Dec 31, 2010

2011: Happy Risk Year!

Life is full of Risk..  We can not deny or totally exclude risk. Have you ever thought about living a (professional) life without taking any risk? What kind of life would that be?

There's this great actuarial risk quote of the famous economist John Maynard Keynes that states:

On the long run, we are all dead.....

So if you want some 'return' in life, you might as well take 'somewhat' risk before you 'certainly' die.

A nice illustration of total risk aversion is the 2004 movie "Along came Polly" were Reuben Feffer (actor Ben Stiller) is an actuary who, since his job involves analyzing risk for insurance purposes, likes living life in complete safety and free from any unnecessary risk.

This movie urges to ask yourself a simple question:

What's the risk of a riskless life?

Living life without risk if for dummies! Optimize the risk-return in your life.

Risk Guidelines
At the end of 2010 some simple Maggid 'Risk Guidelines' for 2011:
  1. As long as there are no risks that'll kill you on the 'middle' or 'short' term: Take risk if you like the return outlook.

  2. Think about how much bad luck or suffering you're willing to accept for a desired return.  Key question here is:
    Why does a marathon runner punish his body every day for weeks on end for an individual race?

  3. Take a small risk every day! Invest small 'good things to do' by helping others without expecting a return. Soon you'll harvest some of your sowed investment seeds.....

Riskless Investment
Remember..., the only one riskless investment in life is.....


Anyhow, make 2011 a happy and healthy risk year!

Related Links:
- "Watch the movie 'Along came Polly' online !
- Learning about Risk and Return: A Simple Model of Bubbles and Crashes 

Dec 26, 2010

Discounting the future

Actually, who are we actuaries to pretend that we can discount the future? Who's able to predict the future 50 years or more ahead in case of a pension fund?  No, we're not crystal ball discounters, we're risk managers 'pure sang'. And as discounting risk managers we're pretty sure about two things:
  1. The increasing uncertainty (fogginess) of future cash flows slowly kills its discounted predictability in time

  2. Risk free discount rates doubtlessly include the risk of changes in future discount rates, but nevertheless vary in time.

    Risk free discount rates are volatile and are unpredictable on the long run.
Historical development
Let's take a look at discounting developments from a helicopter's perspective...
A few decades ago, discounting was simple:

Discounting Around 1980
Whether you were in the insurance or pension business, way back in the last century actuarial business was simple. All you had to do as an actuary, was discounting the assets and liabilities at an explainable 'long term average' and 'realistic save' (whatever this means in today's perspective) discount rate and it was done. Subtracting discounted liabilities from the discounted assets, also resulted in a clear undiscussable equity size:(E= A - L) and - in case of a pension fund, the coverage ratio : (CR=A/L).  

Discounting Around 1990
As computer and calculation capacity increased around 1990, actuarial models became more complex. Instead of as single projected cash flow, more complex cash flows and scenarios entered the actuarial model scene. With more sophisticated computer calculation power we were able to calculate and underpin risk-return investment scenario's that led more to more risky 'risk controlled' investment policies.

'Risk' was translated into (replaced by?) 'volatility' and 'volatility' was translated into 'variance'. Thus future risks where estimated on basis of projected historical variance and (later) with help of VaR models.

However, 'Risk' was mainly defined on (and restricted to) the left side of the balance sheet: the assets. In line with this view, the insurer's  equity could be simply expressed as : E= A - kA.σA - L  (mp= minimum position) , or in case of a pension fund, the coverage ratio: CR=(A - kA.σA) / L   (mp).

Discounting Around 2000
More than a decade later, beginning 2001, fair value accounting and market value broke through. Not only stocks had to be valued at Market Value, but also bonds. As a consequence the volatility of the left side of the balance sheet increased more than ever.

As actuaries we thought we would be save on the right side of the balance sheet were things were steady and calm as always... However, a few years later the 'Actuarial Sleeping Beauties' were kissed to life as Market (consistent) Value was introduced with regard to discounting liabilities. This development fired the starting gun to a swapping right size of the balance sheet.

Now insurers (minimum) equity got squeezed up between two volatility monsters, assets and liabilities:  E= A - kA.σA - L -kL.σL (mp).
Pension funds had to become real acrobats to manage their new wobbly coverage ratio: CR= (A - kA.σA ) / (L + kL.σL)     (mp).

No wonder pension funds and insurers got into trouble when the credit crises caused the final blow.....

Rebuilding stability
In Europe insurers are trying to rebuild stability by means of "Solvency II". Pension funds are trying to find their way out by suggesting more conditional pension rights. Some have even suggested to steer (valuate?) pension funds on basis of a kind of "moving average method" (asset returns or coverage ratio).

Other  'actuarial pension experts' have told me that we should stick to market value and accept the consequences, e.g. just accept that coverage ratios can stay below minimal level for several months, without anyone panicking..... Simply explain to pension fund members that the pension fund is long term well funded and there's no reason for panic if the coverage ratio breaks down for a short period....

Don't Panic......
This reaction reminds me of a weird family experience, when we where on holidays many years ago in a village called Ballyheigue (west(ern) Ireland).

Don't panic!
That afternoon my wife, the kids an I arrived in Ballyheigue. We stayed in a lovely local hotel near the fantastic west coast of Ireland.

The local assistant manager welcomed us and pointed out that there was a small minor (2x!) problem that could occur: Last week, at irregular moments, the hotel alarm had gone off several times, this could probably happen again. Reassuringly, he explained  that in the unfortunate case the alarm would go off, we shouldn't panic and just stay calm, as it would probably be a false alarm.....

That night we confidently went to bed early......

Then, at 01.30 AM that night, suddenly the fire alarm goes off. An ear piercing sound cuts through our ear drums... Within 2 minutes we - all hotel guests including my family - are all outside, despite the reassuring words of the hotel assistant earlier that night.


From this simple experience we can conclude that 'reassuring words' don't help in panic circumstances. Ergo, it's impossible not to panic in case coverage ratios go down for several months....

Convincing people 'not to panic' in case of 'clear panic signs' is an almost impossible task.  Once one mentions the word 'panic', all human systems get in a kind of  non stoppable alarm mode. It's like the famous scene from Fawlty Towers :

Related Links:
- Pension Actuary's Guide to FINANCIAL ECONOMICS (2006)
- Pension contracts and developments in pensions in The Netherlands (2009)
- One of those superb hotels in Ballyheigue: White Sands Hotel

Dec 20, 2010

Goodhart's Law

Back in 1975 professor Charles Goodhart stated:

Goodhart's Law
Any observed statistical regularity will tend to collapse once pressure is placed upon it for control purposes

More in general Goodhart's Law is Goodhart's law is a generalized social science expression of the so called 'Lucas Critique'. Named after Robert Lucas who argues that it is naive to try to predict the effects of an (economic) change entirely on the basis of relationships observed in historical data.

Actuarial examples...
Some remarkable actuarial examples of Goodhart's Law are:

Early 2009 Goodhart proclaimed : “One of the lessons of the recent crisis, a lesson for bankers and for regulators, is, hire fewer mathematicians (actuaries) and physicists who build models on the basis of data that they can observe over relatively short period, and hire a few more historians who know what can go wrong even if they don’t necessarily have a good data basis to put into particular models”.

Although Goodhart is probably right, actuaries should keep an eye on the process....

Future developments are a function of Data, Probability, Uncertainty, Experience and above all Common Sense.

Just like the Roman God Janus, actuaries should look at the future, with the past in mind. And to do just that, we need all the help in the world, especially from historians....

Related links:
- Performance Persistence of Dutch Pension Funds (2010)

Dec 11, 2010

Actuarial Thought Leadership: What is success?

What is success? Are you a successful actuary?

Simple questions, easy to answer you would think. Right?


To illustrate the deeper  meaning and the nuance of success, let's take a look at the next 'Best Practice of Success'. A real life story from Joshua Maggid.....

'Best Practice of Success'

That day, together with my new colleague James, I entered the Pension Board's holy board room. All eight pension board members welcomed us with a hopeful smile and a firm handshake.

After introducing James as our company's brand new super professional, an unbeatable actuary and a seasoned specialist in asset liability matters, all seemed set for a successful presentation by James. Todays subject: Board decision on the new - next year's - asset allocation.

As expected, in a more than splendid and fluently short presentation, James handled everything a pension fund board member could possible think of or ask for. From headlines to all the important details. In roughly half an hour James showed his outstanding technical skills and impressed all board members. They were flabbergasted. What a knowledge, this was what one would call real Thought Leadership!

After James finishes his presentation, silence fills the board room. A kind of holy silence... Every board member is overwhelmed by James' stunning presentation. The Pension Board President quietly  looks around and breaks the profound silence as he softly says: "Thank you James.... Gentleman... (a lack of ladies in pension fund board rooms still teases us)...., is there anyone who has a question?......  (silence continues..) .  If not..... Do we all agree on James' new asset allocation proposal? (silence continues, some board members nod their head..). Does anyone disagree with James' proposal?.....(no one replies verbal or non verbal)... If not... Thank you for your continuing support. As a pension board, we've just agreed to the new asset location for next year... Congratulations!.... Dear advisory actuaries - James in particular - thank you for your effective presentation and corresponding proposal."

As always after I visit a client with a colleague, we meet shortly after in a nearby coffee shop to evaluate the meeting as well as each other's performance, irrespective of any form of hierarchy.

When I meet James shortly after the successful pension fund board meeting in the local Starbucks, he comes in walking with a smile....

"Peace of cake ", he opens our conversation. "What do you mean?, I ask him. "Well, making a $ 0.2 million turnover in a 30 minutes presentation, without any questions or comments, seems like a dream. I couldn't have done any better. I surpassed myself. This was one of my most successful presentations ever", James replied.

I looked him in the eye as I dropped an uneasy silence..... "This was as bad as it could get", I answered James. "How do you mean, 'Bad'? It was great, everyone agreed on my proposal, no questions at all.", James responded agitated.  

"Well - in short - It was YOU that took the decision and not the board. That's whats wrong", I stated. James again: "That's not true, I only advised, the board took the decision, not I. Let's keep things clear here, please!".

"No", I answered, "It was actually you!.... You took the actual decision. And if things in practice turn out different from your proposal (as most likely will be the case), this pension board will blame you for a wrong advice two years from now.......  

By demonstrating your enormous technical power in a half hour monologue, you've overpowered the board in such a way that they could not raise any questions or give comments without the risk of showing a form of incompetence or loss of face.

As we discussed in our preparation, you should have presented at least three different scenarios. Each scenario with a a different risk appetite. You should interactively have helped the board with choosing a well understood risk-return scenario. Asking questions, wrapping up opinions, leading the discussion to a point where the board feels that they've clearly understood what's on the table and 'feels comfortable' with the common decision taken."

James replied with anger: "When I have to do it that way, my presentations would take two hours and my preparation as well.  Above all, I have to deal with ten similar clients next week. I simply don't have the time to pick it up the way you suggest."

Moral of the story
From the above example it's clear that 'short term success' is not the same as 'long term success'.

To prevent ending up only in the reality of our own believes, constructive peer reviewing each other's performances is key to keep delivering long term top quality.

So don't forget to discuss your 'actuarial eggs' with one of your actuarial colleagues.....

It takes 'new ethics' actuaries (and quants) to make pension fund business successful again.
Are you that actuary?

Related links:
- Making Decisions in the Pension Fund Board Room (PDF,2010)
- Investmentmentor:
   expectation, a force that will release either success or failure

Dec 6, 2010

Actuarial Simplicity

What is simplicity? What's the power of simplicity?

It was Johann Wolfgang von Goethe ( listen), a German writer (poet), but also a polymath (!), who

And indeed Goethe was right, in (actuarial) science and  practice it's the challenge of overcoming (transcending) this paradox of simplicity and complexity.

The art of actuarial mastership
As models become more and more complex, it takes the art of actuarial mastership to condense this complexity into an outlined, understandable and (for the audience) applicable outcome.

A 'best practice example' of condensing complexity into a powerful inspiring statement, is Einseins famous equation E=MC2 :

Like Paulo Coelho states in his blog about Einstein:
A man (actuary) should look for what is, and not for what he thinks should be. Any intelligent fool can make things bigger and more complex… 

It takes a touch of genius – and a lot of courage to move in the opposite direction.

Or, to quote Einstein:

Everything should be as simple as it is, but not simpler

How to cut through the actuarial cake?
Just three simple examples on how to cut through the complex actuarial cake. Examples that might help you to simplify complexity:

1. Think more simple

A perfect example of 'thinking more simple' is finding the solution of the next math problem (on the left), grabbed from an old high school math test.

Can you solve this problem within 10 seconds?

Found it? Now move your mouse over the picture or click it, to find the refreshing simple answer.....

Remember however not to oversimplify things. Sometimes problems need the eye of the actuarial master to identify important details...

2. Visual Results
Second example is to visualize the outcome of your models instead of power-point bullet conclusions or explaining how complex your model really is.

A nice example is the online dollar-bill-tracking project "Where's George?" from Research on Complex Systems, that measures the flow of dollars within the U.S. (over 11 millions bills, 3109 counties).
About 17 million passengers travel each week across long distances. However, including all means of transportation, 80% of all traffic occurs across distances less than 50 km.
One picture says it all and 'hides' the complex algorithms used, to get  stunning results.

On top of, George collects relevant data about 'human travel' that could be used for developing models of the spread of infectious diseases.

Just take look at the video presentation of George called Follow the Money to find out how to extract simple outcomes from complex models.

One of the simple results (by Brockmann) of this project is that the probability P(r) of traveling a distance (r, in km)  in a short period of time in days (max 14 days) can be expressed as a power law, i.e.:

P(r)= r -1.6

 3. Listen better
Every (actuarial) project outcome fails if there's no well defined goal at first.

Main problem is often, that the client isn't really capable of defining his goal (or problem) very precise and we - actuaries - start 'helping' the client.  In this 'helping' we are imposing our thoughts, beliefs and experiences onto others, by what we think 'is best' for the client. The outcome might often be an actuarial solution that fits the problem in our own actuarial head, but fails to meet the clients problem.

Main point is that we - as advisors - don't really listen well.
Of course that doesn't apply to you as an actuary personally, but it does apply to all other qualified actuaries, doesn't it?

Just to test if you're part of that small elite troop of 'well listening qualified actuaries' (WLQAs), just answer the next simple Client Problem:

Client: I'm confused about 'distances'. It turns out that measuring the distance between two points on earth is really complicated math, as the world is round and not flat.

But even in a 'flat world' I find measuring distance complicated. As an actuary, can you tell me:

What’s the shortest distance between two points in a flat world?

O.K. Now think for a moment.....

Have you got the answer to this complex client problem?

Now that you're ready with your answer, please click on the answer button to find out the one and only correct answer.
The answer is: the shortest distance between two points is zero
Hope you safely (without any mental damage) passed the above WLQA-test......

A Simple Application
A nice demonstration of actuarial simplicity is the well known 'compound interest doubling rule' that states that an investment with compound interest rate R, doubles itself in N≈72/R years.

So it'll take (p.e.) approximately N≈ 12 (=72/6) years to double your investment of $100 to $200 at an compound interest rate of 6% p.a.

While the precise equation of the doubling time is quite complex to handle, it's approximating equivalent, N≈72/R, is simple applicable and will do fine for small size compound interest rates.

It's our actuarial duty and challenge to develop simple rules of thumbs for board members we advice. We actuaries have to master the power of simplicity. Let's keep doing so!

Related links:
- The Complexity of Simplicity
- Where's George?: Wikipedia
- The scaling laws of human travel (2006)

Dec 3, 2010

God’s Definition of Risk

To snap things in the right perspective, now and then it's good practice to consider how actuarial science really started:

Yes, like Laplace stated in his masterwork 'Théorie Analytique des Probabilités', it all began with 'games of chance'... and - today -  perhaps it still is.....

From 'gaming', probability theory developed to 'actuarial science' and finally to 'risk management'.

Risk Levels
Today we distinguish three main types of risk levels:

Risk Level 1
In fact what we are modeling mostly, are the risks we know, the 'known risks'... These risks are the familiar operational, financial and compliance risks

Risk Level 2
These are the strategic risks. Risks related to new markets, mergers and acquisitions, investments, but also business development, brand and reputation risks.

Risk Level 3
These are the unpredictable, the so called 'unknown, unknown risks'.

The Rumsfeld definitions of risk levels
A similar more humorous, but also interesting definition of risk levels, has been given by the United States Secretary of Defense  Donald Rumsfeld  during the Iraq War:
  1. Known Knowns
    There are known knowns; there are things we know that we know
  2. Known Unknowns
    There are known unknowns; that is to say, there are things that we now know we don’t know
  3. Unknown Unknowns
    But there are also unknown unknowns; there are things we do not know we don’t know."

If we're honest, we'll have to admit that even our 'known known' and 'known unknown' risks in our models in reality have a high 'unknown unknown' origin.

Or, as Barry du Toit at Riskworx shows in an excellent paper called 'Risk, theory, reflection: Limitations of the stochastic model of uncertainty in financial risk analysis' : our stochastic model of uncertainty is powerful but limited.

It's (p.e.) an illusion to use 'standard deviation' as a stand alone measure for risk. We must be aware to apply our models without a healthy portion of 'common sense'. Or, to put it in air-plane words:

The danger inherent in 'altimeter usage' is that its unquestioning use will stop pilots from using a range of more intuitive risk measures, such as looking out of the window!

God’s definition of risk
There is no ultimate "God’s definition of risk", we'll have to manage with our limited models as a help to our Risk Insight. Success!

Sources and related links:
- Limitations of the stochastic model of uncertainty in financial risk analysis
- Laplace: analytic theory of probabilities (English)
- Strategic Management of Three Critical Levels of Risk
- Managing Projects in the Presence of Unknown Unknowns

Nov 29, 2010

Longevity Swaps: The Next Bubble

Last century our Human Footprint Index (the relative human influence in each terrestrial biome on Earth) increased exponentially.

According to the Human Footprint Index, not only Europe (left picture), but also India and the North East of the U.S.  are  'humanized'.......  Step by step we - human beings - are 'amazingly' filling up every little corner of the world.

Just a few more years and - as a species - we'll be 'omnipresent'.

Yes, we are crowding this good old earth at an immense speed, as our health increases and we keep living longer every year. The social and financial effects of this population growth will be enormous.

Nevertheless we're very unsure about how our population will grow in the future...

Key point is that population growth will strongly differ per region and country. The growth in the western countries will be driven by the aging population, while the growth in developing countries, like Africa, will be driven by new births. In the' aging countries' population growth will undermine our social and first pillar pension systems....

Pension Fund Transform
This aging society development implies that our mature pension funds will have to transform from pension-saving to pension-paying.

Secondly 'longevity risks' become more and more important and can not be 'financed' anymore from the declining funding margin.

Example: The Longevity Trap
Let's take a simple example.

Rule of Thumb Nr. 1
In the so called developed countries, every year we live, our life expectancy increases (on average) with 3 months! Or, as Harry de Quetteville from the Telegraph stated it more humorous:

For every year we live, we are only really nine months closer to death!

Rule of Thumb Nr. 2

This rule of thumb states the financial impact of longevity:

One year increase in life expectancy from age 65 equates to approximately a 3% to 5% increase in pension value liabilities.

Combining  rule I and II leads to the conclusion that on average the pension liabilities of mature pension funds currently urge for a yearly 1% increase of liabilities, just for financing the cost of extended longevity.

A decade ago, the slowly increasing 'sniper costs' of extended longevity could easily be financed out of the pension fund's margin.

Nobody (not even an actuary!!!) could imagine that longevity would become a substantial issue.

Later that decade, disappointing stock returns and low long term liability discounting rates shrinked the pension margin and even turned it negative. This pension margin reduction put the cost of extended longevity in quite a different perspective. The 'Actuary Longevity Trap' had become a fact!

What really had happened was that the high returns and interest rates of recent decades masked the (increasing) costs of extended longevity.

'Once bitten, twice shy', one would think.... But not for actuaries, as
the next bubble is coming up........

Longevity Swaps
The Next Bubble

Not only pension funds but also Life insurers are facing significant longevity risks as mortality rates are still declining. Reinsurance companies like Swiss Re and Münchener Rück try to fight the underestimated longevity effects of pension funds with so called ‘Longevity Swaps’.

The essence of a longevity swap is that a pension fund trades the - due to longevity - uncertain estimated future pension payments until death (floating leg) against the actual future pension payments for the scheme’s pensioners payments (fixed leg).

Why a Longevity Swap is a bubble?....

The Longevity Swap only transfers the risk to a counter party (reinsurer), but this counter party in general doesn't have a complementary risk to match the accepted risk of the longevity swap. The counter party bases his underwriting only on a more 'safe' calculation. 

This implies that whoever is sitting at the end op the swapping chord, will finally pay the bill (systematic risk!) in case longevity risks are structurally being kept underestimated. Now if one thing is a fact, it is that - for decades - longevity risks are underestimated en this underestimating behavior will continue in the future, as we actuaries are apparently ignorant at this point.

Just like the high interest rates in the past masked the actual cost of the extended longevity, current longevity swaps wrap' long term unsure and underestimated  future mortality rates' in interest-discounted derivatives. 

Whatever reinsurers are discounting after 30-50 years at interest rates above 2% doesn't really count anymore in terms of present value. but will reveal itself in the coming decades....

By the way, is a 90% (asymmetric?) confidence level resulting in a 11 year life expectation spread in 2050 consistent with a 97,5% or 99,5% confidence level used as basis for a longevity swap?

Probably not.........

But who cares about consistency, when 'short money' is on the table?
You? (Hope you do..)

We're left with no other conclusion than that it will turn out that longevity swaps in their current form are the new systematic risks of the future!

Any solutions? 
The only solution to prevent longevity swaps from becoming a bubble is to find complementary 'matching' risks that compensate the accepted risk (profile).

It's hard to find matching risk profiles for the reinsurer. The fact that longevity mainly applies to older people (top around age 80-85) makes it hard/impossible to compensate longevity risks with mortality risks at younger ages.

Perhaps a kind of solution could be that pension funds could offer the relatives of a pensioner the possibility of insuring (life insurance) the calculated liability of the pensioner (or the remaining annuities until the age of 80) at the moment of death  (a kind of liability legacy life insurance).

Perhaps some creative actuaries have some other ideas? Please let me know...

Sources & Related Links:
- Life Tables United States Social Security Area (2005)
- The Human Footprint Index Graphics
- World Population Growth
- Wapedia: World Population
- A model for longevity swaps
- Understanding Modeling and Managing Longevity Risk
The pros and cons of longevity hedging(2010)
- Longevity Risk in Pension Annuities (2005)
- Increasing Longevity: Effects on Pension (2009)
- Longevity swaps as an investment (2010)
- Pensions: Change management (2009) 
- Pensions: On the wrong track? (2009)

Nov 22, 2010

What's that, an actuary? Kamikaze Investors

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

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

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

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

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

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

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

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

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

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

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

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

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

Nov 17, 2010

How to prevent cutting pension benefits?

Continuing increase of lifespan, low interest rates and stock market under-performance are the cause of pension fund's funding ratios (FR) falling to a level of underfunding (< 100%).

Sure..., it's questionable whether valuing assets an liabilities at market value is the best way to value a pension fund (after all, a 'run on the pension fund' is not possible!). However, changing a pension fund's 'valuing method' to a more artificial method (e.g. 5 years average risk free discount rate) seems no realistic option to prevent underfunding. It would be perceived as a cosmetic brew and no solution at all for sponsors that have to consolidate pension obligations in their balance sheet.

Left without alternatives, pension funds are forced by law (and the regulator) to take action. There seems to be no other choice, than to 'cut pension rights'....  Or is there?

Conditional Benefits
A quite simple and effective solution is to split up current an future Pension Benefits (PB) in a guaranteed (certain) part PBcertain (99,9% confidence level) and a conditional part PBconditional .

The Liabilities of the the conditional part Lcond, can be used to act as a Reserve to guarantee the liabilities of the guaranteed pension benefits  Lcertain. In this approach all inflation, longevity and investment results are absorbed by the conditional part Lcond.
As a consequence, the funding ratio (FR) of the pension fund gets 'cured'....

Let's see how this turns out for a healthy pension fund without a shortage:

What in fact is happening here, is that we use the cooperational characteristics of a pension fund to finance its own equity (Reserve + Lcond). As no shareholders are involved, all equity is owned by the members of the pension fund, who profit not by means of dividend, but in the form of conditional pension benefits.

Now have a look at that same pension fund with a shortage on basis of conditional pension benefits:

Undoubtedly this 'new pension model' situation looks much better than the old model and certainly better than the pension balance sheet after cutting pension benefits:

Just imagine what 'reforming a pension fund on basis of conditional pension rights' could mean for your pension fund.

When life gets difficult, we have to turn to simple actuarial solutions....

Nov 5, 2010

How Rewards Pay Out

Let's take the 'Candle Test' as constructed by the psychologist Karl Duncker (1930).

Just take a look at the materials on the left picture.

A candle, a box of thumbtacks, and a book of matches.

Here's the simple task:

Attach the candle to the wall so that it doesn't drip onto the table below.

(Please, don't read any further until you solved this challenge....)

Here's the solution:

Empty the box with thumbtacks. Place the candle in the emptied box. Fix that box to the wall using the thumbtacks. Place the candle in the box.

If you managed to find this solution (without cheating) within 4 minutes, you're still an enlightened actuary.

If not? Don't mind, things will get better after reading this blog.

To find the solution you had to overcome what is called “functional fixedness”: You had to see beyond the thumbtack box as purely a container for the thumbtacks.

Rewarding Performance
In the sixties Sam Glucksberg used the 'Candle Test' to test the impact of extrinsic motivational factors on the problem solving ability.

Glucksberg created two groups of participants. The first group was told they would be timed to establish norms for how long it would typically take people to solve this sort of puzzle. The second group of participants were offered $5 each, if the time they took to solve the problem was in the top 25% of all those tested. The fastest achievement would be rewarded with $20.

The outcome of this experiment was that it took the extrinsically incentivized second group on average three and a half minutes longer to solve the problem. Obviously the incentives narrowed the participants minds and blocked them to think literally 'out of the box'....

From this experiment it became clear that rewards fail and work contrarily in case of complex situations.

Similar experiment....
Then, Glucksberg took a similar experiment in a slightly different way.
He presented two new groups the situation on the left picture.
Can you predict the outcome this time?

This time, the rewarded group defeated the non-incentivized group by miles....

Why???? Because the tacks were OUT of the box !!!!

By placing the thumbtacks out of the box and placing the thumbtack box empty on the table, Glucksberg had changed the problem.

Instead of achieving a heuristic task (i.e. a complex task that requires analysis and experimenting with possibilities to develop a solution), the problem was reduced to a more algorithmic problem (i.e. the solution comes down to a set of simplistic steps down a single pathway to one conclusion).

To summarize: financial short-term rewarding of complex tasks leads to output reduction instead of a better performance.

More than actuaries, professionals like quants, investment managers and bank managers are rewarded on short-term output, while - at the same time - their professional challenges and objectives are complex like a Gordian knot.

A way out
If we want to get out of the current economic crisis, we'll have to stop rewarding short term results one way or the other. Our complete (economic) system should be rebased on rewarding long(er) sustainable results and well calculated risk. Don't wait any longer, just start today at your department.

The issue of "not getting the 'right' professionals if we don't pay enough" is a fable. No matter how professionals like CEOs, Bank managers or actuaries are: if they just go for the short-term money and aren't intrinsically motivated to make this world a little better with their gifts and skills, please let them leave.

Tip: Include rewarding in your risk models!

Let's conclude with an interesting video by Dan Pink who examines the puzzle of motivation, explaining that traditional rewards aren't always as effective as we think.

Related/Used sources:
- Carrots and sticks
- Functional_fixedness

Oct 23, 2010

Actuarial Word Clouds

We all know the saying 'one picture is worth a thousand words'....

What if that picture also contained words itself?
Such a Word-Picture must be worth at least a million words.....

What if that Word-Picture is also an Actuarial-Word-Picture?
This kind of picture must be worth a billion words!

Enough balderdash..., there's a fabulous online application, called Wordle, to empower and spice up your traditional power-point presentations.

Wordle uses words and their frequency to turn them into a Word-Cloud - or better - a Word-Picture.

You may use Wordle on any group of words or even a RSS-feed.
So in fact Wordle creates a weighted summarized and visualized impression of what you, your document or your employer is. 

Here are some examples of Wordle voor the RSS pages of two actuarial giants....

Let's start with Mercer:

Towers Watson

And now for some Towers Watson's...

Actuary Info
Let's conclude with an example of a more modest and smaller actuarial giant: Actuary Info

Presentation Tip
Next time you give a presentation,  instead of summing up the standard dry bullet points, replace them by a Wordle cloud.

Your audience will be spellbound , 'turn their head', 'look for expected words' and 'immediately grasp the relative size of the issues mentioned'. All resulting in (1) you - the presenter - will have much more attention and (2) the facts shown on your slides will be longer remembered, because the are 'your visualized words' and therefore will be better memorised...

An AON Example...
Let's end with a simple example from AON's 2010 Risk Survey:

I. Traditional (PPT) Slide Presentation

Risk Quantification Tools Used (2010)
(to measure demonstrable Value Received from ERM Efforts)
  • Qualitative tools 59%
  • Industry benchmarks 34%
  • Earnings/Cash flow/Value at Risk 27%
  • No use of risk quantification in ERM process 23%
  • Actuarial analysis 13%
  • Stochastic/Monte Carlo simulation 13%
  • Not specified 7%

II. Wordle Presentation

Now..., get your head in the 'Actuarial Word Clouds' an have even more success with Wordle!!!

- Download: AON Risk Survey (2010)
- Wordle

Oct 18, 2010

Voltaire: Diplomats, Ladies and Actuaries..

Actuaries understand the difference between 'being sure' and telling it....
Some of us are Diplomat, Lady and Actuary in One.... what a dazzling combination...

Diplomats, Ladies and Actuaries
When a diplomat says yes, he means ‘perhaps’;

When he says perhaps, he means ‘no’;
When he says no, he is not a diplomat.

When a lady says no, she means ‘perhaps’;
When she says perhaps, she means ‘yes’;
When she says yes, she is not a lady.
- Voltaire 1694-1778 quoted in Escandell 1993 -

When an actuary says yes, (s)he means 'probably'
When (s)he says probably, (s)he means 'sure'
When (s)he says 'sure', (s)he is not an actuary.
- Joshua Maggid Actuary Info 2010 -

Oct 15, 2010

Questioning Solvency II?

Every now and then, when you're in the middle of some-, any- or every-thing, it's wise to sit back and ask yourself some basic questions:

Is what I'm doing still adding value?
If so, what's that value and for who?
If not, how can I add value one way or the other?
If not, stop!

A Solvency example...
Suppose you're up to your neck in a solvency II project and you've not really seen your family for two weeks. Just sit back, relax and simply ask yourself the next questions:

  1. Why are we implementing Solvency II
    (Better: What's the goal of Solvency II)
  2. Are the reasons for implementing Solvency II valid and sound?
  3. Is it possible and profitable to define and measure detailed risks at company level?
  4. What's the RETURN on Solvency II for policyholders and shareholders?

The official (CEA) answer to question I reads in short:
We implement Solvency II because the current framework is too simple and does not direct capital accurately to where the risks are.

Key question (II) is: Are "too simple" and "more detailed directing capital" valid or sound reasons........?

A more valid reason for implementing Solvency II would be something like:
Recent decades have shown an increase of Insurance Companies Bankrupts (or Insolvencies) to a level of x% p.a. (measured in value instead of numbers). Solvency II intents to bring down this x% risk to (x-y)% in Z years by means of a more detailed capital-risk approach.

The estimated costs of this yearly y% reduction by implementing and maintaining Solvency II, are estimated at z% p.a. .

Main challenges implementing S II at company level

  1. Capital allocation
    At an individual company level, the effect of Solvency II on shareholder and client value will only be negative. More 'dead capital' has to be allocated, decreasing shareholder value and decreasing clients profit share.

  2. Revenues
    Pricing Solvency II, will increase premium/contribution levels. However higher contribution levels will have a negative net impact on sales and revenues.

  3. Capital Inadequacy
    On top of, the extra solvency created by Solvency II will turn out to be inadequate at an individual company level in case the deTAILed risks actually affects (hits) a company. A more (inter)national reinsurance program could bring help here. However, these kind of reinsurance programs turn out to be expensive. Moreover, take care that these deTAILed risks don't turn out to be systemic risks in the end....

It's clear that the Solvency II goals are not smart formulated. Nevertheless, Solvency II seems an irreversible process.

Therefore the key question is:
How can you use Solvency II to add (long term) value to your clients and shareholders?

The art of asking the right question
Now you've replaced your fuzzy feeling and foggy discussions about the goal of Solvency II, by a leading question.

Answering and discussing this question will turn out the way to create efficiency and joy in your project and time for your family.

A lot of colleague actuaries can help you on discussing and answering this question.

Start discussing this question in the company board's next meeting!

Risk management Moral
In fact Risk Management in general is more the art of asking the right question instead of giving the right answer. This is well argumented by Professor Stefan Scholtes (University of Cambridge), who states that what we need is a complementary balance between modelling and intuition; models that relate to and enforce our mental abilities, not replace them.

We actuaries can learn from that. Actuarial questioning turns out key. Next time you have to give a (Board) presentation, start by asking the right (effective) questions instead of giving answers straight away.

One last tip: Never ask 'Why questions', instead ask 'What questions'....

Related links
- CEA Why Solvency II?
- Prof. Stefan Scholtes: The art of asking the right question
- Asking the right questions

Oct 3, 2010

Pension Fund Humor: Ask an Actuary!

The art of Pension Fund management....

original picture source

Investment Strategy: The Price of Doubt

Most actuaries have seen it happen: A perfect designed investment strategy......., turning into a real nightmare. How could it come that far? What happened?

Life of an actuary...
Let's dive into a real life simplified actuarial case....:

As the actuary of your company, you've developed a perfect ALM study. Together with the head of the investment department, you've been able to convince your Board of the new developed 'Investment Strategy'. A consequent mix of 50% Bonds and 50% stocks, resulting in an average expected 6% return on the long term, turned out to be the best (optimal) investment mix given the risk appetite of your Board and the regulatory demands. All things are set for execution.

Now let's see how your strategic plan would develop (scenario I) and how it would probably be executed by the Board (scenario II) over the next ten years.

Although your investment strategy plan was designed on a rational basis and the execution of this plan was also intended to be a rational process, in practice they are not.....

Let's follow the discussion in the Board from year to year...

Year 1
The company's average portfolio return performs according plan (6%). Stocks: 8%, Bonds 4%, on average 6%. The Board concludes they have the right strategy. You, as an actuary, agree.

Year 2
Compliments from the Board. Stocks perform even higher (10%), leading to a 7% average return.
You sleep well that night.

Year 3
Another fabulous Stock performance year. A stock return of 20%, leading to an average return of 12%! Some Board members start to doubt and question your ALM-model. They are arguing that if stock prices are that high three years in a row, they would like to profit more from this development. They suggest to adjust the asset mix in favor of stocks. Your ALM model should me more flexible.

You are defending your Asset Liability Model to the grave, but after extensive discussions all board members agree that a slight 'temporary' adjustment to 70% stocks and 30% bonds would be 'worth the risk' to profit from this high stock return. With great reluctance, you agree....

Year 4
Although the performance of stocks is not as high as the year before, it's still relatively high (15%) and leads to an average return of 11.7%, which is 2.2% (!) higher than the 9.5% return that would have been achieved with a 50/50% mix.  The Board concludes that it took the right decision last year, to adjust the asset mix to 70/30%.

You - as the responsible actuary - warn again, but the facts are against you. Disappointed and misunderstood you return to your office as the President of the Board tries to cheer you up by thanking you for your 'constructive response' in the board meeting. You abstain from joining the festive Board Party that evening.

Year 5
Stocks are dramatically down to 0%, leading to an average mixed return of 1.2% this year.
The board meeting this year is chaotic. Some members support you as the 'responsible actuary' to readjust the asset mix to the original mix of 50/50%. Others argue that this stock dip is only temporary and that this year's average return is only 0.8% lower than would have been achieved with a 50/50% mix. On top of, most members strain that this year's 0.8% negative return is still lower than the 2.2% positive difference of last year. After two stressful board meetings, the Board decides to stick to their 70/30% investment mix.
The board president's eye fails to meet you, as you leave the board room that night.

Year 6
What was most feared, has become true.. A negative stock return of 10%, leading to an average return of -5.8% ....   When you walk into the board room that night, all eyes are on you as the 'responsible actuary'. You hold your breath, just like all other board members. After a short moment of silence the board president states that he proposes to bring back the asset mix to the original 50/50% mix. Without further discussion this proposal is accepted. There's no board party this year.

Year 7
Negative stock returns have increased to 15%, leading to an average return of -5.5% this year.
Some Board members fear that if stock prices will be down for another few years, the average 'needed' return of 6% will not be met. They doubt the current strategy.

Also the Regulator and some Rating Agencies insist on higher confidence and solvency levels with corresponding measures to be taken. Both are not positive and doubt the outlook on stock returns on the long term...

After a long meeting that night, the Board chooses for reasons of 'savety' (!) to adjust the asset mix to 30/70% in favor of the still 4% stable performing Bonds (Better something than nothing (!) ).

Again... you explain that night, that changing the asset mix following actual market performance, is the worst thing a company can do....  But again, you lose the debate.

The power of emotion is greater than the power of rationality. Now not only the Board seems against you, but the Regulator as well. Who wants to fight that! After all, 'ethical' rule number one is 'complying with the Regulator'. That evening you brainwash yourself and reprogram your attitude to 'actuarial follower' instead of 'actuarial leader'.

After two Johnnie Walkers you see the future bright again and seem ready for the new year.

Year 8
To everybody's surprise stocks performed extremely well at 25% this year. As a result the average return reaches a satisfying performance of 10.3%. With 'mixed feelings' board members take notice of the results. What nobody dears to say and everybody seems to think is: 'Had we stuck to our 70/30% asset mix, the performance would have been: 18.7% (!)......'

The Board President cautiously concludes that the Board took the right decision last year, leading to a proud 10.3% return this year. Compliments to everyone, including the actuary! Supported by your 'converted' mind, the 30/70% asset mix is continued. That evening you accept the invitation to the board party. Lots of Johnnie Walkers help you that night to cope with the decisions taken.

Year 9
Stocks perform at 20%, leading to an 8.8% average mixed return. No Board member dears to raise questions about the possibility of readjusting the asset mix to a 'more risky' (what's that?) one. After all, the overall performance is still higher than the needed 6%. So who may complain or doubt the new 'On the Fly Strategy'? Who cares or who dears? You go to bed early that night.

Year 10
Stocks returns have come down to a more 'realistic' level of 7%. As a consequence the average return is down to 4.9%, way down beneath the critical level of 6%. Board members have to strike a balance. Some of them doubt again. Continuing the 30/70% asset mix will not bring them the needed long term 6% objective return. Adjusting to a 50/50% mix probably will, but is more risky. What to do?

All eyes are on you as the 'final advising actuary'. With restrained pride you state: "Dear colleagues, what about our good friend, the original '50/50% asset mix'. Can we confirm on that?" Without anyone answering, the President takes a look around.... His gavel hits the table and the decision seems to have been taken.

That night you decide to change Johnnie Walker for a well deserved glass of 'actuarial wine': a simple  'Mouton Rothschild 1945' (at the expense of the Board of course). You enjoy the moment and the pleasure of being an actuary. Even after the Rothschild you realize that the decade price of doubt was high: 0.9% p.a. ...

When you go to bed for a good night sleep, you smile...., as some little voice in your head tells you that next year this madness decade-cycle will probably start again...

Sep 26, 2010

Equity Returns and Mean Reversion

One of the most triggering questions - given the current crisis - is:

Will equity returns recover?

Mean Reversion
In 2009 the S&P-500 index - as most stock market indices - reached the lowest level since the turn of the century. In less than two years time world stock indices had dropped around fifty percent of their value. Since then, stock indices increased about forty percent.

It's tempting to think that this recovery could have been predicted in advance. This suspected predictable effect of recovering stock prices returning to their long-term average, is called: 'Mean Reversion'.

More explicitly: 'Mean Reversion of stock prices' is the effect that abnormal stock prices gradually return to their long-term historical average or equilibrium price.

Reversion Speed
In a 2010 working paper, the Dutch regulator DNB provides an answer to this question of recoverability.  In this paper, authors Spierdijk, Bikker and Van den Hoek analyze 'mean reversion in international stock markets' in seventeen developed countries during the period 1900-2008.

One of the outcomes of this study is not only an interesting country spread between 'mean returns' and volatility (risk, standard deviation), but also a mind boggling country difference in 'reversion speed' (rs).  Reversion speed can be defined as the 'yearly interest speed to return to the long-term average. RS differs strongly per country, as the next slide shows:

Ranked by average return (all %):

Reversion conclusions
The DNB study concludes that in the period 1900-2008:
  • Average Return
    The average World Stock Return is estimated at 8.0% with a volatility of 16.7% (S.D.).

  • Half-Life Reversion Period (HLRP)
    It takes 'World Stock Prices' on average about 14 years  to absorb half (!) of a shock (HLRP), with a confidence interval of [10 years -21 years]

  • High Half-Life Uncertainty
    The uncertainty of the half-lives estimates is very high. This is due to the fact that the lower bounds for the corresponding median unbiased estimators are close to zero. The upper bounds of the confidence intervals for the half-lives are therefore very high.

  • Mean Reversion, a Trading Strategy?
    The relative low value of the mean reversion rate, as well as its huge uncertainty, severely limits the possibilities to exploit mean reversion in a trading strategy

Concluding Remarks
We should keep in mind that - no matter how well investigated - historical data - as always - only have a limited predictive power.

Looking with a 'actuarial eye' at the volatile annual development of the S&P-500 returns and their moving averages, it's hard to deny some kind of visual proof of an increasing volatile yearly return and a structural declining 10- or 15-years average return.....

This 'visual proof', combined with the results of the 'DNB Mean Reversion paper',  is perhaps the best indicator that the future average long term World Stock return of 8% is probably way too optimistic and still includes too much the optimist mood and hope of the last decades of the 20th century...

S&P-500, averages annual returns and inflation 1950-2010

Distribution Rate
Inflation Real
Price Change
Total Return
1950's 13.2% 5.4% 19.3% 2.2% 10.7% 16.7%
1960's 4.4% 3.3% 7.8% 2.5% 1.8% 5.2%
1970's 1.6% 4.3% 5.8% 7.4% -5.4% -1.4%
1980's 12.6% 4.6% 17.3% 5.1% 7.1% 11.6%
1990's 15.3% 2.7% 18.1% 2.9% 12.0% 14.7%
2000's -2.7% 1.8% -1.0% 2.5% -5.1% -3.4%
1950-2009 7.2% 3.6% 11.0% 3.8% 3.3% 7.0%

Key question is : What would be a save 'long-term total return of stocks' as a base for an investment strategy, without the 'Hope Bubbles' of the last two decades of the last century?

Probably a long term stock return of about 6% would turn out to be a save basis for a kind of investment reversion strategy......
However, now we know where we are going, it's absolutely necessary to know where we are now? Unfortunately.... we don't know.... ;-) 

Sources, related links:
- DNB 2010: Mean Reversion in International Stock Markets
- (Dutch) DNB-2010: Herstel aandelenmarkten is niet vanzelfsprekend
- Wikipedia: S&P-500 Annual Returns 
Simple Stock Investing: S&P-500 historical data