Devising an investable index

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There has been a growing emphasis
on pension fund liability
management and creating a
portfolio of assets to match these liabilities.
The popular press has published
several recommendations to
protect pension fund solvency
through the immunisation of liabilities.
Recommendations have ranged
from the approach of the Boots Pension
fund, which converted the entire
portfolio of assets into fixed income
assets (since revised to include a small
allocation to non-fixed income
assets), to a complete abandoning the
strategic asset allocation policy in
favor of a totally tactical policy, to
duration extension combined with
‘portable alpha’.
However, the principal challenge to
developing an optimal policy for
managing the assets-to-liabilities
ratio (called the funded ratio) has
probably more to do with (a lack of)
understanding of the liabilities than
in developing innovative investment
policies. Through a series of short
notes, we explore how innovative
investment policies can be used to
cause the funded ratio to grow over
time, but first we develop a simple
process by which liabilities can be
understood and monitored on an
intra-year basis.
This renewed interest in asset-liability
matching is mainly caused by the
rapid decline in interest rates, which
led to an increase in most pension
fund liabilities on a mark-to-market
basis. Unfortunately for most pension
funds, this decline in rates coincided
with a decline in many stock
markets. The fall in the value of assets
at a time when the value of liabilities
was increasing led to a dramatic
decline in the ratio of assets to liabilities.
This ratio is often what regulators,
CFOs and members are looking
at to judge whether a plan is “safe”.
Further, new accounting standards
imply that pension fund losses can
affect the corporate pension fund
sponsor. For these three reasons,
many pension plans worldwide are
adjusting their investment and hedging
strategies to reduce the impact of
a declining (and volatile) funded
Pension funds often find it difficult
to express the desired approach and
implementation of liability-driven
investments to their asset managers.
The main problem pension managers
encounter is in setting an appropriate
investable benchmark which reflects
the liabilities.
Here we describe a simple, stable
and accurate benchmark to mimic liabilities
based on daily available
Lehman swap indices. The only input
needed is the projected annual liability
cash flows. The website provides a free trial of
software to help pension funds make
effective decisions. We use the work
done at the €17bn Bedrijfstakpensioenfonds
Metalektro in the Netherlands,
also known as the PME Pension
Fund (, to
clarify our views.
Chart 1 presents a typical actuarial
example of projected pension benefit
cash flows. We restrict ourselves to
the nominal liabilities.
Now the board appointed executive
faces the question: How to manage
assets against this set of cash flows?
To effectively manage a pension
fund, one needs to measure and monitor
these nominal liabilities. A
related question is: how to measure
and monitor liabilities relevant to
investment decisions that need to be
made? Previously, an annual
approach was sufficient, but in
today’s world a more frequent valuation
is needed, especially if one wants
to manage the funding ratio effectively
on an intra-year basis. In turn,
that leads to the challenge of translating
the above cash flows to quoted
market instruments.
The standard approach to develop
as a benchmark is relatively simple,
but it is harder to implement in practice.
It forces managers to accept
either a high tracking error, or a very
costly implementation.
Effectively, each future cash flow is
nothing but a zero coupon bond with
a given maturity. When viewed this
way, the manager needs to invest in
such bonds in the appropriate
notional amount. For example, if the
estimated cash flow due in 2016 is
€750,000 , then the manager needs
to find a zero coupon bond with that
maturity and invest the relevant
amount to earn a payout equal to
€750,000. The relevant amount to
invest today to achieve such a payout
in December 2016 would be determined
by the zero coupon bond rate
for that maturity.
Using the cash flows demonstrated
in chart 1, it can be concluded that the
present value of liabilities is €15bn
with a duration of 15-14 years, as
shown in the table. However, the difficulty
of this approach is that such
pure instruments do not exist, and,
hence either a theoretical zero
coupon portfolio can be constructed
but not implemented, or an alternative
portfolio can be constructed
from zero coupon as well as coupon
bearing bonds (or by boot-strapping
the zero coupon curve implied by
these bonds).
It is not that hard to construct such
a portfolio for any set of liability cash
flows from the universe of Eurozone
government bonds, though
inter/extra polation techniques have
to be used for the 30+ years cash
flows. The theoretical bond portfolio
can be marked to market daily and,
hence, give clients an effective esti-mate of their liability performance
intra-year. The bigger problem is that
with many cash flows, over multiple
years and of moderate amounts, the
liability benchmark involves small
allocations to multiple securities,
making the benchmark unwieldy and
difficult for the average board member
to grasp, so an alternative
approach using swaps (see below) is
more appropriate.
Managing a tailor-made portfolio
of 50 zeros does not seem to exceed
current computing power. The real
issue is that the zero coupon bond
approach does not lead to clean and
transparent pricing and would also be
costly to implement. Furthermore,
the obtained benchmark relying on
the valuation of (zero coupon)
bonds, may contain a credit spread
element (as there is no unique Eurozone
government yield curve,
because different issuers have
(slightly) different credit qualities)
and is hence less objective than standard
benchmarks. For that reason,
PME adopted a different approach
using the most liquid fixed income
markets instruments: swaps.
The swap curve is the pricing benchmark
in the euro market and therefore
the best starting point for index
construction. The plain vanilla
(coupon bearing) interest rate swaps
market offers excellent benchmarks.
For instance, each of the Lehman
Bellwether indices has a long track
record. If the above cash flows could
be replicated by using a set of these
indices, an objective and investable
benchmark could be achieved.
Under the swap method, an
optimisation technique is used to
determine optimal weights to a portfolio
of Lehman indices such that
this swap portfolio will mimic, to a
large degree, the performance of
In such a situation, a chosen set of
indices is used to find an optimal mix,
and typically the swaps selected are of
the standard plain vanilla coupon
bearing variety and maturity (ie, oneyear,
two-year, five-year, 10-year,
and 20-year). The procedure to
determine the weight of each
Lehman index in the liability benchmark
is to use historical yield curve
data from 1999-2005 and find the
portfolio that gives sufficiently low
tracking error relative to the valuation
of liabilities. In the case of pension
cash flows modelled in the chart,
optimal weights to the various indices
are as follows:
First, this is a very simple portfolio
of some key liquid instruments and,
hence, lends itself to acceptance by a
board. This portfolio of Lehman
indices has an annualised tracking
error of 0.30% relative to the liabilities
over the historical simulation
period. An alternative check is to
compare the durations of both portfolios
– and as shown in table 1, the
difference is minimal.
One can argue that it is better to
optimise the weights over some
future simulations, using a Monte
Carlo technique, but such a proposal
only changes the method, not the
approach to estimating an appropriate
liability benchmark. Chart 2
shows how liabilities evolved from
1999-2005 with changes in interest
rates, and chart 3 demonstrates the
close tracking of the portfolio of
swaps over this period.
There are other caveats; sometimes
such an optimisation can provide
negative weights to certain swap
maturities (eg, the 12-month or oneyear
recommended allocation) and
sophisticated clients can see this as
either a short position or a forward
starting swap. This is a very simple
portfolio to monitor and track and
mark-to-market as frequently as
other assets. Effectively, one can now
track, on an intra-year basis, the
annualised growth in the surplus as
the difference between the annualised
return on assets minus the
annualised return on liabilities.
An additional benefit of using the
swap-based approach is that very little
capital is required to hedge the
investable liability index through
swaps or other derivative instruments.
Many pension funds mandate setting
aside capital for hedging liabilities
(through fixed-income investments)
or return generation (through equity
or alternative investments). Then,
because they feel there is a leverage
constraint (ie, the weights allocated to
these instruments have to add up to
100%), they act as if there is tension
between these objectives. Of course,
this is not the case. The real concern
should be overall funding risk, and the
ability to effectively hedge liabilities
with derivatives is an attractive proposition
that frees up capital for return
This note set out to demonstrate
how innovative pension plans can
convert actuarial projections of pension
benefits into an appropriate
investable benchmark, allowing plan
sponsors a better measure of the performance
of their liabilities (and
assets) on an intra-year basis.
In future notes we extend our Metalektro
case to explain how one can
control a €17bn portfolio in a very
cost efficient way by using advanced
web-enabled techniques. In the past
three and a half years, PME has used
this approach to ensure one of the
highest returns of all Dutch pension
funds, which include over 800 pension
funds, in a very competitive market.
More important, using this
approach of tracking liabilities effectively
has allowed PME to control
and improve its overall solvency.
Jan Willem Stuijvenberg is founder
of Stuijvenberg Financial Services
and Arun Muralidhar is chairman of
Mcube Investment Technologies

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