An Asset and Liability Management System for Towers Perrin-Tillinghast

Transcription

1 An Aet and Liability Management Sytem for Tower Perrin-Tillinghat John M. Mulvey Gordon Gould Clive Morgan Department of Operation Reearch and Financial Engineering and Bendheim Center for Finance Princeton Univerity Princeton, New Jerey Tower Perrin 1515 Arapahoe Street Denver, Colorado Tower Perrin 175 Bloor Street South Tower, Suite 1501 Toronto, Ontario M4W 3T6, Canada Tower Perrin-Tillinghat employ a tochatic aet-andliability management ytem for helping it penion plan and inurance client undertand the rik and opportunitie related to capital market invetment and other major deciion. The ytem ha three major component: (1) a tochatic cenario generator (CAP:Link); (2) a nonlinear optimization imulation model (OPT:Link); and (3) a flexible liability- and financial-reporting module (FIN:Link). Each part improve over exiting technology a compared with traditional actuarial approache. The integrated invetment ytem link aet rik to liabilitie o that company goal are bet achieved. For example, US WEST aved $450 to $1,000 million in opportunity cot in it penion plan by following the advice of the aet-and-liability ytem. T ower Perrin i the larget employer of actuarie in the world (850 actuarie) with over 8,000 total employee, office in 69 countrie, and well over $1 billion in annual revenue. The company provide information and conulting ervice concerning benefit to 10,000 national and international client, including 379 of the world larget companie, and 799 of the Fortune 1,000 companie. A primary emphai i penion plan. In addition, the Tillinghat ubidiary upport the inurance indutry throughout the world. The Tillinghat actuarial ytem Copyright 2000 INFORMS /00/3001/0096/$ X electronic ISSN FINANCE INVESTMENT FINANCIAL INSTITUTIONS INSURANCE INTERFACES 30: 1 January February 2000 (pp )

2 TOWERS PERRIN (TAS) i ued by over 40 percent of lifeinurance companie in the US. Tower Perrin-Tillinghat employ a uite of tochatic financial-planning model to provide guidance to manager of penion plan and inurance companie. The ytem imulate aet-and-liability deciion acro a long-term, multiperiod planning horizon typically five to 15 year. The ytem ha been under development ince 1991 and i now employed in over 16 countrie, motly European and Englih-peaking countrie. It i the mot extenive global invetment ytem for actuarial tudie; it ditinguihing feature reult from a collaborative eight-year effort between an operation reearcher (Mulvey) and Tower Perrin worldwide conulting taff. The aet-and-liability management (ALM) ytem applie to two major domain: (1) deigning and managing penion plan, and (2) integrated financial rik management for inurance companie. In both cae, the ytem imulate an aet policy with liability deciion to maximize the company wealth or penion-plan urplu, while maintaining a afe level of operation. The optimization module elect the bet dynamic policie for the inurance company or the penion plan. For defined-benefit penion plan, the primary goal are to deign the plan and to manage the penion urplu o that the company will meet it obligation to it employee, to minimize the company contribution over time, and to maximize the growth in the plan urplu. For inurance companie, the three primary goal are to help the inurance companie to provide inurance product at a fair price to individual and corporation, to generate reaonable profit for hareholder (or dividend for mutual companie), and to maintain capital adequacy and rik management o that the company remain olvent in the long run. Evaluating penion plan and inurance companie i complicated becaue of the long time horizon, the number of partie with divere interet who are affected, and extenive government regulation. In mot developed countrie, regulation require an annual actuarial analyi. Actuarie evaluate the oundne of a penion plan or an inurance company and can require cah contribution from the company for a penion plan in deficit or from tockholder or outide invetor for an undercapitalized inurance company. Such contribution (or their abence) can have a major impact on a company profit or loe. For example, everal aeropace companie have improved their profit by 40 percent over the pat five year through improved penion management. The actuarial profeion cloely monitor it member and certifie them through periodic tet, educational requirement, and other mean. The Tower Perrin tochatic invetment ytem i employed widely. Several hundred large US and international companie run the ytem for penion plan, approximately 40 percent of US life inurance companie ue the related Tillinghat TAS ytem, and Tillinghat ha a major preence in property-caualty inurance. Multinational companie, uch a Unilever and IBM-Europe, employ the global ytem for modeling their worldwide penion plan on a conitent bai. January February

3 MULVEY ET AL. In thi paper, we dicu the nature of penion planning and integrated financial planning. We focu on penion-plan application in order to limit the dicuion. Mulvey, Correnti, and Lummi [1997] dicu a related model in the inurance indutry. Inurance model poe a tructure imilar to penion plan, but they include many additional variable and contraint due to the complexity of integrating a large financial organization. Modeling Framework The Tower Perrin invetment ytem imulate aet-allocation policy in conjunction with liability deciion over a multiyear planning horizon. Integrating aet and liability deciion help the company achieve it goal. The ytem ha three major element: a tochatic cenario generator, a deciion-rule or policy imulator, and an optimization module (Figure 1). The firt two element form the corporate (or penion-plan) imulation module and are deployed before the optimization algorithm earche for the bet compromie policy given the relevant buine, policy, and regulatory contraint. In effect, the optimization run the imulation by identifying deciion trategie that bet fit the propoed objective function over a multiperiod planning horizon. For example, we will make recommendation about the optimal dynamicinvetment rule for tock, bond, cah, and penion contribution over differing economic environment. Three feature ditinguih the Tower Perrin approach, a compared with uch alternative a the Frank Ruell ytem [Cariño et al. 1994]: (1) it reliance on a core et of tructural economic factor for Figure 1: The three element of aet-andliability modeling mut be conitently linked to a et of core economic factor. The tochaticmodel determine value for the economic factor prior to analyzing the deciion policie. driving both aet return and liability movement, (2) a et of policy rule that underlie the deciion-making procee, and (3) a full actuarial analyi of penion deign and cah-flow liabilitie for each economic cenario. The core economic factor link aet and liabilitie. For example, interet-rate change affect aet return and the preent value of liability cah flow. We ue a et of tructural tochatic differential equation to model the economic factor. While thi approach complicate calibrating the model parameter [Mulvey, Morin, and Pauling 1999], we believe that a tructural model depict the relationhip between aet and liabilitie better than impler method, uch a thoe relying on a covariance or vector autocorrelation matrix for aet return. We apply a et of policy rule. The model recommendation are een by penion-plan adminitrator, beneficiarie, employee, regulator, and other intereted partie. Policy rule provide intuition regarding the recommendation and allow for extenive enitivity analyi. INTERFACES 30:1 98

4 TOWERS PERRIN Penion plan have grown in complexity. There are many choice in plan deign. For example, traditional defined-benefit and defined-contribution plan are now upplemented by cah-balance and related hybrid plan. A cah-balance plan i a portable penion (meaning that employee can tranfer their balance to another company) that accumulate each year by a credited amount. Each employee plan gain in value by a certain percentage of alary plu a credit for money already in the plan. The company et it own aet allocation but i required to fund the cah balance of each employee upon termination. The credited amount can be contrained by cap and floor (minimum and maximum). Actuarie are particularly uited to aiting companie to chooe a benefit program that fit it need. ALM Sytem Variable and Equation The ALM invetment ytem conit of t {0,1,2,3,...,T} time tage. The firt tage repreent the current date. The end of the planning period, T, i called the planning horizon. Typically, for a penion plan, we aim for a long-term horizon five to 15 year in the future with quarterly or annual time tep. We generate a et of {1,2,3,...,S} cenario for the future coure of the economy, the capital market, and other uncertaintie. Stochatic cenario can be depicted by mean of a cenario tree diagram (Figure 2). In uch a tree, at each node, the ytem render deciion regarding the aet mix, the amount of payment to penion beneficiarie, and poible cah contribution. A complete path in the cenario tree equate with a ingle cenario {S} (Appendix). At the beginning of each period and for Figure 2: Within a cenario tree for modeling uncertaintie, the deciion are made at each node of the tree depending upon current information. each cenario, the invetment ytem render policy deciion regarding the aet mix, liability value, and etablihing and achieving goal. Between time tep, uncertaintie take over. For example, interet rate might increae becaue of an increae in inflation, and the bond and tock market might react in a negative manner. We ue a ytem of tochatic differential equation to model all tochatic parameter over time. Thee relate a et of key economic factor to the other component, uch a aet-and-liability return [Mulvey 1996, and Mulvey and Thorlaciu 1998]. For a penion plan, the primary deciion variable deignate aet proportion, liability-related deciion, and penion payment: x j,t: invetment in aet j, time t, cenario. y k,t: liability payment k, time t, cenario. u : contribution l, time t, cenario. l,t The penion-plan urplu i calculated in two way. For determining regulatory contribution, we aume that current and retired employee define the target population. For thi group, we calculate the amount of money needed to atify a legal definition of a penion urplu. Cah flow January February

5 MULVEY ET AL. are calculated by actuarie who etimate the life pan of employee, their alarie at retirement date, and myriad other factor. We omit thee detail. Thi approach goe by the title accumulated benefit obligation (ABO). A econd approach for determining a urplu i to aume that the company will continue to exit over time, adding new employee while other reign, retire, and o forth. Thi method require additional aumption regarding the company future; the reulting urplu i determined by the projected benefit obligation (PBO) method. Thee calculation provide a more robut definition of the company ability to meet it future goal. However, the ABO i appropriate for determining company contribution. In either cae, the etimated cah flow (for future penioner) are dicounted at an appropriate rate to derive the plan urplu: The urplu i the market value of aet minu the market value of liability cah flow. For mot aet, we can readily dicover market value, ay, by checking the current price in a newpaper. However, for penion liabilitie and private market aet, we mut etimate the fair value. Typically, thi require dicounting cah flow by an appropriate dicount rate. For penion benefit, typical US regulation require dicounting at an invetment-grade corporate bond rate. Thu, interet rate are critical; the full yield curve mut be modeled in a conitent fahion (Appendix). At each time period, t, the ALM model maximize an objective function, f(x), by moving money between aet categorie, making ditribution to the beneficiarie, and contributing cah to the penion plan. There are numerou candidate for the objective function. In addition, we impoe contraint on the proce, for example, by limiting the tock-aet ratio, addreing tranaction cot whenever aet are bought or old, and taking advantage of invetment opportunitie. Our goal i to find a feaible deciion policy that maximize a temporal objective function. Since we are dealing with temporal uncertainty, the optimal olution, like all feaible olution, encompae a et of path or trajectorie for the penion-plan urplu acro each of the cenario. To give an idea of the model tructure, we lit two baic equation for the flow of fund: Equation (1) for the jth aet category: xj,t 1 (xj,t r j,t) pj,t q j,t (1 t j) (1) for aet j, time t, cenario, where r j,t return for aet j, time t, cenario, p j,t ale of aet j, time t, cenario, q j,t purchae of aet j, time t, cenario, t j tranaction cot for aet j, and Equation (2) for the cah flow: x (x r ) q l,t l l,t l, j,t j j,t j k,t p (1 t ) y j l,t l u. (2) The model avoid looking into the future in an inappropriate fahion. To prevent thi, we add pecial contraint called nonanticipatory condition. The general 1 2 form of the contraint i x x for k j,t j,t INTERFACES 30:1 100

6 TOWERS PERRIN all cenario 1 and 2 that inherent a common pat up to time t. In word, cenario that hare a common path will have nonanticipatory contraint for variable occurring on the hared path. Any financialplanning ytem mut addre thee condition, either explicitly or implicitly. Special purpoe algorithm are available for olving the reulting convex or nonconvex optimization model [Ziemba and Mulvey 1998]. Penion-Planning Objective A major element of aet-and-liability management i to trade off rik and reward at variou temporal juncture. It i natural to expect that invetment poeing volatility will generate greater expected return over time than aet with lower level of volatility. The temporal iue complicate the deciion proce ince long-term horizon provide a cuhion to recoup loe; thu volatile aet may be, in fact, afer in term of contextual rik than le volatile aet. An example i the tock-cah comparion: tock provide higher expected return but are more volatile than cah. We mut conider the time horizon when meauring contextual rik, that i, the chance of meeting the invetor goal. An integrated ALM ytem provide an ideal method for undertanding the temporal rik-reward trade-off and for evaluating the probability of meeting company goal. There are many metric for financial rik, jut a there are alternative meaure of profitability or return. For an inurance company, we might conider the chance of a lo over the next year. Or we might et a profitability target and evaluate the probability of miing the target. In both cae, rik increae a a function of probability. An improved alternative for evaluating rik for an inurance company i to etimate the entire probability ditribution of hareholder equity at each time period, along with other meaure of financial well-being. In the cae of a penion plan, we meaure the dicounted contribution and the plan urplu at the end of the planning horizon. Typically, we equate reward with expected value. We have particular interet in the penion plan urplu at the horizon: Expected urplu p * z, S where p i the probability of cenario, z i the penion urplu under cenario, time T, and S i a et of repreentative cenario. We are intereted in rik at the horizon and include a number of alternative meaure, including emi-variance, downide rik, and urplu variance. In addition, we can how the trajectory path for the penion plan under any of the generated cenario. Policy Rule A a ditinguihing feature, the Tower Perrin ytem etablihe a et of policy rule for managing invetment, liability payment, and penion contribution. We define a policy rule a a pecified formula or et of rule for all the deciion a a function of the tate of the world at each time period and cenario. A a imple example, we might put a fixed proportion (ay 70 percent) of the penion urplu into an S&P500 index fund with the remaining aet aigned to a fixed-income bond portfolio that mimic the penion liabili- January February

7 MULVEY ET AL. tie. Thu at each time period, the ytem mut calculate penion urplu baed on dicounted cah-flow projection, determine the exce of aet over market value of liabilitie, and rebalance the invetment portfolio to achieve the deired target ratio. We call thi particular policy rule fixed proportional urplu (FPS). Numerou alternative policy rule are available for teting. The optimization module compare policy rule and determine the bet combination of rule and parameter etting. For example, in the FPS rule the parameter defining equity proportion will be found via optimization. Policy optimization provide a natural approach for analyzing longterm invetment problem. The rule can be a complex a the invetor like. Policy rule atify the nonanticipatory contraint in an implicit ene. In addition, the approach implifie the tochatic programming model ince it reduce the number of deciion variable over treebaed tochatic programming method and it can readily parallelize the optimization problem. In addition, enior manager can readily grap policy rule. A a diadvantage, the reulting model i likely to be nonconvex. Penion Planning Example A defined-benefit penion plan for a large US company encompae iue that affect a range of takeholder. The company mut et it benefit policy o that both retired and working employee are properly compenated and fairly treated. The term properly and fairly are ubject to alternative interpretation. The invetment policy mut conider the long-term nature of the planning horizon. At the ame time, penion planner mut atify the prudent-man rule. The company mut follow numerou regulation crupulouly government, tax, accounting, and o forth. Clearly, there are a variety of perpective on the rik-reward trade-off. To addre thee iue, Tower Perrin developed the Retirement Plan Financial Management approach. It combine an aement of the plan liabilitie and aet to help determine benefit, funding, invetment, and accounting policie that are conitent with a company overall goal. Thi methodology applie to all component of a company retirement program including penion, aving, and retiree benefit. Some of the key financial meaure that are typically included in a company tatement of objective are: Future cah-contribution requirement; Long-term portfolio return relative to interet-crediting rate (for cah-balance plan); Poible reduction to hareholder equity; Recovery of plan cot in rate (for regulated companie); Future cah-flow need for benefit payment; Funded tatu; and Financial expene. A penion-plan deign hould addre the four area benefit deign, funding policy, invetment trategy, and accounting policy that affect the company financial health a meaured by the tatement of objective. Thee financial lever link together and link to the company broader buine objective (Figure 3). Benefit deign include the type of plan utilized and the level of benefit each plan INTERFACES 30:1 102

8 TOWERS PERRIN Figure 3: The four element of penion-plan deign hould together fit the company goal. Each element hould ait in achieving the company buine objective. provide. The funding policy cover the amount of capital the company contribute in advance to upport promied benefit. The invetment trategy control the invetment of the capital allocated by the funding policy. The accounting policy recognize the annual corporate expene and balance-heet reerve. A fundamental objective i to minimize or at leat manage cah contribution, financial expene, or otherwie-defined financial rik uing thee lever. Adopting a ytematic proce help the company fulfill it financial dutie to hareholder and it fiduciary dutie under it regulatory guideline, uch a the Employee Retirement Income Stability Act (ERISA). Recently, our client have ued the financialmanagement proce to: Shape funding requirement to reduce exceive funding requirement in any ingle year; Evaluate the need to cap the interet crediting rate in a new cah balance plan; Determine the optimal aet allocation aimed at maximizing return on the plan urplu; Develop funding, accounting, and invetment policie to minimize the probability of future reduction in hareholder equity; Determine the financial and cah-flow impact of offering lump um to penionplan participant at retirement; Shape the financial-expene pattern to compre pike and reduce year-to-year volatility; and Analyze the probable impact on the financial tatement of actuarial aumption. The following three real-world cae tudie contain detail that are imilar to many penion plan. Example A Company A retirement plan ha been fully funded for many year. A a reult, it ha not made cah contribution in recent memory. Becaue of everal acquiition, the retirement plan will likely no longer be fully funding in a few year. In fact, a imple determinitic forecat projected that a cah contribution in exce of $60 million would be required in the year While the company accepted the fact that it would have to contribute cah, it wanted to minimize the probability that it would have to contribute more than $60 million in any ingle year of the next five. Following our analyi, the company adopted a new funding policy to hape it future cah contribution. The new policy reduced the probability that the cah contribution would exceed $60 million in any of the next five year from 58 percent to 18 percent. The new funding policy included two key change from the current policy: the aet-moothing method wa reet o January February

9 MULVEY ET AL. Figure 4: The range of cah contribution depend upon the reolution of the uncertaintie and the invetment policy over the planning horizon. The current policie for Company A provide a wider range of outcome than the recommended policie. that invetment gain during the pat few year could be recognized more quickly, and the company committed to an annual contribution of three percent of payroll. We conidered changing the invetment trategy. However, our analyi howed that while thi offer a long-term olution, changing the allocation to a more aggreive portfolio mix would not ignificantly affect reult during the company fiveyear time horizon. Thu, the accounting change fit the company need (Figure 4). Example B Company B adopted a cah-balance plan with a contribution credit of five percent of pay, plu interet credit on the account balance equal to the return on oneyear Treaury bill plu one percent. Company B wa concerned that during a period of high inflation, the interetcrediting rate would exceed the actual return on the trut aet, cauing the plan funded tatu (urplu) to decline. Thu, the company wanted to etimate the implication of applying a cap on the annual interet-crediting rate. After our review, the company decided not to adopt a cap for the following reaon: Over the long-term there wa only a mall rik that the interet-crediting rate would exceed the actual return on the trut aet. A cap would do little to further reduce thi rik. A cap would detract from the employee-perceived value of the cah-balance plan, epecially in year that the cap applied (Figure 5). Example C Company C converted it traditional penion plan to a cah-balance plan and wihed to reevaluate it aet allocation. The company two key financial objective were to maximize the plan urplu and to minimize the rik that the funded tatu would fall below 100 percent over the next five year. A common approach would be to determine the aet-allocation trategy by optimizing the expected return on the plan portfolio of aet relative to the tandard deviation of portfolio return (Figure 6). INTERFACES 30:1 104

10 TOWERS PERRIN Figure 5: Adding a cap to the penion plan will have little impact on Company B financial health. It will detract from the perceived value of the plan to the participant. However, becaue a plan aet and liabilitie are both affected by common economic variable, an aet-only approach i inappropriate. Intead, we employ the urplu efficient-frontier optimization tool. It define rik and reward in term of the plan urplu value. Company C defined rik a the likelihood of falling below 100-percent funded, and it defined reward a the expected funded tatu. A comparion of the aet mixe identified on the aet-only efficient frontier with the urplu frontier for Company C howed that the aet-only optimal olution lie off the efficient frontier and i dominated by other olution on the urplu-efficient frontier (Figure 7). Although the company current mix i efficient relative to the aet-only frontier, it i inefficient relative to Company C tated objective (Table 1). The company adopted the recommended aet allocation. Operation Reearch Contribution The Tower Perrin project ucce can be attributed to innovation baed on operation reearch method. Four area have benefited from interaction among the team of operation reearcher, econometrician, and financial actuarie. Solution of Nonconvex Optimization January February

11 MULVEY ET AL. Figure 6: The aet-only efficient frontier how the optimal combination of rik and reward for the penion-plan aet. Company C current policy (diamond) lie on the aet efficient frontier. The policy-optimization framework give rie to nonconvex program [Ziemba and Mulvey 1998]. Thi property hinder the earch for optimal olution to tochaticfinancial-planning model over multiperiod horizon. Mot multiperiod financial-deciion and policy rule lead to nonconvex nonlinear program. To addre thi iue, the integrated ytem tart the earch with a carefully choen et of point, near to the top of the efficient frontier. It find ubequent point by moving down the efficient frontier while atifying the linear contraint. Thee heuriticmethod have proven effective in practice for many of Tower Perrin client. Calibration of Stochatic Equation via Nonlinear Optimal Fitting An eential element of any planning ytem i parameter etting. For intance, the mean reverion parameter for interet rate ha an impact on the average level of return for fixed-income aet (Appendix). We addre the iue from everal tandpoint. Firt, there hould be a connection between hitorical reult and the overall pattern of the generated cenario. The ditribution of equity return, for intance, hould be compared with the cumulative ditribution over hitory. Major dicrepancie hould be reviewed and accepted or rejected baed on the actuarie judgment. In general, the Tower Perrin model fit ummary tatitic, uch a variance, covariance, autocorrelation, cro-correlation, and the interquartile range. Thee value provide indicator of the overall volatility and interrelationhip of market over the planning period. The actuarie and economit input critical et of tatitic directly into the model. Thee parameter et general trend and average. For intance, the growth in equity earning i determined by expert judgment in each country. Certainly, the actuarie mut account for pat performance when they fix thee value. But they mut be able to take a tand when they are convinced that hitorical average mut be modified. The total parameter-etting exercie combine the judgment of the actuarie and economit with a formal calibration tool. The tool fit hitorical pattern of ummary tatitic, while meeting the target et by the econometric taff a cloely a poible. The optimal fitting program require a nonconvex optimization olver and a routine for running CAP:Link [Mulvey, Morin, and Pauling 1999]. Operation reearcher have much to offer in the calibration of tructural tochatic forecating model. Contructing Repreentative Scenario The cenario et mut repreent a rea- INTERFACES 30:1 106

12 TOWERS PERRIN Figure 7: The urplu efficient frontier how the optimal combination of rik and reward for the penion-plan urplu. Company C current policie are inefficient with repect to it urplu. onable range of outcome, depending upon the invetor need. We minimize the number of cenario by employing variance-reduction method including antitheticvariable. In addition, we can evaluate the model recommendation by running thee through a proce that we call tratified filtered earch [Ziemba and Mulvey 1998]. Here, the goal i to generate a erie of cenario that minimize the ampling error and maximize confidence in the reulting efficient frontier and aet allocation. A econd iue i the error that arie in ampling cenario within the optimization module. We addre thi iue by adjuting the number of cenario ampled depending upon the invetor need. In many cae, a et of 500 cenario ha proven adequate for invetor intereted in tandard rik-reward analyi, uch a urplu efficient frontier. Additional cenario can be generated a needed when there i particular interet in rare event. For intance, the Tillinghat property caualty ytem require a large number of cenario (over 10,000) due to it emphai on rare catatrophe ariing from large hurricane and earthquake. To validate the model, we pend a great deal of time evaluating cenario for reaonablene. We often look at individual cenario to undertand the connection between variable, for example, the level of interet rate and the accompanying level of inflation (Figure 8). Although interet January February

13 MULVEY ET AL. rate increae over the period 1997 to 2005, the real rate of interet interet rate minu inflation decreae during thi period, until eventually, long interet rate pike in 2005, cauing real interet rate to increae. The high level of real rate then puhe down inflation and interet rate follow. Pattern of thi type are judged reaonable by the economic taff. The ALM ytem poee interactive feature that allow uer to eaily ee connection between any et of variable. SytematicStre Teting While economic theory can help actuarie in etting valid aumption, no guiding law govern the future tate of the world economy. Thu, unlike engineer who depend upon phyical law, financial engineer mut take extra care when following the recommendation of financialplanning ytem. In thi environment, we employ a proprietary tre-teting procedure. The method filter cenario that fit pecified pattern. US WEST Application US WEST ha increaed it penion urplu by $450 to $1,000 million over alternative trategie baed on running the financial-planning ytem. Thi client ha a large penion portfolio, over $12 billion (1997), with a ratio of aet to liabilitie equal to 150 percent, and a plan covering 106,000 participant. The company employ the ALM ytem regularly to undertand the impact of poible change in the invetment mix and to explore modification to the penion-plan deign. During the fall 1997, Tower Perrin, in conjunction with US WEST, employed it tre-teting procedure. In addition to tandard analye, US WEST pay cloe attention to factor that could decreae it current ample urplu. It want to continue participating in the upide of the trong US equity market but i concerned about protecting it urplu from unpleaant urprie. We developed a ytematicapproach for identifying cenario that lead to poor performance acro the planning horizon of 10 year. Once we locate the caue of the cenario, we et up the CAP:Link ytem to filter cenario that fit a et of decriptor. For example, a combination of dropping equity market and falling interet rate i the mot devatating for a penion plan. We create a et of cenario that fulfil thi requirement. In 1997, we generated four et of 500 cenario: (1) normal condition; (2) equity market crah, that i, a two-year equity dropping at leat 10 percent per year; (3) an equity bear market, that i, compound equity return le than three percent over the next 10 year; and Aet Only Recommended Large cap US equity 35% 55% Small cap US equity International equity Corporate bond year Treaurie 0 20 Total 100% 100% Table 1. The urplu-optimal invetment mix (recommended) i better than the aet-only olution ince it achieve the company goal with le rik. INTERFACES 30:1 108

14 TOWERS PERRIN Figure 8: Over the planning for a ingle cenario, the economic factor hould diplay enible relationhip to each other. Future inflation will often depend upon the real rate of interet. Negative real rate will caue inflation to increae, wherea poitive real rate will puh future inflation lower a hown. (4) diinflation, that i, long-bond yield average le than 3.5 percent over the next 10 year. For implicity, we compared three invetment trategie the current equity/bond mix, an equity hedged mix, and a long-bond trategy (Figure 9). The current olution wa more robut over the four et of cenario. Baed on thee and imilar reult, US WEST decided to maintain the exiting aet allocation. The cot to hedge the equity expoure would have caued an expected urplu decline of over $2.5 billion. The long-bond trategy hould be avoided a well. While contribution were le likely with improved aetliability matching, the expected urplu would alo have declined by over $2.5 billion over the next 10 year. The reulting cot aving wa ignificant. The cot to hedge the US equity portion would have been a $450 million reduction in urplu over the pat 18 month. The opportunity gain realized by not moving $4.8 billion of equity into bond i $1.01 billion, repreenting an equity return of 40 percent veru bond return of 19 percent over 18 month. The ubequent rik-reward analyi howed the benefit of thee deciion to the financial health of the US WEST penion plan. In ummary, we reran the invetment ytem under filtered et of treful cenario to develop contingency plan for the penion plan. US WEST ha uccefully employed thi dynamictre analyi and ha maintained a ubtantial equity poition over the pat few year. The ALM ytem give it confidence that it penion plan will be able to maintain a ubtantial urplu. A tochatic framework i eential for undertanding the temporal rik/reward iue for a large, complex penion plan. Concluion Tower Perrin tochatic planning ytem ha had a major impact on the actuarial profeion and on many penion plan. Actuarial conultant throughout the world ue the ytem in evaluating penion plan and inurance companie. Linking aet and liability deciion i difficult for mot invetor. The integrated ALM ytem provide an intuitive approach for coordinating thee element. The invetor can concentrate on the primary tak to balance the goal of the variou group, for example, maximizing the urplu of the penion plan, while maintaining retirement benefit, and protecting the company balance heet. Over the pat year, the financialervice indutry ha been moving toward conolidation and merging of diparate organization. A prominent example i Citigroup, formed by combin- January February

15 MULVEY ET AL. Figure 9: The outcome of three trategie over the tandard 500 cenario and three treful cenario et. The current policy ha the bet rik-reward relationhip. ing Traveler and Citicorp (with Smith Barney and Salomon Brother a diviion). European companie are well along the ame path. Thi trend will accelerate a Congre replace depreion-era regulation, uch a the 1933 Gla-Steagall Act. Thee conglomerate financial organization need to integrate their deciion. Companie mut undertand the rikadjuted return for each operation. A financial company mut alo be able to identify rik factor that pan the organization, giving rie to correlated rik. The Tower Perrin ALM ytem can be extended to cover buine-related activitie. A a conequence, the property caualty (PC) diviion of Tillinghat Tower Perrin ha developed an integrated rikmanagement ytem for the PC indutry. Alo, Renaiance Reinurance, in conjunction with Tillinghat, ha developed an integrated rik-management ytem [Lowe and Stanard 1996]. Financial companie have traditionally been managed a decentralized buinee, with occaional meeting between diviional executive to et policy and target. The ituation i reminicent of manufacturer and retailer in the 1960 and 1970 with their production, inventory, and tranportation ubytem. Integrated logitic i the norm for thee companie today. A imilar change will take place in the management of financial organization. The Tower Perrin ytem provide a prominent example of the advantage of integrating aet and liability deciion within a common framework. APPENDIX The cenario generated by CAP:Link INTERFACES 30:1 110

16 TOWERS PERRIN contain key economic variable, uch a price and wage inflation, interet rate for different maturitie (real and nominal), tock dividend yield and growth rate, and exchange rate through each year for a period of up to 40 year. We model return on aet clae and liability projection conitent with the underlying economic factor, epecially interet rate and inflation. The model imultaneouly determine economic variable for multiple economie within a common global framework. Long-term aet-and-liability management i the primary application. The global CAP:Link ytem form a linked network of ingle-country module. The three major economic power the United State, Germany (now the EU), and Japan occupy a central role, with the remaining countrie deignated a home or other countrie. We aume that the other countrie are affected by but do not affect the economie of the three major countrie. The baictochaticdifferential equation are identical in each country, although the parameter reflect unique characteritic of each particular economy. We can readily include additional countrie in the framework by increaing the number of other countrie. Within each country, the baic economic tructure i uch that variable at the top of the tructure influence thoe below, but not vice-vera (Figure 10). Thi approach eae the tak of calibrating the model parameter. The ordering doe not reflect cauality between economic variable but rather capture ignificant comovement. Linkage acro countrie occur at variou level of the model for example, interet rate and tock return. Thee connection are dicued by Mulvey and Thorlaciu [1998]. Roughly, the economic condition in a ingle country are more or le affected by thoe of it neighboring countrie and by it trading partner. The degree of interaction depend upon the country. The tructure i baed on a cacade format. Module above and equal to that level can affect each ubmodule within the ytem. Briefly, the firt level conit of hort and long interet rate, and price inflation. Interet rate are a key attribute in modeling aet return and epecially in coordinating the linkage between aet return and liability invetment. To calculate a penion plan or an inurance company urplu, we mut be able to dicount the projected liability cah flow at a dicount rate that i conitent with bond return, under each cenario. Alo, ince dynamic relationhip are eential in rik analyi, the interet-rate model form a critical element. The econd level entail real yield, currency-exchange rate, and wage. At the third level, we focu on the component of equity return: dividend yield and dividend growth. Return for the remaining aet clae form the next level, with fixed-income aet reflecting the term tructure of interet rate and other mechanim. We project each economic variable by mean of a tochatic differential equation, relating the variable through time and with the tochatic element of the equation and to other variable and factor at the ame or higher level in the cacade. A critical feature for a global cenario generator i the currency module. Several iue complicate modeling currencyexchange rate. Firt, currencie mut enforce the arbitrage free condition among pot exchange rate and among forward rate with differential interet rate. The econd iue concern ymmetry and numeraire independence. We mut create a tructure in which the ditribution of currency return from country A to country B ha the ame ditribution a return from B to A. Both iue limit the form of the currency-exchange model, epecially when integrating three or more currencie. To avoid thee problem, we focu on the trength of each country currency. Ex- January February

17 MULVEY ET AL. Figure 10: The tochatic differential equation are arranged in a cacade tructure. Factor at the higher level of the cacade affect thoe below, but not vice vera. Each country ha the identical tructure with it unique parameter. change rate follow a the ratio between the trength of any two countrie. The abolute trength of any currency i a notional concept; the relative level reflect the difference in the exchange rate [Mulvey and Thorlaciu 1998]. We lit two of the key differential equation (for hort and long government pot rate) to give example of the type of equation that we employ in the CAP:Link ytem. Modeling economic factor i critical. The two equation define the path of interet rate over the planning horizon. There are even parameter: mean reverion level (l l and u l ), drift term (a r and a 1 ), volatility term (r r and r 1 ), and a correlation value for the Wiener term (Z r and Z l ). While the tochatic model i more complex than one baed on a imple regreion tructure, an ALM ytem mut poe conitent linkage between aet and liabilitie. A factor approach eem to be the mot appropriate method for providing thi conitent linkage. Short interet rate: dr a (r r ) dt r r dz t r l t t r r Long interet rate: di a (l l ) dt l r dz t q l t t l l Reference Cariño, D. R.; Kent, T.; Myer, D. H; Stacy, C.; Sylvanu, M.; Turner, A.; Watanabe, K.; and Ziemba, W. T. 1994, The Ruell-Yauda Kaai model: An aet liability model for a Japanee inurance company uing multi-tage tochatic programming, Interface, Vol. 24, No. 1, pp Lowe, S. P. and Stanard, J. 1996, An integrated dynamic financial analyi and deciion upport ytem for a property catatrophe reinurer, Caualty Actuarial Society Forum, ummer. Mulvey, J. M. 1996, Generating cenario for the Tower Perrin invetment ytem, Interface, Vol. 26, No. 2, pp Mulvey, J. M.; Correnti, S.; and Lummi, J. 1997, Total integrated rik management: Inurance element, Princeton Univerity SOR INTERFACES 30:1 112

18 TOWERS PERRIN Report, No , Princeton, New Jerey. Mulvey, J. M.; Morin, F.; and Pauling, B. 1999, Calibration of tochatic cenario generator for DFA, Caualty Actuarial Society Forum, ummer, and Annal of Operation Reearch, Vol. 85, pp Mulvey, J. M. and Thorlaciu, E The Tower Perrin global capital market cenario generation ytem, in Worldwide Aet and Liability Modeling, ed. W. T. Ziemba and J. M. Mulvey, Cambridge Univerity Pre, Cambridge, UK. Ziemba, W. T. and Mulvey, J. M., ed. 1998, Worldwide Aet and Liability Modeling, Cambridge Univerity Pre, Cambridge, UK. Stephen P. Lowe, FCAS, MAAA Principal, Chief Actuary Tillinghat-Tower Perrin, Foretal Centre, 175 Powder Foret Drive, Weatogue, Connecticut , write: Inurance companie are increaingly recognizing the need to build dynamicfinancial model to upport the management of rik and capital. A cornertone of thi proce i the generation of the economic cenario. We are uing Global CAP:Link for thi purpoe, with great ucce. Global CAP:Link provide cenario for the key economic variable that drive the behavior of the aet and liabilitie. Equally important i that the cenario extend acro multiple period, which i critical when modeling longterm, non-tradable inurance contract. We are uing Global CAP:Link, in conjunction with our TAS financial modeling oftware to ait inurer in looking at a number of critical iue. 1. We have analyzed alternative invetment trategie, given an inurer liabilitie. Thee project entail the contruction of aet/liability efficient frontier. 2. We have analyzed alternative portfolio hedging trategie, in the form of different reinurance treatie that the inurer might buy to protect itelf from advere claim experience. 3. We have analyzed the impact of alternative debt/equity ratio on rik and return for an inurer intereted in the efficiency of it capital tructure. We expect the ue of tool uch a Global CAP: Link to explode in the next few year, and to fundamentally alter the way inurer manage rik and capital. Our client are excited by the reult we have obtained; mot importantly, they are acting on the recommendation temming from them. J. Stanford Willie, PhD, Vice Preident, US WEST Invetment, Management Company, 7800 Eat Orchard Road, Suite 290, Englewood, Colorado 80111, write: One of the mot unique feature of the Tower Perrin Sytem i the linkage between the aet and liability component of the model underlying the ytem. Many ytem available in the marketplace focu only on the aet ide of the problem and imply determine a mix of aet that attempt to maximize expected return and/or minimize volatility of return. They ignore the importance of the liability performance in the evaluation of total rik. Even in the cae where thee ytem take the liabilitie into account, the forecated performance i often inconitent with the imulated aet performance and i, we believe, unreliable, epecially over multi-period. With the Tower Perrin Sytem, there are direct linkage between the variou model component underlying the ytem. Thee linkage give u confidence that the outcome are reaonable and truly reflect the rik/reward trade-off we are making in January February

19 MULVEY ET AL. our invetment deciion. Another important apect of the Tower Perrin Sytem i it flexibility relative to the analyi of variou penion fund objective, a topic of particular interet to enior management. At US WEST, we want to increae our urplu poition, but we alo want to minimize corporate contribution and avoid large loe. With the Tower Perrin Sytem, we can analyze the impact of changing our aet allocation on each of thee objective function. We can alo look at a particular aet allocation and analyze the impact of variou extreme economic condition. We have found thi cenario generation capability to be a very powerful tool for aet allocation. And, becaue it allow u to pecifically quantify rik relative to achieving our objective, it i a powerful tool for communicating to enior management. Alo, traditional method of aet allocation baed on mean-variance optimization are enitive to the aumed parameter, uch a return, rik, and correlation of individual aet clae. Often, aet mixe that are unpalatable, or eentially uninvetable, are found to be optimal. Furthermore, ince we cannot know thee parameter with much preciion, and given the enitivity of the analyi to thee parameter, the output of any mean-variance optimization mut be viewed with coniderable caution. We have found the Tower Perrin imulation methodology to be far le enitive to the aumed parameter of the individual aet clae than the traditional meanvariance approach and, therefore, more ueful. In ummary, becaue of the flexibility and reliability of the Tower Perrin Sytem, US WEST Invetment Management Company ha ignificantly improved it deciion-making ability relative to total fund management. We have been able to conduct more thorough, ophiticated, and ueful analyi, which ha led to more thoughtful deciion. The ytem ha alo given our enior management a better undertanding of, and more confidence in, the nature of our invetment trategie. We believe the ytem i worthy of the Edelman Award. INTERFACES 30:1 114