Abstract
This paper examines the inflation expectations, monetary policy credibility, and dollarization. Country fundamentals have explained variation in sovereign spreads, but external factors play an important role. This paper assesses the role of and prospects for bank-lending from a cyclical and structural perspectives. A model calibrated for Uruguay, a financially dollarized economy, suggests that reserves are nearing optimal prudential levels. The results of a modified Merton framework, applied to the case of the Uruguayan banking system, appear to be promising for countries without equity markets.
VI. Has the Financial System Become More Resilient to Shocks? An Analysis Adapting the Merton Framework to a Country without Equity Market Data
By Marcos Rietti Souto
A. Introduction
1. Following substantial restructuring and enhanced supervision in the aftermath of the 2002 crisis, financial sector soundness indicators have strengthened considerably. The banking system is now profitable and has become better capitalized. It is also highly liquid, though this partly reflects a sharp reduction in lending. Nonperforming loans have fallen to 2 percent of total loans (excluding the housing bank) and non resident deposits, which proved volatile in the face of negative external developments, are well below pre-crisis levels. In addition, the regulation and supervision of the financial system has improved significantly. However, despite low short-term risks, important medium term vulnerabilities remain, particularly stemming from high dollarization (see also FSAP 2006).
2. This paper assesses the extent of remaining vulnerabilities of the banking sector using a variant of the Merton framework (1973, 1974). To this end, the study constructs a set of credit risk indicators, which are then used to compare banks' risk profile at the time of the 2002 banking crisis with today's conditions, and examines the impact of potential shocks on the various risk indicators. In contrast to the Merton framework, which uses market data to capture the collective views and expectations of market participants, this paper uses book value data from balance sheets due to the absence of market data in Uruguay. The approach still incorporates volatility into the estimations, a key feature of the Merton framework for capturing non-linearities in the credit risk indicators, especially during periods of distress.
3. Despite the simplifying assumptions, the methodology captures well several stylized facts of the 2002 banking crisis and suggests that the system has become more resilient. In particular, it identifies, as early as the first quarter of 2002, a deterioration in the credit risk indicators of the banking sector and, when applied to the corporate sector, a significant distress event toward the last quarter of 2002. The methodology also points to a substantial improvement in credit risk indicators since the 2002 crisis, in line with the restructuring process pursued over the last years. Consistent with the conclusions of the stress tests of the 2006 FSAP and the 2007 update prepared by the authorities, it shows that, notwithstanding important remaining vulnerabilities, banks have become more resilient to shocks. Thus, the methodology used in this paper appears to have the potential of being a useful toolkit to many economies that lack (or have shallow) equity markets.
B. The Merton Framework
4. The Merton framework offers clear advantages over traditional vulnerability analyses, including by incorporating volatility explicitly into the estimations.1 The approach relies on observable market information on the value and volatility of liabilities (and equity) to derive the value of non-observable quantities, such as the asset value and asset volatility. This information is then combined to estimate risk indicators, such as the distance-to-distress (a measure of how far a firm is from defaulting), default probability, credit spread, and expected losses given a default. In contrast with more traditional vulnerability analyses, this framework incorporates market volatility when estimating credit risk. Volatility is crucial in capturing nonlinear changes in risk, especially during times of stress when small shocks can gain momentum and trigger systemic repercussions.
5. The basic idea is to model a firm's equity as a (junior) contingent claim on the residual value of its assets. In the event of default, all the firm's assets are used to pay the senior stake holders (e.g., debt holders); otherwise equity holders receive the difference between the value of assets and debt. Thus, the equity of the firm can be seen as a call option on the residual value of the firm's assets. This framework enables a rich characterization of a firm's (or sovereign's) balance sheet and the derivation of several credit risk indicators (e.g., distance to distress, default probability, and credit spreads) (Figure 1).
The Merton Framework
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
The Merton Framework
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
The Merton Framework
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
6. With information on the market value and volatility of equity and the value of debt, it is possible to estimate the implied value for assets and volatility through the Black and Scholes option formula. Firms are assumed to default whenever the value of assets fall below a given “distress” barrier. It is then possible to estimate a set of credit risk indicators, including distance-to-distress, default probability, credit spread, and expected losses in the event of default.2
7. Given the lack of an equity market in Uruguay, this study incorporates volatility into the estimation of credit risk indicators by using book value data. While this reduces to some extent its forward-looking nature, the approach still retains key characteristics, such as proper analysis of asset volatility. Moreover, balance sheet data appears to capture well changes in the financial health of Uruguayan banks during the sample period, without particularly long lags.
C. The Stress Tests
8. This section summarizes the main results of stress tests conducted by the 2006 FSAP and updated by the authorities in 2007. It then assesses whether the banking system has become more resilient since the 2006 FSAP.
The 2006 FSAP stress tests
9. The 2006 FSAP stress tests focused on the impact of shocks on banks' capital adequacy (CAR) and liquidity ratios.3 The institutions included all private banks, cooperatives, finance companies, offshore banks, and the state owned Banco de la República Oriental del Uruguay (BROU); these institutions represented 80 percent of the financial system assets. The stress tests were performed on exposures, on a bank-by-bank basis, as of June 2005. They included sensitivity analysis with respect to the interest rate, exchange rate, and credit risk, as well as macroeconomic scenarios involving a domestic supply shock (severe weather conditions), a current account shock (corresponding to a drop in Argentine GDP of 10 percent), and a capital account shock (corresponding to a rise in the three-month Libor to seven percent per year) (Table 1).
2006 FSAP: Stress Tests Assumption
GDP gap where long-term GDP growth is equal to 3 percent.
The country risk was calibrated according to similar historical episodes.
2006 FSAP: Stress Tests Assumption
| Risk factor | Current Account Shock | Capital Account Shock |
|---|---|---|
| Δ Real exchange rate | 5% | 12% |
| Δ Argentina private consumption | −10% | −10% |
| Δ Argentina nominal exchange rate | 45% | 45% |
| Δ Argentina real exchange rate | 30% | 30% |
| Δ Foreign prices | −5% | −13% |
| Δ Domestic prices | 7% | 15% |
| Δ Nominal exchange rate | 17% | 48% |
| Δ GDP 1/ | −4% | −8% |
| Country risk 2/ | 500 to 550 b.p.s. | > 600 b.p.s. |
GDP gap where long-term GDP growth is equal to 3 percent.
The country risk was calibrated according to similar historical episodes.
2006 FSAP: Stress Tests Assumption
| Risk factor | Current Account Shock | Capital Account Shock |
|---|---|---|
| Δ Real exchange rate | 5% | 12% |
| Δ Argentina private consumption | −10% | −10% |
| Δ Argentina nominal exchange rate | 45% | 45% |
| Δ Argentina real exchange rate | 30% | 30% |
| Δ Foreign prices | −5% | −13% |
| Δ Domestic prices | 7% | 15% |
| Δ Nominal exchange rate | 17% | 48% |
| Δ GDP 1/ | −4% | −8% |
| Country risk 2/ | 500 to 550 b.p.s. | > 600 b.p.s. |
GDP gap where long-term GDP growth is equal to 3 percent.
The country risk was calibrated according to similar historical episodes.
10. The 2006 results indicated that banks have improved considerably, but remained vulnerable to severe shocks. Following these large shocks, several institutions would be undercapitalized or with their CAR falling below the minimum required capital ratio, particularly under the capital account shock scenario. However, banks appeared to be resilient to moderate fluctuations in the exchange rate, interest rate, liquidity, and credit reclassification, with only few institutions having their CAR falling below the minimum required capital ratio.
The stress test update
11. The 2007 update of the stress tests indicate that banks are more resilient to economic shocks. The exercise was updated using December 2006 data for shocks that yielded the worst results in the 2006 FSAP. The current account shock results in a drop of the average CAR of 4 percent now, against 8 percent in the 2006 FSAP; the capital account shock yields a drop of 10 percent, against 22 percent in the 2006 FSAP (Figure 2). Liquidity ratios dropped modestly in the 2007 update, compared to the 2006 FSAP exercise. Under the current account shock scenario, liquidity ratios for assets and liabilities maturing in 30 days or less fell, on average, 43 percent in both 2006 FSAP and 2007 update; under the capital account shock scenario, these ratios fell, on average, 48 percent in the 2006 FSAP and 45 percent in the 2007 update. Similar drops in liquidity ratios are observed for assets and liabilities maturing in 90 days or less (Figure 3).
Capital Adequacy ratio after stress shocks
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
Capital Adequacy ratio after stress shocks
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
Capital Adequacy ratio after stress shocks
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
Liquidity ratios after stress shocks
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
Liquidity ratios after stress shocks
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
Liquidity ratios after stress shocks
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
D. The Modified Merton Framework
12. This section uses the modified Merton framework to assess whether credit risk indicators capture well the main stylized facts of the 2002 banking crisis and the ensuing recovery. Also, the framework is used to estimate the impact of current and capital account shocks, replicating those defined in the stress tests, in an effort to incorporate volatility as an additional dimension to these tests, which rely only on assets and liabilities levels.
Estimating risk indicators
13. To estimate credit risk indicators, it is key to adjust balance sheet data to better reflect underlying values and volatilities.4 First, beyond the deterioration in assets reflected through provisions, the data was adjusted by the expected losses arising from companies facing the same shocks. Second, the data was adjusted to take into account the liquidity/capital support provided during the 2002 crisis (US$2.4 billion), which was masking the decrease in total assets value and volatility in the published financial statements (Table 2).
Total Government Assistance to Banks 1/
(In millions of U.S. dollars, as of August 2002)
Includes assistance in pesos, evaluated at Ur$28.8/US$.
Total Government Assistance to Banks 1/
(In millions of U.S. dollars, as of August 2002)
| Total | Public Banks | Private Banks | ||
|---|---|---|---|---|
| Total assistance | 2,417 | 1,228 | 1,189 | |
| Of which: in pesos | 33 | 10 | 23 | |
| Capitalization | 33 | 0 | 33 | |
| Central bank | 563 | 258 | 305 | |
| Article 36/37 | 391 | 258 | 133 | |
| Overdraft | 173 | 0 | 173 | |
| FFSB (Jun. 2002) | 449 | 0 | 449 | |
| FSBS (Aug. 2002) | 1,373 | 970 | 403 | |
Includes assistance in pesos, evaluated at Ur$28.8/US$.
Total Government Assistance to Banks 1/
(In millions of U.S. dollars, as of August 2002)
| Total | Public Banks | Private Banks | ||
|---|---|---|---|---|
| Total assistance | 2,417 | 1,228 | 1,189 | |
| Of which: in pesos | 33 | 10 | 23 | |
| Capitalization | 33 | 0 | 33 | |
| Central bank | 563 | 258 | 305 | |
| Article 36/37 | 391 | 258 | 133 | |
| Overdraft | 173 | 0 | 173 | |
| FFSB (Jun. 2002) | 449 | 0 | 449 | |
| FSBS (Aug. 2002) | 1,373 | 970 | 403 | |
Includes assistance in pesos, evaluated at Ur$28.8/US$.
14. The expected losses from the corporate sector were estimated using the modified Merton framework. Despite the limitations of the methodology (see appendix for the technical details), the results appear to be in line with the stylized facts: in 2002, there was an increase in expected losses from companies that defaulted, owing partially to a higher volatility of total assets; in subsequent years, once the volatility of assets declined and the balance sheet accounts improved, expected losses returned to the pre-crisis levels (Figure 4).5
Expected losses given default in the corporate sector.
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
Expected losses given default in the corporate sector.
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
Expected losses given default in the corporate sector.
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
15. The adjusted book value data for 12 banks were used to estimate time series for credit risk indicators for the banking sector.6 With the adjusted set of assets and assets' volatilities, a time series of default probabilities for each individual bank was estimated—with the default probability of the banking sector estimated by applying, to the individual default probabilities, a weighted average (based on each banks' proportion of total assets).
16. The estimated default probability (EDF) of the banking system using the modified Merton framework appears to be sensible. The framework predicts a near-zero 1-year default probability (with volatility measured over total assets) prior to the 2002 crisis; this suggests that the 2002 shock was largely unanticipated (in line with the results found in Chapters II and III). However, beginning in March 2002, the estimated default probability starts to increase, reaching 45 percent in September 2002. Since then, the default probability has declined substantially, to near zero by end-2006 (Figure 5). This is consistent with a reduction in assets volatility and the substantial “clean-up' in banks portfolios associated with the restructuring process.
Banking sector default probability
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
Banking sector default probability
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
Banking sector default probability
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
Using the modified Merton framework
17. The modified Merton framework can be used to simulate the impact of potential shocks on the EDF. This simulation provides a basis to assess the strength of the improved risk indicators beyond the traditional stress tests. In particular, given that volatility is a key parameter of the EDF, the near zero probability of default is to a large extent the result of the currently low volatility environment. Since standard stress tests only provide information on banks' assets and liabilities levels following shocks, this paper simulates assets' volatilities consistent with the after-shock level of assets. For this purpose, a historical relationship between total assets and their volatility is constructed for all banks to estimate the after-shock assets' volatilities (Figure 6).
The relationship between assets and assets' volatility in Uruguay
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
The relationship between assets and assets' volatility in Uruguay
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
The relationship between assets and assets' volatility in Uruguay
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
18. A simulation of a 2002 crisis-like scenario shows that banks have become more resilient to shocks, further confirming the thrust of the FSAP's stress tests results.7 Using the FSAP's severe capital and current account shocks, the default probabilities reach 24 percent and 14 percent respectively, far below the 45 percent default probability predicted by the model for the peak of the 2002 crisis. However, default probabilities under a 2002 crisis-like stress scenario remain significant, thus underscoring the need to further reduce vulnerabilities in the banking system (Figure 7).
The default probability for the banking sector has stabilized since 2002 and remains at lower levels even when facing significant shocks.
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
The default probability for the banking sector has stabilized since 2002 and remains at lower levels even when facing significant shocks.
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
The default probability for the banking sector has stabilized since 2002 and remains at lower levels even when facing significant shocks.
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
E. Concluding Remarks
19. The results of a modified Merton framework, applied to the case of the Uruguayan banking system, appear to be promising for countries without equity markets. While the methodology is based on balance sheet information, and not on market valuations, the time series for the estimated asset volatilities and default probabilities seem quite sensible. Indeed, they track well the deterioration of the system during the 2002 crisis. The modified Merton framework also proves useful to simulate the effects on individual banks of possible changes in macroeconomic conditions—and, by incorporating volatility into the analysis, improves upon conventional stress tests that rely only on asset and liability levels.
20. While still significant, the analysis suggests that vulnerabilities have continued to decline, further confirming the FSAP stress tests results. The estimated default probability reaches only half the level measured at the peak of the 2002 crisis, even under a substantial shock to the capital account; and the impact of a shock to the current account is even smaller. The results also show, however, that important vulnerabilities remain. Thus, it will be essential to continue deepening financial sector reforms over the medium-term.
References
De Brun, J., N. Gandelman, H. Kamil, and A. C. Porzecanski, 2006, “The Fixed-Income Market in Uruguay,” (Mimeo; Universidad ORT Uruguay).
Dwyer, D. W., G. Guo, and F. Hood III, 2006, “Moody's KMV RISKCALC™ V3.1 US Banks Modeling Methodology,” Working Paper, Moody's/KMV.
Financial Sector Assessment Program, 2006, Appendix 2: “Stress Testing the Banking Sector, International Monetary Fund.
Gapen, Michael T., Dale F. Gray, Cheng Hoon Lim, and Yingbin Xiao, 2005, “Measuring and Analyzing Sovereign Risk with Contingent Claims,” IMF Working Paper 05/155, (Washington: International Monetary Fund), available on the web at: http://www.imf.org/external/pubs/ft/wp/2005/wp05155.pdf.
Gapen, Michael T., Dale F. Gray, Yingbin Xiao, and Cheng Hoon Lim, 2004, “The Contingent Claims Approach to Corporate Vulnerability Analysis: Estimating Default Risk and Economy-wide Risk Transfer,” IMF Working Paper 04/121 (Washington: International Monetary Fund), available on the web at: http://www.imf.org/external/pubs/ft/wp/2004/wp04121.pdf.
Gray, Dale F., and Matthew T. Jones, 2006, “Measuring Sovereign and Banking Sector Risk in Indonesia: An Application of the Contingent Claims Approach,” in Indonesia, Selected Issues Papers, IMF Country Report no. 06/318 (Washington: International Monetary Fund).
Gray, D. F., R. C. Merton, and Z. Bodie, 2006, “A New Framework for Analyzing and Managing Macrofinancial Risks of an Economy,” NBER Working Paper No. 12637, Oct. 2006 (Cambridge, Massachusetts: National Bureau of Economic Research).
Hull, J. C., 2000, Options, Futures, and Other Derivatives (New Jersey: Prentice Hall, 4th ed.).
International Monetary Fund, International Financial Statistics, various issues (Washington: International Monetary Fund).
Merton, Robert C., 1973, “Theory of Rational Option Pricing,” Bell Journal of Economics and Management Science, Vol. 4, 141–83.
Merton, Robert C., 1974, “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” Journal of Finance, Vol. 29 (May), pp. 449–70.
Merton, Robert C., 1977, “An Analytic Derivation of the Cost of Loan Guarantees and Deposit Insurance: An Application of Modern Option Pricing Theory,” Journal of Banking and Finance, Vol. 1, pp. 3–11.
Mitton, T., 2006, “Why Have Debt Ratios Increased for Firms in Emerging Markets,” Working Paper (Brigham: Young University).
Seelig, S., 2006, Resolving the Banking Crisis in Uruguay (Mimeo; International Monetary Fund).
Appendix—Estimating Risk Indicators for the Corporate and Banking Sectors
Estimating Corporate Sector Expected Losses
The main challenge consists in generating a consistent time series on total assets to estimate volatilities on total assets returns. This challenge arises because the sample size (number of firms) in the dataset changes over time. An estimate of total assets as the sum across all firms at each point time, may capture variations in total assets that are simply due to changes in the dataset sample. To control for this fact, Mitton (2006) suggests to estimate the following panel regression for the average firm within the firm:
where Firmi represents firm-fixed effects and Yeart represents a full set of year-specific dummy variables. The time series on the total assets is then constructed as:1
This estimate provides a complete time series for (annual) total assets covering the period of 1994–2006, which makes it possible to estimate returns as continuously compounded, that is rt = In(TAt / TAt−1). To estimate volatilities, it is then possible to use an exponentially weighted moving average (EWMA):
where rt is the return on the total assets at time t, λ is the decay factor (we are using λ = 0.95, following common practice), and σt2 is the volatility at time t.
It is instructive to express the distance-to-distress in another (approximated) way:
where TA is the total assets, DB is the distress barrier, and σTA is the volatility of total assets. The numerator of expression (5) is component 1, which represents the distance of total assets to the distress barrier, as a fraction of total assets (how far from distress). The denominator, σTA, is component 2. Figure A1 depicts the evolution of the components of distance to distress for the corporate sector.
Uruguay's corporate sector: components of distance to distress
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
Uruguay's corporate sector: components of distance to distress
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
Uruguay's corporate sector: components of distance to distress
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
It is clear that: (i) volatility increased substantially in 2002, consistent with the banking crisis that led to a depreciation of the peso, and adversely affecting companies with a substantial exposure to FX rate risk; (ii) after 2002, volatility declines, but still remains above pre-crisis levels; and (iii) component 1,
With information on assets, assets volatility, interest rate, and liabilities, it is possible to obtain the expected losses, given default (Merton, 1977):
where P represents the expected losses, B represents the distress barrier, r is the risk-free interest rate, t is the maturity (for the sake of simplicity, we are looking into 1-year ahead measures), A is the total asset, and d1 and d2 are known parameters in the Black and Scholes formula.2
Estimating Banking Sector Default Probability
To estimate volatility for banks' total assets, it is first necessary to construct a time series of return on assets as rt = In (TAt / TAt−1). Then, like for the corporate sector, volatilities are estimated using the EWMA updating expressions:3
It is also possible to estimate volatilities using time series on return on deposits. Since changes in deposits may be viewed as a measure of customer's confidence in the bank, it may be a better proxy for ‘market-related' volatility. We use both sets of volatility to estimate risk indicators. Both approaches yielded similar results.
The liquidity shock hitting the banking sector in 2002 is captured. Liquid assets were drained at a fast pace in an effort to meet the increasing deposit withdrawals that followed the Argentinean crisis. Following this event, volatilities remained at low levels, reflecting the restructuring of the banking sector. The second hump in deposits volatilities reveal a second run of depositors that took place early in 2003 (Figure 12A2).
Uruguay's banking sector volatilities
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
Uruguay's banking sector volatilities
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
Uruguay's banking sector volatilities
Citation: IMF Staff Country Reports 2008, 046; 10.5089/9781451839418.002.A006
Once asset volatility has been estimated, it is then possible to estimate distance-to-distress and default probability for each bank individually.4 Risk indicators for the banking sector can be obtained as weighted averages of individual banks, weighted by banks total assets.
See Gapen et al. (2004, 2005) and Dale and Jones (2006) for examples of application of the Merton framework to government, banking, and corporate sectors' balance sheets.
Technical details are provided in Gapen et al. (2004, 2005).
For more details on the stress tests' assumptions, see Appendix 2 of the Uruguay FSSA, February 2006.
A capital injection to the banking system, for example, would mask the real volatility in the assets being depleted to meet the deposit withdrawals from a deposit run.
The sample of firms used to construct a time series on total assets and estimate their volatility is taken from De Brun et al (2006) and covers the period 1995–2005.
The twelve banks covering 70 percent of the system are BROU, Banco A.C.A.C., Discount Bank, Santander, Frances Bank, HSBC, Surinvest, Citibank, ABN Amro Bank, BankBoston, Lloyds Bank, and Banco de La Nacion Argentina. Quarterly balance sheet data is available for 2000–2001 and monthly data for 2002M1 to 2006M12.
This is not surprising since the results from the stress tests are used to shock the modified Merton framework.
There are also missing observations for 2002 and 2006. To obtain the value for 2002, the average values for total assets for 2000, 2001, 2003, and 2004 are used. To obtain the value for 2006, the average growth on total assets from 2003 to 2005 is used.
See Hull (2000) for the precise formulae and definition.
For banks we also use λ = 0.95.
See Gapen et al (2004, 2005) for details on the formulas.
