MAT 480
Pension Funding & Valuation
• Overview of upcoming classes:
– Focus on Obligations / Promises / Liabilities
• Defined Benefit plan one of the very few longterm employee related liabilities a company
might carry
– Background to Pension Plans & Retirement
Security
• Origins of plans and evolution over time
– Plan Designs
MAT 480
Pension Funding & Valuation
• Overview of upcoming classes:
– Actuarial Valuations and Cost Methods
• How do we calculate the liability, and for what
purposes? Under what laws?
• What annual expenses do we incur?
– Evolution of Pension Reform and Protection Laws
– Simulation of the creation of an enterprise
– Books to be used and referenced
The parties to a Retirement Benefit…
• The Plan Participant
– Wants a secure retirement
– Wants an income stream he/she cannot outlive
– Wants to pass longevity risk on to someone else
• The Plan Sponsor / Employer
– Wants to provide a secure retirement
– Wants to attract and retain quality employees with strong benefits
• The Plan Sponsor or Insurance Company
– Can provide longevity insurance…
• IF… the portfolio of risks is large enough
• IF… the portfolio of risks is independent
• IF… they can call upon the Central Limit Theorem / Law of
Large Numbers
Back to the Basics
•
Plan Sponsors and/or insurers can take on additional risks because variance
decreases inversely to the number of risks
•
Example:
Let X1 = Risk Payoff of a unit amount with a Bernoulli distribution
•
“Risk Payoff” can be many different benefits:
Life Insurance
Disability Insurance
Retirement Benefit
X1 ~ Bernoulli (p = .2)
P(X1 = 1) = .2
P(X1 = 0) = .8
E[X1] = .2
Var[X1] = .2(.8) = .16
Back to the Basics
• Plan Sponsors and/or insurers can take on
additional risks because variance decreases
inversely to the number of risks
• If two similar Risk Payoffs are combined by the
insurer, what is the expected value and variance
of the average payoff?
Let Y = (X1 + X2) / 2 --- “Risk Payoff for 2 insureds”
P(Y = 0) = .64; P(Y = 1/2) = .32; P(Y = 1) = .04
Back to the Basics
• Plan Sponsors and/or insurers can take on additional risks
because variance decreases inversely to the number of
risks
• If two similar, independent Risk Payoffs are combined by
the insurer, what is the expected value and variance of the
average payoff?
E[Y] = E[X1 + X2] / 2 = .2
Or…. 0(.64) + 1/2(.32) + 1(.04) = .2
Var[Y] = ¼ Var[X1] + ¼ Var[X2] = ¼ (.16) + ¼ (.16) = .08
Or… E[Y2] = 0(.64) + ¼(.32) + 1(.04) = .12
E[Y2] – (E[Y])2 = .12 - .22 = .12 - .04 = .08
Same expectation, but half the variance
Back to the Basics
•
Plan Sponsors and/or insurers can take on additional risks
because variance decreases inversely to the number of risks
•
If N similar Risk Payoffs are combined by the insurer, what is the
expected value and variance of the average payoff?
Let Y = Σ[ (Xi) / n ]
P(Y = 0) = (.8)n ; … ; P(Y = n) = (.2)n
E[Y] = E [ Σ[ (Xi) / n ] ] = 1/n (n) E(Xi) = E(Xi) = .2
Var[Y] = Σ (1 / n2 ) Var (Xi) = (1 / n2 ) (n) Var (Xi) = (1 / n) Var (Xi) = (1 /
n) .16
Same expectation, but variance reduced by a factor of…. 1 / n
Back to the Basics
• Plan Sponsors and/or insurers can take on additional risks
because variance decreases inversely to the number of
risks
• As n grows large, the reduction in variability very
pronounced. This enables the insurer to take on a portfolio
or risks with a much more predictable outcome range.
• “Sufficiently diversified liabilities may in fact have their
random nature dramatically reduced and become nearly
deterministic. This is especially true of retirement liabilities
for a large group.” (Gajek and Ostaszewski, p. 159)
• Upcoming: evolution of the insurance company market for
this risk….
Growth of Pension Plans
• Large explosion of employer benefits in the 20th
century
• Rapid growth in pension plans since the 1940’s
in the U.S. due to:
– Union movement demanding benefit plans
– Strong post-war economy giving company stability
• 1970’s: 75% of all retirement plan assets in pension plans
– Government legislation
– Tax assistance to companies who set up pension plans
• U.S. Market size today
– 28,000 plans; $2.4 T in assets
– 275 plans over $1 B in assets, totaling about 50% of all plan assets
Largest Plans
•
•
•
•
•
•
Federal Retirement Thrift Savings Plan, $325.68 B
California Public Employees' Retirement System, $244.75 B
California State Teachers' Retirement System, $155.74 B
New York State Common Retirement Fund, $150.11 B
Florida State Board of Administration, $134.35 B
Largest corporate plan: General Motors Co., $117.81 B
http://www.pionline.com/article/20130204/PRINTSUB/302049974/dc-plans-snag-a-bigger-piece-of-the-top-1000
Pension Plans as a Social Planning Tool
• In some ways, it can make an organized society better if
a basic minimum economic standard is created
• Delicate balance of “Capitalism” and “Good Social
Policy”
• “What would our society be like if the elderly, the
widows, and the disabled had no income?”…. Old Age,
Survivors, Disability Income Plan is created by the US in
1935
• Commonly called “Social Security”
An “optimal” retirement:
The Three-Legged Stool
Government
Sources
Individual Savings
Financial Planners
often talk about
retirement income
coming from three
distinct sources:
Pension Plans
Growing “fourth leg” = PRWI
Retirement Systems Worldwide
• How are different countries
addressing retirement security?
• United States
– Baby boom generation implies higher average age
– Social Security system, though not funded well
– Strong incentives for employers to create employee
programs
– Incentives for individual savings, but negative
savings rate
Retirement Systems Worldwide
•
•
How are different countries addressing retirement security?
United States – trying to cure our spending habits…
•
2005: “The government reported last week that consumers last year spent
all they earned and then some, pushing the personal savings rate into
negative territory at minus 0.5 percent.
The savings rate has only been negative for a full year twice before, in
1932 and 1933, when Americans were struggling with huge job layoffs
during the Great Depression.”
•
An upward trend has occurred over the past few years…
US Personal Savings Rate
http://research.stlouisfed.org/fred2/series/PSAVERT/
Retirement Systems Worldwide
• How are different countries addressing retirement security?
Need to investigate country demographics…
•
http://www.census.gov/population/international/data/idb/informationGateway.php
Retirement Systems Worldwide
Retirement Systems Worldwide
Retirement Systems Worldwide
Retirement Systems Worldwide
• How are different countries addressing retirement
security?
http://www.census.gov/population/international/data/idb/country.php
• Kenya (see upcoming slides)
– Civil servant savings plan created but withdrawn due to low participation
– Current pension system will have many pensioners in coming years
– Post-retirement poverty is an issue
• Similar issues in Nigeria and South Africa
• Younger population country: Mexico
• Older population country: Greece, Italy
Retirement Systems Worldwide
• How are different countries
addressing retirement security?
• Kenya
•
Retirement Systems Worldwide
• How are different countries
addressing retirement security?
• Kenya
•
Retirement Systems Worldwide
• How are different countries
addressing retirement security?
• Kenya
•
Retirement Systems Worldwide
• How are different countries
addressing retirement security?
• Kenya
•
Retirement Systems Worldwide
• How are different countries addressing
retirement security?
• Other examples?
A common financial planning concept
• The “Replacement Ratio”
– Ratio of income level post-retirement to income level pre-retirement
– Financial planners would estimate that a ratio of between 70% to 80%
should be a minimum goal
• Assumes that certain expenses (mortgage
payments, college tuition, etc) are all preretirement expenses
• Social Security will help with only part of this…
so pension plans and personal savings become
very important
Common Pension Plan Arrangements
• Single Employer Plan
– Most common
– One employer creates / administers / funds
• Multiple Employer Plan
– Often used when several employers have small numbers of
employees
– Administration cost spread over all companies
• Multi-Employer Plan
– Typically associated with unionized labor
– Union members can change employers without losing
pension rights and benefits
Defined Benefit Plans
• Use a well-defined formula, with employee specific
information, to determine retirement benefit
• Employee information could be items such as:
– Years of Service
– Salary History
• What formula items would be helpful to incent
continued service?
• Employers carry investment risk – they must direct
the investments of their contributions to meet the
benefits they promise
Defined Benefit Example:
Unit Benefit Per Year of Service
• Annual retirement benefit of $152 per
month per year of service
Position
Age
Salary
Years of
Service
Annual
Retirement
Benefit
Marketing Manager
35
$40,000
10
$152 x 12 x 10
= $18,240
Chief Actuary
55
$80,000
15
$152 x 12 x 15
= $27,360
Defined Benefit Example:
Salary Percentage Per Year of Service
• Annual retirement benefit of 5% of current
compensation at retirement per year of service
Position
Age
Salary
Years of
Service
Annual
Retirement
Benefit
Marketing Manager
35
$40,000
10
.05 x $40,000 x
10 = $20,000
Chief Actuary
55
$80,000
15
.05 x $80,000 x
15 = $60,000
Salary-Based Defined Benefit Plans
• Annual retirement benefit can be
based on salary in many different
ways:
– Ending salary at retirement
– Career average compensation
– Final average compensation over last X years
• What is fair / unfair about these
different methods?
Example: COUNTRY Financial
Defined Benefit Plan
• Employees eligible once one year of
service is completed in which 1,000
hours is worked and attained age 21
• Vested in plan once five years of
service completed
Example: COUNTRY Financial
Defined Benefit Plan
• Monthly Retirement Benefit Calculation
Calculate A = Average Monthly Earnings during five
highest consecutive years of income out the ten
years immediately preceding retirement
Calculate B = Min (Years of Service, 32)
Life with 10 Year Certain Benefit = 1.65% x A x B
Example: COUNTRY Financial Defined
Benefit Plan
• Need to be 55 and five years of service to
receive any benefits
• Reduction factors apply for retirement before
age 65, except if completed 20 years of
service then non-reduced benefit at age 62
• Many employees with long service retire at 62
with mainly maximized benefit (except for a
potentially increasing earnings component)
Two other defined benefit types
• “Flat Benefit”
– Retirement benefit is a function solely of compensation, but not
service
• Example: Annual Retirement Benefit = 55% of final
compensation (no matter how long you have been employed)
• “Fixed Benefit”
– Retirement benefit is not a function of compensation or service
• Example: Annual Retirement Benefit = $30,000 (no matter
what you earned or how long you have been employed)
U.S. Insurance Company interaction with DB
plans
• Employers take some clear risk in DB plans
–
–
–
–
Investment
Salary inflation
Employee persistency
Retiree mortality
• Some employers may choose to turn over the retiree payment
longevity risk to a life insurance company
• Large number of retirees can help minimize the overall risk to
the insurer
• In a future class we’ll review typical size of Employer Liability vs.
the cost of a Purchase Premium for a Pension Risk Transfer
U.S. Insurance Company Market
• Market for the “Pension Risk Transfer (PRT)” market has
considerably consolidated over the last 20 years
–
–
–
–
Plan sponsor fully transfers investment and longevity risk
Removes administrative, actuarial and investment management expenses,
Eliminates Pension Benefit Guaranty Corporation premiums for purchased
participants
Removes pension liabilities from the balance sheet, diminishes both accounting
and funding volatility
• Well developed and regulated in UK
• 10 Insurance Companies essentially make up 100% of PRT
Market
–
American General, John Hancock, Mass Mutual, MetLife, Mutual of Omaha, New York
Life, Pacific Life, Principal, Prudential, Transamerica
U.S. Insurance Company Market
• Department of Labor Interpretive Bulletin 95-1 is published in
October 2008 to require fiduciary standards on both DB and DC
plans
• http://www.retire.prudential.com/media/managed/compbulletinfinalrules-annuityselection-dc.pdf
U.S. Insurance Company Market
• Two large ones in Fall 2012
• Prudential completes pension transfer
agreement with General Motors Co.; 110,000
members; $25B
–
http://news.prudential.com/article_display.cfm?article_id=6415
• Prudential completes pension risk transfer
transaction with Verizon; 41,000 members;
$7.5 B
–
http://news.prudential.com/article_display.cfm?article_id=6449
Defined Contribution Plans
• Most widely recognized and used
plan in the U.S. is the 401(k) plan
– Named after the section of the IRS code that allows
contributions to be made pre-tax
• Similar plans for public employees
are Section 403(b) plans and Section
457 plans
401(k) plan specifics
• Allow participant to contribute a portion of
compensation on a before-tax basis
• Sometimes referred to as “Salary Reduction”
plans
• Entire payout, including interest, is taxable when
received during retirement
401(k) plan specifics
• Employer often makes matching contributions
– Some employers may require match to be placed in certain investments
• Allows employee direction of investments in
most cases
• No investment risk borne by the employer
• Automatic enrollment processes now permitted
• Maximum deferral amount is $17,500 in 2013;
$23,000 if 50 or older (“catch-up” contributions)
Example: COUNTRY Financial
401(k) Plan
• Automatic enrollment, with opt-out
• Allows participants to defer between 2% and
75% of any paycheck
– Amounts can be changed via administration website by employee
via ID and password
• Allows investments to be made in 17 different
funds, across a range of risk categories,
including target retirement date funds
• All investments directed by participant
Example: COUNTRY
Financial 401(k) Plan
• Company match in 2012 is basically 50 cents on each
dollar you contribute up to 6% of pay – maximum match
therefore is 3% of pay
• Company match not applicable to earnings above a high
compensation limit ($250,000 in 2012), and not
applicable to “catch-up” contributions
• Match is done evenly as you contribute throughout the
calendar year
Longevity Wars:
DB vs. DC vs. Mutual Funds vs.
other??
•Huge competition at times geared towards capturing
individual and employer retirement plans
•Mutual Fund Companies want their “fair share”
•Example: Fidelity Income Replacement Funds℠…
•http://personal.fidelity.com/global/search/inquira/resultsind
ex.shtml?question=income replacement funds
•Funds designed especially for use during retirement
•What are the risks and rewards?
Longevity Wars:
DB vs. DC vs. Mutual Funds vs.
other??
•Longevity Annuity
•http://money.cnn.com/retirement/guide/annuities_longevity.moneymag
/index.htm
•Small premium outlay, delayed payout stream
•Growing incentives to include within qualified plans like 401(k) or
individual IRAs
•Reverse Mortgage
•http://en.wikipedia.org/wiki/Reverse_mortgage
•Translate home equity into retirement income stream
So which type of pension plan is
better?
• Depends on what the employer wants to emphasize and
what types of employees the employer wants to attract
• Defined Contribution: Emphasizes accumulation over
retirement benefit; passes off risk to employee; portable
• Defined Benefit: Emphasizes retirement benefit over
accumulation; requires investment management;
encourages employee continuation in service
• Ancillary benefits: additional benefits for pre-retirement
disability, or death benefits (both pre- and postretirement)
Cost considerations for companies
• Employee mix & attraction
– Younger employees may desire mobility of defined
contribution
– Many years to retirement makes defined benefit fairly
inexpensive
• Inflation considerations
– Renegotiating of union plans will cover this
– Final average compensation plans can cover
adequately
– Career average compensation plans may not
– Index benefits or not?
The cost of pension plans
• Most of what actuaries in the pension field do has to do
with defined benefit plans
• The need to reduce investment uncertainty and the need
to appropriately fund the plan take a lot of actuarial
expertise to manage
• Until about 7 years ago, pension funding was a known
risk, but accounting methods kept much of the focus off
of US corporation balance sheets
The cost of pension plans
• The Pension Protection Act of 2006
• Improves funding rules for employer-sponsored
defined benefit plans; stronger focus on having a
funding target equal to present value of accrued
benefits
• Discounting of liability changes from 30-year
Treasury bonds to 3 different corporate bond rates
specific to timing of plan benefits
• Ability to smooth assets over 5 year period greatly
reduced; must be between 90% and 110% of market
value
The cost of pension plans
•
•
•
•
US Corporation pension funding dilemma:
http://www.mercer.com/press-releases/1332250
2008:
Pension plans sponsored by the largest US companies see a
decline in funded status (the ratio of assets to liabilities) from
104 percent at year-end 2007 to 75 percent as of December 31,
2008.
• Aggregate surplus of $60 billion at the end of 2007 to be
replaced an estimated aggregate deficit of $409 billion at the
end of 2008.
• Why? Poor equity returns
The cost of pension plans
•
•
•
•
US Corporation pension funding dilemma:
http://www.mercer.com/press-releases/1404710
2010:
Funded status to approximate 80 percent as of
December 31, 2010 despite strong equity returns
• Low interest rates for discounting the liability now
additionally part of the valuation issue
• Some movement away from equity investments to
mitigate funding volatility
The cost of pension plans
• US Corporation pension funding dilemma:
•
http://www.mercer.us/press-releases/1430655
• October 2011:
• Funded status to approximate 75 percent
• Continued low interest rates
• http://www.mercer.com/press-releases/1494670
• December 2012:
• Funded status to 72% (even as equities up 10-15% in
2012)
The cost of pension plans
The cost of pension plans
The cost of pension plans
• State pension funding dilemma:
• http://www.wilshire.com/BusinessUnits/Consulting/I
nvestment/2010_State_Retirement_Funding_Report.
pdf
• Very large promises made
• Asset performance in recent years subpar
• Revenue sources inconsistent
• Leads to large underfunding of plans
Basics of Actuarial Valuations
• Why are valuations needed?
– Provide security to all participants
– Relate costs of a pension plan to the working years as a cost of production
vs. pay-as-you-go
– Tax relief to companies as a government incentive
• “Normal Cost” = annual funding amount
– Analogous to life insurance net premium
• “Actuarial Liability” = amount held for future benefits
– Analogous to life insurance reserve
Basics of Actuarial Valuations
• Important ages to keep in mind
– “e” – Age at entry into plan – the age
where benefits begin accruing
– “a” – Age at inception of plan – some
plans may give credit for past service (a >
e)
– “x” – Age at which valuation is performed
– “r” – Age for normal retirement
Basics of Actuarial Valuations
• Individual Cost Methods
– Each individual in a plan is reviewed separately
– Sum of all individual liabilities is total plan liability
– Costing can be increasing or level as age
increases
• Aggregate Cost Methods
– Costing more based on the entire plan instead of
individual components