Showing posts with label formula. Show all posts
Showing posts with label formula. Show all posts

Jun 18, 2010

Risk Symptoms Matrix

On INARM (International Network of Actuarial Risk Managers) ERM advisor Dave Ingram raises the simple question:

What must managers who are not modelers know about models?

Perhaps this question is one of the most relevant questions in Risk Management and the Actuarial profession. It's a key question that should be discussed on Board Level in every (financial) area.

Also this question is relevant in setting up and managing complex projects like Solvency II, ERM, Pension Fund Risk Management, ALM and even "In control" projects.

The answer
Now let's try to answer this intriguing question

Managers are experts in 'decision taking'. Modelers are experts in reducing and simplifying complexity to decidable parameters.

Now the Quality (Q) of a management decision (D) is defined by the equation:

[ Q(D)= Q(Manager) x Q(Modeler) ],

where Modelers are responsible for the Quality of the Input (data) of the model [Q(Input Model)] and the Quality of the modeling process itself [Q(Modeling)].

More refined, we may therefore define :

Q(D)= Q(Manager) x Q(Input Model) x Q(Modeling)

Luckily, not all Q's are independent!
Both Managers and Modelers can raise the Quality of the outcome of the Decision process by asking each other "What If" questions.

By asking WI-questions with regard to the 'Input of the Model" [Q(Input) = data, decision parameters] and examining the output, Modelers are able to raise the Quality of their (technical) Modeling by improving their technical Model [Q(Modeling)].

Moreover, decision parameters are not set in stone. So by asking WI-questions, Modelers become more aware of the Management Decision Consequences (MDCs), helping them to develop and simplify decision parameters to the most adequate, understandable and possible simplified form. Or as Albert Einstein quoted it:

"Everything should be made as simple as possible, but not simpler"

On the other hand, by asking WI-questions, Managers can study the effects of various decisions they might take in different (simulated future) circumstances (as roughly described by the Manager).

This process improves the decision taking skills of a Manager and therefore improves the Quality of the Decisions taken by Managers [Q(D)] in general. At the same time, the Modeler may use the given information from the Manager to improve his Model and (future) data as well.

We may conclude that the answer to the question 'What managers, who are not modelers, need to know about models' is:

Nothing, as long as Manager and Modeler intensively communicate with each other, ask WI-questions, are not afraid to admit their weakness or doubts, challenge each other and don't manipulate each other!

Perhaps an ever more tricky question to answer is:

"What must managers who are also modelers know about models?

Possibly Dave Ingram has the answer to this question....

Aftermath What happens when communication between Managers and modelers fails, is well illustrated in the Gulf of Mexico Oil Disaster, where BP CEO Tony Hayward stated before congress:
- “I simply wasn’t involved in the decision-making.”
- “Clearly an engineering judgment was taken.”

It's easy to spot failing Management-Modeler relationships by means of the next 'Management-Modeler Symptoms Matrix'.....

If you happen to be a modeler in the upper left quadrant, get out as fast as you can!

May 7, 2010

Online Murphy Risk Calculator

Risk is like quantum mechanics:

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

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

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

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

Probably one of the more intriguing risk quotes is :

"Anything that can go wrong, will go wrong"

by the famous Edwin Murphy.

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

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

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

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

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

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

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

The correct formula according to Phil is:

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

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

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

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

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

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

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

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

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

Good Luck with Murphy's calculator!

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

Sep 7, 2009

Swine Flu Counter update Sept 2009

Here you'll find the September 2009 update of the

Global Swine Flu Counter

Although there is still an increasing risk of underreporting, the counter has been renewed on basis of the latest available global reports as provided by Wikipedia/ECDC.

Swine Flu under Control?
The September 2009 developments suggest the Swine Flu development is under control, as the reported infections changed from a exponential growth recent months, to more linear growth in August 2009. In September the increase of infections was already declining.

New Model
The above developments are the main reason why data in the Swine Flu calculator have now been modelled by a logistic function.
Well considered curve fitting at ZunZun, showed a Gompertz function (with offset) resulted in a satisfying approximation :

Life actuaries will be familiar with good old Gompertz. The Gompertz equations are - by the way - also used to model Plant Desease Progres.

The number of death have now been modelled ruffly as 1.8% of the infected people a month earlier [Death=0.018*I(t-30)]

Results update
The results the new approximation show that the number of reported infections increases asymptotically towards a limit of about 323,000.

Correspondingly, the number of death, , increases to a limit of ruffly 6000.

All provided the actual controlled development continues and no new mutation of the H1N1 will develop in the next months.....

The risk of underreporting is not negligible . Modeling on basis of excluding the September data would result in a limit of 528,000 infects and about 9500 deaths. We'll just have to wait how H1N1 develops.....
But as becomes clear, the explosion of swine flue cases looks under control.

If necessary, the counter will be updated again on a on a regular basis. The latest data you'll find in this XLS spreadsheet.

Install Swine Flu Counter
How to implement this Swine Flu Counter on your web site?

  • Put the next HTML-script (without the outer quotes) just before the end of the body tag:' <script language="javascript" type="text/javascript" src=""> </script>'

  • Put the next HTML-line (without the outer quotes) where you want the Swine Flu table to appear on your site :
    ' <div id="swineflutable"></div> '

  • Ready!

Jul 4, 2009

H1N1 Swine Flu Projection

Strange... a lot of (WHO) swine flu talk and information on the Internet, but no worldwide projections or estimates....

The risk of underestimating the so called H1N1 (Swine Flu) virus is not unthinkable.

Worldwide Projection H1N1 Virus

You don't have to be an actuary or mathematician to make a sound projection of the number of people that will be infected (or die) within the next months. All it takes is 'basic high school' and a common spreadsheet.

Let's make a simple worldwide projection of the expected cases (infections) based upon the WolframAlpha data-set:

The purple line illustrates the development of the number of infections worldwide, the dotted purple line illustrates the expected projected development until the end of july 2009.

With one view it's clear is that during the next months the H1N1 virus spread will be enormous. By the end of July 2009 the number of worldwide infections will rise to almost 0.5 million. The spread of the virus will probably be enforced by the fact that a lot of people have their holidays and therefore travel by plane or bus.

As one would aspect, the development of the number of infections is exponential. The (natural) logarithm of the expected cases (dashed red line) is almost a linear curve. You may find more information of data and projections in the next XLS spreadsheet.

Big Explosion
If no additional prevention actions will be taken, a big explosion of the virus starts just after the holiday period in 2009.

It is questionable if the planned vaccinations for October or later will be in time.Perhaps it's better to have a vaccination, or take Tamiflu, than a vacation in July or August.

Global Infection
If no adequate rigid measures will be taken within the next months, the future of humanity could be serious at stake:

Unrestrained exponential growth on basis of the the current growth-path, will lead to a more or less complete global infection by the end of January 2010.

By then ruffly 36 million people worldwide, will have died. If the mortality rate doesn't stabilize (as it currently appears) at 0.45% of the infected people, the effects could be worse.

As the famous 'Wheat and chessboard problem' already illustrated, exponential growth is a dangerous underestimated killer. It's just like a tsunami: when you notice it, it's too late to act.

Let's trust governments are not underestimating this Swine virus threat.

Happy holidays!

Related Links:
- World Population Density
- U.S. Death rates influenza virus 1918
- Visual Flu Tracker
- LinkedIn: InArm: Important remarks by Dave Ingram

Important Notice