CHAPTER Different Stakeholders’ Risks in DB Pension Funds Theo Kocken and Anne de Kreuk CONTENTS 8.1 I ntroduction 8.2 Various Embedded Options in Pension Funds 8.2.1 P arent Guarantee 8.2.2 I ndexation Option 8.2.3 P ension Put 8.2.4 Other Embedded Options 8.3 Valuing Risks as Embedded Options 8.4 A pplications 8.4.1 R isk Management 8.4.2 P ension Redesign 8.4.2.1 Employer versus Participants 8.4.2.2 Distribution of Risks among Participants 8.4.3 Mergers, Acquisitions, and Value Transfer Mechanisms 8.5 C onclusions Appendix References 168 170 170 171 172 173 173 176 177 178 178 179 180 180 81 83 R isk s r ing a mong st a keh ol der s is one of the defining characteristics o f pens ion f unds Defined benefit ( DB) p lans t ypically i nclude covenants ensuring that plan sponsors will compensate the pension fund in case of a funding deficit At the same time, retirees and employees may bear some of the risk, for instance through conditional indexation, i.e., indexation 167 © 2010 by Taylor and Francis Group, LLC 168 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling with inflation that may be forgone whenever the funding level falls below a certain threshold or whenever inflation is above a certain level The payoffs r elated t o t he r isks bo rne b y t he va rious st akeholders resemble payoffs of options, which stakeholders have written to the pension fund Option pricing models may help determining the value of these options as well as the sensitivity to market-related variables such as interest rates, inflation, and the funding ratio, which can be particularly helpful in pension fund governance This is highly relevant in today’s DB and collective defined 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 t his chapter, t he approach of using embedded options to va lue t he 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 technique will be discussed: • Risk ma nagement: m ore i nsight i nto t he r isks ma kes i t e asier t o 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 8.1 INTRODUCTION Defined benefit ( DB) pens ion f unds a re a mong t he m ost co mplex r isksharing institutions ever created Many different structures of risk sharing exist and many different stakeholders (employers, retirees, and employees) are t ypically i nvolved A ll st akeholders a ssume d ifferent r isks Unlike a corporate balance sheet, where it is clear who owns the equity (and therefore takes the highest risk and first loss accordingly) and who is the owner of senior debt, there is little k nowledge about the risks assumed by each stakeholder in pension funds Often, 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 The fact t hat not every stakeholder assumes t he same risks is in itself understandable, s ince so me st akeholders a re be tter eq uipped t o abso rb © 2010 by Taylor and Francis Group, LLC Different Stakeholders’ Risks in DB Pension Funds ◾ 169 risks t han o thers I t i s, h owever, st riking t hat t here i s o ften rdly a ny insight into the objective market value of these risks On top of that, there is usually no explicit compensation agreement This 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 r isk takers seems to accelerate The ageing population also causes a decr easing effectiveness of the contribution rate policy As a result of the withdrawal of the employers as risk takers and the decreasing effectiveness of the contribution rate policy, managing the indexation ambition and all other risks in the pension funds will be an even greater challenge in t he future than it is today A number of employers have already transformed their pension funds into a st andalone co llective defined co ntribution s cheme, e g., t he co llective s cheme is co ntinued, b ut t he em ployer wi thdraws as a r isk-bearing pa rty This automatically gives another risk profile for the beneficiaries B ecause the schemes still are collective, the intergenerational risk sharing between the participants is ma intained This sho ws t hat s ome p ension f unds alr eady have to deal with a changing design of the pension fund model and therefore changing risks for the different stakeholders, which requires a different risk management approach Given the recent market turmoil, funding ratios have come down, corporate tings w ere o ften d owngraded d ue t o h ighly l everaged ba lance sheets, and volatilities went up Therefore, even more t han before, a b etter quantification 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) The risks assumed by various parties in a p ension fund are formulated in t erms o f o ptions—contingent c laims—which st akeholders ve written to the pension fund These options have a cer tain value that can be determined bas ed upon t he s ame techniques as a pplied in t he financial markets to price financial options Most variables that are relevant to pension funds have a basis in financial markets Examples are government bonds, risky assets such as equity and corporate bonds, and the liabilities that are related to interest rates Therefore, the embedded options approach provides reliable market consistent values, which can be used to help valuing the risks for the different stakeholders and determining the sensitivity to market-related variables © 2010 by Taylor and Francis Group, LLC 170 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling The 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 balance be tween r isk a ssumptions a nd return entitlements I n S ections through 8.4, the following is described: • Examples of embedded options are discussed in Section 8.2 • After the embedded options are defined, the valuation of the different embedded options is described by looking at a case concerning a simplified but realistic pension fund • Finally, some applications of this concept to risk management and 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 relevant options t hat can be defined in pension f unds A d istinction can be made between the risks of the employer and the risks of the beneficiaries (employees and retirees) Furthermore, the comparison of the risks of the different groups of beneficiaries is interesting 8.2.1 Parent Guarantee The main embedded option the employer often writes to the pension fund is t he “ parent g uarantee.” This i s t he g uarantee t o su pport t he pens ion fund in case of funding shortfalls The parent guarantee is defined as the explicit additional mandatory payment by the parent company to a previously stipulated and agreed funding ratio.* Figure 8.1 gives an example of the payoff profile of the parent guarantee from the viewpoint of the pension fund This payoff profile shows that the Loss sponsor 50 60 70 80 90 100 110 120 130 Funding ratio FIGURE 8.1 The payoff profi le of the parent guarantee * Throughout this chapter, we consider the nominal funding ratio © 2010 by Taylor and Francis Group, LLC 140 150 Different Stakeholders’ Risks in DB Pension Funds ◾ 171 parent guarantee can be viewed as an embedded option on the funding ratio of a pension fund The value of this option depends on the volatility of the funding ratio On top of t hat, t he va lue depends on t he creditworthiness of t he parent company I f t he pa rent co mpany d oes n ot ve su fficient f unds a t t he moment the pension fund wishes to exercise the option, the agreed payment cannot be done In case of a low funding ratio, the parent company will contribute extra funds, causing the funding ratio to rise Therefore, 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 beneficiaries write to the pension fund is the “Indexation option.” Indexation is the adjustment of pension rights to inflation Different k inds of embedded options exist t hat are related to indexation that is either conditional or capped In the Netherlands, for example, cuts in indexation are often linked to t he f unding ratio, t he so-called conditional i ndexation I n c ase o f co nditional i ndexation, t he m embers o f a pension f und w rite a n option on t he f unding r atio I f t he f unding r atio drops below a c ertain level, the members are obliged to (partially) waive indexation of their entitlements In the United Kingdom, indexation cuts are linked to the inflation level itself Indexation is often capped at a certain level, usually 2.5% or 5% Figure 8.2 shows the payoff profiles of the indexation options The two examples discussed here, indexation conditional on the funding level and Loss of indexation (relative to the inflation level) (a) Funding ratio Loss of indexation (b) FIGURE 8.2 indexation Inflation The payoff profi le o f ( a) c onditional i ndexation a nd ( b) c apped © 2010 by Taylor and Francis Group, LLC 172 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling indexation capped at t he inflation level a re shown i n Figure 2a a nd b respectively, again from the viewpoint of the pension fund The value of the conditional indexation option depends on the level of the funding ratio and the level of the inflation Therefore, in Figure 8.2a the value of the option is given relative to the level of inflation for different levels of the funding ratio, i.e., when the funding ratio is low, the loss of inflation that the participants face is 100% of the inflation level The value of the capped indexation option depends on the inflation level In case of indexation cuts, the funding ratio will rise due to decreasing real liabilities Therefore, 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 eneficiaries w rite t o t he pens ion f und i s t he “ pension put.” The pension put is t he option on a “ joint default”event, wh ich is a deficit 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 i n t he Netherlands The co ntract be tween t he spo nsor a nd t he pension f und i s often a greed for a fi xed period of t ime a nd extended afterward 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 beneficiaries In Figure 8.3, the payoff profile of the pension put is given in cas e of a default of t he parent company, again f rom t he vie wpoint of t he p ension fund The va lue o f t he pens ion p ut depen ds o n, a mong o thers, t he defa ult probability of the sponsor as a function of time, recovery rates, and correlation between financial markets and default probability A “joint default” Loss participant in case of default of company Funding ratio FIGURE 8.3 The payoff profi le of the pension put © 2010 by Taylor and Francis Group, LLC Different Stakeholders’ Risks in DB Pension Funds ◾ 173 will imply write-offs of the pension entitlements, which is defined as the “payout” of the embedded option Therefore, 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, often partly paid by t he employees, wh ich deviate f rom t he ac tuarial cost p rice of t he annuities provided to the beneficiaries In other words, contributions fluctuate annually as a f unction 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 contributions can on average be set below this price In times of bad performance, it is often agreed that contributions can increase and exceed the actuarial cost price If contributions are partly paid by the employer and partly by employees, 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) The co ntribution o ptions p layed a n i mportant r ole i n t he pa st; h owever, 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 beneficiaries due to t he g reying society, cha nging t he contributions s l ittle i mpact Therefore, this set of options will not be addressed here any further Many o ther em bedded o ptions a re i mplicitly p resent 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 defined in defined benefit pension funds—or collective defined contribution pension 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 identified in pension funds In this section, embedded options are measured u sing a rbitrage-free o ption p ricing tech niques a nd a ssuming complete markets (see for example Nijman and Koijen 2006) Furthermore, the assumption is made that the different stakeholders have defined very explicit contracts (options) between them and the pension fund This is a very strong assumption, since in many cases the pension deal is not very well specified This 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 © 2010 by Taylor and Francis Group, LLC 174 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling The options are path dependent* and quite complex The most appropriate m easurement tech nique i s t herefore M onte C arlo s imulations o f market co nsistent a nd a rbitrage-free sc enarios a nd t aking 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 t hat provides t he g uarantee to t he nominal pension obligations (the pa rent g uarantee de scribed i n Section 2), ben eficiaries wh o 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) The contribution rate is fixed 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 r isk free in this case, and 50% equity investments The nominal funding ratio equals 100% The 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 The analysis in the following text is based on different 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 beneficiaries assume no risk at all: The sponsor has provided a guarantee and is assumed default free In this case, the beneficiaries are entitled to full inflation indexation of the liabilities under all scenarios They simply bear zero risk In the second co lumn, t he B B r ating o f t he spo nsor i s t aken i nto acco unt, p utting slightly more risk on the beneficiaries’ plate through the pension put, which is the option on a “ joint default” event In the third column, beneficiaries TABLE 8.1 Values of the Embedded Options for Different Kinds of Risk Sharing (% of Liability Value) Type of Pension Fund Parent guarantee (sponsor covenant) Pension put Indexation option Sponsor share [% total risk] Full Indexation + Default Free Sponsor (%) 29.7 100 Full Indexation + “Default Risk” Sponsor (%) Conditional Indexation + “Default Risk” Sponsor (%) 28.6 17.8 4.8 3.1 11.3 55 86 * The 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”) © 2010 by Taylor and Francis Group, LLC Different Stakeholders’ Risks in DB Pension Funds ◾ 175 are confronted w ith both t he potential default of t he employer a s well a s indexation cuts in situations of low funding ratios The va lues i n t he t ables i n t his sec tion a re ex pressed a s a per centage of the value of the liabilities at t = Table 8.1 shows that for this specific 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 a s t he pos sibility o f i ndexation c uts I n t his c ase, t he ben eficiaries assume almost half of the risks (45%) by accepting conditional indexation and the default risk of the sponsor The option values depend on various parameters, such as the composition (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 co mpared t o t he ben eficiaries, both in absolute and in relative terms Table p rovides a n i nsight i nto t he i mpact o f 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 beneficiaries are taking is higher in embedded option value terms than the risk assumed by the employer This picture is completely reversed in the case of a supporting employer with a high credit rating TABLE 8.2 Option Values (% of Liability Value) as a Function of Asset Mix Composition Equity % of Total Assets Type of Option 30% 50% 70% Parent guarantee Pension put Indexation option Sponsor share (% total risk) 15.2 2.5 12.3 51 17.8 3.1 11.3 55 22.7 3.8 10.4 61 * The credit rating of the sponsor in Table 8.2 is BB, the funding ratio is again 100% † The funding ratio in Table 8.3 is 100%, the asset mix contains 50% equity © 2010 by Taylor and Francis Group, LLC 176 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling TABLE 8.3 Option Values (% of Liability Value) as a Function of Employer’s Credit Rating Employer’s Credit Rating Type of Option CCC BB A Parent guarantee Pension put Indexation option Sponsor share (% total risk) 8.7 10.0 12.1 28 17.8 3.1 11.3 55 21.3 0.3 11.0 65 TABLE 8.4 Option Values (% of Liability Value) as a Function of Actual Funding Ratio Current (Nominal) Funding Ratio Type of Option 80% 100% 120% Parent guarantee Pension put Indexation option Sponsor share (% total risk) 34.0 3.4 13.4 67 17.8 3.1 11.3 55 9.1 2.6 6.4 50 Many other variables determine t he va lue of t hese options, a ke y one being the actual funding ratio Table 8.4 compares the various option values at different 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 b y t he spo nsor i s r elatively h igh co mpared to the beneficiaries’ risk absorption This is due to the fact that the indexation opt ion c annot i ncrease t hat m uch w ith lo wer f unding le vels (the i nflation 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 different p arameters i nfluence t hese va lues, g enerates ma ny n ew a pplications, for example in risk management, pension redesign, and in case of a merger or acquisition In this section, the most important applications are discussed * The credit rating of the sponsor in Table 8.4 is BB, the asset mix contains 50% equity © 2010 by Taylor and Francis Group, LLC Different Stakeholders’ Risks in DB Pension Funds ◾ 177 8.4.1 Risk Management The sensitivity of the different embedded options to market variables such as real or nominal interest rates can be de termined A nother i mportant measure is t he sensitivity to more implicit market-related variables such as the funding ratio Furthermore, the embedded options are sensitive to the pension fund’s assets Embedded o ptions c an be t reated s imilarly t o “ normal” o ptions, including the risk management of these options Analyzing the sensitivities to t he ma rket va riables t hat i nfluence t he options g ives i nsight i nto the different risks of the stakeholder In this section, the sensitivity of the options’ values toward the nominal funding ratio is discussed In the case of conditional indexation, for example, the stakeholders of a pension fund are exposed to both nominal and real interest rates Given the nature of the indexation option, the risk associated with nominal or real rates very much depends on the solvency of the pension fund In c ase o f a l ow f unding r atio, l ittle i nflation-linked i ndexation i s expected to be paid in the future and the pension fund is mainly sensitive to nominal interest rates At very high funding levels, indexation is very likely to be granted many years ahead and the pension fund is mostly sensitive to real interest rates For nonextreme f unding ratio situations, t he indexation option is sensitive to both nominal and real interest rates This sensitivity c an o nly be de termined b y k nowing t he i ndexation o ption’s value and its first order derivative as a function of the two relevant types of interest rates Figure 8.4 provides an example of how the interest rate sensitivities (both sensitivity to real as well as to nominal yield changes) of the liabilities of a pension fund change as a function of the funding ratio.* This approach is useful to determine the optimal hedge in case a pension fund wants to minimize interest rate risk or—as is often s een i n practice—if there is a need for a liability benchmark against which risk and return are measured In practice, interest rate risk is one of the dynamic market fac tors t hat a pens ion f und ma y wa nt t o i nvest i n, i n o rder t o obtain an optimal risk-return profile Usually this profile is optimized in a going concern ALM context In this case, the sensitivity analysis is useful to understand the outcomes and compare against the risk-minimizing hedge position (liability benchmark) An analysis of the higher order derivatives (the “delta” and “vega”) of the options toward the nominal funding ratio is given in Appendix 8.A.1 * For a thorough explanation of the values in this example as well as the values in the following examples, see Kocken 2006, Chapters and © 2010 by Taylor and Francis Group, LLC 178 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling 12.00 Real yield sensitivity 10.00 8.00 6.00 4.00 Nominal yield sensitivity 2.00 0.00 60 70 80 90 100 110 120 130 Nominal funding ratio 140 150 160 170 FIGURE 8.4 Nominal a nd r eal i nterest r ate s ensitivities o f t he c onditionally index liabilities 8.4.2 Pension Redesign As discussed in Section 8.4.3, embedded option theory can explain many of the risks borne by stakeholders in a pension fund By showing the risks per stakeholder, possible tensions between stakeholders are also revealed that a re caused by mismatches between t he risks t hat a re taken a nd t he compensation for taking these risks In case of tensions, the pension system could be n onsustainable i n t he long r un A l ogical next step i n t he applications of the embedded options methodology would be (re-)designing t he pension f und such t hat t he risk taken is rewarded appropriately By evaluating the impact of policy adjustments in a pension fund on the various embedded options and, if necessary, trying to steer with different po licy i nstruments ( asset a llocation, co ntribution r ate po licy, e tc.), changes can be made t hat are acceptable to all stakeholders This creates more stable relations between stakeholders The different relations between stakeholders can cause different types of redesign It is interesting to look at the employer as a risk taker versus the beneficiaries as risk takers, but the relation between the different (groups of) beneficiaries can also be analyzed 8.4.2.1 Employer versus Participants The balance sheet size of a pension fund often exceeds the capitalization of the sponsor New accounting rules, the ageing population, and an increasing sc arcity o f r isk c apital f or co mpanies l ead t o a g rowing p ressure t o shift more risk in DB pension plans from the employer to the participants © 2010 by Taylor and Francis Group, LLC Different Stakeholders’ Risks in DB Pension Funds ◾ 179 This results in individual or collective defined contribution (DC or CDC) funds In current practice, the financial side of the risk transfer is arranged through negotiations whose outcomes are rarely based on clear and objective criteria Using the embedded options approach to determine the economic value an employer should pay into a pension fund when he wants to retreat (partly) as a risk taker and transfer the risks to the beneficiaries (see Hoevenaars et al 2009) can strongly improve the negotiation process Both the value of the guarantees regarding accrued rights as well as future rights to be accrued can be objectively determined by using embedded options The way in which t he pa rticipants should subsequently d istribute t he risks is another question, which, incidentally, can also be a nswered with the aid of the techniques applied here 8.4.2.2 Distribution of Risks among Participants As mentioned earlier, in many pension contracts, the values of the options written by the different groups of participants differ a lot, compared to the compensation that is granted in return for taking these risks Often the actives bear much more risks than the retirees This is economically sensible because they have much more human capital to cushion these risks than retirees Apart from a s mall group of pension funds that did ma ke very explicit agreements on surplus entitlements, there are often no clear agreements on who i s entitled t o t he upside Therefore, a re distribution of w ealth f rom t he ac tive m embers t o t he r etirees s occ urred, wh ich sometimes involves 30% or more of the value of the liabilities (see Kocken 2007) This situation may trigger the actives to retreat as risk takers from the pension fund, just as many employers were already triggered to retreat as risk takers by the same asymmetric risk-return profile An obvious solution for this intergenerational risk is to grant clear entitlements to potential surpluses in proportion to the value of the risks, as expressed i n ter ms of embedded option va lues In other words, ex-post, but not ex-ante wealth distribution Retirees, who may assume some limited risk but not act as the residual risk takers, can for example be given some potential in the upside but only partially A larger share will then go to the actives, who also assumed the largest residual part of the risks This can be set up in such a way that all upside sharing is well balanced in proportion to the risk taking and is thus in line with how these risk-returns would trade in the market As a result of the decreased funding ratios due to the current crisis, the case of cutting rights of participants is widely discussed in the Netherlands © 2010 by Taylor and Francis Group, LLC 180 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling at the moment Currently most pension funds not have a clear view on the va lues of t he em bedded o ptions i mplicitly a ssumed by t he d ifferent groups of participants and the decisions to cut rights will cause tensions between the different groups of participants in many cases An objective risk management approach by using embedded options at an early state in this process would help the pension funds in determining whose rights to cut and to what extent the rights should be cut 8.4.3 Mergers, Acquisitions, and Value Transfer Mechanisms Not only for the different stakeholders in the pension funds it is interesting to know the value of their risks, but also external parties can be interested For example, in case of a merger or acquisition of the parent company this may prove valuable in defining how (groups of) participants and the corresponding risks move from one pension fund to another CFO’s a re i nterested i n what k ind of r isks t hey a ssume a nd what t he value of these risks is when acquiring a firm with a DB pension fund With the knowledge provided by the embedded option technique, the CFO can assess what kind of policy measures applied to the pension fund can result in acceptable risks in case a target firm, including its obligation to the pension fund, would be acquired 8.5 CONCLUSIONS In this chapter, we have seen that the current risk-sharing pension fund system see ms n onsustainable i n t he l ong r un, d ue t o te nsions bet ween the stakeholders implied by imbalances in risk and return for the various stakeholders The embedded options approach d iscussed here c an be u sed to va lue the r isks bo rne b y t he st akeholders—active m embers, r etirees, a nd employers—in a pension fund Using embedded options to value the risks borne by the various stakeholders can be applied in many different decision making situations, such as: • Evaluating the impact of policy adjustments in a pension fund on the various embedded options and, if necessary, trying to steer with different policy instruments (asset allocation, contribution rate policy, etc.) to make the changes acceptable to all stakeholders • Determining the economic value an employer should pay into a pension fund when he wants to retreat as a risk taker in the pension fund and transfer the risks to the beneficiaries © 2010 by Taylor and Francis Group, LLC Different Stakeholders’ Risks in DB Pension Funds ◾ 181 • Determining t he en titlements o f t he d ifferent s takeholders to a potential f uture su rplus i n t he pens ion f und, p roportional t o t he risks they assumed • Determining the claim a pension fund has on a corporate when considering a merger APPENDIX 8.A.1 SENSITIVITY OF THE DELTA AND VEGA OF THE EMBEDDED OPTIONS TO THE NOMINAL FUNDING RATIO The sensitivity of the option value to changes in the funding ratio can be determined This is essentially similar to the concept of “delta” in risk management, though the funding ratio itself is not a r eal market variable This reveals the extent to which the stakeholders are exposed to changes in the funding ratio Figure 8.5 provides an indication of the delta values (sensitivities of the option values to changes in the funding ratio) for two relevant embedded options in DB schemes with conditional indexation: the indexation option and the parent guarantee.* The delta profi le of the parent guarantee is quite different from the profi le of the indexation option The indexation option has very specific features because its value is limited at both the upside and the downside Delta (absolute values) 1.0 Parent guarantee 0.8 0.6 0.4 0.2 Indexation option 0.0 80 90 100 110 Nominal funding ratio 120 130 FIGURE 8.5 Delta characteristics as a function of the funding ratio * The delta values in this example are negative, but for clarity, the absolute (positive) values are presented © 2010 by Taylor and Francis Group, LLC 182 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling Equally important from a risk management perspective is the change in the value of the different embedded options resulting from changes in the volatility of the pension fund’s assets (i.e., the “vega” value) This reveals how st akeholders a re i mpacted b y cha nges i n, e.g , t he a sset a llocation (and thus the volatility) of a pension fund Figure 8.6 shows the vega value of the parent guarantee and the indexation option Vega va lues a re ex pressed i n ter ms o f t he va lue o f t he pens ion f und and w ill be pos itive or negative depending on whether t hey a re considered f rom t he perspec tive o f t he pa rent co mpany o r t he pens ion f und For ex ample, t he pa rent g uarantee i s pos itive f or t he pens ion f und (for all funding ratios) and is therefore negative for the parent company This implies t hat, i n t his ex ample, t he co rporate spo nsor w ill p refer a l ower volatility t o r educe t he va lue o f t he pa rent g uarantee.* I t i s i nteresting to observe t hat for a l ow f unding ratio, t he vega va lue of t he indexation option is positive for the beneficiaries (and negative from the pension fund perspective) This reveals a serious conflict of interest between the position of the employer (seeking a lower risk profi le) and the beneficiaries (seeking a higher risk profile) in case of a low funding ratio Another noteworthy aspect is the magnitude of the vega value, which can be quite large For example, vega can exceed 3% of the liability value The reason for this is the fact that these options are somewhere between Sensitivity to 1% change in volatility (% of liabilities) Parent guarantee Indexation option 0.500 4.00 Parent guarantee 3.00 0.000 2.00 –0.500 1.00 Indexation option 0.00 FIGURE 8.6 70 80 90 100 110 120 Nominal funding ratio 130 140 –1.000 150 Vega characteristics as a function of the funding ratio * It should be noted that this example abstracts from other options available to t he employer such as the contribution rate option that can have a positive vega value © 2010 by Taylor and Francis Group, LLC Different Stakeholders’ Risks in DB Pension Funds ◾ 183 a s ingle, v ery l ong-term o ption a nd a ser ies o f a nnual f orward-starting options This implies that a corporate sponsor, with a large pension fund relative to its c apital va lue, c an easily i ncrease t he va lue of its equity by 20%–30% b y r educing r isk i n i ts pens ion f und This ex plains t he d rive toward risk reduction manifested by many employers The insights described earlier can be used to hedge the risks of the different stakeholders A hedge that is set up to improve the corporate perspective, however, may be detrimental from the beneficiaries’ perspective and adjustments in t he pension agreement may be n ecessary The embedded option technique is very useful in creating a s ituation where a co mbination of hedging and pension redesign is beneficial to all parties involved REFERENCES Hoevenaars, R., T.P Kocken, and E Ponds 2009 Pricing risk in corporate pension plans: Understanding the real pension deal Rotman International Journal of Pension Management, 2(1), Spring 2009: 56–62 DOI: 10.3138/rijpm/2.1.56 Kocken, T.P 2006 Curious Contracts Pension Fund Redesign for the Future Tutein Nolthenius, ‘s-Hertogenbosch, the Netherlands Kocken, T.P 2007 Constructing sustainable pensions Life & Pensions, July 2007: 35–39 Nijman, T.E and R Koijen 2006 Valuation and risk management of inflation-sensitive pension rights In Fair Value and Pension Fund Management, N Kortleve, T.E Nijman, and E Ponds (Eds.), Elsevier Publishers, Amsterdam, the Netherlands Winkel, R April 3, 2009 Heibel over Pensioenpijn bij Super de Boer (Quarrel over pension pain in Super de Boer) Het Financieele Dagblad, April 3, 2009: 13 © 2010 by Taylor and Francis Group, LLC ... ion funds, b ut t he se t abo ve co vers t he ma in o ptions t hat c an be defined in defined benefit pension funds or collective defined contribution pension funds to a certain extent 8. 3 VALUING... Francis Group, LLC Different Stakeholders’ Risks in DB Pension Funds ◾ 179 This results in individual or collective defined contribution (DC or CDC) funds In current practice, the financial side of... 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 8. 1 INTRODUCTION Defined