Sustainable Discount Rates

Steering pension funds on a 'one point' Coverage Ratio is like trying to proof global warming on a hot summer day...... It's useless.

Why?

First of all the complete pension fund balance sheet is based on market value.

As there is no substantial market for pension liabilities, this implies that pension liabilities have to be valued on basis of some kind of arbitrary (artificial) method.

In the U.S. this has led to the (irresponsible) high discount rate of 8% for state pension funds based on the 'expected' long term return without a kind of correction (subtraction) for 'risk'.

In de Dutch market, pension funds have to rate their liabilities on basis of a maturity dependable risk free interest rate, the ‘Nominal interest Rate Term Structure’ (RTS), as ordered by DNB (the Dutch Regulator).

Here's the outcome of this risk free interest rate (RTS) over the past 10 years, including the 10-y average RTS...

Ever since DNB ordered this 'artificial discounting method', pension fund board members didn't get a good night sleep. As the RTS juggles on a daily basis, every morning pension members wake up with the latest 'RTS news surprise of the day'.

You can play the RTS juggle (worm) here:

As coverage ratios are based on the RTS, they shuttle hither and thither as well and executing a long term pension fund strategy becomes more or less like riding the famous (market) bull in a rodeo show.

On a Dutch IPE congress, Angelien Kemna - chief investment officer of the €270bn asset manager APG - warned that the current swap-curve discount criterion forces pension funds to take unwise "significant long-term measures".

Kemna favors an average yield curve or a more straightened version of the current one for discounting liabilities.

The new Dutch Pensions Agreement foresees that pension funds can choose their own discount rate, as pensions are no longer guaranteed!

Indeed, it's time to stop this complex discount circus. But it's also time to stop 'one point estimate' Coverage Ratio steering.

A new look
Let's take a look at a characteristic discount rate dependence of a traditional pension fund like ABP.

Valuing ABP at an (derived average) RTS of 2.69%  (September 2011), ABP's discounted assets fail to meet the discounted liabilities, leading to a coverage ratio of around 90%.

However this kind of risk free valuing is - for sure - too conservative, as ABP's aims at an underpinned strategic expected return of 6,1% on the long term and has a convincing track record of  5 and 10-year moving average returns:

Returns (%) Pension Fund ABP 2993-2010
Year	1993	1994	1995	1996	1997	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010
Yearly Return	16.5	-1.0	16.4	11.8	11.9	12.9	10.0	3.2	-0.7	-7.2	11.0	11.5	12.8	9.5	3.8	-20.2	20.2	13.5
5Y MA Return					10.9	10.2	12.6	9.9	7.3	3.4	3.0	3.3	5.2	7.2	9.7	2.7	4.2	4.4
10Y MA Return										7.1	6.6	7.8	7.5	7.3	6.5	2.9	3.8	4.8

Or in Graphics:

As long as a pension fund (like ABP) continues to perform (on 5 or 10-years moving average) rates that outperform the (derived average) risk free discount rate, it's seems ridiculous to force such a pension fund to discount at a 'risk free rate', as this obliges the fund to change his strategic asset mix to a less risky mix and an suboptimal return.
In turn, these suboptimal returns will lead to an asset shortage. With a vicious cycle of decreasing risk as a fatal result in the end.

Sustainable Discount Rates
In an excellent discussion paper (2006) Jürg Tobler-Oswald proves that the optimal discount rate lies between the risk free rate (RFR) and the investment strategy’s expected return (ER) depending on how good the hedge against the fund’s cash  flow  provided by its investments  is:

Discount Rate₁ = RFR + F_{Cash Flow}(RFR-ER)

Another - more simple and practible - discount rate could be defined as the average between the free discount rate and the X-year (e.g. X=5, or 10) Moving Average Return of the last X-Years (MAR(X)).

Discount Rate₂ = [ RFR + MAR(X) ] /2

As long as MAR(10), MAR(5) and ER stay larger than the interest rate that matches a coverage ratio of 100%, discounting by means of one of the new sustainable discount methods seems sound and safe......

Whats left is that the average (geometric) risk premiums during the last 10 years have turned out negative:

Historical Equity Risk Premiums (ERP)
	ERP: Stocks minus T.Bills		ERP: Stocks minus T.Bonds
Period	Arithmetic	Geometric	Arithmetic	Geometric
1928-2010	7.62%	5.67%	6.03%	4.31%
1960-2010	5.83%	4.44%	4.13%	3.09%
2000-2010	1.37%	-0.79%	-2.26%	-4.11%

This implies (moreover) that it is important that the discounting rate of a pension fund should be based on a sustainable sound weighted mix of:
(1) proven historical performance
(2) a 'save' risk free rate
(3) realistic future return assumptions


Related Links/ Sources
- Kemna IPE article (2011)
- An investment based valuation approach for pension fund cash flows (2006)
- Ignoring the risk in risk premium in State Pensions(2011)
- DB: What went wrong? (2011)
- Actuary.org: Pension Fund Valuation and Market Values (2000)
- Aswath Damodaran: Equity-risk-premiums-2011-edition
- Dutch: ABP coverage ratio

What's a Greek Tragedy?

As actuaries we do not believe in miracles, or do we?

According to a 'strictly confidential' document from the Troika (= EC, IMF & ECB), Greek's Debt/GDP ratio suddenly raised from 149% to 186% in 2013!

This new insight causes a 'potential need for additional official financing' ranging up to €440 billion!! (are you still with me?)

Let's take a look at how Debt/GDP ratio developed in the past and the new optimistic Troika forecast (red line).

Just to help the Troika, I've added a non-miracle 'Maggid' forecast based on simple and more realistic economic principles.

Not a word in the Troika report about the drivers and cultural changes that are necessary to achieve a long term decrease of the Debt/GDP ratio. Everything is based on  suggestive mathematical art.

Continue throwing good money after bad, is not the way forward. Greece will first have to show that it is not only willing, but also achieving debt reduction. Current measures are insufficient. Start for example to raise retirement age to 65 as a beginning...

Let's pray European leaders give up Keynesian miracle thinking and take the right decision:

Stop helping Greece to finance their debt, unless Greece shows strong progress in reducing debt itself every month .

If not.., the line 'A Greek Tragedy' will get a new meaning....

Sources/Links:
- Troika report
- Zerohedge: Greece
- Retirement around the globe blog

Humor: Actuary Scrooge

Today's Brainer:What's the difference between a pension fund and an investment fund?

Actuary $crooge shows...

source

On Line DIY European Stress Test

Thomson Reuters' Breakingviews now presents an on line DIY stress test. Change the Tier 1 ratio and haircuts of the PIIGS countries and find out the capital shortfall of Europe and the shortfal of individual European banks.

An explanation can be found here and there is also an Excel spreadsheet.

Enjoy stress testing!

What's a world without Jobs?

On Wednesday night 5th October, Apple co-founder, former CEO and chairman Steve Jobs, passed away..



Steve Jobs' life is an example to all of us. In an excellent and catching speech, Steve urged graduates to pursue their dreams and pick up the opportunities in life's setbacks at the university's 114th Commencement on June 12, 2005.



What - besides Steve's phenomenal contributions to computer technology and marketing - did Steve contribute to the profession of Risk Management?

Steve Jobs' Risk Management Lessons
Here are (derived from his 2005 Stanford speech) some inspiring lessons from Steve. Lessons we can apply 'one to one' on Risk Management (my comments in Italic):

• Connect 'the dots' in life
  It's impossible to connect the dots looking forward,you can only connect them looking backwards, later in life.  Do so!
  
  
  
  To turn Risk Management into an opportunity, we can't look in a crystal ball. We'll have to explore and have to allow ourselves some experiments and non-conventional ideas to finally see the bigger picture that turns marginal new business developments into one new final integral success!
  
  Try to develop 'Risk Oversight' (connecting the dots) as Risk Oversight is negatively related to risk and positively related to shareholder value (Research Stanford University).
  
  
• Trust
  You have to trust that the dots will somehow connect in your future.
  Believe in something and follow your heart, even if it leads you of the well-worn path..
  
  Make Risk management supportive and not dominant to what you want to achieve in life or business. It's positive when  companies Ideas and Vision sometimes conflict with inner and outer notions.
  
  To grow a plant (company)  in soil (society) is takes opposite 'nutrients' (and circumstances) like water and sun that feed your seed (idea).
  
  
  
  
  Accept that your heart, gut feeling and helicopter view are sometimes more leading than the rationale of your Risk management (what your brain thinks). The more and the longer you are able to manage this paradox, the more likely success will come your way eventually. 
  
  Keep all the above decision elements in ('a paradoxical') place. Remember  Shareholder Value and Sustainability are a function of Risk, so don't pull the plug too soon!
  
  
• Love and Loss
  
  
  Making mistakes is an inherent part of life and doing business.
  
  If you (or something you started) fails, start over!
  
  The effect of less sureness by 'starting over', inspires for exploring new directions and becoming creative again.
  
  'Love what you do' is the most important leading statement to proceed in life and business.
  
  'Sometimes life hits you with a brick'. Don’t lose faith.Your time is limited, so don’t waste it living someone else’s life.
  
  Risk Management exists by the grace of losses that occur. Accept that as a fact. Therefore, if no losses occur anymore, your Risk Management program is actually dead without a clue. It will certainly fail eventually.
  
  
  
  Getting knocked down by a 'brick' like in the current financial crisis, is a sign that we have to redesign our Risk Management programs instead of intensifying existing programs like Basel II /III and Solvency II. Get out!
  
  New Risk Management will have to focus on how to prevent and to DEAL with risk, instead of sophisticated capitalizing risk as Dead Risk Capital. Rather than focus on reducing risk, risk-transformation — that is, capitalizing risk in such a way that its value creation potential is maximized - seems the right way forward.
  
  
• Death
  If you live each day as if it was your last, someday you'll most certainly be right. Remembering you'll die is the most important tool to help you make the big choices in life. Because almost everything — all external expectations, all pride, all fear of embarrassment or failure - these things just fall away in the face of death, leaving only what is truly important.
  
  Remembering that you are going to die is the best way to avoid the trap of thinking you have something to lose.
  
  
  
  
  Risk Management is about making choices and giving up less important issues for more important.
  It's about generating focus on what really matters for sustainability or results, instead of trying to manage everything.
  
  Good Risk management therefore urges for CEO and Board rewards that reflect the downside risk of a company's default instead of just rewarding upward and short term profit.
  
  Company bonuses should therefore be positive as well as negative performance related.  

 Remember, just like Steve Jobs, Risk Management is about 'failing better than anyone else' .....


Related/Sources:
- Steve Jobs: He Thinks Different (2004)
- Was Steve Jobs Practicing Proactive Risk Management? (2010)
- The Role of the Board in Corporate Risk Oversight (Stanford University 2010)
- Dead Risk Capital

Pension Gamification

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

Life is a Game

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

Small Population Compliance Samples

My last post, Compliance Sample Size, demonstrated the set up of an efficient sample method for compliance tests in case of large populations.

What if population size is relatively small ?, some actuaries asked me....

In this case you can ( instead of the beta distribution) make use of the hypergeometric distribution for calculating confidence levels.

Here's the same example as I used in my blog 'Compliance Sample Size', but now for a population of 100 .


'Compliance Check' Example (N=100)
As you probably know, pension advisors have to be compliant and  meet strict federal, state and local regulations.

On behave of the employee, the sponsoring employer as well as the insurer or pension fund, all have a strong interest that the involved 'Pension Advisor' actually is, acts and remains compliant.

PensionAdvice
A professional local Pension Advisor firm, 'PensionAdvice' (fictitious name), wants 'compliance' to become a 'calling card' for  their company. Target is that 'compliance' will become a competitive advantage over its rivals.

You, as an actuary, are asked to advise on the issue of how to verify PensionAdvice's compliance....... What to do?

• Step 1 : Compliance Definition
  First you ask the board of PensionAdvice  what compliance means.
  After several discussions compliance is in short defined as:
  
  
  1. Compliance Quality
     Meeting the regulator's (12 step)  legal compliance requirements
     ('Quality Advice Second Pillar Pension')
     
     
  2. Compliance Quantity
     A 100% compliance target of PensionAdvice's portfolio, with a 5% non-compliance rate (error rate) as a maximum on basis of a 95% confidence level.
  .
  
• Step 2: Check on the prior believes of management
  On basis of earlier experiences, management estimates the actual NonCompliance rate at 8% with 90% confidence that the actual NonCompliance rate is 8% or less:
  
  If management would have no idea at all, or if you would not (like to) include management opinion, simply estimate both (NonCompliance rate and confidence) at 50% (= indifferent) in your model.
  
  
• Step 3: Define Management Objectives
  After some discussion, management defines the (target) Maximum acceptable NonCompliance rate at 5% with a 95% confidence level (=CL).
  
  
• Step 4: Define population size
  In this case it's simple. PensionAdvice management knows for sure the portfolio they want to check for compliance, consists of 100 files: N=100.
  
  This is how step 2 to 4 look in your spreadsheet...
  
  
  
  
  
  
• Step 5 : Define Sample Size
  Now we get to the testing part....
  
  
  
  
  
  Before you start sampling, please notice how prior believes of management are rendered into a fictitious sample (test number = 0) in the model:

• In this case prior believes match a fictitious sample of size 25 with zero noncompliance observations. 
• This fictitious sample corresponds to a confidence level of 77% on basis of a maximum (population) noncompliance rate of 5%.

[ If you think the rendering is to optimistic, you can change the fictitious number of noncompliance observations from zero into 1, 2 or another number (examine in the spreadsheet what happens and play around).]


To lift the 77% confidence level to 95%, it would take an additional sample size of 20 - with zero noncompliance outcomes (you can check this in the spreadsheet).
As sampling is expensive, your employee Jos runs a first test (test 1) with a sample size of 10 with zero noncompliance outcomes. This looks promising!
The cumulative confidence level has risen from 76% to over 89%.


You decide to take another limited sample with a sample size of 10. Unfortunately this sample contains one noncompliant outcome. As a result, the cumulative confidence level drops to almost 75% and another sample of size 20 with zero noncompliant outcomes is necessary to reach the desired 95% confidence level.

You decide to go on and after a few other tests you finally arrive at the intended 95%cumulative confidence level. Mission succeeded!

Evaluation
The interesting aspects of this method are:

1. Prior (weak or small) samples or beliefs about the true error rate and confidence levels, can be added in the model in the form of an (artificial) additional (pre)sample.
   
   
2. As the sample size increases, it becomes clear whether  the defined confidence level will be met or not and if adding more samples is appropriate and/or cost effective.
   

This way unnecessary samples are avoided, sampling becomes as cost effective as possible and auditor and client can dynamically develop a grip on the distribution. Enough talk, let's demonstrate how this works.

Another great advantage of this incremental sampling method is that if noncompliance shows up in an early stage, you can

• stop sampling, without having made major sampling cost
• Improve compliance of the population by means of additional measures on basis of the learnings from the noncompliant outcomes
• start sampling again (from the start) 

If - for example -  test 1 would have had 3 noncompliant outcomes instead of zero, it would take an additional test of size 57 with zero noncompliant outcomes tot achieve a 95% confidence level.  It's clear that in this case it's better to first learn from the 3 noncompliant outomes, what's wrong or needs improvement, than to go on with expensive sampling against your better judgment.

D. Conclusions

On basis of a prior believe that - with 90% confidence - the population is  8% noncompliant, we can now conclude that after an additional total sample of size 40, PensionAdvice's noncompliance rate is 5% or less with a 95% confidence level.

If we want to be 95% sure without 'prior believe', we'll have to take an additional sample of size 25 with zero noncompliant outcomes as a result.

E. Check out: DOWNLOAD EXCEL
You can download the next Excel spreadsheets to check the Demo or tot set up your own compliance test:

- Small population Compliance test DEMO
- Small population Compliance test BLANK
- Large population Compliance test

Enjoy!

Compliance: Sample Size

How to set an adequate sample size in case of a compliance check?

This simple question has ultimately a simple answer, but can become a "mer à boire" (nightmare) in case of a 'classic' sample size approach.....

In my last-but-one blog called 'Pisa or Actuarial Compliant?', I already stressed the importance of checking compliance in the actuarial work field.

Not only from a actuarial perspective compliance is important, but also from a core business viewpoint:

Compliance is the main key driver for sustainable business

Minimizing Total Cost by Compliance
A short illustration: We all know that compliance cost are a part of Quality Control Cost (QC Cost) and that the cost of NonCompliance (NC Cost) increase with the noncompliance rate. 

Mainly 'NC cost' relate to:

• Penalties or administrative fines of the (legal) regulators
• Extra  cost of complaint handling
• Client claims
• Extra administrative cost 
• Cost of legal procedures

Sampling costs - on their turn -  are a (substantial) part of QC cost.

More in general now it's the art of  good practice compliance management, to determine that level of maximal noncompliance rate, that minimizes the total cost of a company.



Although this approach is more or less standard, in practice companies revenues depend strongly on the level of compliance. In other words: If compliance increases, revenues increase and variable costs decrease.

This implies that introducing 'cost driven compliance management' - in general - will (1) reduce  the total cost and (2) mostly make room for additional investments in 'QC Cost' to improve compliance and to lower variable and total cost.

In practice you'll probably have to calibrate (together with other QC investment costs) to find the optimal cost (investment) level that minimizes the total cost as a percentage of the revenues.

As is clear, modeling this kind of stuff is no work for amateurs. It's real risk management crafts-work. After all, the effect of cost investments is not sure and depends on all kind o probabilities and circumstances that need to be carefully modeled and calibrated.

From this more meta perspective view, let's descend to the next down to earth 'real life example'.

'Compliance Check' Example
As you probably know, pension advisors have to be compliant and  meet strict federal, state and local regulations.

On behave of the employee, the sponsoring employer as well as the insurer or pension fund, all have a strong interest that the involved 'Pension Advisor' actually is, acts and remains compliant.

PensionAdvice
A professional local Pension Advisor firm, 'PensionAdvice' (fictitious name), wants 'compliance' to become a 'calling card' for  their company. Target is that 'compliance' will become a competitive advantage over its rivals.

You, as an actuary, are asked to advise on the issue of how to verify PensionAdvice's compliance....... What to do?

• Step 1 : Compliance Definition
  First you ask the board of PensionAdvice  what compliance means.
  After several discussions compliance is in short defined as:
  
  
  1. Compliance Quality
     Meeting the regulator's (12 step)  legal compliance requirements
     ('Quality Advice Second Pillar Pension')
     
     
  2. Compliance Quantity
     A 100% compliance target of PensionAdvice's portfolio, with a 5% non-compliance rate (error rate) as a maximum on basis of a 95% confidence level.
  
  The board has no idea about the (f)actual level of compliance. Compliance was- until now - not addressed on a more detailed employer dossier level.
  Therefore you decide to start with a simple sample approach.
  
  
• Step 2 : Define Sample Size
  In order to define the right sample size, portfolio size is important.
  After a quick call PensionAdvice gives you a rough estimate of their portfolio: around 2.500 employer pension dossiers.
  
  You pick up your 'sample table spreadsheet' and are confronted with the first serious issue.
  
  
  An adequate sample (95% confidence level) would urge a minimum of 334 samples. With around 10-20 hours research per dossiers, the costs of this size of this sampling project would get way out of hand and become unacceptable as they would raise the total cost of  PensionAdvice (check this, before you conclude so!).
  
  Lowering confidence level doesn't solve the problem either. Sample sizes of 100 and more are still too costly and confidence levels of less than 95% are of no value in relation to the clients ambition (compliance= calling card).
  The same goes for higher - more than 5% - 'Error Tolerance' .....
  
  By the way, in case of samples for small populations things will not turn out better. To achieve relevant confidence levels (>95%) and error tolerances (<5%), samples must have a substantial size in relation to the population size.
  
  
  
  
  You can check all this out 'live', on the next spreadsheet to modify sampling conditions to your own needs. If you don't know the variability of the population, use a 'safe' variability of 50%. Click 'Sample Size II' for modeling the sample size of PensionAdvice.

• Step 3: Use Bayesian Sample Model
  
  
  The above standard approach of sampling could deliver smaller samples if we would be sure of a low variability.
  
  Unfortunately we (often) do not know the variability upfront.
  
  Here comes the help of a method based on efficient sampling and Bayesian statistics, as clearly described by Matthew Leitch.
  
  A more simplified version of Leitch's approach is based on the Laplace's famous  'Rule of succession', a classic application of the beta distribution ( Technical explanation (click) ).
  
  The interesting aspects of this method are:
  
  1. Prior (weak or small) samples or beliefs about the true error rate and confidence levels, can be added in the model in the form of an (artificial) additional (pre)sample.
     
     
  2. As the sample size increases, it becomes clear whether  the defined confidence level will be met or not and if adding more samples is appropriate and/or cost effective.
This way unnecessary samples are avoided, sampling becomes as cost effective as possible and auditor and client can dynamically develop a grip on the distribution. Enough talk, let's demonstrate how this works.

Sample Demonstration

The next sample is contained in an Excel spreadsheet that you can download and that is presented in a simplified  spreadsheet at the end of this blog. You can modify this spreadsheet (on line !) to your own needs and use it for real life compliance sampling. Use it with care in case of small populations (n<100).

A. Check on the prior believes of management

Management estimates the actual NonCompliance rate at 8% with 90% confidence that the actual NonCompliance rate is 8% or less:



If management would have no idea at all, or if you would not (like to) include management opinion, simply estimate both (NonCompliance rate and confidence) at 50% (= indifferent) in your model.

B. Define Management Objectives

After some discussion, management defines the (target) Maximum acceptable NonCompliance rate at 5% with a 95% confidence level (=CL)



C. Start ampling
Before you start sampling, please notice how prior believes of management are rendered into a fictitious sample (test number = 0) in the model:

• In this case prior believes match a fictitious sample of size 27 with zero noncompliance observations. 
• This fictitious sample corresponds to a confidence level of 76% on basis of a maximum (population) noncompliance rate of 5%.

[ If you think the rendering is to optimistic, you can change the fictitious number of noncompliance observations from zero into 1, 2 or another number (examine in the spreadsheet what happens and play around).]

To lift the 76% confidence level to 95%, it would take an additional sample size of 31 with zero noncompliance outcomes (you can check this in the spreadsheet).
As sampling is expensive, your employee Jos runs a first test (test 1) with a sample size of 10 with zero noncompliance outcomes. This looks promising!
The cumulative confidence level has risen from 76% to over 85%.



You decide to take another limited sample with a sample size of 10. Unfortunately this sample contains one noncompliant outcome. As a result, the cumulative confidence level drops to almost 70% and another sample of size 45 with zero noncompliant outcomes is necessary to reach the desired 95% confidence level.

You decide to go on and after a few other tests you finally arrive at the intended 95%cumulative confidence level. Mission succeeded!



The great advantage of this incremental sampling method is that if noncompliance shows up in an early stage, you can

• stop sampling, without having made major sampling cost
• Improve compliance of the population by means of additional measures on basis of the learnings from the noncompliant outcomes
• start sampling again (from the start) 

If - for example -  test 1 would have had 3 noncompliant outcomes instead of zero, it would take an additional test of size 115 with zero noncompliant outcomes tot achieve a 95% confidence level.  It's clear that in this case it's better to first learn from the 3 noncompliant outomes, what's wrong or needs improvement, than to go on with expensive sampling against your better judgment.

D. Conclusions

On basis of a prior believe that - with 90% confidence - the population is  8% noncompliant, we can now conclude that after an additional total sample of size 65, PensionAdvice's noncompliance rate is 5% or less with a 95% confidence level.

If we want to be 95% sure without 'prior believe', we'll have to take an additional sample of size 27 with zero noncompliant outcomes as a result.

E. Check out
Check out, download the next spreadsheet. Modify sampling conditions to your own needs and download the Excel spreadsheet.


Finally
Excuses for this much too long blog. I hope I've succeeded in keeping your attention....


Related links / Resources

I. Download official Maggid Excel spreadsheets:
- Dynamic Compliance Sampling (2011)
- Small Sample Size Calculator

II. Related links/ Sources:
- 'Efficient Sampling' spreadsheet by Matthew Leitch
- What Is The Right Sample Size For A Survey?
- Sample Size
- Epidemiology
- Probability of adverse events that have not yet occurred
- Progressive Sampling (Pdf)
- The True Cost of Compliance
- Bayesian modeling (ppt)

Humor: Actuarial Stress Test

Calvin and Hobbes as Manager and Actuary....

Original source: Tonks17
Homepage UK Calvin and Hobbes

Pisa or Actuarial Compliant?

When we talk about actuarial compliance, we usually limit this to our strict actuarial work field.
In a broader sense as 'risk managers', we (actuaries) have a more general responsibility for the sustainability of the company we work for.

Compliance is not just about security, checks, controls, protection, preventing fraud, ethical behavior. Moreover  compliance is the basis of adequate risk management and delivering high standard service and products to your companies clients.

Pisa Compliant
No matter how brilliant and professional our calculations, if the data - on which these calculations are based on -  are 'limited', 'of insufficient quality' or 'too uncertain', we as actuaries will finally fail.

Therefore , building actuarial sandcastles is great art, however completely useless. Matthew 7:26 tells us :  it's a foolish man who builds his actuarial house on the sand....

And so, let's take a look if we have indeed become 'Pisa Compliant' by checking if our actuarial compliance is build on sand or on solid ground. In other words: let's check if actuarial compliance itself is compliant...nd.

Actuarial Data Governance
To open discussion, let's start with some challenging Data Governance questions:

• Data quality compliance
  How is 'data quality compliance' integrated in your actuarial daily work? Have you addressed this issue? And if so, do you just rely on statements and reports of others (auditors, etc), can you agree upon the data quality standards (if there are any). In other words: are the data, processes and reports you base you calculations on, 100%  reliable and guaranteed? If not, what's the actual confidence level of your data en do you report about this confidence level to the board?
  
  
• 
  Data quality Conformation
  Have you checked your calculation data  set on bases of samples or second opinions?
  
  And if so, do you approve with the methods used, the confidence level and the outcome of the data audit? 
  
  Or do you just 'trust' on the blue eyes of the accountant or auditor and formally state you're "paper compliant"?
  
  Did you check if  client information, e.g. pension benefit statement, are not only in line with the administrative data, but also in line with insurance policy conditions or pension scheme rules?
  
  
• Up to date, In good time
  To what quantitative level is the administrative data  'up to date' and is it transparent?
  
  Do you receive administrative backlog and delays reporting and tracking and if so, how do you translate these findings in your calculations?
  
  
• Outsourcing
  From a risk management perspective, have you formulated quantitative and qualitative demands (standards) in outsourced contracts, like 'asset management', 'underwriting'  and 'administration' contracts?
  
  Do you agree on these contracts, do 'outsourcing partners' report on these standards and do you check these reports regularly on a detail level (samples)? 

And some more questions you have to deal with as an actuary:

• Distribution Compliance
  Is the intermediary and are the employers and customers your company deals with, compliant? What's the confidence level of this compliance and in  case of partially noncompliance, what could be the financial consequences? (Claims)
  
  
• Communication Compliance
  Is communication with employees, customers, regulators, supervisors and shareholders compliant? Has your board (and you!) defined what compliance actually means in quantitative terms?
  
  
  
  Is 'communication compliance' based on information (delivery and check) or on communication?
  
  In this case, have you've also checked if  (e.g.) customers understood what you tried to tell them?
  
  Not by asking if your message was understood, but by quantitative methods (tests, polls, surveys, etc) that undisputed 'prove' the customer really understood the message.
  
  
  
  Effective Communication Practice
  Never ask if someone has understood what you've said or explained. Never take for granted someone tells you he or she 'got the picture'.
  
  Instead act as follows: At the end of every (board) presentation, ask that final and unique question of which the answer  assures you, your audience has really understood what your tried to bring across.

Checking Compliance

Now we get to the quantitative 'hard part' of compliance:

How to check compliance?

This interesting topic will be considered in my next blog.... ;-)

To lift a little corner of the veil, just a short practical tip to conclude this blog:

Compliance Sample Test
From a large portfolio you've taken a sample of 30 dossiers to check on data quality. All of them are found compliant. What's the upper limit of the noncompliance rate in case of a 95% confidence level?

This type of question is a typical case of:

“If nothing goes wrong, is everything alright?”

Answer.

The upper limit can be roughly estimated by a simple rule of thumb, called 'Rule of three'....

'Rule of three for compliance tests'

If no noncompliant events occurred in a compliance test sample of n cases, one may conclude with 95% confidence that the rate of  noncompliance will be less than  3/n.

In this case one can be roughly 95% sure the noncompliance rate is less than 10% (= 3/30). Interesting, but slightly disappointing, as we want to chase noncompliance rates in the order of 1%.

Working backwards on the rule of three, a 1% noncompliance rate would urge for samples of 300 or more. Despite the fact that research for 46 international organizations showed that on average, noncompliance cost is 2.65 times the cost of compliance, this size of samples is often (perceived as) too cost inefficient and not practicable.

Read my next blog to find out how to solve this issue....

Related Links:
- Actuarial Compliance Guidelines
- What Is The Right Sample Size For A Survey?
- Epidemiology
- Probability of adverse events that have not yet occurred
- The True Cost of Compliance (2011)
- 'Rule of three'
- Compliance testing: Sampling Plans (accounting standards) or Worddoc

Humor: Merkozy, It's too late

Comparing 5 year exchange rates USD/EUR (decline : 17%) and USD/CNY (decline 21%) clearly shows the negative outlook of the US Dollar.

Both U.S. and Europe, are facing severe debt problems they can not solve with more debt.

Desperate actions
President Obama tries to stimulate economy by creating 1.5 mln new jobs with a $ 450 billion investment (American Job Act).

In Europe president Merkel (Germany) and Sarkozy (France) have joint their strengths and totally different characters into 'one personality', to create not only a strong financial but also economic European union.

This new economic union is necessary to establish a firm grip on the measures that weak financial European countries like, Greece, Italy, Ireland, Spain and Portugal have to take to recover from their debt.

It's too late
Unfortunately there's no support for such an initiative. Unluckily, no Merkozy will be able to prevent Europe from a financial meltdown.

The  only way out seems a European split in relative strong and weak countries.

Make up your mind on the geographic spread of the assets of your company. Get out before it's too late....

Irrational Risk

Actuarial work is demanding..., so you're arriving late at your hotel that night. The hotel manager has only two rooms left. These two rooms are exactly the same, except for one aspect: The fire alarm.....

The manager tells you that in the event of a nighttime fire due to the usual causes, guests in Room 1, equipped with Alarm 1, have an actuarial calculated  2% chance of dying. Guests in Room 2, equipped with Alarm 2, have only a 1% chance of dying.

However - things in life are always complicated -  there's a slight problem.....

According to the manager...... The wiring of Alarm 2 is such that it sometimes causes electrical fires that increase the risk of dying in a nighttime fire by an additional 0.01%.

In other words, Alarm 1 is associated with a 2% risk of death and Alarm 2 is associated with a 1% + 0.01% (betrayal) risk of death.

What room do you choose as a professional actuary?

Outcome
According to a study by Gershoff and Koehler, most participants choose the room with Alarm 1. This,  even though this room 1 has double the increased risk of fire death, according the researchers. Reason: most participants found the tiny risk of "betrayal" (product malfunction) much more frightening than the much larger risk of actually dying.  When people get upset by a tiny risk, they often paradoxically choose the much larger risk.

Personally I think a more imaginable risk 'weighs' stronger than a non-specific abstract risk and in general people are unaware of conditional probability effects......

Conclusion

This simple example proofs that emotion has a strong influence on risk decisions.

Just like in our actuarial profession, risk decisions are often irrational.

It is our duty as actuaries to demystify and to rationalize risk. However, sometimes we're victim of the same emotional bias....




Read more about this interesting subject on:

- Vaccination and betrayal aversion (2011)
- Safety First? The Role of Emotion in Safety Product Betrayal Aversion (2011)

- The Risk-as-feelings hypothesis in a Theory-of-planned-behaviour
- Behavioral economics: the missing link in the financial crisis-  
- Decisions are Never Emotional

U.S. Debt Autopsy

Coming back from vacation, the world seems lost. You don't need to be an actuary to grasp that the recent decision to lift the U.S. debt ceiling is first class trickery and completely inadequate.

What the Chinese rating agency Dagong already concluded back  in November 2010, is only now (August 5, 2011) reluctantly and partly followed by S&P:

U.S. AAA status = Dead.

It's interesting to see which countries Dagong rates lower than  the three famous rating Agencies in the U.S.  (download complete Dragon report).

Meanwhile Dagong downgraded the U.S. again to an ordinary A-status on august 2, 2011.

The arguments for country degrades (as the U.S.) are as much clear as simple: if lifting debt ceilings is not at the same time combined with serious debt reduction measures (spending cuts), you go DOWN!

The outlook on the U.S. is still negative.

Outlook
Let's take look at what happened during 2011 and what 2012 will bring..

This chart instantaneously makes clear what's happening:

• Jan 2011 -  half May 2011
  Although  the whole world can figure out that the original debt ceiling of  $14.294 trillion will be reached within a few months, no measures or actions are taken by the U.S. Treasury to prevent a debt default,.
  
  
• May 16, 2011 - August 1,  2011
  Treasury Secretary Timothy Geithner informs Congress he will start tapping into federal pension funds on Monday to free up borrowing capacity as the nation hits the $14.294 trillion legal limit on its debt.
  
  By these and (possible) other optical actions the actual debt is kept artificially stable, slightly above the first ceiling. Of course the factual debt will (non reporting or visible) continue to keep growing.
  
  
• August 1&2, 2011
  The U.S. House of Representatives and the U.S. Senate pass the Budget Control Act on Aug 2, 2011.The debt ceiling is immediately raised by $400 billion, to $14.694 trillion.
  
  A second debt ceiling increase allows the current new ceiling to grow by an additional $500 billion, to $15.194 trillion, so that government can pay its bills until the end of February 2012.  However, Congress has the authority to reject this second increase.
  
  
• August 5, 2011 - March 2012
  
  TresuryDirect reports show the debt catch-up effects on August 5, 2011.
  
  Already $271 billion of the $400 billion debt ceiling lift turns out to be 'consumed'. Another $129 billion is left.
  
  As my two year old son can calculate: If no measures will be effective, around mid September 2011 a new ceiling crisis and media lift-show shall start.
  
  After agreeing in  September to the second ceiling of  $15.194 trillion the muppet debt show will start again in March 2012, when the second ceiling will break.

The party is over
I'm not a pessimistic person by nature, but the U.S. is running out of possible solutions. 

It looks like the financial space flight program is over. 

We'll have to build a society on new ethical financial principles.

If real measures stay out and claims on other countries or banks (as was the case with the sub prime debacle) are limited, the U.S. will unfortunately default in the end.

This U.S. default will take along most western countries.

It will result in a worldwide financial meltdown.

They only way out that seems left is:

Inflation

Let's hope for the best or a miracle. God bless America!



Related Links and Resources:
- Spreadsheet (Excel) with 2011 Debt Data
- S&P Report, August 5, 2011
- TreasuryDirect (U.S. Debt development)
- Debt Ceiling Increase of 2011
- Alert - Just So We Don't Get Confused As To The Source Of Our Little Problem

Humor: Actuarial Mind

In July 2011 holidays  - instead of blogs - are ahead...

Just chew this month on the next actuary no-brainer:

The smartest actuary in the world

The Pope, a well seasoned actuary and a student nurse are flying on an airplane. The captain comes back and says that he has some bad news and some really bad news. The bad news is that the plane is going to crash! As he puts on a parachute and jumps out he says that the really bad news is that there are only 2 more parachutes.

The actuary says: “I am the smartest man in the world. I've just calculated my life expectancy to be more than fifteen years. Excuse me...” With that he puts on a parachute and jumps out.

The Pope says: “Well, my child, I would love to live, but I believe that my time is up. Please take the other parachute and save yourself.”

The student nurse says: “Not to worry Holy Father. Right now the smartest man in the world is trying to find the rip-cord on my back pack!”