QIS: Longevity Risk Sharing

In a recent discussion about the future and fundamentals of the Dutch pension system I discussed the importance of solidarity.

As expected, the participants quickly came up with the various forms of solidarity, including solidarity between:

– higher and less educated people

– women and men

– old versus young people

Longevity Risk Sharing

Remarkably non of the participants had any idea about the financial impact of one of the most fundamental forms of risk sharing in case of a life annuity: Longevity Risk Sharing. Let's call it in general 'mortality solidarity'.

When asked, most participants strongly underestimated the impact of mortality (mortality share) as part of the yearly payment in the form of a life annuity. On the other hand, they overestimated the impact of 'return'.

Some of the participants had the idea that they would be 'better of' with a traditional individual investment plan in combination with a little more investment risk (and return) ...

Life Annuity Composition
So let's do a mini QIS (Quantitative Impact Study) of 'mortality solidarity' by examining the development of the composition of an annual lifetime annuity, regarding three basic elements: Mortality, Return and Desaving.

Here is the result for a Dutch man, age 65, with a lifetime annuity based on an average 5% yearly return:

Translated in table form:

	Yearly Payment Composition				Cumulative Composition
Age	Mortality	Return	Desaving		Mortality	Return	Desaving
65	16%	51%	33%		16%	51%	33%
66	17%	50%	34%		16%	50%	34%
67	18%	48%	34%		17%	50%	34%
68	19%	46%	34%		17%	49%	34%
69	21%	45%	35%		18%	48%	34%
70	22%	43%	35%		19%	47%	34%
71	24%	41%	35%		20%	46%	34%
72	26%	39%	35%		20%	45%	34%
73	28%	38%	35%		21%	45%	34%
74	30%	36%	34%		22%	44%	34%
75	32%	34%	34%		23%	43%	34%
76	34%	33%	33%		24%	42%	34%
77	36%	31%	33%		25%	41%	34%
78	38%	30%	32%		26%	40%	34%
79	41%	28%	31%		27%	40%	34%
80	43%	27%	30%		28%	39%	34%
81	45%	25%	29%		29%	38%	33%
82	48%	24%	29%		30%	37%	33%
83	50%	22%	28%		31%	36%	33%
84	52%	21%	27%		32%	36%	32%
85	55%	20%	26%		33%	35%	32%
86	57%	18%	25%		34%	34%	32%
87	60%	17%	23%		35%	33%	31%
88	62%	16%	22%		36%	33%	31%
89	65%	15%	20%		37%	32%	31%
90	67%	14%	19%		39%	31%	30%
91	69%	13%	17%		40%	31%	30%
92	72%	13%	16%		41%	30%	29%
93	73%	12%	15%		42%	29%	29%
94	75%	11%	14%		43%	29%	28%
95	77%	11%	12%		44%	28%	28%
96	78%	10%	12%		45%	28%	27%
97	79%	9%	11%		46%	27%	27%
98	80%	9%	11%		47%	26%	26%
99	82%	8%	10%		48%	26%	26%
100	83%	8%	10%		49%	25%	25%
101	84%	7%	9%		50%	25%	25%
102	85%	7%	9%		51%	25%	24%
103	85%	7%	8%		52%	24%	24%
104	86%	6%	8%		53%	24%	24%
105	87%	6%	7%		54%	23%	23%

Observations

As is clear from the table above :

• Already at the start the start of the annuity, at age 65, 16% of the yearly payment is due to mortality risk sharing and 'only'  51% is related to the 'return'.
• As a pension member continues to live, the  'mortality share' of the annual payment increases. At the age of 83 already 50% of his annuity is due to mortality effects and the 'return share'  is already down to 22%.
• As from age 77 of, the 'mortality effect' on the annual payment exceeds the 'return effect'.
  
  

Conclusion

From some simple calculations, we can conclude that longevity (mortality) solidarity is a fundamental part of a life annuity.
 

AfterMath

Make your calculations with other interest rates, ages or life tables with the Pension Calculator (Excel).

You may download the pension calculator HERE

Links/Sources

- Solidarity: Sticking together or ..(Google Books, P. de Beer)

- Benefit of collective schemes (IPE)

- HFC: Pension Challenge

- Download the Excel Pension Calculator

DCF: Discounted Crash Flow

I remember in a 2007 client panel discussion I was chocked to hear that three large company CFOs of name and fame, without blinking an eye, stated that they were running their company on basis of a narrow quarterly time schedule, no longer. Long term investments? Out of the question. Pension obligations? Rather not, please... Project payback periods: 3-6 months, in exceptional cases a maximum of a year.

What was happening?
How come, CFOs have become that short term focused?

Answers
It's easy to come up with answers that pass the buck:

• Extraordinary shareholder demands
• Bonus Structure,
• Greed, Grab Culture

However, despite and behind all this, there is a deeper cause.

Thinking concept
This short term focus, that is not limited to CFOs, is the logical consequence of the way our thinking and modeling has developed during the last decades:

• we try to exclude risk at any price, instead of managing it.
• we struggle and sometimes even fear to transform long term cash flows into discounted cash values or NPVs

According to a 2002 survey, more than 85% of the CFOs say they use NPV-analysis in at least three out of four decisions.
As actuaries we're also part of this family of Discounted Cash Flow (DCF) Experts. Some of us might even have thought there's nothing more to learn about DCF...

Of course we understand every technical detail of our DCF-model, but let's take a look at some classical aspects of the DCF technique from a different angle. I'll call this angle the I-View, with the I of Important.....

DCF properties
As we know the value of a future cash flow (cf ) , depends strongly on the choice of the discount rate (r) and the moment in time (t) of the cash flow. The further away (in time) the cash flow and the higher the discount rate, the lower the DCF value.



I-View
From an I-View perspective one might say that in the DCF of a constant cash flow, the contribution of the cash flow in year 10 is ruffly half as Important (UnImportant-effect) as a cash flow in year one, assuming a discount rate of 7%.

Another way of saying: This one off cash flow is only of 51% Importance to us.

Although this might not surprise you, a often heavy underestimated effect is that the UnImportant-effect rapidly increases in case a particular discounted cash flow in year (t) is part of and expressed as a percentage of a discounted fixed term (or perpetual) cash flow stream. This is illustrated in the next graph (base: r= 10% discount rate).


De relative contribution of a cash flow t, soon loses more and more Importance when it's part of a constant cash flow stream. As the term of this cash flow increases to infinity, the relative contribution of any 'one year cash flow' becomes rapidly UnImportant.

I-View 1: Discount Rate Adjustments
As we know, the choice of the discount rate depends on the type of cash flow. Cash flows with substantial risks are often discounted with an adjusted (higher) r, according to the (CAPM) formula:

r = r_f + β×(r_m - r_f)

with: r_f = risk free rate, r_m = expected return on the market and β = (beta) a measure of the (opposed to the market) cash flow risk.

It's obvious this CAPM-method amplifies the mentioned 'UnImportant-effect' of long term cash flows.

In times of financial crisis, when we're inclined to become more risk averse, the 'UnImportant-effect' grows even more, as we are inclined to adjust r for fear:

r = r_fear + r_f + β×(r_m - r_f)

Moreover in general, the longer the cash flow term, the higher the (compound) expected risk, and therefore the higher the discount rate (r). Instead of a constant r, there's a need for a variable r, r_t, that increases in time, intensifying the 'UnImportant-effect'.

I-View 2: Discount Rate of Liabilities
Another DCF example: A pension fund has extremely long term liabilities. A cash flow of - let's pick - 50 years ahead, is no exception, but only accounts for about 14% of its cash flow in the discounted liabilities of the pension fund (abstracting from mortality and assuming a discount rate of 4%), and is therefore implicit considered (rated) less Important compared to more recent cash flows. Because there's no real or substantial market for long term cash flow pension obligations, r is even harder to define. Increasing r for this risk is like putting the cart before the horse: The UnImportance effect will increase. For internal valuation r should be decreased instead of increased, but how.....?

I-View 3: Short term Ruin Probability Nonsense
A third effect is that a 0.5% yearly ruin probability sounds safe, but nevertheless compounds up to a risk of 14% over a period of 30 years and even more on the long term.

Years	Cum.Ruin Risk
1	0.5%
10	4.9%
20	9.5%
30	14.0%
40	18.2%
50	22.2%
60	26.0%
70	29.6%
80	33.0%
90	36.3%
100	39.4%

FCLTOS, Financial Companies with Long Term Obligations, like banks, insurance companies or pension funds are by definition companies that have to stay ruin proof on the long term. Managing these kind of companies on short term ruin and certainty models is completely nonsense.

However, there's nothing much FCLTOS can do about it. A long-term certainty level of 99.5% (0.5% ruin risk) over a period of 40 years would imply a yearly certainty level of 99.9875% (0.0125% ruin risk). Even if it would be possible to minimize the technical risks to such a low level, it would be overshadowed by unquantifiable external outside risks (e.g. nature disasters). Anyhow, government regulators should define a target with regard to an appropriate choice of a long-term certainty level and should distinguish between short term and long term certainty in their models.

These examples illustrate that the management FCLTOS, giving these DCF-like methods, do not have another choice than to focus on the near future (5-10 years) and - by method - are not obliged and therefore also not will focus on the long term effects.

Navigating
Managing FCLTOS, is like navigating an oil tanker from A to B between the ice floes. You have to avoid the short term (nearby)
risks (the ice floes) while at the same time keep sight and hold direction on your long term target (port B) in order to succeed.

Translated to a pension fund: manage your liquidity on the short term and your solvency and coverage-ratio on the long term. Any captain of an oil tanker would certainly be discharged immediately when he would make a dangerous change in course today to avoid an actual clear, but in the future certainly changing (moving targets) ice floe situation 50 km ahead. Yet, government regulators and supervisors are forcing pension fund 'captains' to undertake such ridiculous actions.

Steering on short term recovery plans , publishing and publicly discussing coverage-ratios and finally 'valuing pension funds' solely on market value (given that the market for extreme {> 30 years} long term assets and liabilities is extremely 'thin' and volatile), is therefore dangerous and apparently wrong (nonsense) and leads to discounted crash situations.

But there's more that contributes to discounted crash management......

One off negative cash flow in the future
Let's compare two (almost) equal cash flows, CFa and CFb:
- CFa: 30 year constant cash flow of yearly $1,
- CFb: like CFa, but in year 25 a one off negative cash flow : -$1

Although a negative cash flow of $1 in year 25 will probably ruin the activities an cash flows in later years, the NPV of the two cash flows only differ slightly and the calculated IRR of CFb (9.76%) is also just slightly lower than the IRR of CFa (10%).

One might argue that because CFb is obviously a more risky cash flow, the adjusted r has to be raised. This is true, but nevertheless intensifies the so called UnImportant-effect: the relative weight of the 'year 25 cash flow' in the NPV decreases.

Last but not least, what explains the short term attitude and those extreme short periods of several years or months, some CFOs practice as a time frame to run and control their company ?

Certainty Erosion
These extreme short periods are the consequence of the No. 1 concern for CFOs:

The fundamental and increasing lack of ability to forecast results

Let's do some rule of thumb exercise....

Assume the certainty level of calculating a sound financial forecast in the next period (year, quarter, month) is estimated by a CFO at C%.

Now take a look at the next table (on the right) that shows the average extrapolated certainty level (AC) over a number of periods P.

In formula:


Some examples from the table:

• A CFO that estimates the 'next quarter result' with a certainty level of 70% (C=0.7), will probably not burn his fingers by presenting a full year forecast with an average expected certainty level of 44%.
• A CFO of a company hit by the current financial crisis, estimates the certainty of his companies January results at 60%. The board announces it's not able to estimate the full year result. Right they are, with a 60% monthly certainty level, the full year result would have a certainty level of only 12%.....
• Even a CFO with a superb forecast certainty level of 90%, will be cautious with a 5-year forecast (certainty level 74%).
• A 'best of class actuary' that estimates the certainty level of his data at 90% on a yearly basis, will have a hard time in answering question about the certainty level of his projections over 14 years (50%?).

The I-View consequence of this 'compound certainty development' is that even at high levels of (yearly) certainty, the (average) certainty of cash flows after already a few years in the future, erodes.

The effects of Certainty Erosion are enormous. The wall of haziness that is created in a few years - at even high levels of certainty - is astonishing. Never 'believe' a long term one point forecast. Always request variance and certainty level(s) of presented forecasts.

Conclusion
We may conclude that DCF is a superb technique as such to analyze and value cash flows. To prevent ending up in a 'crash flow', DCF has to be implemented by professionals who realize that the essential point of DCF is not just the technique itself, but the way the parameters, used in the DCF-models, are defined.

In order to be able to really take responsibility in managing a company, the Board of a company should be involved in the selection and consequences of the deeper and underlaying DCF-parameters. Enough work for actuaries it seems....

Related Links:
- Some comments on QIS3, (Long term certainty levels)
- Quantifying Unquantifiable Risks
- NPV

Longevity escape velocity

Aubrey de Grey, a British biomedical gerontologist, states in his book "Ending Aging," that that the fundamental knowledge to develop effective anti-aging medicine mostly already exists.

In a Ted Show presentation he states:

Why should we cure aging?

Because it kills people!

Age damage
There are seven types of aging damage :

Damage rising with age	Proposed as contributing to aging by
Cell loss, cell atrophy	Brody (1955) or earlier
Extracellular junk	Alzheimer (1907)
Extracellular crosslinks	Monnier and Cerami (1981)
Cell senescence	Hayflick (1965)
Mitochondrial mutations	Harman (1972)
Lysosomal junk	Strehler (1959) or earlier
Nuclear [epi]mutations (cancer)	Szilard (1959) and Cutler (1982)

Although, for more than 25 years, science suspiciously didn't seem to develop, all kind of medicines to repair these damages are already within reach for mice.

Age damage for human beings is strongly age related:



As the chairman of the Methuselah-Foundation, De Grey stimulates scientists to develop medicines that repair age damage for this living generation.

Experiments on mouses showed that medicines didn't only slow down the aging process, but could reverse it as well (condition: start in time!). It turns out that every time a new medicine is developed and applied, it restores - above a certain threshold of reserve capacity - the lost reserve capacity for about 50%.

This would imply that if new medicines for human beings would be developed within the next decade and the rate of developing new medicines will be fast enough to stay 'ahead of the game', all people of 50 years and younger would be able to live a thousand years or more and people just slightly older could still live for hundred years or more.

In 2006 Technology Review announced a $20,000 prize for any molecular biologist who could demonstrate that De Grey was wrong. Nobody succeeded!

If De Grey is right, actuaries don't even have to start calculating new life expectancies or other (financial) consequences. Life insurance and pension will have to be redefined.
Even stronger: We'll have to redefine our life!

Sources: Ted Show presentation, Pres. 1, Pres 2

Related links:
A model of aging as accumulated damage matches observed mortality ...

European Mortality

The Groupe Consultatif Actuariel Europeen published end 2005 a study, which for the first time compares how companies in different European countries measure life expectancy for their pension schemes. It reveals vast differences in mortality assumptions and indicates that practice across the EU varies widely when assessing company pension liabilities.


As you may see from some examples to the left, a wide area of classic mortality formulae in the different European countries passes by.

It's clear that that mortality assumptions in company pension schemes vary from
country to country, due to variations in underlying population mortality as well as in
variations of the profile of typical membership of a company pension scheme. However, the
variations in mortality assumptions are much greater than would be justified by these
factors alone.

Some of the variation is due to the fact that some countries incorporate an allowance
for expected future improvements in mortality, while others use tables that relate to mortality observed over a period in the past, without allowing for the fact that life expectancy continues to increase.

The total actuarial deficit with regard to (future) longevity in company pension schemes is substantial.


As a 'Survey of Actuarial Education in Europe' showed, not only mortality rates differ, but also the the education of different European actuarial professionals.

In short, work enough for actuaries.

More information:

• Mortality findings revealed
  
• Executive summary (pdf 70Kb)
• Full report (pdf 1.67MB)

Netherlands: Rapid increase life expectancy

Last year, female life expectancy at birth was 82.3 years, as against 78.0 years for men. Life expectancy has risen dramatically since 2002.

Life expectancy at birth

Mortality down since 2002

Female life expectancy at birth was 82.3 years in 2007, i.e. 4.3 years more than for men who have a life expectancy of 78.0 years at birth. Since 1980, the gender gap has narrowed. Male and female life expectancy increased by 5.5 and 3.1 years respectively. The situation has improved considerably after 2002. Despite the ageing population mortality has annually declined since 2002. Such a long period of declining mortality is unprecedented in the Netherlands. In 2007, mortality was over 9 thousand (nearly 7 percent) down on 2002.

Declining mortality by age, 2007 relative to 2002

Situation favourable for people in their seventies

The decline in mortality was quite evenly spread across all age groups, but was particularly noticeable among people in their seventies. In 2007, mortality in the age group 70-80 declined by over 5 thousand (nearly 13 percent) relative to 2002. This decline is largely the result of the reduced risk of dying from cardiovascular diseases.

Lower risk of dying by age, 2002-2007

Lower mortality risk for 50 to 80-year-old men

In recent years, the mortality risk declined significantly for both genders. For men aged between 50 and 80, the risk of dying dropped more than for women in the same age bracket. Among the very old, the situation is more favourable for women.

Female life expectancy at birth, 2006

Netherlands not in leading position

Dutch women marginally improved their position on the European record list, but in countries like France and Spain female life expectancy is considerably higher. Belgian and German women also had a somewhat higher life expectancy in 2006. In relative terms, the position of Dutch men on the European life expectancy list is better and comparable to the position French and Spanish men. Swiss, Swedish and Norwegian men, however, enjoy a considerably higher life expectancy.

Source : CBS , by Joop Garssen and Koos van der Togt

Longevity risk solved

Holiday news today...

An unknown Dutch actuary (don't quote me !) claims to have found the definitive solution for what's called 'longevity risk'.

Instead of a traditional non-comprehensive actuarial equation, the proof is one of those rare, and sometimes dangerous or wrong, visual proofs in (actuarial) mathematics.



Anyway, have a nice holiday!