Attachment_2_-_SE_PIMS_System_Description.pdf

Pension Insurance Modeling System

PIMS System Description

Version 1.0 Revised: Updated May 3, 2019 i

Table of Contents

Contents 1 Pension Insurance .................................................................................................... 1-1

1.1 Introduction ....................................................................................................... 1-1

1.2 A Description of Pension Insurance .................................................................. 1-2

1.3 The Nature of Pension Insurance ...................................................................... 1-4

1.3.1 Temporal Variation .................................................................................... 1-4

1.3.2 The Pricing Problem ................................................................................ 1-13

1.4 Prior Attempts to Model Pension Insurance ................................................... 1-16

1.4.1 The Pension Put ....................................................................................... 1-16

1.4.2 Mathematical Solutions ........................................................................... 1-17

1.4.3 Simulation Approach to an Options Model ............................................. 1-19

1.5 The Pension Insurance Modeling System ....................................................... 1-21

2 Description of the Model ......................................................................................... 2-1

2.1 Introduction ....................................................................................................... 2-1

2.2 The Model Strategy and Specification .............................................................. 2-1

2.2.1 Expected Cost of Insurance in the Current Period ..................................... 2-3

2.2.2 Expected Cost in the Next Period as Viewed from the Current Period ..... 2-5

2.3 Structural Equations and Model Specifications ................................................ 2-8

2.3.1 Economy Level .......................................................................................... 2-8

2.3.2 Firm Level ................................................................................................ 2-10

2.3.3 Plan Level ................................................................................................ 2-16

2.3.4 PBGC Level ............................................................................................. 2-20

2.4 The PIMS Simulation ...................................................................................... 2-20

2.4.1 Starting Values ......................................................................................... 2-20

2.4.2 The Simulation ......................................................................................... 2-22

2.4.3 Illustrative Results ................................................................................... 2-23

3 The Actuarial Valuation Process ............................................................................. 3-1

3.1 Introduction ....................................................................................................... 3-1

3.2 Pension Protection Act of 2006 (PPA) .............................................................. 3-4

3.2.1 Limitations of the PIMS Valuation Forecast ............................................. 3-6

3.2.2 At-Risk Plans ............................................................................................. 3-1 ii

3.2.3 Transition and Effective Date .................................................................... 3-1

3.2.4 Workers, Retirees, Employer Recovery Act of 2008 (WRERA) .............. 3-2

3.2.5 Pension Relief Act of 2010 ........................................................................ 3-2

3.2.6 Moving Ahead for Progress in the 21st Century (MAP-21) ....................... 3-3

3.3 Actuarial Valuation Concepts ........................................................................... 3-6

3.3.1 Benefits ...................................................................................................... 3-6

3.3.2 Liabilities ................................................................................................... 3-7

3.3.3 Plan Costs/Funding Method ....................................................................... 3-8

3.4 Valuations in PIMS ........................................................................................... 3-9

3.4.1 Participant Data .......................................................................................... 3-9

3.4.2 Actuarial Assumptions ............................................................................. 3-10

3.4.3 Plan Provisions......................................................................................... 3-11

3.4.4 Plan Assets ............................................................................................... 3-12

3.4.5 Funding Method ....................................................................................... 3-13

3.4.6 Funding Calculations ............................................................................... 3-13

3.4.7 Calculation of the Variable Rate Premium .............................................. 3-14

3.5 Plan Termination Valuation ............................................................................ 3-15

3.6 PBGC Annual Valuation for Financial Statement .......................................... 3-17

3.7 Internal Revenue Code (IRC) Funding Rules in PIMS ................................... 3-17

3.7.1 Minimum Contribution ............................................................................ 3-18

3.7.2 Maximum Deductible Contribution ......................................................... 3-19

3.7.3 Limitations on Pay and Benefits .............................................................. 3-19

3.7.4 Amortization Bases (Minimum Required Contribution) ......................... 3-20

4 The PBGC in PIMS ................................................................................................. 4-1

4.1 Introduction ....................................................................................................... 4-1

4.2 PBGC Initial Values .......................................................................................... 4-1

4.2.1 Liabilities ................................................................................................... 4-1

4.2.2 Assets ......................................................................................................... 4-2

4.2.3 Treatment of “Probables” .......................................................................... 4-3

4.2.4 Premiums ................................................................................................... 4-3

4.2.5 VRP for Plans with Low Bankruptcy Probability...................................... 4-3

4.2.6 Taking a Claim ........................................................................................... 4-4

4.2.7 Participant Data Adjustments .................................................................... 4-4

4.2.8 Asset Adjustment ....................................................................................... 4-4 iii

4.3 Advancing the PBGC ........................................................................................ 4-5

4.4 Asset Investment Options.................................................................................. 4-5

4.5 User Variations .................................................................................................. 4-6

4.6 Items Not Modeled ............................................................................................ 4-6

5 The PIMS Exogenous Variable Equations .............................................................. 5-1

5.1 Introduction ....................................................................................................... 5-1

5.2 Modeling Assumptions: Exogenous Variables ................................................. 5-1

5.2.1 Mean Reversion versus Random Walk ...................................................... 5-1

5.2.2 Interest Rate ............................................................................................... 5-2

5.2.3 Random Walk Model ................................................................................. 5-5

5.2.4 Stock Returns ............................................................................................. 5-5

5.2.5 Firm-Specific Variables ............................................................................. 5-6

5.2.6 Plan-specific Asset Returns ....................................................................... 5-6

5.3 The Exogenous Variable Equations .................................................................. 5-7

5.3.1 Error Components ...................................................................................... 5-7

5.3.2 Standard Errors on the Economy Parameters ............................................ 5-8

5.3.3 The Data ..................................................................................................... 5-8

5.4 Estimation of the Economy and Firm Level Equations .................................... 5-9

5.5 Estimation of the Error Components Equations .............................................. 5-11

Table 5-1: Economy and Firm Equation Parameter Estimation Results ............... 5-12

5.6 Estimation of the Plan Asset Return Equations .............................................. 5-15

6 Modeling Bankruptcy .............................................................................................. 6-1

6.1 Introduction ....................................................................................................... 6-1

6.2 Identifying and Characterizing Bankruptcy ...................................................... 6-3

6.3 A Logit Model of Bankruptcy ........................................................................... 6-4

6.3.1 Leverage ..................................................................................................... 6-5

6.3.2 Cash Flow .................................................................................................. 6-6

6.3.3 Firm Size (Employment)............................................................................ 6-6

6.3.4 Funding Ratio............................................................................................. 6-7

6.3.5 Financial and Utility Industries .................................................................. 6-7

6.3.6 Scope of Data ............................................................................................. 6-7

6.4 Empirical Results .............................................................................................. 6-9

6.5 The Bankruptcy Model Versus Commercial Debt Ratings ............................. 6-12

6.6 The Bankruptcy Equation in the September 30, 2009 PBGC Closing............ 6-14 iv

7 The PIMS Simulation Process ................................................................................. 7-1

7.1 Introduction ....................................................................................................... 7-1

7.2 PIMS Entities .................................................................................................... 7-1

7.3 PIMS Input Data Types ..................................................................................... 7-3

7.4 Simulation Parameters....................................................................................... 7-5

7.4.1 Initial Values .............................................................................................. 7-5

7.4.2 Temporal Parameters ................................................................................. 7-5

7.4.3 Policy Parameters....................................................................................... 7-6

7.5 PIMS Simulation ............................................................................................... 7-6

7.6 PIMS Output ................................................................................................... 7-11

1-1

1 Pension Insurance

1.1 Introduction

The Pension Benefit Guaranty Corporation (PBGC) was created by the Employee

Retirement Income Security Act of 1974 (ERISA) to insure private defined benefit (DB) pension plans in the U.S. The single-employer program is designed to insure participants in plans that terminate with insufficient assets to pay insured benefits.0F

1 Although many insured defined benefit plans are adequately funded, there are a significant number of plans that are highly underfunded. Potential claims against the PBGC typically arise from the forfeiture of pension obligations by plan sponsors with underfunded defined benefit pension plans that file Chapter 7 or Chapter 11 bankruptcy petitions with the relevant districts of the U.S. Federal Bankruptcy

Courts. These bankruptcies can potentially increase the liabilities of the PBGC.1F

2 If such a plan is terminated, the PBGC takes over the plan, makes up the shortfall and becomes a debtor in the proceedings.

This chapter presents a discussion of the conceptual background for developing a simulation model of pension insurance. Subsections present simplified examples of how the pension insurance system operates, compare pension insurance with other types of insurance, review previous theoretical and numerically-based studies of pension insurance, and present the distinctive features of the Pension Insurance Modeling System (PIMS) model developed at the

PBGC.

1 There is also a multi-employer program covering about 1,500 multi-employer plans. This version of PIMS (SEPIMS) deals solely with the single- employer program that dominates the PBGC balance sheet.

2 Firms that enter bankruptcy and who sponsor underfunded pensions do not necessarily make a claim against the PBGC. An insurable event often occurs if the plan sponsor enters Chapter 7 bankruptcy proceedings. Alternatively, a judge might decide to terminate the plan in a Chapter 11 bankruptcy proceeding if he or she determines that the firm cannot be reorganized without terminating an underfunded plan. More typically, the PBGC negotiates a plan termination (and recoveries) with other creditors in bankruptcy proceedings.

1-2

1.2 A Description of Pension Insurance

Benefits and service levels are frozen as of the date of plan termination (“DoPT”). Thus, service grow-ins for early retirement eligibility, or cost-of-living adjustments are ignored after the termination date. Certain reductions are made to reflect maximum levels of benefit guarantees,2F

1 and these amounts are payable in nominal terms starting at the eligible age of retirement allowed by the plan. Furthermore, any benefit improvements during the five years prior to termination are “phased-in”, depending on the number of complete years these amendments were in place prior to DoPT. Current retirees continue to receive their benefits (less any reduction to guaranteed levels).

To illustrate how the insurance works, consider a simplified, one-person plan. Based on service attained at the date of plan termination, the sole worker is entitled to the annual benefits flow (B). For simplicity, assume that benefits fall within the PBGC guarantee, the worker is at retirement age at the time of the termination, and lives forever. If the nominal interest rate is denoted as (i), then termination pension liabilities (LT)3F

2 are equal to:

(1-1) LT = B / i.

If the market value of plan assets is denoted by (A), then underfunding for termination liabilities, (U), is positive if A < LT:

(1-2) U = LT – A ≥ 0.

If the plan sponsor enters bankruptcy with underfunding, and the PBGC proceeds with

1 There is an overall limit on the monthly guarantee which is indexed to the social security wage index. In 2012, the limit was $5,118.75 per month. The guarantee applies to the age 65 benefit in the form of a single life annuity. If retirement occurs before age 65, the guarantee is actuarially reduced to reflect the increased periods of payment. In addition, benefit increases in the plan made within five years of termination are phased into the guarantee. Certain other supplements paid by the plan only for periods prior to normal retirement age may not be guaranteed.

2 The concept of termination liability denotes that no further service accrues and no further benefit increase amendments are made to the plan. It represents the present value of benefits earned as of the date of plan termination.

1-3 the termination, the PBGC assumes responsibility for the plan, makes up the shortfall (U) and enters a claim for this amount as a bankruptcy debtor. The PBGC recovers an amount (R) from this process where R is often positive but is usually significantly less than the amount of the claim:

(1-3) 0 < R ≤ U.

Thus, the net claim absorbed by the agency is:

(1-3) C = U – R ≥ 0

Since its inception, and the PBGC has accumulated 4,769 Single Employer claims with liabilities valued in 2016 dollars of $102.4 billion. In FY 2016, $5,659 million in monthly benefits were paid to 829,000 retirees and 559,000 deferred annuitants were entitled to receive benefits upon attaining retirement age. Twenty-two thousand single-employer defined pension plans, covering approximately 28.6 million participants, paid a total of $6.4 billion in premiums for plan year 2016. These premiums consisted of a $64 fixed charge per participant and a variable rate premium of $30 per $1,000 of plan underfunding4F

1, the latter subject to a cap of

$500/participant. Table 1-1 lists selected PBGC statistics.

1 The Deficit Reduction Act of 2005 (DRA) provides that the fixed change is indexed to increases in the average national wage.

For FY2009, the fixed premium increased to $34.

1-4

Table 1-1: PBGC Single-Employer Program, FY 2016

Participants Entitled to Monthly Benefits

Retirees and beneficiaries1/

Deferred vesteds1/

842,000 652,000

Benefit Payouts

Payments

$5,384 Million

Premiums Total Number of covered participants Average premium per annum, per participant2/

$6.379 Million

28.6 Million

$223

TRUSTEED PLANS

Insufficient Pension Terminations (cumulative through 2016)

Number

4,769

PBGC Net Position after absorbing claims, FY 2012 Assets Liabilities Deficit

$97.3 Billion

$117.9 Billion $20.6 Billion

Sources: PBGC Annual Report, 2016 and PBGC unpublished data.

1 Retirees and beneficiaries exclude participants in “probable” terminations at year end. Deferred vesteds include participants in probables.

2 The premium schedule is $69 per annum per participant for FY2017, plus $34 per $1,000 in underfunding.

Table 1-1 primarily summarizes statistics on plans the PBGC has already trusteed.

However, the focus of the Pension Insurance Modeling System (“PIMS”) is estimating expected claims generated from Single Employer plans which have not been trusteed by the PBGC. The last section of Table 1-1 shows a big source of this future risk–the total underfunding of insured plans which have not been trusteed by the PBGC. The model analyzes industry trends, company financials, and macroeconomic data in order to assess the future risk of the Agency assuming the unfunded liabilities from future distress terminations.

1.3 The Nature of Pension Insurance

1.3.1 Temporal Variation

As background to analysis of the pension insurance system, it is appropriate to examine

1-5 the proper way to calculate the economic price of pension insurance. If market risk in the insurance and expense of the operation are ignored, this is equivalent to determining the premium, or set of premiums, that equate the present value of expected revenues to its present value of expected losses. In some insurance lines, like fire, theft, or life, prices are relatively easy to determine. Losses are fairly predictable; experience is comprised of a large number of small claims, and claim experience does not vary significantly from year to year. Thus, economic prices can be established within a tight confidence. Further, while losses are expected to change over time due to inflation and trends that affect claims (like the spread of smoke and burglar alarms, increases in life expectancy, and so on), they are not characterized by large temporal variation.

Pension claims do not follow this pattern. As shown in Figure 1-1, historical gross claims to the PBGC evince a large temporal variation, ranging from claims as low as $28.6 million in 1984 to $11.2 billion in 2005 (nominal dollars). The volatility of claims partly reflects the occasional bankruptcy of sponsors of large underfunded pension plans, as well as changes in underfunding over time.

1-6

Figure 1-1 shows that the PBGC's ten largest claims have accounted for 62 percent of its total claims.

Figure 1-1: PBGC Gross Claims

Source: PBGC Pension Insurance Data Book 2008

$0

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

Pre-1985 1985 - 1989

1990 - 1994

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

Top 10 Claims

All Other Claims

Dollars in Millions (Current Dollars)

Total Claims 1975 - 2008

38.3% 61.7%

1-7

Figure 1-2 shows the concentration of underfunding over the years 1998 to 2006. The ten companies with the highest amount of underfunding in a given year have represented from 10 percent to 33 percent of total underfunding in that year. As these claims and underfunding statistics illustrate, the financial condition of the PBGC is sensitive to the financial failure of a relatively small number of firms.

Figure 1-2: Concentration of Underfunding

1-8

Figure 1-3 shows the variation in underfunding from 1990 through 2006. Pension liabilities reflect fixed dollar benefit obligations, and thus, underfunding depends importantly on long-term interest rates (see Equation 1-1). Pension plan assets are primarily invested in stocks and bonds and are therefore sensitive to changes in interest rates and stock returns.

Figure 1-3: Defined Benefit Underfunding and Interest Rates

These characteristics of the program suggest that pension insurance is more like disaster insurance than automobile insurance. Significant claims events occur infrequently, and thus, future claims are not predictable within a small standard error based on past experience. A good parallel example is flood insurance where claims are small as long as rain and snow patterns are

"normal," a situation which characterizes most years. If severe precipitation patterns affect heavily populated areas, claims can be dramatically higher than suggested by past experience.

Source: Internal Revenue Service Form 5500 Series Filings for single-employer plans. Data for plan years prior to 1999 include only plans with 100 or more participants

0%

1%

2%

3%

4%

5%

6%

7%

8%

Vested Underfunding Interest Rate

Dollars in Billions (Current Dollars) PBGC Interest Rates

1-9

Hurricane and earthquake insurance claims exhibit similar characteristics. However, unlike these forms of casualty insurance, large waves of claimants to the PBGC will not be required to renew their policies and make future premiums – often adjusted prospectively for adverse experience under the casualty insurance model. Rather, the future premium cash flow from ongoing plans is very unpredictable, especially with soft and hard frozen plans waiting for interest rates to rise and terminate their plans.

In the case of pension insurance, claims may remain within a reasonable range for long periods. There is some probability, however, that macroeconomic conditions will generate large amounts of underfunding (i.e. “the perfect storm”), producing a wave of distress terminations.

The problem is suggested by the claims history shown in Figure 1-1 where the annual variation of gross claims is very high relative to its average value.5F

1 More importantly, it is unlikely that PBGC’s historical experience reflects all possible future outcomes. Without some understanding of the stochastic processes affecting claims, we cannot attach a probability to the likelihood that future experience could be twice as high or half as much as the average of past experience.

The insurance pricing problem posed by large temporal variation can be mitigated if the price (premium) could be reset each period – or at least vary yearly by the plan’s funded percentage (e.g. the variable premium rate varied with the funded percentage of the plan). In this case, pension insurance would be more like one-year term life insurance that must be renewed annually. Consider the issuance of a $100,000 one-year term life insurance policy to an individual who passes the initial physical exam. The premium is set based on the age, sex and

1 The mean value of the gross claims shown in Figure 1-1 is approximately $2,050 million; the standard deviation is $2,931 million.

1-10 perhaps other characteristics of the insured. If the probability of death over the policy period is p then, ignoring administrative costs, the economic premium in period one for the term insurance, (PTERM

1), is simply the probability of death times the face value of the insurance (I):

(1-5) PTERM

1 = p1 I.

If p is five percent, and I is $100,000 then the economic premium is $5,000. Upon advancing one period, the individual buys a new term policy. The price depends on the results of the physical exam at that time.

The one-year term insurance offers protection against sudden death, say due to accidents, or fatal events such as a massive heart attack or stroke. However, it offers little protection against death from other sources. For example, if terminal cancer is detected during the second physical exam, or the insured is in intensive care from a near-fatal heart attack, the price of the insurance during the second period might be close to the face value of the insurance - that is, if the probability of death is 90 percent then the premium is now 90 percent times $100,000, or

$90,000. In effect, term policies cannot effectively insure against death, following a long illness.

Individuals can obtain life insurance protection against most sources of death by purchasing an annual renewable term life insurance policy.6F

1 Upon passing the first physical exam, the insured is entitled to automatic renewals of the same level of insurance regardless of the insured's physical condition at the time of the renewal.7F

2 The policy is canceled only for nonpayment of premiums. Premium increases in these policies can reflect increases in age, 1 Most policies impose some restrictions on death by suicide and from actions in which the individual puts himself at extraordinary risk, for example, by skydiving.

2 Some restrictions may be imposed such as maintenance of non-smoking status, reasonable weight limits, etc. Increases in the face value of the insurance require that the insured pass a physical exam at the time the additional amount is requested. The insured can reduce the face value amount at any time.

1-11 inflation, and changing life expectancies among all insured, but cannot change specifically for any particular insured. These policies protect against death due to cancer, heart ailments, and other circumstances where death may occur long after the initial onset of the condition.

Assuming that the face value of the insurance policy, I, is constant over the entire period of the contract, the economic price for term renewable insurance depends not only on the probability of death in the first period, but on the conditional probability of death in second period, third period and so on. For example, if the policy is specified to be effective for two periods, ignoring administrative costs, and assuming a zero interest rate, the economic premium of the policy purchased at the beginning of period 1 is:

(1-4) PRENEW

1 = [ p1 + (1 - p1)p2 ] I.

Thus, if p1 is five percent, p2 is ten percent, and I is $100,000, the expected cost of the insurance is $14,500.

Pension insurance more closely follows the term renewable model. Under the current pension insurance program, all privately sponsored defined benefit pensions are required to have

PBGC insurance, and the PBGC is required to provide the insurance to all defined benefit plans.8F

PBGC's current premium structure depends only on the plan’s number of participants and its underfunding (representing the face value or economic loss that the insurance is protecting). No adjustments are made for the credit worthiness of the plan sponsor. This characteristic parallels renewable life insurance in the sense that premiums cannot be increased upon the onset of serious financial difficulty of the insured.9F

1 There are a few exceptions such as plans sponsored by professional groups with fewer than 25 participants.

2 This is not to say that an economic premium could not consider the characteristics of a firm or industry that make it more likely that financial difficulty might be encountered at some future point, much like a life insurer takes into account smoking habits of

1-12

The life insurance parallel breaks down in two ways. First, in most life insurance policies, the insured cannot increase the face value of the insurance without approval of the insurer. If additional insurance is awarded, its price is influenced by the current medical condition of the insured. In the case of pension insurance, insured plan sponsors can increase benefits and reduce plan contributions (subject to Internal Revenue Code minimum funding rules) without approval of the PBGC.10F

1 In the past, firms that began to experience financial difficulties and experienced reductions in bond ratings could obtain higher levels of insurance at the same price as plan sponsors with the highest bond ratings, by increasing benefits. However, the Pension Protection Act of 2006 (“PPA06”) put restrictions on underfunded plans (less than

80%) being able to improve plan benefits. Claims to the PBGC typically show falling funding ratios prior to the time the PBGC assumes control of the plan (see Figure 1-4).

its insured in pricing life insurance policies.

1 PBGC's insurance coverage for benefit increases are restricted by phase-in rules upon a plan termination. Operation of funding rules in a model of pension insurance is summarized in Chapter 3. Often, even required minimum funding contributions are not paid during periods prior to the onset of bankruptcy. These “due and unpaid contributions” become part of the defunding in the bankruptcy process.

0%

20%

40%

60%

80%

100%

Termination Year minus 3

Termination Year minus 2

Termination Year minus 1

Termination Year

Figures are based on data from 50 large plans trusteed by PBGC. Funding ratio calculations are based on a common (5 percent) interest rate to adjust liabilities for all years.

Figure 1-4: Pre-Termination Funding Ratios of Large Trusteed Plans FY 2001-

1-13

Second, in the case of life insurance, the face value of insurance is predetermined. In the case of pension insurance, even if the plan sponsor does not directly cause underfunding to increase in a given year, the value of the insurance is volatile. To illustrate, consider underfunding (U) in period one in a typical insured plan:

(1-5) U1 = LT1 - A1.

Underfunding, and hence, the value of the insurance in some future period (t), depends importantly on variation in several factors. These include the rate of return on assets, the long-term interest rate, contributions to the plan, and changes in the size and structure of the firm's work force (which significantly affects the structure of pension plan liabilities).

1.3.2 The Pricing Problem

The pricing or valuation of a term-renewable pension-insurance policy with a highly uncertain face value is a complex task. Exposure depends on initial conditions (i.e., the funding in the plan and the credit worthiness of the plan sponsor) and on the stochastic process that determines the future value of underfunding and the probability of bankruptcy. It also depends on the minimum and maximum funding rules (set out in the Internal Revenue Code) that act to temper plan funding. The losses (claims) that develop from the pension insurance program are thus not characterized by a single deterministic number, but by some distribution that depends on the stochastic behavior of many variables.

Some aspects of the distribution of claims are predictable. The distribution is bounded to the left by zero. Since there is no natural upper limit, we expect and observe that the distribution of claims is naturally skewed to the right.11F

1 Furthermore, because of the large temporal variation

1 The distribution approximates a log normal form.

1-14 of the insurance program described above, we also expect that the standard deviation will be quite large in relation to its mean value. The distribution of PBGC net claims from 1975 to 2008 is shown in Table 1-2.

Table 1-2: Distribution of PBGC Net Claims, 1975-2008

In its simplest form, the model attaches loss estimates to the illustrative distribution. We could then determine the premium required to ensure, for example, a zero deficit for the PBGC with a 75 percent (or 90 percent or 50 percent) probability, and estimate the relationship between losses and various plan characteristics.12F

1 Various policy questions can be considered as well, for example, how changes in funding and guarantee rules affect the loss distribution.

If there were no market risk in pension insurance then these calculations serve as a basis to calculate economic prices. That is, gains and losses that are randomly distributed can be diversified, and thus, ignoring administrative costs, the economic premium structure is

1 For example, the premium could vary by plan type (flat dollar amount, salary-based benefit or combination formula benefits) or by plan asset allocation. Also, premiums could be based solely on underfunding or depend on firm characteristics that reflect long-term bankruptcy risk.

1975-1979 545 36 5 --- --- 586 1980-1984 537 66 18 --- --- 621 1985-1989 451 66 15 5 --- 537 1990-1994 534 137 17 6 --- 694 1995-1999 309 118 16 --- --- 443 2000-2004 346 245 84 22 2 699 2005-2008 98 119 41 7 5 270

TOTAL 2,820 787 196 40 7 3,850

Percent of Total 73.2% 20.4% 5.1% 1.0% 0.2% 100.0%

Sources: PBGC Fiscal Year Closing File (9/30/08) and PBGC Case Management System.

Claim values and distributions are subject to change as PBGC completes reviews and establishes termination dates.

Due to rounding of individual items, percentages may not add up to 100% .

Fiscal Year

PBGC Trusteed Terminations by Fiscal Year and Size of Claim (1975-2008) Single-Employer Program

SIZE OF CLAIM

Less than $1 Million $1-$9 Million $10-$99 Million $100-$999 Million $1 Billion or More Total

1-15 determined by the present values of expected losses across pension and sponsor characteristics.

The randomness assumption is reasonable for other volatile insurance contracts, such as those covering natural disasters. There is no reason to believe that floods or earthquakes are correlated with overall wealth in the economy. The same cannot be said of pension insurance.

Pensions typically hold substantial equity in their portfolios, and leverage ratios, and thus bankruptcy rates are importantly affected by firm’s equity value. Thus, if stock returns are negative, underfunding and bankruptcy probabilities - and thus, pension insurance claims - are expected to increase across the insured population (with some lags).

This prospect means that investors that back the insurance require some premium to compensate them for holding undiversifiable risk. This feature of the insurance adds a layer of complexity to determining its market price. Put simply, there are two components to the price of the insurance: one to cover expected losses (plus administrative expenses); and one to pay for the hedging strategy that is required to offset the correlation of losses to market factors.

One approach to handling the market risk problem follows the basic Capital Asset Pricing

Model (Sharpe 1964), in the sense that a loss beta is estimated which serves as a basis to reduce the discount rate for expected losses. This approach is developed in a series of papers that deal with insurance that has a market risk component,13F

1 and is discussed in the case of pension insurance by Petersen (1995).

An equivalent way to think about the problem is to assume that the insurer takes a short position against market risk. For example, in the case of stock exposure, if the sensitivity of

1 See William Farley (Spring 1979); Alan Klaus and Stephen Ross (September 1982); J. David Cummins (March 1991); Stewart Myers and Richard Cohn (1987).

1-16 losses to stock exposure can be determined then, in principle, the insurer can take a (dynamic) short position in stocks. If stock values decline, gains from the short position are expected to offset the increase in losses caused by the decline. If the short position is appropriately chosen, the relationship between the insured’s operating position and stock returns essentially is eliminated, in an expected sense. The expected cost of this strategy is the negative of the expected excess return on stocks, times the short position. In this approach, the economic premium is the stream of expected losses discounted at the riskless rate plus the cost of the short position.14F

One convenient way to think about the price is to consider pension insurance as a sort of put option: under some conditions, companies have the option to put its underfunding to the

PBGC. The economic price of the insurance is the collective value of these puts. The put value accommodates both the expected losses and the cost of taking a short position.

1.4 Prior Attempts to Model Pension Insurance

1.4.1 The Pension Put

Sharpe (1976) was the first to characterize pension insurance as a "put option." This term was particularly appropriate when ERISA was enacted in 1974. The insurance event as read literally from the 1974 statute seemingly awarded plan sponsors the right to unilaterally "put" or transfer their underfunded pensions to the PBGC in return for 30 percent of the sponsor's net worth.

In this way, the pension put worked like a put option on a publicly traded security: what price should be charged when an investor holding stock currently valued at $100 receives the

1 The riskless rate is used because the insurer has eliminated his exposure to market risk by taking a short position.

1-17 right to put the stock to a risk taker at $90 anytime over the ensuing six months? Models that attempt to impute an insurance value to option contracts are referred to as "options pricing models."15F

1 Sharpe portrays a similar pricing solution for the PBGC.

In fact, the PBGC originally enforced the statute more stringently than Sharpe envisioned. It did not accept pension terminations of underfunded pensions unless the firm was in serious financial distress; virtually all significant claims were paid only when plan sponsors were in bankruptcy (Ippolito 1989). In 1987, this operational reality was codified in the Pension

Protection Act contained in the Omnibus Budget Reconciliation Act of 1987. These changes, however, do not vitiate the thrust of Sharpe's model; they merely alter the nature, and thus the price, of the put option. The firm has an option to put underfunding to the PBGC conditional on becoming seriously financially distressed and entering bankruptcy proceedings. What researchers have attempted to do is determine the insurance value of this conditional option.

PPA helped mitigate the growth of the “put” amount by forcing underfunded plan sponsors from satisfying their minimum required contribution using the credit balance (prevented if < 80% funded in the prior year) and ultimately forcing sponsors to freeze benefit accruals when the plan’s funded ratio drops below 60%.

1.4.2 Mathematical Solutions

The difficulty of modeling the correct price for pension insurance is suggested by considering the pricing solution to the stock option referenced above. It turns out that for this simple option, the mathematical solution is complex (Black and Scholes 1973).16F

2 As in the case of stock options models, changing equity values and interest rates are key factors in options

1 Perhaps the most well known is the Black-Scholes (1973) options pricing model.

2 One of Black’s insights was to recognize that the differential equation that described the put option was similar to the heat equation in physics; this insight allowed him to readily describe an explicit solution to the problem.

1-18 models of pension insurance, but so are many other events. These include the probability of bankruptcy, and actions of the plan sponsor itself (benefit increases, growth or reduction in employment size, and, most importantly, contributions made to the pension plan).

Contribution rules are discussed in more detail in Chapter 3. Stated simply, the Internal

Revenue Code specifies a complex set of rules that determine minimum and maximum funding contributions. These rules depend on the type of pension plan, its demographic characteristics, the actuary's assumptions (retirement ages, separation rates, payment options etc.), and the amount of underfunding. OBRA ’87 and the Pension Protection Act of 2006 helped force underfunded plans to step up to the plate and accelerate their required contributions. However, subsequent legislation – WRERA17F

1, PRA18F

2, and MAP-2119F

3 – have partially weakened the stronger funding requirements under PPA. Nonetheless, the current funding rules can still result in minimum and maximum contributions that are volatile over time.20F

4 Over the past 35 years, many have tried to model pension insurance. The volatility of underfunding, and the consequent minimum funding rules that constrain it, imply that the path of insured underfunding cannot be characterized by a well-behaved functional form. These complexities make tractable mathematical solutions unfeasible. Marcus (1983) attempted such a solution by dramatically simplifying the nature of the insurance contract. In the Marcus framework, plan sponsors have assets and liabilities subject to a stochastic process. Bankruptcy is mechanically defined as the state when firm assets fall below firm liabilities. Marcus models pension assets and liabilities as variables with steady drift, plus random shock. The value of the insurance is determined primarily by market volatility; funding rules that temper the variation are not a feature of the

1 Workers, Retirees, Employer Recovery Act of 2008 2 Pension Relief Act of 2010 3 Moving Ahead for Progress in the 21st Century 4 Petersen (1994) identifies volatility of cash contributions as a primary reason why some firms do not offer defined benefit plans.

1-19 model.21F

1 In addition, the Marcus model implicitly awarded the PBGC the amount of overfunding upon a plan termination (which, by law, cannot occur).

Pennacchi and Lewis (1994) updated and improved on the Marcus model (most notably by eliminating overfunding awards to the PBGC). They also allow for deterioration of plan funding prior to termination. However, there are no funding rules; bankruptcy is not empirically determined; and plan characteristics are static over time. As in the Marcus model, a solution is obtained by greatly simplifying the nature of the contract.

For example, Pennacchi and Lewis solve the market risk problem by using a so-called

Martingale pricing theory. In this approach, the riskless rate is used to discount future streams, but this too-high discount rate is offset by setting the return on stocks equal to the riskless rate plus noise (thereby setting the expected excess return to zero). In a model with funding rules, however, this approach develops problems because the misrepresentation of stock returns gives incorrect funding ratios, and thus, generates improper contribution flows.22F

Bodie and Merton (1994) solve a pricing structure for the PBGC using a mathematical options pricing model but they solve the problem as if pension insurance were a term policy, not a term-renewable policy. Thus, they look at the problem one year at a time, and set new prices dependent on the financial condition of the sponsor in each period.

1.4.3 Simulation Approach to an Options Model

Estrella and Hirtle (1988) abandon the goal of obtaining an explicit deterministic solution of the pension insurance problem. This decision allows them to incorporate more realistic

1 In a version of the model for which an explicit solution is found, contributions are shown to be deterministic over time. In other versions, contributions can be proportional to underfunding.

2 Also see George Pennacchi (1997); Peter Abken (1987); J. David Cummin, Richard Phillips, and Stephen Smith (1997).

1-20 assumptions. They designed a stochastic model where uncertainty is replicated by multiple draws of random error terms from a joint distribution.

The firms in their database are those that report financial and pension data in the

Compustat database. Each firm has one pension plan that is a composite of all the defined benefit plans sponsored by these firms.

Plan assets and firm assets are the only stochastic variables in their model. Other variables such as plan liabilities are deterministic. Bankruptcies are determined mechanically when firm assets drop below some predetermined critical level.23F

1 They use a set of simplified funding rules to constrain underfunding. Importantly, they treat the interest rate as a constant, thereby omitting an important source of uncertainty that characterizes the pension insurance program. Nevertheless, their model represents an important step toward determining potential losses from pension insurance.

The Estrella and Hirtle model only accounts for actual losses resulting from terminations of underfunded pension plans. They do not address the issue how the insurer hedges the market risk, and thus, they do not develop a pricing model. This is the appeal of an analytical solution to the pension insurance problem: it takes advantage of options models already solved for other applications, and it develops a price that accounts for the cost of handling market risk. The

Estrella and Hirtle approach does a poor job of modeling the essence of the put option.

However, as noted by Sharpe (1987), it is difficult if not impossible to formally test the predictive accuracy of formal analytical models. Therefore, the burden is high to ensure that the

1 The authors report that their bankruptcy rule was determined by applying a statistical model that used Compustat data on firm assets, debt, and retained earnings.

1-21 model replicates pension put option behavior as closely as possible. Furthermore, making the model operative for policy guidance requires careful specifications of the insurance contract, realistic characterizations of pension plans and firm behavior, and reliable data.

The simulation approach has the potential to produce a rich distribution of financial outcomes but does not yield an economic price without specification of a hedging strategy. In this volume, we set out to properly portray the underwriting risk in the pension program, leaving the hedging strategy for future research. We concentrate on specifying in some detail the levels of exposure and risk that realistically can develop for a sample of pension plans in the insurance program.

We wish to be able to characterize the distribution of potential losses and the associated distribution of PBGC net worth that reflects a wide variety of potential conditions that can develop in the market for pension insurance. For many management questions facing the agency, this model adequately describes outcomes with corresponding probabilities; for example, it can give the probability that the deficit is more than $x billion in ten years. The model also can be used to evaluate the impact of different funding rules and other legislative initiatives on the financial condition of the agency.

In the future, we will be conducting work to lay the groundwork for a hedging strategy that offsets at least a large part of the of the market risk that characterizes the solution. Once such a strategy is found, we can determine the price of the insurance directly.

1.5 The Pension Insurance Modeling System

The Pension Insurance Modeling System (PIMS) is a simulation model that attempts to quantify the financial uncertainty facing the PBGC by modeling the major components of the

1-22 pension insurance system. The model is similar in approach to that of Estrella and Hirtle, but more refined. Whereas the Estrella and Hirtle model was intended to be analytically suggestive in nature, PIMS is designed to provide realistic information to assist in evaluating the future financial condition of the PBGC, and to provide information to help assess the quantitative impact of legislative efforts to modify the insurance program. With these applications in mind, PIMS pays attention to the underlying details that characterize the pension insurance contract, the pension plans insured by the PBGC, and the underlying data that importantly affect PBGC exposure.

Following previous models, PIMS uses plan sponsor data from the Compustat database.

These data include time series on market assets, book debt, equity value, cash flow, employment, and industry affiliation. Unlike previous models, however, PIMS has an empirical estimate, based on historical Compustat and other data, of the individual probability of bankruptcy. A firm sponsoring a DB plan has a chance to go bankrupt each year depending on firm financial characteristics and external economic factors in each period of the simulation. In addition, PIMS relies on unusually rich pension data.

The quality of the pension plan data used in PIMS is comparable in detail to the information used by actuaries to determine the plan sponsor's required contributions. Plan data are taken from the Form 5500 (Schedule B/SB and attachments) submitted annually to the

Internal Revenue Service.

Important plan data are captured, including age-service matrices of active workers, numbers of retirees, benefit payouts, layoff and retirement age actuarial assumptions, and so on.

Benefit formulae are taken from attachments to the Form 5500, and the amortized funding

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