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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
- The dog and the frisbee
- 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

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%
Start	Net Yearly Return Rate
Age	0%	1%	2%	3%	4%	5%	6%	7%	8%
25	2692	3669	5019	6898	9521	13192	18336	25553	35681
30	2345	3113	4134	5503	7342	9812	13133	17601	23612
35	1999	2584	3335	4304	5555	7171	9257	11949	15421
40	1654	2084	2614	3273	4092	5109	6370	7933	9867
45	1311	1610	1964	2388	2896	3502	4225	5085	6107
50	972	1163	1380	1632	1921	2254	2635	3072	3570
55	638	744	860	989	1132	1291	1465	1657	1868
60	312	355	400	448	499	554	612	674	738

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%
Start	Net Yearly Return Rate
Age	0%	1%	2%	3%	4%	5%	6%	7%	8%
25	3687	4914	6566	8814	11889	16112	21933	29978	41124
30	2947	3859	5051	6624	8707	11468	15138	20021	26526
35	2309	2968	3803	4872	6241	7994	10240	13119	16809
40	1760	2218	2781	3479	4344	5413	6735	8368	10382
45	1288	1590	1949	2381	2897	3515	4251	5127	6168
50	882	1066	1277	1523	1807	2134	2512	2944	3440
55	536	633	741	862	998	1149	1316	1502	1706
60	243	281	321	364	411	461	515	573	634

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'
Start	Net Yearly Return Rate
Age	0%	1%	2%	3%	4%	5%	6%	7%	8%
25	137%	134%	131%	128%	125%	122%	120%	117%	115%
30	126%	124%	122%	120%	119%	117%	115%	114%	112%
35	116%	115%	114%	113%	112%	111%	111%	110%	109%
40	106%	106%	106%	106%	106%	106%	106%	105%	105%
45	98%	99%	99%	100%	100%	100%	101%	101%	101%
50	91%	92%	93%	93%	94%	95%	95%	96%	96%
55	84%	85%	86%	87%	88%	89%	90%	91%	91%
60	78%	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%
Start	Net Yearly Return Rate
Age	0%	1%	2%	3%	4%	5%	6%	7%	8%
25	1130	1507	2013	2702	3645	4939	6724	9190	12607
30	1047	1371	1795	2354	3094	4076	5380	7115	9427
35	951	1223	1567	2007	2571	3293	4219	5405	6925
40	841	1059	1328	1662	2075	2586	3217	3997	4959
45	713	880	1079	1318	1604	1946	2354	2839	3415
50	566	684	820	977	1160	1370	1612	1890	2208
55	399	471	552	642	742	855	979	1117	1269
60	210	242	277	314	355	398	445	494	547

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 25 69% 30 64% 35 59% 40 52% 45 45% 50 36% 55 26% 60 14%

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:

MORE ABOUT EXCEL PENSION CALCULATOR

Enjoy your pension, beware of inflation....

Links & Sources:

- Download Excel Pension Calculator (virus free)

- The scourge of multiple hidden pension pots (2012)

- Survey:Individual Differences in Pension Knowledge (2011)

- Kurt Gödel's incompleteness theorems

- EU Inflation Monster

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:

Everything is simpler than you think 

and at the same time more complex than you imagine

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)