Transcript Modigliani, Miller and Microinsurance

Global Retirement Crisis and the
Four Pillars System
Presentation for the conference celebrating the 10-th Anniversary of the
Foundation of the Institute of Applied Mathematics, Middle East Technical
University, Ankara, Turkey
by
Krzysztof Ostaszewski, Actuarial Program Director
Professor of Mathematics, Illinois State University, Normal, Illinois, U.S.A.
Research Director for Life Insurance and Pensions, The Geneva Association,
Geneva, Switzerland
The Four Pillars
• Social security or social assistance, i.e., universal public
system of pensions or pension-like benefits, created as a
social insurance system, or a welfare benefits system
delivering results similar to social insurance.
• Occupational pensions, where pension benefits for
individuals are delivered by employers, with possible support
of private insurance companies.
• Savings, where individuals save and invest for their own
retirement, using financial intermediaries, including private
insurance companies, which can provide increased security
of their benefits and mitigate longevity risk.
• Continued employment, with barriers to partial employment
that have existed worldwide, either from governments or
from employers, reduced or even removed.
Pillar 1: Social Insurance and social
assistance for the elderly
• Social insurance:
– Benefits set by law (statutory benefits).
– Premiums (taxes) set by law (statutory premiums)
– Typically run on pay-as-you-go basis.
• U.S. Social Security system accumulated a
Trust Fund of approximately $2.5 Trillion,
invested in special issue Treasury Bonds.
• Common complaint: Social insurance is “not
funded.”
The difference is not in “funding” but
in pricing of capital assets
• Hypothetical system of retirement savings
– All taxes invested in special issue government
bonds, earn interest at a rate prescribed by law.
– Upon retirement, withdrawals from account taxed
or subsidized to equal to the amount prescribed
by law.
• Money saved for retirement is always placed
in some capital assets, and those capital assets
are then sold to fund retirement.
Pillar 2: Employment-Based Pensions
• U.S. design for private sector plans, prescribed by Employee
Retirement Income Security Act of 1974
– Form a separate trust fund that will pay pension benefits.
– Employer must provide regular funding as prescribed by plan
actuary, with reports filed with the Department of Labor.
– Plan liabilities calculated by plan actuary.
– Since 2006 Pension Protection Act, must establish clear path to
funding, and must use market-related three-segment yield curve
for calculation of actuarial present value of benefits.
– Trust fund assets invested in a diversified portfolio, typically about
60% stocks and 40% bonds.
• Pension plans provided by states and municipal
government do not have such strict funding requirements,
use Government Accounting Standards. Also use actuarial
valuation.
Actuarial valuation of pension plans
• Accrued benefit funding methods. These
methods focus on maintaining a certain level
of funding. They are security driven, in that
they attempt to establish and maintain a
sound relationship between the fund assets
and the accruing liabilities. The funding
requirement is then the contributions
required to achieve the funding objective. The
two most important methods within this
category are Current Unit Credit and Projected
Unit Credit.
Actuarial valuation of pension plans
• Prospective benefit funding methods. These
methods define a certain level of
contributions. They are contribution driven,
and the primary objective is stability of such
contributions. These contributions then define
the targeted level of the fund at any point in
time. The three most important methods
within this category are Entry Age, Attained
Age and Aggregate.
The funding method does not
affect the true overall cost, unless
it changes people’s behavior
• Cost to plan sponsor =
Total benefits paid to plan beneficiaries
- Member contributions to the plan
- Investment income earned by the pension fund
+ Expenses incurred in the operation of the plan
and the fund.
Modigliani-Miller: Financing alone will
not create value
• It will only create value if:
– Tax benefits or lower regulatory costs are realized,
or
– Bankruptcy costs are lowered, or
– Agency costs are reduced, in particular if new
economic projects of positive value are funded,
and the value is not lost through information
asymmetry, moral hazard, or other agency costs.
Projected Unit Credit Method has
become dominant
Premium (Normal Cost) = Payment for value of benefit accrued
for this year’s service, with value projected to retirement
including salary increases. Example: Employee earning $60,000
gets 2% of final salary benefit for this year’s service, with 3%
annual salary increases,
15 years from retirement, will have final
14
salary 60000 ×1.03 . Normal
Cost is then calculated as
14
(12)
0.02 ×60000 ×1.03 × 15 E50 ×a65 . Note that discount rate(s) and
mortality may be prescribed by law or chosen by the actuary.
Accrued liability (AL) is calculated based on accrued benefits.
Unfunded actuarial liability (UAL) = AL – Actuarial Value of Assets
(F). May result in supplemental funding, subject to review
through: Expected UALt+1 = (UALt + NCt)(1+i) – Contribution with
interest – Benefit payments releasing the liability.
Comparison with life insurance
• Accrued liability <-> Reserve
• Normal Cost <-> Premium
• Recall standard recursive reserve formula
( kV + P )(1+ i ) = qx+k ×bk+1 + px+k × k+1V.
• Reserve, a.k.a., technical provisions.
• Unlike life insurance, assumptions and
valuation may be adjusted.
• Unlike life insurance, positive amount of
surplus is not required.
Solvency II and Pensions
• EU’s Solvency II will impose capital
requirements on insurance firms.
• Solvency Capital Requirement (SCR): capital
required to ensure that the insurance firm is
able to meet its obligations over the next 12
months with a probability of at least 99.5%.
• Minimum Capital Requirement (MCR):
Threshold for regulatory intervention.
Intended as 85% percentile, bounded
between 25% and 45% of SCR.
Capital rules for insurance and
pensions
• Historically
– Life insurance firms used relatively low valuation rate,
and were required to hold capital. Capital paid with
excess of earned rate over valuation rate, plus its own
earned rate.
– Pensions plans used relatively high valuation rate
(60% stocks and 40% bonds portfolio), and were
allowed to have negative surplus, amortized with part
of normal cost and all of supplementary cost.
• Solvency II proposal: Treat plan sponsor commitment to
contribute as a “shadow capital”
Defined Contributions Plans taking over
Key issue for defined
contribution plans
• Under constant force of mortality and constant force
of interest, an amount A purchases an annual
lifetime benefit of A ( m + d ) .
• In 1987, you could take the force of interest to be
9%, and force of mortality at age 65 maybe 3%,
million dollars bought as much as $120,000 p.a.
• In 2011, you could take force of interest to be 1.5%,
force of mortality at age 65 maybe 2.5%, million
dollars buys $40,000 per annum. Actually, in the U.S.
market rate is about $30,000.
Pillar 3: Private savings including life annuities
• This is the only area of retirement systems where market
valuation of the cost of retirement is the rule.
• Perceived as expensive and inaccessible to many.
• Standard problem with insurance
– The contribution to the society from the insurance
industry is to make more risky activities possible.
– But for this process to work, insurance must be priced
properly to control moral hazard.
– If customers are not complaining about insurance
being too expensive, the actuary is not doing his/her
job.
– If insurance is too cheap, calamities result.
What is the risk addressed in
providing pensions?
• Are life annuities insurance?
• It is common to say that life annuity is an
insurance policy against living too long.
• Allow me to propose another perspective: Life
annuity is insurance against the risk of having
to withdraw from labor force.
• Withdrawal from labor force is a risky
decision: One may gain or lose human capital
when unemployed.
Role of financial intermediaries
• What is the role of financial intermediaries in
the economy?
• Banking often perceived as spread business. It
is, in fact, derivative securities business.
• Life insurance is the business of creating
derivative securities (life insurance and
annuity) on human capital.
Pillar 4: Continued Employment
• Most developed economies in the 1950s created
incentives for workers to leave the labor force
between ages 55 and 65.
• But now, normal retirement age is being increased in
most countries.
• Forced retirement amounts to confiscation of human
capital.
• Taxation of pension benefits or reduction of them for
working retirees is a partial confiscation.
Interest rates in the last 25 years, UK, France, USA,
Germany, Japan, and Switzerland, sources: Oliver
Wyman and Oxford Economics
Real GDP growth in the same countries, sources: Oliver
Wyman and Oxford Economics
220
Growth in social spending, EU 15,
(source: OECD)
Real public social spending
210
Real GDP
200
190
180
170
160
150
140
130
120
110
100
1990
1995
2000
2005
07
United States (source: OECD)
220
Real public social spending
210
Real GDP
200
190
180
170
160
150
140
130
120
110
100
1990
1995
2000
2005
07
Japan (source: OECD)
220
Real public social spending
210
Real GDP
200
190
180
170
160
150
140
130
120
110
100
1990
1995
2000
2005
07
Public spending since the 2008 crisis, USA
(source: OECD)
150
30
28
140
26
24
130
22
20
120
18
16
110
14
12
100
10
90
8
2007
2008
2009
2010
2011
2012
United Kingdom (source: OECD)
150
30
28
140
26
24
130
22
20
120
18
16
110
14
12
100
10
90
8
2007
2008
2009
2010
2011
2012
Longevity (source: World Bank)
The effect of the 2008 Credit Crisis
• Pillar 1: Public finance systems in trouble.
Extensive financial suppression imposes
additional cost on the real economy. And weak
economy reduces tax collections.
• Pillar 2: Employers move away from providing
pension guarantees, derisking is the word of the
day.
• Pillar 3: Low rates of return and very high cost of
retirement benefits.
• Pillar 4: Reduced employment opportunities.
The Four Pillars should work in concert
• Pillar 1: By providing minimum standard of
living guarantees it can enhance incentives to
work, and reduce incentives to lobby.
• Pillar 2: Can enhance accumulation of human
capital.
• Pillar 3: Provides market signals for the entire
retirement system.
• Pillar 4: Efficient societal use of human capital.
No savior in finance
• The last 25 years have been market by nearly
revolutionary financial innovation.
• Some of it has unraveled in the 2008 Credit
Crisis.
• But finance alone does not create value, value
is created in the real economy.
• The Four Pillars should serve the real
economy: taxes, bankruptcy and agency costs.
Does this matter for Turkey?
Ratio of working-age population between 15 and 64 to
the rest of population (source: Japan’s Central Bank)
What is the optimal way to
pay off a liability?
• Consider a liability that requires a stream of
payments such that the present value at time
t
0 of payment at time t is Lt. Define ALt = å Li .
i=1
Also let AL0 = 0.
• Problem: Derive an optimal series of
payments, with Pt being the present value at
time 0 of payment to be made at time t – 1
(insurance premium is paid at the beginning of
the year).
Optimal with respect to what?
• Constraint 1: Present values of premiums form
an non-increasing sequence:
other
Pt ³InPt+1
.
words: Funding should not be allowed to be
just postponed (or: No Lucy Ricardo Method
of Funding).
• Constraint 2: APt = P1 + ...+ Pt ³ ALt . In other
words: No negative reserve.
• Minimize: APt – ALt for every t.
Solution
• Consider F(t) = ALt and extend it to be
piecewise linear and continuous, with the
smallest number of points of nondifferentiability possible.
• Let F*(t) be the smallest concave majorant of
F(t). Then the derivative of F*(t) provides the
optimal funding for this liability.
Limitations
• This result is deterministic.
• It does not need to assume one interest rate,
we can use a yield curve for present value
calculation.
• For large pension groups cash flows become
close to being deterministic.
• Purely financial result, while funding involves
a choice of securities in the portfolio, creating
agency problems.
Demographics
• The retirement challenges of developed economies
have been mostly presented as a demographic issue.
• But it is not demographic issue, it is entirely an issue of
pricing of capital assets.
• When the first public universal pension system was
introduced in Germany, life expectancy was in the range
of 46. Now it is around 80 in most developed
economies. Retirement is more expensive, but paid
mostly the same way as before.
• It has become dramatically more expensive following
the 2008 Credit Crisis.
Why do people not know the
cost of retirement?
• Imagine if shoes were provided by stateowned stores, at prescribed times, with every
citizen paying for them through a payroll
deduction.
• Would citizens know the price of shoes under
those circumstances?
• Would you blame them if they did not?
• What if the state-owned store coexisted with
small bazaar-like markets for shoes?
Advice of the Polish Plumber
• Central actor in the debate in France over the
European Union constitution, which was roundly
rejected by French voters in 2005.
• Solutions proposed for the retirement systems
problems following the Credit Crisis of 2008 all
concentrate on finance:
– Quantitative Easing
– Stimulus
– Temporary tax incentives
Cut the pipe three times and it is still too short?
Copernicus Retirement Model
• Copernicus died on May 24, 1543 in Frombork,
Poland.
• On that day, we was presented an advance copy
of De Revolutionibus Orbium Coelestium, his main
work.
• He was in very bad health, but could review the
book and make some corrections.
• On the day of his departure he was still working
on that piece of work that defines him as one of
the great contributors to the mankind’s body of
knowledge.