Dec 30, 2014

Human Development Index 1980 - 2013

Now that the year 2014 is coming to an end, let's take a look at the Human Development Index (HDI) over the years 1980 - 2014.

The HDI is a tool developed by the United Nations to measure and rank countries' levels of social and economic development.

The HDI is based on four criteria:

  1. Life expectancy at birth 
  2. Mean years of schooling 
  3. Expected years of schooling 
  4. Gross national income per capita. 

The HDI makes it possible to track changes in development levels over time and to compare development levels in different countries.

How does your country rank on HDI?

Wish you all a nice Sylvester evening tomorrow!

Dec 21, 2014

Actuarial Readability

As an actuary, accountant or financial consultant, deep knowledge, expert skills and experience are key to writing an interesting article or paper advice.

However, no matter how much you're an expert, finally you're as good as you can get your message across to your audience.

The art of the expert is to simplify the complexity of his/her research into simple, and for the audience understandable text.

In practice this implies that the expert will have to measure the readability of his papers before publishing.

The two most important issues to tackle are 'readability' and 'text-level'.

Although there are many sorts of tests, both topics are simply covered by the so called  Flesch-Kincaid Readability Test.

Let's take a look ate the two simple test formulas of this test:

Flesch-Kincaid Readability Test

Flesch Reading Ease Score

FRES = 206.835 – (1.015 x ASL) – (84.6 x ASW)

Flesch-Kincaid Grade Level

FKGL = (0.39 x ASL) + (11.8 x ASW) – 15.59

ASL  = average sentence length
number of words divided by the number of sentences

ASW = average number of syllables per word

number of syllables divided by number of words

Texts with a FRES-score of 90-100 are easily understandable by an average 5th grader and scores between 0 and 30 are best understood by college graduates.

Some examples of readability index scores of magazines:
- Reader's Digest Magazine: FRES = 65
- Time magazine: FRES = 52
- Harvard Law Review: FRES = 30

The FRES-test has become a U.S. governmental standard. Many government agencies require documents or forms to meet specific readability levels. Most states require insurance forms to score 40-50 on the test.

Where to test your documents?

Besides matching the FRES and FKTL scores in your document, as a guideline try to establish the next English text-test-characteristics
  • Average sentence length 15-20 words, 25-33 syllables and 75-100 characters.
  • Characters per word: < 7
  • Syllables per word: 1.5 - 2.0
  • Words per sentence: 15 - 20

This blog text resulted in scores:
- Flesch-Kincaid Reading Ease 64.7
- Flesch-Kincaid Grade Level 7.2
- Characters per Word 4.4
- Syllables per Word 1.5
- Words per Sentence 11.8

As an example we test the readability of one of the articles of the Investment Fallacies e-book, as published by the Society of Actuaries (SOA) :

By Max J. Rudolph, published in 2014

The readability outcome is as follows:

Readability Score 'The Best Model Doesn’t Win'

Reading Ease
A higher score indicates easier readability; scores usually range between 0 and 100.

Readability Formula

Grade Levels

A grade level (based on the USA education system) is equivalent to the number of years of education a person has had. Scores over 22 should generally be taken to mean graduate level text.

Readability Formula
Average Grade Level

Text Statistics
Character Count 7,611
Syllable Count 2,531
Word Count 1,495
Sentence Count 98
Characters per Word 5.1
Syllables per Word 1.7
Words per Sentence 15.3

Actuarial Texts
With regard to public financial or actuarial publications a FRES-score of around 50 assures, that your publication reaches a wide audience. Even in case you're publishing an article at university level, try to keep the FRES-score as high as possible.

If you write an academic paper, you may use the online application Word and Phrase to measure the percentage of academic words. Try to keep this percentage below 20% to keep your document readable. The publication 'The Best Model Doesn’t Win' would score 17% on academic words......

Next time you write a document or make a PPT presentation, don't forget to


Nov 9, 2014

Retirement Age Development

Due to the continuous ageing process and a strong ongoing growth of life expectancy, countries need to increase their formal retirement age.

Actuarial calculations show  in general that - in order to keep pensions affordable - the formal pension age for future generations will eventually have to increase to the age of 71 or even 75 years.

However, lifting up the retirement age is not an easy process, as people have grown up with the concept of a steady retirement date, all their life. As if 'work is slavery' and life only really starts at your pension date, when you abruptly stop working and live a life behind the window of your apartment...

However THE pension date doesn't exist, it's an illusion, a fata morgana...

Not only that retirement increases the age-related decline of health and cognitive abilities for most workers, it also increases your mortality rate, as a RP-2000 Mortality Study shows:

Secondly, nobody - not even an actuary - can predict the outcome of a pension plan over a period of 60-70 years. Pension dates and and long term pension outcomes are by definition unsure.

OECD Retirement Ages
What we can do is keeping the retirement age in pace with the development of our life expectation. This is exactly what some OECD countries have done, as the next chart shows:

Of  course, the optimal retirement planning depends on several economic en demographic developments in a country.

On the OECD page you can play and compare several pension-related variables across different countries.

Enjoy playing and learning from these OECD data.

- Unhealthy Retirement (2014)
- Does working longer increase your lifespan? (2010)
- OECD Page

Oct 6, 2014

Future Role of THE Actuary

To quote a leading Dutch actuary (Jeroen Tuijp):

THE Actuary doesn't Exist!

But what is, or could be the role of an actuary in the next decade?

Perception: What's an actuary?
The answer to the question "What's an Actuary?", strongly depends on who you are asking.

Some examples of possible answers:

  • Accountant: An Actuary helps to estimate and understand discounting the assets and liabilities
  • Board Member: My Actuary is my premium and liability adequacy advisor, he manages risk
  • Risk Manager: Our Actuary helps me to identify hidden risks and estimate embedded options
  • Investment Manager: Our Actuary helps me to define ALM and investment models
  • Administration Officer: I ask our Actuary for advice on how to administrate in an efficient way
  • ICT Manager: The actuary is responsible for defining the equations in our system
  • Marketing Manager: Our actuary is the driving force behind product development
  • Supervisory Board Member: Our Actuary is the lock on the door

The perception of the professional  contribution of an actuary not only depends on the view in the eye of the beholder, but also on the wide variety of roles that actuaries fill in all kind of organisations.

Some examples of the endless list of the many different (actuarial) roles and positions that actuaries fill in:
  1. Certifying Actuary, Advisory Actuary, Valuation Actuary
  2. Pension Actuary, Investment Actuary, General Insurance Actuary, Health Actuary, Life Actuary, Claims Actuary, Public Pension Actuary, Reinsurance Actuary
  3. Risk Manager, Capital & Solvency (II) Manager, 
  4. Marketing Manager, Head Product Development, Head Financial Control

On top of, the actuarial work field comprises a list of detailed professional disciplines, such as:
  • Regulation: Solvency (II) , Basel,
  • Technical Life Topics: Mortality, Longevity, Healthy Life years, 
  • Technical Non-Life Topics: Car & House Insurance, Catastrophe Risk, Health Insurance, 
  • Investment Topics: ALM, Risk Return Policies, Tail Risks, Economic Risks
  • Long list: Compliance, Resilience, Tax, Ethics, Financial Reporting,  Reinsurance, etc...

All of these viewpoints and wide professional manifestations make it hard to classify and compartmentalize actuaries, especially in and around boardrooms. Yet, actuaries are nearly in every field present, often without being identified or recognized as such!

An actuary is what we call 'The Elephant in the Room', or perhaps better formulated:

THE Actuary is the Multi-Perceived Elephant in the Boardroom

Despite of the wide range of positions actuaries can fulfill, it becomes harder and harder for actuaries to follow a career path that leads to a boardroom position as CXX...

Why is it so hard for an actuary to end up as CEO or COO of a company?

The simple answer to this question is:

Thinking in Stereotypes

Because actuaries are good at mathematics, people in general as well as professionals continue to view and stigmatize them as Overspecialized Nerds and Brilliant Autistics. This way of (wrong) stereotype thinking identifies actuaries often as 'problematic communicators' and 'non-managers'. As a consequence, the managerial qualifications of a lot of actuaries are unfortunately overshadowed by their outstanding professional technical skills.

Thinking in stereotypes is a phenomenon that is around us everywhere, as is shown in Herge's comic book "The Valley of the Cobras". In this book the (quixotic) 'Maharajah of Gopel' is vacationing in the french ski-resort of Vargése. Suddenly the Maharajah discovers his pearl necklace has been stolen and he needs a detective to track down his necklace.The rest of the story is shown in the short comic strip below (click to enlarge):

Conclusions and lessons Learned
THE future role of THE Actuary doesn't exist. As an actuary, fill in every professional role that attracts and fits you. Try it out, to discover you can fill in more than one role in the many healthy life years  ahead of you......

Finally some wrap up ground rules to keep in mind:

  1. Never think in stereotypes as an actuary!
  2. If you are an actuary and have the ambition to become a CEO, CFO or CRO of a company: Act, Dress, Speak and Behave accordingly, as other people probably will keep thinking in stereotypes
  3. If you meet other actuaries: Talk and behave like an actuary
  4. Ground Rule Number One: Always Stay Yourself!


Jul 6, 2014

Understanding Confidence Levels in Time

What's the right understanding of the concept of 'confidence level' for a financial institution?

That's not an easy question....

A short (popular) definition of confidence level in terms of Solvency and Basel regulation would be:

The probability that a financial institution doesn't default within a year.

In this blog I'll discuss and compare three more or less accepted confidence levels (CFLs):

  1. Dutch Pension Funds: CFL= 97.5% 
  2. Life Insurers (Solvency II): CFL = 99,5%
  3. Banks (Basel II/III): CFL = 99.9%

Understanding Confidence Level
Before we get into the details, let's first shine a light on a widespread misunderstanding regarding the concept of 'confidence level'.

To make the concept of confidence level more understandable, one might argue as follows:

  1. The confidence level of a Dutch pension fund is defined as 97.5%
  2. This implies that there's a one years probability that the pension fund has an one year default probability of 2.5% (= 100% - 97.5%)
  3. This implies that the pension fund on average defaults once every 40 years (= 1 / 0.025)

This method of reasoning is completely


The mistake that's been made is more or less the same as the next two fallacies:
  1. If one ship crosses the ocean in 12 days. 12 ships will cross the ocean in one day
  2. I fit in my jacket, my jacket fits in my suitcase, therefore I fit in y suitcase

The probability of a pension fund with a confidence level of 97,5% going default, can be approximated by a simple Poisson distribution as follows:

From this we can conclude:

  • In 40 years the pension fund has a 63% default probability.
  • The probability that the pension fund defaults more than once is 26%
  • The probability that the pension fund defaults exactly once in a 10 years period is 19.47% 

Insurer Confidence Level
For an insurance company with a confidence level of 99.5% the results are:

So even an insurer has a 4.88% default probability in a 10 years period on basis of a 99.5% confidence level. Keep this in mind if you take out a life insurance policy!!!

Banking Confidence Level
It starts getting serious when it comes down to a 99,9% confidence level for banks:

Comparing the default probability of (Dutch) pension funds, insurers and bank on the long run:

Although this blog gives some more insight about the consequences of confidence levels on the long run, the real question of course is: what's the price you have to pay to avoid default risks?
That's something for another blog.....

- Spreadsheet with tables used in this blog

May 18, 2014

Bonds: a Crisis Risk Indicator?

As a risk professional you've learned to classify an increase in bond's interest volatility (or standard deviation) as an indicator that bonds have become more risky. Right you are....

Now, with this knowledge, let's take a look at the next chart, presenting the long-term (10Y) interest rate of some of the leading EU member states from January 1993 to April 2014:

This chart clearly shows that :
  • Since the introduction of the Euro in 1999, country spreads start declining
  • Interest rates converge to the year of the famous (Lehman) crisis in 2008
  • After the 2008 crisis, rating agencies wake up and spreads explode again

Let's take a look in more detail, by some log scale zooming......

To find out if the convergence of interest rates really is a kind of early warning crisis indicator, let's add some more EU countries to the chart.

Now the picture becomes clear: A structural decline in bond's standard deviation is not a decline in risk, but more the opposite....

As standard deviation decreases, (crisis) risk increases!

We can check this by looking at the cross-country standard deviation development in time:

These charts, presented on a vertical linear and log scale basis, clearly  illustrate that as soon as the standard deviation hits the 0.2% level, crisis can be expected soon.

Not only is the 0.2% SD-level an early warning indicator for the 2008 crisis that started with the bankruptcy of the Lehman Brothers bank, but it's also an indicator of 'Dot Com' crisis in 2000....

Meanwhile... as from February 2012, standard deviations are declining  again. Time to worry?

Key questions are:
  • when will standard deviation hit the 0.2% floor again? 
  • and when it does, will there be another crisis?

Remember lesson number 1 in risk management: Crises are unpredictable!
Nevertheless, once 0.2% SD  turns up: fasten your investment seat bells....

- Spreadsheet of charts used in this blog
- EU Interest Rates
- Big Picture Chart

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.

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!


Mar 30, 2014

Chief Actuary Officer

Let's take a look at the governance of financial institutions from a risk management perspective:

Governance Risk Management

Traditional governance focuses on the organisation-structure, decision-structure, influence and power-weights of all stakeholders. Governance Risk Management focuses on how to optimize and monitor risk and value creation for all stakeholders.

Financial Risk Management Monitoring
After defining a companies Mission, Risk Appetite and Strategic Plan, the year-targets and key indicators are not only translated into a tight budget (b) of 'sales targets' and 'profits', but also into 'balance sheet budget targets' (b).

It takes a real well defined 'Governance Risk Management' to split the balance sheet into such parts (Assets, Liabilities & Capital) that responsible officers in the company are able (and can take responsibility) to monitor the actual values (a) monthly or quarterly to the final or adjusted budget values (b).


Officer Role Division
In a well managed and structured financial company the risk-financial roles of the companies officers can be defined as follows:

  1. CIO
    The Chief Investment Officer is primarily responsible for managing the asset actuals A(a) versus the (adjusted) budget A(b). So the CIO has to manage [A(a)-A(b)] in terms of value and within defined  the investment risk budget.
  2. CAO
    Although often unremarked, an important part of the role of the Chief Actuary Officer is to manage the actual liabilities L(a) versus the (adjusted) Liabilities budget L(b).
    This is no easy job, as most longevity and (risk free) discounting of the liabilities are hard to influence.
    Wrapping up: The CAO is responsible for managing [L(a)-L(b)].

    Often the role of the CAO seems to be limited to insurers or pension funds. However, also banks need an actuarial officer, as more and more (product) risks on the bank's balance sheet become economic, demographic and bio-related (mortality, disability, lifestyle).  
  3. CRO
    Often the Chief Risk Officer is seen as someone at arms length reporting about risks to the (supervisory) board. However, one of the main roles of the CRO is to monitor Capital and Capital Requirements. He/She is responsible for realizing the sustainability of the company by managing the (adjusted) Capital budget C(b) while being confronted with continuously changinge Capital actuals C(a). So the CRO is responsible for monitoring [ [C(a)]-C(b)].  

AIRCO Management
Once the targets are set and responsibilities are defined, the hard part of managing a financial institution starts: Cooperation between the Actuarial, Investment, Risk and Capital Organisation (AIRCO) Chiefs.

During a budget year, all individual defined AIRCO budgets and actuals continuously change in practice.
As capital risk development is the complex result of Asset and Liability volatility, capital management and monitoring by (primarily) the CRO manager becomes extra complex. Especially in market crises situations (tail risks), where traditional (linear) correlations between AIRCO components fail by definition. It's the responsibility of the CRO to continuously balance between all stakeholders interests in narrow cooperation with the CAO and CIO, while staying on track with regulatory requirements.

This task is not easy, as AIRCO Management is not a one dimensional mission or game:
  • Run-off
    Often AIRCO Management is merely based on regulatory AIRCO requirements, based on run-off portfolios and one-year period confidence levels (e.g. 99.5% [Solvency-II] or 99,9% [ Basel-II/III] ).
  • Continuous business model 
    However this run-off approach is only based on a kind of default situation with a very low probability (< 1%). It's much more likely (> 99%) that a financial company will exist for more than one year.

    Therefore, adding one or more variations of 'continuous business model approaches' to the existing run-off approach on a board's table, will give the board a more (realistic) insight on the heavy an balanced decisions to be taken to continue and control a sustainable risk-return strategy. 

To manage the complex of AIRCO effects, it's often helpful to set up an Asset Liability Capital Team (ALC-Team) within a financial institution. Main task of this team is to manage risk and returns across all AIC-axes in line with the strategic plan, the defined risk-return appetite and actual regulatory requirements.

The ALC-Team consists of the CAO, CIO an CRO and could in practice be chaired by the board's CFO, or CFRO.
This ALC-Team :
  • proposes board adjustments and monitors the risk-return targets and matching policy
  • makes clear what the often paradoxical and/or conflicting effects of risk-return management are for all stakeholders on basis of different future business continuity models (e.g. Run-off, Continuous business, etc.)
  • Makes clear and advises what measures the board can take due to the impact on ALC of different business models views, changes in economic risks and changes in regulation.
  • operates on basis of ALC reporting information,"Own Risk Assessment" reports, external Economic Risk Reports and external Regulatory Change Information.

One of the most tricky pitfalls in capital management is that a financial institution tries to solve all budget variances and regulation changes only by adjusting its investment policy.

If adjusting is done 'on the fly', without considering the risk-return targets and (even worse) through the mental filter of just one of the stakeholders interests (e.g. 'shareholder value), a financial company implicitly risks to lose track of the overall strategic business targets.

If an economic or regulatory change influences the risk-return objectives, all possible instrumental options to respond, have to be taken into account. One of the most forgotten instruments to respond to market changes, is 'product management' or (new) 'product development'.

Yet, nevertheless the fact that existing (product) contracts are (short term) often hard to adapt, 'product management' is one of the most vital instruments to apply regarding the management of long term risk-return objectives.

Therefore AIRCO Management requires a planned an controlled Stakeholder Management Process in a financial institution.

Stakeholder Value (Risk) Management
Managing a company's stakeholder value implies that the effects of the economic, regulatory and own-company changes on the risk-return objectives are continuously balanced across all stakeholders (Shareholders, Clients, Asset Managers, Board/Employees).

Apart from 'HR value management', regarding possible board and employee reward and benefits adjustments, the instruments to manage and  balance Stakeholder Value:

A-1  Asset Value management
C-1. Capital Management
C-2  Shareholder Value management
L-1  Product Value Management
L-2  Client Value management

are presented in the next chart:

Managing a financial institution in this challenging financial decade (2010-2020) is a complex operation with multidimensional regulation and business risk-return targets. Financial Boards have to manage more truths at the same time in a highly volatile economic risk-return environment.

Surviving in this complex world urges boards to step from a traditional predictable managing approach to a more responsive managing approach, where stakeholders value is continuously monitored and adapted to the real world environment.

This new 'survival approach' urges to improve communication, process information and reporting across Assets, Liabilities and Capital Management within the organisation.

Establishing an ALC-Team approach could be a first step to improve the control on risk-return management within the organisation across all stakeholders and actively using all 'stakeholders value tools' in a balanced way.

Last but not least, the role of the Chief Actuary Officer should be more clearly defined. The CAO is, in line with Client Value objectives, primarily responsible for an adequate liability en product management, that's key in balancing the risk-return objectives of a financial institution.


- Cartoon: Government Risk Management by Todd Nielsen
Risky Business – Making Phenomenal Decisions
   (While Not Forgetting the Risk)

Mar 1, 2014

Too Big to Tail

At the end of 2012 the author of the famous book The Black Swan and professor of risk engineering at the NYU, Nassim Nicholas Taleb, published his new book Antifragile.

Antifragile is a term Taleb defines to describe things that benefit more (have more upside) from random events or shocks, than they are harmed by (have downside).

In other words, antifragile things are those that benefit from stress and disorder.

Inevitably, this  ' E=MC2 ' book will change the foundations of Risk Management coming decade. Antifragile should be qualified as 'compulsory reading' for all actuaries, CFO's, CEO's and risk or investment managers.

It's impossible to summarize Taleb's Antifragile insights in a single blog, Therefore I'll focus on some examples and the major principles.

Also I would like to point at two more less known and 'mathematical based' text-books(downloadable and in progress) that are related to his popular (non-mathematical) book Antifragile:
  1. Taleb Textbook: Fat Tails Math, Probability and Risk in the Real World
  2. Taleb Textbook: Fat Tails and (Anti)fragility 

What's Investment Risk?
In a presentation ("Actuaris: From Backroom to Boardroom"; Dutch) to over 200 actuarial professionals at 'Actuarieel Podium' on October 1st 2013 in Utrecht, Jos Berkemeijer discussed, questioned and challenged some major actuarial profession principles. One of these actuarial principles is the:

Concept of Investment Risk

Inspired by Taleb's view on investment risk, I asked my audience to rank the next randomly presented stock charts in order of decreasing risk.

Can you manage?

As expected, most actuaries chose Stock Chart I or II as 'most risky'. Apart from a few Taleb-conscious actuaries, all of them chose Chart III as 'least risky'.

And that last choice is indeed the choice we're trained to qualify as least risky. The way we're brought up, is that risk equals volatility, ultimately resulting in a dangerous and wrong conclusion: non-volatility = 'no risk'.

However, according to Taleb, the opposite is true: Chart III represents the most risky stock.


Because the company or investment fund that's behind Stock Chart III doesn't have any real experience with 'managing risk' at all !!

Taleb's Turkey
In another way, Stock Chart II is risky as well. Chart III shows limited risk and exponential growth.
As Isaac Newton already stated: What goes up must come down
Therefore Stock III is a risky investment as well, despite it's limited volatility.

The fact that Chart II Stocks must come down is well illustrated by Taleb's Turkey example   

"A turkey is fed by a butcher.  Every day it is confirmed to the turkey and the turkey’s economics department and the turkey’s risk management department and the turkey’s analytical department that the butcher loves turkeys. And every day brings more confidence to that statement. 
The butcher will keep feeding the turkey until a few days before Thanksgiving. Then comes that day when it is really not a very good idea to be a turkey.

So with the butcher surprising it, the turkey will have a revision of belief—right when its confidence in the statement that the butcher loves turkeys is maximal and “it is very quiet” and soothingly predictable in the life of the turkey.

This example also makes clear that black swans are not just big negative impact events. The events of a black swan event depend on the position of the observer.

Least Risky
At the end we have to conclude that, despite the largest volatility, Stock III is the least risky investment, because the company or investment fund behind this stock chart, has learned to 'deal' with risk.

Dealing with investment risk is just like raising your child. You try to protect your child against life threatening events (defaults), while at the same time you encourage it to take limited (non life threatening) risks, so it may learn to prevent and absorb damages (losses) in order get better in resisting future other risks. 

Or.., to put it in a philosophical way, as defined by rabbi Anthony Glickman:

 “Life is long gamma.”
“Life benefits from volatility and variability”

Antifragile Essentials
Now after this popular intro, let's conclude with some fundamental principles of Taleb:
  1. Antifragile
    An investment portfolio (strategy) can be qualified as 'Antifragile' if it benefits more form shocks (high-impact events or extreme volatility, up to a certain level) than it suffers.

  2. Optionality & Investment Strategy
    • What makes you antifragile?
      Executing a option strategy
    • Traditional investment strategies: 'too much focus'
      Traditional investment strategies (e.g. Mean-Variance optimization, profit maximization or risk budgeting) all have explicit goals ('focus') that make their performance outcomes very parameter and model dependent. Because 'medium' risks can be subjected to huge measurement errors, the often 'medium' or 'moderate' risk attitude of these strategies can become catastrophical.

      Traditional investment strategies are not designed to explicitly cope with Negative Black Swans events. Neither are they designed to profit from 'disorder clusters': volatility, uncertainty, disturbances, randomness and stressors.

      Most important: traditional investment strategies are not set for maximal profiting of Positive Black Swans!
    • Barbell strategy
      The essence of an 'optionality investment strategy' ('barbell strategy') can be formulated as a 'dual attitude' of extreme risk aversion by playing it ultimate safe in some areas (robust to negative Black Swans) and extreme 'risk loving' by taking a lot of small risks in others (open to positive Black Swans), hence achieving antifragility.

      As a consequence this barbell-strategy reduces the downside risk, e.g. the elimination of the risk of ruin. In fact any strategy that removes the risk of ruin is a kind of barbell strategy. It's a strategy of limited loss and large possible outcome.
    • More Data, Better Outcome?
      Quit contrary to what we as actuaries would expect, Taleb explains in his book Antifragile that the more data you get, the less you know what’s going on, and the more iatrogenics (damage from treatment in excess of the benefits) you will cause.

Some risks are simply too small or too big to Tail. Try to approach them in an Antifragile way.....

Although the new insights and theories of Taleb are quit appealing, there's still a lot of work to do to make it work in practice.

Fortunately, you may read Taleb's book Antifagile online, or simply download it.


Taleb Links

Other Link