Chapter 14 insuring defined benefit plans in germany

CHAPTER 14 Insuring Defined Benefit Plans in Germany Ferdinand Mager and Christian Schmieder CONTENTS 14.1 I ntroduction 14.2 Pensions-Sicherungs-Verein VVaG in Germany 14.3 Risk Profile of the PSVaG 14.4 Risk-Adjusted Premiums Based on the U.K Model 14.5 C onclusion References 316 317 321 324 328 29 I n Ger ma ny, t he boo k r eserve s ystem i s t he co mmon m ethod o f financing occ upational pens ion p lans H ence, t he pens ion l iabilities are u nfunded b y na ture, b ut m utually a nd co mpulsory i nsured b y t he Pensions-Sicherungs-Verein VVaG (PSVaG) against bankruptcy In 2002, the PSVaG introduced reduced premiums for pension fund–based plans, which are commonly used by large German firms This reform could lead to adverse selection problems in the future The use of risk-adjusted premiums could be a means to avoid or mitigate this We use Deutsche Bundesbank’s balance sheet database to analyze the risk profile of t he portfolio of pension provision i nsured by t he PSVaG Next, we apply the risk-adjusted premium scheme of the 2005 established UK Pension Protection Fund to the PSVaG We find that the caps on the risk-adjusted premiums applied by the PPF can be a means to make use of the advantages of risk-adjusted premiums, namely, to strictly limit moral hazard and adverse selection and, at the same time, to account for the fact that substantially increased premiums could directly influence the default 315 © 2010 by Taylor and Francis Group, LLC 316 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling probability of SMEs in a negative way The outcome of a st udy by Gerke et al (2008) could be used to set the caps at an appropriate level Keywords: Unfunded pensions, pension insurance, mutual insurance association, book reserve system, adverse selection, PensionsSicherungs-Verein VVaG (PSVaG), pensions protection fund (PPF) 14.1 INTRODUCTION Occupational pension systems constitute t he second pillar of pension systems, complementing the public pension system (Pillar 1) and private pension systems (Pillar 3) Together with private pension plans, occupational pension systems have grown in their importance during recent years The plans vary widely in design and importance across countries Specific institutions that insure defined benefit pension plans are an important element to ensure the sustainability of the Pillar s ystems against bankruptcy of the sponsoring company Such institutions do, however, exist only in a few countries Sweden and Finland were the first to establish pension insurance systems i n t he e arly 1960s, followed by t he United S tates a nd G ermany i n 1974, and Japan in 1989 In the United Kingdom, the first such insurance system wa s i ntroduced i n 995 a s a co nsequence o f t he Ma xwell sc andal, in which 30,000 employees lost their pensions when the pension fund assets were pledged as collateral As a result of the severe underfunding of many pension plans and several large bankruptcies, the U.K government established the pension protection fund (PPF), which became operational in April 2005 Recently, discussions as to whether to change the premium system in order to avoid potential adverse economic effects (such as moral hazard a nd adv erse sel ection) w ere a lso co nducted i n o ther co untries (including the United States and Germany) The financial literature is almost exclusively focused on the U.S Pension Benefit Guarantee Corporation (PBGC) Since its inception, several authors have pointed out the moral hazard problems created by nonrisk-sensitive premiums and the pricing problem, which can be linked to a conditional put option (Sharpe, 1976; Treynor, 1977; Niehaus, 1990) The full conceptual complexity of t he pension i nsurance system is add ressed w ithin a n integrated framework by Boyce and Ippolito (2002), who use the stochastic pension insurance modeling system (PIMS) introduced by the PBGC in 1998 to analyze its risk profile as well as a variety of pricing plans The Pensions-Sicherungs-Verein VVaG (PSVaG) is the German counterpart to the PBGC in the United States The PSVaG currently charges flat insurance premiums In 2002, it introduced reduced premiums for pension-fund-based © 2010 by Taylor and Francis Group, LLC Insuring Defined Benefit Plans in Germany ◾ 317 plans (taking i nto account t heir lower r isk profile), wh ich a re meanwhile commonly used by large German firms, in line with international practice This reform could lead to adverse selection problems in the future In 2005, the management of the PSVaG took notice of this issue and announced the need f or (further) ad justments o f i ts p ricing s ystem The i ntroduction o f risk-adjusted premiums could be a means not only to avoid adverse selection effects, but also to take into account the potential moral hazard effects In t his chapter, we apply t he r isk-adjusted pricing scheme of t he U.K PPF to t he PSVaG, simulating a lso sc enarios of i ncreased f unding levels by l arge G erman firms to demonstrate adverse selection effects We find that the caps on the risk-adjusted premiums applied by the PPF can be a means to make use of the advantages of risk-adjusted premiums in avoiding adverse economic effects, and, at the same time, to account for the fact that substantially increased premiums could directly influence the default probability of small- a nd medium-sized companies (SMEs) i n a n egative way The outcome of a study by Gerke et al (2008), who use credit risk techniques to analyze the risk structure of the PSVaG and discuss risk-adjusted pricing schemes based on expected losses and risk contribution to worstcase loss scenarios, could be used to set the caps at an appropriate level.* This cha pter i s o rganized a s f ollows: I n Section 14.2, w e o utline t he German occupational pension insurance system Section 14.3 provides information on the risk profile of the PSVaG In Section 14.4, we apply the U.K system of risk-adjusted premiums to the PSVaG and analyze whether this system could be useful for the PSVaG Section 14.5 provides a conclusion to the text 14.2 PENSIONS-SICHERUNGS-VEREIN VVAG IN GERMANY Germany is one of the few countries where the internal funding of pension obligations via book reserves is an accepted standard.† When pensions are internally financed, t he co mpanies acc rue boo k r eserves co rresponding * The only other quantitative study on the PSVaG has been carried out by Grünbichler (1990), who exemplarily calculates risk-adjusted insurance premiums for a sample of 22 large listed corporations using a Merton-type approach (Merton, 1973, 1977) † The German system of internally financed pension plans emerged in the aftermath of the Second World War Like all other economic sectors, the banking industry was devastated and the capital market defunct External financing was hardly available In addition, the Allied forces imposed marginal tax rates of up to 0% on company profits By disclosing a l iability for f uture pension payments, taxation (as well a s wages) could be deferred a nd t he retained f unds could be used for re construction I n m any c ases, p ension pl ans were ne gotiated w ith work c ouncils i n l arge firms and established through collective agreements Thus, from today’s perspective, the internal financing of pensions can be regarded as an important component of the “Wirtschaftswunder.” © 2010 by Taylor and Francis Group, LLC 318 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling to t he present va lue of pension commitments a s l iabilities i n t heir ba lance sheets and write off the accruals from their taxable income.* Book reserves are systematically considered as a way to keep cash flows as long as possible w ithin t he firm to finance t he own original business.† Ther eby, the firms’ pension plans are integrated into the corporate financial structure The reporting of pension liabilities follows strict rules They are calculated using a uniform discount rate of 6% and standardized biometric assumptions As no separate funding is required, pension provisions in the balance sheet take the form of unsecured debt Today, the accrual of book reserves is still the most widespread method of financing occ upational pens ion p lans i n G ermany F or ma ny y ears, pensions were not protected in the event of bankruptcy unlike in the case of funded plans, where the pension fund is used to pay out what is due to the pensioners in t he event of ba nkruptcy In t he case of a boo k reserve system, only the remaining corporate assets can be used to serve pension obligations, which can, in fact, lead to a shortfall Therefore, an obligatory bankruptcy i nsurance s ystem wa s se t u p a nd i nstitutionalized t hrough the PSVaG i n 974, t he s ame y ear wh en t he P BGC wa s f ounded The creation of both i nstitutions wa s accompanied by ex tensive new legislation governing occupational pension plans Like in the United States, the setup of the system in Germany was very much influenced by the failure of a c ar manufacturer (Studebaker in the United States and Borgward in Germany) In Germany, the insurance system was a way to maintain the necessary public support for the book reserve system In 2008, the PSVaG protected pensions with a total notional value of €277 billion.‡ Unlike t he PBGC, for ex ample, t he PSVaG i s not a f ederal a gency It was established by the Confederation of German Employers’ Associations (BDA), the Federation of German Industries (BDI), and the Association of German Life Insurance Corporations The PSVaG operates as a p rivate * Income tax does not fall due until the pensions are actually paid and the book reserves are drawn down The overall very complex tax effects have been controversially discussed in the German finance literature † In principle, a company running a (Anglo Saxon type) funded pension plan could sell off the pension fund assets, use the proceeds to repay corporate debt and draw the present value of its pension l iabilities on b alance sheet Thereby, it move s to a ( German t ype) book reserve system The opposite process is also possible (Gerke et al., 2006) The book reserve system can also be interpreted as a form of funding with an extreme asset allocation It is comparable to a pension fund which only holds unsecured bonds issued by the sponsoring company ‡ From 2002 on, some Luxembourgish companies have also been covered by the PSVaG They account for less than 1% of all insurants © 2010 by Taylor and Francis Group, LLC Insuring Defined Benefit Plans in Germany ◾ 319 mutual i nsurance a ssociation w ith co mpulsory m embership f or a ll firms running pens ion p lans, wh ich m ight be adv ersely a ffected i n t he c ase o f bankruptcy.* Unlike the PBGC or the newly established PPF in the United Kingdom, the PSVaG does not meet the payments from a central fund In the case of bankruptcy, the PSVaG purchases annuities from a consortium of private life i nsurance companies covering t he present va lue of a ll pensions t hat are already paid.† Hence, the PSVaG is financed by ex post insurance premiums that cover the annual costs of the insurance plan and ensure its ongoing solvency.‡ The rates are calculated by dividing the annual costs of the previous 12 months by the amount of insured pension liabilities, which leads to volatility in premiums Currently, t he i nsurance premiums of PSVaG not reflect t he i ndividual default risk of the insured firms Therefore, the book reserve system provides l ong-term financing a t cost s i ndependent o f t he b usiness r isk There is no cap on annual premiums It is generally assumed that a catastrophic loss can be smoothed out in the long run as pension liabilities can be met on a pay-as-you-go basis (e.g., Heubeck, 1985) and that the taxpayers p rovide n o i mplicit h edge f unction F rom 1975 t o 004, t he a nnual insurance premiums ranged from 0.03% to 0.69%, averaging 0.23% of the insured l iabilities (see Figure 14.1).§ With some exceptions, most cla ims result from the bankruptcy of SMEs In t he United States, premiums constitute cha rges on a flat r ate basis ($30 per pa rticipant), wh ich had t o be r aised se veral t imes i n t he pa st Additionally, there is a variable component of $9 per $1000 of underfunded vested benefits as a risk component Although the PBGC is not funded * The insured event is bankruptcy The Employee Retirement Income Security Act of 1974 in the United States originally used a termination insurance concept † The consortium is made up of about 60 insurance companies Entitlements are not prefinanced until they are due The original idea of not prefinancing entitlements was again to keep the assets as long as possible within the companies, where they could be used more efficiently The cost of a bankruptcy case is thereby smoothed over up to 30 years The present value of entitlements to be financed in the future amounts to approximately 1% of all insured pensions Additionally, the PSVaG operates an equalization fund with a target funding level of the moving year average cost of annual pension insurance It is drawn on in years with high pension insurance costs ‡ At the beginning of e ach year a rou gh estimate based on re cent experience is made and an initial premium is charged in advance § The p ension i nsurance s ystem w as not a ffected by t he G erman re unification in 990 Occupational pension schemes did not exist in Eastern Germany and are even today by far less common Direct pension promises were vested and insured only after 10 years In fact, we could identify only about 30 firms from Eastern Germany with pension provision above €100,000 © 2010 by Taylor and Francis Group, LLC 320 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling Premium in percent of liabilities 0.80% Mean : 0.23% Median : 0.21% Std dev : 0.14% 0.70% 0.60% 0.50% 0.40% 0.30% 0.20% 0.10% 03 20 05 20 07 01 20 99 20 97 19 95 19 93 19 91 19 89 19 87 19 85 19 83 19 81 19 79 19 77 19 19 19 75 0.00% Year FIGURE 14.1 The PSV aG’s a nnual i nsurance p remiums ( From P ensionsVersicherungs-Verein VVaG (2008), Annual report 2008.) by tax revenues, it is a f ederal agency, a nd t hereby a co ntingent l iability of the government and the taxpayers In the United Kingdom, 80% of the premiums are risk-adjusted based on the firms’ default probabilities and the funding status of the pension plan (see Section 14.4) Recently, the German legislation governing occupational pension plans and private pension contracts was reformed comprehensively, ma inly to reduce dependency on the public pay-as-you-go pension system, which is being increasingly strained by an aging population The German capital market is well developed and the funding of pension plans constitutes an international st andard The o riginal i dea f or b uilding u p boo k r eserves by i nvesting t he necessary a ssets i n t he own firm may become obsolete in the future Many large firms that can afford to so are funding their pension l iabilities a nd c anceling t hem i n t heir ba lance sh eets acco rding t o U S-GAAP o r I nternational A ccounting S tandards/International Financial Reporting Standards (IAS/IFRS),* namely, by establishing contractual trust agreements (CTAs).† In 2002, pension funds were introduced as an alternative way to finance pension obligations, taking into account the changes in the occupational pension systems in Germany If properly funded, boo k r eserves c an be o utsourced t o pens ion f unds n ontaxably * In part the funding is motivated by change in international rating methodologies See Gerke et al (2006) † The most prominent example is the Siemens Pension Trust, with assets in excess of €10 billion In the case of C TAs, the pension liabilities still appear on t he pension sheet under German accounting rules © 2010 by Taylor and Francis Group, LLC Insuring Defined Benefit Plans in Germany ◾ 321 Pension f unds a re a lso co vered b y t he PSV aG, b ut t he p remiums a re reduced to one-fift h of those of (unfunded) pension provisions due to the vastly different exposure of the PSVaG Within the changing institutional environment, adverse selection effects can be ex pected, as firms that can afford funding will tend to so, leaving the remaining group of insurants to deteriorate in quality By consequence, in May 2005, the management board of the PSVaG declared that the financing system needed to be changed The proposed reforms i nclude t he i mmediate p refinancing o f a ll en titlements i n t he case o f ba nkruptcy, a n en forced p refi nancing o f e xisting en titlements and an additional mechanism to smooth annual premiums In the future, the reformed system could be the basis for risk-adjusted premiums The management board has justified its proposed reforms by pointing to the risk of declining premium contributions and to the fact that funding of pensions is now widely accepted in Germany (PSVaG, 2005; Gerke and Heubeck, 2002) 14.3 RISK PROFILE OF THE PSVAG What se ts t he PSVaG a part f rom o ther financial i nstitutions is t hat i ts insurance portfolio can be o bserved “ from t he outside.” T he pension liabilities a ppear a s pens ion p rovisions o n t he l iability s ide o f i nsured firms’ balance sheets Given t he defa ult r isk o f t he i nsured firms, they can—in credit risk terms—be modeled as unsecured loans In fact, the PSVaG does not follow a rigorous work-out process and the recovery rate is typically below 5% In order to analyze and simulate the PSVaG’s credit risk profile, we use the balance sheet database of Deutsche Bundesbank and include all firms with pension provisions into our analysis.* In the next step, this “raw” data set has been edited in order to best match the PSVaG portfolio, namely, by using historical insurance losses, the annual total volume of insured pensions, and the size and default information structure of the PSVaG portfolio Below, w e b riefly o utline t he u nderlying m ethod f or m easuring t he credit portfolio risk of the PSVaG * Our initial sample directly represented about 70% of all book reserves insured by the PSVaG We excluded companies with book reserves of less than €100,000 from the analysis as they represent le ss t han h alf a p ercent of t he tot al e xposure of t he P SVaG For c omprehensive details see Gerke et al (2008) © 2010 by Taylor and Francis Group, LLC 322 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling In t he f irst step , w e de termine t he a nnual p robability b y defa ult* (PD) o f e ach PSVaG co unterpart ba sed o n a b inary l ogit m odel.† We assume that the recovery rate is 5%, i.e., a loss given default (LGD) of 95% Second, we use a Merton-type one-factor model (which is also underlying the Basel II framework) to arrive at an ex ante forecast of the portfolio loss probability distribution f unction (loss PDF) as a means to monitor the inherent risk of a credit portfolio.‡ We thereby calculate the expected loss (EL) and unexpected loss (UL) for the PSVaG portfolio The EL denotes the average portfolio loss to be expected ex ante, while the U L i s u sually def ined a s t he d ifference be tween a spec ific h igh quantile value of the Loss PDF and the EL and thereby reflects worstcase loss levels In this study, we use the Value-at-Risk (VaR) and the expected shortfall (ES) as suggested by Artzner et al (1999) as quantile values of the Loss PDF We refer to confidence levels similar to those used in the banking and insurance industry and to a t ime horizon of one year In o rder t o de termine t he po rtfolio’s U L, w e per form M onte C arlo simulations with 100,000 runs Figure 14.2 shows the Loss PDF for the PSVaG with all portfolio losses above 3% treated as a “tail” cluster (i.e., as a group of worst-case losses) The Loss PDF is highly skewed to the right, what indicates that there is a h igh probability of low losses around t he EL and a low, yet nonnegligible probability of very high losses (worstcase tail risk) * In the case of the PSVaG, default is defi ned as bankruptcy † We use six regression variables: four fi nancial ratios and two sector dummies to distinguish the default industry, industrials from the trade sector and the remaining industry sectors We also included year dummies in order to c ontrol for m acroeconomic effects, For t he default data subsample, we use balance sheet data with a time gap of 12–24 months prior to default Due to m issing bankruptcy data equitation we appl y a we ighted logit procedure to c orrect the bias toward underreporting bankruptcies For a comprehensive description see Gerke et al (2008) ‡ The c redit r isk d efault pro cess i s mo deled b ased on a s tylized Me rton-type a sset v alue model (Merton, 1974) with one common systematic risk factor and the remaining disturbance being idiosyncratic We assume that each fi rm’s creditworthiness is represented by its asset value, which fluctuates over time and reflects the actual state of the fi rm’s creditworthiness We control for asset values falling below a certain barrier (usually the liabilities of a fi rm) during a year time horizon, what implicates a default event The asset values of larger firms tend to h ave a h igher correlation with the systematic factor, i.e., implying that they are more strongly influenced by macroeconomic developments We refer to three discrete si ze g roups to c apture c orrelation e ffects For a c omprehensive d escription s ee Gerke et al (2008) © 2010 by Taylor and Francis Group, LLC Insuring Defined Benefit Plans in Germany ◾ 323 9000 50 75 90 95 Mean : 0.39% Median : 0.098% Std Dev : 0.87% 8000 7000 Frequency 6000 5000 4000 3000 2000 1000 8% 6% 4% 0% 2% 2 8% 6% 4% 0% 2% 1 8% 6% 4% 2% 0 0% Portfolio loss (in %) Loss p robability d istribution f unction f or t he PSVaG p ortfolio The vertical lines indicate the x% quantiles of the PSVaG losses The line with the label “50”, for example, refers to the median loss FIGURE 14.2 The E L (0.39%) i s lower t han i n a n average c redit portfolio of a ba nk, despite the low recovery rate.* The reason for that is that large firms typically exhibit (very) low default probabilities paired with (very) high exposures, as the PSVaG does not set an upper limit to individual exposures At a confidence level of 99.9%, the VaR of the PSVaG portfolio is about 9% of the insured portfolio exposure and the ES is 11.5% Hence, the VaR (and the ES) exceeds the EL (0.39%) by more than 20 times (in the case of the ES almost 30 t imes), indicating that the PSVaG faces the risk of very high losses in case of accumulation in an unfavorable year This outcome shows that the occurrence of a worst-case loss event might even question the existence of the PSVaG, also as such a l oss event would be more than 10 times higher than the highest historical losses incurred during the last 30 years.† Although w orst-case l osses ma y t herefore a ppear ex traordinarily high, a comparison with the historical premiums underpins the robustness of the calculated loss PDF Over the past 30 years, the historical premiums ranged from around the 15% loss quantile (0.03%) to the 87% * Moody’s (2001, p 6), for example, underlies average net loan provisions of 0.77% for German banks du ring t he p eriod 1989–1999 w hich i s more t han t wo t imes t he ave rage lo ss of t he PSVaG during the same period † For a comprehensive analysis, see Gerke et al (2008) © 2010 by Taylor and Francis Group, LLC 324 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling loss quantile (0.69%) of the loss distribution Had AEG’s looming bankruptcy not been averted by an out-of-court settlement in 1982, the corresponding loss of more than 2% would have exceeded the 95% quantile However, when i nterpreting t his outcome of a y ear loss scenario, it has to be taken into account that pension insurers have a higher degree of flexibility than deposit insurers, for example In the case of the occurrence of an insured event (i.e., bankruptcy), it is not the full pension liability that falls due, but merely monthly pension payments Hence, the PSVaG does, in principle, have the policy option to stop buying annuities and to switch to a pay-as-you-go system A worst-case loss event (as it could occur in the course of the current economic crisis) could thereby be smoothed out over decades Alternatively, the PSVaG could prefinance extreme losses up to a certain confidence level by building up a reserve fund The target funding level could be t he difference of the VaR of the 99.0% and the 99.9% confidence level, for ex ample Accordingly, t he corresponding loss could be added to the annual premium over a reasonable lengthy time period An additional ex ante policy option would be reinsurance The PSVaG could, for example, issue a catastrophic bond, where the principal is lost for the investors in case the loss of the PSVaG exceeds a certain predefined level 14.4 RISK-ADJUSTED PREMIUMS BASED ON THE U.K MODEL The PSVaG’s current uniform pricing faces two issues: first, the plan crosssubsidizes firms and thereby distorts a fair competition (moral hazard problem), a s po inted o ut b y t he M onopolkommission (2004) S econd, u niform premiums can lead to adverse selection problems due to the existence of the alternative treatment for funded plans, particularly for large, cash-rich firms The m ost r ecent ex ample o f h ow r isk-adjusted p remiums c an be implemented i s t he U K P PF.* T he 009/10 pens ion p rotection l evy decomposes i nto a sch eme-based l evy ( 20% o f t he t otal) a nd a r iskbased levy (80% of the total) The risk-based levy is calculated by multiplying the underfunding (risk) of a pension scheme by the short-term default risk of the sponsoring firm The PPF groups the plan sponsors into 100 different risk bands and assigns default probabilities to each of t he ba nds T he r isk-based p remium i s add itionally sub ject t o t wo caps First, there is an upper bound for default probabilities set at 15% Second, t he ma ximum r isk-based levy is c apped at t he level of 1% of * A c omprehensive d escription c an b e fou nd on t he home page of t he P PF ( www pensionprotectionfund.org.uk) © 2010 by Taylor and Francis Group, LLC Insuring Defined Benefit Plans in Germany ◾ 325 the l iabilities S caling ensu res t he f ixed p roportion o f sch eme-based to risk-based levy and the redistribution of capped risk-based levies to uncapped schemes The total amount is scaled up or down to the levy set by the board of the PPF In the next step, we apply the insurance pricing scheme of the PPF to the po rtfolio st ructure o f t he PSVaG a nd co mpare t he r esults w ith t he current nonrisk-adjusted, uniform PSVaG pricing scheme.* To so, we map the PSVaG portfolio exposure into the 100 risk bands used by the PPF and assume that pension liabilities are unsecured (i.e unfunded), subordinated debt.† O ur r isk a nalysis s be en done ba sed on ten subg roups, clustering ten risk bands each (1–10, 11–20, etc.) Table 14.1 shows the distribution of the PSVaG pension plans according t o t he default probabilities (or fa ilure scores u sed by t he PPF) of TABLE 14.1 PSVaG: Distribution of Risk-Adjusted Premiums vs Uniform Premiums (i.e., Liabilities) Failure Scores Probability of Default 100–91 90–81 80–71 70–61 60–51 50–41 40–31 30–21 20–11 10–1 0.01%–0.13% 0.15%–0.28% 0.30%–0.43% 0.44%–0.63% 0.65%–0.94% 0.98%–1.38% 1.47%–2.02% 2.09%–2.57% 2.69%–4.11% 4.495%–29.26% Number of Plans (in %) 18.72 13.31 10.48 10.34 12.12 11.61 8.23 4.72 5.96 4.54 100 Liabilities (in %) 29.31 33.44 11.46 6.37 7.74 6.92 2.16 1.03 0.68 0.89 100 RiskBased Levy Only (in %) RiskBased Levy, Capped (in %) 5.43 14.96 8.48 7.32 13.43 17.95 7.81 5.13 4.94 14.54 100 7.25 19.96 11.31 9.77 17.92 20.00 6.27 2.98 1.96 2.58 100 RiskBased and Scheme Levy, Capped (in %) 11.66 22.65 11.34 9.09 15.88 17.38 5.45 2.59 1.71 2.24 100 Source: O wn calculation * One ge neral d ifference b etween t he P SVaG i nsurance pre mium a nd c redit pr icing i s t hat the for mer i s d etermined e x p ost, w hen t he lo sses h ave o ccurred, w hereas r isk-adjusted credit pricing is based on ex ante expectations of potential losses Nevertheless, as the PSVaG membership i s c ompulsory a nd of a lon g-term n ature, one c ould a lso i magine a n e x p ost allocation of lo sses i n a r isk-adjusted w ay to t he PSVaG members i n order to avoid c rosssubsidization a nd potential adverse economic effects resulting f rom t hat The PPF sets t he annual levy to meet the expected costs of the scheme in the long term † http://www.pensionprotectionfund.org.uk/0910_determination_appendix_3.pdf © 2010 by Taylor and Francis Group, LLC 326 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling their sponsors, t he portion of plans fa lling into t he respective cluster (column ), t he po rtion o f pens ion l iabilities per cl uster ( column , which represents uniform premiums), and three different risk-adjusted premiums (columns 5–7) About half of all firms insured by the PSVaG have a failure score of 60 or higher (and a default probability of less than 1%) which is usually referred to as investment grade They represent about 80% of the total exposure of the PSVaG Under the current uniform insurance pricing scheme this exposure is proportional to the annual premiums The 10% of the firms with the lowest failure score (and a default probability of 4.5% and higher) account only for 1.6% of the total exposure or annual premiums, respectively Under a fully risk-based pricing scheme, the distribution of premiums would alter considerably (column 5): For the group of firms with the best rating (failure score 100–91), the premium would decrease by about 80% on a weighted average basis, whereas it would increase by about 15 times for the group with the lowest rating (failure score 10–1) For about 10% of the plan sponsors (failures scores 70–61) representing about 6% of the exposure, the premium would remain about the same When applying the caps (and redistribution of the capped premiums) the change in the premium structure is less pronounced (column 6) The fixed 20% proportion of scheme-based levies further decreases the dispersion of premiums compared to uniform pricing (column 7) For the group with the lowest rating the premiums would increase by about 150% and for the group with the highest rating there would be a decrease by about 60% The long-run existence of the PSVaG as a mutual insurance organization crucially depends on how it is accepted by its members It is estimated that about half of the pension provisions in Germany of the DAX30 corporations have been funded by assets over the last years (Rhiel and Stieglitz, 2007) Risk-adjusted premiums, taking into account the probability of default and the funding status of the insurants, are one way to mitigate adverse selection effects and are consistent with generally higher risk awareness among financial institutions (moral hazard problem) For t he following analysis we assume for simplicity reasons t hat t he DAX30 corporations f und t heir insured pension liabilities by 50% a nd 100%, r espectively, a nd t hat t his l eads t o a p roportional r eduction o f their i nsurance premiums Table 14.2 shows t he relative cha nge i n t he distribution of premiums across the different risk bands compared with uniform pricing © 2010 by Taylor and Francis Group, LLC Insuring Defined Benefit Plans in Germany ◾ 327 TABLE 14.2 Change in the Distribution of Levies across the Risk Banks Failure Scores 100–91 90–81 80–71 70–61 60–51 50–41 40–31 30–21 20–11 10–1 Risk-Based Levy Only (in %) Risk- and Scheme-Levy, Capped (in %) 50% Funding −85 −65 −27 +16 +75 +131 +297 +510 +792 +1895 −64 −42 +4 +54 +121 +141 +192 +227 +227 +227 Risk-Based Levy Only (in %) Risk- and Scheme-Levy, Capped (in %) 100% Funding −90 −80 −28 +18 +77 +85 +353 +683 +1046 +2463 −71 −63 +15 +76 +150 +122 +267 +369 +369 +369 Source: O wn calculation As shown in Table 14.2, in t he case of no caps a nd 50% f unding (riskbased l evy o nly), t he r elative co ntribution o f t he l owest-ranked g roup o f plan sponsors (10–1) increases by almost 19 times (compared to 15 times in the case where large firms not fund, see Table 14.1), whereas the relative contribution of t he h ighest-ranked g roup decl ines by 85% (column 2) I n case of full funding, the increase for the lowest-ranked group goes further up to 24.6 times (column 4) In the case of a scheme-based levy with caps, the change remains substantially less pronounced, with an increase for the lowest-rated group by 227% (50% funding) and 369% (100% funding) At first g lance, i t a ppears t hat la rge firms w ith a l ow p robability o f default seem to have cross-subsidized the majority of small- and mediumsized firms d uring dec ades, l eading t o r elatively l ow a verage p remiums charged by the PSVaG However, the concentration of risk with very large insurants comes at the expense of a high VaR, i.e., very high losses would occur if one or more of the very large insurants default at the same time, a fac t wh ich m ight ve be en f orgotten a s n o ma jor l oss occ urred o ver decades.* Hence, there were also the large industrial firms, with pension provisions that constitute up to a quarter of the balance sheet total, which made use of the book-reserve system and relied on the public support for this specific financing system * The looming insolvency of AEG in 1982 was averted but nevertheless let to the highest cost of the insurance scheme in the history of the PSVaG © 2010 by Taylor and Francis Group, LLC 328 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling It is questionable whether a partial “opting out” as allowed under the 2002 revised PSVaG pricing scheme (via a reduction of the premiums for funded pension plans by 80%), namely, by asset funding over a short period of time, represents the costs of the insurance over its life cycle in a fair manner In fact, risk-adjusted pricing systems seem to be a fa ir alternative The key question becomes how they should be shaped The caps on full-fledged risk-based premiums as applied by the PPF accounts for the fact that very high i nsurance p remiums co uld d rive firms with weaker ratings, i.e., typically SMEs, towards bankruptcy, which is an effect that is to be avoided from a socioeconomic perspective The question t hus becomes how t he premium cap should be se t The outcome of t he st udy by Gerke et a l (2008), who d iscuss r isk-adjusted pricing schemes for the PSVaG based on expected losses and risk contribution to high portfolio loss scenarios, respectively, could be used to set the c aps at a j ustifiable level for G ermany a nd would t hereby ma ke u se of t he relatively st raightforward pricing method of t he PPF built on t he grounds of sophisticated risk analysis.* One could focus the decision on the increase of risk premiums to be paid by SMEs, for example, which have been found by Gerke et al (2008) to increase by about +46% in the case of a risk contribution to high portfolio losses pricing scheme as compared to +195% in the case of an expected-loss-based pricing scheme In addition, the experience gained in studies on the PBGC (Boyce and Ippolito, 2002) can be taken into account Further, it should be questioned whether a pricing system which relies on annual funding measures captures the risk of a sharply declining funding status right before insolvency 14.5 CONCLUSION We a nalyze t he po rtfolio r isk st ructure o f t he PSVaG w ith a ben chmark data set of Deutsche Bundesbank We estimate the portfolio loss distribution function of the PSVaG The loss distribution is highly skewed with an expected loss that is lower than that in an average credit portfolio of a bank, due to the low risk profile of large firms with very high insured exposures However, r esulting f rom t he r isk co ncentration o f t he la tter, t he PSVaG portfolio faces a substantial tail risk, i.e., implying that there is a small, but nonnegligible probability of portfolio losses which are by 20 times and more in excess of the historical levels However, in a worst-case loss scenario, the * The only other quantitative study on the PSVaG has been carried out by Grünbichler (1990), who exemplarily calculates risk-adjusted insurance premiums for a sample of 22 large listed corporations using a Merton-type approach (Merton, 1973, 1977) © 2010 by Taylor and Francis Group, LLC Insuring Defined Benefit Plans in Germany ◾ 329 PSVaG does, in principle, and unlike banks, have the policy option to switch to a pay-as-you-go system At least (moderate) cases of worst-case loss events could thereby be smoothed out over decades During r ecent y ears, t he ma nagement boa rd o f t he PSVaG ex pressed the need to change the financing system The management board justifies the need for reform with the risk of a declining insurance volume and the fac t t hat n owadays t he f unding o f pens ions i s w idely acc epted The reformed system could be the basis for risk-adjusted premiums, which can serve two main purposes: first, to avoid moral hazard effects and second to avoid adverse selection problems faced by the PSVaG due to the alternative pricing scheme for funded pensions introduced in 2002 To analyze the effect of risk-based premiums, we apply the levy schedule of U.K.’s PPF to the portfolio structure of the PSVaG Under an expected loss pricing scheme, the levies would vary extremely But in fact, the caps as applied by the PPF (essentially also a limitation of the maximum annual risk-adjusted premium t o 1% of t he pens ion l iabilities) g reatly l imit t he dispersion of levies A simulation of the additional effect of adverse selection faced by the PSVaG via pension funding reveals that its magnitude is on a level for the issue to be carefully taken into account in the future The findings of Gerke et al (2008) could be used to set the level of the premium cap at an adequate level, taking into account the socioeconomic effects, na mely, t he r isk t hat subst antially h igher p remiums co uld l ead to an increased number of bankruptcies of SMEs directly resulting from PSVaG insurance.* Given that the German public pay-as-you-go pensions system is increasingly strained, this is in contrast to the political interest in favor of an expansion of occupational pensions In order to set the premium cap, one might a lso benchmark the riskbased premiums used by deposit insurance systems In Germany, the private banks and cooperative banks use risk-based pricing systems since 1998 and 2004, respectively The maximum premiums are limited to 2.5 times and 1.5 times, respectively, of those banks in the lowest risk bracket REFERENCES Artzner, P., F Delbaen, J.-M Eber, and D Heath, 1999, Coherent measures of risk, Mathematical Finance, 9(3): 203–228 Boyce, S and R A Ippolito, 2002, The cost of pension insurance, Journal of Risk and Insurance, 69: 121–170 * In f act, we id entified s everal c ases of sm all c orporations i n ou r s ample were r isk-adjusted premiums would exceed their equity © 2010 by Taylor and Francis Group, LLC 330 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling Gerke, W a nd K H eubeck, 2002, G utachten zur k ünftigen Funktionsfähigkeit durch den Pensions-Sicherungs-Verein VVaG, Betriebliche Altersvorsorge, 57: S433–S491 Gerke, W., F Mager, a nd A Rö hrs, 2006, P ension f unding, in solvency r isk and the rating of corporations, Schmalenbach Business Review, Special issue 2: 35–63 Gerke, W., F Mager, T Reinschmidt, and C Schmieder, 2008, Empirical risk analysis of pension insurance: The case of Germany, The Journal of Risk and Insurance, 75(3): 763–784 Grünbichler, A., 1990, Zur Ermittlung risikoangepaßter Versicherungsprämie für die betriebliche Altersvorsorge, Zeitschrift für Betriebswirtschaft, 60: 319–341 Heubeck, G., 1985, Fina nzierungsverfahren der I nsolvenzsicherung und ihr e Auswirkung im Z eitablauf, in Pensions-Sicherungs-Verein (ed ): 10 J ahre Insolvenzsicherung der b etrieblichen Al tersvorsorge in D eutschland, Cologne, Germany, pp 56–72 Merton, R C., 1973, Theory of rational option pricing, Bell Journal of Economics and Management Science, 4: 141–183 Merton, R C., 1974, On the pricing of corporate debt: The risk structure of interest rates, Journal of Finance, 29: 449–470 Merton, R C., 1977, An analytical derivation of the cost of deposit insurance and loan guarantees, Journal of Banking and Finance, 1: 3–11 Monopolkommission, 2004, W ettbewerbspolitik im S chatten na tionaler Champions, Baden-Baden Moody’s Investor Services, 2001, M oody’s RiskCalc ™ for private companies: The German model, Rating Methodology, May 2001 Niehaus, G R., 1990, The PBGC’s flat free schedule, moral hazard, and promised benefits, Journal of Banking and Finance, 14: 55–68 Pensions-Sicherungs-Verein VVaG (PSVaG), 2005, PSVaG sieht die Notwendigkeit, das Fina nzierungsverfahren a uf v ollständige K apitaldeckung umzust ellen, press release of May 17, 2005, www.psvag.de Pensions-Sicherungs-Verein VVaG (PSVaG), 2008, Annual report 2008 Rhiel, R a nd S tieglitz, R , 2007, P raxis der Rec hnungslegung f ür P ensionsver pflichtungen nach IAS 19 und FAS 87, Der Betrieb, 60: 1653–1657 Sharpe, W F , 1976, C orporate p ension f unding p olicy, Journal of F inancial Economics, 3: 183–193 Treynor, J L., 1977, The principles of corporate pension finance, Journal of Finance, 32: 627–638 © 2010 by Taylor and Francis Group, LLC ... Group, LLC Insuring Defined Benefit Plans in Germany ◾ 317 plans (taking i nto account t heir lower r isk profile), wh ich a re meanwhile commonly used by large German firms, in line with international... of all insurants © 2010 by Taylor and Francis Group, LLC Insuring Defined Benefit Plans in Germany ◾ 319 mutual i nsurance a ssociation w ith co mpulsory m embership f or a ll firms running pens... billion In the case of C TAs, the pension liabilities still appear on t he pension sheet under German accounting rules © 2010 by Taylor and Francis Group, LLC Insuring Defined Benefit Plans in Germany