Chapter 8 different stakeholders’ risks in DB pension funds

Option pricing models may help determining the value of these options as well as the sensitivity to market-related variables such as inter-est rates, infl ation, and the funding ratio, w

Different Stakeholders’ Risks in DB Pension

Funds

Theo Kocken and Anne de Kreuk

CONTENTS

8.4.2.2 Distribution of Risks among Participants 179 8.4.3 Mergers, Acquisitions, and Value Transfer Mechanisms 180

Risk s har ing a mong st akehol der s is one of the defi ning

character-istics of pension f unds Defi ned benefi t (DB) plans t ypically include covenants ensuring that plan sponsors will compensate the pension fund in case of a funding defi cit At the same time, retirees and employees may bear some of the risk, for instance through conditional indexation, i.e., indexation

with infl ation that may be forgone whenever the funding level falls below a certain threshold or whenever infl ation is above a certain level

Th e payoff s r elated t o t he r isks bo rne b y t he va rious st akeholders resemble payoff s of options, which stakeholders have written to the pen-sion fund Option pricing models may help determining the value of these options as well as the sensitivity to market-related variables such as inter-est rates, infl ation, and the funding ratio, which can be particularly help-ful in pension fund governance Th is is highly relevant in today’s DB and collective defi ned contribution (CDC) landscape in countries with mature

or developing retirement industries

Ultimately, valuing the various options embedded in the pension fund may also help in designing pension systems, which are robust for future changes in demography and market structure, such that each stakeholder will be fairly compensated for the risks borne in the pension fund

In this chapter, the approach of using embedded options to value the risks a nd co rresponding r ewards o f t he va rious st akeholders w ill be explained Furthermore, some applications of the embedded options tech-nique will be discussed:

Risk ma nagement: m ore i nsight i nto t he r isks ma kes i t e asier t o

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manage the pension funds’ risks

Improved decision making in case of pension fund buyouts or

•

pension fund redesign

Improved decision making in case of mergers and acquisitions

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8.1 INTRODUCTION

Defi ned benefi t (DB) pension f unds a re a mong t he most complex r isk-sharing institutions ever created Many diff erent structures of risk isk-sharing exist and many diff erent stakeholders (employers, retirees, and employees) are t ypically involved A ll stakeholders assume diff erent risks Unlike a corporate balance sheet, where it is clear who owns the equity (and there-fore takes the highest risk and fi rst loss accordingly) and who is the owner

of senior debt, there is little knowledge about the risks assumed by each stakeholder in pension funds Oft en, risk is measured for pension funds, but only as a whole, typically expressed in, e.g., the risk of funding shortfall However, this does not equal the risk borne by each of the stakeholders

Th e fact that not every stakeholder assumes the same risks is in itself understandable, s ince some st akeholders a re be tter eq uipped t o absorb

risks t han others It is, however, st riking t hat t here is oft en ha rdly a ny insight into the objective market value of these risks On top of that, there

is usually no explicit compensation agreement Th is may create incentives for some groups to retreat as a risk taker and will eventually cause a serious threat to the sustainability of the collective risk-sharing pension system Employers around the world have felt the impact of the greying society and the process of withdrawal of employers as risk takers seems to accel-erate Th e ageing population also causes a decreasing eff ectiveness of the contribution rate policy As a result of the withdrawal of the employers as risk takers and the decreasing eff ectiveness of the contribution rate policy, managing the indexation ambition and all other risks in the pension funds will be an even greater challenge in the future than it is today A number

of employers have already transformed their pension funds into a st and-alone collective defi ned contribution scheme, e.g., the collective scheme

is co ntinued, b ut t he em ployer wi thdraws as a r isk-bearing pa rty Th is automatically gives another risk profi le for the benefi ciaries Because the schemes still are collective, the intergenerational risk sharing between the participants is ma intained Th is shows that some pension funds already have to deal with a changing design of the pension fund model and there-fore changing risks for the diff erent stakeholders, which requires a diff er-ent risk managemer-ent approach

Given the recent market turmoil, funding ratios have come down, cor-porate ra tings were o ft en d owngraded d ue t o h ighly l everaged ba lance sheets, and volatilities went up Th erefore, even more than before, a b et-ter quantifi cation of the risks that the various parties assume, enabling a more meaningful and focused risk management, may be very valuable

An objective way to deal with the multi-stakeholder risk situations that arise in p ension f unds is t he em bedded o ptions a pproach (s ee K ocken 2006) Th e risks assumed by various parties in a pension fund are formu-lated in t erms o f o ptions—contingent c laims—which st akeholders ha ve written to the pension fund Th ese options have a cer tain value that can

be determined based upon the same techniques as a pplied in t he fi nan-cial markets to price fi nannan-cial options Most variables that are relevant to pension funds have a basis in fi nancial markets Examples are government bonds, risky assets such as equity and corporate bonds, and the liabilities that are related to interest rates Th erefore, the embedded options approach provides reliable market consistent values, which can be used to help valu-ing the risks for the diff erent stakeholders and determinvalu-ing the sensitivity

to market-related variables

Th e main focus in this chapter is to show the use of embedded options

as a tool to get more sustainable pension contracts by creating a better bal-ance between risk assumptions and return entitlements In Sections 8.2 through 8.4, the following is described:

Examples of embedded options are discussed in Section 8.2

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Aft er the embedded options are defi ned, the valuation of the diff

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ent embedded options is described by looking at a case concerning a simplifi ed but realistic pension fund

Finally, some applications of this concept to risk management and

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pension redesign are shown

8.2 VARIOUS EMBEDDED OPTIONS IN PENSION FUNDS Before analyzing the values of the embedded options and looking at the applications, it is useful to give a description of some of the most rele-vant options that can be defi ned in pension funds A d istinction can be made between the risks of the employer and the risks of the benefi ciaries (employees and retirees) Furthermore, the comparison of the risks of the diff erent groups of benefi ciaries is interesting

8.2.1 Parent Guarantee

Th e main embedded option the employer oft en writes to the pension fund

is t he “parent g uarantee.” Th is is t he g uarantee to support t he pension fund in case of funding shortfalls Th e parent guarantee is defi ned as the explicit additional mandatory payment by the parent company to a previ-ously stipulated and agreed funding ratio.*

Figure 8.1 gives an example of the payoff profi le of the parent guarantee from the viewpoint of the pension fund Th is payoff profi le shows that the

* Th roughout this chapter, we consider the nominal funding ratio.

Loss

sponsor

50 60 70 80 90 100

Funding ratio

110 120 130 140 150

FIGURE 8.1 Th e payoff profi le of the parent guarantee

parent guarantee can be viewed as an embedded option on the funding ratio of a pension fund

Th e value of this option depends on the volatility of the funding ratio

On top of that, the value depends on the creditworthiness of the parent company I f t he pa rent co mpany d oes n ot ha ve su ffi cient f unds a t t he moment the pension fund wishes to exercise the option, the agreed pay-ment cannot be done

In case of a low funding ratio, the parent company will contribute extra funds, causing the funding ratio to rise Th erefore, the option has impact

on the asset side of the fund rather than on the liability side

8.2.2 Indexation Option

An option that the benefi ciaries write to the pension fund is the “Index-ation option.” Index“Index-ation is the adjustment of pension rights to infl “Index-ation Diff erent kinds of embedded options exist that are related to indexation that is either conditional or capped In the Netherlands, for example, cuts

in indexation are oft en linked to the funding ratio, the so-called condi-tional i ndexation I n c ase o f co ndicondi-tional i ndexation, t he m embers o f a pension fund write an option on the funding ratio If the funding ratio drops below a certain level, the members are obliged to (partially) waive indexation of their entitlements In the United Kingdom, indexation cuts are linked to the infl ation level itself Indexation is oft en capped at a cer-tain level, usually 2.5% or 5%

Figure 8.2 shows the payoff profi les of the indexation options Th e two examples discussed here, indexation conditional on the funding level and

Funding ratio (a)

Loss of

indexation

(relative to the

inflation level)

Inflation (b)

Loss of indexation

FIGURE 8.2 Th e payoff profi le o f (a) c onditional i ndexation a nd ( b) c apped indexation

indexation capped at the infl ation level are shown in Figure 8.2a and b respectively, again from the viewpoint of the pension fund

Th e value of the conditional indexation option depends on the level of the funding ratio and the level of the infl ation Th erefore, in Figure 8.2a the value of the option is given relative to the level of infl ation for diff erent levels of the funding ratio, i.e., when the funding ratio is low, the loss of infl ation that the participants face is 100% of the infl ation level Th e value

of the capped indexation option depends on the infl ation level

In case of indexation cuts, the funding ratio will rise due to decreasing real liabilities Th erefore, the option has impact on the liability side of the fund rather than the asset side

8.2.3 Pension Put

Another opt ion b enefi ciaries w rite to t he pension f und i s t he “pension put.” Th e pension put is the option on a “ joint default”event, which is a defi cit in the pension fund at the same time as a default of the employer Please note that in some countries, such as the Netherlands, a sponsor also has the right to withdraw as a risk taker A recent example is the case

of the Super de Boer pension fund (see Winkel 2009) Super de Boer is a supermarket cha in in t he Netherlands Th e contract between t he spon-sor and the pension fund is oft en agreed for a fi xed period of time and extended aft erward In this case, the sponsor will not extend the contract with the pension fund because they cannot come to an agreement about the way in which the pension fund is managed If no clear statements are made on the costs for the sponsor of withdrawing, this will give the same implications as a default of the sponsor for benefi ciaries

In Figure 8.3, the payoff profi le of the pension put is given in case of a default of the parent company, again from the viewpoint of the pension fund

Th e va lue of t he pension put depends on, a mong others, t he default probability of the sponsor as a function of time, recovery rates, and corre-lation between fi nancial markets and default probability A “joint default”

Funding ratio

Loss participant

in case of default

of company

FIGURE 8.3 Th e payoff profi le of the pension put

will imply write-off s of the pension entitlements, which is defi ned as the

“payout” of the embedded option Th erefore, the option has an impact on the liability side of the fund rather than the asset side

8.2.4 Other Embedded Options

Many pension funds receive contributions from the employer, oft en partly paid by the employees, which deviate from the actuarial cost p rice of the annuities provided to the benefi ciaries In other words, contributions fl uc-tuate annually as a function of the funding ratio If no risks were taken in the pension fund, the required contribution would equal the actuarial cost price Because of the risks being taken, within the pension scheme contribu-tions can on average be set below this price In times of bad performance, it

is oft en agreed that contributions can increase and exceed the actuarial cost price If contributions are partly paid by the employer and partly by employ-ees, both employer and employees have written options to the pension fund (because the contribution they pay is higher than the actuarial costs price in case of a low funding ratio), but they also received options from the pension fund (because contribution will be cut in case of a high funding ratio)

Th e contribution options played a n i mportant role i n t he pa st; how-ever, n owadays l ittle co ntribution ste ering c an be ex pected S ince t he active employees are usually only a small portion of the total benefi ciaries due to the greying society, changing the contributions has little impact

Th erefore, this set of options will not be addressed here any further Many o ther em bedded o ptions a re i mplicitly present i n t he pens ion funds, b ut t he se t abo ve co vers t he ma in o ptions t hat c an be defi ned

in defi ned benefi t pension funds—or collective defi ned contribution pen-sion funds to a certain extent

8.3 VALUING RISKS AS EMBEDDED OPTIONS

In Section 8.2, we have seen several examples of embedded options that can be identifi ed in pension funds In this section, embedded options are measured u sing a rbitrage-free option pricing tech niques a nd a ssuming complete markets (see for example Nijman and Koijen 2006) Furthermore, the assumption is made that the diff erent stakeholders have defi ned very explicit contracts (options) between them and the pension fund Th is is a very strong assumption, since in many cases the pension deal is not very well specifi ed Th is assumption, however, will make it even more clear that there is a need for such explicit pension contracts, which are easier valued and therefore more transparent for all stakeholders

Th e options are path dependent* and quite complex Th e most appro-priate m easurement tech nique i s t herefore M onte C arlo s imulations o f market consistent a nd a rbitrage-free scenarios a nd taking t he ex pected value under this risk neutral measure

Below, a case is discussed that is based on a risk-sharing pension fund with

a sponsor that provides the guarantee to the nominal pension obligations (the pa rent g uarantee de scribed i n Section 8 2), benefi ciaries who acc ept conditional indexation (the indexation option described in Section 8.2) as well as the possibility of a default by the employer (the pension put described

in Section 8.2) Th e contribution rate is fi xed to keep the case transparent For ex pository r easons, t he pens ion f und ba se c ase a pplies a s imple asset allocation of 50% government bonds, which are assumed to be risk free in this case, and 50% equity investments Th e nominal funding ratio equals 100% Th e sponsor’s debt is assumed to be BB rated

In the case study, the sensitivity to the assumptions is tested by letting

go one of the assumptions Th e analysis in the following text is based on diff erent models that are discussed extensively in chapters two, three and four of Kocken (2006) and are not repeated here

Table 8.1 starts with (column 1) a situation in which benefi ciaries assume

no risk at all: Th e sponsor has provided a guarantee and is assumed default free In this case, the benefi ciaries are entitled to full infl ation indexation

of the liabilities under all scenarios Th ey simply bear zero risk In the sec-ond column, t he BB rating of t he sponsor is taken into account, putting slightly more risk on the benefi ciaries’ plate through the pension put, which

is the option on a “ joint default” event In the third column, benefi ciaries

* Th e value of the options does not only depend on the current values of the market variables, but also on realized values of the market variables in the past (their “path”).

TABLE 8.1 Values of the Embedded Options for Diff erent Kinds

of Risk Sharing (% of Liability Value)

Type of Pension

Fund

Full Indexation + Default Free Sponsor (%)

Full Indexation +

“Default Risk”

Sponsor (%)

Conditional Indexation + “Default Risk” Sponsor (%)

Parent guarantee

Sponsor share

are confronted with both the potential default of the employer as well as indexation cuts in situations of low funding ratios

Th e values in the tables in this section are expressed as a per centage

of the value of the liabilities at t = 0 Table 8.1 shows that for this specifi c situation, the parent guarantee has a value that is close to 30%, in case the possibility of default of the parent is excluded However, it is interesting to see the impact of corporate default risk and especially explicit risk sharing such as t he possibility of indexation cuts In t his case, t he benefi ciaries assume almost half of the risks (45%) by accepting conditional indexation and the default risk of the sponsor

Th e option values depend on various parameters, such as the composi-tion (and hence the volatility) of the asset mix and the credit rating of the sponsoring company Table 8.2 provides some insight into the impact of asset allocation on the embedded option values, with lower equity (higher bonds) and higher equity (lower bonds) allocations.*

Table 8.2 reveals that more risk taking in the asset mix of the pension fund that is discussed in this case leads to more additional risk assumed

by t he employer compared to t he benefi ciaries, both in absolute and in relative terms

Table 8 3 provides a n i nsight i nto t he i mpact of va riations i n c redit rating on the option values.†

Table 8.3 explains the importance of credit risk and the impact on who assumes what risk: In case the employer has a low credit rating, the amount

of risk that benefi ciaries are taking is higher in embedded option value terms than the risk assumed by the employer Th is picture is completely reversed in the case of a supporting employer with a high credit rating

* Th e credit rating of the sponsor in Table 8.2 is BB, the funding ratio is again 100%.

† Th e funding ratio in Table 8.3 is 100%, the asset mix contains 50% equity.

TABLE 8.2 Option Values (% of Liability Value) as a Function of Asset Mix Composition

Equity % of Total Assets

Parent guarantee 15.2 17.8 22.7 Pension put 2.5 3.1 3.8 Indexation option 12.3 11.3 10.4 Sponsor share

(% total risk) 51 55 61

Many other variables determine the value of these options, a ke y one being the actual funding ratio Table 8.4 compares the various option val-ues at diff erent funding ratios.*

It is clear from Table 8.4 that at very low funding levels, far below fully funded st atus, t he r isk a ssumed by t he sponsor i s relatively h igh com-pared to the benefi ciaries’ risk absorption Th is is due to the fact that the indexation opt ion c annot i ncrease t hat much w ith lower f unding levels (the infl ation can only be lost, regardless of the shortfall level), where the corporate sponsor has to complete the entire shortfall

8.4 APPLICATIONS

Knowing the values of embedded options and knowing in what way dif-ferent p arameters i nfl uence t hese va lues, g enerates ma ny n ew a pplica-tions, for example in risk management, pension redesign, and in case of

a merger or acquisition In this section, the most important applications are discussed

* Th e credit rating of the sponsor in Table 8.4 is BB, the asset mix contains 50% equity.

TABLE 8.3 Option Values (% of Liability Value)

as a Function of Employer’s Credit Rating

Employer’s Credit Rating

Parent guarantee 8.7 17.8 21.3 Pension put 10.0 3.1 0.3 Indexation option 12.1 11.3 11.0 Sponsor share

(% total risk) 28 55 65

TABLE 8.4 Option Values (% of Liability Value)

as a Function of Actual Funding Ratio

Current (Nominal) Funding Ratio

Parent guarantee 34.0 17.8 9.1

Indexation option 13.4 11.3 6.4

Sponsor share

(% total risk) 67 55 50