MAT 480Pension Funding & Valuation

• Overview of upcoming classes:– Focus on Obligations / Promises / Liabilities

• Defined Benefit plan one of the very few long-term employee related liabilities a company might carry

– Background to Pension Plans & Retirement Security• Origins of plans and evolution over time

– Plan Designs

MAT 480Pension 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 InsuranceDisability InsuranceRetirement Benefit

X1 ~ Bernoulli (p = .2)

P(X1 = 1) = .2P(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) = .08Or… E[Y2] = 0(.64) + ¼(.32) + 1(.04) = .12E[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

Financial Planners often talk about retirement income coming from three distinct sources:

Government Sources

Individual Savings

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 Ratehttp://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 pre-retirement 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/compbulletin-finalrules-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/

resultsindex.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 post-retirement)

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