Showing posts with label simplicity. Show all posts
Showing posts with label simplicity. Show all posts

Jan 20, 2013

SMPLFCTN

As an actuary, you probably grew up with that famous quote of Einstein:

Everything Should Be Made as Simple as Possible,
But Not Simpler.

However, as 'Quote Investigator' shows, there is no direct evidence that Einstein crafted this aphorism...

Hmmmm.... Never mind.... as this quote is clearly redundant and therefore can be simplified....

So, it's enough to stick to the subjective concept of 'keep it simple'.....

'Simple', simply means 'easy to understand'.  

If we would try to present or explain something 'too simple', we are in fact making it harder to understand and therefore 'more complicated'.

Example
If we try to explain that we can estimate the area of a circle (approx. 3.14159...; radius=1) in practice by a n-sided polygon, a three year old child ;-) will buy your simplification in case of  a 12-sided polygon.




Oversimplified, or Worse: Desimplified
In case of a square (4-sided polygon), he'll probably raise his eyebrow, as you oversimplified the topic. And in case of a triangle you'll probably have lost him completely. You desimplified and thereby complicated your case to the opposite of what you untended : a clear understanding.



Simplification Criterion
Keep in mind that, like in the case above, you must develop a criterion when you simplify things. In the above example, a criterion could (e,g) be that the area of the polygon shouldn't differ more than 10% of the original circle and must have a relative simple (round) answer. This criterion would lead to a 12-sided polygon as an adequate simplification example.


And of course, we have to test this ex-ante 12-sided criterion in practice by means of a questionnaire.


Simplification is Complicated
However, 'simplification' as process, is not simple at all. In practice simplification can be used to reduce things that are:
  1. complicated (not simple, but knowable) or 
  2. complex (not simple and never fully knowable) 
In an article called 'Simplicity: A New Model',  Jurgen Appelo tries to simplify the complex world of simplicity linked concepts. He states that simplification means 'make understandable', which means moving it vertically, from the top of the model to the bottom in the following Appelo-illustration.

Anyhow, there's much to learn about simplicity related topics.....   

Let's finish with an excellent example of a need for simplification : 

Simplifying 'Complexity of financial regulation'
In an excellent presentation, Executive Director Financial Stability of the Bank of England,  Andrew Haldane, pleas and argues to simplify financial regulation.

It turns out that the growing number of regulation rules and principles (e.g. Basel III) has an adverse effect on taming the crisis.

Also 
the traditional Merton-Markowitz approach that assumes a known probability distribution for future market risk and enables portfolio risk to be calculated and thereby priced and hedged, offers no help to solve the current crisis.
Haldane concludes that "More simple regulation  based on 'Optimal choice under uncertainty' is necessarily. Haldane concludes:

"Modern finance is complex, perhaps too complex.  Regulation of modern finance is complex, almost certainly too complex.  That configuration spells trouble.

As you do not fight fire with fire, you do not fight complexity with complexity.  Because complexity generates uncertainty, not risk, it requires a regulatory response grounded in simplicity, not complexity. 


Delivering that would require an about-turn from the regulatory community from the path followed for the better part of the past 50 years.  If a once-in-a-lifetime crisis is not able to deliver that change, it is not clear what will.  


To ask today’s regulators to save us from tomorrow’s crisis using yesterday’s toolbox is to ask a border collie to catch a frisbee by first applying Newton’s Law of Gravity.
"


Haldane's (2012) presentation called 'Ensuring Long-Term Financial Stability', or more popular 'The dog and the frisbee', is a breakthrough in managing, modeling and controlling Risk and financial future results. It's a MUST read for actuaries and board members in the financial industry.

Finally
From now in, actuaries can simply start 'helping' as a border collie!

Sources/Links
- BOE Presentatie Andrew Haldan
- Risk models must be torn up
- Mathematica: Play with Polygons
- Einstein's Simple Quote Investigated
- Complex versus Complicated
Complicated vs complex vs chaotic
- Simplicity a new model

Nov 17, 2012

Pension for Contribution

People are lost if it comes down to their pension. A recent (2012) Friends Life survey found that 68% of Britons do not know the collective value of their pension funds.....

This result is in line with a Dutch 2011 survey, that concludes that 66% has no knowledge of their pension.

Pension illiteracy is clearly a worldwide phenomenon. Pensions are a 'low interest' product. Unfortunately - nowadays - in the double sense of the latter words.

As an actuary, people often ask me at a birthday party : I'm paying a 1000 bucks contribution each year for my pension, but does it pay out in the end? Can you tell me?

Unfortunately most actuaries, including myself, answer this question by telling that this is a difficult question to answer straightforward and that the pension outcome depends on topics like age, mortality, return, inflation, gender, indexation, investment scheme, asset mix, etc., etc.....

Simplifying
To make a breakthrough in this pension communication paradox, let's try to create more pension insight with a simple approach. But remember - as with everything in life - the word 'simple' implies that we can not be complete as well as consistent at the same time. After all, Kurt Gödel's incompleteness theorems clearly show that nothing in life can be both complete and consistent at the same time.

Thanks to God and Gödel, we can stay alive on this planet by simplifying everything in life to a level that our brains can comprise. We'll keep it that way in this blog as well.

How much pension Benefits for how much contribution?
First thing to do, is to give the average low pension interested person on this planet an overall hunch on what a yearly investment of a 1000 bucks(first simplification: S1)until the pension age of 65 year (S2) delivers in terms of a yearly pension as of age 65 in case of an average pension fund.

If we state 'bucks' here, we mean your local general currency. We denote 'bucks' here simply as $, or leave it out. So $ stands for €, ¥ , £ or even $ itself.

Now let's calculate for different pension contribution start ages (S3)what a yearly contribution of $ 1000 (payable in months at the beginning of each month; S4), pays back in terms of a yearly pension (payable in months at the end of each month; S5) on basis of a set of different constant return rates (S6). The calculation is on a net basis (so without costs; S7), a Dutch (2008) mortality table (S8) and without any inflation (S9), any pension indexation (S10), any contribution indexation (S11), or any tax influence (S12).

Here's the simple table we're looking for:

TABLE 1
Yearly Pension at age 65 on basis of 1000 yearly contribution
Pension Indexation=0%, Contribution Indexation=0%, Inflation: 0%
StartNet Yearly Return Rate
Age0%1%2%3%4%5%6%7%8%
252692366950196898952113192183362555335681
30234531134134550373429812131331760123612
3519992584333543045555717192571194915421
40165420842614327340925109637079339867
45131116101964238828963502422550856107
5097211631380163219212254263530723570
5563874486098911321291146516571868
60312355400448499554612674738

In a graphical view on a logarithmic pension benefits scale, it looks something like this:

Example
To illustrate what is happening, a simple example:
When you join your pension fund at age 40 and start saving $ 1000 a year (the first of every month: $ 83.33) until your 65, you'll receive a yearly pension benefit of $ 4092 yearly ( $ 341 at the end of every month) from age 65 of, as long as you live.

From this table, we can already draw some very basic conclusions:
  • To build up a substantial pension, it pays out if you start early in life
  • The pension outcome is heavily dependent on the yearly return of your pension fund
  • Most pension funds operate on basis of a 'general employee and/or employer contribution' instead of individual employee contributions.
    This implies that younger employees pay more than they should have paid on an individual basis and older employees less. In other words, younger employees subsidize older employees. How much more, you can derive from the tables above and by comparing the individual contributions to the general contribution level of the pension fund.


Pension Indexation
As we all want to protect our pension against inflation, let's calculate the outcome of a 'real pension' instead of a 'nominal pension'. As long term yearly inflation rates vary between 2% and 3%, we make the same calculation as above, but now the yearly pension outcome (as from age 65) will be indexed with 3% (fixed) at the end of every year and the yearly contribution paid, will also be yearly indexed with 3%.
Here's the outcome:

TABLE 2
Yearly Pension at age 65 on basis of 1000 yearly contribution
Pension Indexation=3%, Contribution Indexation=3%, Inflation: 0%
StartNet Yearly Return Rate
Age0%1%2%3%4%5%6%7%8%
2536874914656688141188916112219332997841124
302947385950516624870711468151382002126526
35230929683803487262417994102401311916809
401760221827813479434454136735836810382
45128815901949238128973515425151276168
5088210661277152318072134251229443440
555366337418629981149131615021706
60243281321364411461515573634

To get grip at the comparison between a real and a nominal pension, we express the real pension (3% Indexed Pensions and Contribution) as a percentage of the nominal pension:

TABLE 3
Yearly Pension at age 65 on basis of 1000 yearly contribution
'3% P&C-Indexed Pensions' as percentage '0% P&C-Indexed Pensions'
StartNet Yearly Return Rate
Age0%1%2%3%4%5%6%7%8%
25137%134%131%128%125%122%120%117%115%
30126%124%122%120%119%117%115%114%112%
35116%115%114%113%112%111%111%110%109%
40106%106%106%106%106%106%106%105%105%
4598%99%99%100%100%100%101%101%101%
5091%92%93%93%94%95%95%96%96%
5584%85%86%87%88%89%90%91%91%
6078%79%80%81%82%83%84%85%86%

From this last table we can conclude that if you start saving for your pension below the age of 40 your indexed savings weight up to the indexed pension. Above the age of 45 it is the other way around.

The above figures are the kind of figures (magnitude) you'll find on your benefits statements. You can compare in practice whether your benefit statement is in line with the above tables....

The Inflation Monster
In the last given example, pension is 3% inflation protected as from the moment of retirement.

However, if pension is not also yearly fully indexed (in this case: 3%) during the contribution period, there still is a major potential inflation erosion risk left.

In this case it's interesting to examine what the value of a 3% indexed pension in combination with a 3% indexed contribution is worth in terms of actual money, as inflation would continue at a constant 3% level each year. Here's the answer:

TABLE 4
Yearly Pension at age 65 on basis of 1000 yearly contribution
Pension Indexation=3%, Contribution Indexation=3%, Inflation: 3%
StartNet Yearly Return Rate
Age0%1%2%3%4%5%6%7%8%
251130150720132702364549396724919012607
30104713711795235430944076538071159427
3595112231567200725713293421954056925
4084110591328166220752586321739974959
457138801079131816041946235428393415
5056668482097711601370161218902208
5539947155264274285597911171269
60210242277314355398445494547

What we notice is a substantial inflation erosion effect as the pension fund participants get younger.
Let's zoom in on an example to see what we can achieve with these tables.

Example
  • From table 2 we can conclude that - at a 4% return rate - a 40 year old starting pension fund member, with a $ 1000 dollar yearly 3% indexed contribution will reach a 3% yearly indexed pension of $ 4344 yearly at age 65.
  • From table 4 we can subsequently conclude that, based on an inflation rate of 3%, this $ 4344 pension has a 'real' value of $ 2075, if it's expressed in the value money had when the participant was 40 years old (so, at the start).
  • From table 4 we can also conclude that in order to 'compensate' inflation erosion for this pension member, the pension fund has to achieve a return of around 7.4%.
    This follows from simple linear interpolation:
    7,4% = 7% + 1% * (4344-3997)/(4959-3997)

I'll leave other examples to your own imagination.

The effect of a constant inflation on a pension is devastating, as the next table shows

TABLE 5
Inflation Erosion
  • Pension indexation=3%
    as of age 65
  • Contribution indexation=3%
  • Inflation=3%
Start
Age
Inflation
Erosion
2569%
3064%
3559%
4052%
4545%
5036%
5526%
6014%
From table 5 it becomes clear that Inflation erosion is indeed substantial.
If you have a fully indexed pension from age 65 (who has?) of and you're N years away from your retirement, an inflation of i% will erode your pension with E%. In formula:
         
Example
Set inflation to 3%. If you're 40 years old and about to retire at 65, you've got 25 years (N=25=65-40) ahead of you.

If your pension of let's say $ 10,000 a year is not indexed during this period, you can buy with this $ 10,000 no more than you could buy today with $ 4,800.

Your pension is eroded due to inflation with 52% = 1- 1.03^-25. So only 48% is left.....

Finally
I trust these tables and examples contribute a little to your pension insight. Just dive into your pension, it's financially relevant and certainly will pay out!
Remember that all results and examples in this blog are approximations and simplifications on a net base (no costs or taxes are included). In practice pension funds or insurers have tot charge costs for administration, asset management, solvency, guarantees, mortality risk, etc. . This implies that in practice the results could differ strongly with the results as shown in this blog. The examples in this blog are therefore for learning and demonstration purposes only.

The above calculations were made in a few minutes with help of the Excel Pension Calculator that was developed in 2011 and updated in 2012.
With help of this pension planner you can calculate all kind of variations and set different variables, including different mortality tables (or even define your own mortality table).

You can download the pension calculator for free and make your own pension calculations.
More information about pension calculating with this simple pension calculator at:


Enjoy your pension, beware of inflation....

Links & Sources:

Dec 6, 2010

Actuarial Simplicity

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

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


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)