Chapter 3 performance and risk measurement for pension funds

CHAPTER Performance and Risk Measurement for Pension Funds Auke Plantinga CONTENTS 3.1 I ntroduction 3.2 Liability-Driven Investing and Pension Liabilities 3.3 Liability-Driven Risk and Performance Attribution 3.3.1 P erformance Measure 3.3.2 R isk Measures 3.3.3 B enchmark 3.3.4 P erformance Attribution 3.4 An Application of the Model 3.5 Conclusion and Discussion References 72 72 76 76 76 77 78 80 83 T his ch a pter p r opos es a n a ttribution m odel f or m onitoring t he performance and risk of a defined benefit pension fund In order to facilitate easy interpretation of the results, the return is expressed as a percentage of the value of the liabilities The model is based on a liability benchmark t hat re flects t he r isk a nd return cha racteristics of l iabilities As a r esult, t he a ttribution m odel f ocuses t he a ttention o f t he po rtfolio managers on creating a portfolio that replicates liabilities The attribution model allocates differences in return between the actual and benchmark portfolio to decisions relative to the benchmark portfolio In addition, the model decomposes risks according to the same structure by using a measure of downside risk 71 © 2010 by Taylor and Francis Group, LLC 72 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling 3.1 INTRODUCTION Pension funds around the world suffered dramatically from falling stock markets in the period 1999–2003 as well as during the current 2008–2009 financial crisis Many pension funds have become underfunded, and face funding ratios well below 100% In both periods, stock markets performed badly a nd i nterest r ates d ropped considerably These a re conditions t hat have a ser ious impact on pension f und ba lance sheets, by decreasing t he market value of the assets and increasing the market or fair value of the liabilities Ryan and Fabozzi (2002) provide evidence of the existence of large mismatches between assets and liabilities in the 200 largest U.S definedbenefit plans prior to the first pension crisis For example, in 1995 the assets of these 200 pension funds yielded an average positive return of 28.70%, which was insufficient to match with the liability return of 41.16% Liability-driven in vesting i s a n in vestment p hilosophy t hat im plies managing a ssets r elative t o l iabilities.* W ith l iability-driven i nvesting, pension f unds c an reduce t heir ex posure to financial crises by reducing the mismatches between assets and liabilities In order to encourage pension funds to adopt liability-driven investment strategies, i t i s n ecessary t o r edesign per formance a nd r isk m easurement systems The best way to accomplish this is by adopting a so-called liabilitydriven benchmark for performance and risk management In this study, we discuss a performance and risk measurement system that f ocuses o n l iability-driven i nvesting W ithout a ppropriate per formance and risk measurement, liability-driven investing will be difficult to manage as portfolio managers will be tempted to focus on traditional asset-only benchmarks We propose a number of new elements in measuring per formance a nd r isk for pension f unds The first new element is by measuring the performance of a pension fund relative to the value of the liabilities in order to focus on the societal objective of a pens ion fund as the provider of reliable pensions The second new element is that we propose to use a decomposition of downside risk consistent with the decomposition of performance 3.2 LIABILITY-DRIVEN INVESTING AND PENSION LIABILITIES Liability-driven investing is a strategy aimed at reducing a pension plan’s risks by choosing assets that serve as a hedge for the risks implicit in the liabilities This i s o nly pos sible f or a l imited se t o f r isk fac tors t hat a re * See, for example, Leibowitz (1986), Siegel and Waring (2004), and Waring (2004) © 2010 by Taylor and Francis Group, LLC Performance and Risk Measurement for Pension Funds ◾ 73 present bo th i n t he a sset po rtfolio a nd t he l iability po rtfolio The most important of these risks are the interest rate risk and the inflation risk.* Some other risks in the liability portfolio are difficult to hedge with traditional a sset cla sses, such a s t he mortality r isk or t he operational r isk Those types of risks can be reduced by, for example, reinsurance, or simply by creating an a dditional s olvency buffer f or u nexpected l osses I n t his study, we implement liability-driven investing using cash flow matching Cash flow matching is a robust strategy for dealing with any type of term structure movement Practical considerations may result in choosing for a less robust solution, such as duration matching Pension claims in a defined-benefit plan are largely determined by the wages earned by the beneficiaries and the number of years of employment With a final pay system, the pension claims are based on the wage earned in the last year However, it is also common to have claims as a function of past wages earned, such a s t he average wage earned during t he years of em ployment A co rrect va luation o f t he l iabilities i s c rucial i n ma naging pens ion f unds The va lue o f l iabilities ser ves a s a ben chmark f or the level of assets needed to ser vice the future cash flows of the pension fund The valuation starts with an appropriate estimate of the future cash flows resulting from the current promises made to beneficiaries Next, the present value of these cash flows is calculated using a d iscount rate This discount rate is a c rucial element i n t he l iability-driven benchmark We propose to use the risk-free rate on government bonds as the discount rate In combination with a matching strategy and sufficient assets, this means that the liabilities will be met with certainty.† From the perspective of the beneficiary, a va luation ba sed on t he r isk-free government bond r ates is the preferred alternative since it provides the opportunity to create riskless pension claims It is important to see that the resulting value is not the market value of the liabilities, but the value of a risk-free cash flow desired by the beneficiaries If the present value of the liabilities based on government bond r ates exceeds t he va lue of t he a ssets, it i s clear t hat t he t rue market value of the liabilities is less, unless the sponsor provides a credible guarantee to make up for any deficits The return on the cash flow matching strategy is the minimum acceptable return (MAR) to be achieved on the assets (see Sortino et al., 1999) If the assets not yield this return, the future pension benefits cannot be * Another factor is currency risk, which we ignore in this chapter by assuming that the pension fund has single currency pension liabilities † The conditions for creating an immunized portfolio are specified by Redington (1952) © 2010 by Taylor and Francis Group, LLC 74 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling realized without further sponsor contributions The actual realization of reliable pensions depends on the investment strategy In order to keep the focus of portfolio managers on the objective of the pension beneficiaries, the cash flow matching strategy, which gives the best chance of realizing the objective, has to be embedded in the asset benchmark Elton and Gruber (1992) provide a t heoretical justification for the use of matching strategies in the context of a mean–variance framework For a pension fund with assets A and present value of liabilities L, the return on surplus is rs = St +1 A(1 + ) − L(1 + rl ) −1 = −1 St A−L (3.1) The r iskless st rategy, F, is to invest an amount, L, i n a po rtfolio of c ash flow–matched a ssets, a nd t o i nvest t he r emainder i n t reasury b ills The return of this strategy is rF = ( A − L)(1 + rf ) + (L − L)(1 + rl ) − = rf A−L (3.2) Similarly, the return on a risky strategy R is rR = A(1 + rR ) − L(1 + rl ) L − = rR + (rR − rl ) A−L S (3.3) Any co mbination o f t hese t wo po rtfolios r esults i n a po rtfolio o n a straight l ine connecting F and R i n t he mean st andard de viation space, similar to the capital market line in the CAPM However, the underlying portfolios are different and depend on the leverage and liability returns Consequently, different investors have opportunity sets The actual choice for an asset portfolio depends on the risk aversion of the pension fund Pension funds have a multitude of participants that also have different interests Therefore, t he q uestion h ow t o ch oose a l evel o f r isk a version for the pension fund that is representative for all participants is not easy and perhaps even impossible to answer In many of the surplus optimization models, the surplus is owned by the plan sponsor, and the criterion for choosing an asset portfolio is to maximize the utility of the surplus.* As stated by Erza (1991): “A defined benefit pension plan is effectively an operating d ivision o f t he spo nsor.” W ith pens ion f unds bei ng o perating divisions of sponsors, conflicts of interest with the beneficiaries may arise * See, for example, Elton and Gruber (1992), Erza (1991), or Sharpe and Tint (1992) © 2010 by Taylor and Francis Group, LLC Performance and Risk Measurement for Pension Funds ◾ 75 Beneficiaries have a d ifferent perception o f r isk From a ben eficiary’s point of view, any asset portfolio is risk-free as long as the pension fund allocates an amount Al ≥ L to a cash flow–matched portfolio In addition, the st rategy for t he su rplus a ssets As should return above t he t hreshold level −As/S If returns on the surplus asset are below the threshold value, the surplus assets become negative and this decreases the value of liabilitydriven in vestments B eneficiaries ve o nly l imited i nterest i n r eturns above that required to service liabilities, since they usually not share in the surplus returns The different perspec tives on r isk by t he sponsor a nd t he beneficiaries motivate a d istinction be tween su rplus a ssets a nd l iability-driven a ssets As long as the sponsor is willing to choose an asset portfolio that is risk-free from t he perspec tive of t he beneficiaries, t he potential conflict of i nterest is not relevant By separating the assets in two portfolios, one dedicated to liability-driven investments and one to surplus-driven investments, the participants can easily monitor the value of the portfolio dedicated to service their claims Participants or their representatives should be able to observe whether large differences exist between the value of liabilities and liabilitydriven a sset portfolios If la rge d ifferences ex ist, t his is a sign t hat t he fund has potentially a la rge exposure to risk In combination w ith a r iskmonitoring system, this safeguards the continuity of the pension fund In constructing a liability-driven investment portfolio, it is important to make a distinction between nominal and real liabilities The liabilities of pension funds can be nominal, real, or a mixture of nominal and real Nominal liabilities are promises to pay future cash flows expressed in nominal terms Real liabilities are promises to pay future cash flows with a fixed purchasing power Each type of liability should be matched with the appropriate type of asset Nominal liabilities can be matched with nominal government bonds and real liabilities can be matched with inflation-linked bonds such as TIPS Since each type of liability requires a different type of instrument, it is convenient to create separate asset portfolios for each type of liability We use cash flow matching as the strategy to construct the benchmark In practice, duration matching and other factor immunization strategies are f requently u sed a s a n a lternative f or r easons o f flexibility Duration matching opens t he possibility to create a ma tched portfolio even i f t he sum of the maturities of the liability cash flows exceed the largest available asset maturity However, matching based on duration may not shield against c ertain n onparallel s hifts o f t he ter m st ructure Ther efore, we believe t hat i n co nstructing t he ben chmark, c ash flow matching is the best alternative as it provides the best track of the value of the liabilities © 2010 by Taylor and Francis Group, LLC 76 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling Duration matching can be used to create the actual asset portfolio As a result, de viations be tween t he r eturn of t he duration a nd t he c ash flow matching strategy are measured in the performance attribution model 3.3 LIABILITY-DRIVEN RISK AND PERFORMANCE ATTRIBUTION In developing benchmarks and a performance attribution model, we value the assets based on their market values, and the liabilities as the present value of the expected cash flows using the nominal- and real-term structures of interest rates This results in the following stylized balance sheet: Assets Surplus assets Nominal assets Real assets Liabilities As Anl Arl Surplus Nominal liabilities Real liabilities S Ln Lr Managing the performance and risk of pension fund assets relative to its liabilities s i mplications f or t he per formance a nd r isk m easures, t he benchmark and the attribution model 3.3.1 Performance Measure The performance measure should be chosen consistent with the objective of the pension fund in mind The main objective of a pens ion fund is to provide ben efits to its members This suggests that we should focus on measuring the performance from the perspective of the liabilities We propose to measure the performance by scaling the changes in surplus by the liability value as opposed to scaling by assets or scaling by surplus From a mathematical point of view, scaling is irrelevant for the decomposition However, the major advantage of scaling by liability value is that losses are expressed in terms of liability value, so beneficiaries can directly relate to the magnitude of losses A l oss of 10% for an underfunded pension plan implies that, roughly speaking, a beneficiary is likely to receive 10% less in pension payments.* This measure of pension fund performance is closely related to the funding ratio return proposed by Leibowitz et al (1994) 3.3.2 Risk Measures Since the sponsor and the beneficiaries have different perspectives on risk, it makes sense to use two risk measures The difference in asset and liability * This is different from the surplus approach proposed by Ezra (1991) and Sharpe and Tint (1990) © 2010 by Taylor and Francis Group, LLC Performance and Risk Measurement for Pension Funds ◾ 77 returns is a general measure of risk, as it focuses on changes in the value of surplus This measure is relevant for both parties involved in the pension fund We use a d ownside risk measure as suggested by Sortino and Van der Meer (1991) i n order to accommodate de viations f rom normality i n the return distribution The downside risk measure is calculated based on a simulated distribution of possible outcomes: n DR = ∑ x =1 ⎛ ∆S ⎞ ιx ⎜ x − rmar ⎟ ⎝ L ⎠ n (3 4) where ιx is a dummy variable with value for all ∆Sx/L < rmar ∆Sx/L is the change in surplus in simulation run x scaled by liability value rmar = n is the number of simulation runs If the surplus return is negative, asset returns are lower than liability returns Beneficiaries a re ma inly co ncerned w ith l osses a s fa r a s t hey dec rease the value of their benefits This motivates a second downside risk measure, based on a more conservative minimal acceptable rate of return: rmar* = − S (3 L 5) which i s t he t hreshold r eturn t hat d ifferentiates b etween en ding w ith a positive or a negative surplus value In calculating downside risk measures, we need a distribution of asset and liability returns Using historical numbers is not very meaningful in constructing such a d istribution since the nature of assets and liabilities may change over time Therefore, we use a simulation model in the spirit of the value-at-risk models used in banking There is a va st literature on how t o c reate such m odels, wh ich i s be yond t he scope of t his st udy At this point, it suffices to state that the measures are calculated over the outcomes of the different simulation runs 3.3.3 Benchmark The benchmark for the pension fund is a weighted average of the benchmark return for the surplus investments and the two groups of liabilitydriven investments (Table 3.1) © 2010 by Taylor and Francis Group, LLC 78 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling TABLE 3.1 Benchmark Composition and Return Portfolio Surplus-driven assets Benchmark Weight Benchmark Return p s Nominal liability-driven assets Real liability-driven assets w = S/A rsp wnlp = Ln /A rnlp wrlp = Lr /A rrlp The benchmarks for the liability-driven assets are based on replicating the return and risk of the liabilities Given that defined-benefit pensions are fi xed in terms of nominal or real benefit, we use portfolios of bonds that are cash flow–matched with the liabilities The return on the portfolio matched with the nominal liability is rnlp, and the return on the portfolio matched with the real liabilities is rrlp 3.3.4 Performance Attribution The ba sis for t he per formance attribution model is t he benchmark spec ified abo ve i n co njunction w ith t he dec ision p rocess w ithin t he pens ion fund C onsistent w ith our portfolio a nd benchmark st ructure, we d istinguish between active decisions within one of the asset portfolios and active decision with respect to the allocation to each of the asset portfolios Active decisions w ithin one of t he asset portfolios refer to t he decision to have a portfolio with a different composition as compared to the benchmark For the surplus-driven assets, this could be the decision to invest in an actively managed fund For the liability-driven assets, this is the decision to invest in, for example, bonds with different maturities or to i nvest in bonds with a d ifferent c redit qu ality The a llocation m ismatches a re t he de viations between the market value of the asset portfolios and the value of the liability portfolios that they aim to cover In Table 3.2, we summarize the main sources of return We express the active return and the return on allocation mismatches in terms of our proposed performance measure TABLE 3.2 Decision Process Surplus-driven assets Liability-driven nominal assets Liability-driven real assets Allocation mismatches Actual Return Benchmark Return Active Return r as r ps [rsa − rsp ]S/L rnla rnlp [rnla − rnlp ]Ln /L rrla rrlp [rrla − rrlp ]Lr /L [( As − S)rsa + ( An − Ln )rnla + ( Ar − Lr )rrla ]/L © 2010 by Taylor and Francis Group, LLC Performance and Risk Measurement for Pension Funds ◾ 79 We construct a performance attribution model by analyzing the incremental i mpact of i ndividual d ecisions on b enchmark re turns This is accomplished by creating expressions for the realized surplus returns and the benchmark su rplus returns a nd t aking t he d ifference between t hese expressions The realized surplus return in money terms is ∆S a = As rsa + An rnla + Ar rnra − Ln rnlp − Lr rrla (3.6) where ∆Sa i s t he r ealized cha nge i n su rplus va lue S ince pens ion f unds should be managed in the interest of the pension beneficiaries, we calculate the surplus return relative to the value of the liabilities, which results in the following expression: ∆S a As a An − Ln a Ar − Lr a Ln a L = rs + rnl + rrl + (rnl − rnlp ) − r (rrla − rrlp ) (3.7) L L L L L L The benchmark is based on cash flow matching As a result, the allocation to the three asset classes equals As = S, An = Ln, and Ar = Lr The benchmark return is defined as ∆S p S p Ln p L = rs + (rnl − rnl ) + r (rrlp − rrl ) L L L L (3.8) where ∆Sp is the change in surplus based on the benchmark portfolio With perfect ma tching, rnlp − rnl = an d rrlp − rrl = I n p ractice, de viations a re likely to occur for several technical reasons, such as mortality risk and small mismatches between the liabilities and the benchmark portfolios may result in small positive or negative returns For analyzing the investment performance of a pension fund, this is not a major concern By calculating the difference between Equations 3.7 and 3.8, we calculate the difference between the return on the actual portfolio and the benchmark Since the liability returns are present in both Equations 3.7 and 3.8 it cancels out in the difference As a result, we are able to construct the following performance attribution: (rsa − rsp ) S L A − S a An − Ln a Ar − Lr a ∆S a − ∆S p rs + rnl + rrl =+ s L L L L L L + n (rnla − rnlp ) + r (rrla − rrlp ) L L © 2010 by Taylor and Francis Group, LLC (i) (ii) (iii) (3.9) 80 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling where component (i) is the return added by means of active management with the surplus portfolio, component (ii) is the funding allocation mismatches, and component (iii) is the return on the maturity mismatches of both nominal and real duration mismatches In addition to performing a return attribution model, we present a risk attribution model where we decompose the difference in downside risk between the actual and the benchmark portfolio into components consistent with Equation 3.9 In order to this, we use the decomposition of downside risk proposed by Reed et al (2008) Reed et al (2008) have shown how each asset i contributes to the total downside risk of a portfolio p: DR i = DR n wi (rmar − ri , x )(rmar − rp, x ) (3 n x =1 Σ 10) where x is an integer identifying a particular scenario wi is the market value of asset i as a fraction of total assets ri,x is the return of asset i rp,x is the portfolio return in scenario x n represents the total number of scenarios The su m of t he i ndividual contributions i s eq ual t o t otal d ownside r isk DR A similar decomposition can be made for the decisions in the pension fund by recognizing that each decision is a long-short portfolio reallocating money from one part of the portfolio to another 3.4 AN APPLICATION OF THE MODEL In this section, we provide an illustration of the performance and risk attribution model proposed in Section 3.3 We consider a hypothetical pension fund with a mix of real and nominal liabilities Consistent with our attribution model, the fund has divided its assets in three different portfolios: surplus assets, nominal, and real liability-driven assets The surplus assets are invested in risky investments such a s stocks Nominal and real assets are fixed income securities in terms of nominal or real terms The duration of the assets is shorter than the duration of the corresponding liabilities The market value of assets and the value of the liabilities are presented in Table 3.3 From Table 3.3 we can infer that the funding ratio is 133%, which indicates a well-funded pension plan Participants in the pension fund should © 2010 by Taylor and Francis Group, LLC Performance and Risk Measurement for Pension Funds ◾ 81 TABLE 3.3 Balance Sheet of Pension Fund Assets Value Liabilities Value 80 40 40 Surplus Nominal liabilities Real liabilities 40 50 70 Surplus assets Nominal liability-driven assets Real liability-driven assets notice that there are substantial allocation mismatches between the size of the liabilities and the corresponding liability-driven asset portfolios Asset values are based on market values The value of the liabilities is calculated as the present value of the PBO cash flow estimates discounted against respectively the nominal and real interest rates with the appropriate maturity Suppose that the returns realized over a r eporting year are given in Table 3.4 The return on surplus assets was very bad, although it was only marginally worse than the benchmark Both nominal and real liability-driven asset portfolios show small positive returns However, the liability-driven benchmark portfolios have large positive returns Based on the information in Table 3.4, the performance of the pension fund is decomposed using Equation 3.9 The result is presented in Table 3.5 We presented the nominal and the real part of component (iii) separately as (iiia) and (iiib) The actual performance of −53.15% is a measure of the change in surplus as a per centage of liability va lue The benchmark a lso lost −17.79% but t his is not enough to result i n a n egative su rplus va lue TABLE 3.4 Returns on Actual and Benchmark Portfolio Actual Portfolio (%) Surplus assets Nominal liability-driven assets Real liability-driven assets TABLE 3.5 Benchmark Portfolio (%) −54.3 2.7 −53.4 14.8 0.3 20.2 Performance Attribution of Pension Fund Benchmark performance Active decision i ii iiia iiib Actual performance © 2010 by Taylor and Francis Group, LLC −17.79% −0.29% −18.38% −5.05% −11.63% −35.36% −53.15% 82 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling since t he i nitial su rplus wa s 33.3% a s a per centage of t he l iability va lue The loss due to active decisions equals 35.36%, and half of this loss is due to the allocation mismatches In particular, the fact that the pension fund had an excess allocation to surplus assets was a bad decision In this example, risk analysis is not really necessary since the example is a doom scenario, making participants painfully aware of the risks they have taken However, if returns are positive due to favorable decisions or good luck, participants tend to forget about risk When the risks are not obvious from last year’s realization, a decomposition of risk is very useful In order to make this possible, it is necessary to create a distribution of outcomes One way to this is to use a simulation study, where the factors of concern are modeled The simulation study used in this example generates economic scenarios for the real- and nominal-term structure of interest rates as well as for a passive stock index and an actively managed portfolio of stocks Based on this model, we calculated returns for the actual and benchmark asset portfolios We used conservative estimates for t he equity r isk premium The summary statistics of these portfolios are presented in Table 3.6 We u se E quation 10 f or c alculating t he co ntribution o f e ach dec ision to the downside risk of the portfolio The c alculations a re done on a simulated distribution of 500 possible outcomes using an ALM model As stated before, the simulation model is not discussed here, since it is not really relevant for applying the proposed attribution model, and it would involve discussing many technical issues.* The outcomes of these calculations are presented in Table 3.7 TABLE 3.6 Summary Statistics of Actual and Benchmark Returns Actual Portfolio Surplus Nominal Real Benchmark Portfolio E[r] (%) S (%) E[r] (%) s (%) 1.65 2.29 0.01 30.01 4.98 0.22 1.64 4.60 1.81 29.91 11.80 11.87 Note: This t able presents t he average return and its st andard deviation of the actual and benchmark portfolios in t he simulation st udy The st udy is bas ed o n 500 simulation runs * This does not suggest that the choice of the model is irrelevant © 2010 by Taylor and Francis Group, LLC Performance and Risk Measurement for Pension Funds ◾ 83 TABLE 3.7 Downside Risk Attribution Benchmark 7.1% Active decisions i ii iiia iiib 0.0% 7.2% 0.4% 0.5% 8.1% Actual portfolio 15.2% The simulation study indicates that the actual portfolio has more than twice as much risk as the benchmark portfolio The contribution of active decisions to the actual portfolio risk is 8.1% The choice for an active portfolio of su rplus a ssets s a lmost no i mpact on t he total downside r isk However, the benchmark choice for the surplus asset portfolio generates almost lf o f t he t otal po rtfolio d ownside r isk The a ttribution m odel shows that the increase in the downside risk is mostly due to the allocation m ismatch, wh ich contributes 7.2% t o t he d ownside r isk The duration mismatches in the nominal and real liability-driven portfolios have a moderate impact on the portfolio risk 3.5 CONCLUSION AND DISCUSSION Bad stock ma rket per formance c aused ser ious d ifficulties for defi nedbenefit pension plans at t he beg inning of t his new c entury A lthough fi nancial markets appear to be the main source of risk, the performance and risk management of pension funds were not able to deal with this Th is cha pter p roposes a per formance a nd r isk a ttribution m odel t hat is m ore a ligned w ith t he o bjective o f t he ben eficiaries S ince pe nsion funds are designated institutions for providing reliable pension to individuals, the reliability of these pensions should be the primary objective of the pension fund Our proposed benchmark implies zero risk for the beneficiaries The sponsor can take more risk by choosing an appropriate surplus asset portfolio, as long as the risks of the surplus asset portfolio not carry over to the liability-driven asset portfolios We a lso proposed a risk attribution model based on downside risk We illustrated our model with an example of a stylized pension fund and a simulation model The ex ample i s t ypical for ma ny pension f unds a s it has an excess exposure to risky assets The model shows how pension fund managers can easily identify risky decisions and evaluate the impact of these © 2010 by Taylor and Francis Group, LLC 84 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling decisions on its ability to service future pension claims In using this model, it is important to develop a realistic model to generate economic scenarios of stock and bond prices In this chapter, we did not discuss these modeling issues Nevertheless, the choice of the economic model is important REFERENCES Elton, E J and M J Gruber, 1992, Op timal investment strategies with investor liabilities, Journal of Banking and Finance, 16, 869–890 Erza, D., 1991, Asset allocation by surplus optimization, 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van der Meer, and A Plantinga, 1999, The Dutch triangle, Journal of Portfolio Management, 26(1), 50–58 Waring, M B., 2004, Liability-relative investing, Journal of Portfolio Management, 30(4), 8–20 © 2010 by Taylor and Francis Group, LLC ... example, Leibowitz (1986), Siegel and Waring (2004), and Waring (2004) © 2010 by Taylor and Francis Group, LLC Performance and Risk Measurement for Pension Funds ◾ 73 present bo th i n t he a sset... may arise * See, for example, Elton and Gruber (1992), Erza (1991), or Sharpe and Tint (1992) © 2010 by Taylor and Francis Group, LLC Performance and Risk Measurement for Pension Funds ◾ 75 Beneficiaries... proposed by Ezra (1991) and Sharpe and Tint (1990) © 2010 by Taylor and Francis Group, LLC Performance and Risk Measurement for Pension Funds ◾ 77 returns is a general measure of risk, as it focuses