Default Risk at Risk

What's the default rate of Europe?
Let's try to answer this question by examining the (spread on) 10 year Government Bonds for different European countries.

Some simple observations:

• A Diverging Europe
  The above chart clearly shows that EU-country interest rates are diverging. The 'spread' between relative financial healthy countries and their weaker brothers is increasing.
   
• A strong EU Base?
  Key (rhetorical) question  is whether the low interest rates of countries like Denmark, Sweden and Germany are the result of their strong economic performance or the effect of fact that other EU-countries are in real trouble...
   
• Rewarding Debt
  The current real interest rate of  relatively 'healthy' countries (interest rates less than 2%) is negative at long term inflation levels between 2% and 4%.
  Negative real interest rates imply a non-sustainable  debt rewarding economic system for governments and banks. Perhaps most important: in a negative real rate economy financial institutions like pension funds, lose their rationale for existence!!
  
  
• Risk Free Rate?
  Also remarkable is that these low interest rates are far under what was once qualified as risk free rate (3%-6%, whatever.....)

Risk Free Rate In order to be able to calculate a country's default probability, we need to estimate the so called 'risk free rate'. As I've Illustrated earlier (how to catch risk)  the idea of a 'risk free rate' is an illusion: Every asset has some kind of risk Relative Risk However risk could be relatively defined from one country to another. In order to do so, let's analyze a more worldwide picture (table on the right) of 10-y bond rates on June 1 2012. From this table we may conclude that the best risk free country 10-year  bond rate is the 0.55% Swiss rate. As we know that even this rate is not completely free of risk, let's not settle for the traditional  mistake of  'one point estimates', but calculate a country's default risk on basis of different risk free rate levels, varying between 0% and +1%. Calculating Country Default Risk A country's semiannually paid default risk (dh) can be calculated from a country's 10-year (semiannually paid) Bond Rate (semiannually paid coupon rate = ch ) and a semiannually paid Risk Free Rate (semiannually rate = rh) on basis of the next relationship: leading to: Expressed in the yearly semiannually paid coupon rate (c=2.ch) and risk free rate (r=2. rh): Finally resulting in a formula (1) regarding the one year default risk (d):

Country 10Y Bond (%) Greece 30.83 Pakistan 13.27 Brazil 12.55 Portugal 12.03 Hungary 8.71 India 8.5 Ireland 8.21 South Africa 8.2 Colombia 7.6 Peru 6.76 Spain 6.56 Indonesia 6.51 Mexico 6.04 Russia 6 Italy 5.92 Poland 5.45 Israel 4.46 Thailand 3.78 South Korea 3.69 Malaysia 3.55 New Zealand 3.54 China 3.38 Czech Republic 3.27 Belgium 2.94 Australia 2.9 Norway 2.38 France 2.36 Austria 2.12 Canada 1.76 Netherlands 1.61 United States 1.58 United Kingdom 1.57 Finland 1.49 Singapore 1.46 Sweden 1.29 Germany 1.2 Denmark 1.03 Hong Kong 1 Japan 0.82 Switzerland 0.55

Now, let's calculate the default risks for the top-5 worrisome EU countries given a risk free rate of 0%:

	Greece	Portugal	Ireland	Spain	Italy
10Y Bonds	30.8%	12.0%	8.2%	6.6%	5.9%
1YR Default Risk , r=0%	24.9%	11.0%	7.7%	6.3%	5.7%
1YR Default Risk , r=1%	24.2%	10.1%	6.8%	5.3%	4.7%

As is clear from this table, in practice there's no substantial impact-difference between a 0% or a 1% risk free rate, with regard to calculating a one year default rate.

This helps us to define a really simple rule of thumb to translate a 10Y Bond rate (c) into 1 year default rate (d) at a 0% 'free interest rate level' :

Examples

• 10Y Bond rate = 30% =0.3
  d= 0.3 -0.3*o.3/2 = 0.3 - 0.045 =0,255 ≈ 25%
   
• 10Y Bond rate = 10% =0.1
  d= 0.1 -0.1*o.1/2 = 0.1 - 0.005 =0,095 ≈ 9.5%
   
• Higher risk free rates  (r>0%)
  At higher than 0% risk free rates, simply subtract the risk free rate from the default rate, to find the default rate at that higher risk free rate.
  Example: Risk free rate = r =1%, 10Y Bond Rate = 30% : d ≈ 25%-1% ≈ 24%
   
• Compare country relatively default rates
  10Y Bond Rate Ireland = 8.21%
  10Y Bond Rate Greece = 30.8%
  Probability (d) that Greece defaults relatively more than Ireland:
  d ≈ 0.31 -0.5*0.31^2 -8 ≈ 0.18 ≈ 18% (more exact formula 1: 18.62%)

Of course we have to realize that all this hocus-pocus 'default math' is only based on strongly artificial managed market perceptions.... Probably the real default rates of Greece are much higher than 25%. In other words:

                               Default Risks are at Risk

N-year default probability
For those of you who still believe that financial Europe will survive, let's calculate default probabilities for more than one year. In formula the N-year default probability (d_N) can be defined as:  d_N = 1-(1-d)^N

Conclusion

There's no hope for a Greece Euro-survival. Main problem is that even if Greece's debts would be covered by the stronger EU countries, Greece is not in the position of realizing a financial stable and positive economy.

Other financial weak and 'temporarily more or less out of the spotlight' countries like Portugal, Ireland and Spain will follow. No matter the development of default rates, it's an illusion to think that Germany is financial able to carry Europe through this crisis. Perhaps it's time to introduce country linked euros like the DE-Euro.......

Related Links
- Download Excel Spreadsheet used for this blog
-  On line Bond Default Probability Calculator
- Greece’s bond exchange
- Actual 10Y Government Bonds (all countries)
- The Greek debt crisis and the hypocrisy of the EU bureaucrats (2010)