent debt instruments. The framework is based on a resolution of the equity premium puzzle—which refers to many standard economic models’ inability to explain the high premium on a diversified portfolio of equities over that of “risk-free” government securities —and helps explain why these instruments have had limited success so far. The hindrance may well reflect not what investors know they don’t know but rather what investors do not know that they do not know. Under rational expectations, lenders know that the realization of future GDP is uncertain, but they fully understand the single probability distribution governing the possible outcomes. This notion of risk, or uncertainty, within the model is the typical uncertainty considered in macroeconomics. Alternatively, we consider investors who mistrust their forecasting model and consider the possibility that their forecasts may be biased in some unknown direction. They entertain different models that are statistically close to their baseline model and could also ft the data reasonably well. This type of uncertainty applies for instance when data are limited or when investors fear that some of the model ingredients are not correct but are only approximations. We analyze how lenders’ concern about model misspecification—that models may miss some unknown unknowns—could affect the desirability of issuing state-contingent debt instruments.

We evaluate prices and welfare effects of state-contingent debt using a standard quantitative model of sovereign debt and strategic default, augmented with international lenders with a preference for robustness to model misspecification. These lenders have in mind a statistical model to evaluate future outcomes, but do not trust it fully. Therefore, they consider alternative possible models and seek actions that would perform well under all of these alternative models.

For the commonly used threshold state-contingent bond structure (for example, the GDP-linked warrants issued by Argentina in 2005, Greece in 2012, and Ukraine in 2015 pay only when GDP growth meets a certain threshold), there is an “ambiguity” premium in bond spreads that can explain most of the residual labeled as novelty premium. As investors seek robust decision rules that perform well under all known and unknown unknowns, they act as if the probability of bad states is higher and demand compensation for holding bonds that do not pay when times are bad. This additional premium source leads to welfare losses for the issuing sovereign.

Robust Investors Have a Distorted View of the World

When investors have concerns about model misspecification, they may consider alternative probability models that are difficult to distinguish from their main forecasting model with limited data. How large a distortion they consider measures the lack of trust in the main model. Now, depending on which actions they plan to take (for example, purchasing the state-contingent bond of a certain country), some of this unease will lead to worse expected payofs. To address the lack of trust in the model, they may then want to use the worst-case forecast to price bonds. This would support an investment strategy that is robust to specification errors.

For example, if robust investors are considering the purchase of a bond that pays only if the country’s GDP surpasses a particular threshold, they will look very closely at how they forecast GDP. When they price the bond using the worst-case model, robust investors overestimate the probability of low-repayment scenarios. Under the worst-case distribution, GDP will fall short of the threshold more often than under the baseline. In this sense, the investors are endogenously pessimistic.

A key insight from our research is that the design of state-contingent bonds influences how robust lenders distort their forecasts. Our results suggest that events that are very unlikely will probably remain unlikely after disturbances that are statistically difficult to detect. By contrast, likely events offer much more scope for the distortion of their probability of occurrence. The types of bonds countries have issued in the past stipulate non-repayment with high probability (that is, the government would pay only in relatively good times) and thus are particularly sensitive to probability distortions. As a result, these instruments are ultimately priced by models in which non-repayment is much more likely, inducing the large spreads we see in the data.

Design Matters

With rational expectations, modifying a bond structure in a way that keeps expected repayments the same does not affect its price. With robustness, however, variation in expected repayment enables different probability distortions. These then feed into ambiguity premiums and contribute to higher spreads.

The optimal design of state-contingent debt depends on the investors’ degree of robustness. Figure 2 shows at each level of GDP the stipulated repayments optimally designed for each type of lender. Regardless of the degree of robustness, optimally designed debt always promises higher payments when GDP is high, effectively sharing the country’s risk with its lenders. This feature is dampened as lenders become more robust. When lenders fully trust their model (and are no longer concerned with robustness), they are willing to provide insurance to the country by allowing zero payments in a large range of (low) GDP values, compensated by high payments when the country does well. But when they do not trust their model and want to guard against misspecification, lenders prefer bond structures that offer more security. They value not having to stand by their forecast when they have little faith in it. Moreover, when robustness is extreme, the government would like to minimize the contingency in stipulated repayments. But ex post default risk also gives rise to contingency. Therefore, for bad states, the government promises as much as it can credibly commit to repay. In contrast to the commonly used threshold bond, the optimal design generates substantial welfare gains, although these gains are decreasing with the level of robustness.

Optimal Debt Design

Citation: IMF Research Perspectives 2021, 001; 10.5089/9781513585789.053.A002

Sources: Authors’ calculations.Note: noncont. = noncontingent.

• Download Figure
• Download figure as PowerPoint slide

View Full Size

Optimal Debt Design

Citation: IMF Research Perspectives 2021, 001; 10.5089/9781513585789.053.A002

Sources: Authors’ calculations.Note: noncont. = noncontingent.

• Download Figure
• Download figure as PowerPoint slide

Optimal Debt Design

Citation: IMF Research Perspectives 2021, 001; 10.5089/9781513585789.053.A002

Sources: Authors’ calculations.Note: noncont. = noncontingent.

• Download Figure
• Download figure as PowerPoint slide

Conclusion

Robustness helps explain the prices of state-contingent debt. We link the typical design of these instruments to their prices: thresholds in good times, with no payments whatsoever for a large share of possible contingencies, are particularly susceptible to the probability distortions (or endogenous pessimism) of robust lenders. Our model calibrated to data with noncontingent debt can account only for the prices of state-contingent bonds issued by Argentina in its 2005 debt restructuring. Our findings account for the scant use of these instruments in practice and shed light on their optimal design. This provides valuable lessons as interest in these instruments peaks again with governments around the world facing higher debt and an uncertain economic outlook due to COVID-19.