Wikibooks is a Wikimedia community for creating a free library of educational textbooks that anyone can edit.
Since the start in 2003, Wikibooks has grown to include over 35000 pages (year 2009) in a multitude of textbooks created by volunteers.
Chess A great example of Wikibooks is the Wikibook Chess.
In exactly 12 chapters a variety of aspects like, Playing, Notating, Tactics, Strategies, Openings and Endgames, are clearly explained.
Wikibook of Actuarial Science There is also a Wikibook of Actuarial Science. Although all the required chapters of 'Actuarial Science' are already there and structured, the content has to be taken care of.
So, if you like to contribute? Work for voluntary actuaries!
Actuarial Models Collective (organizing) mechanisms are important stuff for actuaries. For example, they play an essential role with regard to all kind of solidarity aspects in pension- and insurance-contracts.
Moreover, collective rational or even emotional behavior often plays a decisive role in our society, as may be clear from the 2009 credit crisis turmoil and the escalating bonus madness.
Be aware, study "collective behavior mechanisms" and take them into account when you set up your actuarial risk model.
Since 2008, according to Milliman, the average funding ratio of the top 100 US (largest) Pension Funds has fallen from 99,6% to 71,7%.
Dutch pension funds developments are comparable.
One way of the other, pension funds have to plan their way out of this financial crisis.
On january 29, 2009, on a NETSPAR meeting, Theo Nijman, Professor Investment Theory of the Tilburg University, gave a presentation called Optimal design of recovery plans.
Nijman's recovery model
Summarized, Nijman shows several recovery options:
Do nothing:
Hope that financial markets will recover and the interest rates will rise
Reduction, if no recovery plan can satisfy the criteria:
Reduction of guarantees
Recovery by Maggid
Although all kind of (IRS) regulations are in place, basically there's no reason for panic....
Everything in life is based on trust. So are our (ALM and VAR) models.
This implies that the only way out, is to stick to our models and their corresponding strategies as much as possible, which means in principle: Do nothing.
However, what we do need to do, is to (re)define and maintain our indexation strategy as follows:
Yearly negative indexation
This strategy implicates that for pension funds with funding ratio's of 80% or less, we'll have to apply "yearly negative indexation".
One off reduction of entitlements is not necessary in this situation and would be 'clumsy', unless the funding ratio would be less than 60% (you have to draw the line somewhere).
In fact this 'negative indexation' is not really new, it's just that we haven't been in this kind of situation before and because we didn't think we would end up in this scenario, we didn't develop any policy. Let's do it now!
Yearly negative indexation is in fact no more than the logical natural opposite of (positive) indexation.
In good times there's positive indexation en in bad times negative indexation, it's a simple as that. Books closed.
Redefine risk strategy?
Last but not least: if we never ever want to end up in a (crisis)situation like this again, we should redefine our risk strategy and select an asset mix that fits to a lower risk/return level.
The question is, when it's the the right time to reallocate, will you actually do it?
UK According to IPE more than 90% of UK Defined Benefit (DB) schemes are underfunded. The aggregate funding position of almost 7,800 schemes reported a deficit of £218.7bn at the end of February 2009.
NL The situation in the Netherlands is hardly better.Figures from the Dutch regulator,DNB, show around half of the country’s 650+ pension schemes are under-funded. The Dutch government has extended the recovery period for pension funds from three to five years. The main question is: "Is that long enough?"
How Defined Benefit Plans work(ed)
Pension funds, especially DB schemes, have to face that their worst dreams, a complete doom scenario, is becoming true :
First the subprime market collapsed
Then, as trust broke down, the stock market went down as well
Titanic lessons Just like the 'unsinkable' Titanic was protected by compartments, we had protected our pension schemes with diversification. And just like the Titanic, we actuaries, asset managers, and quants made a fundamental mistake. We underestimated the correlation between the different compartments (bonds, subprimes, stocks). One hit in the vital front compartment was enough to draw our pension dreams to the bottom of the ocean.
Optimistic view But let's not stay pessimistic.
Do you know how long it took the market to recover after 1929? .....
ONLY 25 YEARS!
Global Investment Returns Yearbook 2009 And there are more reasons to stay positive about the equity results on the long term, as is shown in the very interesting downloadable Credit Suisse Global Investment Returns Yearbook 2009, that analysis returns from 1900 until the end of 2008.
As this yearbook shows us in more detail, it is only a matter of statistical faith, that equity performance on the long term will recover.
So the only thing we can do is, just like a sick patient: stay cool, rest (don't move), don't panic and wait until trust and the markets recover.
In an earlier TED Show psychologist Barry Schwartz illustrated in a humorous and catching way the effects od "Too much choice".
Now, in another TED Show video called, "The real crisis? We stopped being wise", he shows us that the current financial crisis can't be solved by more rules or incentive policy.
Schwartz pleads for a new approach based on a Obama's approach to solve the current financial crisis. Already before his inauguration Obama said:
“We must ask, not just is it profitable, but is it right”
Schwartz: "In his inaugrual address, Barack Obama appealed to each of us to give our best, as we try to extragate ourselves form the current financial crisis. But what did he appeal to? He did not, happily, follow in the footsteps of his predecessor and tell us to just go shopping. Nor did he tell us , 'Trust us, trust your country. Invest. Invest. Invest.' Instead, what he told us, was, to put aside the childish things. And he appealed to virtue.
Two reasons motivate less? Schwartz brilliantly illustrates the common wrong notion that if you have one reason for doing something and you are given a second reason for doing the same thing, it seems only logical that two reasons are better than one, and you are more likely to do it.
This is not always true. sometimes two reasons to do the same thing seem to compete with one another instead of complementing, and they make people less likely to do it.
Schwartz illustrates this in the next example:
In Switzerland, back about 15 years ago, they were trying to decide where to site nuclear waste dumps. There was a national referendum and some psychologists went around and polled citizens who were very well informed. And they said, “Would you be willing to have a nuclear waste dump in your community?” Astonishingly, 50% of the citizens said “Yes.” They knew, or thought, it was dangerous, they thought it would reduce their property values, but, it had to go somewhere, and they had responsibilities as citizens.
The psychologists asked other people a slightly different question. They said, “If we paid you six weeks salary, every year, would you have a nuclear waste dump in your community?” Two reasons: it is my responsibility and I am getting paid. Instead of 50% saying yes, 25% said yes.
What happens is that the introduction of the incentive gets us to a point that, instead of asking, “What is my responsibility?”, all we ask is “What serves my interest?”
When incentives don’t work, when CEOs ignore the long term health of their companies in pursuit of short term gains that will lead to massive bonuses, the (wrong) response is always the same: get smarter incentives.
So, in general, adding more or better incentives will not motivate us more or increase our responsibility!
Actuarial lesson As actuaries we often try to find as many reasons as possible to convince a board of taking the right decision. Perhaps we should emphasize more on finding and communicating that one and only reason to take the right decision: a prudent, healthy and solid decision (investment) that benefits all stakeholders on the long and short term, in a balanced way.
A priest and an Actuary were rounded up for execution by the French Revolution.
The priest had been taken over to the Guillotine and was asked if he had any last words. He said 'If I am innocent, let the Lord God Almighty prevent this execution!'
Everybody laughed until the Guillotine failed to come down on three consecutive tries due to a malfunction. So according French law, the priest was set free.
Then the Actuary had to be executed. He climbed the guillotine and calmly laid down his head on the block. Again the very same malfunction occurred on the first two tries, at which point Actuary looked up, examined the guillotine and exclaimed: "I think I see the problem"
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.
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.
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
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).
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.
Coastline Formula & Valuation What can we learn from this fractal coastline measurement with regard to valuations?
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!
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!
Aubrey de Grey, a British biomedical gerontologist, states in his book "Ending Aging," that that the fundamental knowledge to develop effective anti-aging medicine mostly already exists.
Age damage
There are seven types of aging damage :
Damage rising with age
Proposed as contributing to aging by
Cell loss, cell atrophy
Brody (1955) or earlier
Extracellular junk
Alzheimer (1907)
Extracellular crosslinks
Monnier and Cerami (1981)
Cell senescence
Hayflick (1965)
Mitochondrial mutations
Harman (1972)
Lysosomal junk
Strehler (1959) or earlier
Nuclear [epi]mutations (cancer)
Szilard (1959) and Cutler (1982)
Although, for more than 25 years, science suspiciously didn't seem to develop, all kind of medicines to repair these damages are already within reach for mice.
Age damage for human beings is strongly age related:
As the chairman of the Methuselah-Foundation, De Grey stimulates scientists to develop medicines that repair age damage for this living generation.
Experiments on mouses showed that medicines didn't only slow down the aging process, but could reverse it as well (condition: start in time!). It turns out that every time a new medicine is developed and applied, it restores - above a certain threshold of reserve capacity - the lost reserve capacity for about 50%.
This would imply that if new medicines for human beings would be developed within the next decade and the rate of developing new medicines will be fast enough to stay 'ahead of the game', all people of 50 years and younger would be able to live a thousand years or more and people just slightly older could still live for hundred years or more.
In 2006 Technology Review announced a $20,000 prize for any molecular biologist who could demonstrate that De Grey was wrong. Nobody succeeded!
If De Grey is right, actuaries don't even have to start calculating new life expectancies or other (financial) consequences. Life insurance and pension will have to be redefined.
Even stronger: We'll have to redefine our life!
Do you recognize this? Sometimes you spend hours copying a simple table from a WORD-document, Internet Page or PDF-file to your (Excel) spreadsheet. What should take about two minutes work, ends in frustration. Finally you decide to fill your spreadsheet by hand.
These times are over. With the next simple javascript application, called
Let's be humble and take a look at home. The home of actuaries, accountants and last but not least 'quants'.
Gewußt oder nicht gewußt? Actuaries and accountants have failed in foreseeing the credit crisis. Together, we have greatly underestimated the developments and put our head in the sand. We've also failed to bring the emerging crisis to a possible end through enhanced cooperation with each other or by sending out common strong signals. In short: "Wir haben es nicht gewußt!"
Without an adequate technical substantiation, we have trusted business plans promising ROEs of 15% and more. This, while we all know that the average risk-free rate is still about 10% below this level and that such high returns can certainly not be made without taking additional risk.
VaR Model As an article in The Actuary shows, we got intimidated and overruled by the quants with their Value at Risk (VaR) models. The consequences of the advices of these magic mathematicians and their VaR models are well explained in an excellent article called 'Risk Mismanagement' in the New York Times.
It specifically cuts them off. A 99% VaR calculation does not evaluate what happens in the last 1%.
This makes VaR relatively useless as a riskmanagement tool and potentially catastrophic when its use creates a false sense of security among senior managers and watchdogs. " Quote:
VaR is like an airbag that works all the time, except when you have a car accident
Also, according to Bloomberg, the risk-taking VaR model is broken and everyone is coming to the realization that no formula or rating system can substitute for old-fashioned 'due diligence'.
Quantum mechanics Because of the complexity of these new VaR-like models, experienced actuaries, accountants, managers and supervisors were all afraid to ask deeper questions or to admit that they didn't totally understood these complex models that were presented as 'simple manageable board instruments' with 'simple steering parameters'. Just like nobody is eager to admit that 'quantum mechanics' is hard to understand and therefor every amateur quantum guru can say what he wants, because nobody checks it.
Consequences This way, indirect and by our advice and our models, CEOs and CFOs of large companies and pension funds got the (wrong) impression that 'complex financial markets' were based on 'a sound statistical model', where (annual) deficit risks of 2.5%, 0.5% or 0.1% are exactly calculable and moreover also acceptable.
Whatever, lessons learned, new opportunities for actuaries to set a new benchmark for '21 century riskmanagement'.
However..., stay careful, to catch a tiger by the tail is risky!
How can you be against something that's fair, like "Fair Value"? What could be wrong, valuating a company at market value?
IceComp Case Let me take you along in a story about IceComp, a fictitious ordinary wholesaler in ice creams.
The daily demand for ice creams turns out to be in line with the outside temperature. In an average summer, with an average temperature of 16°C (about 60°F), IceComp sells 10 million ice creams a year. Annual turnover the past 10 years, $ 20 million with a net margin of 10%.
In order to regulate demand and to maximize profit, IceComp defines the daily ice cream selling price (P) in line with the market by the formula:
P = DAYTEMP / 8
So at 32°C an ice cream will sell at $ 4 and at 16°C it will sell at $ 2 a piece. To always deliver on time, IceComp keeps an average stock of about 2 million ice creams. Based on on the average selling price of the last 10 years, this stock is valued in the balance sheet at $ 4 million, resulting in a fair and trustworthy P&L, that reflects the actual sales level at current prices.
Two years ago, inventory (stock) valuation based on market prices ('fair value'), i.e. the price daily selling price of an ice cream, became mandatory. From that moment on, things started to go wrong.
Consistent with the daily temperature, the daily inventory value starts to oscillate heavily, with explosions and variations up to $ 6 million per month. To the 'surprise' of all stakeholders, equally strong alternating monthly gains and losses are reported. It's crystal clear, the company is no longer 'in control'.
The national supervisor interferes and demands extra securities (funds). Now the monthly P&L of IceComp starts to oscillate even more, as the investment results of the extra securities, that principally do not have anything to do with the core business of IceComp, also start to vary on basis of 'fair value' (market prices) valuation.
Ultimately, lack of confidence from share- and stakeholders drives IceComp into bankruptcy.
Conclusion What was meant to be 'intentional Fair', turns out to be 'Unfair' in practice. Valuing balance sheets on bases of daily prices is like playing 'Russian roulette'. It can be compared to making 'climate statements', based on the daily weather forecast.
The analogy to banking, pension and insurance business may be clear. Don't base valuation methods on daily prices, but on a, per product or market defined, 'moving average market price' for a fixed chosen period (depending on product or market cycle).
The current (credit) crisis calls for development of new valuating principles by auditors and actuaries.
Did you know there are more than 100 "new year's days" in a calendar year? It just depends on where you live or what you believe.
Before 1752, Americans celebrated New Year's Day on March 25th (Lady Day according to the old Celtic religion and the Feast of the Annunciation according to the Christian religion).
Great Britain and its colonies changed their New Year's celebrations to January 1st when they changed from the old Julian calendar to the Gregorian calendar in 1751.
Although the S&P 500® 1988-2007 Index had an annualized return of 12%, the average equity fund investor (in equity mutual funds) only generated a 5% return and market timers, who tried to outsmart the market by timing their inflows and outflows, generated an annualized loss of 1%.
*Measures returns of investors in equity mutual funds. Source: Bureau of Labor Statistics, DALBAR
Greed and Fear When the asset strategy has been chosen and implemented, it comes down to strong nerves, to hold this strategy.
But nothing human is strange to us. Who can resist the pressure of shareholders, advisors or analysts to question the current strategy after 2 or 3 years of extremely high (or low) stock returns?
In straightening out and defending your policy, stakeholders and advisors will often argue that you're a rearview mirror actuary or board member. They'll stress that the actual situation is not comparable with any situation in the past.
However, always keep in mind the words of Sir John Templeton (1912-2008) :
So how successful are you, in cashing in on your emotions an withstanding pressure?
Still, if you nevertheless give in and are going to change your bond/stock ratio based on fear, greed or hype, all bets are off. Example
As is clear form the example above, when your strategy is vulnerable to heart cries, you'll end up in the famous Pork Cycle , which - in this case - leads to a return level beneath that of risk free assets. The price of Greed and Fear! Lesson When you've set your assets according your chosen asset strategy, only change this strategy when the underlying long term asset-modeling parameters substantially change. In every other case, don't decide on basis of 'heart over head'.
Define and allocate equity (as security) for an 'up front' defined period of time in wich you're willing to except lower or even a defined maximum negative performance. Agree this strategy up front with the supervisory board and national Supervisors.
Lyndon LaRouche, economist, long-range forecaster, risk manager 'avant la lettre' and one of the initiators behind the SDI-project (Strategic Defense Initiative) in the 80s.
With firm quotes like "there has been no economic growth on this planet, since the end of the 1960s. None, if you measure the right magnitudes", he takes stand in the sometimes overoptimistic and misleading world we've created.
Back in 1995, in Germany, he stated "We are at the end of an epoch".
He warned that a global financial bankruptcy and collapse would be under way and introduced in an econometric form his 'famous' "Typical Collapse Function" or "Triple Curve"to illustrate that power statement.
In his daring view, he describes the interplay of the three curves (non mathematical directionalities) that characterize the collapse process:
Physical-economic input/output (bottom curve) The productivity and functioning of the physical economy, upon which all human existence depends;
Monetary aggregates (middle curve) The increase in monetary aggregates (approximately represented by money supply measures; injections)
Financial aggregates (upper curve) Growth—which can become hyperbolic growth—in financial aggregates of all kinds: run-up of debts and other obligations, speculation in currencies, stock markets, futures (derivatives), etc.
As in the case of a "typical collapse function," the interaction of the upper two curves sucks the underlying physical economy dry.
But at a certain critical point (around 2000 in the USA), no matter how much money is injected in the economy, the financial bubbles cannot be kept aloft! The rate of rate of growth of monetary aggregates becomes higher than the rate of rate of growth for financial aggregates. In graphical terms, this is the "inevitable crossover" point of the middle, monetary curve, breaking up through the top financial curve.
Although this looks like intuitive econometric science, LaRouche illustrates this with some striking examples.
In the year 2000 LaRouche stated that compared with a worldwide GDP of about $41 trillion, the total amount of financial aggregate in short-term obligations was over $400 trillion. In other words, at least 10 times the amount of the total annual product of the world as a whole at that time. "
Outstanding obligations: $1.4 quadrillion, derivatives, short-term obligations of speculative nature
This mess is coming down.
System will be put into bankruptcy, by governments
And than to realize that there are still leading prominent professionals that like to make us believe that it's just some limited subprime issue. Regretful, it's the other way around. Subprime will just turn out to be the proverbial little stroke that'll fell the great oak.
According to IPE, Frans Ballendux, former business leader of Mercer Investment Consulting in the Netherlands, is starting his own investment consultancy business.
The Groupe Consultatif Actuariel Europeen published end 2005 a study, which for the first time compares how companies in different European countries measure life expectancy for their pension schemes. It reveals vast differences in mortality assumptions and indicates that practice across the EU varies widely when assessing company pension liabilities.
As you may see from some examples to the left, a wide area of classic mortality formulae in the different European countries passes by.
It's clear that that mortality assumptions in company pension schemes vary from country to country, due to variations in underlying population mortality as well as in variations of the profile of typical membership of a company pension scheme. However, the variations in mortality assumptions are much greater than would be justified by these factors alone.
Some of the variation is due to the fact that some countries incorporate an allowance for expected future improvements in mortality, while others use tables that relate to mortality observed over a period in the past, without allowing for the fact that life expectancy continues to increase.
The total actuarial deficit with regard to (future) longevity in company pension schemes is substantial.
As a 'Survey of Actuarial Education in Europe' showed, not only mortality rates differ, but also the the education of different European actuarial professionals.
The Netherlands are the overall winner in the Euro Health Consumer Index 2008, launched today in Brussels at a press conference hosted by the Health Consumer Powerhouse.
The Euro Health Consumer Index is the annual ranking of national European healthcare systems across six key areas: Patient rights and information, e-Health, Waiting time for treatment, Outcomes, Range and reach of services provided and Pharmaceuticals.
In a Harvard Business Review called "Why satisfied customers defect", Jones & Sasser explain that even a 80% 'satisfied clients score', is no guarantee for sustainable success.
Common management misconceptions are:
A client satisfaction level below complete or total satisfaction is adequate.
It's not profitable to invest in changing customers from 'satisfied' to 'completely satisfied'.
Their conclusion is that, in most cases, 'complete customer satisfaction' is key in order to secure customer loyalty and generate sustainable financial performance.
Loyalty & Satisfaction Despite of what sometimes intuitively is assumed, the relationship between loyalty and satisfaction is in most cases not linear, but depends on the competition level of a specific market segment.
In a Dutch presentation, called "CRM Myths", direct marketing professor Janny Hoekstra confirms this relationship and shows that even 'satisfied clients' are in the so called 'indifference zone'.
The 'art of client management' is obviously to create 'Apostles' and to avoid creating 'Terrorists'.
So stimulate, instead of discourage, your clients to give you feedback and to complain, because this is the only way to create new apostles.
NPS A relatively new and, according to Harvard (The One Number You Need to Grow), probably better method to measure client loyalty is the 'Net Promoter Score' (NPS). Simply score your clients on a 0-10 points scale on the question: "Would you recommend company X ?'
Now simply calculate the NPS score (%) as: NPS = Promoters%(rating 9&10)- Detractors%(rating 6 or less)
NPS scores of 75% or more prove world class loyalty.
Loyalty effect Another, intuitively driven, perception is that the more customers are loyal, the more they generate profit.
In general this seems true, however as Hoekstra shows: not every 'more loyal' client is also per definition 'more profitable'.
Investing in 'True friends' appears essential and eventually pays out.
Customer Lifetime Value Actuaries that combine marketing an actuarial sciences could help by defining and calculating what is called: The Customer Lifetime Value (CLV)
The CLV of a specific client(group) could be defined as the discounted value of the yearly margin (m = profits - costs), with discounting rate (i) and the (client) retention rate (r).
CLV:Rule of thumb In the strongly simplified case with constant margin, the CLV - as a rule of thumb - could be defined as the margin (m) multiplied with the so called margin multiple = r/(1+i-r).
Example: Discount rate = i =12%, Retention rate = r = 90%, results in a CLV of approximately 4 times the yearly margin.
As is clear from the formula and table above, the choice and impact of the discount rate is only significant in combination with a high (>90%) retention rate.
Modeling and creating Client Value is not only in the interest of the shareholder, but moreover a case of creating creating added value for clients, in particular 'best satisfied clients'.
As actuaries we all know investment Banking is a complex business. This Youtube video explains the essentials of Investment banking in about 8 minutes.
Be sure to study the video seriously, it will be the best study investment you've done in years.
Credit Crisis Indicators: Treasury, Libor, Ted, Paper & Bonds.
The creditmarkets indicators give a better measure of the crisis than the stock markets. NYT gathered five ways to measure the recent disruptions in the credit markets.
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Wikibooks is great!
Chess
In 1967 he revived the original formula, earlier developed by 
The constant D also stands for 'Dimension' and in 1975 Mandelbrot develops this Dimension- idea to what is called the 
The Euro Health Consumer Index is the annual ranking of national European healthcare systems across six key areas: Patient rights and information, e-Health, Waiting time for treatment, Outcomes, Range and reach of services provided and Pharmaceuticals.
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