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

Actuarial Fallacies

Just some light stuff, to chew the cud during holidays...

A good friend tells you that a certain 'John Nevermet' is an introverted professional and is either an actuary or a salesman.

Which one do you think John most probably is?

If your first thought was: an actuary, congratulations(!), you just got caught in what is called a classical

Thinking Trap

Most people - not actuaries of course ;-) - are tempted to think John is almost certainly an actuary.On the other hand, they think of a salesman as 'outgoing', 'extrovert' or maybe 'pushy', but certainly not as 'introvert'. Wrapped up : John is an actuary....

Sorry, but - as you know - this logic conclusion is definitely wrong. It neglects the fact that salesmen outnumber actuaries at most 100 to 1. Before you would even start to consider John's character, you should have concluded that even when all the actuaries were introvert, there would only be a small 1% probability that John is actually an actuary (only in the unlikely case that less than 1% of the salesmen would be introvert, this option would be logically to consider).

Top 10 Thinking Traps
This foregoing simple example is just one of the fabulous Top 10 Thinking Traps Exposed by Luciano Passuello.

On his blog Litemind, Luciano explains in a 5 minute 'must read' called 'How to Foolproof Your Mind' the next interesting and most harmful Thinking Traps, including suggestions on how to avoid each one of them. :

1. Anchoring Trap: Over-Relying on First Thoughts
   Your starting point can heavily bias your thinking
   
2. Status Quo Trap: Keeping on Keeping On
   We tend to repeat established behaviors
   
3. Sunk Cost Trap: Protecting Earlier Choices
   Sunk cost shouldn’t influence a decision, but it does
   
4. Confirmation Trap: Seeing What You Want to See
   Being less critical of arguments that support our initial ideas
5. Incomplete Information Trap: Review Your Assumptions
   Overlooking a simple data element can mislead our intuition
   
6. Conformity Trap: Everybody Else Is Doing It
   Other people’s actions do heavily influence ours
   
7. Illusion of Control Trap: Shooting in the Dark
   The tendency to overestimate our personal control
8. Coincidence Trap: We Suck at Probabilities
   A “miracle” is - given enough attempts - possible!
   
9. Recall Trap: Not All Memories Are Created Equal
   “Special events” have the potential to distort our thinking
   
10. Superiority Trap: The Average is Above Average
    People have much inflated views of themselves
    

Thinking traps are a special form of fallacies.

Example
A nice and triggering example of a composition fallacy is:
I fit into my shirt... My shirt fits into my luggage...
Therefore I fit in my luggage...

Can you tell what's going wrong here?
Yes? Then get ready for the next fallacy phase.

Although there a complete list of fallacies, another new interesting subset could be defined as 'Actuarial Fallacies'....

Actuarial Fallacies
Except for a 1988 homonymous, humorous intended, nevertheless still actual and relevant document by Charles L. McClenahan, nothing much has been published on actuarial fallacies.

Apparently fallacies are not an issue on the Actuarial Globe.

Therefore, I'll confine my remarks to a few actuarial events, of which each one could easily be nominated for the fictional 'Grand Actuarial Fallacy Prize':

1. Longevity risk can be easily managed
   Longevity slowly but steadily increases. It's not a yearly smashing or impressing risk, but over the years it has the characteristics of a killing sniper: when you finally discover the accumulated longevity loss after a few years, it's almost too late to handle and take appropriate measures.
   
   Actuaries could have foreseen a few decades ago that the average life span would keep rising and adequate measures had to be taken at once. Instead, actuaries failed to catch the implications of the rise in longevity and were caught by the proverbial 'boiling frog effect'. In short: actuaries failed to act in time....
   
   
2. Stocks are a hedge against fixed-income liabilities
   Already in 1994 in a document called 'On The Risk of Stocks in the Long Run', nobody else than Zvi Bodie already proved that stocks are not a hedge against fixed-income liabilities even in the long run.
   
   
3. Credit Crisis
   Actuaries have failed in foreseeing the credit crisis. We have greatly underestimated the developments and put our head in the sand. We have trusted business plans promising ROEs of 15% and more.Read more in Actuary-Info's : "Wir haben es nicht gewußt!"
   
   
4. VAR Model
   As an article in The Actuary shows, we got intimidated and overruled by the 'magic' quants with their Value at Risk (VaR) models. We did and do know better as actuaries, but missed the boat. Actuaries should be more than professionally trained in giving 'push back'.
   
   
5. The relationship between risk and return
   As we know this risk-return relationship is central to strategy research and practice.
   
   In measuring risk as the variance of a series of accounting-based returns, Bowman obtained the puzzling result of a negative association between risk and mean return.The expected positive association between risk and return turns out to be elusive.
   
   Henkel explains in two must-read articles 'Risk-Return Fallacy' (2000) and The Risk-Return Paradox for Strategic Management: Disentangling True and Spurious Effects the problems and solutions in this field.
   
   Instead of only following what's happening on the other side of the balance sheet, actuaries should mobilize themselves and add some new insights!
   
   Asset Actuaries, please rise!
   
   
   Es ist nicht genug zu wissen, man muss auch anwenden
   - Johann Wolfgang von Goethe -
   
   

Now that we've unmasked several fallacies, in special the 'introvert actuary fallacy', let's conclude our fallacy course with a 'lessons learned?' actuarial anecdote:

Why it's better to work with an imperfect actuary
We all know: A perfect actuary draws perfect conclusions form perfect datasets.

Then of course : A perfect actuary certainly draws "wrong conclusions" from imperfect data.

It's a fact that the data are always imperfect.

So that we can conclude that there is at least a small chance that an imperfect actuary may draw the right conclusion.


That's why it's better to work with an imperfect actuary.

Client Quote
As we know, clients are always right. Remarkably, the next client quote seems to stress the mentioned successful outcome of the imperfect actuary:
I once had an actuary tell me that, because the future is uncertain, his numbers were almost certainly wrong, but he believed they were less wrong than guessing outcomes with no analysis.

You think - by now - you know everything about fallacies?
Well, test it by taking the next fallacy Quiz:

How logical are you?

Success!

Original source :
The November 1983 Random Sampler article Actuarial Fallacies

Hypegiaphobia

What's that spell? Hypegiaphobia?

Yes, Hypegiaphobia is the unpronounceable 'short' for:

A fear of responsibility

In a 2008 white paper, called Hypegiaphobia, KPMG stresses the importance that organizations want to be and must be 'in control' of a multitude of risks and therefore make enormous sacrifices to achieve this goal.

CEO, management and employees have to comply to so many simultaneous goals, and the consequences of not being compliant on a single issue are that high, that people fear to take individual responsibility in a organization.

In search of the balance between rules and trust, KPMG calls upon the parties involved to provide more space for individual responsibilities. In the mentioned white paper KPMG answers two key questions:

• Are the high investments in risk management effective and do they really lead to a lower risk profile?
  
  
• Does risk management overshoot its goal and produce undesirable effects, such as reduced entrepreneurial spirit, increasing litigation, a culture of fear and a potentially adverse effect on the competitive position?

Trust Rules
Moreover, in 2009 KPMG extended their view on Hypegiaphobia by publishing a document called 'Trust Rules'.

Guts, vision and trust go hand in hand in a time of increasing litigation.

Unplug
Lately, numerous persons and organizations in the Netherlands have had the guts to “unplug”. Unplug is a new work style by which numerous (compliance) issues are handled in unconventional ways :

• Getting rid of unnecessary rules, of fixed places and times
• Dealing better with knowledge
• Collaborating more
• Taking more personal responsibility

All this with a a single focus: The client.

Principles
To organize trust and to be able to trust, KPMG has formulated (on basis of client interviews) nine principles they call trust rules (mark: the noun has turned into a verb) :

1. Make contact personal
2. Define common goals
3. Set the right example
4. Build trust with sensible rules
5. Share responsibility and trust
6. Stay on course and keep calm, even when things go wrong
7. Rely on informed trust, not on blind trust
8. Be mild on misunderstanding but crush abuse
9. Dare to experiment and learn from experience

Risk
In a document called Signs of Safety, risk is defined as an increasingly defining motif of the social life of western countries.

However, risk is almost always seen as negative, as something that must be avoided.

Killing Black Swans
To put it simply: everyone is worried about been blamed and sued for something. Thus organizations have become increasingly risk-averse to the point of risk-phobia. Elimination of every Black Swan risk at any price, seems the unrealistic and never ending target.

New solutions
The challenge for management, actuaries and accountants is to see and define Risk in terms of a potential big win and investment instead of only a potential big loss. This also means that - as a society - we have to reformulate rules and laws in a way that risks can be taken in such a way that failure, bankruptcy are or catastrophes are not (nearly) completely excluded anymore.

Often economies of scale lead to the rise of international (financial) companies that overshadow individual countries in terms of VAR.
If country governments of such 'inhabited' international enterprises are convinced that an eventual bankruptcy of such a company would create great collateral damage and therefore is not an realistic option, things will have to change. In these cases governments have no other choice than to order by law:

• a limitation of (international) company size
• a limitation of reciprocal contracts between big companies
  

or...

• to demand and allow companies to restructure themselves in such a way that, in case of a catastrophe, only a part of the company goes bankrupt and not the company as a whole
  

In these cases state (re)insurance is not a preferable solution. Pricing this risk would be too expensive or - even worse - not charging for this risk would lead to a situation where management can take every risk they want, because in case of a bankruptcy, the government would back up anyhow.

Risk-Phobia Virus
As actuaries we're extremely vulnerable to the 'risk-phobia virus'.
Let's not get caught by this virus or hide in the bush, but take a calculated risk and go out to present our new solutions that make the difference in tomorrows risky world. Risk..., a never ending issue....

Links: Hypegiaphobia Video , List of phobia's, Dutch nine trust rules
Sources: Signs of Safety

Actuary Core Qualities

Apart from an official outstanding actuarial education, what core qualities does an actuary need to be successful?

Summarized, here are some of the main qualities:

• Great Mathematical skills and experience
• Outstanding multi level, oral and written communication skills
• Interpersonal and social skills
• Being able to downgrade complex problems to simple decisions to be taken
• Self-motivated, ambitious, creative, independent, team worker
• Conflict solving capabilities; Empathic but also decisive
• Professional integrity, commercial outlook
• A professional discussion partner for professionals in other areas as Pension, Investment, Health, Risk, Governance, ICT, Finance, Administration, Marketing, HR, Legal & Fiscal affairs, etc.

To put is simply: an actuary has to be a kind of 'White Raven', a 'one in a million professional'.....

However, actuaries are just like humans, they do not only have their core qualities, but also their pitfalls.

Besides, how can you find out what your core quality is?

Core Quality Test
Well, the simple answer is that -thanks to Daniel Ofman - you can find out in a one minute online test what your core quality is.

This test doesn't only defines your core quality, but also your pitfall, challenge and allergy.

TAKE THE CORE QUALITY TEST

Now you know what your qualities and pitfalls are, you may as well start working on them!

Links: Core-Qualities
Sources : Wiki, RSS,

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

H1N1 Swine Flu Projection

Strange... a lot of (WHO) swine flu talk and information on the Internet, but no worldwide projections or estimates....

The risk of underestimating the so called H1N1 (Swine Flu) virus is not unthinkable.

Worldwide Projection H1N1 Virus
You don't have to be an actuary or mathematician to make a sound projection of the number of people that will be infected (or die) within the next months. All it takes is 'basic high school' and a common spreadsheet.

Let's make a simple worldwide projection of the expected cases (infections) based upon the WolframAlpha data-set:



The purple line illustrates the development of the number of infections worldwide, the dotted purple line illustrates the expected projected development until the end of july 2009.

With one view it's clear is that during the next months the H1N1 virus spread will be enormous. By the end of July 2009 the number of worldwide infections will rise to almost 0.5 million. The spread of the virus will probably be enforced by the fact that a lot of people have their holidays and therefore travel by plane or bus.

As one would aspect, the development of the number of infections is exponential. The (natural) logarithm of the expected cases (dashed red line) is almost a linear curve. You may find more information of data and projections in the next XLS spreadsheet.

Big Explosion
If no additional prevention actions will be taken, a big explosion of the virus starts just after the holiday period in 2009.



It is questionable if the planned vaccinations for October or later will be in time.Perhaps it's better to have a vaccination, or take Tamiflu, than a vacation in July or August.

Global Infection
If no adequate rigid measures will be taken within the next months, the future of humanity could be serious at stake:



Unrestrained exponential growth on basis of the the current growth-path, will lead to a more or less complete global infection by the end of January 2010.

By then ruffly 36 million people worldwide, will have died. If the mortality rate doesn't stabilize (as it currently appears) at 0.45% of the infected people, the effects could be worse.

As the famous 'Wheat and chessboard problem' already illustrated, exponential growth is a dangerous underestimated killer. It's just like a tsunami: when you notice it, it's too late to act.

Let's trust governments are not underestimating this Swine virus threat.

Happy holidays!

Related Links:
- World Population Density
- U.S. Death rates influenza virus 1918
- Visual Flu Tracker
- LinkedIn: InArm: Important remarks by Dave Ingram

Important Notice

• The 'July 2009 estimation', based on new more reliable and accurate WHO data, you may find on Swine Flu Counter.
  
  
• You'll find the latest (Sept 6, 2009) estimation and Swine Flu Counter on Swine Flu Counter Update-sept-2009

Central Bank Risk Management

Facing 2009, leads us back 300 years in history, when funding 'credit demand' was one of the main reasons for founding Central Banks in England (1694), the USA (1790) and the Netherlands (1814).

Let's go back in history and have a short look at the situation in the Netherlands 200 years ago...

More history DNB
English, Dutch

Monetary Stability

Nowadays the importance of monetary stability is just as important as a few eras ago. It cannot be underestimated.

The years of the gold standard are behind us. Question is: are there any stable new alternatives?

Learning from the past, one way or the other, we will have to introduce new trustful standards. Maintaining the current situation will probably not lead to a sustainable financial system on the long term.

To stress the importance of a stable standard, just take a look at the development of the next Federal Reserve Balance Sheet:


The above graph clearly shows that Central Bank Risk Management is not an unimportant issue....

Fed Example
Example: As more 'bad loans' and up on the U.S. federal balance sheet, to prohibit downgrade U.S. credit rating , the FED - one way or the other - will have to standardize itself.

Central Banks are monitoring themselves
The past has shown that self-regulation in private financial markets doesn't work. Be confident, it won't work on a Central Bank level either: balance size figures and federal stakeholder interests have grown to enormous proportions.

Central Banks are in fact regulating and monitoring themselves and - except for the Eurosystem - they don't fully comply to international accounting standards as well, a risk society clearly cannot permit itself.

Split up Central Banks
To regain control of central banks, governments will have to split their Central Banks into:

• A regular "Reserve Bank" (monetary function) and a
• An objective independent Regulator, that regulates private banks as well as the State Bank.

If a Central Bank is also operating as a State Bank, this Bank should also be separated from the Reserve Bank business, to guaranty an objective monetary policy by the Reserve Bank in a specific country.

In the mean time, Central Banks will have to become innovative and come up with a collectively supported new standard alternative. They have to act fast, before the market creates his own new wild and probably risky standards out the financial market chaos.

Actuaries and Economists could work together to develop such a stable risk-free standard.

Pension Fund Death Spiral

In a very simplified model (Pensions Dynamics, PPT), professor of investment strategy, Alan White, concludes that defined benefit pension plans probably cannot succeed on the long term.

Death Spiral
White shows that every pension fund with a non risk-free asset approach, will eventually encounter a “Death Spiral” which will lead to the collapse of the fund. The only solutions are:

• Raising contribution rates
• Lowering promised pension benefits.

Assumptions
All conclusions are based on the next summarized main assumptions:

• Compensation growth: 2% per year
• Pension contribution: 15% of yearly compensation
• Yearly retirement income objective: 70% of his final salary
• Risk-free rate of interest is 3%;Risk premium on the risky assets: 3%
• Annual volatility of the risky assets: 15%
• Time horizon: 100-year
• Risky Assets investment part : 60% of the portfolio
• Corresponding final pay pension defined as 20 year annuity
• Required minimum average Pension Fund asset value in steady state
  - at 3% return: €/$ 47,200
  - at 6% return: €/$ 23,600

Frequency Distribution Outcome
One of the most striking outcomes of this study is the fact that as we look farther in to the future of the simulated pension fund, the amplitude of the frequency distribution of asset values appears to be dropping to zero. The chance that (average) asset values will be between $10,000 and $100,000 gets smaller and smaller.

The reason for this is that the probability of very high asset values and the probability of entering a collapsed state (the collapsed funds are not shown in the next figure) both increase as we expand out time horizon. As a result the probability that assets remain in the intermediate interval, is reduced.

Another interesting facts are:

• Asset values appear to become more sustainable as the part 'risky assets' increases
• Collapse rates for growing pension funds are, (almost) independently of the asset mix, negligible.
• Collapse rates for more mature (steady state) pension funds are substantial and increase to deadly percentages as the time horizon increases from 50 to 100 years.

Remarks
Although Whites model is perhaps oversimplified and can be easily criticized, it clearly shows the essential principles of running a pension fund.

In a commentary, Rob Bauer (ABP, University of Maastricht) argues White's conclusions. Nevertheless, interesting stuff, that stimulates actuarial insight.

Links
Interesting corresponding links:

• Longer Horizons Can Handle Riskier Holdings
• Stochastic Interest rate models (2008)
• The calculus of retirement income

Influenced Decisions

As sincere actuaries, we all think our decisions are made in a pure professional and rational manner. Upon our turn, the board we advise, takes decisions based on our 'objective' unbiased advices.

Too bad, nothing is less is true! Decisions are strongly influenced by the way we present our proposals.


Influenced Decisions
In a splendid TED Video Presentation called 'Are we in control of our own decisions' (half an our fun and learning!) , Dan Ariely, an Israeli professor of behavioral economics and head of the eRationality research group at the MIT Media Lab, shows the astonishing effect of how decisions can be fundamentally changed by adding dummies in proposals:

First experiment
Ariely tested the next ad on the website of the Economist.com on a group of 100 MIT students:

As expected, most students wanted the combo deal (84%). Students can read, so nobody wanted the middle option.

But now, if you have an option nobody wants, you can take it off. Right? So Ariely tested another version of this ad on another group of students, eliminating the middle option. This is what happened:

Now the most popular option (84%) suddenly became the least popular (32%). And the least popular (16%) became the most popular (68%) option.

What happened was that the 'useless' option in the middle, was useless in the sense that nobody wanted it. But it wasn't useless in the sense that it helped people figure out what they wanted. In fact, relative to the option in the middle, which was get only the print for $125, the print and web for $125 looked like a fantastic deal. And as a consequence, people chose it.

The general idea here is that we actually don't know our preferences that well. And because we don't know our preferences that well we're susceptible to all of these influences from the external forces.

Second experiment
People believe that when they see somebody, they immediately know whether they like that person or not. Ariely decided to put this statement to the test.

He showed his students a picture of Tom and a picture of Jerry (real people in practice). Then he asked "Who do you want to date? Tom or Jerry?" But for half the people he added a slightly less attractive (photoshopped) version of Jerry. For the other half of the students he added a slightly less attractive (ugly) version of Tom.

Now the question was, will ugly Jerry and ugly Tom help their respective, more attractive brothers?

The answer was absolutely YES. When ugly Jerry was around, Jerry was popular. When ugly Tom was around, Tom was popular.


Conclusions: The Dummy Effect
What can we conclude from these two experiments?

When a board has to take a decision between two main proposals, their decision might be positively influenced by adding a third 'slightly less attractive version' (the dummy) of the proposal you - as an actuary - value as most favorable.

The danger that you - unaware of this dummy-effect - add slightly other proposals is substantial, as - in searching for the best decision - you'll be naturally inclined to add a few solutions nearby the optimal solution.

From now on...
Now that you've become aware of this dummy-effect, your next board proposals will be 'cleaner' than before and 'undummied'. Also you'll have a more enriched look at third party (or employee) proposals that are on your or on your boards table. From now on your board advise will not only focus on the technical or actuarial matters, but also include a professional opinion about the way a proposal is structured and presented.

Good luck in developing proposals.....

Links
- Book Predictably Irrational by Dan Ariely
- MIT Center for future banking