130 ◾ Pension Fund Risk Management: Financial and Actuarial Modelinginterdepen-dent entities, with diff erent degrees of relationships between many actors.. In order to be risk oriented
Trang 16.6.4 Measuring Attractiveness by a Categorical-Based
6.6.5 Agent-Based Combined System Dynamics Models 1436.6.6 Agent-Based Modeling and Fuzzy Logic 144
Trang 2130 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling
interdepen-dent entities, with diff erent degrees of relationships between many actors Th e governance of a soc ioeconomic a nd political environment under a pension fund’s perspective is considered as a complex system in which the interactions among the actors infl uence the governance and the governance infl uence their interactions, in a recursive way In order
to be risk oriented and to cope with the peculiarities of complex systems,
asset and liability management (ALM) models of pension funds problems incorporate, among others, stochasticity, liquidity control, populational
dynamics, a nd dec ision delays to be tter forecast a nd foresee so lvency
in the long term Once ALM was established as a fac tor-based model, a research consisting of 25 Brazilian pension funds chosen from among 313 that together had almost 70% of total segment assets of such entities was made so as to identify risk factors and to represent their cause-and-eff ect relationships Th en, t o m odel u ncertainties o r t o enab le m ulti-criteria analysis, m ethods such a s a nalysis o f p rospective a nd r etrospective
scenarios, s ystem dy namics, agent-based mo delling, Bayesian a
naly-sis, Markov chains, and measuring attractiviness by a categorical-based
evaluation technique (Macbeth) were presented and discussed In
con-clusion, t his cha pter e vidences t he power o f a m ulti-paradigm m odel
to study complex environments and off ers a way to manage a dy namic ALM problem
6.1 INTRODUCTION
Pension funds are nonfi nancial institutions with a nonspeculative nature, and thus, assets and liabilities management is diff erent from those of fi nan-cial institutions, and so is risk management Due to the long-term nature
of fi nancial assets and because most pa rts of liabilities must be linked to pensions released on the occasion of workers’ retirement, pension funds are exposed to many risks that are diffi cult to be dealt with
investment policies that looks for an optimal allocation strategy and acts
to seek sustained growth along with a socially responsible behavior Th ei r complex goal is to off er benefi t plans and to get an adequate income return
in a way to assure an actuarial equilibrium in the long term
deci-sions about asset allocations, pension costs, populational dynamics, ematical provisions, ac tuarial equilibrium, and s o on As a fac tor-based model, ALM studies usually address many factors mostly qualitatively and
math-© 2010 by Taylor and Francis Group, LLC
Trang 3subjectively Th e corporate governance of a p ension fund includes a s et
of practices that may optimize its performance and protect all eco nomic agents involved, such as in vestors, employees, sponsors, and other inter-ested parties
Once ALM facili tates decisio n-making p rocesses in a p ension f und, methods and techniques such as prospective and retrospective scenarios, multi-criteria analysis for decision-making processes, agent-based models combined with system dynamics (SD) models, fuzzy logic, Bayes theorems, Monte Carlo simulation, and Markov chains help to estimate and calibrate many parameters and insert stochasticity in the model
6.2 MODELING OF PENSION FUND DYNAMICS
Essentially, a pens ion fund needs to decide periodically how to allocate investments over diff erent asset classes and what would be t he contribu-tion rate in order to fund its liabilities Modeling is an important part of
a decision-making process Beginning with the key relationships among variables, models try to capture the best understanding of the current situ-ation and to project available data so as to forecast the future, considering our interference or the absence of it
achieving at least one of the following goals:
1 Identify and estimate risk factors
2 Imitate populational dynamics
3 Characterize prices evolution to get a prospective cash fl ow
4 Control solvency and liquidity
5 Model changeable factors to get their systemic complexity
6 Design stochastic scenarios and maintain stochastic control
7 Control and charge shortfalls
8 Calculate asset and liability durations
9 Analyze hedging strategies
10 Produce assets allocation based on estimated liabilities
11 Produce pension payment over time on a long-term basis
Trang 4132 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling
12 Produce quantitative information for the board of trustees
13 Produce insurance pricing
14 Optimize social insurance policies
qualitative and quantitative methods and techniques that ensure adequate data for the analysis process
6.3 ASSET/LIABILITY MANAGEMENT
Once e ach ben efi t p lan ha s d iff erent l iabilities a nd o bjectives, pens ion funds need to produce a high-income return to correspond to long-term actuarial expectations and to pay diff erent kinds of benefi ts ALM more usually refers to the projections of assets and liabilities over a long-term period, co mmonly o ver 30 y ears, co nsidering d iff erent s cenarios a nd under a stochastic modeling
ALM may be seen as a met hod to manage risks and uncertainties in pension funds so as to ensure adequate solvency and liquidity over time Considering their long-term obligations, pension funds’ planning horizon
is large and generally address solvency and liquidity by many policies.Acceptable and prudential investments, clear contribution criteria, and actuarial assessments over time are practices that aim to assure annually the equilibrium between accumulation and future payments to the partic-ipants of the plan If a shortfall or surplus occurs, many actions to assure actuarial equilibrium take place Th e process requires a g reat amount of information about the organization, its operations, and the performance
of the market It comprises
1 Th e analysis of an organization’s balance sheet
2 Many actions and controls to manage credit, liquidity, market, and operational risks
3 Th e use of statistical and mathematical methods to predict or cast the future or to defi ne a fi nite number of scenarios so as to model uncertainty
fore-Many b iometric, demographic, eco nomic, a nd administrative fac tors in ALM models treat some degree of uncertainty Actuaries, directors, and economists in pension funds must interact with each other to decide over
© 2010 by Taylor and Francis Group, LLC
Trang 5allocation processes based on subjective information and variable
Deterministic modeling involves using a single “best guess”
mislead-in a pa rticular context a re systematically identifi ed, a nalyzed, assessed,
drivers of decision, their inherent risk factors, and many typical actions to better comprehend a pension fund’s dynamics over time
ALM studies are generally combined to one or more mean–variance models or techniques to quantify fi nancial risks: Markowitz portfolio the-ory, capital asset pricing model (CAPM), asset pricing theory (APT), value
at risk—V@r, Sharpe, duration, and many others Generally, attempting to predict the future based on past behavior or to take the present value of a future position, they try to know more about time series, and thus mitigate risks and reduce uncertainties
A stochastic programming model for ALM is dynamic since the mation on the actual value of uncertain parameters is revealed in stages From Drijver et al (2002), it is assumed that
1 Because of the risks of underfunding, decisions on asset mix, bution rate, and remedial contributions are made once a year
2 Uncertainty is modeled through a fi nite number of scenarios given
by a scenario tree Each scenario demands a complete set of decision variables at each time period because like the total asset value, the portfolio market value is given by the value of investments in each asset class and by the total value of liabilities
Trang 6Accumulation ↑ Strategic asset allocation ↑ High-income
(market risks)
A portfolio with more risky assets is structured due to the need
of credibility and to correspond to participants expectations
↓ Low-solvency (liquidity risks)
Interest on new adhesions to reduce costs and to get more income
↑ Higher returns over investments
Loans and other facilities to add value to participants and attract more of them
Maturity ↓ Strategic asset allocation ↓ Low-income
(market risks);
A portfolio with less risky assets is structured to assure liquid yields to pay liabilities
↑ Assure punctual payments
↑ High-solvency (liquidity risks)
Th e adhesions are generally closed
↓ Lower returns Th e loans follow a historical behaviour to maintain credibility
and participant satisfaction All stages Authorize new benefi ts
plan
Legal risks: out of the limits fi xed
by the regulation
Assure prudential investments
Better manage the assets Compliance Market monitoring Low costs Legal obligations and schedule Actuarial assessments Good solvency Bad corporative governance Emphasis on actuarial constraints and the plan’s equilibrium Higher yields Reducing transaction costs A program to maintain good internal controls is desirable in order
to assure better corporate governance Economies of scale through volume of transactions and controlling the information fl ow to better decide and act accordingly the needs
FIGURE 6.1 Inherent risks by maturity stage of a b enefi t plan (Adapted from Chaim, R.M., Combining ALM and system
dynam-ics in pension funds, in 24th International Conference of System Dynamdynam-ics Society, Proceedings of th e 24th International Conference,
Nijmegen, the Netherlands, 2006, Wiley Inter Science Available at: http://www.systemdynamics.org/conferences/2006/proceed/papers/CHAIM315.pdf, accessed April 15, 2009.)
© 2010 by Taylor and Francis Group, LLC
Trang 7In a changing and complex environment, pension funds wealth ment needs a m ore robust investment a llocation approach t han a st atic mean–variance analysis Cariño et al (1994) proposed a m ultistage sto-chastic dynamic ALM model that includes stochastic controls and short-fall penalties Also, techniques like Brownian motion have been used in the search for better results (Kaufmann, 2005).
manageBoulier et al (1996) consider that “stock returns are uncertain in effi cient ma rkets, so st ochastic co ntrol w ould h elp i n fi nding t he o ptimal investment policy, as well as the adequate level of contribution” (Cariño
-et al., 1994) Kaufmann (2005) used stochastic volatility models with jumps to estimate quartiles of fi nancial risks for a 2-week period
Due to uncertainty, it is diffi cult to quantify risk, especially in some special cases In t his way, Aderbi et a l (2006) studied t he properties of expected shortfall from a fi nancial risk management’s point of view “As a measure for assessing the fi nancial risks of a portfolio,” they conclude that
“expected shortfall appears as a na tural choice to resort to when v@r i s unable to distinguish between portfolios with diff erent riskiness” (Aderbi
et al., 2006) Expected shortfall may be defi ned as “the average loss when value-at-risk is exceeded” giving “information about frequency and size of large losses” (Kaufmann, 2005)
responses to risks of diff erent nature rather than a mere reaction nism t o t hose l imited e vents de tected It i s about ma naging t he f uture rather than administering past events, and it must be directly connected
mecha-to actions that aim mecha-to assure good governance of a pension fund
6.4 PENSION FUND GOVERNANCE
Governance is a system composed of a great number of interdependent entities, with diff erent degrees of relationships As complex systems, there would be many interactions among diverse actors that may cause relevant discrepancies on their institutional performances
Liability management decisions must consider uncertain outcomes of events relevant to a pension fund business environment such as regulation, multiple accounts, multiple horizons for diff erent goals, provisions for end
SD’s feedback loop method to represent the dynamic of a typical pension fund and some organizational processes involved Th e symbol “+” means that factors are directly related, and “−” when they are inversely related
It is possible to verify that many cause relations between variables,
expressed by feedback loops R1, R2, B1, B2, and B3, which may explain
Trang 8136 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling
some pension f und’s dy namics a nd c an a id to plan ac tions to a ssure a better governance:
R1—Good solvency (new participants → contributions → asset allocation →
capital gains → credibility → new participants) More attractive plans could enhance contributions by means of new participants or more sponsors that may generate more accumulation Th is way, more credibility could attract more participants and, once there is more money, the solvency tends to get better by, for example, the share and reduction of estimated costs of the plan
R2—Accumulation (a sset a llocation → capital gains → asset allocation)
is a s ituation where money produces money A c apital gain means more money to invest Th is could lead to an exponential growth or decay phe-nomena in the future, depending on capital gains or losses
B1—Credibility (new participants → contributions → asset allocation →
transaction and risk management costs → new participants): More tive plans may attract more pa rticipants a nd t hen t he costs tend to get higher Th is dynamic may reduce adhesions
attrac-Contributions
New participants
Fractional growth rate
Maturity delay Pension payments
Shortfall costs
Transaction and risk management costs Expect liability New benefit plan
+ +
+
+
+ +
+ –
FIGURE 6.2 Pension funds—typical dynamics
© 2010 by Taylor and Francis Group, LLC
Trang 9B2—Good wealth (transaction and risk management costs → asset
alloca-tion → shortfall costs → transacalloca-tion and risk management costs): If there were costs, there would be less money to invest and, consequently, lower shortfall costs that may reduce costs If they reduce, there would be more money, much shortfall costs, and more costs Th is ba lancing dy namic could explain actions that aim to reduce costs
B3—Benefi t payments (ne w pa rticipants → exp ect lia bility → p ension
payments → transaction and risk management costs → new participants) describe the process of accumulating funds and paying benefi ts It includes actions and practices to control the pension fund’s liquidity and solvency
based models it is necessary to defi ne t he world i n ter ms of va riables,”
“to imagine the world in terms of variables, to understand rates of change,
to think at a s ystem level and to understand causation in a s ystem” (de Santos, 1992) Macroeconomics, biometrics, and actuarial classes of vari-ables must be h olistically considered Many random variables identifi ed
by Rocha (2001) were returns over investment, interest rates, tive taxes, capacity factor of salaries and benefi ts, and the rates of increase
administra-in salaries, all of them beadministra-ing economical factors
Appendix 6.A.1 shows many factors identifi ed by conducting research with fi nancial ma nagers a nd ac tuaries a nd t heir i nterrelation o n a motricity-dependence ba sis (Godet, 2 004) a s a wa y t o cla ssify t hem t o explain result variables On the basis of this, the causation between vari-
It is possible to verify many cause relations among variables and the
6.5 POPULATIONAL DYNAMICS
is the lower cost of the former due to loss sharing among participants In both cases, there are many risk factors Th ere are many particular risk fac-tors that explain the system behavior once a defi ned benefi t plan reaches maturity As the number of active participants decrease and pension pay-ments increase, it becomes more important to hedge against liquidity risks ALM served an important role in elici ting requirements to better elabo-rate benefi t and investment plans and to review the predictions underlying choice preferences It had a signifi cant impact on the structure and param-eterization of the fi nal simulation model
Trang 10138 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling
According to Winklevoss (1977, p 56), a population of a pension plan members consists of many subpopulations, for example, active employees, retired employees, vested terminated employees, disabled employees, and
u-ences over the costs of a plan Th e word “S” means that factors are directly related a nd beha ve i n t he s ame s ide a nd “ O” wh en t hey a re i nversely related, behaving in the opposite side
As pens ion f unds a re t ypically a m ulti-decrement en vironment (Winklevoss, 1977, pp 10–22), the causal loop diagram in Figure 6.4 shows the dynamics of a benefi t plan Credibility reinforce new adhesions made by
word of mouth and ad campaigns (R1); many decrements like mortality (B1), withdrawal (B2), disability (B3), and retirement (B4) are the balancing ways
to reduce this population, and thus the costs of the benefi t plan (Winklevoss,
1977, pp 10–22) Some details about each decrement follows:
R1—Credibility means that people become more and more interested in
adhering to a benefi t plan of a pension fund Th is means more assets come from the participants and the organizations that are sponsors of the benefi t
Actuarial interest rate Contributions
Present value of future benefits
Present value of future contributions
Salary increases
Expected return –
+
Plan´s estimated costs
+
+ +
+
+
Plan’s attractivity –
Pension costs – –
–
Liabilities +
Actuarial goals + +
Perfomance of the plan +
–
–
Long-term inflation –
– +
–
Mortality rate New participants+
–
+
Average age of participants and relatives +
Mathematical provisions Actuarial goals
+ +
Withdrawal/
termination rate –
Disability rate Retirement rate
– –
Withdrawal/
termination
–
FIGURE 6.3 Actuarial factors and their interrelationship in an ALM Model
© 2010 by Taylor and Francis Group, LLC
Trang 11plan Credibility generates confi dence that tends to foster new adhesion
of new participants
B1—Mortality decrements: “…among active employees prevents the
attain-ment of a r etireattain-ment st atus a nd hence t he receipt of a pens ion benefi t, while mortality among pensioners acts to terminate the payment of their pension benefi t” (Winklevoss, 1977, p 12)
B2—Withdrawal d ecrements: Th is de crement i s a lso c alled ter mination
decrement as well as the mortality decrement, “…prevents employees from attaining r etirement a ge a nd r eceiving ben efi t u nder t he p lan … t here are a m ultitude of fac tors entering i nto t he de termination of employee termination rates, but two factors consistently found to have signifi cant relationship are age and length of service Th e older the employee and/or the longer his period of service, the less likely it is that he will terminate employment” (W inklevoss, 1 977, p p 1 5–16) A ccording t o W inklevoss (1977, p 18), “disability among active employees, like mortality and with-drawal, prevents qualifi cation for a retirement benefi t and, in turn, lowers the cost of retirement.”
B3—Disability decrements: “…a typical disability benefi t might provide an
annual pension, beginning aft er a waiting period, based on the employee’s benefi ts acc rued t o d ata, o r o n h is p rojected n ormal r etirement ben efi t When disability benefi ts are provided outside the pension plan, it is com-mon to continue crediting the disabled employee with service until normal
Population
Withdrawal decrement Mortality
decrement
New
participants
S S
R1
Disability decrement
Retirement decrement
Trang 13retirement, at which time the auxiliary plan’s benefi ts cease and the employee begins receiving a normal pension” (Winklevoss, 1977, pp 18–19);
B4—Retirement d ecrement: “…the r etirement dec rement a mong ac tive
employees initiates the pension payments” (Winklevoss, 1977, p 21).Figure 6.5 shows a system dynamic stock and fl ow diagram to manage the population dy namics of a pens ion f und Credibility is a fac tor t hat
obtained by expert opinions
to mortality, disability, withdrawal, and retirement risks A p ensioner is exposed just to mortality risks An exp ected population aging ratio uses historical data and calculates the aging index Th is dynamic is essential to
an ALM model to estimate the total assets and the fl ow of liabilities, thus maintaining good solvency and preventing against liquidity risks
According to Edmonds (2003), in cases in which the fi eld of study is suffi ciently complex, it is impractical or even impossible to rely only on mathematical models, like diff erential equations Th erefore, the construc-tion of an agent-based model appears to be the most suitable way to assess the impact of the socioeconomic and political issues on pension fund par-ticipants and nonparticipants
Wagner (1986) argues that a combination of factors such as uncertainty, dynamic interactions among many actors, subsequent events, and complex interdependencies among system variables makes it diffi cult to analyze the
Active
Plan’s maturity
Expected population aging of the plan Aging ratio
Maintained benefits ratio
Total participants
Aging index Retirement ratio
Disability ratio
Cessation Credibility ratio
Adhesions
Mortality decrements
FIGURE 6.5 Population dynamics—stock and fl ow diagram
Trang 14Dynamic Asset and Liability Management ◾ 141
problem To cope with the complexity of pension systems, one can use the combination of many simulation approaches like agent-based models, sys-tem dynamics, and discrete event simulation (econometric model) Th ey all require a co mbination of many qualitative and quantitative methods and techniques in order to organize and represent information necessary
to control risks and uncertainties
6.6 MULTI-PARADIGM APPROACH TO GET
A DYNAMIC ALM MODEL
Uncertainties sometimes mean risks and their associated probabilities of occurrence, which must be defi ned in tangible operational terms Many methods and techniques try to fi t a theoretical distribution to observed data and give ways to a d ynamic model to forecast the possible results
by estimators and probabilities A multi-paradigm approach based on a combination of subjective methods and techniques that, by nature, are scenarios st udies inc lude AHP, M acbeth, a nd a pproaches lik e syst em dynamics, ag ent-based mo deling, f uzzy logic, M arkov c hains, M onte Carlo simulations, and Bayesian nets may enhance ALM capability so as
to be dynamically risk oriented
6.6.1 Prospective and Retrospective Scenario Analyses
According to the Centre for Tax Policy and Administration (CTPA, 2001), risk management implies abilities to infl uence or control future events Future studies focus on the context in which the problem under analysis is intro-duced and try to identify events that may frustrate organizational goals
It can be seen as a formal process in which risk factors of a particular context are systematically identifi ed, analyzed, assessed, and prioritized Among o thers, t he process a ims t o en hance t he co mprehension o f t he system’s environment and their interconnections, treat effi ciently uncer-tainties, facilitate information fl ows, a nd integrate ma ny organizational sectors
According t o Ma rshall (2002, p p 78–80), m odels ba sed o n sc enario analysis try to comprehend impacts of events over the organization Th ey basically are stories that describe and determine the combination of risk events (Marshall, 2002, p 78) Th e author refers to multiple and prospec-tive scenarios as a way to cope with uncertainties and market turbulences
In such environments, it is diffi cult to defi ne strategies and it is necessary
to use tools capable of minimizing their eff ects over the organization
© 2010 by Taylor and Francis Group, LLC