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Discussion ofDiscussion of ““On Asset-Liability Matching and Federal On Asset-Liability Matching and Federal

Deposit and Pension Insurance”Deposit and Pension Insurance”

by Zvi Bodieby Zvi Bodie

Deborah LucasDeborah Lucas

Northwestern University and NBERNorthwestern University and NBER

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OverviewOverview

Decomposing PBGC’s Risk ExposureDecomposing PBGC’s Risk Exposure

What Does a Matched Portfolio Look Like?What Does a Matched Portfolio Look Like?

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PBGC’s Risk ExposurePBGC’s Risk Exposure

Results drawn from:Results drawn from:

“ “The Risk Exposure of the Pension Benefit The Risk Exposure of the Pension Benefit Guarantee Corporation” Guarantee Corporation”

CBO study by Kiska, Lucas and Phaup CBO study by Kiska, Lucas and Phaup available at available at www.cbo.govwww.cbo.gov

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PBGC’s Risk ExposurePBGC’s Risk Exposure

Two conditions must be met simultaneously for PBGC to Two conditions must be met simultaneously for PBGC to assume pension plans:assume pension plans: 1. Firm bankruptcy1. Firm bankruptcy 2. Under-funded pension plan2. Under-funded pension plan

The probability of a joint occurrence is much lower than the The probability of a joint occurrence is much lower than the probability that a pension plan is under-funded.probability that a pension plan is under-funded.

Fair premium for below-investment grade firms would have to be Fair premium for below-investment grade firms would have to be 18.5 times higher to match the current cost for investment-grade 18.5 times higher to match the current cost for investment-grade firms.firms.

The fair price of PBGC premiums includes a significant The fair price of PBGC premiums includes a significant charge for market risk, as both bankruptcy and under-charge for market risk, as both bankruptcy and under-funding are correlated with market downturns. funding are correlated with market downturns.

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PBGC’s Risk ExposurePBGC’s Risk Exposure PBGC insurance is a compound put option.PBGC insurance is a compound put option.

It can be valued using options pricing methods.It can be valued using options pricing methods.

Monte Carlo model takes into account the Monte Carlo model takes into account the evolution over time of:evolution over time of: Firm assets (stochastic)Firm assets (stochastic) Firm liabilities (deterministic)Firm liabilities (deterministic) Pension assets (70% stocks and 30% bonds)Pension assets (70% stocks and 30% bonds) Pension liabilities (deterministic)Pension liabilities (deterministic) and interactions with program rulesand interactions with program rules

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CBO Estimates of PBGC’s DeficitCBO Estimates of PBGC’s Deficit

Accumulated DeficitAccumulated Deficit, as , as of September 30, 2004 of September 30, 2004

$23.3 billion$23.3 billion

Prospective Net CostsProspective Net Costs

Over 10 years Over 10 years

Over 15 years Over 15 years

Over 20 years Over 20 years

$63.4 billion$63.4 billion

$95.7 billion$95.7 billion

$118.6 billion$118.6 billion

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Cost ComponentsCost Components

PBGC’s PBGC’s Prospective Net Prospective Net CostsCosts Over 10 Years Over 10 Years Under Current Law Under Current Law

$63.4 billion$63.4 billion

Limit a plan’s investment Limit a plan’s investment in in equities equities to to 30 %30 % of of plan assets (from 70%) plan assets (from 70%)

-$9.9 billion-$9.9 billion

Make permanent the Make permanent the increase in discount increase in discount ratesrates for calculating for calculating pension liabilities pension liabilities

+$8.1 billion+$8.1 billion

Fair premium multipleFair premium multiple 6.5x current rate6.5x current rate

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Summary of FindingsSummary of Findings

As Bodie suggests, more closely matching pension assets As Bodie suggests, more closely matching pension assets and liabilities significantly lowers PBGC’s projected costs.and liabilities significantly lowers PBGC’s projected costs.

But even with a matched portfolio, the model predicts that the But even with a matched portfolio, the model predicts that the PBGC will bear considerable costs.PBGC will bear considerable costs.

Reason is that termination liabilities are systematically greater Reason is that termination liabilities are systematically greater than current liabilities (i.e.,required funding levels). than current liabilities (i.e.,required funding levels).

We assume 20 percent mark-up of liabilities over assets at We assume 20 percent mark-up of liabilities over assets at

termination, following Pennachi and Lewis, and historical termination, following Pennachi and Lewis, and historical experience experience

e.g., U.S. Air > 90% funded in year prior to termination, <45% funded e.g., U.S. Air > 90% funded in year prior to termination, <45% funded at termination at termination

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Summary of FindingsSummary of Findings

Costs not arising directly from asset-Costs not arising directly from asset-liability mismatch can be attributed to liability mismatch can be attributed to regulatory forbearance, and to accounting regulatory forbearance, and to accounting conventions.conventions.

Forcing firms to fund to level of termination Forcing firms to fund to level of termination liabilities would result in systematic over-liabilities would result in systematic over-funding. funding.

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The S&L analogy revisitedThe S&L analogy revisited Similarities:Similarities:

Mismatch in market sensitivity of assets and liabilities Mismatch in market sensitivity of assets and liabilities creates potentially huge costs for the insurer.creates potentially huge costs for the insurer.

Regulatory forbearance exacerbates problem.Regulatory forbearance exacerbates problem.

Differences:Differences: Much less severe moral hazard due to compound option. Much less severe moral hazard due to compound option.

Sound companies have very little chance of putting their Sound companies have very little chance of putting their plan to the PBGC. plan to the PBGC.

Little evidence that distressed companies gamble more Little evidence that distressed companies gamble more with pension plan assets. with pension plan assets.

Significantly lower projected costs. Significantly lower projected costs.

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What perpetuates the mismatch?What perpetuates the mismatch?

Why don’t healthy companies use more bonds in Why don’t healthy companies use more bonds in funding their pensions, reducing volatility?funding their pensions, reducing volatility?

Why are policymakers reluctant to lower PBGC Why are policymakers reluctant to lower PBGC costs via restrictions on asset-liability mismatch?costs via restrictions on asset-liability mismatch?

Tentative answers: Tentative answers: Firms follow established norms.Firms follow established norms. The investment strategy that minimizes risk has not The investment strategy that minimizes risk has not

been fully articulated. been fully articulated.

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Is the best hedge a bond portfolio?Is the best hedge a bond portfolio?

Bodie’s example:Bodie’s example: Pension liability of $1000 in 10 yearsPension liability of $1000 in 10 years Put away present value = $1000/(1+r)Put away present value = $1000/(1+r)10 10 in risk-in risk-

free bondsfree bonds This is a perfect hedgeThis is a perfect hedge

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The optimal hedge portfolio with The optimal hedge portfolio with wage indexationwage indexation

Typical DB pension promises a fraction of terminal Typical DB pension promises a fraction of terminal wages, a random variable.wages, a random variable.

e.g., annual pension = .4 x wagee.g., annual pension = .4 x wage1010

Now the best hedge is the portfolio maximally correlated Now the best hedge is the portfolio maximally correlated with wagewith wage1010

If wages and stock returns are correlated, the optimal If wages and stock returns are correlated, the optimal portfolio will contain stocks was well as bonds.portfolio will contain stocks was well as bonds.

How much stock? It depends…How much stock? It depends…

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Finding the best hedge portfolioFinding the best hedge portfolio When wages and stocks are correlated, the value of the When wages and stocks are correlated, the value of the

pension liability can be modeled as a derivativepension liability can be modeled as a derivative..

The value of the pension liability, and the hedge portfolio, The value of the pension liability, and the hedge portfolio, can be found using can be found using options pricingoptions pricing methods. methods.

The The optimal portfolio is dynamicoptimal portfolio is dynamic, changing over time with the , changing over time with the demographics of the labor force.demographics of the labor force.

Bonds still play a big roleBonds still play a big role:: Firms with predominantly retired workers should invest predominantly Firms with predominantly retired workers should invest predominantly

in bonds.in bonds. Firms with young workers should invest more in stocks.Firms with young workers should invest more in stocks. When workers separate from the firm, their benefit becomes like a When workers separate from the firm, their benefit becomes like a

bond. bond.

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An exampleAn example The following joint process for stocks, human capital and wages The following joint process for stocks, human capital and wages

generates:generates: 1. an almost a zero correlation between wage growth and stock returns 1. an almost a zero correlation between wage growth and stock returns

at a one-year horizonat a one-year horizon 2. a correlation of .11 between wage growth and stock returns over 3 2. a correlation of .11 between wage growth and stock returns over 3

years, and .36 over five yearsyears, and .36 over five years

The aggregate value of stock evolves according to:The aggregate value of stock evolves according to:

The aggregate value of human capital evolves according to:The aggregate value of human capital evolves according to:

Wages evolve according to:Wages evolve according to:

)()5.(exp 2sssstht dzhhdivrSS

ttt

twwwtht WS

S

HThdzhhHH

*)()5.(exp 2

)( ttwtht WHhrWW

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An example An example parametersparameters

Inputs (annual)

mean stock return 0.05payout rate on human capital 0.02dividend yield 0.02std dev stock return 0.18std dev idio wage return 0.02std dev idio own firm return 0.2mean growth human capital 0.02speed of reversion to target 0.1speed of reversion in wages 0.5sensitivity to own-stock return 0target human to physical capital 2risk-free rate 0.02

Inputs DB Pensioncompare 0.00initial replacement rate 0.00years of earnings 35Separation and Mortalitymortality rate <= age 65 0.003mortality rate > age 65 0.05separation rate x < age 35 0.06separation rate age 34 < x < age 46 0.045separation rate age 45 < x < age 56 0.04separation rate age 55 < x 0.05

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An example -- An example -- resultsresults

Initial wage replacement rate 0.6 0.5 0.3 0Years to retirement 5 10 20 35

pv liability using correct risk adjustment 0.218 0.179 0.109 0.040pv liability discounting at risk-free rate 0.220 0.189 0.138 0.074pv liability discounting at average stock return 0.189 0.140 0.076 0.026initial share in stocks to get avg discount rate 0.063 0.195 0.389 0.589

share of cohort making it to 65 with the firm 0.766 0.5948 0.371 0.1694

Bottom line: Optimal share in stocks increases with employment horizon.

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Final thoughtsFinal thoughts

Asset-liability mismatch is a major source of risk, Asset-liability mismatch is a major source of risk, but restricting investments to bonds may not be but restricting investments to bonds may not be the right answer. the right answer.

Any policy that seriously addresses the PBGC Any policy that seriously addresses the PBGC funding gap will likely accelerate the switch from funding gap will likely accelerate the switch from DB to DC pensions.DB to DC pensions.

Hence, the costs of PBGC insurance must be Hence, the costs of PBGC insurance must be considered in the broader context of the goals of considered in the broader context of the goals of an employer-based retirement savings system.an employer-based retirement savings system.