Glide path ALM: A dynamic allocation
approach to derisking
Authors: Kimberly A. Stockton and Anatoly Shtekhman, CFA
Removing pension plan risk through “derisking” investment
strategies has become a major focus for pension plan sponsors.
Vanguard researchers propose that sponsors can benefit by
incorporating derisking logic directly into their asset-liability
models, thus providing more practical, actionable results.
Changes in pension law and other factors have left
plan sponsors more exposed to pension plan risk. As
a result, many have made “derisking” the foundation
of their investment strategies. This approach involves
reducing risk through asset allocation changes as the
funding ratio improves, with the goal of stabilizing the
portfolio once full funding is achieved, at which point
higher investment returns offer little benefit to the
sponsor. (Overfunding of the plan is not rewarded,
because, except in limited situations, assets can be
used only to fund plan liabilities.)
The issue: Plan sponsors are seeking to reduce
exposure to pension plan risk by incorporating
derisking investment strategies.
The challenge: Asset-liability models, widely used by
plan sponsors, are often based on several static asset
allocations. Yet, derisking approaches suggest that
portfolio allocation should change if the plan’s funding
ratio rises.
Vanguard conclusion: Our glide path ALM approach
incorporates derisking logic directly into the assetliability model. This provides a number of benefits to
plan sponsors.
Asset-liability modeling (ALM) has long been the
preferred tool used by sponsors to assess a plan’s
strategic asset allocation relative to its liability. ALM
studies typically look at a number of static allocations
to forecast the potential risks, returns, and costs
to the plan. Yet a derisking strategy entails making
substantial changes in the portfolio as the plan
moves toward full funding.
Our glide path ALM approach combines traditional
ALM with derisking by incorporating a dynamic
asset allocation. Specifically, we forecast market
and pension metrics over the investment strategy
planning period, with asset allocations changing as
funding level thresholds, or “triggers,” are reached.
This approach creates a more applicable and
actionable result for plan sponsors.
This article uses a case-study approach to explain
our methodology and to illustrate how a typical
pension plan would employ glide path ALM to
derisk. We present our quantitative and qualitative
tools—including a risk-adjusted G-ALM score we
created—for evaluating progress and the likelihood
of success.
Note: This article is adapted from a 2012 Vanguard research paper by the same authors and title; available at http://vanguard.com/glidepathALM.
Vanguard Investment Perspectives > 1
Case-study plan characteristics
Initial funding ratio: 84%.
Initial assets : $4,169.4 million.
Initial liability: $4,938.1 million.
Plan status: Closed.
Liability discount rate: 5.4%.
Normal cost: $75 million.
Liability duration: 12.6 years.
The case study
As with any ALM process, the glide path ALM
begins with a forecast of plan assets, liabilities,
and other metrics. Our asset simulation model,
the Vanguard Capital Markets Model® (VCMM),
employs a regression-based Monte Carlo simulation
approach to generate forward-looking distributions
of expected long-term returns for global equities,
fixed income, and other asset classes. For this study,
we analyzed a closed plan with an 80% equity/
20% fixed income starting allocation1 (see details
in the accompanying box).
Using the asset forecast and plan metrics, we
created a liability-driven investing (LDI) efficient
frontier for our plan. The frontier is based on the
highest expected return for a given level of liability
tracking error over five years.2
Next, to facilitate the derisking process, we
decided on three “phase” portfolios from the
efficient frontier. As shown in Figure 1, we chose
portfolios from across the frontier. Moving from right
to left, the portfolios reduce risk in steps, gradually
decreasing the equity exposure to about one-third of
the portfolio while increasing the bond allocation and
lengthening its duration to achieve greater hedging.
For example, the Phase 1 portfolio here is 45% U.S.
equity, 20% international equity, 20% extendedduration U.S. Treasury bonds, and 15% U.S. longterm bonds. The Phase 3 allocation is 30% U.S.
equity, 5% international equity, 15% extendedduration Treasury bonds, and 50% U.S. long-term
bonds. In practice, specific portfolios should be
chosen on the basis of desired duration hedge
ratios and the plan sponsor’s willingness and ability
to take risk.
Important: The projections or other information generated by the Vanguard Capital Markets Model
regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect
actual investment results, and are not guarantees of future results. VCMM results will vary with each
use and over time. The VCMM projections are based on a statistical analysis of historical data. Future
returns may behave differently from the historical patterns captured in the VCMM. More important,
the VCMM may be underestimating extreme negative scenarios unobserved in the historical period
on which the model estimation is based.
1 Although the typical pension plan asset allocation is closer to 55% equity/45% bonds, we chose this more aggressive starting allocation for the study because it
better illustrates the derisking process.
2 Liability tracking error is measured here as the return volatility relative to liability volatility.
2
> Volume 12
Figure 1.
Case study: Efficient frontier and phase portfolios
a. Efficient frontier for expected return and tracking error
based on VCMM simulations
10%
Current
portfolio Phase 1 Phase 2 Phase 3
9%
Return
b. Allocations: Current portfolio and phase portfolios
selected from efficient frontier
U.S. equity
48%45%30%30%
8%
International equity 32
7%
Aggregate
U.S. bond market 20000
Phase 1
Phase 2
6%
Phase 3
●
Current portfolio
●
●
5%
4%
20
20
5
Extended-duration
Treasury bonds 0
20
20
15
Long-term U.S. bonds 0
15
30
50
Current duration
hedge ratio 6%
44%
56%
64%
3%
1
6
11
16
21%
Liability tracking error
Note: Duration calculation is point-in-time and assumes that the equity duration is 0 year.
Source: Vanguard, from VCMM simulations.
As funding-level thresholds are reached, plans make
the transition to the next phase portfolio, which will
have lower tracking error and a higher liability hedge
ratio. The transitions are driven purely by funding
level, and not by time. Therefore, the year in which
a plan moves to a new phase varies. Starting-phase
portfolios also can vary, depending on the initial
funding status. Sponsors of underfunded plans
could choose to make a large contribution to improve
their status and begin in Phase 2 or even Phase 3.
However, the need for the glide path arises from the
practical reality that large one-time contributions are
not often a viable option for plan sponsors.
Setting the triggers and finding
the glide path
The next step in the glide path ALM process is
determining at what funding levels the plan will
move to a lower-risk allocation. Funding-level
triggers are plan-specific and should be based on
a number of factors, such as plan status, sponsorcompany constraints, and risk aversion (for a
detailed discussion, see Inglis and Sparling, 2012).
In practice, determining the appropriate trigger can
be an iterative process based on close dialogue
between the plan sponsor and the advisor.
Vanguard Investment Perspectives > 3
Figure 2.
Funding-level thresholds for derisking
Phase 1
Phase 2
100%
Phase 3
110%
Source: Vanguard.
Figure 3.
Glide path ALM: Annual probability
of holding each phase portfolio
Note, however, that the portfolio does have
a measurable chance of reaching each phase
trigger earlier. The full spectrum of these portfolio
probabilities will be used to drive the funding
metric forecasts.
100%
Probability
80
60
Estimating metrics based on probabilities
40
20
0
Year 1
Year 2
Year 3
Year 4
Year 5
Phase 1
Phase 2
Phase 3
Notes: Based on VCMM five-year simulations. Calculations assume that
portfolio holds the Phase 1 allocation at the start of year 1.
Source: Vanguard, from VCMM simulations.
For our case-study plan, we chose the fundinglevel thresholds shown in Figure 2. Based on these
thresholds, we used VCMM simulations to determine
the probability that this plan would be in each phase
(portfolio) over the five-year study horizon—in other
words, the likelihood of reaching a funding-level
trigger each year.
4
The results are shown in Figure 3, where the
height of each color reflects the probability of
the plan’s being in that phase during a given
year. Because our case-study plan starts out very
underfunded, it is most likely to maintain a Phase 1
portfolio in years 1–3. Not until year 4 is the plan
expected to be sufficiently well-funded to trigger a
transition to the lower-risk Phase 2 portfolio. A move
to Phase 3 appears most probable in year 5, when
the plan is expected to be much better funded.
> Volume 12
Next, we evaluated the pension metrics for the
current portfolio and the glide path portfolio.
Note that the pension metrics for the glide path
are estimated based on the portfolio probabilities as
they change over time. This is a critical component
of our approach, because we are attempting to
estimate what the plan will experience over the next
five years. Given the uncertainty in future asset and
liability returns, we cannot be sure when the plan
will move between phase portfolios. As a result, we
base the metrics forecast on the probability of its
being in each phase portfolio each year.
For example, in year 2, the probability of being in
Phase 1 is 80%, so the VCMM uses the Phase 1
allocation for 80% of the portfolio assets. The Phase
2 probability is 15% in year 2, so the VCMM applies
that allocation to 15% of the assets. And the final
5% of assets are assigned to the Phase 3 allocation.
In this way, plan sponsors receive a forecast that
emphasizes the highest-probability metrics but also
reflects other potential outcomes.
Figure 4.
To further illustrate the decline in risk as a plan
moves along the glide path, we estimated fundingratio distributions each year for both the glide path
portfolio and the current portfolio. Figure 5, on
page 6, shows the range between the left and right
tails (the 5th and 95th percentiles) of distributions
for each portfolio. The lower, flatter track of the glide
path portfolio relative to that of the current portfolio
indicates that it is reducing the distribution of
outcomes. The range shrinks because both risk
and expected return are curtailed.3
Liability tracking error: Glide path
portfolio versus current portfolio
20%
16
12
8
4
0
Year 1
Year 2
Year 3
Year 4
Year 5
Current
Glide path
Note: Liability tracking error here is calculated as the standard deviation across
all VCMM asset-liability simulations each year.
Source: Vanguard, based on VCMM simulations.
Because the glide path ALM is primarily a tool
to help sponsors assess the derisking process,
expected liability tracking error is a key metric to
evaluate. In Figure 4, we compare expected liability
tracking error for the glide path portfolio to that of
the plan’s current portfolio (80% equity/20% fixed
income).
Two points are clear from Figure 4. First, the
tracking error with the glide path portfolio, even in
the first year, is expected to be dramatically lower
than for the current portfolio. This translates to lower
funding-ratio and balance-sheet volatility. Second,
tracking error declines over time with the glide path
portfolio. This is not surprising, given that the asset
allocation is changing from high to low risk as it
moves into the later phases. Recall that in year 5 the
portfolio consists primarily of the Phase 3 allocation,
which has the highest duration hedge ratio.
Figure 5 shows the expected (50th-percentile)
results for funding ratios and tracking error. The
glide path portfolio has lower expected funding
ratios because of the risk–return trade-off; yet,
even with its considerably lower risk, this portfolio
is still expected to end in full funding.
Navigating the trade-offs
Figure 5 illustrates some of the trade-offs that
plan sponsors must face in managing plan assets.
When addressing deficits, sponsors basically have
two ways to improve the funding level: They can
contribute more to the plan, or they can own a
higher-risk asset portfolio in hopes of earning more
return. In the end, sponsors must consider the same
trade-off all investors do: Increasing potential return
usually means taking on more risk.
This decision is not black-and-white, and there are
ways to customize the fit. Glide path ALM planning
gives plan sponsors additional “dials” to use in
assessing the risk–return trade-off. For example, the
glide path ALM process can help answer questions
such as:
• How large should the initial contribution4 be, and
will that affect the beginning portfolio?
• What will subsequent derisking portfolios look
like, and should the derisking process end with
immunization (i.e., matching the plan’s cash
flow, duration, or other metrics with those of
the liability)?
3 As noted earlier, this lower upside potential should not be problematic for pension funds once full funding is in view, because too high a surplus then represents
uncompensated risk. Again, this illustrates the primary benefit of derisking: managing risk in pension funding ratios and limiting large contribution surprises.
4 The initial contribution is a cash lump sum that is added to the assets backing liabilities at the beginning of the planning period.
Vanguard Investment Perspectives > 5
Figure 5.
Funding-ratio ranges and 50th-percentile
metrics for glide path portfolio and
current portfolio
a. The difference in “tails”: Funding-ratio ranges,
95th–5th percentile
No hard rules govern the decision process. Rather,
it should be based on a steady communication flow
between the plan sponsor and the advisor.
120%
Funding-ratio range
100
80
60
40
20
0
Year 1
Year 2
Year 3
Year 4
Year 5
Current
Glide path
b. E
xpected funding ratios and liability tracking error
Expected funding ratio (50th percentile)
Year 1
Year 2
Year 3
Year 4
Year 5
Current
82% 86% 93%100%106%
Glide path
82
87
92
96
100
Expected tracking error
Year 2
Year 1
Current
15.4%16.7%16.7%16.9%16.6%
Glide path
11.6
11.8
Year 3
10.9
Year 4
10.1
Year 5
8.9
Notes: The funding-ratio range in the chart represents the difference between
the 95th- and 5th-percentile results each year. Liability tracking error here is
calculated as the standard deviation across all VCMM asset-liability simulations
each year.
Source: Vanguard, based on VCMM simulations.
6
> Volume 12
• At what funding levels (triggers) should the
derisking portfolios begin, and at what frequency
should they change?
To illustrate the trade-off dynamics of a glide path
approach, we estimated annual tracking error,
contributions, and return for our case-study plan
using the glide path portfolio over the five-year time
horizon. As shown in Figure 6, the glide path risk
reduction is not free, although the trade-offs are not
necessarily proportional. Both risk and return will
decline over time as the portfolio becomes more
highly correlated with liabilities. But here risk declines
more than return. Contributions can initially be higher
for the glide path than for riskier portfolios. But
contributions are expected to decline over time
as full funding is reached. At that point, the plan
maintains a more conservative asset allocation
to substantially lower its chance of becoming
underfunded again. Tracking error in year 5 is
expected to be about 25% lower than in year 1,
in order to reduce risk but still maintain full funding
for this plan.
The G-ALM score: A risk-adjusted measure
For pension plans that implement a glide path
derisking approach, forward-looking estimates
are important for managing the trade-offs just
discussed, and specifically for anticipating the
timing of next steps. Forecasts of pension metrics
are one component of this, but we think it is also
helpful to evaluate the chances of success on a
risk-adjusted basis.
Figure 6.
Glide path trade-offs: Contributions,
tracking error, and return
$300
12
250
10
200
8
150
6
100
4
Contributions ($ millions)
Portfolio return and tracking error
14%
50
2
0
0
Year 1
Year 2
Year 3
Year 4
Year 5
Liability tracking error
Return
Contributions
Notes: Contributions and return are 50th-percentile annual results. This analysis
uses a proxy for minimum contribution requirements based on the seven-year
amortization of funding shortfalls defined by the Pension Protection Act. Liability
tracking error here is calculated as the standard deviation across all VCMM
asset-liability simulations each year.
Source: Vanguard, based on VCMM simulations.
To that end, we created a G-ALM score, a riskadjusted measure of success for pension plans
derisking in phases based on funding-ratio thresholds.
Specifically, we forecast the probability (Pb) of meeting
a funding target objective (FT ) and the liability tracking
error (LT ) for sponsors with planning horizon (t). The
risk score is:
G-ALM(t) =
PbFT(t)
LT
The G-ALM score can be interpreted much like
other risk-adjusted return measures. The best way
to evaluate the score is relatively: over time, or
based on alternate asset allocations, funding level
objectives, or other variables. For example, it might
be useful to compare the score with a shorter/smaller
bond allocation to the score with a longer/larger bond
allocation in the glide path portfolios. We intend the
score to be another tool for plan sponsors to use
when evaluating the trade-offs we have described.
Figure 7, on page 8, shows the G-ALM scores
for our plan assuming that contributions are made,
asset allocations are dynamic, and the funding-ratio
objective is 110%. We also include the probability
of meeting the funding-ratio objective and trackingerror results on which the score is based. We
compare scores for the glide path allocation to
scores with the current allocation at four different
initial funding ratios. In general, the score improves
as the initial funding ratio rises, because this
increases the probability of meeting the funding
objective in the numerator. However, initial funding
ratios affect which portfolio, glide path or current,
results in a higher G-ALM score.
For this plan, scores are higher for the glide path
portfolio than for the current allocation when initial
funding ratios are 100% or greater. With these
beginning ratios and a 110% objective, the glide
path portfolio is more “efficient” in terms of the
relevant success/risk measure. Given a 100% or
107% starting ratio, the return benefit offered by
the current portfolio is not sufficient to overcome
the benefit of lower tracking error by the glide path
portfolio, resulting in a higher G-ALM score for the
glide path.
To illustrate the trade-off here: With a 100% initial
funding ratio, the probability of being 110% funded
at the end of the period is 34% for the glide path
portfolio and 53.7% for the current portfolio. At the
same time, the expected tracking error is 9.5% for
the glide path portfolio and 16.6% for the current
one. This means that for the glide path portfolio,
expected tracking error is about 43% lower, while
the probability of reaching the funding-ratio objective
is only about 37% lower than for the current
portfolio. In other words, the return loss is less than
the risk reduction, so the glide path score is higher.
Vanguard Investment Perspectives > 7
Figure 7.
G-ALM scores at different funding levels
Scores represent probability of reaching 110% funding
divided by expected liability tracking error over five years.
Initial funding
status
G-ALM scores
3.5
107%
4.4
3.2
100
Conclusion
3.6
With changes in the pension governing laws, a
new pension management strategy—derisking
based on funded status—has been widely embraced
by consultants and plan sponsors. Derisking lays out
a glide path for reducing portfolio risk as the funding
ratio rises, reflecting the view that as the advantage
of higher expected returns diminishes, portfolio risk
should diminish as well.
2.8
90
2.6
2.6
84
2.2
Current
Glide path
Probability of reaching 110% funding in year 5
Initial funding status
84% 90%100%107%
Current
44.9%47.8%53.7%57.9%
Glide path
24.4 27.434.039.9
Liability tracking error
However, the G-ALM score does not always suggest
immediate derisking. If a plan like this wants to
obtain a funding surplus without making a large initial
contribution, the initial funding ratio will be lower, and
in that case the sponsor may value higher expected
returns more and risk reduction less. In that situation,
the benefit of higher expected returns—a greater
probability of meeting the funding objective—
outweighs the detriment of higher tracking error.5
Initial funding status
84% 90%100%107%
Current
17.2%16.9%16.6%16.5%
Glide path
11.2
10.6
9.5
9.0
Notes: This analysis uses a proxy for minimum contribution requirements based
on the seven-year amortization of funding shortfalls defined by the Pension
Protection Act. Liability tracking error here is calculated as the change in assets
relative to the change in liabilities. The calculation includes estimates for normal
cost (the portion of the cost of projected benefits that is allocated to a specific
plan year).
We suggest combining derisking with ALM studies,
the process most plan sponsors use to forecast
and evaluate plan risk, return, and costs in order to
make investment decisions. Although derisking
approaches suggest that portfolio allocation should
change dramatically if the funding ratio rises, few of
today’s ALMs account for this. As our case study
illustrates, incorporating the derisking logic directly
into the ALM provides a number of benefits to plan
sponsors.
Glide path ALM assists with strategic decisions and
provides more practical, actionable output. Forecasts
of funding-ratio volatility, downside risk, and costs
made with dynamic asset allocation provide a better
understanding of the potential financial impact, and
ultimately, produce results more closely aligned to
the concerns and questions of senior management.
Source: Vanguard, based on VCMM simulations.
5 We also calculated G-ALM scores for this plan using the same assumptions but with a 100% funding objective, rather than 110%. With that funding-level
objective, the return hurdle is not as high, and the risk reduction trumps the return reduction for the glide path portfolio. Using the 100% funding objective,
the G-ALM score is higher for the glide path portfolio at each of the four initial funding ratios.
8
> Volume 12
References
Bosse, Paul M., 2010. Pensions—Dynamic IPS:
A Plan for Action. Valley Forge, Pa.: The Vanguard
Group.
Bosse, Paul M., and Francis Vincent, 2010. Pension
Risk Control: Is There a Better Way? Valley Forge,
Pa.: The Vanguard Group.
Stockton, Kimberly A., 2008. How a Pension Plan’s
Funding Level Should Influence Its Investment
Strategy. Valley Forge, Pa.: The Vanguard Group.
Stockton, Kimberly A., and Anatoly Shtekhman, 2012.
Glide Path ALM: A Dynamic Allocation Approach to
Derisking. Valley Forge, Pa.: The Vanguard Group.
Bosse, Paul M., Nathan Zahm, and Evan Inglis, 2011.
Derisking and Pension Expense: Not All Bad News.
Valley Forge, Pa.: The Vanguard Group.
Stockton, Kimberly A., Scott J. Donaldson, and
Anatoly Shtekhman, 2008. Liability-Driven Investing:
A Tool for Managing Pension Plan Funding Volatility.
Valley Forge, Pa.: The Vanguard Group.
Inglis, R. Evan, and Jeffrey Sparling, 2012. Pension
Derisking: Start With the End in Mind. Valley Forge,
Pa.: The Vanguard Group.
Wallick, Daniel W., Roger Aliaga-Díaz, and Joseph
Davis, 2009. Vanguard Capital Markets Model. Valley
Forge, Pa.: The Vanguard Group.
Vanguard Investment Perspectives > 9
About the Vanguard Capital Markets Model
The Vanguard Capital Markets Model (VCMM) is a proprietary financial simulation tool developed and
maintained by Vanguard’s Investment Counseling & Research and Investment Strategy Groups. The VCMM
forecasts distributions of future returns for a wide array of broad asset classes. These include U.S. and
international equity markets, several maturities of the U.S. Treasury and corporate fixed income markets,
international fixed income markets, U.S. money markets, commodities markets, and certain alternative
investment strategies. The asset-return distributions shown in this article are drawn from 10,000 VCMM
simulations based on market data and other information available as of December 31, 2011.
The VCMM is grounded in the empirical view that the returns of various asset classes reflect the
compensation investors receive for bearing different types of systematic risk (or beta). Using a long span
of historical monthly data, the VCMM estimates a dynamic statistical relationship among global risk factors
and asset returns. Based on these calculations, the model uses regression-based Monte Carlo simulation
methods to project relationships in the future. By explicitly accounting for important initial market conditions
when generating its return distributions, the VCMM framework departs fundamentally from more basic
Monte Carlo simulation techniques found in certain financial software. The reader is directed to the
research paper Vanguard Capital Markets Model (Wallick, Aliaga-Díaz, and Davis, 2009) for further details.
The primary value of the VCMM is in its application to analyzing potential client portfolios. VCMM assetclass forecasts—comprising distributions of expected returns, volatilities, and correlations—are key to
the evaluation of potential downside risks, various risk and return trade-offs, and diversification benefits
of various asset classes. Although central tendencies are generated in any return distribution, Vanguard
stresses that focusing on the full range of potential outcomes for the assets considered, such as the
data presented in this article, is the most effective way to use VCMM output.
10
> Volume 12
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