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)

Why Life Cycle Funds are Second Best

Life Cycle Funds (LCFs) are seen as the ideal solution for pension planning. Unfortunately they aren't..... They're Second Best....

Pension Funds solutions (PFs), are far more superior to LCFs, as will be shown in this blog with regard to the performance of a pension plan.

Life Cycle

A Life Cycle approach presumes that, while your young and still have a long time before retirement, you can risk to invest more than an average pension fund in risky assets like stocks, with an assumed higher long term return than bonds,

As you come closer to the retirement age, you'll have to be more careful and decrease your stock portfolio incrementally to zero in favor of (assumed) more solid fixed income asset classes like government bonds.

A well known classic life cycle investment scheme is "100-Age", where the investment in stocks depends on your age. Percentage stocks = 100 -  actual age.
E.g.: If you're 30 years old, your portfolio consists of 70% stocks and 30% bonds.

Here's what the average return of a life cycle '100-Age' investment looks like when you start your pension plan at the age of 30 and assume a long term 7% average yearly return on stocks and 4% on bonds.
The return of this life cycle fund is compared to a pension fund with continuously 50% in stocks.

Key question is however, is the younger generation also risk minded and the older generation risk averse?

As often in life and also in this case, what would be logical to expect, turns out just to be a little bit more complicated in practice....

Misunderstanding:Younger people have a high risk attitude
Research by Bonsang (et al.; 2011) of the University of Maastricht and Netspar shows that on average 25% of the 50+ generation is willing to take risk.

 The research report shows evidence  that  the  change  in  risk  attitude  at  older age  is driven by 'cognitive decline'.  About 40 to 50% of the change in risk attitude can be attributed to cognitive aging.

Unfortunately other recent research also shows that only 30% of people under age 35 say they're willing to take substantial or above-average risks in their portfolios (source:Investment Company Institute).

This implies that -  although they would theoretically be better of on the long run - younger people will certainly not put all their eggs in one basket, by investing all or most of their money in stocks.

Pension Fund Investment Horizon
In contrast to individual pension member investors, a pension fund has a long term perspective of more than 20-50 years as new members (employees) keep joining the pension fund in the future. Therefore a pension fund can keep its strategic allocation in stocks relatively constant over time instead of decreasing it.

This implies that a pension fund on the long term has an advantage (longer horizon) above a life cycle fund. Let's try to find the order of magnitude of this difference.


Comparing a Life Cycle fund with a Pension Fund
First of all, we have to take into account that younger people will not over invest in stocks.

Let's assume:

• A 30 year old 'pension plan starter', retiring at age 65
• Contribution level   (€, $, £, ¥,): 1000 a year
• A long term 7% average yearly return on stocks and 4% on bonds
• Life Cycle Investment scheme
  A modest 50% stocks, with a yearly 2% decrease as  from age 50
• Pension Fund Investment Scheme
  A constant 50% investment in stocks (and 50% in bonds)
• Inflation 3%, Pension and Contribution indexation: 3%

 This leads to the next yearly return of these portfolios, as follows:

To find out the overall difference in return between LCF en PFS, we calculate the Return on Investments (ROI) of both investment schemes with help of the:

Pension Calculator

The outcome looks like this:

As you can see the ROI outcomes (left axis) on the investments (yearly contribution) from 'dying age' 65 to age 69 are negative as the cumulative payed pensions (compared to your contribution) didn't (yet) result in a positive balance. Or to put it in another way, if you die between age 65 and 69, you died too early to have a positive return on your paid contribution.

Overperformance
The right axis shows the difference between the LC ROIs and the PF ROIs.
As you may notice,  the pension fund has a structural yearly overperformance of more than 0.3%  and an average overperformance between 0.4% and 0.5% per year.

Overperformance expressed in pension benefits
Expressed in terms of yearly pensions the differences are as follows:

Investment Scheme	Pension at 65	Relative
LC 55year -2% p/y	11673	83%
LC '100-Age'	12304	93%
PF 50% stocks	13172	100%

For a 40 year old pension plan starter, the differences are:

Investment Scheme	Pension at 65	Relative
LC 55year -2% p/y	5359	82%
LC '100-Age'	5578	92%
PF 50% stocks	6040	100%

Conclusion

Investing in life cycle funds ends up in a 7% to 18% lower pension than investing in a pension fund with 50% investment in stocks.


So..., Be wise and choose a pension fund for your investment if you can!


Aftermath
Of course, every pension vehicle has its pros and cons ... So do Life Cycle AND Pension Funds.....

Related Links/Sources
- CNNMoney:The young and the riskless shun the market (2011)
- Cognitive Aging and Risk Attitude (2011)
- America’s Comm. to Ret.Security: Investor Attitudes and Action (2012) 
-  “Saving/investing over the life cycle and the role of pension funds” (2007)
- Excel Pension Calculator Blog
- Benny AND Boone Comic Strips
- Study: Public employee pensions a bargain (2011)

Excel Pension Calculator

Why isn't there just a simple pension Excel calculator on the internet, so I can do my own pension planning?

Well..., from now on there is!

Simply download the Excel Pension Calculator (allow macro's !!) and get an idea of how much you'll have to invest to end up with the pension benefit level of your dreams.... or less... ;-)

Or..., just fill in how much you can afford to invest monthly and see for yourself what pension benefit level is within reach, based on expected return rates, investment methods and inflation.

Just to give a small visual impression of the calculator...

Press on 'Calc' buttons to calculate the variable to the left, while leaving all other variables constant.

Graphics

Also some modest graphics are available. A small example....

Take a look at the next graph that shows how your yearly pension is yearly  funded by:

1. the yearly desavings (= dissavings) from your saving account
2. the yearly addition from the pension fund (= estimated savings of pension fund members that will die in this year)
3. the yearly return on your saving account

Notice the immense impact of the (yearly increasing) addition of your pension fund (= savings of the active members who are expected to die in a particular year and contribute to the savings of your account) compared to the other components (desavings and returns).

Options

The calculator offers several interesting options:

• Set the calculator to 'Saving Account' instead of 'Pension Fund' to notice the difference in outcomes between these two systems.
• Switch to the life table of your choice (p.e.  the country where you live)
• Set and name your own personal Life Table or Investment Scheme
• Simulate longevity effects by manipulating the Life Table Age Correction field

The Excel Pension Calculator has much more features. More than I can handle in this blog. Just download the calculator and play with it to really touch base and to learn what pension is all about....

- Download the Excel Pension Calculator

Enjoy!

Disclaimer: This pension Calculator is just for demonstration purposes. The accuracy of the calculations of this calculator is not guaranteed nor is its applicability to your individual circumstances. You should always obtain personal advice from qualified professionals. Also take notice of the disclaimer in the Excel Pension Calculator.

P.S. I : On request a Quick Start tip

1. Download Calculator and open Excel Spreadsheet

2. Don't forget to"Enable Macros" !! 
3. Enable iterative calculation; Set Max. Iterations=1000, Max. Change=0.4

3. Change 'Start Age  Contribution' to your actual age

4. Notice that the amount 'Saving Surplus at age 120:' changes

5. Press the 'Calc' button next to 'Contribution' to calculate your Contribution

6. Or, Press the 'Calc' button next to 'Pension'  to calculate your yearly pension

7. Set any other Field as you like and press any of the 'Calc' Buttons   

P.S. II : New update, version 2012.2 on April 4,  including a single premium option.
P.S. III: New update, version 2012.3 on April 20, drop down menus (under Excel-2010) now also operate under Excel-2007 versions...

Pension Gamification

For years you deny it, then you doubt it, then you know for sure:

Life is a Game

This blog is specially written for (1) those who are still in the denial phase and (2) 'actuarial life gamers' who just want to enjoy actuarial gaming....

Pension Game
Games are an excellent way to involve people (employees) in a complex and (two fold)  'low interest product' like pension.

Pension games stimulate clear communication and understanding of pensions (The Nest Phrasebook:Clear communication about pensions Version 1.1).

Games, like the above pension game, conquer the world more and more.

Gamification
It looks like everything that has to be sold or communicated, succeeds better with the help of a game. Gamification gets people more engaged, helps change behaviors and stimulates innovation. In other words:

Gamification rules our life

As an example of gamification, Gartner cited the U.K.’s Department for Work and Pensions, which created an innovation game called Idea Street to decentralize innovation and generate ideas from its 120,000 people across the organization. Idea Street is a social collaboration platform with the addition of game mechanics, including points, leaderboards and a “buzz index.”

The employees went wild for it. Within 18 months, Idea Street had approximately 4,500 users and had generated 1,400 ideas, 63 of which had gone forward to implementation.

Other gamification examples are the U.S. military’s “America’s Army” video-game recruiting tool, and the World Bank-sponsored Evoke game, which crowdsources ideas from players globally to solve social challenges.

All and more of this in the 2011 report of  Gartner that states that by 2015, more than 50% of organizations tat manage innovation processes will gamify those processes.

Consequences

Mainly as a consequence of the overdose of gamification in our society, people get confused and lose sight on the difference between reality and illusion. 

This confusion is exacerbated by the fact that negative effects of the current financial crisis have been 'managed away' in stead of letting people and organizations 'perceive' and 'experience' the (negative) financial consequences of their handling.

The 'Hocus Pocus Society'

This way, we gradually created a 'Hocus Pocus Society' where all our (actuarial) models and convictions are doomed to fail as the 'game of life' seems to be to:

• challenge the established (good governance) rules to raise profit and returns to an unrealistic level, by introducing uncontrolled and uncontrollable mechanisms and financial instruments like 'market value', 'derivatives', 'sub-prime mortgages', 'High Frequency Trading', etc.
• try - at the same time - to capture and control these volatile 'unwanted' effects of these mechanisms and instruments by an overdose of hypocritical additional regulation (Solvency (II), Governance, etc.)
• transfer and lay back fundamental complex risk to consumers and communicating this in such a (so called) 'transparent' but oversimplified 'way', that consumers for sure lose their trust in financial institutions as a whole.
• end up in new, for the financial institutions, 99,9% risk free financial products and offerings on the marketplace with a non corresponding stock holders dividend level.

This illusory way of communication about pensions is well demonstrated in the next 'Pension game' video: The myth of your (401K) pension





Way out

To get out of this down spiral cycle in the fiancial industry, we'll have to learn from other industries.

Just like in the case of introducing new medicines , new financial products will have to meet a number of tests and need explicit approval by in and external regulators before they are allowed to be  introduced on the market place.

Anyhow: Don't end up like a 'Hocus Pocus Actuary' and game up your actuarial life!



Related and additional links:
- Idea Street
- Gartner: Over 50% firms may gamify processes 
- Youtube: The Pension Game
- The Annuity Game - Heads Government Wins Tails Pensioner's Lose
- 5 Cent "Old Age Pension" Dice Game 


Calculators:
- life expectancy calculator
- Retirement Withdrawal Calculator

Compliance: Sample Size

How to set an adequate sample size in case of a compliance check?

This simple question has ultimately a simple answer, but can become a "mer à boire" (nightmare) in case of a 'classic' sample size approach.....

In my last-but-one blog called 'Pisa or Actuarial Compliant?', I already stressed the importance of checking compliance in the actuarial work field.

Not only from a actuarial perspective compliance is important, but also from a core business viewpoint:

Compliance is the main key driver for sustainable business

Minimizing Total Cost by Compliance
A short illustration: We all know that compliance cost are a part of Quality Control Cost (QC Cost) and that the cost of NonCompliance (NC Cost) increase with the noncompliance rate. 

Mainly 'NC cost' relate to:

• Penalties or administrative fines of the (legal) regulators
• Extra  cost of complaint handling
• Client claims
• Extra administrative cost 
• Cost of legal procedures

Sampling costs - on their turn -  are a (substantial) part of QC cost.

More in general now it's the art of  good practice compliance management, to determine that level of maximal noncompliance rate, that minimizes the total cost of a company.



Although this approach is more or less standard, in practice companies revenues depend strongly on the level of compliance. In other words: If compliance increases, revenues increase and variable costs decrease.

This implies that introducing 'cost driven compliance management' - in general - will (1) reduce  the total cost and (2) mostly make room for additional investments in 'QC Cost' to improve compliance and to lower variable and total cost.

In practice you'll probably have to calibrate (together with other QC investment costs) to find the optimal cost (investment) level that minimizes the total cost as a percentage of the revenues.

As is clear, modeling this kind of stuff is no work for amateurs. It's real risk management crafts-work. After all, the effect of cost investments is not sure and depends on all kind o probabilities and circumstances that need to be carefully modeled and calibrated.

From this more meta perspective view, let's descend to the next down to earth 'real life example'.

'Compliance Check' Example
As you probably know, pension advisors have to be compliant and  meet strict federal, state and local regulations.

On behave of the employee, the sponsoring employer as well as the insurer or pension fund, all have a strong interest that the involved 'Pension Advisor' actually is, acts and remains compliant.

PensionAdvice
A professional local Pension Advisor firm, 'PensionAdvice' (fictitious name), wants 'compliance' to become a 'calling card' for  their company. Target is that 'compliance' will become a competitive advantage over its rivals.

You, as an actuary, are asked to advise on the issue of how to verify PensionAdvice's compliance....... What to do?

• Step 1 : Compliance Definition
  First you ask the board of PensionAdvice  what compliance means.
  After several discussions compliance is in short defined as:
  
  
  1. Compliance Quality
     Meeting the regulator's (12 step)  legal compliance requirements
     ('Quality Advice Second Pillar Pension')
     
     
  2. Compliance Quantity
     A 100% compliance target of PensionAdvice's portfolio, with a 5% non-compliance rate (error rate) as a maximum on basis of a 95% confidence level.
  
  The board has no idea about the (f)actual level of compliance. Compliance was- until now - not addressed on a more detailed employer dossier level.
  Therefore you decide to start with a simple sample approach.
  
  
• Step 2 : Define Sample Size
  In order to define the right sample size, portfolio size is important.
  After a quick call PensionAdvice gives you a rough estimate of their portfolio: around 2.500 employer pension dossiers.
  
  You pick up your 'sample table spreadsheet' and are confronted with the first serious issue.
  
  
  An adequate sample (95% confidence level) would urge a minimum of 334 samples. With around 10-20 hours research per dossiers, the costs of this size of this sampling project would get way out of hand and become unacceptable as they would raise the total cost of  PensionAdvice (check this, before you conclude so!).
  
  Lowering confidence level doesn't solve the problem either. Sample sizes of 100 and more are still too costly and confidence levels of less than 95% are of no value in relation to the clients ambition (compliance= calling card).
  The same goes for higher - more than 5% - 'Error Tolerance' .....
  
  By the way, in case of samples for small populations things will not turn out better. To achieve relevant confidence levels (>95%) and error tolerances (<5%), samples must have a substantial size in relation to the population size.
  
  
  
  
  You can check all this out 'live', on the next spreadsheet to modify sampling conditions to your own needs. If you don't know the variability of the population, use a 'safe' variability of 50%. Click 'Sample Size II' for modeling the sample size of PensionAdvice.

• Step 3: Use Bayesian Sample Model
  
  
  The above standard approach of sampling could deliver smaller samples if we would be sure of a low variability.
  
  Unfortunately we (often) do not know the variability upfront.
  
  Here comes the help of a method based on efficient sampling and Bayesian statistics, as clearly described by Matthew Leitch.
  
  A more simplified version of Leitch's approach is based on the Laplace's famous  'Rule of succession', a classic application of the beta distribution ( Technical explanation (click) ).
  
  The interesting aspects of this method are:
  
  1. Prior (weak or small) samples or beliefs about the true error rate and confidence levels, can be added in the model in the form of an (artificial) additional (pre)sample.
     
     
  2. As the sample size increases, it becomes clear whether  the defined confidence level will be met or not and if adding more samples is appropriate and/or cost effective.
This way unnecessary samples are avoided, sampling becomes as cost effective as possible and auditor and client can dynamically develop a grip on the distribution. Enough talk, let's demonstrate how this works.

Sample Demonstration

The next sample is contained in an Excel spreadsheet that you can download and that is presented in a simplified  spreadsheet at the end of this blog. You can modify this spreadsheet (on line !) to your own needs and use it for real life compliance sampling. Use it with care in case of small populations (n<100).

A. Check on the prior believes of management

Management estimates the actual NonCompliance rate at 8% with 90% confidence that the actual NonCompliance rate is 8% or less:



If management would have no idea at all, or if you would not (like to) include management opinion, simply estimate both (NonCompliance rate and confidence) at 50% (= indifferent) in your model.

B. Define Management Objectives

After some discussion, management defines the (target) Maximum acceptable NonCompliance rate at 5% with a 95% confidence level (=CL)



C. Start ampling
Before you start sampling, please notice how prior believes of management are rendered into a fictitious sample (test number = 0) in the model:

• In this case prior believes match a fictitious sample of size 27 with zero noncompliance observations. 
• This fictitious sample corresponds to a confidence level of 76% on basis of a maximum (population) noncompliance rate of 5%.

[ If you think the rendering is to optimistic, you can change the fictitious number of noncompliance observations from zero into 1, 2 or another number (examine in the spreadsheet what happens and play around).]

To lift the 76% confidence level to 95%, it would take an additional sample size of 31 with zero noncompliance outcomes (you can check this in the spreadsheet).
As sampling is expensive, your employee Jos runs a first test (test 1) with a sample size of 10 with zero noncompliance outcomes. This looks promising!
The cumulative confidence level has risen from 76% to over 85%.



You decide to take another limited sample with a sample size of 10. Unfortunately this sample contains one noncompliant outcome. As a result, the cumulative confidence level drops to almost 70% and another sample of size 45 with zero noncompliant outcomes is necessary to reach the desired 95% confidence level.

You decide to go on and after a few other tests you finally arrive at the intended 95%cumulative confidence level. Mission succeeded!



The great advantage of this incremental sampling method is that if noncompliance shows up in an early stage, you can

• stop sampling, without having made major sampling cost
• Improve compliance of the population by means of additional measures on basis of the learnings from the noncompliant outcomes
• start sampling again (from the start) 

If - for example -  test 1 would have had 3 noncompliant outcomes instead of zero, it would take an additional test of size 115 with zero noncompliant outcomes tot achieve a 95% confidence level.  It's clear that in this case it's better to first learn from the 3 noncompliant outomes, what's wrong or needs improvement, than to go on with expensive sampling against your better judgment.

D. Conclusions

On basis of a prior believe that - with 90% confidence - the population is  8% noncompliant, we can now conclude that after an additional total sample of size 65, PensionAdvice's noncompliance rate is 5% or less with a 95% confidence level.

If we want to be 95% sure without 'prior believe', we'll have to take an additional sample of size 27 with zero noncompliant outcomes as a result.

E. Check out
Check out, download the next spreadsheet. Modify sampling conditions to your own needs and download the Excel spreadsheet.


Finally
Excuses for this much too long blog. I hope I've succeeded in keeping your attention....


Related links / Resources

I. Download official Maggid Excel spreadsheets:
- Dynamic Compliance Sampling (2011)
- Small Sample Size Calculator

II. Related links/ Sources:
- 'Efficient Sampling' spreadsheet by Matthew Leitch
- What Is The Right Sample Size For A Survey?
- Sample Size
- Epidemiology
- Probability of adverse events that have not yet occurred
- Progressive Sampling (Pdf)
- The True Cost of Compliance
- Bayesian modeling (ppt)

What's that, an actuary? Kamikaze Investors

'Housing' is probably one of the most complex assets and also one of the most interesting.

Wake up...
At the next birthday party when somebody asks you the regular line: 'What's that, an actuary?....'  Don't answer the obligatory way, but demonstrate your actuarial risk management abilities in an interactive way....

Just ask who of your birthday friends would call himself a private - non professional - risky investor?........

After some hesitation and discussion, probably all of them will answer something like:  'No, I would not dare to risk much money, I put most of my savings in a 'safe - as possible - bank account'.

Than, your next question is: "Who owns a house?"
Now, probably more than 60% of your friends will raise their finger......

Congratulations! Now you may congratulate this 60% of your friends with the fact that they are probably a more risk taking investor than an average pension fund, because they are most likely (by far) overfunded  in the asset category "Housing".

After grasping the point of your little quiz, most of your friends will first laugh, than think, and after a while some of them will ask you what they should do about being a Kamikaze-investor?

Now you get to the tricky part of being an actuary:

1. Never tell anyone what to do, 
2. Just show them the possible scenarios
3. Point out and quantify the risks, and 
4. Help them take their own decisions 

House-Pricing
 A lot of research has been done around House pricing and risk.

Although their seems to be a positive relationship between interest rate and housing-price growth, the housing risk is much more complicated than that.

Also housing prices differ strongly by country, as the next Economist table shows:

And because as actuaries, we're little Kamikaze-investors as well, the Economist has developed an interactive application to get sight at the housing-price development in your country relative to others.

Have fun with this House-Price Calculator

Related links:
- Economist House-Price Development Calculator 
- Housing consumption-based asset pricing and residential mortgage default risk. (2009) 
- Home Values and Household Debt Present Global Risks
- Running on funds: Complete (2007) Fitch Table

Online Murphy Risk Calculator

Risk is like quantum mechanics:

If you think you understand Risk, you don't understand Risk
Maggid after : Feynman

If you are not completely confused by Risk, you do not understand it
Maggid after : John Wheeler

Sure, risk is hard to tackle. The more you learn about risk, the more you become aware of it's sneaky characteristics (clustering, tails, etc).

This is why becoming a qualified actuary takes an incredible amount of time, hard study and many years of experience.  As masters in Risk, actuaries understand the limits in modeling and calculating Risk.

Murphy

Probably one of the more intriguing risk quotes is :

Murphy's Law

"Anything that can go wrong, will go wrong"

by the famous Edwin Murphy.

A quote that keeps an actuary mind busy....  After all, as actuaries it is our duty to quantify and explain uncertainty (as much as is possible) in board rooms and on the accounting table. Not only when decisions have to be taken, but also after things turned out wrong or different from what we thought. This is - to put it mildly - no 'easy task' and it's not getting easier in the near future.....


Just like Murphy, actuaries experienced last decades that (statistic) bad luck often collaborates with bad timing. What drives God (i.e. quantum mechanics or 'Murphy probability') to confront us - (poor) actuaries - with 'fair value volatility', 'longevity explosions', 'subprime defeats', 'imploding real estate market's and 'extraordinary solvency demands by supervisors', all at the same time time?


(Un)Luckily, help is on the way....  In 2004 British Gas commissioned some scientists to create a formula to predict Murphy's Law, also known as Sod's Law.

Murphy's Formula
In a 2005 study, based on a survey of 1,023 adults, Murphy’s Law was shown 'statistically significant'. The final report also supplied a formula for predicting occurrences of Murphy’s Law. Here it is....


Let U, C, I, S, and F be integers between 1 and 9, reflecting respectively comparative levels of Urgency, Complexity, Importance, Skills, and Frequency in a given set of circumstances. Let A, which stands for Aggravation, equal 0.7 (Please, don’t ask why). The likelihood (L) of Murphy’s Law obtaining under those circumstances, on a scale of 0 to 8.6, turns out to be:

L = [((U + C + I) x (10 - S)) / 20] x A x 1 / (1 - sin (F / 10))

Murphy's Formula strikes itself
Unfortunately, Murphy's law suffered from self reference, as one of the  authors, the mathematician Phil Obayda, commented on a 2004 blog that this formula is wrong.

The correct formula according to Phil is:

 P= (((U+C+I) * (1-S))/2) * A * (1/(1-Sin F))

with P = probability of Sod's Law Occuring and U, C, I, S and F values greater than 0 and less than 1, keeping the mysterious A = 0.7.

Murphy's formula simplified
Simplifying this last formula leads to Maggid's formula for the probability (%) of Murphy hitting you, whenever you perform a task:

Although application of this formula is not (yet) an obligated part of the actuary's Code of Professional Conduct, please check this equation anytime you're about to defend an actuarial advice on a Board's table.

How to use Murphy's formula: an Actuarial Example
Let's do a simple exercise to demonstrate the power of Murphy's formula:

You've developed a risk model of the Stock market. In a meeting the Chair of the board asks you how certain you are of your model being right. You know the difference between risk and uncertainty, so you say "one moment please" and pick up your pocket calculator while reflecting: This is a ´U=3, I=9,C=10,F=3´ situation, and I'm a S=9 actuary. That calculates as P=10.4% of Murphy hitting me. Within 20 seconds you (over)confidently answer: I`m about 90% sure of my model!

The Chair of the Board looks desperate... His eyes reflect: ´Is 90% good or bad?` You didn't realize your model was that important to the board.  But.. if that's so, 'Importance' should not be rated at I=9 but at I=10, raising the failure probability to almost 11%. Now you start doubting yourself : What if you overestimated yourself? What if you're only a AA-Actuary (level S=7) instead of a AAA (level S=9)? This would increase the probability of failing to 31.3%. Suddenly you realize you're only one step away from a major personal actuarial meltdown.
You get yourself together, regain your self confidence, realize you're one of the best actuaries in the world (S=10) and full of confidence you reply the questioning eyes of the Chair with: "Sir, I'm almost 100% certain my model is right.

The Board is relieved and content. You're an actuary they can trust. Now they can decide without hesitation.

So next time you want to know the failure probability of a task, use the next Online Murphy Calculater.

Good Luck with Murphy's calculator!

Used sources/Links:
- Sod’s Law: A Proof
- Newyorker: Murphy At the Bat
- The Engineering of Murphy's Law?
- Legend, Inc. Murphy's Laws
- The Stock Market: Risk vs. Uncertainty
- Murphy's Online Calculator

Swine Flu Counter update Sept 2009

Here you'll find the September 2009 update of the

Global Swine Flu Counter

Although there is still an increasing risk of underreporting, the counter has been renewed on basis of the latest available global reports as provided by Wikipedia/ECDC.

Swine Flu under Control?
The September 2009 developments suggest the Swine Flu development is under control, as the reported infections changed from a exponential growth recent months, to more linear growth in August 2009. In September the increase of infections was already declining.

New Model
The above developments are the main reason why data in the Swine Flu calculator have now been modelled by a logistic function.
Well considered curve fitting at ZunZun, showed a Gompertz function (with offset) resulted in a satisfying approximation :



Life actuaries will be familiar with good old Gompertz. The Gompertz equations are - by the way - also used to model Plant Desease Progres.

The number of death have now been modelled ruffly as 1.8% of the infected people a month earlier [Death=0.018*I(t-30)]

Results update
The results the new approximation show that the number of reported infections increases asymptotically towards a limit of about 323,000.

Correspondingly, the number of death, , increases to a limit of ruffly 6000.

All provided the actual controlled development continues and no new mutation of the H1N1 will develop in the next months.....

Risk
The risk of underreporting is not negligible . Modeling on basis of excluding the September data would result in a limit of 528,000 infects and about 9500 deaths. We'll just have to wait how H1N1 develops.....
But as becomes clear, the explosion of swine flue cases looks under control.

If necessary, the counter will be updated again on a on a regular basis. The latest data you'll find in this XLS spreadsheet.

Install Swine Flu Counter
How to implement this Swine Flu Counter on your web site?

• Put the next HTML-script (without the outer quotes) just before the end of the body tag:' <script language="javascript" type="text/javascript" src="http://sites.google.com/site/boooming/actuary/swine-flu-2009-update1.js"> </script>'
  


• Put the next HTML-line (without the outer quotes) where you want the Swine Flu table to appear on your site :
  ' <div id="swineflutable"></div> '
  
  
• Ready!

Swine Flu Counter update 06-07-2009

Want a simple global Swine Flu Counter on your web page?

You may find the old (July 6, 2009) Counter/Calculator Here.
There is already a new counter on a more recent model available.
Look at : Swine Flu Counter Update-sept-2009

The (old) counter is based on a 'July 6, 2009 estimation' as described on Actuary-Info. However, now the data have been updated based on the official, more reliable and accurate WHO reports.



If necessary, counters will be updated again on a on a regular basis. The latest data you'll find in this XLS spreadsheet.

Install Swine Flu Counter
How to implement this old Swine Flu Counter on your web site?

• Put the next HTML-script (without the outer quotes) just before the end of the body tag:' <script language="javascript" type="text/javascript" src="http://jos.blogspot.googlepages.com/swine-flu-2009.js"> </script>'
  


• Put the next HTML-line (without the outer quotes) where you want the Swine Flu table to appear on your site :
  ' <div id="swineflutable"></div> '
  
  
• Ready!

Remember, you may only install one counter on your website, either the old or the new.

Paradox
The best what could and will happen with regard to the original swine flu model and corresponding counter, is that they don't turn out to be valid. This way the model and counter will have proven their 'reason for existence'. Simply just by contributing to the necessary awareness and prevention measures to diminish or stop the exponential swine flu infections growth.

Contrary, developing but not publishing models or counters will create a lack of warning and attention and would therefore prove the (exponential) model to become true. This is the inevitable paradox of modeling with our without follow up actions.

This paradox is the main reason why an 'actuarial advice' should therefore alway be presented in a (minimal) "two-way scenario" form:

• Estimation of results without follow up actions
• Estimation of results including advised follow up actions

Anyway, have fun with your Swine Flu Counter!

Joshua Maggid

ADD July 18, 2009
On July 16, 2009 WHO reports:

• Further spread of the pandemic, within affected countries and to new countries, is considered inevitable.
• This assumption is fully backed by experience. The 2009 influenza pandemic has spread internationally with unprecedented speed. In past pandemics, influenza viruses have needed more than six months to spread as widely as the new H1N1 virus has spread in less than six weeks.
• The increasing number of cases in many countries with sustained community transmission is making it extremely difficult, if not impossible, for countries to try and confirm them through laboratory testing. Moreover, the counting of individual cases is now no longer essential in such countries for monitoring either the level or nature of the risk posed by the pandemic virus or to guide implementation of the most appropriate response measures.

In short: now h1n1 really gets important and probably is running out of hand, WHO stops reporting.....
Let's see if we can find another source....

ADD July 21, 2009
Wikipedia's 2009 flu pandemic reports (based on ECDC reports, as WHO reports fail) an accumulated number of 143,652 reported infections and 899 deaths on July 21, 2009. As the WHO has decided not to registrate the number of infections anymore (as from july 9) and, except for the US, reports are based on confirmed laboratory test results, the actual number of infections will be much higher.

That's why, as long as the actual deaths are in line with the modelled estimated death, the 'July 6th exponential model', used as basis for the swine flu counter, seems still realistic and valid!

ADD Sept 06, 2009
The data have structurally changed from exponential to linear.
Take a look at the new counter at:

Swine Flu Counter Update-sept-2009