Showing posts with label risk. Show all posts
Showing posts with label risk. Show all posts

Apr 22, 2012

Investment Herding Risk

What was suspected, has now been proved:

Investment Herding Exists!

Dutch Pension Funds are active Traders
In a 2011 research document called "Herd behavior and trading of Dutch pension funds", researchers Rubbaniy, Lelyveld and Verschoor of the Dutch Erasmus University in Rotterdam, provided evidence that repudiates the popular belief that - in specific - Dutch pension funds are long-term passive institutional traders.

De facto Dutch pension funds are active traders and trade about 8.5%  of their portfolio on a monthly basis!

Conclusions
Main conclusions of Rubbaniy (et al.) are:
  • Significant feedback trading strategies, both momentum and contrarian
  • Robust herding behavior in investments of Dutch pension funds
    Overall (LSV) herding level of 8.14% (significant at 1% level !!)
    On average if 100 PFs are active in the same security in the same month, there are 8.14 more PFs trading on the same side of the market than what would be expected under null hypothesis of random selection of securities.
  • Herding asymmetry in buying and selling of securities
    Across asset classes there is a higher degree of herding in less-risky assets.
  • Recent financial crises have a positive impact on both turnover and herding while it negatively affects feedback trading.


Explanations
Possible explanations of these herding effects are:
  • Possibly outsourcing of portfolio management and small PFs imitation of large PFs’ lead to the same kind of asset allocation strategy.
  • Many small Dutch PFs often hire the same large and reputed asset management firms for their portfolio management and are likely to have same asset allocation of their portfolios. 
  • Even if they do their own portfolio management, small Dutch PFs may mimic the investment behavior of large PFs - a widespread belief about the small investors - and thus, add to (LSV) herding measure.

Remarks
Let's conclude with some remarks....

  • Dangerous Big Brother Hedge
    Although large PFs (investors) have some 'economics of scale' and budget for experimenting on a small scale with (alternative) non-conventional investments, their investment strategy probably strongly differs from a small PF, as liabilities, sponsor obligations and pension benefits conditions are often are fund specific. 

    Therefore, following a large PF asset strategy as a small PF, is extremely dangerous and will eventually not turn out to be the 'big brother hedge' the fund was aiming at.
     
  • Unfounded First Mover Risk
    Key question remains if all this herding, hedging and active trading results in an outperformance above a long term sustainable asset-location strategy.

    Probably not. But although investors pretend tot act on a rational basis, in reality irrational and conformist behavior take the upper-hand. Small investors often don't dare to formulate a unique fund specific asset allocation strategy because of 'first mover risk'.

Keep care and formulate yur own specif pension fund strategic asset mix!

Related Links & Sources
 - "Herd behaviour and trading of Dutch pension funds" (2011, PDF)
 - Momentum or Contrarian Investment Strategies:
    Evidence from Dutch Institutional Investors (2011)
- Momentum and Contrarian Stock-Market Indices

Mar 14, 2012

Life is Nonlinear, so is Risk!

From the day we were born, we've learned to survive in a complex world by applying linear mechanisms in life:
  • On a short time scale things don't change much
  • The future can be predicted by extrapolation of the past
  • Every event now, must have a cause in the past
  • Results are a (linear) combination of events in the past

Linear Thinking
In line with our linear culture, we - actuaries, (risk) managers, investment consultants or asset managers, etc. - have applied this way of linear thinking in our professional field:
  • Mean reversion: Returns continue to go back to an average value over time
  • Volatilities are more or less constant in time
  • Increasing volatility is a good predictor of an upcoming financial crisis
  • Standard deviation is similar to risk or volatility
  • If a distribution is complex, a normal distribution nevertheless will do fine
  • Tail risks are not really interesting or can't be modelled anyway

More detailed psychological linear thinking in the Risk area...

  • Peer Risk: If all other professionals (institutions) are using a certain method or investment strategy, why should I take the risk of developing a new one?
  • First Mover Risk: Why should I act first and carry all research investments?
  • Supervisory Compliant:If the regulator prescribes new regulations, I'll apply those regulations as if it is my own risk appetite.
  • Big Brother Hedge Risk: I base my investment strategy at a save distance on the biggest leader in the market. Might trouble arise, the Regulator first has to deal with my Big Brother.
  • Regulation Risk: Regulation (change) is perceived as a given fact and not viewed or managed as a kind of risk
  • Risk of Free Rate Risk: There must be some kind of risk free interest rate.

Thinking long term and two steps deeper, it's obvious that applying any of the above mentioned linear thinking methods will likely be the nail in the coffin of any financial institution.

Linear thinking and modelling make our daily life more simple. Unfortunately, 'too simple' to cope with financial markets reality on a long term. 

Metamorphosis by Escher...
If we are lucky, (market) circumstances only change slowly and we're able to adapt the value of the variables in our linear models gradually, while  keeping our traditional way of linear thinking and modeling.  We act just like the famous graphic artist Escher shows us in Metamorphosis...

If we are less 'lucky' (as we are in2012), our linear models all of a sudden seem to fail. Covariances and volatility increase. Systemic risk shows up everywhere and a 'risk free rate' turns out to be an illusion. Our risk dashboard is on fire and we'll have to admit: our linear MPT models are failing.




Navigation Risk Parable
Why is it so so hard to admit that our linear models fail?

Suppose you developed a 2D linear (x,y)-navigation app in your Florida flatland office. Your app works fine for years. Than you decide to visit Black Hills & Badlands of South Dakota. Suddenly your app seems to fail in the mountains. Travel times and distances on your display suddenly seem wrong.

You realise you urgently need to develop a nonlinear 3D (x,y,z)-navigation app.... However, you don't do it.

Why not?

Well, first of all your old linear 2D app worked fine for years and on short trips the app still works (approximately) fine.

Besides, nobody of your Californian friends uses a 3D app and developing a new nonlinear app is very expensive.

Well, it's time we realise that most developments in life are in fact nonlinear.
If the stakes are high, like in the investment business, linear models will eventually lead us to a disaster.

Summarised, we might conclude:

If life is Nonlinear, so why aren't our models?

New Solutions
What alternatives do we have for our old linear model?

Although there are many nonlinear models, I'll emphasize on two interesting nonlinear based models in this blog.

I. Predicting economic market crises using measures of collective panic
Is there an adequate predictor of a market crisis?

Using new statistical analysis tools based on complexity theory, the New England Complex Systems Institute (NECSI) performed a new research on predicting market crashes.

As we know volatility is a measure of risk. So one would expect an increase of volatility also to be an adequate predictor of a financial market crash. Unfortunately this is not the case, as is shown in the recent NECSI study. While volatility increases at the beginning of a crisis, it is unreliable as an adequate indicator of a nearby market crash.

What also is not true, is that a market crash is often triggered by market panic justified, or not justified, by external (bad) news.

The NECSI research indicates that it's the internal structure of the market and not an external crises, that's primarily responsible for a market crash.

It turns out that the number of different stocks that move up (U) or down (D) together is an indicator of the mimicry ( 'collective flight'; herding) within the market. When mimicry is high, many stocks follow each other's movements.

This "co-movement" of stocks  is an indicator of a nervous market that is ripe for panic. The existence of a large probability of co-movement of stocks on any given day, is a measure of systemic risk and vulnerability to self-induced panic.

So, rather than measuring volatility or correlation, the fraction of stocks that move in the same direction turns out to be a successful predictor of a market crash..

NECSI researchers showed that a dramatic increase in market mimicry occurred during the entire year before each market crash of the past 25 years, including the recent financial crisis.




II. Worst-Case Value-at-Risk of Non-Linear Portfolios 
We all know that VaR lacks some desirable theoretical properties:
- Not a coherent risk measure.
- Precise knowledge of the distribution function is critical
- Non-convex function of w → VaR minimization intractable
- To optimize VaR we have to resort to VaR approximations
- Normality assumption is unrealistic → may underestimate the actual VaR.

Zymler, Kuhn & Rustem of the Department of Computing Imperial College London now developed a nonlinear alternative for VAR, called



Worst Case Var


Two variations on WCVar lead to practical applications:

  1. Worst-Case Polyhedral VaR (WCPVaR)
    A polyhedral VaR approximation for portfolios containing long positions in European options expiring at the end of the investment horizon

  2. Worst-Case Quadratic VaR (WCQVaR)
    A suitable VaR approximation for portfolios containing long and/or short positions in European and/or exotic options expiring beyond the investment horizon.

Here's an example of WCQVar's results against  WCVar (plain) and the good old 'Monte Carlo Var' we mostly use in linear modeling. This graph needs no further comment.....



Using the WCQVar leads to more realistic modeling results. WCQVar-techniques can also be used for for index tracking leads to spectacular results (see pdf).

Worst-Case Value-at-Risk of Non-Linear Portfolios

Finally
After so many years of relative successfully using linear models, it's hard to recognize that we need new models based on new nonlinear approaches.
Therefore we need 'first movers'. Who's willing to take the risk and jump into the nonlinear deep-sea?



Be confident and stay on your happy feet.. after a successful jump, 'herding theory' tells us others will follow...


Sources & Related Links
- Predicting economic market crises using measures of collective panic (PDF)
NECSI Research (2011)
- Self-Induced Panic And The Financial Crisis 
- Worst Case Var Document (PDF; 2011)
- Worst Case Var Document (PDF;2009)
- Order Happy Feet Video 



Nov 10, 2011

How to catch Risk?

Desperate attempts to catch Risk in new regulatory standards like Basel (II/III) for banks and Solvency (II) for insurers seem a dead end street....

What is happening?

That's the question we're about to answer in this blog!

Here are some observations:
  • Risk Weighting
    All new risk valuating standards are based on Risk Weighting. Some assets (or liabilities) are assumed to be more risky than others. In practice, every asset class that has been identified as more or less 'safe', has turned out to be risky after all. E.G., government bonds  where - until the 2011 crisis  in Greece - assumed to be risk free. Unfortunately, nothing could be further from the truth...

    Nothing in life is risk free
  • Tier Ratio's
    Instead of simple 'Equity to Asset Ratios', Tier 1 & 2 ratios where developed. These Tier ratios only take a fraction of the total assets into account. This leads to 'Equity to Risk-Weighted Assets Ratios' that insinuate adequate, substantial and reassuring 10-15% Capital ratios, while - in fact - they're not! These kind of ratios are misleading and create a false sense of safety....

    Tier Ratios lead people up the garden path

  • Tail Hide and Seek
    As more and more risks are valued, regulated and urge for extra capital requirements, financial institutions will try to create extra return on risks that are formally not or only 'light weighted' measured. This way substantial risks are 'pushed' into the tail, fat risk tails are created and the sight on the real risks in the company becomes misty.

    Overregulation decreases the effect of good risk management

Illustration: Comparison 'Deutsche Bank' - 'Bank of America'
To illustrate what is happening, let's compare a giant like "Deutsche Bank" (DB) with the number one on the banking list, the "Bank of America" (BOA).


Financial RatiosDeutsche BankBank of America
(x 1 bn $)              Year:2010200920102009
Assets (A)1906150122652230
Liabilities (L)1855146320371999
Shareholder Equity (SE)4937228231
SE / A - Ratio2.6%2.4%10.1%10.4%
---------------------------------
Risk-Weighted Assets (RWA)34627314561543
Assets (A)1906150122652230
RWA / A - Ratio18%18%64%69%
---------------------------------
Regulatory Capital (RC)4938230226
Risk-Weighted Assets (RWA)34627314561543
Total Capital Ratio 14.1%13.9%15.8%14.7%
---------------------------------
Tier 1 capital4334164160
Risk-Weighted Assets (RWA)34627314561543
Tier 1 Capital Ratio12.3%12.6%11.2%10.4%




















Although both banks have more or less the same 'Tier 1' and 'Total Capital Ratio', their individual risk profile is completely different. 

In the case of DB only 18% of the assets are assumed (marked) risky, while in the case of BOA around 64% is assumed risky and taken into account for a risk weighted solvency approach.

Notice that the simple gross 'Equity to Asset' Ratio (E/A-Ratio, or in short 'EAR')  of DB is only 2.6%, while the similar ratio of BOA is around 10.1%. If DB would be hit by an 5% impact loss, it would be in deep trouble.


Reflections
Our risk models have become too sophisticated and don't cover the area of 'Unkown Risk' enough. Unintentionally rand controversially, risk regulations and models make us implicitly sweep our real risks under the carpet. In principle Risks can be categorized as:

  1. Known Risk Measured
  2. Known Risk Unmeasured
  3. Unknown Risk
  4. Hidden Risk (knowingly or unknowingly)

It's time to admit that no asset or liability is completely free of risk and there's an overall substantial probability that risk - by definition - will hit eventually from an unexpected corner. To put things in perspective: In the 19th century, banks funded their assets with around 40-50% equity.

Conclusion
Including 'Unkown Risk', a simple gross E/A-Ratio (EAR) of a magnitude of 15-25% (across the total assets) would probably be the best kind of guarantee to accomplish a more sustainable financial system in the world. The new EAR could be best defined as the sum of an actuarial underpinned percentage on basis of the underlaying calculable covered risks and a TBD overall 10% 'add up' for unknown risks:

E/A-Ratio = EAR =  EAR[ calculable risk ] + EAR[ unknown risk ]

Until we've included Unkown Risk fully in our risk models, we'll stay in deep trouble.

Aftermath: 'Avatar Ratios'
To rate a company (bank), often it's not enough to look at just the traditional financial ratios. An interesting way to additionally rate a company in a more sophisticated way, is with the help of so - by me - called 'Avatar Ratios'.


Additional to financial ratios, 'Avatar Ratios' tell you more about what the intentions, (real) important issues and the 'drive' of a company and its employees are.

An 'Avatar Ratio Analysis' gives you more or less 'the embodiment' of all what drives a company. It can be constructed by making a word analysis of a crucial document or annual report of a company. In short: You simply download the annual report (or any other company characteristic document) and analyze it with a  'Word Frequency Counter' like WriteWords.

IAA Demo
As a demo, let's analyze the IAA's Strategic Plan




FrequencyWord
21actuarial
10strategic
10develop
8associations
6standards
6priorities
6plans
6objective
6action
5promote
5profession
5member
5international
5iaa
5association
4practice
4maintain
4key
4global
4encourage
4education
3worldwide
3statement
3relationships
3plan
3including
3identify
3establish
3common
3discussion
2world
2values
2supranational
2support
2services
2risk
2relevant
2provide
2program
2professionalism
2professional
2prioritize
2principles
2organizations
2organization
2mission
2march
2management
2links
2issues
2internationale
2help
2fields
2facilitate
2countries
2contact
2conduct
2areas
2area
2approved
2among
2actuaries
2actuarielle
1voluntary
1vision
1understanding
1transparency
1traditional
1stakeholders
1soundness
1society
1social
1skills
1sections
1scope
1scientific
1role
1review
1research
1reputation
1relationship
1regional
1recommended
1recognized
1recognition
1quality
1public
1protection
1promotion
1process
1procedures
1presidents
1offered
1objectivity
1objectives
1needs
1model
1members
1knowledge
1jurisdictions
1involvement
1integrity
1improve
1guidelines
1forums
1forum
1financial
1feasibility
1experiences
1expansion
1examine
1ensure
1enhance
1disciplinary
1developing
1developed
1designation
1decisions
1decision
1credential
1create
1cooperation
1convergence
1contributing
1continuing
1constructing
1code
1changing
1availability
1audiences
1active
1achieve
1accountability
1access

With the help of WriteWords we first create (on line) a frequency table. Next we cut out irrelevant words like 'and', 'the', etc. 

Here are the results:
(1) a  scrollable frequency table of all relevant words
(2) a 'Top 22 words' frequency table



In most cases - like this one - the result of simply putting the first 10 to 15 words in the top of the frequency table behind each other, is astonishing: It creates a kind of 'Identity Statement'. Here's the result for IAA's strategic plan, where even more than 20 words give a beautiful comprised identity statement:

IAA's Strategic Plan (Identity Statement comprised with WriteWords)
Actuarial strategic develop associations. Standards, priorities plans objective action. Promote profession member international. IAA association practice maintain key. Global encourage education worldwide.

Avatar Analysis: Comparison 'Deutsche Bank' - 'Bank of America' 
Let's now go back to our banking case and compare 'Deutsche Bank' (DB) and the 'Bank of America' (BOA) with the help of a simple Avatar Ratio Analysis.

The Avatar Ratio Analys presents the word frequency (absolute numbers) and their relative frequency (= word frequency / total number of word in document). Here is the result:


Avatar RatiosDeutsche BankBank of America
Freq.Perc.
Freq.Perc.
Governance1090.06%250.02%
Risk14580.79%8520.53%
Control2730.15%1560.10%
Total G+R+C18401.00%10330.64%
------------------
Client/Customer3590.20%2500.15%
Shareholder1690.09%1620.10%
------------------
Transparent150.01%20.00%
------------------
Employee1530.08%630.04%
Director400.02%230.01%
------------------
Profit, Income10010.54%8350.52%
------------------
Tot. nr. of words161579100%184048100%


Although I'll leave the final conclusions up to you, here are some remarkable observations:
  • Total number of words
    Both companies (DB and BOA) need an enormous amount of words to explain their environment (clients, shareholders, rating agencies, etc) the essentials about what's going on in their company in a modest calendar year.

    To read an annual report of about 170,000 words, it would take an average reader (reading speed 200 to 250 words per minute) about 10-12 hours.

    Perhaps you, as an actuary, can read faster ( test it!: speed reading test ), but even at a speed of 500 wpm it would be an enormous task (5-6 hours) to fulfill.

  • Governance, Risk & Control
    It's clear that DB puts much more energy (+60%) in communicating about themes as Governance Risk and Control than BOA. Also is clear that DB is far more transparent in its communication than BOA. This does (of course) not imply that BOA's risk and control frame is inferior to DB's. It could even be the opposite. It just shows that (and how) BOA handles and communicates differently (less open) from DB.

  • Profit, Income, Shareholders + Clients and Employees
    DB and BOA weight Profit, Income and shareholders on more or less the same level. Both rank client/customer above shareholders. DB gives 'clients/customers' as well as employees double the attention of BOA!

At last
Next time you report to your board, include an Avatar Analysis of your report in your presentation!

Related Links, Sources:
- The biggest weakness of Basel III (2010)
- The Banker top 1000 list (2011) 
- Word Frequency Counter : WriteWords
- IAA's Strategic Plan  
- Bank of America: Annual Report 2010
- Deutsche Bank: Annual report 2010
- On line speed reading test 
- Spreadsheet containing this blog's DB and BOA analysis

Jun 27, 2011

Impact or Probability?

We all are more than familiar with the definition of Risk:

Risk = Probability × Impact= P×I

This way of measuring risk is a nice, simple, explainable and intuitive way of ordering risks in board or bath rooms, but unfortunately quite useless.

To demonstrate the limits of this kind of typical Risk definition, let's take a look at the next story:

The Risk of bicycling

You decided to start a 3 year math study at City University in London. From your brand new apartment in Southall, it's a 12.5 mile drive to the University at Southhampton Street.  As a passionate cyclist you consider the risk of cycling through London for the next three years.

Based on your googled " DFT's Reported Road Casualties 2009" research (resulting in a cycling death rate of 36 per billion vehicle miles), you first conclude that the probability of getting killed in a cycle accident during your three year study is relatively low : 0.1% (≈ 3[years] × 365[days] × 25[miles] × (36 [Killed]  ÷ 109[vehicle miles]).

Subjective probability
After this factfinding you start to realize it's YOU getting on the bike and it's YOUR 0.1% risk of DYING  in the next three years of your study....

Hmmmm...this comes closer; it makes things a little different, doesn't it? 

Its looks like 'subjective probability' - on reflection - is perhaps somewhat different from 'objective probability'.

While your left and right brain are still in a dormant paradoxical state of confusion, your left (logical) brain already starts to cope with the needs of the right (emotional) half that wants you on that bike at all costs!

Russian Roulette
Now your left brain tells you not to get emotional, after all it is 'only' an additional 0.1% risk. Already your left brain starts searching for reference material to legitimate the decision you're about to take.

Aha!.... Let's compare it with 'Russian Roulette', your left brain suggests. Instead of 6 chambers we have thousand chambers with one bullet. Heeee, that makes sense, you talk to yourself.

With such a 1000 chambers Russian gun against my head I would pull the trigger  without hesitating....  Or wouldn't I?..... No.., to be completely honest, 'I wouldn't risk it', my right brain tells me.

Hé... my left brain now tells me my right brain is inconsistent: It wants me on the bike but not to take part in a equal 'death probability game' of Russian roulette. Why not?

In Control
My left half concludes it must be the 'feeling' of my right side that makes me feel I'm 'in control' on my bike, but not in case of Russian Roulette. That makes sense, tells my left brain me. Of course! Problem solved! My right and left brain finally agree: It's only a small risk and it's I who can control the outcome of a healthy drive.  Besides, this way the health benefits of cycling massively outweigh the risks as well, my right brain convinces me superfluous.


A final check by my right brain tells me: If I can't trust myself, who can I?
This rhetorical question is the smashing argument in stepping on the bike and to enjoy a wonderful ride through London City.
As ever...,


Aftermathematics
After returning from my accidentless bike trip, I enjoy a drink with a colleague of mine, the  famous actuary Will Strike  [who doesn't know him? ;-)].


After telling him my 'bike decision story' he friendly criticizes me for my non-professional approach in this private decision problem. Will tells me that I should not only have analyzed the probability (P), but also the Impact (I) of my decision. Remember the equation: Risk=P×I?

Yes of course, Will is right. How could I forget? ..., the probability of getting a deathly accident was only 0.1%.

Yet, 'when' a car hits you full, the probability of meeting St. Petrus at heaven's gate is 100% and the Impact (I) is maximal (I=1; you're dead ...)

Summarized:

Risk[death on bike;25 miles/day; 3 years] =
Probability × Impact = 0.1% × 1=0.1%
From this outcome it's clear that, even though the Impact is maximal (1=100%) , on a '0% to 100% Risk scale' this 3 year 'London-Bike Risk Project' seems negligible and by no means a risk that would urge my full attention.

I'm finally relieved... it always makes a case stronger to have a taken decision verified by another method. In this case the Risk=P×I method confirmed my decision taken on basis of my left-right brain discussion.  Pff....

Afteraftermath
The next morning, after my subconscious brain washed the 'bike dishes' of the day before, I wake up with new insights. Suddenly I realize I tried to take my biking decision on the wrong variable: Probability, instead of Impact.

Actually, in both cases and without realizing, I took my decision finally on basis of the Impact and the possible 'Preventional Control' (not damage control !!!) I  could exert before and during my bike trip.

I had to conclude that in cases of high Impact (I>0.9), nor my left-right brain chat, nor the 'Risk=PxI' formula lead to a sound decision, because both are too much based on probability instead of Impact. In other words:

In case of high Impact, probability is irrelevant


In case of high Impact, only control counts


From now on this 'bike conclusion' will be engraved in my memory and I will apply it in my professional work as well.



P.S. for disbelievers, the tough ones!
If you're convinced you would take the risk of firing the 1000 chamber  Russian gun against your head, you probably valuate the fun of the bicycle trip higher than probability of the loss of your life or good health.

In this case, suppose someone would offer you an amount of money if you would take part in a 1000 chamber Russian roulette instead of a bicycle tour. At which amount would you settle?

Let's assume you would settle at € 10.000.000 (I wouldn't settle for less). In this case you really value your bicycle trip!!!! 

As we've seen in banking business as well : extreme low probabilities and high impact situations are tricky! That's why stress tests focus on impact and not on probability.

The different faces of Risk
Another issue when looking at risk is that risk is always conditional.
'The' probability of death or 'the' mortality rate doesn't exist. Mortality depends on a number of variables, such as age (the run down state of your DNA quality), the DNA-quality you where born with and lifestyle. Secondly mortality also depends on a number of uncertain events in your life.

To demonstrate this 'Chameleon property' of probability, lets take a look at the probability of a meteor hitting good old earth.

The initial probability of an asteroid devastating the earth within a 10 year time frame is around 0.1%. A typical case of low probability and high impact. Once we've become aware of a spotted meteor in our direction, the probability suddenly changes from a general probability in a time frame to a asteroid specific probability during his actual passage of the earth.
In case of  the asteroid '2011 MD'  that will pass the earth at a minimal distance of 11000 km on June 27, 2011, this specific probability turns out 0.11% (remember the Russian Gun...).

With a diameter of around 8 meter, this asteroid is no big threat to our civilization.

Here's a short impression what's coming flying in on us within the next decades (Source: Nasa; asteroid>50 meter or minimum distance< 100,000km):



Apart from some 'big asteroids' in the next decade, this picture puts our minds at rest. Yet we should keep in mind that most asteroids are discovered only a few weeks before a possibe collaps...


Risk Maps
A nice example of the limits of the Risk=P×I model in combination with a nice aleternative, is demonstrated by Fanton and Neil in in a document called: 'Measuring your Risks: Numbers that would make sense to Bruce Willis and his crew'.

In  their document they analyze the case of the film Armageddon, where an asteroid of the size of Texas is on a direct collision course with the earth and  Harry Stamper (alias Bruce  Willis) saves the world by blowing it up.

Trying to fill in the Risk=P×I model in this Armageddon case is useless.

In this case, Risk is defined as:

Risk =  [Probability of Impact]  × [Impact of asteroid striking the earth]
 
Fanton and Neil conclude:
  • We cannot get the Probability number.
    The probability number is a mix up. In general it makes no sense and it's too difficult for a risk manager to give the unconditional probability of every ‘risk’ irrespective of relevant controls, triggers and mitigants.
  • We  cannot  get  the  Impact  number. 
    Impact (on what?) can't be unconditional defined without considering also the possible mitigating events. 
  • Risk  score  is  meaningless.
    Even  if  we  could  get  round  the  two problems above, what exactly  does  the  resulting  number  mean?  
  • It  does  not  tell  us  what  we  really  need  to  know. 
    What  we  really  need  to  know is the probability, given our current state of knowledge, that there will be massive loss of life.

Instead of the Risk=P×I model,  Fanton and Neil propose (Measuring risks) the use of  causal models (risk maps) in which a risk is characterised by a set of uncertain events.

Each of these events has a set of  outcomes and the  ‘uncertainty’  associated  with  a  risk  is  not  a  separate  notion  (as  assumed  in  the  classic approach).
Every event  (and  hence  every  object  associated  with  risk)  has  uncertainty  that  is characterised by the event’s probability distribution.

Examples:

The Initial risk of meteor strike
The probability of loss of life (meaning at least 80% of the world population) is about 77%:



In terms of the difference that Bruce Willis and his crew could make there are two scenarios: (1) the meteor is blown up and (2) where it is not.




Reading off the values for the probability of “loss of life” being false we find that we jump from 8.5% (meteor not blown up) to 82% (meteor blown up). This near tenfold increase in the probability of saving the world clearly explains why it merited an attempt.

Lessons learned
Use (Bayesian) Risk Maps rather than the Probability Impact Model or Risk Heat Maps, if you want to take decisions on facts instead of your intuition.

P.S. Many thanks to Benedict Escoto, who attended me on a wrong interpretation of the bicycle risk on bases of the Biomed info.
See document: Deaths of Cyclists in London: trends from 1992 to 2006
I rewrote this blog on information of DFT.

Related Links:
- DFT's Reported Road Casualties 2009
- Pedal cyclist casualties in reported road accidents: 2008 
- Is Cycling Dangerous?
- Cycling in London – How dangerous is it? (2011)
- Nasa: Small Asteroid to Whip Past Earth on June 27, 2011
- Nasa: Close (future) asteroid approaches...
- Nasa: Differences between Asteroid, Comet, Meteoroid, etc.
- Nasa: Search asteroid approaches in data base
- Nasa: Impact Probability of asteroids 
- Fanton & Neil: Measuring risks
- Fanton & Neil: Bayesian networks explained (pdf)
- Neil: Using Risk Maps!

Adds:
Using Risk Maps


Deathly bike accedents in London




May 14, 2011

Oversized Supervision?


In April 2011 EIOPA  published  the findings of its 2010 survey:


applicable to the Institutions for Occupational Retirement Provision (IORPs) in the context of the IORP Directive.

The report analyses several interesting differences in reporting among member states.

I'll will confine myself in this blog to two remarkable results....
 
1. Difference in number of Supervision employees per country

It's remarkable (and not directly explainable) to see that the UK and The Netherlands outnumber the other European countries on number of supervision employees....


 
2. Influence Actuarial Reporting

The survey provides a large number of reporting and monitoring issues that aim to monitor or mitigate several types of risk.
I'll provide a short report that shows the connection between some actuarial reports and types of risk.

Clearly the risk of funding is one of the most important issues with regard to actuarial reporting. Perhaps it's even a little bit overweighted......

Anyhow, check your reports with regard to the above risks, especially if your living in an oversized supervision country like the UK or The Netherlands....

Apr 25, 2011

Risk Quotes

I'll not even try to give a definition of 'Risk Management'.
More than the word Risk, Risk Management is full of traps and paradoxes.

Just to mention some.....

Risk Management is...
  • not primarily about risk that can be calculated with a 99,x% confidence level
  • dealing with Risks you know will come, but can't be calculated
  • more about correlation in time than mean estimates and standard deviation
  • more about prevention, foreseeing and managing risk than capitalisation of risk
  • more about taking risks to benefit, than trying to exclude risks
  • fighting risk instead of excluding risk
  • making Plans B and C, in case your confidence level fails

Avoiding Risk
One of the trickiest parts of Risk Management is that we often  are trying to avoid Risk at any price.

By doing so, we introduce a new risk: It gets harder to achieve shareholder and client value.

Often returns will decline because of over-capitalisation and a risk-return unbalance.

Finally we have to compete in new risk areas we're not experienced in. 

It's all well expressed in a cartoon on cartoonstock:

'We've considered every potential risk, except the risks of avoiding all risks.'


Personally I prefer the challenging Risk Management quote of Jos Berkemeijer, that states:

 "Risk Management: the art of foreseeing hindsight."





Better than trying to define Risk or Risk Management, it is to study and get inspired by Risk Quotes.

Therefore I conclude this Blog with a link to the Blog 'Risk Quotes'


You can place a random quote like this one:

Random Risk Quote


on your website or Blog by copying the next javascript code.

<script type="text/javascript" src="http://goo.gl/WdMOK"></script>

Install Instructions
  1. Copy above JavaScript code (select;CTRL-C).
  2. Paste (CTRL-V) the code on your webpage or Blog
    Blogger: Go to Design Tab, Click on Add a gadget;
    Click on 'HTML/Javascript' Gadget
    Paste the above code in the gadget and Save. 

Related Links
- Risk Quotes
- Riskviews: quotes
- Best Risk Management Quotes
- Death of Risk Management

Mar 5, 2011

Supervisory Compliant, is it enough?

Risk management is tricky business... Being 'Officially Compliant', 'Just Compliant' or in other words "Supervisory Compliant", is not enough to help your CEO survive with your company in the complex market battle!

Whether you're an Actuary or Risk Manager of an Insurance company, Bank or a Pension Fund, the risk of being 'Supervisory Compliant' is simply : bankruptcy!

Becoming 'Supervisory Compliant' in complex programs like Solvency-II, Basel III or Legal Pension Fund Risk Frameworks, consumes so much time and effort, that almost no time seems to be left for contemplating or doing the essential Risk Management work properly.

Just being 'Supervisory Compliant' implies:  constantly running after the Supervisor to become  'just in time' officially compliant and not having enough time to think about the (f)actual relevant risks.

Supervisory Compliance becomes very frighting when Risk Appetite and Valuations are rashly based upon the minimum Supervisory requirements, as is (e.g.) the case in the Dutch Pension Fund legal framework. Boards stop thinking about the actual risks and feel compliant and satisfied once the Supervisory Compliance Boxes are checked.

A new look at compliance
Let's take a look from a new point of view at the complete Risk Management Compliance Field:

In basis there are three types of 'being compliant':

  1. Supervisory Compliant
    When you're Supervisory Compliant, you officially comply to all legal Risk Management compliance requirements. Your Supervisor is happy...

  2. Professional Compliant
    You comply to your own professional Risk Management standards. You are happy...  but what about your Supervisor? Comply or Explain....

  3. Success Compliant
    Being Success Compliant implies that all Risk Management requirements that are key to have success - e.g. key to survive in the market on the long run - are met.

Let's zoom in at some specific areas in this chart:

Bias areas
It's perhaps hard to admit, but in our attempt to be complete, we define and manage a lot of (small) risks that do actually exist, but are in fact not really or limited relevant with regard to company continuity.

Distinctive Character area
The Distinctive Character area is perhaps the most interesting area. To get grip on this area urges us to 'Think outside the Circle'.

By doing so we'll be able to manage risks that  our competitors fail to do. Here we can achieve 'Distinctive Character' by managing risks more efficient or by turning risks into profits. Examples are: Derivatives that limit our investment risks. Specialized experience rating (rate making) on your portfolio on basis of characteristic and unique risk profiles.

Tricky area
The tricky area is the area that consists of Supervisory Risks you tend not to find important, but that are very important for achieving success in the market. Tricky areas could e.g. be: Deflation Risk, Longevity Risk or Take Over Risk.

Reversed Thinking area
This is perhaps the most interesting risk area.

To explore this area you'll not only have  to 'think outside of your circle', but - just like in reversed stress tests with Banks - try to think backwards, to find out what could cause a certain event or loss.

This reversed thinking process succeeds best as a group. Group members should be professionals and non-professionals from different types of business, education and background.

A successful group mix could e.g. consist of : an actuary, an accountant, a manager, a marketing manager, a compliance officer, an employee, a client, a shareholder representative and last but not least the receptionist.

Finally.....
Try to find time to manage your company to new heights and stop being just 'Supervisory Compliant'.....

Feb 27, 2011

Gold: Risk or Rescue?

For those of you who are still doubting...we live in a crazy world....

The Dutch Central Bank (DNB) has ordered (by court !) the glass-workers pension fund (SPVG) to decrease its 13% Gold allocation to less than 3% within two months.

DNB and Court arguments in short:
  1. An investment of 13% is not in line with the Prudent Person Rule, which includes the principle that: assets must be invested in such a manner as to ensure the security, quality, liquidity and profitability of the portfolio as a whole.

  2. Gold is a commodity and holding 13%  is classified as 'overweight' in comparison to the 2.7% average that Dutch pension funds have invested in commodities.

  3. 15% allocation in Gold is a 'concentration risk' that could lead to a coverage shortage if the gold price imploded (volatility of Gold is relatively large).

At first, it seems unbelievable that important decisions, with substantial financial impact  - even in Court - are not based on financial facts, but on 'general principles' and the way the market 'used to do it'.

A decision based on an argument that refers to 'the average pension fund,' would more or less imply that pension funds would not be allowed to base their investment strategy on their own specific situation or a changing market outlook. Pension Fund Boards appear to be  'captured' by the market and a Supervisor who obviously has a hard time to develop 'own standards'....

Secondly, DNB actually takes over the investment responsibility of the pension Board. One could wander if DNB is (sufficiently) aware of the possibility that it can be hold financially responsible for the effect of a negative outcome if it turns out in the near future that SPVG has suffered a substantial financial loss, caused by this DNB-designation.

Is Gold really a risk?....  or a rescue?

Checking the facts.... 
Let's just check if DNB's and Court's arguments are valid.....

Yearly Return
We start by comparing the yearly returns of Gold, the S&P-500 Index and '10-Y Treasury Bonds' over the period 1971-2010.

To make Bonds risk-comparable with Gold and the S&P-500 Index, the yearly average Bond interest rate is translated into a yearly Market Value performance. This is done by assuming that each year, all '10-Y Bonds' bought in a specific year are valued, and sold at the average interest rate one year later (approximation).


Here is the result:

To bring some sense and order into this chart, we calculate the 'Moving Compound Annual Growth Rate' (MCAGR).
We start in 2010 and calculate the  compound average yearly return backwards moving up (year by year) to 1971. This is the result:


Now, this looks better... and a bit surprising as well!!! On the long term Gold (μ=9.2%) and the S&P-500 (μ=10.2%) are tending to a rough 9-10% yearly return......  A little bit Surprising is that Bonds (μ=7.6%) get along very well with their big risky brothers...
Take your time to 'absorb' the impact of this chart.....

Risk
Next, we take a look at Risk. We define Risk at first as the Standard Deviation (SD). We directly cut trough to the 'Moving Risk' (Moving SD).
We might conclude here that during recent years there was an increase of risk with regard to the S&P-500 (the 'red' crisis 'Mount K2' is clearly visible). Note that also for a longer period, i.c. the last 30 years, the S&P-500 Risk is substantial higher than the Risk of Gold and much higher than the Risk of Bonds. Only looking at a period of 40 years, Gold shows 'optical' up as more risky (SD=σ=25.8%) than the two other asset categories, Bonds (SD=σ=6.9%) and S&P-500 (SD=σ=18.1%).

However this way of presenting Risk is strongly discussable. Another view of Risk that comes closer to what we naturally 'perceive' as Risk, is to define Risk as only as the Downside Standard Deviation (look up : Sortino ratio ), where all positive yearly returns are eliminated (DSD) or set to zero (DSDZ).....
Let's have a look:
Now, these charts give us a quite a different sight on Risk-reality....
It shows that -on the long term -  not Gold (DSD=Dσ=7.5%) is the riskiest asset, but the S&P-500 (DSD=Dσ=10.6%). Bonds (DSD=Dσ=0.5%), as aspected, have the least volatility and are therefore less risky.

Perhaps the Risk of Bonds is a bit underestimated (very few observations) by the DSD-method (excluding positive yearly returns). In this case the downside deviation of yearly Bond-returns, replacing positive returns by zero, which generates a standard deviation of 3.2%, gives a better indication of a more likely standard deviation on the long run.


Why Gold? 
Although these simple calculations already put the DNB conclusions in a different light, let's get to the main point that should be addressed in defending why Gold should be a substantial part of any Pension Fund portfolio:
 
 Gold Reduces VaR


In a 2010 (october) publication the World Gold Council published a document called Gold: Hedging Against Tail Risk. This interesting report concludes:
  1. Gold is first and foremost a consistent portfolio diversifier
  2. Gold effectively helps to manage risk in a portfolio, not only by means of increasing risk-adjusted returns, but also by reducing expected losses incurred in extreme circumstances such tail-risk events (VaR).
Following this excellent WGC report, let's test the balancing and risk-reducing  power of Gold by analyzing (classical) Risk (SD) in combining Gold with different allocations (0% up to 100%)  in an asset mix with Bonds, respectively investments in S&P-500 stocks.


This chart clearly shows that Gold has the power to reduce the S&P-500 Risk (SD) from18.1% to 13,3% with an optimal asset location mix of  approximately 60% S&P-500 and 40% Gold. 

In case of Bonds the Risk (SD) is reduced from 6.9%  to 4.8% with an optimal mix of 80% Bonds and 20% Gold.

Asset Liability Model (ALM)
In practice it is necessary to optimize, by means of an adequate ALM study, the  allocation mix of stocks, Bonds and Gold. Just as a 'quick & dirty' excercise, let's take a look at the next asset-combination scenarios, based on data over the period 1971-2010:
Just some head line observations:
  • From scenario M1 it becomes clear that even a 100% Bond scenario is't free from Risk. So diversification with other assets is a must.
  • Looking at M2-M5 we find that the optimal mix, defined as the mix that best maximizes Return (Compound Annual Growth Rate)  and Sharpe Ratio (at a Risk free rate of 3% or 4%) and minimizes Risk (Standard deviation), is something something in the order of: 70% Bonds, 15% stock and 15% Gold.
  • Scenarios M6-M8 and M9-M11 take todays most common (but strongly discussable!) practice as a starting point. Most pension funds have allocated around 50% or 40% to Bonds and 50% or 60% in more risky asset categories (stocks, etc.). It's clear that even in this situation Risk can be reduced and Return can be optimized, if Stocks are exchanged to Gold with a maximum allocation of 20% or 30%.

Notifier
Although this 'rule of thumb exercise' on this website provides some basic insights, please keep in mind that finding the optimal mix is work for professionals (actuaries).

A serious ALM Study is always necessary and should not only take into account a broad range of diversified asset categories, but should also focus and optimize on:
  • The impact of the liabilities (duration) and coverage ratio volatility
  • The Timing: Mean values and Standard Deviations are great, but the expected return highly depends on the actual moment of  investment or divestment in the market.
  • Future expectations. In the current market situation (2011) the risk of interest rates going up and therefore Bond market value going strongly down, isn't hypothetical. Secondly, the stock market has been pumped up by trillions of 'investments' (?) in the US economy. Once this crisis-aid definitely stops, the question is if these 'cement investments' will be strong enough to keep stocks up. Personally I fear the worst...
    Not to mention a scenario with declining stock rates in combination with increasing interest rates and inflation......
    Who said the life of an actuary was easy???

Conclusion
We may conclude that:
  • Investing in Gold up to a 10% to 15% allocation, reduces the Risk of a portfolio consisting of Bonds and S&P-500 Stocks substantially. 
  • Gold is less Risky than investing in S&P-500 Stocks

Therefore the 'not with facts' underpinned intervention of DNB looks - to put it euphemistically -  at least strongly discussable....

A wise and modest underpinned allocation of Gold is no Risk, it's a Rescue!

Related Links:
- Spreadsheet with Data used in this Blog
- Prudent person Rule
- IPE: Dutch regulator orders pension scheme to dump gold
- GOLD: HEDGING AGAINST TAIL RISK
- Downside Risk:Sortino ratio
- Dutch Central Bank Orders Pension Fund To Sell Its Gold
- Pension Fund Benchmarking 
- Strategic Risk Managment and Risk Monitoring for Pension Funds

Bonus: Gold, Hedging against Tail Risk Video