04/10/ 01
DEFAULT PROBABILITIES ON EUROPEAN SOVEREIGN DEBT: MARKET-BASED ESTIMATES Laurence S Copeland and Sally-Anne Jones*
Both authors: Cardiff Business School Cardiff CF1 3EU Tel +44 1222 875740 FAX +44 1222 874419 email
[email protected]
Default probabilities on European Sovereign Debt: Market-Based Estimates
Laurence S Copeland and Sally-Anne Jones Cardiff Business School
ABSTRACT This paper attempts to extract real-time market-based estimates of the default probabilities on Government debt for a selection of European countries, using a technique applied by Bierman and Hass (1979) and Fons (1987) in the corporate debt market. The technique involves solving the debt pricing equation for the martingale probabilities which under the no-arbitrage assumption equate the price of risky debt discounted at the riskless rate to the actual price. Results for Belgium, Finland, Ireland, Italy, and Spain suggest default probabilities have tended to decline as EMU has approached.
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The arrival of European Monetary Union (EMU) at the start of 1999 has important implications for the sovereign debt market. In particular, since all existing debts of member countries must now be repaid in Euros, the previously remote possibility of default becomes a significant risk, especially as several countries have entered EMU with levels of debt relative to GDP 1 comparable to those of recently defaulting Asian and Latin American governments. In this context, it is of interest to attempt to compute the default probabilities implicit in the yields on 2 European government bonds. METHODOLOGY To this end, we follow the procedures applied by Bierman and Hass (1975) and later by Fons (1987) to corporate debt. Under this approach, we can view risky debt as being priced by an equation of the following general form, where for simplicity we assume coupons are paid annually:
~ ~ ~ E 0 ( CF1 ) E 0 ( CF2 ) E 0 ( CFN ) B0 = + + .................. + 1+ r (1 + r ) 2 (1 + r ) N
(1)
i.e. the current price of a bond promising to pay cashflows CF1 ……..CF N in each of the next N years is the present value of the expected cashflow stream, where the expectation is computed with respect to the martingale (or risk-neutral) probabilities, while the present value involves only r, the redemption yield on riskless debt of the same maturity and coupon rate. Provided we can identify the cashflows in (1), we can therefore derive the risk-neutral 3 probabilities of default on the promised payments from bond prices. In order to implement this approach in the context of sovereign debt denominated in foreign currencies, we impose a number of further assumptions. First, since we have no sound basis for assuming otherwise, we follow Fons (1987) in imposing a flat term structure on the default probabilities i.e. we set Pt1 = Pt2 = …….= PtN = Pt, where Ptk is the probability of default on the th 4 k payment impled by market prices at time t. Second, we assume that in the event of a default occurring in year k , the payout to bondholders is zero in that year and in all 5 6 subsequent years, k+1 ……. N. We also assume there are no relevant taxes on cashflows. Under these circumstances, we can write equation (1) as:
B0 =
(1 − P )C (1 − P ) 2 C (1 − P) N (C + 100) + + .................. + 1+ r (1 + r ) 2 (1 + r ) N
(2)
The main difficulties in implementing this methodology relate to finding adequate proxies for 1
For example, Mexico’s pre-crisis level of foreign currency debt was only 28% in 1995, compared to levels of nearly 27% and 35% for Italy and Belgium in 1998 and nearly 120% if what were originally domestic curreny debts are included. 2 Little attention has so far been paid to these issues in the published literature, though see Lemmen and Goodhart (1999), who use spreads over corporate swap rates to estimate credit risk premia, and Izvorski (1998), who concentrates on Brady bonds. 3 Of course, if we are happy to make the assumption that bond markets are actually risk neutral, we can identify the probabilities derived in this paper with the “true” default probabilities. 4 The only nonflat term structure of probabilities for which there could be any obvious a priori justification might be one which allowed for a higher probability of default on the final baloon payment. It should be remembered in this regard that sovereign default is far more a matter of choice (that is, of political decision) than are corporate defaults, which are usually imposed by creditors, especially outside the USA. 5 Fons (1987) imposes a constant default payout ratio of 41%, based on the historic level of bankruptcy payouts in his sample of defaulting US corporate debt. We have no comparable dataset for sovereign debt on which to base a nonzero payout ratio. 6 In our sample, Italy is the only country with a withholding tax on coupons, and even there it was abolished for nonresidents at the start of 1997 (see Favero et al (1997)).
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the variables, especially the riskless rate. The obvious candidate is the yield on comparable own-currency borrowing. Thus, we implement (2) by using the yield on German borrowing in DM as the riskless rate in pricing DM -denominated debt issued by other countries (Italy, Spain, Finland, Ireland, Belgium) and similarly the yield on French borrowing in FFr for FFrdenominated debt issued by Spain However, since we are unwilling to introduce a submodel of the term structure at this point, we are restricted to using the redemption yield on riskless debt of similar maturity and coupon to the risky debt priced by equation (2). Unfortunately, this narrows down very significantly the number of bonds we can use, since in each case we require a matched pairing of the two 7 countries’ bonds. In the end, we were left with only 6 matched pairs of bonds from which to compute our probabilities. RESULTS In order to interpret the results summarised in Table 1 and presented in the graphs, note that as of time t, the probability of default at some point in the remaining life of a bond with N coupon payments still outstanding is given by:
P = 1 − (1 − p ) t
t
N
N
= ∑ pt (1− pt ) j −1
(3)
j =1
so that for a bond with 10 years left to redemption, a probability of default on the next annual coupon payment of, say, 0.1% implies about a 1% probability of default up to and including maturity. In the event, as can be seen from the Table, mean default probabilities over the various data periods were estimated at under one third of 1% for Belgium Finalnd and Ireland (all borrowing in DM). For Italy, the figures were much higher: over 4% on average, and never 3 1 less than 2 /4%, and peaking at nearly 5 /2%. For Spain, we had data on debt denominated both in DM and FFr. It is slightly disappointing that the two series yield different estimates of the default probability (0.268% and 0.468% respectively), because they may have been expected to be equal. After all, it is hard to imagine an EU member defaulting on its debt in one case and not in the other. The most likely explanation would appear to be that the estimates of the default risk are contaminated by foreign currency risk, so that DM debt is overpriced relative to FFr debt regardless of the creditworthiness of the borrower. Looking at the time series plots in Figs 1 and 2, we note a number of other points. First, the meetings where the key decisions regarding EMU memebership were made (03/25/98, when the European Commission made its recommendations and 05/02/98, when the Heads of State ratified the decision) appear to have had no perceptible effect, probably because they were anticipated well in advance of the event. On the other hand, as might have been expected, both the market’s assessment of the riskiness of Italian debt and its volatility rose dramatically during the global credit crisis surrounding the Russian default in August 1998. Moreover, although the level has fallen back to precrisis levels in recent months, volatility remains high. The same effects are visible, though less obvious, in Spanish and Finnish borrowing, though not in Irish and Belgian debt markets.
CONCLUSION 7
Kan (1998) offers an alternative solution, in using the yield on supranational debt as his riskless rate. We found this approach unsatisfactory, as the yield on supranational debt in our sample period was often higher than on comparable national borrowing. Kan (1998) also experiments with a term structure model, which creates complications in interpreting his results, but less so than it would here, because he is only concerned with measuring the credit risk premium rather than default probabilities. It is also worth noting that many of these bond issues are relatively small and illiquid. We eliminated from our sample any issues smaller than $500m.
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Apart from the fact that the absolute levels of the probability estimates are lower than might have been expected, the broad downward trend in the series runs counter to the logic of EMU, for the reasons given at the outset. There are two possible explanations. The first is myopia on the part of bond market traders. This explanation is consistent with the widespread and confident anticipation, reflected almost unanimously in media comment, of unhampered yield convergence among EMU members, completely ignoring any consideration of credit risk. An alternative, and in our opinion more persuasive explanation, is that markets are (and always were) well aware of the credit risks of Euro-denominated repayments. However, rational agents may well be taking for granted that, the Maastricht Treaty No-Bailout Clause notwithstanding, the monetary and fiscal institutions of the EU will in practice be unable to withstand the pressure to rescue a member country in danger of default.
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Issuer
Issue Date
TABLE 1: FOREIGN CURRENCY DEBT ISSUES Redemption Currency Coupon Default probabilities N Date N
P = 1 − (1 − p ) t
Belgium Finland Ireland Italy Spain Spain
09/27/94 01/06/93 03/01/89 07/04/97 12/05/94 05/20/94
10/18/99 01/27/00 03/01/99 07/10/07 01/05/00 06/20/01
DM DM DM DM DM FFr
t
= ∑ pt (1− pt ) j −1 j =1
%
Mean
Max
Min
S.D.
7.25 7.50 6.50 5.75 7.00 6.50
0.221 0.246 0.332 4.084 0.268 0.468
0.487 0.629 1.792 5.461 0.647 1.060
0.000 0.001 0.000 2.756 0.020 0.099
0.084 0.080 0.126 0.363 0.098 0.191
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Fig 1: Default Probabilities for Finland, Spain Over Remaining Life of Bond (in %) 1.20
1.00
fnland/dm spain/dm spain/ffr
0.80
0.60
0.40
0.20
Jan-99
Dec-98
Oct-98
Nov-98
Aug-98
Jul-98
Jun-98
May-98
Mar-98
Feb-98
Jan-98
Dec-97
Oct-97
Sep-97
Aug-97
Jul-97
Jun-97
Apr-97
Mar-97
Feb-97
Jan-97
0.00
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Fig 2: Default Probabilities for Belgium, Ireland, Italy Over Remaining Life of Bond (In %)
6.00 belgium/dm ireland/dm italy/dm 5.00
4.00
3.00
2.00
1.00
Feb-99
Jan-99
Nov-98
Oct-98
Sep-98
Jul-98
Jun-98
May-98
Mar-98
Feb-98
Jan-98
Nov-97
Oct-97
Sep-97
Jul-97
Jun-97
Mar-97
May-97
Feb-97
Jan-97
0.00
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BIBLIOGRAPHY
Bierman, H and Hass, J E (1975) An Analytic Model of Bond Risk Differentials, Journal of Financial and Quantitative Analysis, 10, 757-73 Cottarelli, C and Mecagni, M (1990) The Risk Premium on Italian Government Debt 1967-88, IMF Staff Papers, 37, 4, 865-80 Favero, C A, Giavazzi, F and Spaventa, L (1997) High Yields: The Spread on German Interest Rates, Economic Journal, 107, (July), 956-85 Fons, J (1987) The Default Premium and Corporate Bond Experience, Journal of Finance, XLII, 1, 81-97 Izvorski, I (1998) Brady Bonds and Default Probabilities, IMF Working Paper WP/98/16, February Kan, K (1998) Credit Spreads on Government Bonds, Applied Financial Economics, 8, 301-13 Lemmen, J J G and Goodhart, C A E (1999) Credit Risks and European Government Bond Markets: a Panel Data Econometric Analysis, forthcoming in Eastern Economic Journal, April
