The first Actuary

As the story goes, insurance began around 1688 at a coffeehouse in London called Lloyds, where shipman discussed and divided their risks.

That 'explains' the birth of non life insurance.

But what about life insurance?

Who developed the first life table?

Answers...
The answer to this question depends on who you ask...

• Definitely Graunt in 1662 (statistical analyzes of data)
  
• Surely De Witt in 1671 (life insurance tables)
• Undoubtedly Halley: 1693 (life insurance tables)

Depending on what you define as a life table, answering this question often leads to a never ending semantic discussion.

Don't worry, there's help... In his Google-book, "A history of probability and statistics and their applications before 1750", Anders Hald explains the origin and development of life tables.

First Life Tables
An indeed, the 'first' life tables, based on more or less empiric data and interest rates were developed at the end of the 17th century.
The first actuary....
However, already in the 3rd century the Roman jurist Ulpian devised a table for the legal conversion of a life annuity to an annuity certain.
It was pointed out by Greenwood that the valuation (duration) of the annuities was deliberately chosen to high, in order to protect the interests of the legal heir.

This would implie that Ulpian not only did a tremendous job by estimating life annuities, but also developed and applied the first primitive 'Solvency Zero' principles...

With his 'simple table', Ulpian was more than ahead of his time.

So, we may rightfully conclude that the one and only first actuary was a jurist: Domitius Ulpianus, alias Ulpian

Strange that it took more than 1500 years to develop more sophisticated life- and annuity tables.

Related links & Sources:

• Early uses of Graunt's Life Table
• A history of probability and statistics and their applications before 1750
• Early Insurance Mechanisms and Their Mathematical Foundations

Pension Fund Market Valuation ParaDox

Is Market Valuation (MV) the right tool for pension funds?

Mid 2009, the new appointed ABP chairman Nijpels and - previously - the ABP CFO ten Damme (picture on the right), stated that the relatively new method of MV is inadequate for pension funds.

Both think that valuation of pension funds could be better based on a (seven year) moving average interest rate.
Nijpels en Ten Damme are supported in their view by Albert Röell, Chairman of KAS BANK, who advises the Dutch regulator DNB to reassess its policy.

Nevertheless DNB doesn't seem to respond.
Neither Roëll nor the world's third-biggest pension fund gets an answer. Is ABP crying over spilt milk?

Why MV?
At first sight, there seems nothing wrong in calculating the value of a pension fund, on MV basis. Market (consistent) valuation implies that the value of an asset or liability is defined by it's market price. If the market is too thin, a mark-to-model approach can be used....

Clearly MV increased the transparency and accountability of pension funds. However, 2008/2009 show that MV, based on the actual term structure of interest rates, leads to excessive volatility in funding ratios.

Is MV the best method?
Of course MV can be a best practice method in helping to define the pension fund value in case of a merger, a takeover or with regard to managing assets. But is MV also the best method for managing the pension fund as a whole, from a board, regulator or 'pension fund member' perspective?

• Future certainty
  The first fundamental question is :
  
  
  can we define the value of long-term
  ( 60 years or more) cash flows at all?
  
  
  The answer is: No, we can't!. Just take a look at an average CFO, who's proud to present his next quarterly company result with 60% certainty. What would be the certainty of the long-term company result of - let's say - 20 years ahead. Exactly: Almost zero.
  
  It's impossible for anyone, no Nostradamus Actuary included, to predict the compound and correlated long term effects of interest rate, stock market, derivates, inflation, salary increases, mortality, disability, longevity and costs. Therefore, if it's not possible....., don't pretent you can.
  
  
• Pension fund: Not for Sale
  Second important subject for consideration is that a pension fund (in general) is not listed on the stock market. Also, in general, it is not for sale on the market. Therefore, the hourly, daily or monthly calculated MV is only of limited interest with regard to the pension fund's strategy, policy or control.
  
  Neither is MV the right base for monthly adjusting of the contribution rates, funding rates or indexation capacity.

Principles
Simply stated, it's important that a pension fund:

1. can meet its obligations "on the long-term"
2. is sufficiently liquid to pay his annuities "on the short-term"

Moving average
The first statement implies that if you take the funding ratio as steering/testing parameter (there are more!), there is - given the mentioned long term uncertainty - no other option than to base the valuation on a more (term dependent) 'moving average' of interest rates in combination with the moving average value development of other asset classes. The choice of the moving average period is critical.

Dead Money
Even more, if the pension fund is forced to act on basis of MV, it has to keep extra (non-volatile) buffers to withstand the possible effects of non-relevant short-term market fluctuations. On top of this many pension funds tried to downplay their indexation ambition.

The consequence of all this is that MV generates a substantial amount of structural "dead" capital into the balance sheet. "Dead" capital that - besides - is withdrawn from the national economy and therefore weakens the pension fund's country position in the international level playing field.

Paradoxical measures
In case - due to market developments - the MV goes down , short-term prudential constraints (as enforced or stimulated by the regulator) will moreover endanger the long-term objectives of pension funds. Consequently leading pension funds from the frying-pan into the fire.

There's another interesting aspect that pleads against MV. In general (Dutch) pension funds cannot go bankrupt, as they are allowed to cut back on the participants’ entitlements in extreme (emergency) situations. So the key question is what kind of minimum security level we enforce upon ourselves. Just an example to illustrate this:

Example
What would you prefer:

1. 100% of the yearly pension that you have been promised, on basis of a 125% funding ratio
2. 125% of the yearly pension that you have been originally promised, at a 100% funding ratio target

Remember there is no ultimate warranty whatsoever in either situation.

The only difference is that in scenario A the chance that your entitlements will be cut down is slightly smaller than in scenario B. But this last situation is as hypothetic as it can be, as contributions will be raised first, before any cut down scenarios will be considered.

So its better to use the funding ratio surplus for legalized controlled indexation and pension benefits improvement than as 'dead' money.

A final argument in the war against MV for pension funds is the next illustration .....

ParaDox
Let's take a look at a company called ParaDox.... ParaDox produces parasols (sunshades) for the high season.

In winter, ParaDox produces at full speed in order to achieve a top level inventory at the start of the summer.

In winter, however, hardly any parasols are sold. During this cold season the price of the parasols on the market (in the shops) drops to about 50% of the summer price. Even more, parasols sales go 80% down in winter (cf. long-term investment market).

If ParaDox would apply MV based techniques, it would have to depreciate their current stock to 50% of the (summer)value. Surely ParaDox would go bankrupt. No, every sensible human being, including actuaries, would decide that in this situation it's best to value the stock of ParaDox on basis of the 'moving average' (realized) sales price over one or more recent years.
N.B. Even if ParaDox would have one or two 'bad summers', deprecation would not be considered.

If in this ParaDox case it's clear that market valuation (i.c. deprecation) is unwise, the more it must be clear that in a company with long-term obligations and high uncertainties , like a pension fund is, it's naive to operate and steer on basis of MV.

Moving Average Period
Now that's illustrated that the Moving Average Method (MAM) is preferable above the MV method (MVM) for pension funds, there's still one thing to decide: the 'MAM period'.

If the MAM period is chosen too short, it will suffer the same disadvantages as the MVM.

If it's chosen too long, there's the risk of not being able to adapt fast enough to realistic contribution levels, if needed. In this situation there's also the risk of unintentional intergenerational financial effects. However, these effects can be yearly calculated and translated into a sound policy.

From this perspective it seems reasonable to fix the MAM periode to the average duration of nominal pension liabilities, which is (in The Netherlands) about fifteen years (in real terms, it is even longer).

Hope
Let's trust that DNB listens to ABP and KAS BANK, so that 'pension funds' and 'pension fun' become one again!

Related links:
- P&I/Watson Wyatt World 300 Largest Pension Funds
- Market-consistent valuation of pension liabilities (must read!)

Actuagram

If you want something to chew on, something that challenges your actuarial brain and associative power, try to solve the next Actuagram.
This actuarial brain teaser is a mix of an actuarial crossword puzzle and a cryptogram.

How to play the puzzle:

1. Click on the word you would like to solve.
2. Fill in your suggestion, click on OK
3. Only if you do not know the answer, click on the 'solve button'

Can you manage, without using the 'solve button' ?

Congratulations! Actuaries, have fun!

[ If your browser doesn't allow you to play here, click on this link]

Actuagram

by Joshua Maggid
EclipseCrossword © 2000-2007

This interactive crossword puzzle requires JavaScript and a reasonably recent web browser, such as Internet Explorer 5.5
or later, Netscape 7, Mozilla, Firefox, or Safari. If you have disabled web page scripting, please re-enable it and refresh
the page. If this web page is saved to your computer, you may need to click the yellow Information Bar at the top of
the page to allow the puzzle to load.

Actuarial Sustainability Alarm

Recently the European Commission launched the 'Sustainability Report 2009", investigating the long-term (2010-2060)sustainability of public finances.

This report clearly shows the long-term economic effects of the aging society and the continuous increasing life expectancy.

Financing increasing pension and health costs in the next decades, will be a real challenge for almost all European countries. Even more, the current financial crisis and unsure financial outlook urge for severe short term measures in order to prevent much more unpleasant other measures in the next decades.

The report claims that the ability to meet public pensions liabilities is a higher long-term risk for governments than ever before and in most cases reform of member states’ pensions systems is 'must' and can no longer be delayed.

Although the report manly focuses on the increase (the so called delta) of the sustainability gap, I would like to take a look at the development of the aging costs in relation to the debt development of each country.

Development Aging costs
Let's start to take a look at the development of the public pensions liabilities (pension costs) and health costs from a slightly different angle as published in the report:

On average the total aging costs are increasing from 25% in 2010 to about 30% in 2060 on bases of a no-policy-change assumption.But there a countries (BE, EL, LU, SI) that grow way above this average to a level that's even above the current level of countries with high social standards, like Sweden and Finland.

To conquer this development, some member countries are trying to tackling the longevity issue by raising retirement ages.
Not only the pension costs increase, but also the projected long-term increase in healthcare spending is large and constitutes on its own a risk to sustainability.

Countries whose regimes are listed by the report as 'high-risk' in terms of sustainability are: The Czech Republic, Cyprus, Ireland, Greece Spain, Latvia, Lithuania, Malta, the Netherlands, Romania, Slovakia and the UK. In many countries the age-related expenditure is expected to climb quickly against existing financial imbalances.

Development gross debt ratio
As is clear from the next table, the mentioned next decades increase in health and pension costs, in combination with the unhealthy financial situation - due to the credit crisis - cumulates in a clear desperate debt situation for most of the European countries:

The table shows the government gross debt ratio in 2008 and 2009, and the projections for 2010, 2030 and 2060, once the costs of servicing debt and paying for age-related expenditure are taken into account.

As mentioned before, the long-term debt projections have been prepared under a no-policy-change assumption and in partial equilibrium. Given these assumptions, the projections are not robust forecasts and are not meant to be realistic scenarios of what may happen in the future.

The aim of the debt projections is to illustrate the long-term trends and the size of the required remedial action to avoid government debts to enter into an exponentially increasing spiral.

Actuary Involvement
It's clear that the debt and social costs developments are not heading in the right direction..... Actuary involvement to analyze, advice and create new social systems seems necessary.
Actuaries on the bridge, please!

Sources
- IPE
- EC
- Sustainability Report 2009
- Report 2009
- Download: Maggid Excel tables Aging Costs and Debt Development

Best Pension Country 2009

There's a small country somewhere on this globe, called The Netherlands......

This small country does not only turns out to be the European and (probably) World Health Leader 2009, but - by the way - also happens to be the first Pension World Leader 2009, according to a new global research by Mercer.

You might wonder, who's the leader of that small country near the sea? His name is Mr. Jan Peter Balkenende. He's Prime minister for more than 7 years, is said to have no charisma and has proved to be able to lead a country that's loaded with hair-splitters and complaining people who disagree with each other on every possible subject.

Opposite to other European presidents like Sarkozy (France) or Berlusconi (Italy), who perform strongly on basis of their charisma and seem mainly interested in the fair sex, the Dutch Prime Minister Balkenende - just like the German Prime Minister Angela Merkel - is a modest no-nonsense leader, who walks his talk and gets the job done.

For sure he would be the best European President kandidate, to lead Europe through difficult times ahead on basis of dialog, respect and agreement.

Mercer Global Pension Index
Back to the Mercer Global Pension Index outcome.
The research is a first attempt to objectively compare the retirement income systems of eleven countries spread across the world.

Countries where rated in five grades:

Grade	Index value	Description
A	>80	A first class and robust retirement income system that delivers good benefits, is sustainable and has a high level of integrity
B	65–80	A system that has a sound structure, with many good features, but has some areas for improvement that differentiate it from an A-grade system.
C	50–65	A system that has some good features, but also has major risks and/or shortcomings that should be addressed. Without these improvements, its efficacy and/or long-term sustainability can be questioned.
D	35–50	A system that has some desirable features, but also has major weaknesses and/or omissions that need to be addressed. Without these improvements, its efficacy and sustainability are in doubt.
E	<35	A poor system that may be in the early stages of development or a non-existent system.

The overall index value for each country represents the weighted average of the three sub-indices. adequacy, sustainability and Integrity.


Pension Index Outcome 2009
The results of the pension research clearly appoint The Netherlands as the undisputed Pension leader.


Remarkable however, is that none of the participating countries were classified with an A-grade (index value > 80). This can be easily explained by the fact that no one system is strong enough to withstand the challenges of an aging population.

Want to know more? Than listen to to Dr David Knox (WWP Mercer) discussing the Melbourne Mercer Global Pension Index




Or simply download the full report.

Interested in how The Netherlands 'did it'? Just contact Tim Burggraaf, one of the best worldwide consultants of Mercer in The Netherlands. Tim is a Master in Pensions and Life Assurance. No... he's not an actuary... but you wouldn't notice and moreover, he's one of the best interlocutors and speakers you can can get.

Sources :
- IPE
- Melbourne Mercer Global Pension Index

Humor: Actuary Solves Credit Crisis

One upon a time there was a small village depending on only one source of income, tourism... the only problem was - due to the 'crisis' - there were no tourists left...

Every villager had to borrow from an other in order to survive.. several months passed .. everyone felt miserable.

One day a cost conscious actuary, visiting a Risk Conference nearby, arrived in the village.

Heading for a cheap overnight stay, he booked a small room in the only available local hotel. He paid in advance with a 100 dollar note and went to his room to prepare for the conference.

Before the actuary could unpack his bags, the hotel owner had already taken the 100 dollar note, heading his way to pay the butcher.. to whom he owed precisely 100 dollar.

The butcher, in his turn, immediately ran off with the 100 dollar to see the local farmer and paid his debt for all the meat he'd been supplied with...

With the same 100 dollar note, the farmer immediately paid the seed salesman who, right at that time, was visiting the farmer to collect the unpaid 100 dollar bill.

Back in his hotel, the seed salesman closed the circle. In order to settle the hotel bill for that night, he dropped the 100 dollar note on the counter. Just at that moment, the actuary - who'd come down to tell the hotel owner that he didn't like his room - arrives at the counter, picks up his 100 dollar and disappears.

Nothing was spent,
nothing was gained,
nothing was lost.
Nonetheless, thanks to the actuary, nobody in the village had any debts!

Moral
This story shows why it's important for actuaries to attend Risk Conferences and illustrates how actuaries can actively contribute to solving the credit crisis.

Original Sources: Free after newciv, Dutch source Aardbron

Health Leadership 2009

The Netherlands win the 2009 Euro Health Consumer Index (EHCI), for the second year in a row.

Nevertheless, Denmark keeps its runner-up position from last year. Besides The Netherlands and Denmark there are other strong performers like Iceland, Austria and Switzerland, leaving the UK in a disappointing 14th position....

Index performance criteria
The EHCI 2009 groups 38 indicators of quality into six categories: Patient rights and information, e-Health, Waiting time for treatment, Outcomes, Range and reach of services provided and Pharmaceuticals.
Each sub-discipline is weighted for importance to provide the overall Index score.

HCP research director, Dr. Arne Bjornberg, states: The Dutch might have found a successful approach that combines competition for funding and provision within a regulated framework.

Effective Health (Actuarial) Principles
In actuarial context, the success of the Dutch health system is based on a few very simple principles:

• Risk Solidarity
• Risk Equalization
• No Risk Selection
• Free choice of Care Providers & Health Insurer
• Transparent ranking of Care Providers on bases of cost & quality
• Worldwide cover

The Dutch Health Care System
An excellent summary of the Dutch Health Care System can be viewed on YouTube:

Health care In the Netherlands


Of course the Dutch system is no panacea, there are also many challenges and disadvantages.

Just to mention some....

• How to control Hospital costs?
• (The Future of Hospitals in the Netherlands in 2015)
• The increasing and partly unpredictable run-off period of hospital and specialist care claims costs (DBCs)
• How to create a 'healthy' and financial balance between basic and additional (private) health insurance
• How to control the spiraling and increasing health costs of longevity and how to (ethically) control the costs in the last years of our life?

Nevertheless, the Dutch system can be an inspiring example for countries like the US and the UK.


Let's conclude with an interesting development. In an 2009 article called A Strategy for Health Care Reform, Michael E. Porter presents the principles for a new health system, based on the idea that the central focus must be on increasing value for patients.

Related downloads/sources:

• Download the Euro Health Consumer Index 2009 report
• Download the Index Matrix
• Cartoons: Seppo.net
  

Early Retirement hits Mortality

Do early pensioners live longer?

Or, to rephrase this: What's the influence of early retirement on mortality?

The answer has been given in a 2005 BMJ paper called:

Age at retirement and long term survival of an industrial population: prospective cohort study

In a long term (1973-2004) cohort research, the mortality of past Shell Oil employees,who retired at ages 55, 60, and 65, have been studied.

Outcome
The main outcome of this study is that subjects who retired early at 55 and who were still alive at 65 had a significantly higher mortality than those who retired at 65 (hazard ratio 1.37, 95% confidence interval 1.09 to 1.73).

After adjustment, mortality was similar between those who retired at 60 and those who retired at 65 (1.06, 0.92 to 1.22).

So we may (carefully) conclude that working longer, means living longer...

Another interesting question, that hasn't been answered yet, is:
'what's the influence of early retirement on our healthy life years...

Free Course Finance of Aging

The aging of the population raises numerous economic and financial issues for pension funds, insurance companies and governments.
To take wise decisions, expert knowledge in these organizations is crucial. To provide this knowledge a Dutch organization called Netspar initiated courses on an academic level.

Netspar is an independent network for research, education and knowledge exchange in the field of pensions, aging and retirement.

In 2009 Netspar introduced a new course Master's program Economics and Finance of Aging, that can also be followed individually or in tracks.

To make things even easier, Netspar developed the

Free Online Course

Introduction to Economics and Finance of Aging

Lans Bovenberg, professor ar the Tilburg University, introduces you in the interesting world of Economics and Finance of Aging.

This course is completely free and ca be viewed online.

So, whether you're an actuary or not, if you've got a few spare minutes left a day, don't miss this free course......

Polya: Actuaries Good or Bad

As an actuary, were you born 'Good' or 'Bad'? The answer to this question can be given with help of mathematics!

Let's start with a simple model. When you, as a prospective actuarial talent, were born, you had only a limited number of experiences. Let's assume you came to earth quite neutral, with one 'Good' (G) and one "Bad" (B) experience.
At this point in time, your (still unconscious) attitude and therefore expectation of a 'Good' (B) outcome of your next experience, will be 50%.

In line with the expression "You'll always reap what you sow" (Gal 6:7), or associative translated "You'll become what you X" (with X ='Think', 'Eat', 'Are', etc.)", your next experience will indeed turn out to be equally G or B.

Let's assume that providence decided, the outcome is G. Now you've become a more optimistic baby actuary. Your experience-bucket is now filled with two G's and one B (experience), so your subjective 'colored' outlook on G's is 66,66% (2/3=[2 G's/(2 G's + 1 B)]) . You also look back on a relatively Positive Life Score of PLS=66,66% G's.
Would you have experienced a 'B score' instead, it would be the other way around and as a potential pessimist your outlook and PLS would have been lowered to 33,33% .

But happily you're a 66,66% (!) G-Score-optimist and life goes on. According to the same principles, the probability of scoring a new G-experience is now 66,66% instead of 50%.

As you may already notice, your PLS will more and more develop according your personal historical G- an B-experience track record.

A few questions that may rise, are:

• Does your Positive Life Score (PLS) has a limit? And if so, what's that limit?
• Once you're in a pessimistic phase, what are the changes of getting out?

Here is were the help of a great mathematician, George Pólya,

comes in, by modeling the above situation in what is called:

Polya's Urn model
An urn contains G₀ Green (Good) and B₀ Black (Bad) balls. One ball is drawn randomly from the urn and is then placed back in the urn together with an (extra) ball of the same color.

Our Good&Bad exercise turns out to be a simplified two color Polya Urn Model (G₀=1,B₀=1) that is part of a large family of General Urn Models.

Properties
It turns out that this model has the following (translated)properties:

• On any given moment in your life if you do not know what kind of balls have been drawing before, the expectation of drawing a Good or Bad ball (experience) is always G₀ =G0/(G₀ +B₀) =50%.
  
  
• On any given moment in your life, gaining a Good or a Bad experience depends on the track record of G&B experiences in your life. So if you've experienced G Good experiences and B Bad experiences, your changes of experiencing a next Good experience are equal to the track record of your Positive Life Score : PLS_(G+B)=G/(G+B)
  
  
• The relative influence of a G or B experience on the PLS decreases rapidly as the number of total experiences increases. Your PLS has a definitive limit in (life)time with equal changes of outcome on the interval [0,1].
  
  
• As is clear from some simulations, the first 10 to 20 experiences in our life determine whether we'll become an optimist (PLS_(∞)> 0.75) or an pessimist (PLS_(∞)<0,25).
  
  
  
  
  
  
  
  
  
  
• Moreover, the first 5 to 10 experiences in your life already determine the direction of our PLS in life. This means that our parents and teachers have an important role in guiding us in our baby and youngster phase to a positive balanced number of experiences (a more than average PLS).
  
  For example if on a given moment in life you have had 4 Bad experiences and 1 Good, the probability of having a next Good experience is 20%. What's more frustrating is that the probability in this case to get in three steps to a 50% level is only about 3% (=1/5*2/6*3/7) . This illustrates the heavy responsibility of our parents and teachers.
  
  That's why it's for example so difficult to change your religion. Once the first 50 religion experiences have been brought in by your parents, it's hard to change from Budha to Allah or Christ, or the other way around.
  
  The same is true with regard to our actuarial education and experience. Once we've experienced more than 10 years in a row that longevity increases slowly, it will hard to be convinced that longevity will explode one day. As a consequence, the way we are formed - per definition - causes that we will always underestimate the risk of a change, as we unconsciously relate risk more to our paste experience more than (we can) to the future. .
  
  
• Once a more than average PLS in our life is achieved, we're more likely to absorb a Bad experience without getting unbalanced. Parents and teachers can 'let go'.

Keep in mind, Polya's Urn is only a think-model to help you to become aware of the important mechanisms that play a role in becoming 'who you are' or 'what you'll be'.

Change?
Once you become experienced in life and your PLS direction has been set, you can only change this by either a Professional De or Re-programming (PDR) or a, what is called, Life Changing Experience (LCE). In PDR Bad experiences are taken away (i.e. out of the urn) and replaced by Good experiences, to regain trust and a higher confidence (PLS) level. In LCE's, your environmental or physical circumstances suddenly chance in such a way that you are forced to experience only just B (or just G) experiences. Another LCE is created by the change of context. What before were B experiences now turn out to be G experiences (or the other way around).

What if?
There are many other aspects that could be studied in relation to the Polya model. For example:

• What would be the effect if an experience is not just only Good or Bad, but a mix.
• What if a 'Good experience' doesn't trigger extra positive confidence (an extra G) but a negative experience (an extra B).

The answer in both cases is that almost always the PLS-limit=50% !, in other words: You'll become average.

But how does a little bit of extra Bad (or Good) influence the PLS limit? If you want to experiment (online) and learn more about Good and Bad, go and visit

Polya's Urn Experiment

and look up the Math behind Polya's Urn (attachments).

Perhaps Polya's Urn is also a good start to model the stock market.
I'll leave that up to you.
Math helps us to discover who we are or what we become...

God must be an Actuary

Let's dive back in history and take a look at a unusual 'biblical' article in The Actuary of 1986 (Vol. 20, nr. 6 ; page 8).

In a amusing article Mark W. Campbell develops a simple lifespan equation with regard to our 'Greatⁿ Grandfathers'.

This is the original (somewhat restyled) article:

You Should Live So Long

Sir:

In the January issue, Murray Projector quotes Genesis 6:3 as follows:

“And the Lord said: ‘My Spirit shall not abide in man forever, for that he also is flesh; therefore shall his days be a hundred and twenty years.’ “

Mr. Projector suggests the interpretation that 120 years is the maximum age or “omega” for man. This is an interesting idea when one considers the recorded life spans of Noah (of whose generation Genesis 6:3 speaks) and his descendants. The enclosed graph shows these life spans down to Moses, of whom Deuteronomy 34:7 states:

“And Moses was a hundred and twenty years old when he died: his eye was not dim, nor his natural force abated.”

The curve which has been fitted to the data is of the form y = A + B-C^-X. With “A” set equal to 120, the R- squared of the fit is approximately 92% (the R-squared can be increased slightly using a lower value of “A”). This is a remarkably good fit to biological data.

I am not sure what all this means, except that, as always, there is more to the Bible than meets the eye. I welcome the comments of other readers.

Mark W. Campbell

In his original article Campbell doesn't mention the values of the variables A,B and C. However, in the following magazine of The Actuary (nr. 7), Samuel L. Tucker, defines those variables in an equation that 'fits the Campbell curve quite well' :

y=120+830*1.407 ^-x

the variable 'x' stands for the 'xth generation'.

In the same article, nr. 7, Tucker concludes that the Campbell equation overestimates the lifespan and therefore fails in case of earlier great-great grandfathers, back until Adam. He challenges Campbell to develop an integral equation regarding all 26 generation.

26 Generation Equation
Well, here it is. The formula, a logistic equation fitted at ZunZun, is now expressed into our modern western time line (t):
With a= 792.40, b= 1307204394.9 and
c= -0,00881292

In graphics:

The simple formula and good fit undoubtedly prove that:

God must be an Actuary! ;-)

The results in table form:


De equation is again modelled with an age limit of 120, as it appears that, although longevity in modern times is increasing, the 'omega age' (120) seems hard to beat.

More information about our great-great grandfathers at:

Noahs Age

For those who are interested, please download the corresponding spreadsheet.

Have fun in combining actuarial math and the bible.......

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!

Why an actuary succeeds!

What's that special gift an actuary has, that he always succeeds?

Never mind how complex the situation, an actuary always has that one missing magic equation ready to astonish his audience....

Some accuse actuaries of always talking their way out of a problem. They stress that actuaries misuse their formulae to force decisions 'their way'.

We all know that's not true. Yes, an actuary always survives and actuaries are not biased or irrational.

It's the study, our experience and our trained 'gut feeling', that makes us succeed, as the next cartoon shows!

(Click [twice] on the cartoon for the enlarged version, to get a clear sight at the equations)


So now you know why an actuary is not easily daunted!

DCF: Discounted Crash Flow

I remember in a 2007 client panel discussion I was chocked to hear that three large company CFOs of name and fame, without blinking an eye, stated that they were running their company on basis of a narrow quarterly time schedule, no longer. Long term investments? Out of the question. Pension obligations? Rather not, please... Project payback periods: 3-6 months, in exceptional cases a maximum of a year.

What was happening?
How come, CFOs have become that short term focused?

Answers
It's easy to come up with answers that pass the buck:

• Extraordinary shareholder demands
• Bonus Structure,
• Greed, Grab Culture

However, despite and behind all this, there is a deeper cause.

Thinking concept
This short term focus, that is not limited to CFOs, is the logical consequence of the way our thinking and modeling has developed during the last decades:

• we try to exclude risk at any price, instead of managing it.
• we struggle and sometimes even fear to transform long term cash flows into discounted cash values or NPVs

According to a 2002 survey, more than 85% of the CFOs say they use NPV-analysis in at least three out of four decisions.
As actuaries we're also part of this family of Discounted Cash Flow (DCF) Experts. Some of us might even have thought there's nothing more to learn about DCF...

Of course we understand every technical detail of our DCF-model, but let's take a look at some classical aspects of the DCF technique from a different angle. I'll call this angle the I-View, with the I of Important.....

DCF properties
As we know the value of a future cash flow (cf ) , depends strongly on the choice of the discount rate (r) and the moment in time (t) of the cash flow. The further away (in time) the cash flow and the higher the discount rate, the lower the DCF value.



I-View
From an I-View perspective one might say that in the DCF of a constant cash flow, the contribution of the cash flow in year 10 is ruffly half as Important (UnImportant-effect) as a cash flow in year one, assuming a discount rate of 7%.

Another way of saying: This one off cash flow is only of 51% Importance to us.

Although this might not surprise you, a often heavy underestimated effect is that the UnImportant-effect rapidly increases in case a particular discounted cash flow in year (t) is part of and expressed as a percentage of a discounted fixed term (or perpetual) cash flow stream. This is illustrated in the next graph (base: r= 10% discount rate).


De relative contribution of a cash flow t, soon loses more and more Importance when it's part of a constant cash flow stream. As the term of this cash flow increases to infinity, the relative contribution of any 'one year cash flow' becomes rapidly UnImportant.

I-View 1: Discount Rate Adjustments
As we know, the choice of the discount rate depends on the type of cash flow. Cash flows with substantial risks are often discounted with an adjusted (higher) r, according to the (CAPM) formula:

r = r_f + β×(r_m - r_f)

with: r_f = risk free rate, r_m = expected return on the market and β = (beta) a measure of the (opposed to the market) cash flow risk.

It's obvious this CAPM-method amplifies the mentioned 'UnImportant-effect' of long term cash flows.

In times of financial crisis, when we're inclined to become more risk averse, the 'UnImportant-effect' grows even more, as we are inclined to adjust r for fear:

r = r_fear + r_f + β×(r_m - r_f)

Moreover in general, the longer the cash flow term, the higher the (compound) expected risk, and therefore the higher the discount rate (r). Instead of a constant r, there's a need for a variable r, r_t, that increases in time, intensifying the 'UnImportant-effect'.

I-View 2: Discount Rate of Liabilities
Another DCF example: A pension fund has extremely long term liabilities. A cash flow of - let's pick - 50 years ahead, is no exception, but only accounts for about 14% of its cash flow in the discounted liabilities of the pension fund (abstracting from mortality and assuming a discount rate of 4%), and is therefore implicit considered (rated) less Important compared to more recent cash flows. Because there's no real or substantial market for long term cash flow pension obligations, r is even harder to define. Increasing r for this risk is like putting the cart before the horse: The UnImportance effect will increase. For internal valuation r should be decreased instead of increased, but how.....?

I-View 3: Short term Ruin Probability Nonsense
A third effect is that a 0.5% yearly ruin probability sounds safe, but nevertheless compounds up to a risk of 14% over a period of 30 years and even more on the long term.

Years	Cum.Ruin Risk
1	0.5%
10	4.9%
20	9.5%
30	14.0%
40	18.2%
50	22.2%
60	26.0%
70	29.6%
80	33.0%
90	36.3%
100	39.4%

FCLTOS, Financial Companies with Long Term Obligations, like banks, insurance companies or pension funds are by definition companies that have to stay ruin proof on the long term. Managing these kind of companies on short term ruin and certainty models is completely nonsense.

However, there's nothing much FCLTOS can do about it. A long-term certainty level of 99.5% (0.5% ruin risk) over a period of 40 years would imply a yearly certainty level of 99.9875% (0.0125% ruin risk). Even if it would be possible to minimize the technical risks to such a low level, it would be overshadowed by unquantifiable external outside risks (e.g. nature disasters). Anyhow, government regulators should define a target with regard to an appropriate choice of a long-term certainty level and should distinguish between short term and long term certainty in their models.

These examples illustrate that the management FCLTOS, giving these DCF-like methods, do not have another choice than to focus on the near future (5-10 years) and - by method - are not obliged and therefore also not will focus on the long term effects.

Navigating
Managing FCLTOS, is like navigating an oil tanker from A to B between the ice floes. You have to avoid the short term (nearby)
risks (the ice floes) while at the same time keep sight and hold direction on your long term target (port B) in order to succeed.

Translated to a pension fund: manage your liquidity on the short term and your solvency and coverage-ratio on the long term. Any captain of an oil tanker would certainly be discharged immediately when he would make a dangerous change in course today to avoid an actual clear, but in the future certainly changing (moving targets) ice floe situation 50 km ahead. Yet, government regulators and supervisors are forcing pension fund 'captains' to undertake such ridiculous actions.

Steering on short term recovery plans , publishing and publicly discussing coverage-ratios and finally 'valuing pension funds' solely on market value (given that the market for extreme {> 30 years} long term assets and liabilities is extremely 'thin' and volatile), is therefore dangerous and apparently wrong (nonsense) and leads to discounted crash situations.

But there's more that contributes to discounted crash management......

One off negative cash flow in the future
Let's compare two (almost) equal cash flows, CFa and CFb:
- CFa: 30 year constant cash flow of yearly $1,
- CFb: like CFa, but in year 25 a one off negative cash flow : -$1

Although a negative cash flow of $1 in year 25 will probably ruin the activities an cash flows in later years, the NPV of the two cash flows only differ slightly and the calculated IRR of CFb (9.76%) is also just slightly lower than the IRR of CFa (10%).

One might argue that because CFb is obviously a more risky cash flow, the adjusted r has to be raised. This is true, but nevertheless intensifies the so called UnImportant-effect: the relative weight of the 'year 25 cash flow' in the NPV decreases.

Last but not least, what explains the short term attitude and those extreme short periods of several years or months, some CFOs practice as a time frame to run and control their company ?

Certainty Erosion
These extreme short periods are the consequence of the No. 1 concern for CFOs:

The fundamental and increasing lack of ability to forecast results

Let's do some rule of thumb exercise....

Assume the certainty level of calculating a sound financial forecast in the next period (year, quarter, month) is estimated by a CFO at C%.

Now take a look at the next table (on the right) that shows the average extrapolated certainty level (AC) over a number of periods P.

In formula:


Some examples from the table:

• A CFO that estimates the 'next quarter result' with a certainty level of 70% (C=0.7), will probably not burn his fingers by presenting a full year forecast with an average expected certainty level of 44%.
• A CFO of a company hit by the current financial crisis, estimates the certainty of his companies January results at 60%. The board announces it's not able to estimate the full year result. Right they are, with a 60% monthly certainty level, the full year result would have a certainty level of only 12%.....
• Even a CFO with a superb forecast certainty level of 90%, will be cautious with a 5-year forecast (certainty level 74%).
• A 'best of class actuary' that estimates the certainty level of his data at 90% on a yearly basis, will have a hard time in answering question about the certainty level of his projections over 14 years (50%?).

The I-View consequence of this 'compound certainty development' is that even at high levels of (yearly) certainty, the (average) certainty of cash flows after already a few years in the future, erodes.

The effects of Certainty Erosion are enormous. The wall of haziness that is created in a few years - at even high levels of certainty - is astonishing. Never 'believe' a long term one point forecast. Always request variance and certainty level(s) of presented forecasts.

Conclusion
We may conclude that DCF is a superb technique as such to analyze and value cash flows. To prevent ending up in a 'crash flow', DCF has to be implemented by professionals who realize that the essential point of DCF is not just the technique itself, but the way the parameters, used in the DCF-models, are defined.

In order to be able to really take responsibility in managing a company, the Board of a company should be involved in the selection and consequences of the deeper and underlaying DCF-parameters. Enough work for actuaries it seems....

Related Links:
- Some comments on QIS3, (Long term certainty levels)
- Quantifying Unquantifiable Risks
- NPV

Success

We all want to be successful. But what is success?

Success could perhaps be defined as achieving the Result you want by using your core Qualities at the right Time given the right Circumstances (place,people,weather, atmosphere).

In formula: R = Q x T x C

Another way of looking at success has been defined by Hevizi:

It’s not WHAT you know.

It is not WHO you know.

It is not HOW you deliver.

It is ALL of it.

In the new world of tough competition for positions, careers and recognition it is important to remind ourselves that it takes 3 to be successful and compete.

We can look at this as the following formula:

SUCCESS = IQ * EQ * XQ

Success explained
A more sophisticated, humorous yet interesting approach of success has been defined by Alain de Botton in the next TED video. Alain examines our ideas of success and failure:
Is what you define as success really your personal defined success or perhaps the unconscious copied succes definition of somebody else?

He points out that believing in winners and loosers is a narrow and wrong way of defining the world. On top of this, he gives randomness a place in the definition of success and stresses that there can be no success without loss....

Philosophy of Success

Wrapped up, success could be defined as being satisfied and happy with your choices, actions, gains and losses.....

So never give up, discover the secrets of success and enjoy it!

Youtube Success Links:
Quest for success
Success by Deepak Chopra