Solvency II or Basel III ? Model Fallacy

Managing investment models - ALM models in particular - is a professional art. One of the most tricky risk management fallacies when dealing with these models, is that they are being used for identifying so called 'bad scenarios', which are then being 'hedged away'.

To illustrate what is happening, join me in a short every day ALM thought experiment...

Before that, I must warn you... this is going to be a long, technical, but hopefully interesting Blog. I'll try to keep the discussion on 'high school level'. Stay with me, Ill promise: it actuarially pays out in the end!

ALM Thought Experiment

• Testing the asset Mix
  Suppose the board of our Insurance Company or Pension Fund is testing the current strategic asset mix with help of an ALM model in order to find out more about the future risk characteristics of the chosen portfolio.
   
• Simulation
  The ALM model runs a 'thousands of scenarios simulation', to find out under which conditions and in which scenarios the 'required return' is met and to test if results are in line with the defined risk appetite.
   
• Quantum Asset Return Space
  
  
  In order to stay as close to reality as possible, let's assume that the 'Quantum Asset Return Space' in which the asset mix has to deliver its required returns for a fixed chosen duration horizon N, consists of: 
1. 999,900 scenarios with Positive Outcomes ( POs ),
   where the asset returns weigh up to the required return) and 
2. 100 scenarios with Negative Outcomes ( NOs ),
   where the asset returns fail to weigh up to the required return.
    
Choose 'N' virtual anywhere between 1 (fraction) of a year up to 50 years, in line with your liability duration.
 


• Confidence (Base) Rate
  From the above example, we may conclude that the N-year confidence base rate of a positive scenario outcome (in short: assets meet liabilities) in reality is 99.99% and the N-year probability of a company default due to a lack of asset returns in reality is 0.01%.
   
• From Quantum Space to Reality
  
  
  As the strategic asset mix 'performs' in a quantum reality, nobody - no board member or expert - can tell which of the quantum ('potential') scenarios will come true in the next N years or (even) what the exact individual quantum scenarios are.
  
  Nevertheless, these quantum scenarios all exist in "Quantum Asset Return Space" (QARS) and only one of those quantum scenarios will finally turn out as the one and only 'return reality'.
  
  Which one...(?), we can only tell after the scenario has manifested itself after N years.
   
• Defining the ALM Model
  Now we start defining our ALM Model. As any model, our ALM model is an approach of reality (or more specific: the above defined 'quantum reality') in which we are forced to make simplifications, like: defining an 'average return', defining 'risk' as standard deviation, defining a 'normal' or other type of model as basis for drawing 'scenarios' for our ALM's simulation process.
  Therefore our ALM Model is and cannot be perfect.
  
  Now, because of the fact that our model isn't perfect, let's assume that our 'high quality' ALM Model has an overall Error Rate of 1% (ER=1%), more specific simplified defined as:
1. The model generates Negative Scenario Outcomes (NSOs) (= required return not met) with an error rate of 1%. In other words: in 1% of the cases, the model generates a positive outcome scenario when it should have generated a negative outcome scenario
    
2. The model generates Positive Scenario Outcomes (PSOs) (= required return met) with an error rate of 1%. In other words: in 1% of the cases, the model generates a negative outcome scenario when it should have generated a positive outcome scenario
    

The Key Question!

Now that we've set the our ALM model, we run it in a simulation with no matter how much runs. Here is the visual outcome:

As you may notice, the resulting ALM graph tells us more than a billion numbers....At once it's clear that one of the scenarios (the blue one) has a very negative unwanted outcome.

The investment advisor suggests to 'hedge this scenario away'. You as an actuary raise the key question:

What is the probability that a Negative Outcome (NO) scenario in the ALM model is indeed truly a negative outcome and not a false outcome due to the fact that the model is not perfect?

With this question, you hit the nail (right) on the head...

Do you know the answer? Is it 99% exactly, more or less?

Before reading further, try to answer the question and do not cheat by scrolling down.....

To help you prevent reading further by accident, I have inserted a pointful youtube movie:

Answer 

Now here is the answer: The probability that any of the NOs (Negative Outcomes) in the ALM study - and not only the very negative blue one - is a truly a NO and not a PO (Positive Outcome) and therefore false NO, is - fasten your seat belts  - 0.98%! (no misspelling here!)

Warning

So there's a 99.02% (=100%-0.98%) probability that any Negative Outcome from our model is totally wrong, Therefore one must be very cautious and careful with drawing conclusions and formulating risk management actions upon negative scenarios from ALM models in general.

Explanation

Here's the short Excel-like explanation, which is based on Bayes' Theorem.

You can download the Excel spreadsheet here.

There is MORE!

Now you might argue that the low probability (0.98%) of finding true Negative Outcomes is due to the high (99,99%) Positive Outcome rate and that 99,99% is unrealistic much higher than - for instance - the Basel III confidence level of 99,9%. Well..., you're absolutely right. As high positive outcome rates correspond one to one with high confidence levels, here are the results for other positive outcome rates that equal certain well known (future) standard confidence levels (N := 1 year):

What can we conclude from this graph?

If the relative part of positive outcomes and therefore the confidence levels rise, the probability that an identified Negative Output Scenario is true, decreases dramatically fast to zero. To put it in other words:

At high confidence levels (ALM) models can not identify negative scenarios anymore!!!

Higher Error Rates

Now keep in mind we calculated all this still with a high quality error rate of 1%. What about higher model error rates. Here's the outcome:

As expected, at higher error rates, the situation of non detectable negative scenarios gets worse as the model error rate increases......

U.S. Pension Funds

The 50% Confidence Level is added, because a lot of U.S. pension funds are in this confidence area. In this case we find - more or less regardless of the model error rate level - a substantial probability ( 80% - 90%) of finding true negative outcome scenarios. Problem here is, it's useless to define actions on individual negative scenarios. First priority should be to restructure and cut ambition in the current pension agreement, in order to realize a higher confidence level. It's useless to mop the kitchen when your house is flooded with water.....

Model Error Rate Determination

One might argue that the approach in this blog is too theoretical as it's impossible to determine the exact (future) error rate of a model. Yes, it's true that the exact model error rate is hard to determine. However, with help of backtesting the magnitude of the model error rate can be roughly estimated and that's good enough for drawing relevant conclusions.

A General Detectability Equation

The general equation for calculating the Detectability (Rate) of Negative Outcome Scenarios (DNOS) given the model error rate (ER)  and a trusted Confidence Level (CL) is:

DNOS = (1-ER) (1- CL) / ( 1- CL + 2 ER CL -ER )

Example

So a model error rate of 1%, combined with Basel III confidence level of 99.9% results in a low 9.02% [ =(1-0.01)*(1-0.999)/(1-0.999+2*0.01*0.999-0.01) ] detectability of Negative Outcome scenarios.

Detectability Rates

Here's a more complete oversight of detectability rates:

It would take (impossible?) super high quality model error rates of 0.1% or lower to regain detectability power in our (ALM) models, as is shown in the next table:

Required  Model Confidence Level

If we define the Model Confidence Level as MCL = 1 - MER, the rate of Detectability of Negative Outcome Scenarios as DR= Detectability Rate = DNOS and the CL as CL=Positive Outcome Scenarios' Confidence Level, we can calculate an visualize the required  Model Confidence Levels (MCL) as follows:

From this graph it's at a glance clear that already modest Confidence Levels (>90%) in combination with a modest Detectability Rate of 90%, leads to unrealistic required Model Confidence Rates of around 99% or more. Let's not discuss the required Model Confidence Rates for Solvency II and/or Basel II/III.

Conclusions

1. Current models lose power
   Due to the effect that (ALM) models are limited (model error rates 1%-5%) and confidence levels are increasing (above > 99%) because of more severe regulation, models significantly lose power an therefore become useless in detecting true negative outcome scenarios in a simulation. This implies that models lose their significance with respect to adequate risk management, because it's impossible to detect whether any negative outcome scenario is realistic.
    
2. Current models not Solvency II and Basel II/III proof
   From (1) we can conclude in general that - despite our sound methods -our models probably are not Solvency II and Basel II/III proof. First action to take, is to get sight on the error rate of our models in high confidence environments...
    
3. 
   New models?
   The alternative and challenge for actuaries and investment modelers is to develop new models with substantial lower model error rates (< 0.1%).
   
   Key Question: Is that possible?
   
   If you are inclined to think it is, please keep in mind that human beings have an error rate of 1% and computer programs have an error rate of about 3%.......
    

Links & Sources:

- Download this blog's Excel spreadsheet
- Wikipedia: Base Rate Fallacy

- Human Errors

Solvency II: Standard or Internal Model?

Solvency II is entering the critical phase.Time is running out!

But...., as a wise proverb states:

"When The Actuaries Get Tough,

The Tough get Actuaries"

However, the market for actuarial resources is limited and Solvency II Actuaries that  combine strategic and technical knowledge with 'common sense' are like  white ravens.

In the case of Solvency II, actuaries and models are moving forward in a particular way.

Standard Model
Originally, the 'standard model' was foreseen as a simple model for small and mid-size insurers (apart from very small insurers that were excluded). Big insurers, with more developed actuarial models, larger scale and more resources, were expected to work out a more sophisticated 'internal model'.

As the Solvency II Time Pressure Cooker gets up steam, things start turning.

Small and mid-size insurers found out that the 'standard model' was highly inefficient and the wrong instrument to steer adequately on risk management and to determine adequate solvency levels in their company.

Just because of their limited size and product selection, small and mid-size insurers often already have a well tuned risk management system in place and implemented throughout the organization. The manager, actuary (being the risk manager as well) and CFO of such companies therefore have enough time to develop a formal Solvency II 'internal model' that could be easily implemented throughout their organization.

Internal Model
Quit the opposite happens in the world of big insurers.

Big insurers coordinated Solvency II at Holding level and started to challenge their business-units around 2009 to develop and implement Solvency II programs on basis of an 'internal model'.

Collecting homework at the Holding in 2010, it became clear that a lot of technical issues in the models were still unclear. Moreover, models were not integrated (= condition)  in the business and counting up several 'internal models' showed up several consolidated inconsistencies. 

The complexity of developing a consistent risk model turned out to strong. Some big insurers are now considering to fall back on the 'standard model' (or partial model) before it's too late: the shortest errors are the best.

Looking back it's not surprising that big insurers need more time to operationalize a fine tuned risk model. It took specialist Munich Re 10 years to implement an internal model.

This development is also an indication that some big insurers are strongly over-sized. In order to keep up with the speed of the market, big insurers have to be split up into a manageable and market-fit size.


Related Links:

- Surviving Solvency II (2010)
- The influence of Solvency II on an insurer’s strategic policy
- White Ravens and Black Swans (Math Fun)

Questioning Solvency II?

Every now and then, when you're in the middle of some-, any- or every-thing, it's wise to sit back and ask yourself some basic questions:

Is what I'm doing still adding value?
If so, what's that value and for who?
If not, how can I add value one way or the other?
If not, stop!

A Solvency example...

Suppose you're up to your neck in a solvency II project and you've not really seen your family for two weeks. Just sit back, relax and simply ask yourself the next questions:

1. Why are we implementing Solvency II
   (Better: What's the goal of Solvency II)
2. Are the reasons for implementing Solvency II valid and sound?
3. Is it possible and profitable to define and measure detailed risks at company level?
4. What's the RETURN on Solvency II for policyholders and shareholders?

The official (CEA) answer to question I reads in short:

We implement Solvency II because the current framework is too simple and does not direct capital accurately to where the risks are.

Key question (II) is: Are "too simple" and "more detailed directing capital" valid or sound reasons........?


Alternative
A more valid reason for implementing Solvency II would be something like:

Recent decades have shown an increase of Insurance Companies Bankrupts (or Insolvencies) to a level of x% p.a. (measured in value instead of numbers). Solvency II intents to bring down this x% risk to (x-y)% in Z years by means of a more detailed capital-risk approach.

The estimated costs of this yearly y% reduction by implementing and maintaining Solvency II, are estimated at z% p.a. .

Main challenges implementing S II at company level

1. Capital allocation
   At an individual company level, the effect of Solvency II on shareholder and client value will only be negative. More 'dead capital' has to be allocated, decreasing shareholder value and decreasing clients profit share.
   
   
2. Revenues
   Pricing Solvency II, will increase premium/contribution levels. However higher contribution levels will have a negative net impact on sales and revenues.
   
   
3. Capital Inadequacy
   On top of, the extra solvency created by Solvency II will turn out to be inadequate at an individual company level in case the deTAILed risks actually affects (hits) a company. A more (inter)national reinsurance program could bring help here. However, these kind of reinsurance programs turn out to be expensive. Moreover, take care that these deTAILed risks don't turn out to be systemic risks in the end....

Conclusion

It's clear that the Solvency II goals are not smart formulated. Nevertheless, Solvency II seems an irreversible process.

Therefore the key question is:

How can you use Solvency II to add (long term) value to your clients and shareholders?

The art of asking the right question

Now you've replaced your fuzzy feeling and foggy discussions about the goal of Solvency II, by a leading question.

Answering and discussing this question will turn out the way to create efficiency and joy in your project and time for your family.

A lot of colleague actuaries can help you on discussing and answering this question.

Start discussing this question in the company board's next meeting!


Risk management Moral
In fact Risk Management in general is more the art of asking the right question instead of giving the right answer. This is well argumented by Professor Stefan Scholtes (University of Cambridge), who states that what we need is a complementary balance between modelling and intuition; models that relate to and enforce our mental abilities, not replace them.

audio link

We actuaries can learn from that. Actuarial questioning turns out key. Next time you have to give a (Board) presentation, start by asking the right (effective) questions instead of giving answers straight away.

One last tip: Never ask 'Why questions', instead ask 'What questions'....

Related links
- CEA Why Solvency II?
- Prof. Stefan Scholtes: The art of asking the right question
- Asking the right questions

Solvency II Project Management Pitfalls

When you - just like me - wonder how Solvency (II) projects are being managed, join the club! It's crazy...., dozens of actuaries, IT professionals, finance experts, bookkeepers accountants, risk managers, project and program managers, compliance officers and a lot of other semi-solvency 'Disaster tourists' are flown in to join budget-unlimited S-II Projects.

On top of it all, nobody seems to understand each other, it's a  confusion of tongues..... 

Now that the European Parliament have finally agreed upon  the Solvency II Framework Directive in April 2009, everything should look ready for a successful S-II implementation before the end of 2012. However, nothing is farther from the truth.....

Solve(ncy) Questions in Time
The end of 2012 might seem a long way of...
While time is ticking, all kind of questions pop up like:

• How to build an ORSA system and who owns it?
• What's the relation between ORSA and other systems or models, like the Internal Model
• Where do the actuarial models and systems fit in?
• What are financial, actuarial, investing and 'managing' parameters, what distinguishes them, who owns them and who's authorised and competent to change them?
• How to connect all IT-systems to deliver on a frequent basis what S-II reporting needs......?
• How to build a consistent S-II IT framework, while the outcomes from QIS-5 (6,7,...) are (still) not clear and more 'Qisses' seem to come ahead?
• Etc, etc, etc, etc^10

The Solvency Delusion
Answering the above questions is not the only challenge. A real 'Solvency Hoax' and other pitfalls seem on their way....

It appears that most of the actuarial work has been done by calculating the MCR and SCR in 'Pillar I'.

It's scaring to observe that the 'communis opinio'  now seems to be that the main part of the S-II project is completed. Project members feel relieved and the 'Solvency II Balance Sheet' seems (almost) ready!

Don't rejoice..., it's a delusion!  The main work in Pillar II (ORSA) and Pillar III (Reporting, transparency) still has to come and - at this moment - only few project managers know how to move from Pillar I to Pillar II.

Compliancy First, a pitfall?
With the Quantitative Impact Study (QIS-5) on its way (due date: October 2010) every insurer is focusing on becoming a well capitalized Solvency-II compliant financial institution.

There is nothing wrong with this compliance goal, but 'just' becoming 'solvency compliant' is a real pitfall and unfortunately not enough to survive in the years after 2010.

Risk Optimization

Sometimes, in the fever of becoming compliant, an essential part called "Risk Optimization" seems to be left out, as most managers only have an eye for 'direct capital effects' on the balance sheet and finishing 'on time', whatever the consequences......

Risk Optimization is - as we know - one of the most efficient methods to maximize company and client value. Here's a limited (check)list of possible Risk Optimization measurements:

1. Risk Avoidance - Prevent Risk    • Health programs    • Health checks    • Certification (ISO, etc)    • Risk education programs    • High-risk transactions       (identify,eliminate, price)    • Fraud detection       (identify,eliminate, price)    • Adverse selection       (identify, manage, price) - Adjust policy conditions    • Exclude or Limit Risk         (type,term)    • Restrict underwriter       conditions       (excess, term, etc) - Run-off portfolios/products 2. Damage control - Emergency Plans (tested) - Claims Service, Repair service - Reintegration services 3. Risk Reduction - Diversification - Asset Mix, ALM - Decrease exposure term - Risk Matching - Decrease mismatch    AL/Duration - Outsourcing, Leasing 4. Risk Sharing - Reinsurance (XL,SL,SQ) - Securitization, Pooling - Derivatives, Hedging - Geographical spread - Tax, Bonus policy 5. Risk Pricing - Exposure rating, Experience rating - Credibility rating, Community rating - Risk profile rating 6. Equity financing - IPO, Initial Public Offering - Share sale, Share placement - Capital injections

Solvency-II Project Oversight

Just to remind you of the enormous financial impact potential of 'Risk Optimization' and to keep your eye on a 'helicopter view level' with regard to Solvency-II projects and achievements, here's a (non-complete but hopefully helpful) visual oversight of what has to be done before the end of 2012.....

(Download big picture JPG, PDF)

Be aware that all Key Performance Indicators (KPIs), Key Risk Indicators (KRIs) and Key Control Indicators (KCIs) must be well defined and allocated. Please keep also in mind that one person’s KRI can be another’s performance indicator(KPI) and a third person’s control-effectiveness indicator.

Value Added Actions

As actuaries, we're in the position of letting 'Risk Optimization' work.
We're the 'connecting officers' in the Solvency Army, with the potential of convincing management and other professionals to take the right value added actions in time.

Don't be bluffed as an actuary, take stand in your Solvency II project and add real value to your company and its clients.

Related Links:

- A Comparison of Solvency Systems: US and EU
- UK Life solvency falls under qis-5
- Determine capital add-on
- Reducing r-w assets to maximize profitability and capital ratios
- Risk: Who is who?
- Balanced scorecard including KRIs (2010)
- Solvency II, Piller II & III
- Risk Adjusted Return On Risk Adjusted Capital (RARORAC)
- ERM: “Managing the Invisible" (pdf; 2010)
- Unlocking the mystery of the risk framework around ORSA
- Risk  based Performance: KPI,KRI,KCI
- Risk of risk indicators (ppt;2004)
- Defining Risk Appetite
- Risk appetite ING KPI/KRI
- Board fit for S II?
- How to compute fund vaR?
- Technical Provisions in Solvency II
- Insurers should use derivatives to manage risk under Solvency II 
- Solvency Regulation and Contract Pricing in the Insurance Industry
- Overview and comparison of risk-based capital standards 
- Solvency II IBM
- Reinsurance: Munich Re  , Reinsurance solvency II