April 27, 2011

Overview of the Pension Insurance Modeling System (PIMS)

What is PIMS?

• PIMS is a stochastic (i.e., random) simulation model of elements of 

PBGC’s financial statement. In a simulation, key factors affecting PBGC 

are randomly selected, like lottery balls from an urn. After combining 

these random selections, the model assesses what effect they would have 

on PBGC.

• It generates thousands of 10-year projections of PBGC’s future financial 

statements and of the factors influencing the financial statement (such 

as claims, premiums, interest rates, stock returns, etc.). These 

projections depict the broad range of potential outcomes that could 

happen to PBGC and show what future outcomes are most likely to 

occur.

• The random effects in the simulation are based on measures of the 

historical volatility in key factors underlying the insurance, in particular 

interest rates, stock market returns, and corporate bankruptcy rates.

• The results from the different scenarios are compiled to show how 

frequently different types of outcomes are simulated. The frequency with 

which an outcome is simulated (for example, that PBGC attains a 

surplus in the next 10 years), estimates the likelihood of that outcome’s 

actual occurrence.

• PIMS does not predict what will happen to the future, but rather 

estimates probabilities over a range of possible outcomes.

• PIMS is a tool for understanding the risks insured by PBGC.

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April 27, 2011

Overview of the Pension Insurance Modeling System (PIMS)

Why did we develop PIMS?

• PBGC insurance risk has characteristics similar to those of insurances 

for natural disasters, what are called catastrophe insurances. That is, 

large claim events have a significant but relatively low likelihood of 

occurring. This means that historical claim experience provides a poor 

measure of the future probability of large claim events and even of the 

long-term average level of claims. The graph below, showing the annual 

variation in past claim experience, is illustrative of the nature of PBGC 

insurance risk.

• Simulation models are useful tools for evaluating risks of this type 

because they can generate many years worth of possible claim 

experiences.

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April 27, 2011

Overview of the Pension Insurance Modeling System (PIMS)

How does PIMS work?

PIMS starts with:

• Detailed data on a representative sample of PBGC insured 

pensions, including benefit formulae and current plan 

demographics. The data is prepared from the plans’ Schedule B 

filings and from their attachments to the Schedule B.

• Data on the current financial health of the insured plans’ corporate

sponsors.

• A representation of PBGC’s current financial position.

In a PIMS simulation:

• 10 years of future financial market events (stock returns, interest 

rates) are randomly selected according to measures of historical 

market volatilities.

Key Assumptions:

Interest rates. The 30-year Treasury bond yield follows a random 

walk process (i.e., this year’s yield equals last year’s yield plus a 

random disturbance). Corporate bond yields are modeled to 

regress over time to their historic spreads over Treasury yields. 

The real (inflation adjusted) interest rate is set with a fixed

parameter. Inflation is the difference between the Treasury bond 

yield and the real rate. No short term interest rates are modeled.

Stock returns. The S&P 500 return is modeled as a strictly mean 

reverting process (i.e., each year’s return equals 10.4% plus a 

random disturbance).

Correlations. The random disturbances affecting the bond yield 

and stock returns are correlated according to an historical 

estimate. Stock returns are more likely to be high when the bond 

yield is falling and vice versa.

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April 27, 2011

Overview of the Pension Insurance Modeling System (PIMS)

• Pension plans are brought through the simulated financial events, 

experiencing the associated gains and losses. PBGC insurance 

premiums are assessed on plan sponsors, and plans present 

contribution requirements to their sponsors.

Key Assumptions:

Asset returns. Plan investment returns are based on historical 

measures of individual plan returns’ correlations with S&P 500 

returns and 30-year Treasury returns. Data on plans’ actual 

investment allocations are now being reporting in 5500 filings and 

PIMS will soon begin using that information.

Sponsor contributions. For projecting future claims in our 

baseline simulation (used for our annual report projections),

sponsors are assumed to make the minimum contribution required 

by Internal Revenue Code. In the case of a sponsor bankruptcy, 

we assume sponsors fail to make their required contribution from 

the prior year. In calculating projected variable premium 

collections, a higher level of contributions is assumed in order to 

reflect the tendency of many sponsors to fund above the minimum 

in order to reduce premiums (and for other reasons). This 

contribution adjustment is calibrated using data from PBGC’s 

history of premium collections.

Plan participants. Simulated participants retire, separate, and are 

affected by mortality according to actuarial assumptions. The 

number of active participants changes proportionally to total 

employment of the sponsor (see below). 

Benefit and salary levels. Flat benefits grow at the rate of inflation 

plus productivity growth (a fixed parameter). The average salary 

for a given age and service level also grows at the rate of inflation 

plus productivity growth. Salaries also grow with age and service 

to reflect merit and promotion.

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April 27, 2011

Overview of the Pension Insurance Modeling System (PIMS)

• Corporate sponsors are brought through the financial events, and 

also experience random shocks to their financial health according 

to historical measures of the volatilities. They are subjected to 

random chances of bankruptcy depending on their financial health 

measures.

Key Assumptions:

Financial Averages. Each firm’s equity to debt and cash flow to 

asset ratios are affected each year by a regression to long-term 

averages and by random disturbances.

Employment and equity value. Firms’ employment and equity 

values follow random walk processes.

Correlations. The random disturbances affecting the above 

variables are correlated with each other, and are also correlated to 

the random disturbances affecting stock returns and interest rates, 

according to historical estimates.

Bankruptcy. Each firm faces a yearly random chance of 

bankruptcy. Individual firms have differing probabilities of 

bankruptcy which are based on the above financial and 

employment variables and also on the funding status of the plans 

they sponsor.

• PBGC is brought through the financial events, experiencing gains 

and losses accordingly. It receives insurance premiums and

makes benefit payments to trusteed participants. When a sponsor 

experiences bankruptcy and has a sufficiently underfunded plan, 

PBGC receives a claim.

Key Assumptions:

Plan terminations. Plans sponsored by bankrupt sponsors are 

assumed to present a claim to PBGC if they are less than 80% 

funded (by PBGC termination assumptions). Otherwise a standard 

termination is assumed.

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April 27, 2011

Overview of the Pension Insurance Modeling System (PIMS)

What are the outputs of PIMS?

• A typical simulation consists of 5,000 different scenarios (500 unique 

economic scenarios, which PBGC and each plan and sponsor experience 

10 times). 

• Data that can be tracked through PIMS simulations include:

o PBGC claims

o Premiums

o Plan funding levels

o Plan contributions required by funding laws

o Investment gains and losses

Example 1, the distribution of simulated claims over the next decade

0

20

40

60

80

100

120

140

160

180

200

0 10 20 30 40 50 60 70 80 90 100 110 120 130

Number of simulations

(out of 5,000)

Billions of Dollars (present value)

Distribution of Projected Claims 2011-2020

Mean $ 25.0

Median $ 21.3

Std. Dev. $ 16.4

5% $ 6.0

10% $ 8.2

25% $ 13.2

75% $ 32.7

90% $ 46.2

95% $ 56.9

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April 27, 2011

Overview of the Pension Insurance Modeling System (PIMS)

Example 2, the distribution of the PBGC’s financial position after 10 

years

Example 3, testing the sensitivity of results to economic assumptions

0

100

200

300

400

500

600

700

800

900

-160 -140 -120 -100 -80 -60 -40 -20 0 20 40 60

Number of simulations

(out of 5,000)

Billions of Dollars (present value)

Distribution of PBGC's Projected 2020 Financial Position 

Mean $ (24.2)

Median $ (21.3)

Std. Dev. $ 28.7

5% $ (75.5)

10% $ (61.2)

25% $ (41.0)

75% $ (5.3)

90% $ 9.9

95% $ 18.8

Probability of any 

surplus in 2020 18.8%

0%

5%

10%

15%

20%

25%

30%

35%

40%

-160 -140 -120 -100 -80 -60 -40 -20 0 20 40 60

Percent of Total Simulations

Billions of Dollars (present value)

Distribution of PBGC's Projected 2020 Financial Position

Baseline Stochastic Economy Compared to Two Historic Economies

Baseline

1969-78 

Economy

1990-99 

Economy

Mean $ (24.2) $ (40.0) $ (2.3)

Median $ (21.3) $ (37.1) $ (0.8)

Std. Dev. $ 28.7 $ 13.7 $ 12.6

5% $ (75.5) $ (65.5) $ (22.4)

10% $ (61.2) $ (57.3) $ (16.7)

25% $ (41.0) $ (46.4) $ (8.9)

75% $ (5.3) $ (30.6) $ 6.1

90% $ 9.9 $ (25.6) $ 11.7

95% $ 18.8 $ (23.0) $ 14.3

Probability of any 

surplus in 2020 18.8% 0.0% 47.7%

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April 27, 2011

Overview of the Pension Insurance Modeling System (PIMS)

What are applications of PIMS?

• Making financial statement projections to give the Congress a better 

understanding of the range of financial risks faced by PBGC.

• Measuring the effects of possible policy changes. Possible examples 

include:

o Changes to the premium structure

o Changes to funding laws

o Changes to the interest rates used to value liabilities

• Exploring the effects of pension industry trends, such as a possible 

increase in standard terminations.

• Evaluation of risk management strategies.

Who else uses PIMS results?

• The Congressional Budget Office, the Joint Committee on Taxation, the 

Treasury, and the Office of Management and Budget to make estimates 

of the budgetary impact of legislative proposals.

• The Government Accountability Office to analyze and assess the 

condition of the pension insurance program and evaluate possible policy 

and legislative changes.

• Academics and think tanks to study plan characteristics.

• The Society of Actuaries is using PIMS to study defined benefit plan 

issues.

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