Actuarial Limit 100m Sprint

In June 2009 Professor of Statistics John Einmahl and (junior) actuary Sander Smeets, calculated the ultimate record for the 100-meter sprint. The actual World record - at that time - was set by Usain Bolt at 9.69 seconds (August 16, 2008, Beijing, China).

With help of the extreme-value theory and based on 'doping free' World Record data (observation period:1991 to June,19 2008) Smeets and Einmahl calculated the fastest time that a man would be ultimately capable of sprinting at: Limit = 9.51 seconds.

However....
As often in actuarial calculation, once your model is finally set, tested and implemented, the world changes...

Or, as a former colleague once friendly answered when I asked him if his ship (project) was still on course:

My ship's on course......
But the port moves !

In this case, the 'model shifting event' took place in Beijing, exactly one year later, on August 16, 2009: Usain Bolt sets a new astonishing 100m World Record in 9.58 seconds !

Of course 9.58 secs is still within the scope of Smeets' and Einmahl's model limit of 9.51 seconds...

Nevertheless, as a common sense actuary, you can see coming a mile away, that this 9.51 secs-limit will not hold as a final future limit.

As is visual clear, one can at least question the validity of the 'extreme-value theory approach' in this 100m sprint case.

Math-Only Models
In this kind of projections (e.g. 100m world records) it's not enough to base estimations only on historical data. No matter how well historical data are projected into future data, things will mesh up!
Why? Because these kind of 'math-only models' fail to incorporate the changes in what's behind and what causes new 100m World Records. To develop more sensible estimates, we'll have to dive into the world of Biomechanics.

To demonstrate this, let's have a quick -amateur - look at some biomechanical data with respect to Usain Bolt's last World Record:

Let's draw a simple conclusion from this chart:

Hitting 9.50 secs seems possible

Just like Bolt stated in an interview: "I think I can go 9.50-something", appears to be realistic:

• 0.026 secs faster by improving his reaction time to the level of his best competitors: 0.12secs, instead of  0.146secs
• 0.060 secs faster by reaching his maximum speed (12.35 m/s) at V50 and maintaining this speed for the remaining 50 meters. 

Biomechanical explanations
On top of this, Bolt outperforms his competitors on having a higher step length and a lower step frequency. This implies there must be deeper biomechanical factors like body weight, leg strength, leg length & stiffness (etc), that need to be included in a model to develop more realistic outcomes.

Newest biomechanical research ("The biological limits to running speed are imposed from the ground up" ) shows maximum (theoretical?) speeds of 14 m/s are within reach, leading to potential World Records of around 9 secs on the long run.....

Based on this new biomechanical information output in combination with an appropriate chosen corresponding logistic model, we can now predict a more realistic ultimate World Record Estimation (WRE) in time.

Curvefitting at ZunZun with the 1968-2009 data (including Bolt's 9.58 secs record) on basis of a Weibull CDF With Offset (c), led to the next, best fit equation:

 
With: y=WRE in seconds, x=Excel date number, and:
a =  -3.81253229860548
b =  41926.0524625578
c =  8.97894916004274 (=final limit)

As we may learn more about biometrics in the near future, perhaps the ultimate 9 seconds (8.9789 seconds, more exactly) can possibly be reached faster than we currently estimate (year 2200).


Playtime
Now, just play around with (estimate) world records in this Google time series plotter:

WRE Plotter

Finally

As actuaries, what can we learn from this 'sprinting example'?
 

Well... Take a look at estimating future (2030 a.f.) mortality rates.

Just like with estimating World Records, it seems almost impossible to estimate future mortality rates just on basis of extrapolating history.

No matter the quality of the data or your model, without additional information what's behind this mortality development, future estimations seem worthless and risky.

Although more and more factors affecting retirement mortality are being analysed, (bio)genetic and medical information should be studied by actuaries and translated into output that strengthens the devlopment of new mortality estimate models.

Actuaries, leave your comfortable Qx-houses and get started!

Related links and sources:
- Ultimate 100m world records through extreme-value theory
- 90 years of records
- Usain Bolt: The Science of Running Really Fast
- Biomechanics Report WC Berlin 2009 Sprint Men
- BP WC Berlin 2009 - Analysis of Bolt: average speed 
- The biological limits to running speed (2010)
- Limits to running speed in dogs, horses and humans (2008)
- Improving running economy and efficiency
- Factors Affecting Retirement Mortality and Their Impact ... 
- Cheetah Sets New World Record 100 meter sprint2009 (6.130 sec)
- 100m World record data and WRE (xls spreadsheet)

Exceptional Longevity Predictable

A genome-wide association study (Paola Sebastiani et al) based upon 1055 centenarians, showed that Exceptional Longevity (EL)  - living 90 years or more - can be predicted with 77% accuracy!

video

EL Genetic Passport
This research development will have major impact on 'life insurance' and pensions. With an EL Genetic Passport in your pocket, you'll have the power to conclude with 77% certainty whether it's profitable (or not) to buy life insurance or to invest more or less in your pension fund.

Genetic Loss by GAS

To prevent major losses caused by 'adverse selection', life insurance companies and pension funds have no other choice left, than to base life insurance premium prices and pension contributions on 'genetic passport information'.

Just like it's (from a company's perspective) devastating to sell mortgages to people who cannot afford it, it's also killing to sell life annuities to people who have knowledge of getting 90 years or older with 77% certainty.

As Genetic Adverse Selection (GAS) also negatively affects current provisions and value of an insurance company or pension fund, GAS development effects should be included and estimated in actual liability calculations.

Without doubt, GAS will generate large Genetic Losses in the next decades. Perhaps GAS can be qualified as a substantial new kind of risk in Pillar I calculations.


Related links - Sources:
- Science: Genetic Signatures of Exceptional Longevity in Humans
- PDF: Genetic Signatures of Exceptional Longevity in Humans
- BU: Signatures of Human Exceptional Longevity (video)
- Centenarians in some European countries, 2007

Death by Solvency

Risk Management can be a strange and deathly game. Normally one would expect that the more the demand of Probability of Insolvency (POI) is decreased:

• the more Prevention- , Risk-reduction- and Damage-control-measures will be taken
• the less actual Risk and corresponding Loss will actually occur
• the higher the resulting average yearly profit
• the lower the resulting yearly profit volatility

This appears to be true in situations where Risk Management is hardly developed and POI-Demands are relatively modest (5%-2.5%).

Increasing POI-Demands
However, depending on the type of risk, beyond certain POI-Demands (smaller than roughly 2.5%) , the costs of Risk management measures, maintenance and capital requirements become higher than the average expected Loss-reduction, resulting in - on average - lower profits.
Of course, these extra risk management investments and capital requirements can financed by raising consumers prices, but - on balance - this will result a smaller market corresponding with a lower profitability level.

The question can be asked if this still is what we, management and consumers, intended to achieve.......?

Next, in our passion to reduce Risk to an even more extreme low level, we can get carried away completely...

Excessive POI-Demands
When POI-Demands get to levels of 1% or less, a remarkable psychological effect enters the Risk management arena.

Management perceives that the Risk-level is now actually so low that they cannot fail anymore.
In their ambitious goal to outperform the profit level of their competitors, management gets overconfident and reckless. What would you attempt to do if you knew you could not fail?

When POI-Demands are set to levels of 0.5% or less (as they are mostly now in 2010) it becomes almost impossible to beat your competitors with an approach of 'taking more risk'. Even if one would try to manage or hedge these extra risks 'best' in the market. In the long-term, the price of this risk would equal or beat the expected loss.

In this situation some managers get desperate and instead of considering things 'right', they see only one option 'left'....

WAR

'Working Around (the) Rules"

WAR, Working Around the Rules, comprises actions like:

• Taking (extra) risks on non-measurable or non-measured financial transactions, or or 'non-obligated-reporting risks'
• Manipulating, disguising or mitigate risk information, or risk-control reports
• Misuse legally allowed methods and accounting principles to create legally unintended financial effects or transactions

 

It's perhaps hard to admit, but as actual developments show, we've entered the final WAR phase. Some Examples: subprime, Madoff accounting, BP-deep horizon oil failure, bank multipliers, etc, etc.

In all these examples, managers (are pushed to) become over-creative by working around the rules to deliver what they've promised: more profit.

However this approach always results in

1. More short-term profits
2. Less long-term profits
3. Sudden bankruptcy in the end

This development, resembles the 2010 situation in the Insurance and Banking industry where, after each financial debacle, POI-Demands where successively decreased to a 0.5% level  and have resulted in marginal profits and a highly volatile Profits or even losses. Pension Funds (NL: 2.5% POI-Demand) appear to be the next patient the operating table.....

The situation is out of control. Nothing really seems to help anymore....

Solutions

Are there any solution to prevent this solvency meltdown process?
Yes, but that's for another blog as this one is getting too long...

Related links:
- Why excessive capital requirements harm consumers, insurers and...(2010)
- Presentation - Modelling of Long-Term Risk (2010)