Actuarial Proverbs: Will Europe Survive?

According to Eurostat, Europe - especially the Euro (€) 'Coin' Countries that put all their Euro eggs in one basket -  face a difficult time. In a world where money seems to grow on trees, it's hard to take the right measures to prevent Greece from a financial meltdown with unknown consequences.

Questions
Even for actuaries it's hard to understand what's happening and what makes sense or not, It's over our 'actuarial' head....

• Should 'Europe donor countries' support Greece fore more than the '110 billion Euro rescue' in 2010?
  
  
• Is Greece’s 10-year bond rate of 15% an adequate risk premium?
  
  
• Will restructuring Greece's debt solve anything, devaluate the Euro,  or pose other  incalculable risks to the overall Euro zone?

Difficult questions that are hard too answer....


Debt-Deficit Comparison
Let's take an actuarial look at the facts by comparing 2010 Government Debt with Deficit (all in % GDP):

From this chart it's clear that not only Greece is in the danger zone, but also Ireland and the US as well... Moreover, the UK is not free from worries, to put it mildly...

The blind are leading...
Another chart-conclusion might be that the blind are leading the blind'. Relative strong less-weaker countries like Germany and France,  have to carry the financial consequences of cheating and not-performing countries. Above all, we all know: one rotten apple spoils the barrel!!

In fact to save or revive 'Financial Europe' it would take some countries with no debt and a strong positive surplus (= negative deficit) instead of a deficit.

It seems neither sensible nor logical  to restructure another  country's debt if the outlook of the governments debt and deficit of the' helping country' is (slightly less) negative as well. But as we know: only fools rush in where angels fear to tread.

Trying to help other countries that fail to restructure themselves is like banging your head against a brick wall...  No risk premium on government bonds can compensate that...

Countries with a strong relative debt and a deficit should restructure their own country and financial situation at once, before asking ore receiving any outside help.

Growth: The Solution?
Some argue that debt and deficits are not so bad as long as countries are growing. Let's dive into this argument with the next chart (data source: Eurostat):

Indeed, from this 'Growth-Believe' we can now understand why (only) Greece is seen as such a major problem.

From this chart it's also clear that if Ireland and Spain are not going to grow one way or the other, they will become the next big problem. These countries have to take the bull by its horns, before it's too late.

It's throwing caution to the wind when 'debt and deficit countries' with a positive 'Real GDP Growth Rate' try to save sicker country-brothers by lending them money.

Moreover, it's lending money you don't really possess or own, it's like robbing Peter (yourself) to pay Paul....

Combining the two Eurostat charts it becomes clear that that not all 'Garlic Countries' (Mediterranean countries:Greece, Spain, Portugal, Italy) can be lumped together.

Greece is indeed the greatest risk , secondly a non-garlic country: Ireland...
Spain, Portugal and Italy are relatively at arm’s length and could perhaps keep their head above water if they take the right measures in time.

U.S.' Fiscal Gap

Finally, don't forget about the U.S., as the U.S. Real GDP Growth Rate is already declining to 2.3% in Q1 2011.

According to Boston University economist Kotlikoff, the U.S. is broke.  Kotlikoff doesn’t trust government accounting. He uses “Fiscal Gap,” not the accumulation of deficits, to define public debt. This "Fiscal Gap" is the difference between a government’s projected revenue  and its projected spending .

By this measure, the U.S. government debt is $200-trillion – 840 percent of current GDP. 

Conclusions

From all this it's clear Europe is stuck between a rock and a hard place...
Although ECB President Mr. Trichet thinks different, it looks like €-Europe has to choose between two blind goats (Irish saying):

(1) A complete Financial Europe Meltdown in case of endless financing default countries like Greece or

(2) Letting individual default countries go bankrupt, with unsure (systemic) consequences for local banks and other financial institutions that financed or invested in default countries.

How to decide? Guideline:  Of two evils, always choose the less....
As option (1) is clearly putting the cart before the horse, and surely leads to a meltdown, only option 2 is left: QUIT!

Sources and related links:
- Spreadsheet: Used Data, Tables for this blog (xls)
- US Real GDP Growth Rate
- Government Debt and Optimal Monetary and Fiscal Policy (2010)
- English proverbs and sayings (!)
- English deficit (including time table)
- Shadowstats (for the real stats!)
- The U.S. is broke?
- Eurostat: Euro area government deficit at 6.0% GDP (2011) 
- BILD: Interview with Jean-Claude Trichet, President ECB, 15 January 2011

Oversized Supervision?

In April 2011 EIOPA  published  the findings of its 2010 survey:

 REPORT ON REPORTING REQUIREMENTS TO SUPERVISORY AUTHORITIES

applicable to the Institutions for Occupational Retirement Provision (IORPs) in the context of the IORP Directive.

The report analyses several interesting differences in reporting among member states.

I'll will confine myself in this blog to two remarkable results....
 
1. Difference in number of Supervision employees per country
It's remarkable (and not directly explainable) to see that the UK and The Netherlands outnumber the other European countries on number of supervision employees....

 
2. Influence Actuarial Reporting
The survey provides a large number of reporting and monitoring issues that aim to monitor or mitigate several types of risk.
I'll provide a short report that shows the connection between some actuarial reports and types of risk.

Clearly the risk of funding is one of the most important issues with regard to actuarial reporting. Perhaps it's even a little bit overweighted......

Anyhow, check your reports with regard to the above risks, especially if your living in an oversized supervision country like the UK or The Netherlands....

Homo Actuarius Bayesianis

Bayesian fallacies are often the most trickiest.....

A classical example of a Bayesian fallacy is the so called "Prosecutor's fallacy" in case of DNA testing...

Multiple DNA testing (Source: Wikipedia)

A crime-scene DNA sample is compared against a database of 20,000 men.

A match is found, the corresponding man is accused and at his trial, it is testified that the probability that two DNA profiles match by chance is only 1 in 10,000.


Sounds logical, doesn't it?
Yes... 'Sounds'... As this does not mean the probability that the suspect is innocent is also 1 in 10,000. Since 20,000 men were tested, there were 20,000 opportunities to find a match by chance.

Even if none of the men in the database left the crime-scene DNA, a match by chance to an innocent is more likely than not. The chance of getting at least one match among the records is in this case:



So, this evidence alone is an uncompelling data dredging result. If the culprit was in the database then he and one or more other men would probably be matched; in either case, it would be a fallacy to ignore the number of records searched when weighing the evidence. "Cold hits" like this on DNA data-banks are now understood to require careful presentation as trial evidence.

In a similar (Dutch) case, an innocent nurse (Lucia de Berk) was at first wrongly accused (and convicted!) of murdering several of her patients.

Other Bayesian fallacies
Bayesian fallacies can come close to the actuarial profession and even be humorous, as the next two examples show:

1. Pension Fund Management
   
   
   It turns out that from all pension board members that were involved in a pension fund deficit, only 25% invested more than half in stocks.
   
   Therefore 75% of the pension fund board members with a pension fund deficit invested 50% or less in stocks.
   
   From this we may conclude that pension fund board members should have done en do better by investing more in stocks....
   
   
2. The Drunken Driver
   It turns out that of from all drivers involved in car crashes 41% were drunk and 59% sober.
   
   Therefore to limit the probability of a car crash it's better to drink...

It's often not easy to recognize the 'Bayesian Monster' in your models. If you doubt, always set up a 2 by 2 contingency table to check the conclusions....

Homo Actuarius
Let's  dive into the historical development of Asset Liability Management (ALM) to illustrate the different stages we as actuaries went through to finally cope with Bayesian stats. We do this by going (far) back to prehistoric actuarial times.
 

As we all know, the word actuary originated from the Latin word actuarius (the person who occupied this position kept the minutes at the sessions of the Senate in the Ancient Rome). This explains part of the name-giving of our species.

Going back further in time we recognize the following species of actuaries..

1. Homo Actuarius Apriorius
   This actuarial creature (we could hardly call him an actuary) establishes the probability of an hypothesis, no matter what data tell.
   
   ALM example: H₀: E(return)=4.0%. Contributions, liabilities and investments are all calculated at 4%. What the data tell is uninteresting.
   
   
2. Homo Actuarius Pragmaticus
   The more developed 'Homo Actuarius Pragamiticus' demonstrates he's only interested in the (results of the) data.
   ALM example: In my experiments I found x=4.0%, full stop.
   Therefore, let's calculate with this 4.0%.
   
   
3. Homo Actuarius Frequentistus
   In this stage, the 'Homo Actuarius Frequentistus' measures the probability of the data given a certain hypothesis.
   
   ALM example: If H₀: E(return)=4.0%, then the probability to get an observed value more different from the one I observed is given by an opportune expression. Don't ask myself if my observed value is near the true one, I can only tell you that if my observed value(s) is the true one, then the probability of observing data more extreme than mine is given by an opportune expression.
   In this stage the so called Monte Carlo Methods was developed...
   
   
4. Homo Actuarius Contemplatus
   The Homo Actuarius Contemplatus measures the probability of the data and of the hypothesis.
   
   ALM example:You decide to take over the (divided!) yearly advice of the 'Parameters Committee' to base your ALM on the maximum expected value for the return on fixed-income securities, which is at that moment  4.0%. Every year you measure the (deviation) of the real data as well and start contemplating on how the two might match...... (btw: they don't!)
   
   
5. Homo Actuarius Bayesianis
   The Homo Actuarius Bayesianis measures the probability of the hypothesis, given the data.  Was the  Frequentistus'  approach about 'modeling mechanisms' in the world, the Bayesian interpretations are more about 'modeling rational reasoning'.
   
   ALM example: Given the data of a certain period we test wetter the value of H₀: E(return)=4.0% is true : near 4.0% with a P% (P=99?) confidence level.

Knowledge: All probabilities are conditional
Knowledge is a strange  phenomenon...

When I was born I knew nothing about everything. When I grew up learned something about some thing. Now I've grown old I know everything about nothing. Joshua Maggid

The moment we become aware that ALL probabilities - even quantum probabilities - are in fact hidden conditional Bayesian probabilities, we (as actuaries) get enlightened (if you don't : don't worry, just fake it and read on)!

Simple Proof: P(A)=P(A|S), where S is the set of all possible outcomes.

From this moment on your probabilistic life will change.

To demonstrate this, examine the next simple example.

Tossing a coin

• When tossing a coin, we all know: P (heads)=0.5
• However, we implicitly assumed a 'fair coin', didn't we?
• So what we in fact stated was: P (heads|fair)=0.5
• 
  Now a small problem appears on the horizon: We all know a fair coin is hypothetical, it doesn't really exist in a real world as every 'real coin' has some physical properties and/or environmental circumstances that makes it more or less biased.
• We can not but conclude that the expression
  'P (heads|fair)=0.5'  is theoretical true, but has unfortunately no practical value.
• The only way out is to define fairness in a practical way is by stating something like:  0.4999≥P(heads|fair)≤0.5001
• Conclusion: Defining one point estimates in practice is practically  useless, always define estimate intervals (based on confidence levels).

From this beginners  example, let's move on to something more actuarial:

Estimating Interest Rates: A Multi Economic Approach

• Suppose you base your (ALM) Bond Returns (R) upon:
  μ= E(R)=4% and σ=2%
  
  
• Regardless what kind of brilliant interest- generating model (Monte Carlo or whatever) you developed, chances are your model is based upon several implicit assumptions like inflation or unemployment.
  
  The actual Return (R_t) on time (t) depends on many (correlated, mostly exogenous) variables like Inflation (I), Unemployment (U), GDP growth(G), Country (C) and last but not least  (R_[t-x]).
  
  A well defined Asset Liability Model should therefore define (R_t) more on basis of a 'Multi Economic Approach'  (MEA) in a form that looks more or less something like: R_t = F(I,U,G,σ,R_[t-1],R_[t-2],etc.)
  
  
• In discussing with the board which economic future scenarios will be most likely and can be used as strategic scenarios, we (actuaries) will be better able to advice with the help of MEA. This approach, based on new technical economic models and intensive discussions with the board, will guarantee  more realistic output and better underpinned decision taking.

Sources and related links:
I. Stats....
- Make your own car crash query
- Alcohol-Impaired Driving Fatalities (National Statistics)
- D r u n k D r i v i n g Fatalities in America (2009)
- Drunk Driving Facts (2006)

II. Humor, Cartoons, Inspiration...
- Jesse van Muylwijck Cartoons (The Judge)
- PHDCOMICS
- Interference : Evolution inspired by Mike West

III. Bayesian Math....
- New Conceptual Approach of the Interpretation of Clinical Tests (2004)
- The Bayesian logic of frequency-based conjunction fallacies (pdf,2011)
- The Bayesian Fallacy: Distinguishing Four Kinds of Beliefs (2008)
- Resource Material for Promoting the Bayesian View of Everything
- A Constructivist View of the Statistical Quantification of Evidence
- Conditional Probability and Conditional Expectation
- Getting fair results from a biased coin
- INTRODUCTION TO MATHEMATICAL FINANCE