Abstract
This paper develops a comprehensive new framework to measure and analyze sovereign risk. Contingent claims analysis is used to construct a marked-to-market balance sheet for the sovereign and derive a set of forward-looking credit risk indicators that serve as a barometer of sovereign risk. Applications to 12 emerging market economies show the approach to be robust, and the risk indicators are a significant improvement over traditional macroeconomic vulnerability indicators and accounting-based measures. The framework can help policymakers design risk mitigation strategies and rank policy options using a calibrated structural model unique to each economy.
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Notes
See Buiter (1993) for a discussion of the many items on the balance sheet of the public sector, including nonmarketable items such as social overhead capital.
Xiao (2007) shows that an increase in volatility dampens demand for sovereign bonds.
Volatility of sovereign assets can differ across countries for many reasons, including, but not limited to, the level of international reserves on the government's balance sheet, the exchange rate, and variations in government revenue and expenditures. Countries with lower asset volatility are generally able to use larger amounts of leverage with relative comfort whereas countries with higher asset volatility would be better off taking on less leverage.
Foreign currency debt in global markets is predominantly fixed-rate, “bullet” maturity debt that results in easily defined contractual flows. Some global debt is amortizing, but these payments are usually well specified. The main difficulties in estimating debt payments arise when the debt payments are linked to changes in interest rates, exchange rates, or inflation. These forms are more often found in domestic as opposed to global capital markets.
Measuring the balance sheet in U.S. dollars results in variable sovereign assets vs. a fixed distress barrier. Measuring the balance sheet in domestic currency will result in both variable sovereign assets and a variable distress barrier. In either configuration, the contingent claim formulas will produce the same results.
The implicit guarantees to the financial sector, or other entities, could remain on the liability side of the consolidated public sector balance sheet and modeled as implicit put options. For more details, see Merton (1977); Gray, Merton, and Bodie (2002, 2006); Gapen and others (2004); and Van den End and Tabbae (2005). These papers link the sovereign to the contingent claim balance sheets of the banking or corporate sectors. The detailed analysis of the links to other sectors is beyond the scope of this paper.
Support for viewing foreign currency debt as senior can also be found in the literature on “original sin” in Eichengreen, Hausmann, and Panizza (2002).
The analysis also holds in the case of large developed markets such as the United States. While the balance sheet is already measured in dollars, the domestic bondholder is subject to (1) increased debt issuance that dilutes existing bondholders' claims on sovereign assets and (2) an increase in base money, or unexpected inflation risk, which reduces the real value of domestic currency debt. Even though developed markets are not thought to exhibit problems of “original sin” and currency mismatches, domestic currency liabilities of developed countries exhibit equity-like properties through dilution risk.
See Cossin and Pirotte (2001) for a discussion on how the framework can handle multiple layers of liabilities or default sequences. The use of two layers of sovereign liabilities is a reasonable approximation given the observed robustness of the model and the behavior of spreads during periods of stress. Assuming that all money and local currency debt are senior and all foreign currency debt is junior leads to inconsistencies. Crises resulting in depreciation of the exchange rate would cause the “foreign currency junior claim” to grow large compared to domestic currency debt. This is inconsistent with the observation that credit default swap spreads on foreign currency debt increase with sharp depreciations. In situations of large exchange rate appreciation, usually considered beneficial from a credit risk perspective, the value of the “foreign currency debt junior claim” would be very small relative to domestic currency debt, indicating a large expected loss is associated with the domestic currency debt.
This definition of the distress barrier is identical to that used by Moody's KMV in corporate sector default risk analysis (Crosbie and Bohn, 2003). Short-term is defined as one year or less by residual maturity. See Sobehart and Stein (2000) and Sobehart, Keenan, and Stein (2000) for evidence that this approach outperforms other models in estimation of corporate sector credit risk.
See Hull (1993) and Baxter and Rennie (1996) for discrete-time representations.
Here, N(d 1) is the change in the price of domestic currency liabilities with respect to a change in sovereign assets, or ∂V DCL /∂V A . This ratio is also referred to as the option delta. See Hull (1993, p. 38).
The main difficulty in applying Equations (1) and (3) lies in the computation of the cumulative normal distribution. Numerical integration methods can be used to evaluate the distribution directly, computing a finite number of evaluations of the integrand and then summing over these values. Judd (1998) provides a menu of available integration methods, including the Gauss-Hermite quadrature that is often used in conjunction with normally distributed random variables. Alternatively, the distribution can be approximated using a high-order polynomial approximation, as is done in Hull (1993, pp. 226–27). Standard prepackaged routines in Matlab can then be implemented to find the zero roots of the nonlinear equations using iterative methods. A sample Matlab program can be found in Miranda and Fackler (2002, pp. 382–85). Using either of these techniques, Equations (1) and (3) can be solved for the implied value of sovereign assets and sovereign asset volatility.
Risk-neutral valuation is an important factor underlying the derivation of the Black-Scholes option pricing formula whereby the value of the option can be derived by forming a riskless hedge portfolio. Thus, option values do not depend on the investor's or decision maker's attitude toward risk, which is a major benefit of this approach. Alternative balance sheet approaches based on discounted cash flows are subject to serious error not only from errors in cash flow projections but also from errors in choosing the discount rate. See Hull (1993, pp. 221–22) and Chriss (1997, pp. 190–93) for additional discussion of risk-neutral valuation.
Merton (1974) derives similar measures for the pricing of corporate debt. The value of senior foreign currency liabilities can also be obtained using the implicit put option in risky debt (Gapen and others, 2004; Gray, 2004; Chacko and others, 2006; and Gray, Merton, and Bodie, 2006), or
.Variations in the derivative asset price with respect to changes in the underlying parameters that enter the option formula are known as Greek-letter risk measures. Frequently used measures are the option delta, gamma, and vega. See Briys and others (1998, pp. 124–28) for these and other measures of option sensitivities that are used in managing exposures.
Mapping of risk-neutral default probability into actual default probabilities is necessary for rating agencies in the ratings process but is not necessary for valuation purposes. The Merton framework substitutes the risk-free interest rate for the actual expected return in the asset-probability distribution. Because the actual expected return is greater than the risk-free return, the risk-neutral probability of default is higher than the actual probability of default. However, expected returns are not necessary for valuation purposes. The relationship between the risk-neutral spreads and risk-neutral default probability and actual spreads and market-implied default probability, as undertaken in this paper, is examined mainly for robustness purposes. See Merton (1990) for additional discussion.
The historical data for the sovereign risk indicators in Equations (3), (4), (5) to (6) were obtained from the Macrofinancial Risk (MfRisk) model, which applies the contingent claims methodology as described in this paper. The model was developed under a joint research effort between Moody's and Macro Financial Risk, Inc., and applied to 17 countries. At the time of the writing of this paper, access to MfRisk was available only through subscription.
Reported output in Figure 3 is limited to the 12 countries for which credit default swap data were available.
The reported correlations in Table 1 were computed using Spearman's rank correlation instead of conventional correlation. Conventional correlation is inappropriate in this case because it implicitly assumes linear relationships among variables, an assumption that contradicts the nonlinear relationship between variables as found in this paper. Spearman's rank correlation is a less restrictive measure to gauge relationships among variables because it does not impose any linearity assumptions.
The JPMorgan EMBIG index has replaced the EMBI+ index as the preferred index for tracking emerging market credit spreads, but historical EMBIG index data were not available at the time of the writing of this paper.
The countries in the sample include Brazil, Colombia, Korea, Malaysia, Mexico, Philippines, Poland, Russia, South Africa, Turkey, and Venezuela.
MIDP can be obtained from CDS spreads through the following equation:
, where spread is the net one-year credit default swap spread, t is the time horizon (equal to 1 in this case), and R=30 percent is the recovery rate. If the one- year CDS spread is 180 basis points, the implied default probability is 2.5 percent.The countries in the sample include Brazil, Colombia, Korea, Malaysia, Mexico, Philippines, Poland, Russia, South Africa, Turkey, and Venezuela.
The solid line in the figure represents the line of best fit, y=4597.3 exp(–2.3743x), with R 2=0.7957.
Since the scenario and Monte Carlo simulations are based on this hypothetical sovereign balance sheet, we use the results from a panel regression between risk-neutral spreads and EMBI+ spreads applied to the countries in Table 3. The estimated equation between risk-neutral spreads and market credit spreads is ln(EMBI t ) =2.97+0.61 ln (RNS t ).
Although Monte Carlo simulations are able to handle many thousand possible events, they produce a random set of outcomes based on the market characteristics assumed, which may or may not predict potential shocks. The simulation process will only produce as many extreme events as dictated by the distribution assumption of the market variables. To be comprehensive, simulation procedures should be combined with various scenario assumptions to produce a set of stress outcomes.
As discussed in the previous section regarding the computation of implied sovereign assets and volatility, the calibrated inputs of the distress barrier and volatility of domestic currency liabilities are estimates. That is, ς̂ is an estimate of the true volatility of domestic currency liabilities, ς̂, and as such will contain standard error, leading to possible model risk. The presence of standard error otherwise results in confidence intervals around the point estimates of risk for each risk indicator. However, the traditional practices used to compute such estimates in the finance literature as described in this paper do not involve empirical regression estimation, making the construction of standard error bounds problematic. Instead of computing a confidence interval around the expected value of the risk indicator given standard error in ς̂, the construction of probability distributions using Monte Carlo analysis is equivalent to confidence intervals around the expected value of the risk indicator given the estimate of ς̂. The issue is further complicated by the fact that introducing standard errors on ς̂ would result in error bands on the entire distribution of the risk indicators in the Monte Carlo simulation, greatly complicating the exercise.
See Jorion (2000). VaR models estimate the exposure of a portfolio, or the equivalent set of positions, to market risk. The measure captures the expected maximum loss and is usually expressed within a confidence interval.
Two other sovereign VaR measures can be calculated. The first, sovereign capital-at-risk, is an extension of sovereign VaR for the central bank. The probability distribution of the residual value of “capital” or junior claim of the monetary authority is calculated and a confidence level attached to the risk that the monetary authority cannot meet its commitments. Blejer and Schumacher (1999) use a similar construction. The second, sovereign credit-at-risk, is the upper bound on gains or losses due to credit risk, which in this case is the value of the guarantee to the banking system. See Gapen and others (2004) for an example of how this could be modeled.
See Gapen and Papaioannou (2007) for the various motives and implications of reserve accumulation throughout the Asian region.
Simulating the adjusted sovereign balance sheet under the same exchange rate and interest rate distributions and correlation is subject to the critique that these distributions and correlations are derived from market expectations that are likely to change with the shift in policy. The simulations conducted in this paper should be viewed only as illustrating potential impacts from policy changes.
IMF (2000) examines three ratios: reserves to imports, reserves to monetary aggregates, and reserves to public and private short-term foreign currency debt by residual maturity. The report concludes that reserves to short-term foreign currency debt is a superior measure and recommends that a ratio of 1 be a lower bound for adequate reserve coverage.
See Gray (2007) for applications to sovereign wealth management and Gray and Malone (forthcoming) for additional examples. Caballero and Panageas (2005) also examine various instruments and risk mitigation strategies that policymakers could implement in addition to traditional reserve accumulation in a model of sudden stops in capital flows.
This is true whether one uses the simplified distress barrier in this paper (short-term foreign currency debt and interest plus one-half long- term foreign currency debt) or a more sophisticated approach (short-term foreign currency debt and interest plus the present discounted value of long-term foreign currency debt and interest). Both approaches would reflect an increase in sovereign risk if long-term foreign currency debt was traded for equal book value amounts of short-term foreign currency debt. The distress barrier under the second approach, however, would be more sensitive to near-term repayment humps that would carry a higher weight in the distress barrier than a similar payment profile further out on the maturity scale.
.
, where spread is the net one-year credit default swap spread, t is the time horizon (equal to 1 in this case), and R=30 percent is the recovery rate. If the one- year CDS spread is 180 basis points, the implied default probability is 2.5 percent.References
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*Michael Gapen is an economist with the IMF Institute; Dale Gray is a senior economist and Cheng Hoon Lim is a division chief with the IMF Monetary and Capital Markets Department; and Yingbin Xiao is an economist with the IMF European Department. The authors would like to thank Zvi Bodie, Carlos Medeiros, Robert Merton, Linda Tesar, and participants of the JPMorgan Chase seminars at the 2005 Annual Meetings of the Inter-American Development Bank in Okinawa and the Asian Development Bank in Istanbul, the Institute of International Finance Country Risk Workshop, and the IMF Institute for helpful comments and suggestions. We would also like to thank an anonymous referee for helpful suggestions.
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Gapen, M., Gray, D., Lim, C. et al. Measuring and Analyzing Sovereign Risk with Contingent Claims. IMF Econ Rev 55, 109–148 (2008). https://doi.org/10.1057/palgrave.imfsp.9450026
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DOI: https://doi.org/10.1057/palgrave.imfsp.9450026