Optimal corporate pension policy for de…ned bene…t plans in the presence of PBGC insurance Katarzyna Romaniuk Universidad de Santiago de Chile and Université de Paris 1 Panthéon-Sorbonne

ARIA Meeting, August 2012

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Introduction: The corporate pension policy in the literature two views of pension policy (Bodie et al., 1985) traditional and corporate

form of the de…ned bene…t (DB) pension plan’s policy tax considerations (Black, 1980; Tepper, 1981); the Pension Bene…t Guaranty Corporation (PBGC) insurance (Sharpe, 1976; Treynor, 1977); contribution considerations (Black, 1989); asset-liability management (ALM) mechanisms (Black, 1989, vs Bodie, 1990).

interactions between the …rm’s and the pension plan’s decisions Stocks in the pension fund have a leverage-like character (Black, 1980). Low equity investment in the pension fund enables more risk-taking in operating activities or in the capital structure (Merton, 2006). An increase in the pension liability to total assets ratio is associated with a decrease in the debt to total assets ratio (Shivdasani and Stefanescu, 2010). K. Romaniuk (USACH & Université Paris 1) (Institute) Optimal corporate pension policy

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Introduction: The existing literature and our contribution the existing literature both theoretical and empirical elements of response concerning the form of the corporate pension policy however, lack of a general, uni…ed framework in which the fundamental characteristics of this policy would be determined

our objective to build such a setting to analyze the characteristics of and interactions between the …rm’s optimal investment and …nancing policies and the DB pension plan’s optimal portfolio strategy

the modeling foundations based on the continuous-time optimal portfolio problem designed by Merton (1971) integrated balance sheet perspective K. Romaniuk (USACH & Université Paris 1) (Institute) Optimal corporate pension policy

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Introduction: The paper’s organization

1. The model 2. Main results 3. The principles to be followed by equityholders, participants and PBGC in times of non-distress and distress

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The model: The balance sheets

Four balance sheets BS BS BS BS

(1): (2): (3): (4):

non-consolidated …rm-only balance sheet; non-consolidated DB plan-only balance sheet; consolidated balance sheet without the PBGC put; consolidated balance sheet with the PBGC put.

the participants’vs the equityholders’perspective: BS (2) vs BS (3) or BS (4) the non-distress vs the distress consolidated balance sheet: BS (3) vs BS (4)

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ARIA Meeting, August 2012

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The model: The balance sheets (cont.) BS (1) AF

DF XF

BS (2) AP

LP XP

BS (3) AF D F AP LP X F +P

BS (4) AF D F AP LP PP X

AF , D F and X F : the …rm’s assets, debt and equity, respectively; AP , LP and X P : the pension plan’s assets, liabilities and net position, respectively; X F +P : the consolidated balance sheet equity; P P : the PBGC insurance put, whose value at maturity T is P P (T ) = Max (LP (T ) AP (T ); 0); X : the consolidated balance sheet equity if the PBGC put emerges.

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The model: The optimization programs BS (1)

BS (2)

BS (3)

BS (4)

AF

DF XF

MaxEt U (X F (T ))

AP

LP XP

MaxEt U (X P (T ))

AF AP

DF LP X F +P

MaxEt U (X F +P (T ))

AF AP PP

DF LP X

MaxEt [U (X (T ))]

Et stands for the expectation, conditional on the information available in t . U is the utility function.

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ARIA Meeting, August 2012

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The model: The control variables

the …rm decisions: investment and …nancing; control variables: the assets to equity ratio ratio

DF XF

AF XF

and the debt to equity

.

the DB plan decision: portfolio; control variables: the plan’s asset proportions to give to the stock market index S and to the riskless asset η.

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ARIA Meeting, August 2012

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The model: The variables dynamics AF , D F , S, LP , the DB plan´ s ‡ows of contributions c and of withdrawals w di (t ) = µi (t, Y (t ))dt + σi (t, Y (t ))dB i (t ) i (t ) with µi (t, Y (t )) and σi (t, Y (t )) bounded functions of time t and the vector of K state variables Y , and B i (t ) a standard Brownian motion, instantaneously correlated with B j (t ), where i, j = AF , D F , S, LP , c, w . the k-th state variable Yk dYk (t ) = µYk (t, Y (t ))dt + σYk (t, Y (t ))dB Yk (t ) Yk ( t ) the riskless asset η d η (t ) = r (t, Y (t ))dt η (t )

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Main results: The consolidated non-distress environment

When moving from the non-consolidated to the consolidated perspective, the …rm (DB plan) additionally hedges against the DB plan (…rm) variables.

! When moving from the participants’ to the equityholders’perspective, a hedge against the …rm variables emerges in the optimal DB portfolio rule.

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ARIA Meeting, August 2012

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Main results: The consolidated non-distress environment (cont.) The mechanisms driving the consolidated optimal policies In the existing literature, the pension portfolio policy from the corporate perspective has been fundamentally regarded solely as a hedging tool, used to optimize the …rm’s investment or …nancing decisions.

In our more general setting, the …rm and pension plan’s optimal policies are driven by speculative and hedging motives and in each optimal policy, the hedging activity considers, apart from the state variables, both the variables related to the pension plan and those related to the …rm.

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Main results: The consolidated distress environment

In the consolidated environment, when moving from the non-distress to the distress con…guration, the PBGC put emerges in the balance sheet, and all of the terms of the DB plan’s optimal portfolio policy become divided by the delta of the call symmetric to the PBGC put.

! i. When the sponsoring company is approaching distress, its optimal DB portfolio behavior becomes more aggressive. ! ii. Both risk-shifting and risk-management incentives should become stronger, as predicted by Rauh (2009).

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The principles followed by equityholders

The sponsoring company’s equityholders aim to optimize with respect to their wealth, within a consolidated balance sheet setting, using the pension as an optimizing tool in their own interests.

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ARIA Meeting, August 2012

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The principles to be followed by participants and PBGC in times of non-distress and distress

the pension plan participants’choice: sound ALM principles, within a non-consolidated setting

! their overwhelming goal : to receive the pension promised In normal, non-distressed times, the optimal pension portfolio rule from the equityholders’perspective is acceptable to both the participants and PBGC. However, this is no longer the case when the …rm approaches distress.

! The moment for the PBGC to step in is not the sponsoring company’s bankruptcy but when the …rm approaches distress.

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The reform step implied by the model results

our recommendation: The PBGC should immediately gain a control right on pension decisions as soon as the sponsoring company’s …nancial health is threatened. one possibility of reform: to develop the existing Early Warning Program by extending the range of monitoring activities and the PBGC’s control rights

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Conclusion

When a …rm sponsoring a DB plan approaches distress, the PBGC insurance e¤ect materializes and the …rm’s optimal pension portfolio policy becomes aggressive.

! Pension decisions of sponsoring companies near distress should be controlled by the PBGC.

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ARIA Meeting, August 2012

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Conclusion (cont.)

pension portfolio policy to be advocated by the PBGC?

! portfolio restriction to impose on DB plans sponsored by …rms near distress? (Romaniuk, 2012)

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ARIA Meeting, August 2012

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