Long and short of duration

The need for pension funds to
match their assets more closely
to their liabilities has put the
topic of duration at the top of the
Pension funds are faced with the
problem of finding fixed income
instruments with the right durations.
The problem is greatest at the long
end, where there is a shortage of longdated
Governments have tried to help with
the issue of 30- and 50-year bonds.
Companies like Coca Cola, Disney
and IBM have even issued 100-year
paper. Yet the demand for long-dated
bonds outstrips the supply, depressing
bond yields still further.
One solution is to use the duration
of equities to match liabilities. It is
argued that equities are reasonably
long duration assets that are suited to
longer-term liabilities such as pensions.
As part of a diversified portfolio,
equities can do as good a job as bonds,
if not better, at providing the necessary
The concept of equity duration is
relatively recent, and the debate about
its usefulness dates back no more than
20 years. Most of the debate has centred
on how to measure equity duration.
Unlike the measurement of
bond duration, estimating equity
duration is not an exact science. Most
admit it is difficult to measure, and
some wonder whether
it is worth measuring at
The proponents of
equity duration say the
difficulties in estimating
duration should not
detract from its importance
as a tool for pension
fund and asset
managers. They argue
that it is a particularly
useful tool in three
areas: immunisation,
risk management and
tactical asset allocation.
Immunisation means
matching asset and liabilities
in such a way
that they are insensitive
to interest rate movements.
Since equities
account of for a significant
percentage of
many pension plans,
some idea of their duration would be
If equities are sensitive to interest
rate changes, investment managers
need to be able to make allowance for
this sensitivity in their risk managment
Similarly, with tactical asset allocation
investment managers who are
aware of the sensitivity of equities can
take full advantage of any changes in
interest rates.
The idea of duration has been
around for more than 60 years. It is
defined as the sensitivity of a security
to changes in interest rates. The
longer the duration, the greater this
sensitivity is likely to be.
In fixed income analysis, the economist
Frederick Macaulay calculated
duration back in 1938 as the
‘weighted average maturity’ of a
bond, or portfolio of bonds. The
weights are the present values of each
of the anticipated cash flows, both
coupons and principal, as a percentage
of the price of the bond, and the
weight of each cash flow is its contribution
to the total price.
The duration of a bond is therefore
the point around which the weighted
present value is distributed. It has
been described as the ‘centre of gravity’
of an investment’s cash flow. This
why it is the duration rather than the
maturity of fixed income instruments
that matters to pension funds looking
to match their liabilities. The cash
flow characteristics of a bond with a
long duration will coincide with the
cash flow requirements of a long-tern
Although the concept of duration is
usually applied to bonds, it can be
applied to any security with a prospective
payment stream, including equities.
In the case of equities, the dividend
can be seen as the equivalent of
the bond coupon, and the share price
as the equivalent of the bond principal.
Yet there are significant differences
between bond and equity duration,
which may explain why equity
duration is still not widely used by
asset or pension fund managers.
One key difference is the maturity.
The terminal value of equities, unlike
bonds, is not fixed. Another difference
is the certainty of payment.
Bondholders know what interest payments
they will receive. Shareholders
cannot be certain what dividend payment
they will receive.
The most widely used method of
estimating equity duration is the Gordon
model, named after Myron Gordon,
now a professor at the University
of Toronto. This is a version of the
dividend discount model (DDM), a
method for valuing a stock.
According to the model, the
value of equity is based on its
estimated dividend, the equity
discount rate and the dividend
growth rate.
Srikant Dash, index strategist at
Standard & Poor’s in New York, and
Kevin Gardiner, head of global equity
strategy at HSBC in London, have
shown in their paper ‘On the duration
of equity’ how a DDM-based estimate
of European and US equity
duration might have looked over the
past 20 years.
The simplest way of estimating this
in the DDM approach is to treat
equity duration as the inverse of the
actual dividend yield. The dividend
yield suggests that equity duration has
been rising steadily, Dash and Gardiner
says, to around 30 to 40 years in
the US and 20 to 25 years in Europe,
though the rise here is less steep.
The main objection to adopting the
DDM framework as a tool for pension
and asset management is that it tends
to provide unrealistically high estimates
of equity duration – often more
than 50 years for high-growth stocks.
Observation by asset managers what
actually happens to companies suggests
it must be lower.
Long equity durations also turned
asset management practice on its
head by suggesting that the fixed
income portion of a fund manager’s
portfolio could be used to shorten the
overall duration of the asset pool.
In conventional fund management
practice, the equity component of a
portfolio is likely to have much
shorter durations than those estimated
by the DDM.
What bothered proponents of
equity duration was the duration
lengths implied by the DDM. Fifty
years seemed an implausibly long
time. Experience showed that duration
were often much shorter.
In the mid-1980s Martin Leibowitz,
a former CIO of TIACREFF,
was one of the first people to
look at effective equity durations
empirically – that is, on the basis of
experience rather than theory.
Leibowitz suggests a different way
of estimating equity duration empirically,
by looking at historical changes
in equity prices and interest rates. The
method produced far shorter estimates
of duration – on average
between two to six years and 2.8 years
for the US market.
This seemed more plausible to practitioners.
Jim Moore, product manager
for PIMCO’s long duration and
pension products, says: “If you dig
deeper and think through the nature
of some businesses out there, particularly
the cyclical businesses, this makes
more sense. The cyclicality in their
earnings streams is driven by many of
the same factors that affect interest
rates. So you would expect their earnings
streams to drop at the same time
interest rates drop, effectively shortening
“Also, if you think about the nature
of financial innovation,
and the active management
of a firm, there’s a
lot of embedded
optionality that effectively
shortens duration.
So if you look
empirically over the last
25 to 30 years, the
implied duration of
equities is between two
and three years.
“This is logical when
you start to think that
you could create a
coupon paying 30-year
bond that has anything
from a zero to 14-or 15-
year duration or more.
The bond could have a
high duration if the
coupon is fixed and
doesn’t move or - if the
coupon is responding to
interest rates and is influenced by the same factor that’s
driving the discount factor - you could
have a very short duration.”
Two UK economists, Richard
Lewin and Stephen Satchell of,
respectively, the Judge Institute
of Management Studies and the
Faculty of Economics and Politics at
Cambridge University, have tried to
resolve the problem of the wide
divergence of the DDM and Leibowitz
In their paper ‘The
derivation of a new model
of equity duration’, Lewin
and Satchell develop the
idea of equity duration as a
by-product of asset pricing,
and suggest that the equity
premium may be an important
link between the Leibowitz
approach to equity
duration and the more traditional
dividend discount
model DDM alternative.
They base their computation
of equity duration on
the historic correlation
between UK stocks and
bonds. Their methodology
uses this correlation,
together with a measure of
bond market duration, to
arrive at an estimate of
equity duration.
Crucially, they attempt to
resolve the controversial
issue of the average
expected lifetime of equities. The
DDM approach implies equities are
financial assets with infinite lives in
terms of a prospective investment
horizon. This in turn generates excessively
long equity duration estimates.
In some respects, equities do appear
to have infinite horizons. Investors
own businesses, which could theoretically
stay in business indefinitely.
Yet Lewin and Satchell argue that
equities cannot be treated as undated
instruments, with an infinite horizon,
when there is a clearly observable corporate
failure rate of 1% and 2% a year
in the UK.
They therefore calibrated their
model to reflect the fact that
equities behave as assets with
finite horizons. They chose 100 years
as an average lifetime benchmark for
equities. The resulting calculations,
they say, square with the liability
structure of most pension funds,
which have upper liability durations
that are far below the 49-year maximum
contribution period for a male
worker in the UK.
Besides the DDM and the Leibowitz
approach, Dash and Gardiner
identify a third approach to the estimation
of equity duration – what is
called the ‘flow through’ approach.
This is an attempt to build on DDM
to measure the sensitivity of growth to
interest rates.
Leibowitz and a colleague proposed
calculating equity duration by looking
at two factors separately. One factor
is ‘assets in place’, which they term
tangible value. The other is growth
opportunities, which they term franchise
value. The duration equity is the
weighted average sum of duration of
each of these two valuations.
Separating the valuations is useful
because it showed that factors like
inflation affect them differently. Standard
& Poor’s uses these models to
calculate an annual estimate of the
duration of the S&P 500. This ranges
from 15 to 25 years, lower than the
calculations using the DDM but
much higher than the duration of
most government bonds.
Yet Dash and Gardiner suggest that
the flow-through approach has one
serious shortcoming. It finds it difficult
to model the sensitivity of growth
to interest rates.
“If theory and intuition both suggest
stocks are long-duration investments
why are they so insensitive to
changes in interest rates?” they ask.
They suggest several possible
answers. One is that higher interest
rates cause growth to fall, softening
the impact on duration and price sensitivity.
However, they add that the fact that
equity duration cannot be measured
objectively with any precision does
not mean that it is necessarily short.
One way of analysing equity duration
more objectively is to look at how
it might be used at the equity portfolio
level rather than asset allocation
level. Dash and Gardiner suggest that
it might be more useful to focus less
on absolute duration and more on
how duration is ranked across equity
styles and sectors.
“Investors often choose to follow a
growth or value style and we can
imagine some investors opting for a
duration bias. Just as many investors
believe that value outperforms in the
long term, so others might believe
that duration will,” they suggest.
In a given equity sector, duration
will be longer if growth is higher or if
beta (market risk) is lower. In other
words, they say, investors looking for
high duration sectors should look for
growth prospects that are not cancelled
out by a similar level of risk.
They call this style the pursuit of
“growth at a reasonable risk”.
Dash and Gardiner believe that they
can rank sectors of equities according
to their duration characteristics by
calculating their prospective growth
rates and riskiness. The calculate
growth by looking at dividend
growth over the past 10 years, and risk
by looking at beta, the measure of the
market risk that investors face.
Having calculated growth rates and
betas, they then rank the sectors
according to their growth/risk ratios,
which act as a proxy for their duration.
Plotting the sectors of the S&P
Europe BMI in mid-2005 according
to their relative duration, they show
that sectors with a long duration
include food, healthcare and property
– an asset class that is under-represented
in the portfolios of many European
pension funds.
Sectors with short durations
include computer software and
hardware, telecom equipment
and electronics. reflecting the fall out
from the TMT episode has resulted in
very high levels of market risk.
The main drawback to this method,
Dash and Gardiner warn, is that the
past may not be a useful guide to the
Yet duration does appear to be a significant
factor in sector performance,
By splitting duration estimates into
two equal weighted basked to high
and low duration sects, Dash and Gardiner
show that high duration baskets
have mainly outperformed since
So does equity duration explain
some of the effects of style investing?
In particular, can the relative performance
of value and growth stock be
explained in terms of their duration?
Some proponents of equity duration
believe that it can. In their paper
‘Implied equity duration: a new measure
of equity risk’, Patricia Dechow
and Richard Sloan of the University of
Michigan Business School and Mark
Soliman of Stanford Graduate School
of Business argue that the book-tomarket
ratio provides a crude measure
of equity duration.
Eugene Fama and Kenneth French
identified book to value as an important
driver of returns in their threefactor
model. They showed that firms
with low book-to-market ratios have
higher equity betas; in other words,
are more susceptible to market risk.
Dechow, Sloan and Solomon’s
equity duration framework, constructed
from an analysis of financial
statements, suggests that firms have
higher market risk
because equities with low
book-to-market durations
have longer durations,
and so are more
sensitive to expected
return shocks.
They say that their
measure of equity duration
provides a better
ranking of equities; style
characteristics on the
value/growth dimension
than value and growth
index providers such as S
& P, Dow Jones and Russell,
whose growth and
value classifications are
based on “ad hoc reasoning
and data-motivated
statistical procedures.”
So is equity duration of
use to pension funds,
principally for immunising
assets against interest
rate risk? Or have the
behaviour of the market
changed in such a way that equities are
no longer an attractive duration play?
One market change in the past two
years has been the switch from a positive
to negative correlation between
the global equity and fixed income
Bob Litterman, director of quantitative
resources at Goldman Sachs Asset
Management, has argued that, for this
and other reasons, equity duration is
no longer a useful construct for pension
funds – if it ever was one.
He points out that two recent developments
have reduced the usefulness
of relying on estimates of equity durations.
First, long-term instability and
negative correlations between the
bond and equity markets have made
any stable measure of equity duration
Second, a liquid market in derivatives,
such as interest rate swaps, has
enabled pension funds to use derivatives
to hedge against changes in the
overall measure of interest rates measured
by duration.
Litterman says the small and unstable
relationship between domestic
equities and domestic interest rates
“is not an interesting or important
consideration in this broader return
generating context”.
He concludes that the term equity
duration suggests a stable structural
relationship between equity returns
and interest rate changes. “Unfortunately
such a relationship does not
In short, there may be arguments in
favour of pension funds increasing
their exposure to equities in the current
climate, but equity duration is
not one of them.

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