Although the world history contains many examples of countries which haven’t (fully) honoured their obligations, this risk seems to be underestimated in the QIS5 and the level 2 text (especially for European countries). A better understanding what causes a sovereign default and how to determine the capital requirement, will lead to a better internal model and to better risk management. However, due to limited data, there is currently no uniform approach.
Reinhart and Rogoff provide a detailed overview of sovereign defaults (including 1 Dutch default in 1814!) starting from the Napoleonic wars. The authors show that defaults occur in “waves” where long periods without defaults, are followed by periods with a sharp increase in defaults. Hence, looking at historical data, one cannot speak of a “new era” in which a lower number of defaults are applicable. They also point out that defaults are not limited to Latin American and African countries, but have happened in Europe and Asia as well, as shown in Table 1.
They also observe that defaults happen both through impairment of assets, or by the excessive increase of money supply (seignorage). Furthermore, opinions differ if delaying payments automatically triggers a default or if the intention behind a default should be taken into account as well (the Venezuelan default of 1998 did not happen because the government refused to honour payments voluntary, but because the official who was responsible for signing the checks was not present causing delays and hence an automatic default).
The yield (return) on corporate bonds is higher than the return on government bonds as the latter are less risky: in the worst case, the government can decrease its spending and raise taxes to meet its obligations or employ seignorage. Companies are less flexible because a substantial increase in their product prices and reduction of expenditure is usually not an option. The difference in yield between government and corporate bonds is referred to as the spread.
However, before looking into the spread components, one has to agree on a risk-free asset. The AG position paper concludes that a government curve or a swap curve with a credit adjustment is the closest approximation to a risk-free return: the government curve is a natural fit (as a government can fund its way out of a default), the swap-rate is more liquid than the government market which is an attractive characteristic for a risk-free rate.
Of course we can not assume that every government bond is risk-free: a government bond with a low credit rating does have default risk!
The difference between the risk-free rate and the yield on corporate bonds is explained on the basis of the following factors (as outlined in Churm & Panigirtzoglou):
1. Credit risk factors:
1.1 Expected default: this is the extra return investors require on corporate bonds as compensations for the increased risk of default.
1.2 Downgrade risk: the compensation investors require for the risk that a corporate bond is downgraded (e.g. from A to BBB) leading to a decrease in value.
1.3 Increase in credit spread: the risk that although a corporate bond retains the same rating, the difference in yield between corporate bonds and risk-free bonds increases, therefore leading to a decrease in value of the corporate bonds.
2. Non-credit risk factors:
2.1 (Il)liquidity: the market for government bonds is deeper and more liquid than the corporate bond market. Therefore, investors usually incur higher costs when trading corporate bonds. For these additional costs investors require an additional return also known as (il)liquidity premium.
2.2 Tax: government bonds (e.g. municipal bonds) have a preferential tax treatment. Investors require a compensation when investing in corporate bonds instead.
2.3 Regulations: government bonds are more widely accepted than corporate bonds or there might be a preferential treatment towards government bonds. E.g. Solvency II exempts some government bonds from capital charges making them more attractive for insurance companies. Also, in some countries pension funds are required to hold a certain percentage of their assets in (local) government bonds.
An overview of spread-decomposition is given in Figure 1:
In the insurance industry, non-credit risk factors belong to the yield pickup of the insurer: for some products with a predictable cash flow pattern (e.g. annuity) the insurer is able to hold the corporate bond until maturity while matching its liability cashflows. Therefore, the insurer has no need for interim trading and can benefit from the non-credit factors.
This article elaborates on the spread elements of an increase in spread and default.
Because the swap market is more liquid than the government bond market, most insurers use a swap-rate, with a credit adjustment to discount liability cash flows. Nevertheless, if these obligations are backed by government bonds this creates the risk that the interest rate on government bonds in some scenarios is higher than the swap rate. Figure 2 below shows how a 1 x scenario is determined for Philippine swaps and bonds.
However, this method has its limitations:
• A liquidity and credit adjustment is required to compare swaps with government bonds;
• The swap market is still not fully developed everywhere (e.g. Asia), and therefore a lack of appropriate data can occur;
• Lack of data requires a subjective duration choice or the need to apply inter/extrapolation;
• This method calculates the risk in the reduction of spreads and not the probability of a default.
When a government defaults, this does not automatically result in complications for an insurer: the value of the liabilities decreases proportionally with the bond values. However, when an insurer’s assets and liabilities are denominated in foreign government bonds, there is less certainty that the foreign government/regulator uses the same principle. Besides the standard currency risk, there is now a risk of a government default as well. Due to reputational risk, it is not always possible for the insurer to (partially) write down its obligations.
The default risk for corporate bonds is usually estimated by the Probability of Default (PD) and the Recovery Rate (RR) once default has occurred. Structural form models assume a threshold (also called default boundary) after which default occurs. The loss is calculated as follows:
For the PD a standard normal distribution is appropriate and a beta distribution for the RR is common. A Monte Carlo simulation creates random numbers for PD and RR from which you can determine VaR outcome. Rating agencies provide annual reports with PD and RR for each asset type and rating.
Rating data unfortunately have several limitations:
• Lack of historical defaults: Moody’s mentions only 15 defaults between 1983-2010, hence derived PD and RR values might not be robust;
• Changing data set: in 1990 the majority of Moody’s government bonds consisted of investment grade bonds (BBB and higher). As more emerging markets have entered the bond market, the proportion of speculative bonds (BB and below) has increased, as shown in Figure 3. The increase in the number of defaults over time (the first default in the Moody’s data set was only in 1998), shows that counterparties are less risk-free than before. A simple historical average hence does not sufficiently identify the potential future risks;
• Lack of transparency on one-year default probability calculation: specific descriptions of the methods which rating agencies apply are not available. Comparing the 1-year default probabilities of different rating agencies is thus difficult;
• Differences local and foreign defaults: the local credit rating is usually higher than the foreign credit rating because governments can print money to avoid a local default, and because the political and economical costs of a local default are higher. Although the difference between the number of foreign and local defaults declined over the years, the choice between the two ratings remains subjective;
• No historical 1-year investment-grade defaults: the use of a longer history (5 or 10 years) default probability (PDi) therefore leads to better risk assessment. The following formula determines the 1-year default probability (δi):
• The lowest rating category, CCC-C, is a “mixed bag” that contains both countries with a high default chance in the near future (e.g. by end of 2011 Greece) and countries that have already defaulted and have returned to the capital market.
Rating agencies claim that their procedure for assigning ratings is on the same basis for companies and countries. As there is more data available for corporate bonds than sovereigns, the PD and RR corporate data are used instead of the government bond data. Also there are one-year historical defaults for investment-grade corporate bonds which are not available for government bonds. The only adjustment that remains is for the CCC-C rating: countries can default, re-structure and return to the capital market while companies often don’t have that option. A reduction of the CCC-C rating PD for sovereigns compared to corporates is therefore appropriate.
The standard formula in Solvency II has no spread capital requirements for AAA and AA-rated government bonds issued in domestic currency. Especially European government bonds are given a preferential treatment under the standard formula as a capital exemption is given independent of the rating: e.g. both German (AAA-rated) and Greece (CCC) sovereign bonds are capital exempted although the underlying risks differ significantly. However, an internal Solvency II model can make an exception for this and include a sovereign credit capital charge.
Solvency II seems to have an odd relationship with sovereign default risk: QIS5 excludes government bonds in the counterparty default module and instead assigns them to the spread module, which indirectly implies that there is no default can take place on government bonds. Under the current economic climate this seems to be far too optimistic!
Ratings have a prominent role in the Solvency II framework (counterparty, credit spread, and concentration risk). In the default model ratings play a crucial role as well. However, the rash use of ratings is similar to the blind crossing of a busy street when the light is on green: it seems safe until one day it goes wrong, as investors in AAA-rated American mortgage backed securities found out in 2008. The actuarial profession should adopt a more market-based instrument to estimate counterparty risk: market ratings, such as spreads, or CDS, are available for this, although this leads to more volatility. In the meantime, the use of an average rating of different agencies would be the most practical solution.
Actuarieel Genootschap & Actuarieel Instituut. Rapport, Principes voor de Rentetermijnstructuur. “Dé juiste curve bestaat niet”, Actuarieel Genootschap & Actuarieel Instituut, Utrecht, 2009.
Churm, Rohan and Nikolaas Panigirtzoglou, Decomposing credit spreads, Bank of England, London, Working paper no. 253, 2005.
Moody’s, Corporate Default and Recovery Rates, 1983-2010. Moody’s, New York, 2011.
Moody’s, Narrowing the gap – a clarification of Moody’s approach to local versus foreign currency government bond ratings, Moody’s, London, 2010.
Moody’s, Sovereign Default and Recovery Rates, 1983-2010. Moody’s, New York, 2011.
Reinhart, C.M. and K.S. Rogoff. This time is different: A Panoramic View of Eight Centuries of Financial Crises. NBER working paper, 2008.
Remolona, E.M., M. Scatigna and E. Wu (2008), A ratings-based approach to measuring sovereign credit risk, International Journal of Finance and Economics, volume 13.
Standard & Poor’s, Sovereign Defaults And Rating Transition Data, 2010 Update, Standard & Poor’s, New York, 2011.
Webber, Lewis (2007), Decomposing corporate bond spreads, Bank of England Quarterly Bulletin, Winter, pages 533-541.
This article has also been published in the Dutch actuarial magazine “De actuaris” as per March 2012 http://www.ai-ag.nl/download/12897-19-4-art.Houben.pdf and in the AENORM 74 pages 8-11 http://issuu.com/vsaekamer/docs/aenorm_74_definitief/1