Member’s Paper
Rethinking the Funding of Mature
Pension Plans
By Malcolm Hamilton, MSc, FCIA, FSA
Any opinions expressed in this paper are those of the
author and are not necessarily the opinion or position
of the Canadian Institute of Actuaries.
Les opinions exprimées dans cette communication sont
celles de l’auteur et ne sont pas nécessairement les
opinions ou politiques de l’Institut canadien des
actuaires.
Written comments on this paper received at the
Secretariat by August 2007 will be published in the
Proceedings along with the paper.
Les observations écrites sur cette communication
reçues au Secrétariat avant août 2007 seront publiées
dans les Déliberations avec la communication. Un
résumé en français est inclus ci-après.
Month 2007
Document 207XXX
Ce document est disponible en français
© 2007 Canadian Institute of Actuaries
Member’s Paper
April 2007
Rethinking the Funding of Mature Pension Plans
By Malcolm Hamilton, MSc, FCIA, FSA
Abstract
Résumé
This paper examines the funding of mature pension
plans and, in particular, the challenges arising from the
asset/liability mismatch. Funding is treated as an
exercise in stochastic control involving the selection of
a funding target and the development of a set of rules
for adjusting contributions, benefits and/or asset mix to
control funding levels.
Le présent document examine le provisionnement des
régimes de retraite arrivés à maturité et, plus
particulièrement, les défis que pose le non-appariement
des échéances de l’actif et du passif. Le provisionnement
y est traité comme un exercice de contrôle stochastique
qui repose sur la détermination d’un objectif de
provisionnement et l’élaboration d’un ensemble de règles
permettant de rajuster les cotisations, les prestations et/ou
la composition de l’actif afin d’exercer un contrôle sur le
niveau de provisionnement.
Funding targets can be established by government as a
matter of public policy, by plan sponsors pursuing their
financial interests and/or through a collectively
bargained process. Once the target is set the funding
strategy modifies contribution rates, benefit levels
and/or asset mixes to prevent the pension fund from
wandering too far from the target. The success of a
funding strategy is not measured by the proximity of the
funding target to any actuarially calculated amount but
by the success of the strategy in confining the market
value of the pension fund to an appropriate range by
setting contribution rates, benefit levels and/or asset
mixes in acceptable ways.
Les objectifs de provisionnement peuvent être fixés par le
gouvernement dans le cadre de sa politique d’intérêt
public, par les promoteurs de régimes souhaitant atteindre
leurs objectifs financiers ou par le biais d’un processus
négocié par convention collective. Une fois l’objectif
établi, la stratégie de provisionnement consiste à modifier
les taux de cotisation, le niveau des prestations et/ou la
composition de l’actif afin de s’assurer que le niveau de
provisionnement du régime de retraite n’est pas trop en
deçà ou au-delà de l’objectif. La réussite de la stratégie de
provisionnement ne se mesure pas par la proximité de
l’objectif de provisionnement de quelque valeur
actuarielle, mais bien par la mesure dans laquelle la
stratégie parvient à circonscrire la valeur marchande de la
caisse de retraite dans des limites appropriées, en
établissant les taux de cotisation, le niveau des prestations
et/ou la composition de l’actif de façon acceptable.
The paper distinguishes pension plans where benefit
security is a concern from pension plans where it is not.
The paper examines funding strategies for each type of
plan, identifies the essential differences between these
strategies and proposes a framework for the funding of
pension plans in Canada.
The author concludes that, while contribution rate
stability is a worthwhile objective for a funding
strategy, it is not an achievable one. For mature pension
plans with significant equity holdings any viable
funding strategy will force contribution rates to move in
a wide range. Actuarial techniques, such as the
smoothing of assets and/or the selection of amortization
periods, can influence the rapidity with which
contribution rates change but not the range in which
they must ultimately move.
Le document fait une distinction entre les régimes de
retraite pour lesquels la sécurité des prestations est
précaire et les autres régimes. Il examine les stratégies de
provisionnement à l’égard de chaque type de plan,
recense les principales différences entre elles et propose
un cadre de provisionnement pour les régimes de retraite
au Canada.
L’auteur en arrive à la conclusion que, bien que la
stabilité des taux de cotisation soit un objectif valable
dans le cas d’une stratégie de provisionnement, il n’est
pas possible d’y parvenir, car, en ce qui concerne les
régimes de retraite arrivés à maturité qui détiennent un
important portefeuille d’actions, toute stratégie viable de
provisionnement entraînera nécessairement une grande
variation des taux de cotisation. Les techniques
actuarielles, telles que le lissage de l’actif et/ou les
périodes choisies pour l’amortissement, peuvent influer
sur la rapidité avec laquelle les taux de cotisation
varieront, mais non sur l’étendue de leur variation en bout
de ligne.
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April 2007
Rethinking the Funding of Mature Pension Plans
1. OVERVIEW
1.1 Context
Pension plans change as they mature. The retired population grows. The amount flowing into the
pension plan increases at a decreasing rate, then decreases, then turns negative and ultimately
becomes decidedly negative. The pension fund grows more quickly than the covered payroll as
does the risk associated with a particular asset mix. Using the Ontario Teachers’ Pension Plan as
an example, between 1990 and 2006 the ratio of retired to active teachers more than doubled, the
cash flow went from positive to decidedly negative and the pension fund increased from 3 times
the annual payroll of the teaching profession to 10 times the annual payroll of the teaching
profession.
As pension plans mature benefits usually improve – initially because benefits seldom start at the
desired level and later because, in times of abundance, improvements are made simply because
they appear affordable. Plan sponsors mature as well. Pension plans are often started by young,
profitable, growing enterprises. By the time the pension plan matures growth has slowed
(perhaps reversed), profit margins are under pressure and the enterprise is less able to bear risk
than was originally imagined.
Funding and investment policies are founded on beliefs about the way things work. Prominent
among these beliefs are the following:

investing a significant proportion of the pension fund in equities will, in the long run,
increase the rate of return on the pension fund and decrease the cost of the pension plan –
rendering affordable that which might otherwise be unaffordable;

the risk of investing in equities, while significant in the short term, is tolerable in the long
term if properly managed using actuarial techniques; and

the long term cost of a pension plan is a meaningful concept and can be estimated by an
actuary with some precision provided that the plan sponsor/administrator is patient,
steadfast and prepared to endure the inevitable ups and downs of the stock market.
These beliefs served pension plans well in their formative years; first because in a young pension
plan the actuary’s assumptions about future investment returns are more important than how the
pension fund actually performs; and second, because a twenty year bull market made possible a
combination of good benefits and low contribution rates that, in normal times, cannot be
sustained.
Now that the markets are no longer cooperating plan sponsors find themselves in a predicament.
Their pension plans are more expensive than they thought they would be. Actuarial techniques
are not delivering the promised stability. Accountants and investors, suspecting that traditional
financial reporting conceals more than it reveals, are pushing for greater transparency. Many
companies are unable to bear, or prudently run, the risks inherent in their current investment
policies yet they cannot afford to hedge or avoid these risks. In other words, they are painted into
a corner.
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April 2007
Abandoning the stock market in favour of low risk investments is prohibitively expensive when
interest rates are at 40 year lows. Even if riskless investments could be found in sufficient
quantities, the contribution rates needed to support generous pension plans with “safe”
investments can be double today’s already high rates. Given a choice between fluctuating
contribution rates that occasionally become painful and stable contribution rates that are always
painful, plan sponsors, members and plan administrators are opting for the former and hoping for
the best.
As a young actuary, I was taught to set the funding target for a pension plan equal to the present
value of accrued benefits1. The valuation interest rate was the expected long term rate of return
on the pension fund less an unspecified and undisclosed margin for adverse deviation. It was
generally understood that the valuation interest rate was not influenced by bond yields, the latter
being too “short term” no matter how far into the future the bond matured. Changing the
valuation interest rate from one valuation date to the next was discouraged both as a source of
unwelcome volatility and as a tacit admission that the previous valuation interest rate had not
been as “long term” as it should have been. Using different valuation interest rates for different
pension plans on a common date, even plans with similar characteristics, was common practice
and was unavoidable in a world where actuaries inherited clients from predecessors with
differing views.
Since pension liabilities valued at unchanging interest rates were inert and since actuaries
preferred stable contribution rates to volatile ones, actuaries favoured inert asset values. Market
values were conspicuously ill suited to this task; so actuaries developed a variety of smoothing
techniques, each designed to ensure that the actuarial value of assets was disconnected from the
market value of assets just as the actuarial value of liabilities was disconnected from the market
value of bonds. It is as if actuaries believed that smoothed asset values and inert liability
measures were comparable simply because neither bore any resemblance to a market value.
As naïve as these practices now appear, they remain accepted actuarial practice long after they
have ceased to be good actuarial practice.
The failings of traditional actuarial practice revealed themselves in many ways.
1

Failing to increase valuation interest rates when market interest rates were high during
the 1980s contributed to large surpluses in the 1990s, and to the litigation flowing there
from.

Using inconsistent assumptions for different pension plans on a common date caused the
accounting profession to impose its own requirements, thereby facilitating intercompany
comparisons.

Failing to appreciate the importance of securing a pension plan’s wind up liabilities led
regulators to introduce solvency funding requirements that override traditional funding
practice when interest rates are low.

Ignoring market interest rates in the setting of valuation assumptions led many plan
administrators to erroneously conclude that long bonds were risky investments as
compared to the safety of treasury bills, a confusion for which they paid heavily between
1980 and 2000.
Using projected salaries where relevant.
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Finally, the actuary’s alleged ability to deliver stable contribution rates independent of
the investment risk taken by a pension plan emboldened plan sponsors and plan
administrators to take risks that, at least in some instances, they should not have taken.
Asked to choose between the high, stable contribution rates associated with long bonds
and the low, allegedly stable contribution rates associated with equity laden portfolios,
plan sponsors, not surprisingly, chose the latter.
These failings were easily tolerated in a bull market. The consequences – contribution holidays,
low (often negative) pension expenses, large pools of surplus and/or unrecognized gains to pay
for early retirement windows – were widely celebrated in the 1990s but their significance was
less than fully appreciated. Practices that produce large windfalls in good times are often capable
of delivering major disappointments in bad times.
The beliefs and practices that served actuaries well when pension plans were young are ill suited
to a world where mature pension plans wrestle with an uncertain future. Actuaries are too
confident in their ability to stabilize contribution rates by ignoring current events in favour of the
“long term view”. We have been slow to learn that a risk ignored is not a risk avoided and that a
risk concealed is not a risk well managed. Finally, we have been reluctant to acknowledge the
importance of returns during the twenty years following an actuarial valuation and the role that
long term interest rates should play in predicting these returns.
Finally, actuarial practice has been preoccupied with the funding of pension plans that can be
relied upon to continue perpetually as going concerns. The “going concern” approach provides
useful insights but it also has limitations when mature pension plans sponsored by struggling
corporations collide with low interest rates and disappointing equity returns. The actuarial
profession must now rethink the funding of pension plans. What is the goal? Is it to provide for
the orderly accumulation of assets in pension plans that are assumed to continue forever as going
concerns? Is it to secure the pensions promised to plan members when pension plans are wound
up by insolvent corporations? Or should we try to do both, with one emphasised for some plans
at some times and the other emphasised for other plans at different times?
1.2 Mature Pension Plans
For the purposes of this paper, a mature pension plan is one that has achieved the stability
associated with steady growth for a long period of time. The composition of the workforce, the
ratio of retired to active members, the ratio of benefits to payroll, the plan provisions – all are
assumed to have reached a steady state. The plan may still be growing, either because the
membership is growing or because salaries are increasing, but the population is growing slowly,
if at all, while salaries are growing steadily. Any recurring plan improvements (e.g., ad hoc
inflation adjustments or negotiated increases in flat benefits) are assumed to be regular and
pursuant to a long standing practice.
In practice one does not find pension plans that grow steadily and without incident for long
periods of time. Still, mature pension plans are worth studying for several reasons.

As pension plans age they exhibit many of the characteristics of the mature pension plan;
for example they have large pension funds, negative cash flow, a heightened exposure to
investment risk, etc.

Funding practices that do not work for pension plans that grow at a constant rate are
unlikely to work for pension plans that grow sporadically.
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Mature pension plans are easier to analyze than pension plans growing at ever-changing
rates. The strategic alternatives stand out against an unchanging backdrop.
1.3 Actuarial Funding Methods and Intergenerational Equity
Assume for the moment that the rate at which payrolls2, pension liabilities and cash flows grow
in a mature pension plan is g and that the rate of return on the pension fund is R where R is
known and stable. Usually R > g and the existence of a pension fund reduces the contribution
rate required to support the pension plan. Specifically
 Rg 
C  PGR  FUND x 

 1 g 
(1.1)
where
C
is the sustainable contribution rate expressed as a multiple of payroll3
PGR
is the pay-as-you-go contribution rate, i.e. the ratio of pension benefits to payroll,
expressed as a multiple of payroll3
FUND
is the market value of the pension fund expressed as a multiple of payroll.
A larger contribution rate causes the pension fund to grow more quickly than the pension plan’s
obligations. A smaller contribution rate causes the pension fund to grow less quickly than the
pension plan’s obligations. With the passage of time there are three possibilities: the pension
fund can decrease without limit, remain at its current level, or increase without limit. The only
contribution rate that will prevent the pension fund from collapsing or accumulating unlimited
wealth is the one identified in (1.1).
Equation (1.1) establishes a relationship between C , FUND, PGR, R and g. For defined benefit
pension plans, PGR, R and g are usually treated as exogenous variables dictated by plan design,
investment policy, demography and economic conditions. Equation (1.1) then demonstrates that
for any asset value, FUND, there is a sustainable contribution rate, C , that will keep the
pension fund at the same level (as a multiple of payroll). Alternatively, by rearranging the
variables
 1 g 
FUND =  PGR  C  

 Rg 
(1.2)
it is clear that for any contribution rate, C , there is an asset value, FUND, capable of
perpetually sustaining this contribution rate.
In practice, interest rates, inflation rates, rates of return on investment and population growth
rates will change frequently and sometimes dramatically. Still, if terms such as “long term cost”
and “long term rate of return” have any meaning it is in the context of a long term equilibrium
where parameters settle into their expected values. Equations (1.1) and (1.2) capture the
relationship between the variables in this hypothetical equilibrium state.
2
3
In this paper, payroll means the aggregate pensionable earnings of active plan members.
Contributions and benefits are assumed to be paid at the end of the year.
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Traditional actuarial methods identify contribution rates and funding levels that are in some
sense intergenerationally just. For example, the entry age normal actuarial cost method identifies
a contribution rate, NC  R  , that is fair to those who enter the plan in a particular year. If this
cohort’s assets are segregated and if the pension fund earns a rate of return equal to R each year,
a contribution rate equal to NC  R  will support the cohort’s benefits. The cohort will not
subsidize, nor will it be subsidized by, other cohorts.
The use of traditional actuarial methods, particularly in the formative years of a pension plan,
ensures that the early generations do not deliberately burden those who follow. If, as was the
case for the Canada Pension Plan, contribution rates in the early years deliberately confer a
windfall on the first generation, the subsequent adoption of actuarial funding techniques cannot
undo the windfall already enjoyed. If one generation receives a windfall the cost of that windfall
can, at best, be spread evenly over future generations by setting the lowest contribution rate that
can be sustained indefinitely, which is essentially what the 1996 Canada Pension Plan reforms
attempted to do.
Intergenerational equity is more difficult to define and more difficult to achieve in a world with
uncertain investment returns. If intergenerational equity means that each generation supports
itself ex post, i.e. no money flows from one generation or cohort to another, then defined
contribution pension plans become the design of choice. Each cohort is self supporting but there
are large intergenerational differences in contribution rates and/or benefits as each generation
must live within the confines of its own investment experience.
If intergenerational equity means that different generations experience identical or similar
outcomes, i.e., that contribution rates and benefits change little with the passage of time, then
defined benefit plans, which attempt to fix benefits and stabilize contribution rates through large
equity-enhancing intergenerational transfers, appear to be the way to go. Unfortunately, while
defined benefit pension plans can deliver more equal outcomes than defined contribution pension
plans, in a world with changing interest rates and pension fund returns that deviate materially
from the expected levels over long periods (i.e. decades, if not longer), the defined benefit
pension plan can deliver, at best, ex ante intergenerational equity. A well governed pension plan
can do everything possible to ensure that future generations are treated fairly (ex ante equity) but
will not be able to deliver similar outcomes to different generations (ex post equity) because
unforeseeable experience fluctuations must be countered by changes to contribution rates and/or
benefit levels that will be kind to some generations and unkind to others.
While traditional actuarial practice attempts to equitably allocate contribution rates to successive
generations of plan participants, it makes no comparable attempt to equitably allocate risk among
generations. By building the equity risk premium into the valuation assumptions, albeit reduced
by some poorly defined margin for adverse deviation, actuaries allow the first generation of plan
participants to enjoy4 the equity risk premia that are expected to be earned in the future as
compensation for risks borne by future generations. Just as pay-as-you-go funding relies on
future generations to bear much of the cost of the first generation’s benefits, actuarial cost
methods that anticipate equity risk premia rely on future generations to bear much of the
investment risk associated with the first generation’s benefits. The windfall enjoyed by the first
4
As higher compensation (if the employer underestimates the true cost of the pension plan in setting employee
compensation) and/or as reduced contribution rates in a cost shared plan.
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generation, once enjoyed, cannot be recovered and the adoption of different practices at a latter
date can never fully restore intergenerational equity. The best one can hope for is an equitable
future sharing of the burden that has become the pension plan’s legacy.
1.4 Addressing Gains and Losses
There are three options for addressing investment gains and losses.
1. Ignore what has happened in the belief that future gains and losses will undo past losses
and gains.
2. Regularly adapt to the pension plan’s new reality by using (1.1) to recalculate the
sustainable contribution rate, C , based on the new funding level and future expected
returns (in essence, the Canada Pension Plan’s approach).
3. Set a contribution rate that gradually reverses any unexpected gains or losses and
eventually returns the pension fund to its intended level (the approach mandated for most
pension plans).
As will be demonstrated later, the first approach does not work. When ignored, gains and losses
grow at the rate of return on the pension fund and eventually overwhelm the pension plan.
The second approach is the weakest viable option for addressing gains and losses. If the value of
the assets in the pension fund at time t (as a multiple of payroll) is At and the funding target is
FT , then
 Rg 
Ct 1  PGR  
 At
 1 g 
 Rg 
 TCR  
  At  FT 
 1 g 
where TCR, the target contribution rate, equals
 Rg 
PGR  
 FT
 1 g 
This, of and by itself, does not reverse the surplus or deficit over time. It spreads the contribution
impact over all future generations and, by so doing, attempts to stabilize the funding position at
its new level without returning it to its former level.
The third approach tries to return the pension fund to some target level, FT , by setting the
contribution rate equal to (say)
Ct 1  TCR    At  FT 
where  dictates the vigour with which deviations from the funding target are addressed. If the
Rg
funding technique is to succeed,  must exceed 1  g otherwise there is no reason to expect the
funding level to move towards the target.
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1.5 Funding Strategies
For the purposes of this paper a funding strategy consists of a funding target, FT , a target
contribution rate, TCR, an assumed rate of return on the pension fund i (which may be the
expected rate of return on the pension fund or something smaller) and a set of rules for
modifying the contribution rate when, due to good or bad experience, the value of the pension
fund drifts away from its target level. FT , TCR and i are logically connected by the equation
 1 g 
FT   PGR  TCR  

ig 
(1.3)
If the target contribution rate is set equal to NC  i  (the normal cost using an actuarial cost
method and an interest rate equal to i ) then the funding target calculated from (1.3) will equal
the actuarial liability. Thus, the funding strategies examined in this paper admit, as a special
case, the funding targets preferred by Canadian actuaries. Other targets, such as targets based on
a pension plan’s wind up liabilities, are equally admissible.
For the purposes of this paper a funding strategy is viewed as an exercise in stochastic
control. The objective is to control the funding level of a pension plan by setting and adjusting
contribution rates within tolerable limits to confine the value of the pension fund’s assets to an
acceptable range. One cannot decide actuarially whether the funding target should be zero, the
entry age normal actuarial liability or 110% of a pension plan’s wind up liability. This decision
must be made by government as a matter of public policy, by plan sponsors pursuing their own
interests or through a collectively bargained process.
The funding target is an element of the control mechanism. As such, it is logically and
numerically distinct from the actuarial liability calculated for financial disclosure and
accounting purposes. For example, suppose the riskless interest rate is 5% and the expected rate
of return on the pension fund is 7%. Suppose further that the actuarial liability calculated using
the Accrued Benefit Actuarial Cost Method is $10 million using a 5% interest rate and $7 million
using a 7% interest rate. The plan sponsor should disclose a pension liability equal to $10 million
but there is no harm in setting the funding target equal to $7 million5. The difference, $3 million,
is a measure of the liability that is to be discharged by the future bearing of investment risk (i.e.
the investment risks that must be borne to increase the rate of return from 5% to 7%). By adding
equities to the mix the plan sponsor does not change the pension liability; the plan sponsor
changes how the economic burden represented by this liability will be borne. By increasing the
portion of the pension fund invested in equities the plan sponsor reduces the expected level of
future contributions. In exchange, the plan sponsor must live with contribution rates that are
unpredictable and that move in a wide range.
The test of a funding target is not whether it corresponds to the fair value of the accrued pension
obligations or to any other actuarially determined present value. The test of the funding target,
and the test of every other element of a funding strategy, is whether the strategy achieves
the funding objectives, i.e. do funding levels and contribution rates behave in an acceptable
way?
5
Setting aside, for the moment, concerns about benefit security.
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While it is not common to do so, both asset mix and benefits can be used to manage funding
levels either alone or in conjunction with contribution rates. A funding deficiency can be
addressed by increasing contribution rates, increasing the percentage of the pension fund
invested in equities (to boost expected returns recognizing that, where benefit security is a
concern, this might not be prudent) and/or by reducing benefits6.
If the asset mix and benefits are elements of the funding strategy, equation (1.1) becomes
 r  g  
TCR  TBR  FT 


 1 g 1 g 
(1.4)
where
TCR is the target contribution rate as a multiple of payroll,
TBR is the target benefit payout as a multiple of payroll,
FT
is the funding target as a multiple of payroll,

is the target portion of the pension fund invested in equities,
r
is the riskless interest rate, and

is the equity risk premium.
Equation (1.4) links the target levels for benefits, contributions, asset mix and the funding level.
When the funding level drifts away from the target, contribution rates, benefits and/or the
percentage of the pension fund invested in equities can be adjusted to push it back.
As devices for controlling the funding level of a pension plan, contribution rates and benefit
levels are natural substitutes. Both influence the funding level by acting on the cash flow. In the
absence of legal constraints, anything that can be accomplished with one can be accomplished
with the other.
Funding strategies based on asset mix should be viewed as a complement to funding strategies
based on contribution rates and/or benefit levels, not as a substitute for these strategies. The
impact that contribution rates have on funding levels is independent of the size of the pension
fund. The impact that asset mix has on funding levels is proportional to the size of the pension
fund. This means that asset mix is more influential in mature pension plans than in immature
ones, and more influential when a pension plan is overfunded than when it is underfunded.
In this paper asset mix is adjusted to better manage the funding position of a pension plan, not to
improve the investment performance of the pension fund relative to some benchmark, i.e. asset
mix is used as an element of funding policy not as an element of investment policy. Of course,
nothing prevents a pension plan from using asset mix for both purposes at the same time.
1.6 Funding on a Going Concern Basis
Canadian actuaries have long acknowledged two funding objectives.

First, to accumulate assets in a rational, systematic and orderly way for the purpose of
paying benefits.
In which case the pension plan might more accurately be described as a “managed benefit” plan, not a defined
benefit plan.
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Second, to better secure the benefits promised to plan members.
Judging from actuarial practice, the first objective was considered more important than the
second. Actuarial standards were developed for pension plans that continue perpetually as going
concerns. The wind up contingency was ignored7 and benefit security, which is only an issue
when pension plans are wound up by insolvent plan sponsors, was assigned a secondary role.
Benefit security might properly be described as a consequence of actuarial funding practice
not as an objective. When funds are set aside in a systematic way and accumulate in a trust
fund, benefits are unavoidably more secure than they otherwise would have been. However, if
the objective is to secure the benefits payable upon plan wind up, actuaries should attach more
importance to ensuring that pension assets exceed wind up liabilities than has traditionally been
the case.
This subsection addresses the funding of pension plans where benefit security is not a
concern either because the pension plan can be relied upon to continue for long periods as
a going concern or, alternatively, because the sponsor of the pension plan (or some external
agent) can be relied upon to make good any deficiency if and when the pension plan winds
up. In practice few pension plans satisfy these criteria – largely pension plans sponsored by
governments, guaranteed by governments, or sponsored by regulated monopolies providing
essential services. Subsection 1.7 addresses the funding of pension plans where benefit security
is a concern.
Setting a Going Concern Funding Target
From the plan sponsor’s perspective, choosing a funding target and deciding how to invest the
pension fund are financial decisions. If the plan sponsor contributes an additional dollar to a
pension fund which earns a rate of return equal to R on the pension fund’s incremental
investments and if the incremental investment returns are used to reduce the plan sponsor’s
future contributions, the plan sponsor realizes an after tax rate of return equal to R on the
additional dollar contributed to the pension fund. If this is viewed as an attractive after-tax rate
of return after adjusting for risk, the sponsor should increase the funding level8. If, on the other
hand, R is not an attractive after tax rate of return after adjusting for risk, the sponsor should
fund on a pay-as-you-go basis.
In cost shared pension plans9 the issues are somewhat different. An employer can view the
selection of a funding target as an investment decision because the employer treats contributions
as investments (not as expenses) for accounting purposes and because the employer will be
around to receive a return on its investment. The same can be said of plan members collectively
but not of plan members individually. A decision to fund conservatively may be a wise
investment for plan members as a whole but for the cohorts that make the investment knowing
that, by so doing, they will lower the contribution rate for future cohorts but not necessarily for
themselves, the investment loses much of its allure.
7
Other than in the solvency valuations required by regulation since the 1980s and received without enthusiasm by
the profession.
8
Provided, of course, that the sponsor is confident that the additional funding will not produce stranded surplus.
9
In a cost shared pension plan, employees are both contributors and beneficiaries. The term “sponsor” should be
construed as including employees in their capacity as risk bearing contributors.
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April 2007
The target contribution rate TCR  is tied to the funding target  FT  and the asset mix by the
relationship10
 Rg 
TCR  PGR  FT 

 1 g 
(1.5)
where R is the expected rate of return on the pension fund. While it is customary to view the
asset mix as an exogenous variable, for plans that can be relied upon to continue as going
concerns it is sometimes useful to think about the appropriate funding level for each asset class.
Instead of deciding what proportion of a pension fund should be invested in equities   and
then asking how big the pension fund should be  FT  , ask how big the equity fund  FT 
should be and how big the bond fund
 1    FT  should be.
Equation (1.5) then becomes
rg
rg 
TCR  PGR  1    FT 
   FT 

 1 g 
 1 g 
 Bonds  r  g   equities  r    g 
 PGR  




 payroll  1  g   payroll  1  g 
(1.6)
When real interest rates are low, it is difficult to justify holding bonds in the fund of a pension
plan that can be relied upon to continue as a going concern. With real interest rates currently
around 1.5%, any combination of population growth and real salary growth exceeding 1.5% will
cause g to exceed r , in which case increasing the amount invested in bonds will increase the
target contribution rate. Consequently, when real interest rates are low it makes sense to reduce
the funding target and to cut back the portion of the pension fund invested in bonds. Halving the
funding target and reducing the percentage of the pension fund invested in bonds from 50% to
0% will produce lower contribution rates and similar levels of risk while tying up only one-half
of the capital11. Of course in pension plans where benefit security upon wind up is a concern it
would be irresponsible to reduce funding levels, thereby exposing plan members to a significant
loss of benefits upon wind up, simply because it was not economically advantageous to
contribute.
Evaluating Funding Strategies
Sections 2, 3 and 4 use a simple mathematical model to examine going concern funding
strategies. The model looks at a mature public sector pension plan (as these are arguably the only
plans for which benefit security is not an issue) with the following features.

Pensions accrue over 30 years and are paid over 30 years.

Pensions are 50% of final earnings.
For the remainder of this section we will assume, for convenience, that benefits are fixed, hence TBR  PGR.
In a world with changing interest rates (variable r ) and/or unpredictable rates of growth (variable g ), one cannot
be sure that holding bonds will continue to be disadvantageous and this type of strategy would clearly need to be
moderated.
10
11
12
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
April 2007
Pensions are 100% CPI indexed.
To simplify the analysis, pension benefits are fixed on the understanding that one can always
shift some or all of the risks borne by contributors to beneficiaries if the “deal” is structured
appropriately.
The actuarial model is the simplest imaginable. Prices increase by 2.5% per annum. Wages
increase by 3.5% per annum. The workforce grows by 1% per annum. The riskless interest rate is
4.75% and never changes. The equity risk premium is 4%. Equity returns follow a lognormal
distribution with an 18% standard deviation. The task is to devise control mechanisms that work
effectively in this environment. If it is difficult to manage the funding position of a
theoretical pension plan in a simple, stable, well-understood environment then it will be
even more difficult to manage the funding position of a real pension plan in an
environment that is poorly understood and ever changing.
The model ignores interest rate fluctuations because this greatly simplifies the analysis and
because the risks associated with interest rate fluctuations can either be hedged (as they relate to
the accrued benefits of a pension plan) or they are of little consequence (as they relate to the cost
of benefits to be earned in the future – costs which can, and arguably should, be countered by
future adjustments to other compensation elements).
How Long is the “Long Term”?
By observing that

the time-weighted average rate of return on a pension fund will converge to some value
in the very long term, and

pension plans are long term undertakings with obligations that extend more than 70 years
into the future
many actuaries and many plan sponsors have concluded that short term experience fluctuations
are of little consequence. This belief takes many forms.

Equities, while volatile in the short term, are viewed as safe in the long term.

The “long term” cost of a pension plan is assumed to be both stable and predictable.

Techniques that stabilize contribution rates in the short term by ignoring short term
fluctuations (e.g., smoothing, the opportunistic selection of filing dates, maintaining
stabilization reserves, establishing provisions for adverse deviation that can be released in
hard times, ignoring market interest rates in the setting of actuarial assumptions) are
justified by reference to the advantages of ignoring “short term” market fluctuations.
These beliefs become less tenable as pension plans mature. As will be demonstrated in section
3.2, in a mature pension plan the rate of return earned on a pension fund in year t becomes
progressively less important as t increases12. As a rough guideline,

12
13
each year, the rate of return is 2% to 3% less important than the prior year’s rate of
return13,
While in a young pension plan with a positive cash flow, the importance of future returns increases as
Using an “open group” model.
13
t increases.
Member’s Paper
April 2007

after 20 to 30 years the importance of a year is one half of the importance of the first
year, and

the returns in the first 20 to 30 years are as important as the returns in all of the following
years.
A mature pension plan might continue forever as a going concern but for planning purposes its
investment horizon should be viewed as 20 to 30 years. This means, for pension plans with a
significant commitment to equities:

if the next 20 years are particularly good or particularly bad it is unlikely that
subsequent experience will reverse the gains or losses no matter how long one waits
for this to happen; and

since pension investment performance is not predictable over 20 to 30 year periods
(as is obvious from a cursory examination of the last 50 years) the long term cost of
a pension plan is neither stable nor predictable.
The model’s behaviour is consistent with these insights. Fixing the contribution rate at the
target level, or at any other level, ceases to be a viable strategy as soon as returns become
random. Seventy percent of the trials end in ruin while 30% accumulate unmanageable
surplus14. There is very little difference between the time weighted average rates of return in
trials with runaway deficits and the time weighted average rates of return in trials with runaway
surpluses. In many instances, a trial with a runaway surplus will have a lower time weighted
average rate of return than a trial with a runaway deficit. The average return is not as important
to the outcome as is the timing of the good and bad years. Trials that have a run of good
experience early on will often accumulate unmanageable surpluses while trials with a run of bad
experience early on will often accumulate unmanageable deficits because the later years are less
important than the early years.
Changing funding targets and/or the target contribution rates can change the outcome, but not in
a way that produces a viable funding strategy. If one introduces margins for adverse deviation,
more trials end with runaway surpluses and fewer trials end with runaway deficits, but the
probability of a lengthy trial producing a pension fund anywhere near the target level remains
essentially zero. Unless the funding mechanism addresses both surpluses and deficits with
sufficient vigour to confine the funding level to an appropriate range, the funding position
of a pension plan with a significant commitment to equities is inherently unstable.
Viable vs. Preferred Funding Strategies
For the purposes of this paper a viable funding strategy is one that, with a high probability over a
long period of time, confines the asset value to a range bounded by zero at the low end and by
the present value of future benefits (calculated for an open group using the riskless interest rate)
at the high end15. The upper and lower bounds are not terribly important as, once the asset value
14
More trials end with large negative balances than large positive balances because the investment risk grows as the
pension fund grows. The probability of a plan with a surplus losing its surplus is higher than the probability of a
pension plan with a deficit losing its deficit.
15
Remember that the “model” is of an open group with steady population growth. If the fund equals the present
value of future benefits at the riskless interest rate then the plan can permanently suspend contributions and hold
riskless investments.
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April 2007
falls outside these bounds, it tends to move farther and farther from the target, eventually falling
outside any reasonable range.
Actuaries have traditionally been more concerned about the lower bound than the upper bound.
Provisions for adverse deviation, contingency reserves, conservative assumptions, asset valuation
methods that average, over time, less than the market value – all of these techniques are required,
encouraged or tolerated. Actuarial techniques that err in the opposite direction are discouraged or
forbidden. Where benefit security is a concern caution is understandable. However for pension
plans that continue forever as going concerns caution leads to overfunding and, eventually, to
better benefits or lower contribution rates. The first is unwelcome if the benefits are as good as
they should be. The second is unwelcome if the goal is intergenerational equity. Unmanageable
surpluses are a lesser problem than unmanageable deficits, but they are a problem nonetheless.
Viable funding strategies must control surpluses as effectively as they control deficits.
Three criteria are used to select preferred funding strategies from among the many viable funding
strategies.
Transparency16 – a strategy is said to be transparent if over long periods of time the average
funding level, contribution rate, benefit level and asset mix are at the target levels. Many
viable strategies gravitate towards an equilibrium state that is not the target state. For
example, if the target contribution rate and the funding target are actuarially determined
using a conservative interest rate (i.e. a rate less than the expected rate of return on the
pension fund) the equilibrium funding level will be above the target funding level and the
equilibrium contribution rate will be below the target contribution rate. The fact that the
equilibrium states and the targets state are different does not prevent the strategy from being
viable but it does make it less than transparent and this can cause problems. For example,
judges will imagine that surpluses are unexpected windfalls, not the unavoidable
consequence of actuarial assumptions that are deliberately conservative.
Short-Term Contribution Rate Stability – contribution rates are said to be stable in the short
term if they do not drift far from the current level over short periods, i.e. if short term
fluctuations are small.
Long-Term Contribution Rate Stability – contribution rates are said to be stable in the long
term if they do not drift far from the expected level over long periods, i.e. if the range in
which contribution rates move is narrow.
Using Contribution Rates to Control Funding Levels
If the asset mix and benefit level are fixed, funding levels can be controlled by increasing
contribution rates to address deficits and decreasing them to address surpluses. The simplest such
mechanism is
Ct 1  TCR   C  t  FT 
“Transparency” may not be the best word to describe this concept but the author has yet to find a better one. Most
people will assume that a successful funding strategy will, in some sense, hit the targets at which it purports to aim.
If the expected value of the funding level and the expected value of the contribution rate in the long term differ
significantly from the target values then, from the perspective of an interested bystander, the targets aren’t really
targets or the method has failed to achieve its goal.
16
15
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Rg
 2.5% 17, the strategy is not viable. If  C exceeds this level by a small amount the
1 g
strategy is viable18 and contribution rates are admirably stable in the short term, but they move in
a very wide range in the long term. As  C increases, contribution rates become less stable in the
short term and more stable in the long term. When  C is around 5%17, the range in which
contribution rates move in the long term is at its narrowest. Increasing  C beyond this point
causes contribution rates to be less stable in both the short and long terms.
If  C 
The optimal value for  C (in the example used in Sections 3 and 4) is somewhere between 2.5%
and 5% depending on whether it is more important for contribution rates to be stable in the short
term or more important for them to be stable in the long term. With  C = 2.5%, contribution
rates are stable in the short term but the reaction to funding imbalances is so weak that the assets
stray far from the target level in the long run, as do contribution rates. With  C = 5% the reaction
to funding imbalances is more vigorous, contribution rates are more volatile in the short term
but, because they are more volatile, the assets remain closer to the target level and the range in
which contribution rates move in the long term is narrowed.
Since short-term instability can be addressed in a number of ways (using the techniques
discussed in subsection 1.9 and in section 5) while long-term instability cannot,  C = 5% looks
like the best choice. This is approximately one-half of the value associated with the 15 year
amortization of going concern deficiencies enshrined in Canadian legislation and approximately
one fifth of the value associated with the 5 year amortization of solvency deficiencies.
Consequently, today’s statutory funding requirements are more onerous than necessary in a low
interest environment for plans that can be relied upon to continue as going concerns19.
Finally, while  C = 5% minimizes the range in which contribution rates move in the long term,
the range is still very wide. The probability of negative contribution rates and the probability of
contribution rates exceeding twice the target level in a particular year are not negligible. Long
term contribution rate stability is a worthwhile objective but it is not one that can be
achieved in a mature pension plan with a significant commitment to equities.
Contribution Rate Limits
For many pension plans the contribution rate has a natural lower bound. It may be zero (if
surplus withdrawals are impossible), the employee contribution rate (if experience gains are not
shared with employees in a contributory pension plan) or the target contribution rate (if the plan
text or some future regulation prohibits contribution holidays). Any lower bound on contribution
rates impairs the control mechanism and increases the likelihood of runaway surpluses.
If the percentage of the pension fund invested in equities is fixed at traditional levels (40%
to 70%), all viable contribution-based funding strategies involve the periodic withdrawal of
17
Using the model assumptions.
Assuming for the moment that contribution rates can be as large or as small (i.e. as negative) as they need to be to
address deficits and surpluses, respectively.
19
If real interest rates were higher, the optimal  C would be higher and the optimal amortization period for
18
surpluses and deficits would be closer to the 15 years dictated by Canadian legislation.
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Member’s Paper
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surplus. Contribution holidays, even when fully taken the minute there is enough surplus to
support them, will not prevent surplus from attaining unmanageable levels the first time there is a
sufficiently good run of equity returns. The propensity to accumulate unmanageable surplus will
be higher where

the asset mix is more heavily weighted to equities, or

employees contribute (unless employee contributions are suspended when the plan is well
funded), or

the plan membership and/or salaries grow slowly.
As regards the upper bound, contribution rates can be capped at any level higher than the
pay-as-you-go contribution rate without undermining the viability of a funding strategy. A
continuing pension fund will gradually recover from any deficiency as long as contributions
exceed benefits and the rate of return on the pension fund exceeds the rate of growth in the
funding target. There is no need to increase the contribution rate above the pay-as-you-go rate.
However, if the contribution rate is held at or just slightly above the pay-as-you-go rate, recovery
from a sizeable funding deficiency will be very slow and contribution rates will remain at the
maximum level for long periods.
Using Asset Mix and Contribution Rates to Control Funding Levels
By increasing the percentage of the pension fund invested in equities when assets are below the
funding target and decreasing it when assets are above the funding target, the pension fund can
be encouraged to move toward the target.
In theory, asset mix can be used as a replacement for contribution rates in a funding strategy.
Contribution rates would then be fixed at the target level and asset mix would be used to control
the funding level. In practice this does not work because asset mix is relatively ineffective in
addressing deficits. Increasing the percentage of the pension fund invested in equities to 100% as
the funding position deteriorates does little to arrest the decline. It helps, but not by enough to
eliminate the need to increase contribution rates. On the other hand, asset mix is very effective
in addressing runaway surpluses. As long as the percentage of the pension fund invested in
equities is reduced to zero before assets reach the point where the minimum contribution rate
(usually zero) can be sustained in perpetuity by riskless investments, the surplus will be
manageable.
Where surplus cannot be withdrawn from a pension plan, asset mix becomes an essential
element of funding policy. By adjusting both contribution rates and asset mix the plan sponsor
can keep the pension fund in an appropriate range. Contribution rate increases are particularly
important when the funding level is low, as asset mix is ineffective when the amounts invested
are small. Reducing the percentage of the pension fund invested in equities when the funding
level is high is also important, as reducing the contribution rate to zero will not always prevent
investment gains on a large and growing pool of assets from creating a stranded surplus.
1.7 Funding on a Wind Up Basis
Most pension plans cannot safely assume that they will continue forever as going concerns.
Wind up is seldom imminent. It is, however, a possibility and there is no guaranty that the
demise of the pension plan will be foreseen well in advance of the event. The fact that wind up is
possible does not mean, of and by itself, that a pension plan should be funded in contemplation
17
Member’s Paper
April 2007
of wind up. If the future of the pension plan is in doubt but the future of the plan sponsor is not,
the pension plan can be funded as a going concern as long as the plan sponsor can be relied upon
to fund any deficit should the plan wind up.
To fund a pension plan on a wind up basis is not to assume that the pension plan will wind
up in the foreseeable future. It is not the antithesis of going concern funding. Funding on a
wind up basis means that, for as long as the pension plan continues as a going concern, the
funding strategy will try to keep the pension plan’s assets above its wind up liabilities.
Funding on a wind up basis differs from funding on a going concern basis in three respects.

First, since the obligations of a pension plan upon wind up differ from the obligations of
the pension plan while it continues as a going concern, the funding target can be
materially different.

Second, since a going concern funding target frequently takes into account future
investment returns in excess of the riskless rate in the belief that the plan sponsor will
bear the requisite risks and, since the party or parties assuming the pension plan’s
obligations upon wind up will not be prepared to bear these risks or will expect to be
compensated for bearing them, the amount needed to settle the plan’s wind up obligations
will often exceed the going concern funding target.

Third, in the absence of concerns about benefit security the optimal going concern
funding strategy will usually be one that reacts slowly to funding imbalances, thereby
allowing the pension fund to meander in a wide range about some target level. Unless the
target level is well above the pension plan’s wind up liabilities, this means that pension
plans will have large wind up deficiencies for long periods of time and that the
probability of a wind up deficiency, and the expected size of the wind up deficiency, will
be large. A wind up funding strategy must react more forcefully to wind up
deficiencies than a going concern funding strategy reacts to going concern
deficiencies.
Securing Benefits
When a pension plan winds up, benefits are lost for three distinct reasons:
1. Experience losses, in particular disappointing equity returns or liability increases caused
by falling interest rates, can leave the pension plan with less money than it needs to
discharge its obligations.
2. The benefits to which a member is entitled upon plan wind up may be less than the
benefits the member would have received for past service had the plan continued as a
going concern.
3. Recent improvements to the pension plan may not have been fully funded.
The first type of loss – losses associated with poor experience – is the only one that funding
strategies can address.
The benefits to which a pension plan is committed upon wind up may not be as good as the
benefits to which it is committed as a going concern. This is not a funding problem. If the wind
up benefits are less than the going concern benefits, as can happen when pensions are based on
final average earnings, setting money aside to fund the going concern benefit will not secure the
18
Member’s Paper
April 2007
going concern benefit. It simply creates a surplus upon wind up with no guarantee that this
surplus will be used to replace the lost benefits.
If the funding of benefit improvements in arrears is a problem this problem must be addressed
directly, either by preventing plans from improving benefits when they are poorly funded or by
requiring the immediate funding of such improvements or by attaching lower priority, upon wind
up, to paying benefits attributable to recent improvements.
Conflicting Interests
An effective wind up funding strategy should be viable, transparent and produce contributions
that are tolerably volatile in both the short and long term. It should also satisfy two additional
criteria;

First, the expected wind up deficiency should be small.

Second, the expected wind up surplus should not be so large as to be unacceptable to plan
sponsors.
These additional criteria conflict in an obvious way. The wind up funding deficiency is a
measure of the plan members’ exposure to benefit loss upon plan wind up. The wind up funding
surplus is a measure of the plan sponsor’s exposure to surplus forfeiture if the plan winds up in
whole or in part, if the plan is transferred to a successor or if a labour dispute is settled through
arbitration.
As a matter of public policy, it is unwise to have the interests of plan members conflict with
the interests of plan sponsors as they relate to the funding of pension plans. If there is a
conflict, making benefits safer for plan members unavoidably makes pension plans less attractive
to plan sponsors. This conflict complicates the governance of pension plans. Funding decisions
cannot be left entirely to the plan sponsor, as it is in the interest of the plan sponsor to leave
benefits less than fully protected thereby reducing the sponsor’s exposure to surplus forfeiture.
Funding decisions cannot be left entirely to plan members, or to fiduciaries representing the
interests of plan members, as it is in the interest of plan members to choose the highest funding
target that can be endured by the plan sponsor, thereby better securing their benefits and creating
opportunities for future surplus windfalls. Finally, it is hard to see how a board or agency can
successfully balance the conflicting interests of the two parties without alienating one or both.
For these reasons, the author favours a governance structure where funding decisions, including
the judgements made by the actuary in performing his or her work, are made by or for the benefit
of the plan sponsor20 but are appropriately constrained by regulations that ensure that these
decisions do not unreasonably compromise benefit security. Unfortunately the current funding
rules in Canada, as interpreted by the courts, make it exceedingly difficult to find funding
practices that simultaneously protect members from benefit loss and sponsors from surplus
forfeiture.
1.8 Improving the Regulation of Pension Funding
If the primary goal of pension standards legislation is to secure benefits, as is becoming apparent
with the passage of time, the efficacy of a set of funding regulations should first be measured by
20
Including contributors and/or beneficiaries who bear risk.
19
Member’s Paper
April 2007
the expected wind up funding deficiency. The regulator/government21 must decide what
constitutes an acceptable benefit loss upon wind up recognizing that if the number is too large,
public confidence in the pension system will erode while, if the number is too small, plan
sponsors will abandon their plans. The regulator should impose, from among the many funding
standards that produce an acceptable exposure to benefit loss, the one that is least offensive to
plan sponsors. There are a number of criteria that might be used to make this choice. Simplicity
should be preferred to complexity; transparency to opaqueness; stability to volatility. Finally, the
standard should be minimally intrusive, allowing plan sponsors the greatest possible latitude in
choosing funding and investment practices to their liking.
The funding standard imposed by regulation should work for pension plans that follow high risk
investment strategies as well as for pension plans that follow low risk investment strategies. It
should work for pension plans that cut back equities as their funding positions deteriorate (in the
belief that a poorly funded pension plan is less able to bear risk) and for pension plans that
increase their reliance on equities as their funding positions deteriorate (in the hope that a
recovering stock market will painlessly solve their funding problems). The challenge is to find a
funding standard that accomplishes these goals without being unduly complicated and without a
companion set of restrictions on the investment practices of pension plans.
It is not unreasonable for a credit worthy plan sponsor to expect relief from stringent wind up
funding standards. As long as the plan sponsor remains healthy the plan members are not at risk.
Moreover, making large contributions to address funding deficiencies every time the stock
market performs poorly guarantees that, when the stock market performs well, the pension plan
will have a large surplus all or part of which may be forfeit or stranded. Since pension regulators
are not accustomed to evaluating the credit worthiness of plan sponsors and since actuaries are
both inexpert and conflicted in making this assessment, the easiest way to take the credit
worthiness of a plan sponsor into account is to allow actuaries to treat qualifying letters of credit,
up to some prescribed limit, as an asset of the pension plan for funding purposes. Decisions
about creditworthiness would then rest with financial institutions who are competent to make
these decisions and these financial institutions, not plan members, would bear the risk of sponsor
insolvency and would be compensated for so doing.
Options for Enhancing Benefit Security
There are many ways to enhance benefit security.
Shortening the Amortization Periods for Deficits – Shortening the period over which deficits
are amortized improves benefit security in two ways: it reduces the duration and size of
deficiencies when they arise and it increases the probability that the plan will have a surplus
when it is wound up.
Increasing the Funding Target – the higher the funding target relative to a pension plan’s
wind up liabilities the lower the expected benefit loss upon wind up. In this respect, how the
target is situated relative to the pension plan’s wind up liabilities is the only relevant
consideration. The going concern liabilities are irrelevant.
21
In theory, this task could be left to plan members and plan sponsors but, given their conflicting interests and the
disparate interests of active and retired plan members, the author believes that common ground will be hard to find.
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Member’s Paper
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Calculating the Target Contribution Rate – the lower the interest rate used to calculate the
target contribution rate the lower the expected loss on wind up. The target contribution rate is
calculated as follows.
 1 i 
TCRt 1  PGRt 1  FTt 1  
 FTt
 1 g 
ig 
 PGR  
 FT if FTt 1  FTt  FT and PGRt 1  PGR
 1 g 
(1.7)
The interest rate used in this calculation need not be the interest rate used to calculate
the funding target. For example, FT could be the pension plan’s wind up liability
calculated using the riskless interest rate r , while the target contribution rate is calculated
with i  R, thereby fully anticipating the expected return on the pension fund for the year.
Lengthening the Amortization Period for Surplus – if contributions are cut back less abruptly
when the pension fund exceeds the funding target, surpluses will be larger and more
common. By inference, deficits will be smaller and less common. The natural way to
lengthen the amortization period would be to choose the same period as is used for deficits
or, alternatively, to prohibit any reduction in the contribution rate until surplus exceeds a
prescribed threshold, say 10% of the wind up liability.
Any of these devices can be used to lower the expected loss on wind up to the desired level.
None is attractive to plan sponsors as each increases the sponsor’s exposure to surplus
forfeiture. However, some techniques may be more attractive than others.
The Current System
Canada currently has a bifurcated approach to funding regulation. Plan sponsors are required to
calculate both a going concern funding target and a wind up funding target. The result is a
complicated, ineffective jumble of regulations with no obvious rationale.
In general

the funding target is the greater of the going concern liability and the wind up (solvency)
liability, the former largely unregulated and the latter largely prescribed;

wind up deficiencies are amortized over 5 years and going concern deficiencies are
amortized over 15 years. The two are coordinated by treating the present value of going
concern amortization payments during the 5 years following a valuation as an asset for
solvency valuation purposes;

the going concern normal cost is used as the target contribution rate. This means that
there is no logical link between the target contribution rate and the funding target when a
pension plan’s wind up liabilities exceed its going concern liabilities; and

any surplus can be used to reduce the required contribution rate.
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Member’s Paper
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In Ontario, assets and interest rates can be smoothed. Federally regulated pension plans can
smooth assets but not interest rates22. In Quebec, smoothing is forbidden22. All jurisdictions
require triennial filings but permit opportunistic filings unless the plan was badly funded at the
time of the last filing. With the exception of Quebec all jurisdictions permit poorly funded
pension plans to improve benefits and to fund the improvements over 5 years. The funding rules
ignore the financial condition of the plan sponsor and the investment practices of the pension
plan with one exception: a greater commitment to equities can be used to justify lower funding
levels on a going concern basis.
An Alternative
In the interest of simplicity and effectiveness, the author favours the following changes to
funding standards:

the elimination of the going concern funding requirements23,

the establishment of a funding target equal to the pension plan’s wind up liabilities24,

the establishment of a target contribution rate using (1.7) with i  r ,

special contributions equal to 10% of any wind up funding deficiency or, alternatively,
equal to the amount needed to amortize the deficiency over 15 years, and

no restrictions on the use of surplus (on a wind up basis) to reduce the contributions
otherwise required.
If these measures do not lower the expected benefit loss on wind up to an acceptable level
pension plans could be barred from using surplus up to some prescribed threshold, say 10% of
the wind up liability, to reduce their required contributions, as Quebec is about to do.
A pension plan would be permitted to treat the amount payable upon the exercise of a qualifying
letter of credit, up to some prescribed limit, as an asset of the pension plan in exchange for the
plan sponsor contributing, in addition to the amounts otherwise required,

the cost of acquiring the letter of credit to the extent that this cost is borne by the pension
fund, and

interest, at the riskless rate, on the amount of the letter.
Pension plans sponsored by governments25, agencies whose debts26 are guaranteed by
governments and other prescribed institutions would be exempt from the regulatory requirements
22
For solvency valuations.
Plan sponsors would be able to fund on a going concern basis if they chose to do so, provided that contributions
exceed the minimum dictated by regulation (on a wind up basis).
24
If the wind up liability is to be a meaningful concept, pension standards legislation will need to create new options
for pension plans, in particular indexed pension plans, to settle their obligations upon wind up. In the absence of a
viable annuity market, in particular for indexed pensions, this might mean
 establishing a government agency to assume the obligations of wound up pension plans in exchange for a
payment equal to the commuted value of the pensions on a prescribed basis, or
 requiring members to accept lump sums equal to the commuted values of their pensions or, if they prefer,
whatever annuity can be purchased with these lump sums recognizing that the annuity amount and/or the
level of indexing may be less than the plan provides.
25
Excluding individual municipalities.
26
Including unfunded pension obligations.
23
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April 2007
and would be free to choose funding strategies appropriate to their circumstances. Alternatively,
a separate set of regulations might be developed for jointly sponsored pension plans (as that term
is defined in the Pension Benefits Act of Ontario) and for multiemployer pension plans –
regulations that deemphasise the importance of benefit security and that emphasize the
importance of funding pension plans in a way that is intergenerationally fair, at least ex ante27.
There are many advantages to this regulatory approach.

It is simple when compared to the current approach and to most of the alternatives.

The target contribution rate is logically tied to the funding target.

Using the riskless interest rate to calculate the target contribution rate (as opposed to
using the expected rate of return on the pension fund) accomplishes three things:
o first, by ignoring the equity risk premium it introduces a margin for adverse deviation
into the calculation of the contribution rate – a margin that increases with the
percentage of the pension fund invested in equities;
o second, it does so in a way that relieves the regulator of any responsibility for
estimating the equity risk premium; and
o third, the period over which funding deficiencies must be amortized can be
lengthened (say to 15 years) without reducing benefit security because the target
contribution rate has been increased.

It provides an opportunity for financially strong plan sponsors to use letters of credit to
reduce their pension contributions and their exposures to surplus forfeiture, but to do so
at their own expense in a way that enhances benefit security and does not burden
regulators with difficult decisions.

It exempts pension plans for which benefit security is not an issue from wind up funding
requirements that are, for them, unnecessary and unhelpful.
Finally, this approach does a surprisingly good job of implicitly accommodating different
investment policies.
27
While there are legitimate actuarial reasons for distinguishing public sector pension plans (and more generally,
plans where one can reasonably ignore the possibility of benefit forfeiture upon wind up) from private sector
pension plans, there are other reasons, not of an actuarial nature, to be concerned about such a distinction.

Allowing public sector pension plans to be funded at lower levels and/or to react less vigorously to funding
imbalances may confuse governments and the public about the true costs and risks associated with these
plans.

Separate rules for public sector pension plans desensitize governments to the problems afflicting private
sector pension plans and make it harder to change the rules and regulations governing private sector
pension plans when these rules impose unnecessary hardship.
The first concern is, in the opinion of the author, legitimate but misplaced. It is the public sector accounting
standards, not pension funding rules, that conceal the cost and risk of public sector pension plans and it is the public
sector accounting standards, not the funding rules, that must be changed to solve this problem.
The second concern is an important one. When large public sector pension plans need relief from poorly conceived
regulations they have immediate access to decision makers. When private sector pension plans need similar relief
they are invariably ignored unless public sector pension plans have the same problem.
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April 2007

The expected loss on wind up declines as the percentage of the pension fund invested in
equities drops below the normal range (40% to 60%) and as it rises above it. With
riskless investments, deficits do not arise and benefits are secure. If the pension fund is
fully invested in equities the target contribution rate (which ignores the equity risk
premium) is so conservative that the average funding level eventually moves well above
the target level and benefits remain secure.

As a second test, three different approaches to modifying the asset mix of poorly funded
pension plans were examined:
o increasing the percentage of the pension fund invested in equities as the funding
position deteriorates to combat deficiencies with higher expected returns;
o freezing the asset mix at the target level; and
o decreasing the percentage of the pension fund invested in equities as the funding
position deteriorates.
In each case, the expected wind up deficiency was the same, i.e., as long as the target
contribution rate is based on the riskless interest rate, the higher expected returns associated with
equities compensated for the added risk28.
1.9 Managing Contribution Rates in the Short Term
Actuaries and/or their clients use a variety of techniques to manage contribution rates in the short
term. Examples include
Smoothing
–
recognizing investment gains and
gradually rather than immediately
The Selection of Filing Dates
–
choosing the effective dates as at which
valuation reports will be filed
Provisions for Adverse Deviation
–
establishing explicit or implicit cushions in the
funding target and/or the target contribution rate
and changing these to dampen fluctuations
losses
Actuaries and plan administrators are, subject to any constraints imposed by fiduciary duty, free
to apply these techniques opportunistically – for example by filing valuations that reduce
contribution rates while withholding valuations that increase contribution rates (until a filing is
required by law).
While it is difficult to generalize, most of these techniques do what is expected of them. They
give actuaries and/or plan sponsors some control over contribution rates in the short term and
some ability to predict cash flow in the short to medium term. They do nothing to narrow the
range in which contribution rates and funding levels move in the long term. The techniques are
useful in the sense that they enhance control in the short term with no materially adverse
consequence in the long term. They are also dangerous if plan sponsors, confused by the
28
This conclusion may be specific to the example in Section 6.
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April 2007
fact that they have a measure of control in the short term, imagine the long term risks to be
less than they really are and make foolhardy decisions as a consequence.
Consistency
If a pension plan adopts an unbiased29 method of smoothing assets or decides to file valuations
biannually or triennially and if these practices are consistently followed over long periods, the
impact on financial performance is noticeable but not terribly important. If these techniques are
changed from time to time for reasons that have nothing to do with the immediate impact on
contribution rates, the results are not materially different. However, if the techniques are
employed only when they reduce contribution rates, the average funding level can be altered
materially. Used opportunistically, actuarial techniques become less effective at stabilizing
contribution rates and more effective at reducing funding levels.
The fact that the opportunistic use of filing and smoothing techniques depresses funding levels is
not a concern for pension plans that can be relied upon to continue as going concerns. If the plan
sponsor wants to adopt complicated strategies that reduce funding levels rather than simpler
more transparent strategies that accomplish the same thing, no harm comes to plan members. The
same cannot be said of pension plans where benefit security is a concern. For these plans, the
opportunistic use of actuarial techniques can materially increase the members’ exposure to
benefit loss upon plan wind up.
Since both smoothing and triennial filings serve legitimate purposes, there is little harm in
allowing plan sponsors to use these techniques consistently. To prevent opportunism from
undermining the effectiveness of these techniques, pension plans might be allowed to
change filing frequencies and/or smoothing methods only when the change increases
contribution rates.
Transparency
Pension standards legislation ties contributions to the unfunded liability and to the normal cost
identified in the most recent actuarial valuation. Having acknowledged that a pension plan has a
large funding deficiency, the plan sponsor has no alternative but to immediately increase
contributions to the level dictated by regulation. If actuaries are to manage contribution rates in
the short term they must do so by manipulating either the timing of the filings or the balance
sheets presented therein. As a consequence, the balance sheets are often not what they appear to
be. They are not an attempt to accurately represent the financial position of the pension plan on
the valuation date. They are a means to an end – an artifice constructed for the purpose of
arriving at an acceptable contribution rate.
This would not be a problem if the users of actuarial reports looked only at the suggested
contribution rates. It is a problem if users expect the balance sheets to say something meaningful
about the pension plan’s financial condition.
If the regulations were differently constructed, actuarial techniques for managing contribution
rates could be applied directly to contribution rates rather than indirectly through balance sheets.
For example, suppose pension plan sponsors were permitted
29
Unbiased in the sense that the average smoothed value equals the average market value over long periods.
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Member’s Paper
April 2007

to increase contribution rates in uniform steps starting on a date no later than one year
following the valuation date and ending no later than 5 years following the valuation date
subject to a demonstration that this schedule of contribution rates can reasonably be
expected to reduce the funding deficiency by an acceptable amount over an acceptable
period; and

to establish a funding corridor and to ignore, in the setting of contribution rates, surpluses
or deficits within this corridor.
The gradual phasing-in of contribution rate adjustments eliminates the need for smoothing. The
introduction of a funding corridor eliminates the need for the actuary to manipulate provisions
for adverse deviation to build cushions in good times and release them in bad times. With rules
such as these, actuaries would be able to value assets at market and to remove provisions for
adverse deviation from their balance sheets without denying plan sponsors the control they seek.
26