Actuworry: Pension Math

According to Financial News the Pension Crisis is growing in Europe.
Except for Germany, most European countries are in trouble due to the credit crisis and subprime mortgages. On average, funding ratio's are below 100%.

As a lot of pension funds are mature, raising premium levels will not offer any help on the short term. Neither a 'selling stocks strategy' does. As a consequence all pension payments are at risk.

'Primarily' we should have learned from Einstein's Pensions theory:

Nevertheless, as actuaries have to be realistic, Einsteins' Pension Formule is a day after the fair. Let's look at at an other way out of this crisis.

When nothing helps, the only way out seems lowering pension rights and payments. However, this is premature and will most likely cause unnecessary social commotion.

Consider, what would you prefer:
A. $ 10.000 pension with a 100% funding ratio?
B. $ 8.000 pension with a 125% funding ratio?

Actuworry won't help. As actuaries we have to stay cool. The only realistic way out is simply to wait for better times.

Langton's Actuarial Ant

As an actuary, you believe in the consistency of your risk models.

You might think that with 10.000 observations you've got enough stuff to present a consistent statistical model with realistic expectations, variances, etc.

You are aware that the output of your model depends on the quality of the data and the assumptions. In your advice you try to communicate all that to the board in order to support sound and responsible decisions.

In other words, you've got a consistent model and, as an actuary with a professional and consistent life-philosophy, you have everything under control. No great changes will take place?

Well, 

you're probably wrong !

Just like our models, we actuaries, are not consistent

Even if we (or the risk reality we try to model) act in a stable consistent way, we (or risk reality) keep interfering with our environment and our environment responses to us.

At first this response seems meaningless and of no value. You think you're consequent and your work and achievements in life seem relatively stable, perhaps a little bit chaotic and of no great significance. But in repeating your proven receipts, way of doing or procedures endlessly, eventually

Something will change
This change often will not appear as an evolution in your life, but as a kind of revolution, out of the blue and most often unexpected.
Suddenly, just like in the credit crisis, there's an emerging situation. The way you always did it, doesn't turn out right anymore. Your model crashed, you crashed and there was nothing you could do about it. You couldn't have foreseen it, you could not have prevented it the classical way.

That's why we always have to add some non-classical extra 'common sense' safety margin thinking in our models.

Progress?
The other side of this is also true. Fore example, when you study, you'll probably, once in a while, think: what progress am I making?

But don't worry, if you keep on your track, there'll be a day your future suddenly comes to you (out of the blue: as a kind of emergent property) instead of "the you trying to make your future" in this Game of Life.

A good demonstration of this principle is

Langton's ant Langton's ant is an virtual ant that starts out on a grid containing black and white cells, and then follows the following set of rules. If the ant is on a black square, it turns right 90° and moves forward one unit. If the ant is on a white square, it turns left 90° and moves forward one unit. When the ant leaves a square, it inverts the color. The result is a quite complicated and apparently chaotic, but relatively stable, motion. But after about 10.000 moves the ant starts to build a broad diagonal "highway".

So keep in mind "Langton's Actuarial Ant" next time you design a new risk model.

Anyhow, stay on your track as an actuary and remember, whether it's you in life or your models, someday there'll be

a collapse of chaos

Coastline Fair Value

Close your eyes and take a guess at the Australian coast length? Answer : 'Exactly' 25,760 km.

1. Right, according to Wikipedia
2. Wrong! Because the exact coast length depends on the length of your ruler!

If you would measure the Australian coastline with a 1-mm ruler, you would get a length of more than 100 .000 km!

This leads to the question:

Does a 'coastline fair value' exist?

After all, as the ruler gets diminishingly small, the coastline's length gets infinitely large.
This phenomenon is also known as the Richardson Effect (or the coastline paradox).

Coastline Formula?
In 1967 a document called "How long is the coast of Britain?" was published by the great mathematician Mandelbrot

In 1967 he revived the original formula, earlier developed by Richardson :

L(G) = F . G^(1-D)

with

L=length of the coastline as a function of G

G=Ruler length

F=positive constant factor,
D=constant (D>=1). D is a ‘‘characteristic’’ of a frontier, varying from D=1 for a straight frontier to D=1.25 for a very irregular coastline like Britain. It turns out that D = 1.13 for the Australian coast and D=1.02 for the very smooth South Africa coastline.

Fractals
The constant D also stands for 'Dimension' and in 1975 Mandelbrot develops this Dimension- idea to what is called the Fractal Dimension.

Fractals turn out to be the perfect (math) language for describing all kind of natural phenomenas like leaves, trees , etc.

Fractals are even used to describe the stock market, the credit crisis or the coastline of the law.


Coastline Formula & Valuation
What can we learn from this fractal coastline measurement with regard to valuations?

1. Stop changing the rules
   If accounting standards like IFRS , GAAP and IAS or legislation are constantly changing (e.g. amendments) and getting more and more specific, valuing a company becomes like measuring the coastline with different rulers.
   
   In this case management, supervisors, stake- and shareholders lack a sustainable view on their business. You can't justify the results and value of your company if you have to measure yourself with a dynamic ruler!
   
   
2. Stop digging
   More and more deep going risk research will eventually lead to an substantial increase or even 'infinite' Value at Risk.
   
   Therefore it's important to define portfolio-, market- and product-risk- limits and structures first, right from the companies (risk) strategy.
   
   These instruments reduce the needed depth of risk research and therefore increase the control- and efficiency-level of the company.

Try to think scale free and have fun by applying fractals in actuarial science!