Showing posts with label longevity. Show all posts
Showing posts with label longevity. Show all posts

Jun 5, 2011

Short Term Longevity Risk

As well-born actuaries we all know the long term risks of longevity:

Lots of actuaries keep expending their energy on calculations of 50 years ahead mortality probabilities....  And indeed..., this is challenging....

Some research reports predict a decline in life expectation, others and more serious recent reports show a steady increase of life expectation.

Mission Impossible
Fact of actuarial life is that - although long term research is useful and educational - we are no Actuarial Magicians.

We should never suggest that we're able to value a bunch of complex and systemic risks  (liabilities, assets,mortality, costs, demographics, etc) into a reliable consistent model that predicts reality.

It's a farce!

What CAN we do?
Instead trying to compress a complex of long term risky cash flows into one representing unique value, we need to:
  1. Analyze and model the short term risks
  2. Develop a method (system) that enables boards of directors to manage and control their risky cash flows (profit share systems, experience rating, etc.).

Example: Short Term Longevity Risk
As a 2011 report of the National Research Council clearly shows:  The previous 50 years we've seen a 3 months yearly increase of lifespan every calendar year.

Instead of recalculating, checking and pondering this trend, let's take a look at the short term effects of this longevity increase trend.

Effect of 'one year life expectancy' increase 
First we take a look at the cost effect of the increase of 'one year of life expectancy' on a single-premium of a (deferred) life annuity (paid-up pensions)...
( Life table total population: United States, 2003 )

Depending on the discounting interest rate, a one year improvement of longevity for a 65 old person demands a 2,3% to 4,0% increase of the liabilities.

Of course the increase of the liabilities of a portfolio (of a pension fund) depends on the (liability weighted) age distrubution of the corresponding portfolio.

Here's a simple example:

This comes close to the rule of thumb as mentioned by AEGON:

10% mortality improvement adds one year to life expectancy, and one year of life expectancy adds 4% to the required value of a pension fund’s reserves

From the above presented visual sensitivity analysis we may conclude that for general (distributed) portfolio's a 'one year lifetime increase' will demand approximately 4-5% of the actual liabilities.

A three to four months yearly longevity-increase - as is still the actual trend - will therefore demand roughly a substantial 1,5% (yearly) of the liabilities.
This implies that in case your contribution is calculated at 4% and your average portfolio return is 7%, there's 3% left for financing longevity and indexation (=method). As 'longevity growth' in the near future will probably cost about 1,5%, there's  only 1,5% left for indexation on the long run.

Case closed

Related links:
Spreadsheet (xls) with data used in this blog
- Forecasting longevity of Dutch pension scheme members using postcodes
- Increasing life expectancy at pension funds (uvt;2011)
- Life Tables for the United States Social Security Area 1900-2100
- Valuing Pension Fund Liabilities on the Balance Sheet
- No limits to life expectancy?
- Broken Limits to Life Expectancy
- NRC: Explaining divergent levels of longevity (pdf;2011)
- Wolfram Alpha: Longevity U.S.
- AEGON: Longevity Rule of thumb

Sep 11, 2010

Coverage Ratio Solution Space

Dutch pension funds are in deep trouble. The average coverage ratio of many pension funds has fallen to a level well below 100% (underfunded). Some major Dutch pension funds with coverage levels around 90%, called Government to dissuade the planned pension rights cuts.

A delay in pension rights cuts seems justifiable. Key question is the reason for this requested delay. For reasons of reformulating new pension policies and ambitions, delay seems reasonable. With the intention to just 'buy time' in order to continue 'desperate hope' that the markets and low returns will recover, further delay could prove catastrophic.

Facing Reality
Pension funds have to cope with several hurricanes at the same time:
  1. Relatively low interest rates
  2. Underperforming stock market
  3. Underestimated longevity risks
  4. Need for higher confidence levels

Although low interest rates and underperforming stock markets could continue for several years, on the long term interest rates and stock markets will most likely recover, simply because economic growth imply higher returns on the long term.

Underestimating The Longevity Monster
One of the 'big' (?) surprises seems the recent development in longevity. For decades now, actuaries and researchers are structurally underestimating the effect of longevity.

Maggid's Longevity Forecast
Although longevity has been studied a lot, a decrease of the steady growth of the human lifespan in the coming decades will most likely turn out to be idle hope....

Lessons learned, we actuaries will seriously have to take into account that the linear increase of lifespan probably will continue until at least the age of 90 (Maggid forecast). This implies that we'll have to 'spice up' our mainly retrospective life expectancy models and corresponding forecasts with a healthy portion of common sense.

What about the 'risk free' discount rate?
More actu(ari)al trouble is caused by the fact of the low interest rates and sticky stock markets.
Pension funds face the substantial volatility and the low level of the so called "risk free discount rate" that drives the coverage ratio. Paradoxically we could state:

There's nothing more risky than a  'risk free' discount rate

The - artificial - low level risk free interest rate pulls down the coverage ratio of a pension fund.

At the same time it's necessary to level up the existing 97.5% confidence level of pension funds. A 97.5% confidence level implies that a pension fund will turn into default (underfunding) twice in an average person's lifespan.

Despite the fact that a 'twice in a life meltdown' is probably hard to explain to anyone, new upcoming Solvency demands for pension funds will be inevitable in order to create a level playing field on the financial market. Good governance, common sense and upcoming new regulatory initiatives will therefore certainly urge a higher pension fund confidence level like the 99,5% level in the insurance industry (Solvency II) or the 99,9% level in the banking industry (Basel II) .

Sitting Ducks
As is clear from the above image, successfully financing a pension-fund (portfolio) on the long term at the current ambition level, calls - in general - for high (unrealistic) interest rates. The 'solution space' for achieving the necessary  high coverage ratios that match the (new) capital requirements appears to be very narrow.

Therefore (there is no other way), most pension funds have to take time and redefine their (future) ambition instead of playing 'sitting ducks' and hoping for the best.

Used Sources, Links:

- Dutch life expectation 2010-2060
- Japanese life expectation: 86.5 years
- Dutch life expectation 2010-2060
- Japanese life expectation: 86.5 years
- Dutch - De risico's van het leven (risks of life) ...
- Will Life Expectancy Continue To Increase Or Level Off 

Jul 5, 2010

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!

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

Feb 6, 2010

Why VaR fails and actuaries can do better

Perhaps the most important challenge of an actuary is to develop and train the capability to explain complex matters in a simple way.

One of the best examples of practicing this 'complexity reduction ability' has been given by David Einhorn, president of Greenlight Capital. In a nutshell David explains with a simple example why VaR models fail. Take a look at the next excerpt of David's interesting article in Point-Counterpoint.

Why Var fails
A risk manager’s job is to worry about whether the bank is putting itself at risk in the unusual times - or, in statistical terms, in the tails of distribution. Yet, VaR ignores what happens in the tails. It specifically cuts them off. A 99% VaR calculation does not evaluate what happens in the last1%.

This, in my view, makes VaR relatively useless as a riskmanagement tool and potentially catastrophic when its usec reates a false sense of security among senior managers and watchdogs.

VaR is like an airbag that works all the time,except when you have a car accident

By ignoring the tails, VaR creates an incentive to take excessive but remote risks.

Consider an investment in a coin-flip. If you bet $100 on tails at even money, your VaR to a 99% threshold is $100, as you will lose that amount 50% of the time, which obviously is within the threshold. In this case, the VaR will equal the maximum loss.

Compare that to a bet where you offer 127 to 1 odds on $100 that heads won’t come up seven times in a row. You will win more than 99.2% of the time, which exceeds the 99% threshold. As a result, your 99% VaR is zero, even though you are exposed to a possible $12,700 loss.

In other words, an investment bank wouldn’t have to put up any capital to make this bet.

The math whizzes will say it is more complicated than that, but this is idea. Now we understand why investment banks held enormous portfolios of “super-senior triple A-rated” whatever. These securities had very small returns.

However, the risk models said they had trivial VaR, because the possibility of credit loss was calculated to be beyond the VaR threshold. This meant that holding them required only a trivial amount of capital, and a small return over a trivial capital can generate an almost infinite revenue-to-equity ratio.

VaR-driven risk management encouraged accepting a lot of bets that amounted to accepting the risk that heads wouldn’t come up seven times in a row. In the current crisis, it has turned out that the unlucky outcome was far more likely than the backtested models predicted.

What is worse, the various supposedly remote risks that required trivial capital are highly correlated; you don’t just lose on one bad bet in this environment, you lose on many of them for the same reason. This is why in recent periods the investment banks had quarterly write-downs that were many times the firm wide modelled VaR.

The Real Risk Issues
What. besides the 'art of simple communication', can we - actuaries - learn from David Einhorn?

What David essentially tries to tell us, is that we should focus on the real Risk Management issues that are in the x% tail and not on the other (100-x)% .

Of course we're inclined to agree with David. But are we actuaries truly focusing on the 'right' risks in the tail?

I'm afraid the answer to this question is most often : No!
Let's look at a simple example that illustrates the way we are (biased) focusing on the wrong side of the VaR curve.

Example Longevity
For years (decades) now, longevity risk has been structurally underestimated.

Yes, undoubtedly we have learned some of our lessons.

Todays longevity calculations are not (anymore) just based on simple straight on mortality observations of the past.

Nevertheless, in our search to grasp, analyze and explain the continuous life span increase, we've got caught in a interesting but dangerous habit of examining more and more interesting details that might explain the variance of future developments in mor(t)ality rates.

As 'smart' longevity actuaries and experts, we consider a lot of sophisticated additional elements in our projections or calculations.

Just a small inventory of actuarial longevity refinement:
  • Difference in mortality rates: Gender, Marital or Social status, Income or Health related mortality rates
  • Size: Standard deviation, Group-, Portfolio-size
  • Selection effects, Enhanced annuities
  • Extrapolation: Generation tables, longitudinal effects, Autocorrelation, 'Heat Maps'


In our increasing enthusiasm to capture the longevity monster, we got engrossed in our work. As experienced actuaries we know the devil is always in the De-Tails, however the question is: In which details?

We all know perfectly well that probably the most essential triggers for longevity risk in the future, can not be found in our data.
These triggers depend on the effect of new developments like :

It's clear that investigating and modeling the soft risk indicators of extreme longevity is no longer a luxury, as also an exploding increase of lifespan of 10-20% in the coming decades seems not unlikely.
By stretching our actuarial research to the the medical arena, we would be able to develop new (more) future- and shock-proof longevity models and stress tests. Regrettably, we don't like to skate on thin ice.....

Ostrich Management

If we - actuaries - would take longevity and our profession as 'Risk Manager' more serious, we would warn the world about the global estimated (financial) impact of these medical developments on Pension- and Health topics. We would advice on which measures to take, in order to absorb and manage this future risk.

Instead of taking appropriate actions, we hide in the dark, maintaining our believe in Fairy-Tails. As unworldly savants we joyfully keep our eyes on the research of relative small variances in longevity, while neglecting the serious mega risks ahead of us.

This way of Ostrich Management is a worrying threat to the actuarial profession. As we are aware of these kind of (medical) future risks, not including or disclaiming them in our models and advice, could even have a major liability impact.

In order to be able to prevent serious global loss, society expects actuaries to estimate and advice on risk, instead of explaining afterwards what, why and how things went wrong, what we 'have learned' and what we 'could or should' have done.

This way of denying reality reminds me of an amusing Jewish story of the Lost Key...

The lost Key
One early morning, just before dawn, as the folks were on their way to the synagogue for the Shaharit (early morning payer) they notice Herscheleh under the lamp post, circling the post scanning the ground.

“Herschel” said the rabbi “What on earth are you doing here this time of the morning?”

“I lost my key” replied Herscheleh

“Where did you lose it?” inquired the rabbi

“There” said Herscheleh, pointing into the darkness away from the light of the lamp post.

“So why are looking for you key in here if you lost it there”? persisted the puzzled rabbi.

“Because the light is here Rabbi, not there” replied Herschel with a smug.

Let's conclude with a quote, that - just as this blog- probably didn't help either:

Risk is not always apparent,
but its invisibility is no longer an excuse for ignoring it.

-- Bankers Trust on risk management, 1995 --

Interesting additional links:

Jun 7, 2009

Happy Life Expectancy

As we know, Life Expectation can be measured in many ways. The three most common methods are:
  • LE = Life Expectation (standard), the average number of years that a newborn can expect to live.
  • HALE = Health Adjusted Life Expectation, the average number of years that a newborn can expect to live in "full health"
  • HLE = Healthy Life Expectation, the average number of years that a newborn can expect to live in "full perceived health"

As comparisons between LE an HALE show, 'living longer' doesn't necessarily mean 'living longer in good health'. However, it has become clear that a strong Healthy Working Life Expectancy at age 50 or higher is the best guarantee that people will be able to work longer as they live longer.

One step further. Living in "good (perceived) health" doesn't automatically mean that people are living a happy life.

Happiness is one of the most important lifestyle statistics. Optimizing the number of 'happy years' in our life is therefore an important issue.

Happy Life Expectancy
Here is where Prof.dr. Ruut Veenhoven (Publications), comes in.

Veenhoven defines a different HLE as:

In formula:

HLE = LE x Happiness-score/10

The Happiness-score (H) is the average happiness as expressed on a 0-10 scale.

Let's compare the HALE an HLE (Happy Life Expectancy) scores with each other for different (top-30 ranked) countries:

A full list and data is available at the World Database of Happiness.

It's clear that in most top-30 countries we spend about 90% of our life in healthy conditions and only about 70-80% in happy conditions. There room for improvement here! I'll leave the other conclusions up to yourself....

Let's conclude with two other correlated interesting findings:

1. Happy Life Expectancy Determination
What public policies are most conducive to happiness? This requires a view on the determinants of happiness in nations:

It turns out that six societal qualities (wealth, security, freedom, inequality, brotherhood and justice) explain 83% of the differences in Average happiness, 71% of the differences in Inequality of happiness and no less than 87% of the differences in Happy Life Years.
Enough for an interesting discussion between actuaries and politicians, I would say....

2. Wealth and happiness correlation
As expected wealth (expressed in GDP per capita) and happiness (e.g. highly satisfaction) are strongly correlated in clear distinguished regions.
Also the 'mean life satisfaction' turns out to be correlated to different age-groups and countries:

These graphics are food for thought on the relationship between mortality and wealth. More about that soon......