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)

Risk Manager Test

Risk Manager is THE profession of the future.

For all (young) actuaries, econometricians and other talented whizzkids who are considering to become a Risk Manager, here's the ultimate test...

Find out if you really have more risk management talent than an average Duck Risk Manager.

Perhaps even some more experienced Risk Managers dare to risk their reputation by taking the test as well........ 

Risk Manager Test 

Imagine you're a risk manager during World War II...

Allied pilots are bombing targets in Germany. Most bomber airplanes come back with heavy damage, some even don't come back at all. Therefore it is considered important to protect bombers with extra armor.

As there is only very limited supply of retrofitting armor, you as a risk manager are hired to determine where this extra armor is best placed on a plane.

In order to find out the vulnerable parts of the plane, you mark every bullet hole of every plane that comes back from a bombing mission as a red dot on a plane-bullet-hole diagram.

After having observed more than 50 planes coming back, you end up with the next diagram:

Instruction
Please point out in detail the most important places where you as a risk manager, would put the armor on the plane.

READY?.......

To find Out if you passed the Risk Manager Qualification Test please press on the answer button.

ANSWER

Aftermath

The risk manager in this test actually exists. During WWII, the Hungarian-born mathematician Abraham Wald undertook a study with the British Air Ministry to use statistical analysis to help protect bombers flying over enemy territory. The data to be crunched included the number and location of bullet holes on returning aircraft, and the goal was to use this information to determine where to best add armor to the plane's structure.



Sources & Related Links
- Abraham Wald : original Report
- Abraham Wald's Work on Aircraft Survivability by Marc Mangel 
- The hole story: What you don't see will kill you 
- UK Bombers in WWII (pictures)

Strategy Outsourcing

Most Pension Fund Boards are sincerely convinced they define their strategy on basis of their own insights.....

In practice, the leading Investment Consultant - as trusted advisor - often has a strong influence on the board.

Very often the authority of the Investment Consultant is so dominant that it's "not done", permitted or 'seen as wise' to discuss the advice of the consultant. Nor is a second opinion seen as appropriate, as it might be regarded as a matter of distrust in the trusted advisor relationship.....

Unfortunately in these situations it is quite often the Investment Consultant, instead of the Pension Find Board, who implicitly defines the Strategic Plan, Risk Appetite and Asset Mix......

Of course this doesn't apply for YOUR Pension Fund....

In this case DON'T view or download the next power point presentation 'On how Strategic Advice got Outsourced'....
Strategy Outsourcing

Scroll through the presentation by pressing the right arrow button.

Confidence Fallacy
Last but not least: As most Investment Consultants advice more than one pension fund, it is not unlikely that a lot of pension funds get more or less the same kind of advice. This might give pension fund board members a false notion of confidence with regard to their (own) chosen investment strategy.

All the more reason to be extra vigilant that the chosen strategy is finally YOUR strategy and not that of your consultant......

Remember.....  Never Ever Outsource your Strategy!

Related Links 
- Download PDF: On how Strategic Advice got Outsourced
- Donald Duck Search Images