Showing posts sorted by relevance for query calculator. Sort by date Show all posts
Showing posts sorted by relevance for query calculator. Sort by date Show all posts

Mar 30, 2012

Excel Pension Calculator

Why isn't there just a simple pension Excel calculator on the internet, so I can do my own pension planning?

Well..., from now on there is!

Simply download the Excel Pension Calculator (allow macro's !!) and get an idea of how much you'll have to invest to end up with the pension benefit level of your dreams.... or less... ;-)

Or..., just fill in how much you can afford to invest monthly and see for yourself what pension benefit level is within reach, based on expected return rates, investment methods and inflation.

Just to give a small visual impression of the calculator...






Press on 'Calc' buttons to calculate the variable to the left, while leaving all other variables constant.

Graphics
Also some modest graphics are available. A small example....
Take a look at the next graph that shows how your yearly pension is yearly  funded by:
  1. the yearly desavings (= dissavings) from your saving account
  2. the yearly addition from the pension fund (= estimated savings of pension fund members that will die in this year)
  3. the yearly return on your saving account



Notice the immense impact of the (yearly increasing) addition of your pension fund (= savings of the active members who are expected to die in a particular year and contribute to the savings of your account) compared to the other components (desavings and returns).

Options
The calculator offers several interesting options:
  • Set the calculator to 'Saving Account' instead of 'Pension Fund' to notice the difference in outcomes between these two systems.
  • Switch to the life table of your choice (p.e.  the country where you live)
  • Set and name your own personal Life Table or Investment Scheme
  • Simulate longevity effects by manipulating the Life Table Age Correction field

The Excel Pension Calculator has much more features. More than I can handle in this blog. Just download the calculator and play with it to really touch base and to learn what pension is all about....

- Download the Excel Pension Calculator


Enjoy!

Disclaimer: This pension Calculator is just for demonstration purposes. The accuracy of the calculations of this calculator is not guaranteed nor is its applicability to your individual circumstances. You should always obtain personal advice from qualified professionals. Also take notice of the disclaimer in the Excel Pension Calculator.

P.S. I : On request a Quick Start tip
1. Download Calculator and open Excel Spreadsheet
2. Don't forget to"Enable Macros" !! 
3. Enable iterative calculation; Set Max. Iterations=1000, Max. Change=0.4
3. Change 'Start Age  Contribution' to your actual age
4. Notice that the amount 'Saving Surplus at age 120:' changes
5. Press the 'Calc' button next to 'Contribution' to calculate your Contribution
6. Or, Press the 'Calc' button next to 'Pension'  to calculate your yearly pension
7. Set any other Field as you like and press any of the 'Calc' Buttons   

P.S. II : New update, version 2012.2 on April 4,  including a single premium option.
P.S. III: New update, version 2012.3 on April 20, drop down menus (under Excel-2010) now also operate under Excel-2007 versions...

May 7, 2010

Online Murphy Risk Calculator

Risk is like quantum mechanics:

If you think you understand Risk, you don't understand Risk
Maggid after : Feynman


If you are not completely confused by Risk, you do not understand it
Maggid after : John Wheeler

Sure, risk is hard to tackle. The more you learn about risk, the more you become aware of it's sneaky characteristics (clustering, tails, etc).

This is why becoming a qualified actuary takes an incredible amount of time, hard study and many years of experience.  As masters in Risk, actuaries understand the limits in modeling and calculating Risk.

Murphy
Probably one of the more intriguing risk quotes is :


"Anything that can go wrong, will go wrong"

by the famous Edwin Murphy.

A quote that keeps an actuary mind busy....  After all, as actuaries it is our duty to quantify and explain uncertainty (as much as is possible) in board rooms and on the accounting table. Not only when decisions have to be taken, but also after things turned out wrong or different from what we thought. This is - to put it mildly - no 'easy task' and it's not getting easier in the near future.....


Just like Murphy, actuaries experienced last decades that (statistic) bad luck often collaborates with bad timing. What drives God (i.e. quantum mechanics or 'Murphy probability') to confront us - (poor) actuaries - with 'fair value volatility', 'longevity explosions', 'subprime defeats', 'imploding real estate market's and 'extraordinary solvency demands by supervisors', all at the same time time?


(Un)Luckily, help is on the way....  In 2004 British Gas commissioned some scientists to create a formula to predict Murphy's Law, also known as Sod's Law.

Murphy's Formula
In a 2005 study, based on a survey of 1,023 adults, Murphy’s Law was shown 'statistically significant'. The final report also supplied a formula for predicting occurrences of Murphy’s Law. Here it is....


Let U, C, I, S, and F be integers between 1 and 9, reflecting respectively comparative levels of Urgency, Complexity, Importance, Skills, and Frequency in a given set of circumstances. Let A, which stands for Aggravation, equal 0.7 (Please, don’t ask why). The likelihood (L) of Murphy’s Law obtaining under those circumstances, on a scale of 0 to 8.6, turns out to be:

L = [((U + C + I) x (10 - S)) / 20] x A x 1 / (1 - sin (F / 10))

Murphy's Formula strikes itself
Unfortunately, Murphy's law suffered from self reference, as one of the  authors, the mathematician Phil Obayda, commented on a 2004 blog that this formula is wrong.

The correct formula according to Phil is:

 P= (((U+C+I) * (1-S))/2) * A * (1/(1-Sin F))

with P = probability of Sod's Law Occuring and U, C, I, S and F values greater than 0 and less than 1, keeping the mysterious A = 0.7.

Murphy's formula simplified
Simplifying this last formula leads to Maggid's formula for the probability (%) of Murphy hitting you, whenever you perform a task:


Although application of this formula is not (yet) an obligated part of the actuary's Code of Professional Conduct, please check this equation anytime you're about to defend an actuarial advice on a Board's table.

How to use Murphy's formula: an Actuarial Example
Let's do a simple exercise to demonstrate the power of Murphy's formula:

You've developed a risk model of the Stock market. In a meeting the Chair of the board asks you how certain you are of your model being right. You know the difference between risk and uncertainty, so you say "one moment please" and pick up your pocket calculator while reflecting: This is a ´U=3, I=9,C=10,F=3´ situation, and I'm a S=9 actuary. That calculates as P=10.4% of Murphy hitting me. Within 20 seconds you (over)confidently answer: I`m about 90% sure of my model!

The Chair of the Board looks desperate... His eyes reflect: ´Is 90% good or bad?` You didn't realize your model was that important to the board.  But.. if that's so, 'Importance' should not be rated at I=9 but at I=10, raising the failure probability to almost 11%. Now you start doubting yourself : What if you overestimated yourself? What if you're only a AA-Actuary (level S=7) instead of a AAA (level S=9)? This would increase the probability of failing to 31.3%. Suddenly you realize you're only one step away from a major personal actuarial meltdown.
You get yourself together, regain your self confidence, realize you're one of the best actuaries in the world (S=10) and full of confidence you reply the questioning eyes of the Chair with: "Sir, I'm almost 100% certain my model is right.

The Board is relieved and content. You're an actuary they can trust. Now they can decide without hesitation.

So next time you want to know the failure probability of a task, use the next Online Murphy Calculater.









Good Luck with Murphy's calculator!

Used sources/Links:
- Sod’s Law: A Proof
- Newyorker: Murphy At the Bat
- The Engineering of Murphy's Law?
- Legend, Inc. Murphy's Laws
- The Stock Market: Risk vs. Uncertainty
- Murphy's Online Calculator

Sep 2, 2013

Pension Egg Choice

Imagine you're a new pension fund member and your pension fund offers you the next simple proposal regarding your future pension income.

With closed eyes you are allowed to take out two 'pension eggs', either from nest I or nest II. Which nest do you choose?

Think about this proposal and remember: your complete financial old age depends solely on the nest of your choice.




I discussed the above dilemma  last week (august 2013) in a presentation with an across-section of Dutch pension representatives. This dilemma illustrates in a simple way the precarious choice Dutch pension funds and their members have to make in deciding between a traditional Nominal Pension with conditional CPI-indexation (nest I) and a fully CPI-indexed 'Real' Pension (nest II).

Key point is that to achieve a higher Real Pension, you have to put your Nominal Pension 'at risk'.
And who is consciously willing to put 'future income' substantial  at risk?

As 'pension income' is in fact 'deferred income', there's also a kind of implicit understanding that your future retirement income security should be 'in line' with your actual income security and not substantial lower.

Retirement Income Security   Actual Income Security ?

No wonder that all of the 23 attendees at my presentation chose Nest I (Nominal + Indexation) as favorite.

Remark
After the meeting one of the attendees stated that the '10'-valued egg in Nest II should have been valued at at least a value of 20 or higher to create an equal or higher average expectation, as higher risk would implicate also higher return.

I positively smiled for a moment... told him that his remark (and many others that followed) was formally right and suggested that he would test the 'Pension Egg Choice' in his pension board, including an extra voting with an 20-valued egg instead of a 10-valued egg. A day later he called me back and told me the extra voting didn't substantial change the voting outcome.......

Remember that more risk doesn't automatically imply more return. If volatility (risk) increases without a well-argued expected increase in 'average return', the 'compound average return' will (even) decrease with half of its variance.

Worldwide Pension Funds Alert
Not only Dutch pension funds face the Pension Egg Dilemma, but in fact all pension funds worldwide do. To fund their pension liabilities they have to make average returns of more than 5%, 6% or even 7% for more than 50 years on a row or more. And to achieve those kind of return levels with a (nominal) risk free rate and a treasury bill outlook, both varying between 2 to 3.5 percent, implies that they'll have to invest in risky asset classes.

As a consequence the ultimate pension outcome could be lower than on basis of a risk free approach that guarantees a nominal pension. In other words: your Nominal pension is at risk.

Example
To illustrate what is happening, let's look at a 30 year old Dutch pension fund member (Tom) with an retirement age of 65.

The pension fund (theoretically) offers Tom the next options. Tom values these options on basis of a 20 year period:
  1. Option 1
    Tom's contribution is invested in totally risk free assets at 3% (
    orange line), resulting in a sure (€,$,£,¥)  10000 yearly pension
     
  2. Option 2
    Tom's contribution is invested in 30% risk free and 70% risky assets (purple line), resulting in a 25.9% (100%-74.1%) change of an outcome below his yearly 10000 (nominal) pension, but also an almost 50% probability of a pension of around 23904 or more.

    Looking closer at the downside, there's also a 10% probability of ending up with a negative return, corresponding with a yearly pension of 4255 a year or less.

However, Tom suddenly realizes the limitations of a linear model approach. If the 'risk free asset part' of his investment  is really completely independent (can't be dragged down) from the risky part and also insensitive to market conditions, there's a downside risk limitation.  A 30% really 'completely market valued risk free' would in Tom's case  imply a total minimal guaranteed portfolio return of nearly 1% (30% of 3% = 0.9% ≈ 1%) , corresponding with a minimal yearly pension benefit level of around 5645.

In case of 70% risk free investment approach (green line), the downside return risk would be limited to a minimal 2.1% return corresponding with a minimal pension of around 7506, approximately 75% of Tom's nominal pension target.

This 70% risk free approach could be quite acceptable for Tom, as he realizes there'll be no extra return without taking extra risk...

Nevertheless..., pension fund life and its member's choices ain't easy. So Tom asks the pension fund's actuary what his pension outcome would be on a 50 year evaluation basis.... here it is


Now Tom's risk of ending up with a yearly pension outcome of 10000 or less has decreased to a 15.3% (100-84.7). Tom could decrease this downside risk further to 8.6% by choosing a less risky asset mix of 70% risk free and 30% risky assets. However, this drops his upside potential. On average (50%) his pension outlook of around 23904 will drop to a little less than 17850.

Now Tom fully starts to grasp the impact of long term return assumptions...  After all, is assuming a 6% or 7% 50-year return not way to optimistic?

Your own Pension Confidence Level Calculator
As shown in the examples above the key questions are i.a. :
  1. How much of your guaranteed* nominal pension P are you willing to risk to end up with a higher pension P+U
  2. How much uncertainty (100% - confidence) are you willing to accept that your pension is lower than a certain amount?
  3. What's the real (nonlinear) downside risk of my pension?

To find the answers to these kind of questions and to calculate your own pension perspective, you may download the

in Excel.

With the Pension Confidence Level Calculator you may calculate your pension confidence with all kind of asset mixes, co-variances, (pension) ages and several user definable life tables.

Remember the calculations are only illustrative and indicative approximations, to be used for instructional purposes. Ask your pension fund to make a more detailed and personal calculation.

Next
Now that you've experienced that most pension funds need an ambitious return that may put your nominal pension at risk, the question is what to do?

Main problem is that pension funds do not act in this alarming situation. As a kind of sitting duck they play a kind of 'waiting game' in the hope that bond yields and other markets recover.

Meanwhile you could at least do something to get the fuzzy pension picture clear. Simply follow this Cookbook :

Pension Fund Restructure Cookbook
  1. Your Retirement Income is not a one point estimate, so ask your pension fund's actuary:
    • to calculate what future average return rate is needed to (100%) fund the liabilities, given the actual market value of the assets of the pension fund
    • to calculate (estimate) your future pension at different constant future return rates
    • to estimate the probability level of achieving each future return rate or more (confidence level) for the rest of your life, in accordance with the applied actuarial models
  2. Next, ask your actuary to formulate his advised investment risk approach in line with the Pension Eggs presentation as presented in this blog, but now with more nests.
  3. Now let your board and pension members determine their risk appetite by voting which nest they choose
  4. Finally, let the actuary in cooperation with the investment advisory committee, propose an 'investment strategy' that is completely in line with the new defined risk appetite 
  5. Take a decision to (phase-wise) implement this new investment strategy.

Result
Perhaps the outcome of the above exercise will be a lower pension than you expected, but:
  • probably not as low as you would have got if you kept on gambling on uncertain high returns 
  • and certainly not lower than what you need and define as a decent minimum pension income 

Anyhow, enjoy the Pension Confidence Level Calculator....

Links/Downloads

May 4, 2014

Discussing Life-Cycle Pensions & Longevity

In this blog I'm going to discuss two persistent pension topics:

  1. One of the most common misunderstandings in pension fund land is that an individual (member) investment policy weighs up to a collective investment approach.
  2. Is there a rule of thumb that expresses 'longevity risk' in terms of the yearly return?  

1. Collective vs. Individual Investing Approach
In case of a 'healthy pension fund', new members will join as time continues. In a mature pension fund the balance of contributions, investment returns, paid pensions and costs will stabilize over time.

Therefore the duration of the obligations of a pension fund will more or less stabilize as well. The duration of an average pension fund varies often between 15 and 25 years. Long enough to define a long term investment strategy based on a mix of risky equities (e.g. 60%) and fixed income (e.g. 40%). Regardless of age or status, all members of a pension fund profit from this balanced investment approach.




In case of an individual (member) investment strategy, the risk profile of the individual investments has to be reduced as the retirement date comes near. In practice this implies that 'equities' are reduced in favor of 'fixed income' after a certain age. As the age of a pension member progresses, the duration of the individual liabilities also decreases, with an expected downfall in return as a consequence.

Let's compare three different types of investment strategies to get a clear picture of what is happening:

  1. Collective Pension Fund Strategy Approach: Constant Yearly Return
    40% Fixed Income à 4% return + 60% Equities à 6% = 5.2% return yearly
     
  2. Life Cycle I Approach ('100-Age' Method)
    Yearly Return (age X): X% Fixed Income à 4% + (100-X)% Equities à 6%
     
  3. Life Cycle II Approach (Decreasing equities between age 45 and age 65)
    Yearly Return (age X) = MIN(MAX((6%+(44-X)*0.1%);4%);6%)

All visually expressed in the next chart:


Pension Outcomes
Now lets compare the pension outcomes of these three different investment strategies with help of the Pension Excel Calculator on basis of the next assumptions:
- Retirement age: 65 year
- Start ages 20 and 40
- 3% and 0% indexed  contributions and benefits
- Life Table NL Men 2012 (NL=Netherlands)

Results Pension Calculations (yearly paid pension):




Conclusion  I
From the above table we can conclude that switching from a collective investment approach to an individual investment approach will decrease pension benefits with roughly 10%. Think twice before you do so!



2. Longevity Risk Impact
To get an idea of the longevity impact on the pension outcomes, yearly paid pensions are calculated for different forecasted Dutch life tables (Men).

Life Tables



Forecast Life Table 2062 is calculated on basis of a publication of the Royal Dutch Actuarial Association.

The Forecast Life Table 2112 is (non-official; non scientific) calculated on basis of the assumption that for every age the decrease in mortality rate over the period 2062-2112 is the same as over the period 2012-2062.

Pension Outcomes per Life Table
Here are the yearly pension outcomes on basis of the forecasted life tables:













From the above table, we may conclude that the order of magnitude effect of longevity over a fifty to seventy year period is that pensions will have to be cut  roughly by 25%-30%.


Another way of looking at this longevity risk, is to try to fund the future increase in life expectation from the annual returns.

The next table shows the required return to fund the longevity impact for different forecasted life tables:



Roughly speaking, the expected long-term longevity effects take about 0.7%-1.2% of the yearly return on the long run.


Finally
Instead of developing a high tech approach, this blog intended to give you some practical insights in the order of magnitude effects of life-cycle investments and longevity impact on pension plans in general.

Hope you liked it!




Links/Downloads:

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:

Nov 11, 2013

QIS: Longevity Risk Sharing

In a recent discussion about the future and fundamentals of the Dutch pension system I discussed the importance of solidarity.

As expected, the participants quickly came up with the various forms of solidarity, including solidarity between:
– higher and less educated people
– women and men
– old versus young people

Longevity Risk Sharing
Remarkably non of the participants had any idea about the financial impact of one of the most fundamental forms of risk sharing in case of a life annuity: Longevity Risk Sharing. Let's call it in general 'mortality solidarity'.

When asked, most participants strongly underestimated the impact of mortality (mortality share) as part of the yearly payment in the form of a life annuity. On the other hand, they overestimated the impact of 'return'.

Some of the participants had the idea that they would be 'better of' with a traditional individual investment plan in combination with a little more investment risk (and return) ...

Life Annuity Composition
So let's do a mini QIS (Quantitative Impact Study) of 'mortality solidarity' by examining the development of the composition of an annual lifetime annuity, regarding three basic elements: Mortality, Return and Desaving.

Here is the result for a Dutch man, age 65, with a lifetime annuity based on an average 5% yearly return:




Translated in table form:

Yearly Payment CompositionCumulative Composition
AgeMortality Return DesavingMortality Return Desaving
6516%51%33%16%51%33%
6617%50%34%16%50%34%
6718%48%34%17%50%34%
6819%46%34%17%49%34%
6921%45%35%18%48%34%
7022%43%35%19%47%34%
7124%41%35%20%46%34%
7226%39%35%20%45%34%
7328%38%35%21%45%34%
7430%36%34%22%44%34%
7532%34%34%23%43%34%
7634%33%33%24%42%34%
7736%31%33%25%41%34%
7838%30%32%26%40%34%
7941%28%31%27%40%34%
8043%27%30%28%39%34%
8145%25%29%29%38%33%
8248%24%29%30%37%33%
8350%22%28%31%36%33%
8452%21%27%32%36%32%
8555%20%26%33%35%32%
8657%18%25%34%34%32%
8760%17%23%35%33%31%
8862%16%22%36%33%31%
8965%15%20%37%32%31%
9067%14%19%39%31%30%
9169%13%17%40%31%30%
9272%13%16%41%30%29%
9373%12%15%42%29%29%
9475%11%14%43%29%28%
9577%11%12%44%28%28%
9678%10%12%45%28%27%
9779%9%11%46%27%27%
9880%9%11%47%26%26%
9982%8%10%48%26%26%
10083%8%10%49%25%25%
10184%7%9%50%25%25%
10285%7%9%51%25%24%
10385%7%8%52%24%24%
10486%6%8%53%24%24%
10587%6%7%54%23%23%


Observations
As is clear from the table above :
  • Already at the start the start of the annuity, at age 65, 16% of the yearly payment is due to mortality risk sharing and 'only'  51% is related to the 'return'.
  • As a pension member continues to live, the  'mortality share' of the annual payment increases. At the age of 83 already 50% of his annuity is due to mortality effects and the 'return share'  is already down to 22%.
  • As from age 77 of, the 'mortality effect' on the annual payment exceeds the 'return effect'.

Conclusion
From some simple calculations, we can conclude that longevity (mortality) solidarity is a fundamental part of a life annuity.
 

AfterMath
Make your calculations with other interest rates, ages or life tables with the Pension Calculator (Excel).

You may download the pension calculator HERE

Links/Sources

Sep 29, 2011

Pension Gamification

For years you deny it, then you doubt it, then you know for sure:



This blog is specially written for (1) those who are still in the denial phase and (2) 'actuarial life gamers' who just want to enjoy actuarial gaming....

Pension Game
Games are an excellent way to involve people (employees) in a complex and (two fold)  'low interest product' like pension.


Pension games stimulate clear communication and understanding of pensions (The Nest Phrasebook:Clear communication about pensions Version 1.1).

Games, like the above pension game, conquer the world more and more.

Gamification
It looks like everything that has to be sold or communicated, succeeds better with the help of a game. Gamification gets people more engaged, helps change behaviors and stimulates innovation. In other words:

Gamification rules our life

As an example of gamification, Gartner cited the U.K.’s Department for Work and Pensions, which created an innovation game called Idea Street to decentralize innovation and generate ideas from its 120,000 people across the organization. Idea Street is a social collaboration platform with the addition of game mechanics, including points, leaderboards and a “buzz index.”

The employees went wild for it. Within 18 months, Idea Street had approximately 4,500 users and had generated 1,400 ideas, 63 of which had gone forward to implementation.

Other gamification examples are the U.S. military’s “America’s Army” video-game recruiting tool, and the World Bank-sponsored Evoke game, which crowdsources ideas from players globally to solve social challenges.

All and more of this in the 2011 report of  Gartner that states that by 2015, more than 50% of organizations tat manage innovation processes will gamify those processes.

Consequences
Mainly as a consequence of the overdose of gamification in our society, people get confused and lose sight on the difference between reality and illusion. 

This confusion is exacerbated by the fact that negative effects of the current financial crisis have been 'managed away' in stead of letting people and organizations 'perceive' and 'experience' the (negative) financial consequences of their handling.



The 'Hocus Pocus Society'
This way, we gradually created a 'Hocus Pocus Society' where all our (actuarial) models and convictions are doomed to fail as the 'game of life' seems to be to:
  • challenge the established (good governance) rules to raise profit and returns to an unrealistic level, by introducing uncontrolled and uncontrollable mechanisms and financial instruments like 'market value', 'derivatives', 'sub-prime mortgages', 'High Frequency Trading', etc.
  • try - at the same time - to capture and control these volatile 'unwanted' effects of these mechanisms and instruments by an overdose of hypocritical additional regulation (Solvency (II), Governance, etc.)
  • transfer and lay back fundamental complex risk to consumers and communicating this in such a (so called) 'transparent' but oversimplified 'way', that consumers for sure lose their trust in financial institutions as a whole.
  • end up in new, for the financial institutions, 99,9% risk free financial products and offerings on the marketplace with a non corresponding stock holders dividend level.



This illusory way of communication about pensions is well demonstrated in the next 'Pension game' video: The myth of your (401K) pension





Way out
To get out of this down spiral cycle in the fiancial industry, we'll have to learn from other industries.

Just like in the case of introducing new medicines , new financial products will have to meet a number of tests and need explicit approval by in and external regulators before they are allowed to be  introduced on the market place.

Anyhow: Don't end up like a 'Hocus Pocus Actuary' and game up your actuarial life!



Related and additional links:
- Idea Street
- Gartner: Over 50% firms may gamify processes 
- Youtube: The Pension Game
- The Annuity Game - Heads Government Wins Tails Pensioner's Lose
- 5 Cent "Old Age Pension" Dice Game 


Calculators:
- life expectancy calculator
- Retirement Withdrawal Calculator