Download Analysing and Decomposing the Sources of Added

An EDHEC-Risk Institute Publication
Analysing and Decomposing
the Sources of Added-Value
of Corporate Bonds Within
Institutional Investors’
Portfolios
August 2013
with the support of
Institute
Table of Contents
1. Introduction.......................................................................................................... 5
2. The Investment Model......................................................................................... 9
3. Empirical Results................................................................................................17
Conclusion................................................................................................................27
Appendix...................................................................................................................31
References................................................................................................................39
About Rothschild & Cie........................................................................................ 41
About EDHEC-Risk Institute.................................................................................43
EDHEC-Risk Institute Publications and Position Papers (2010-2013).........47
2
This research is supported by Rothschild & Cie in the context of the “The Case for Inflation-Linked Corporate Bonds: Issuers’
and Investors’ Perspectives” research chair.
Printed in France, August 2013. Copyright© EDHEC 2013
The opinions expressed in this study are those of the author and do not necessarily reflect those of EDHEC Business School.
The authors can be contacted at [email protected].
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
Foreword
The present publication, “Analysing and
Decomposing the Sources of Added-Value
of Corporate Bonds within Institutional
Investors’ Portfolios,” is drawn from the
Rothschild & Cie research chair on “The
Case for Inflation-Linked Corporate Bonds:
Issuers’ and Investors’ Perspectives” at
EDHEC-Risk Institute.
The purpose of this research chair is to
support research undertaken at EDHEC-Risk
on the benefits of inflation-linked bonds
from the investors’ perspective as well as
from the issuers’ perspective. The chair
also focuses on comparing and contrasting
investors’ and issuers’ perceptions of
inflation-linked bonds.
The current paper, by Lionel Martellini,
Scientific Director of EDHEC-Risk Institute,
and Vincent Milhau, Deputy Scientific
Director of EDHEC-Risk Institute, provides a
formal analysis of the benefits of corporate
bonds in investors’ portfolios, distinguishing
between the impact of introducing them
in performance-seeking portfolios and the
impact of introducing them in liabilityhedging portfolios.
The authors show that investor welfare can
be improved by the design of performanceseeking portfolios with improved liabilityhedging properties, or conversely by the
design of liability-hedging portfolios with
improved performance properties.
I would like to thank the co-authors, Lionel
Martellini and Vincent Milhau, for their
comprehensive analysis of the benefits of
corporate bonds in investors’ portfolios.
We would also like to extend our warm
thanks to our partners at Rothschild & Cie
for their collaboration on the project and
their support of the research chair.
Wishing you a pleasant and informative
read,
Noël Amenc
Professor of Finance
Director of EDHEC-Risk Institute
An EDHEC-Risk Institute Publication
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Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
About the Authors
Lionel Martellini is professor of finance at EDHEC Business School and
scientific director of EDHEC-Risk Institute. He has graduate degrees in
economics, statistics, and mathematics, as well as a PhD in finance from
the University of California at Berkeley. Lionel is a member of the editorial
board of the Journal of Portfolio Management and the Journal of Alternative
Investments. An expert in quantitative asset management and derivatives
valuation, his work has been widely published in academic and practitioner
journals and has co-authored textbooks on alternative investment strategies
and fixed-income securities.
Vincent Milhau is deputy scientific director of EDHEC-Risk Institute. He holds
master's degrees in statistics (ENSAE) and financial mathematics (Université
Paris VII), as well as a PhD in finance (Université de Nice-Sophia Antipolis).
His research focus is on portfolio selection problems and continuous-time
asset-pricing models.
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An EDHEC-Risk Institute Publication
1. Introduction
An EDHEC-Risk Institute Publication
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Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
1. Introduction
1 - On Friday October 19, 2012,
it was reported that weekly
inflows to investment-grade
corporate bond funds were the
highest in over two decades
with $2.4 billion inflows into
investment-grade corporate
bond funds. Of that total, $1.4
billion flowed to investmentgrade corporate bond mutual
funds, and the rest went into
ETFs.
2 - While the presence of credit
risk in corporate accounts is well
understood and documented,
sovereign credit risk is more
difficult to apprehend given that
sovereign state accounts are
hardly audited. In this context, it
can be argued that investment
grade corporate bond markets
offer better stability and
visibility than sovereign
bond markets.
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An EDHEC-Risk Institute Publication
According to international accounting
standards SFAS 87.44 and IAS19.78, which
recommend that pension obligations be
valued on the basis of a discount rate equal
to the market yield on AA bonds, the most
straightforward way for pension funds
to match liability payments is to build a
portfolio of long-dated, investment grade
corporate bonds. In practice, institutional
investors including pension funds, but also
insurance companies, sovereign funds,
etc., are actually showing an increasing
appetite for corporate bonds, not only for
their liability hedging benefits, but also
for their performance benefits related
to the presence of a credit risk premium,
which is imperfectly correlated with
the equity risk premium.1 This trend has
been accelerated by the recent sovereign
bond crisis, which has made high quality
corporate bonds an attractive alternative,
or at least a complement, to Treasury
bonds in investors’ portfolios.2
This paper provides a formal analysis
of the benefits of corporate bonds in
investors’
portfolios,
distinguishing
between the impact of introducing
them in performance-seeking portfolios
and the impact of introducing them in
liability-hedging portfolios. From a formal
standpoint, our analysis is cast within the
context of the liability-driven investing
(LDI) paradigm, a disciplined investment
framework that advocates splitting an
investor’s wealth between a dedicated
liability-hedging portfolio (LHP) and a
common performance-seeking portfolio
(PSP), in addition to cash (Martellini
(2006), Martellini and Milhau (2012)).
While the LDI paradigm implies that
investor welfare should depend on how
good each building block is at delivering
what it has been designed for (namely
risk-adjusted performance benefits for
the PSP and hedging benefits for LHP),
the intuition suggests that the interaction
between performance and hedging
motives should also play an important
role. We analyse this effect and show
that investor welfare can be improved
by the design of performance-seeking
portfolios with improved liability-hedging
properties, or conversely by the design of
liability-hedging portfolios with improved
performance properties.
To see this, we first introduce a formal
decomposition of investor welfare in terms
of performance and hedging benefits,
and show that a residual term remains,
which can be interpreted as a cross-effect
emanating from the interaction between
performance and hedging motives. This
result, which we call the “fund interaction
theorem”, is important in that it shows
that investor welfare indeed includes
contributions from the PSP and the LHP,
but also cross-contributions related to
the hedging potential of the PSP. When
negative, the cross-contribution signals
the presence of a conflict between the
performance and hedging motives, such
as a short (long) position required for
performance purposes and a long (short)
position required for hedging purposes.
This cross-contribution can be substantial
for some parameter values, and sometimes
equal or superior in magnitude to the
performance and hedging contributions.
The practical implications of the fund
interaction theorem is that investors
will in general benefit from improving
hedging characteristics of the PSP, unless
this improvement is associated with an
exceedingly large decrease in Sharpe
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
1. Introduction
ratio.3 In the end, the net impact will
be positive or negative depending on
the relative strength of the following
two competing effects. On the one
hand, the PSP with improved hedging
benefits can represent a higher fraction
of the investor’s portfolio for a given risk
budget; on the other hand, the PSP with
improved hedging properties may have a
lower performance: hence the trade-off is
between an increase in performance due
to a higher allocation to risky assets, and
a decrease in risk-adjusted performance
due to a lower reward for each dollar
invested.
3 - It is important at this
stage to recognise that the
fund interaction theorem and
the fund separation theorem
are not mutually inconsistent;
in fact they co-exist within
the framework of liabilitydriven investing, which
the aforementioned results
do not contradict, even
though they do advocate
a focus on the interaction
between performance and
hedging motives.
In an empirical analysis, we find that
corporate bonds are particularly wellsuited to improve the PSP/LHP interaction,
given that they have a well-controlled
interest rate risk exposure while providing
an access to an equity-like risk premium.
In other words, they have on the one hand
attractive interest rate hedging benefits
which should help improve the correlation
of the PSP with the liabilities compared
for instance to an equity investment.
On the other hand, they exhibit a higher
expected performance compared to
sovereign bonds due to the presence of a
credit risk premium. These two properties
make them natural candidates for
inclusion in the performance portfolio,
where the primary focus is on achieving
a high expected return, and where a high
correlation with liabilities helps to align
performance and hedging motives, and
also in the liability-hedging portfolio,
where the primary focus is on interest
rate risk hedging, and where the presence
of a credit risk premium also contributes
to aligning performance and hedging
motives more effectively than what is
allowed by sovereign bonds. As recalled
above, if liabilities are discounted at the
risk-free rate plus a spread, corporate
bonds may actually hedge liability risk
better than sovereign bonds do, precisely
because they include a credit spread
component that evolves in line with the
discount rate on liabilities.
The rest of the paper is organised as
follows. Section 2 introduces a formal
framework suited for an analysis of
whether investor welfare can be enhanced
by the introduction of corporate bonds in
performance and/or hedging portfolios.
Section 3 analyses the empirical
implications of this framework, using
monthly data over the period of February
1973-January 2013. Section 4 presents
some conclusions and suggestions for
further research.
An EDHEC-Risk Institute Publication
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Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
1. Introduction
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An EDHEC-Risk Institute Publication
2. The Investment Model
An EDHEC-Risk Institute Publication
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Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
2. The Investment Model
We consider a partial equilibrium model,
with a single investor whose decisions
have no impact on prices. Uncertainty in
the economy is represented by a standard
probability space
, where
is the set of measurable events and
is a probability measure that represents
the beliefs of the investor. Investment
decisions are made at the initial date,
denoted with 0, and the horizon is a
positive date T.
The investment universe consists of N
risky assets whose returns over the period
[0, T] are random as seen from date 0. We
let
denote the N × 1 vector of realised
returns, and and be the expectation
and the covariance matrix of . In other
words, is the vector of expected returns
of the assets, while
is their covariance
matrix. The investor has an initial capital
A0, which he invests in the available assets,
to end up with a terminal wealth AT. In
addition, he is endowed liabilities, which
are represented by a down payment LT at
date T.
2.1 Portfolio Strategies and Investor
Welfare
The portfolio strategies that we consider
in this paper are of the buy-and-hold
type: that is, the investor chooses at date
0 the weights to allocate to the various
assets, and then does not trade until
date T. This assumption may seem at
odds with the industry practice, which
is closer to a fixed-mix strategy: that is,
the portfolio has constant weights over
time, as opposed to having constant
numbers of shares of each asset.
The reason why we focus on the buy-andhold case is because for such strategies,
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An EDHEC-Risk Institute Publication
the moments of terminal wealth are
simple functions of the weights chosen at
date 0. The expectation and the variance
of wealth at date T take the well-known
forms:
(2.1)
It would also have been possible to cast
the model in a fixed-mix framework, as
Hoevenaars et al. (2008) do: assuming
fixed-mix strategies and normal logreturns on securities, and using the loglinear approximation to the intertemporal
budget constraint of Campbell and Viceira
(2001), they are able to relate the moments
of wealth to the constant weights. Our
approach assumes a different form of
strategies, which is perhaps less realistic,
but it does not require any normality
assumption about returns, and it gives
exact, as opposed to approximated,
expressions for the moments of wealth
(see (2.1)). In other words, expressions (2.1)
are model-free as far as the distribution
of asset returns is concerned.
In fact, because of the presence of
liabilities, the investor is not so much
concerned with the uncertainty in wealth
itself as with the uncertainty in wealth
relative to liabilities. Thus, the welfare
measure has to be a function of some
measure of the relative risk of the portfolio.
Two main options have been proposed
in the literature: a focus on the funding
ratio
, or a focus on the surplus AT − LT.
We follow the second approach here,
because the assumptions made above
imply simple expressions for the moments
of the surplus. To write them, we define a
few auxiliary notations: AL is the N ×1
vector of covariances between the risky
assets and liabilities, L is the expected
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
2. The Investment Model
terminal value of liabilities, and
variance of liabilities.
is the
Then:
Finally, the welfare is represented by a
quadratic utility from the surplus, a metric
that depends on a risk aversion parameter
γ:
4 - The LHP that appears in the
optimal strategy maximises the
squared correlation, not the
correlation itself, because this
strategy is derived under the
assumption that short-selling
is permitted, so that a negative
correlation can be virtually
turned into a positive one.
Pension funds often adopt liability-driven
investing strategies, where performance
and hedging are managed separately,
through the allocation to a “performance”
building block and a “liability-hedging”
block. The objective of the performanceseeking portfolio (PSP) is to achieve a high
Sharpe ratio, while that of the liabilityhedging portfolio (LHP) is to replicate
the value of liabilities as accurately as
possible. Thus, it is natural to restrict our
attention to pairs of blocks that satisfy
the following conditions:
maximum Sharpe ratio portfolio and the
portfolio that maximises the squared
correlation with liabilities.4 The building
blocks that we consider in this paper are
not theoretical constructions that achieve
the maximum Sharpe ratio or the highest
squared correlation, and they only satisfy
(2.2). In what follows, we denote with
and
the terminal wealths
achieved by investing the capital A0 in
solely one building block.
The
following
proposition
gives
expressions for the moments of the
surplus under the strategy (2.3). This
result is straightforward, as it is merely
a rewriting of the expectation and the
variance in the case where there are
only two assets, namely a PSP and an
LHP. Nevertheless, it is useful to justify
the subsequent attempts to improve the
performance of the LHP and the hedging
properties of the PSP.
Proposition 1
Consider strategy (2.3). The expectation
and the variance of the surplus are given
by:
(2.2)
where λ stands for the Sharpe ratio and
ρ·,L for the correlation with liabilities. The
LDI portfolio is a combination of the two
building blocks:
(2.4)
(2.3)
Such a strategy can be rationalised in an
expected utility framework (see Martellini
and Milhau (2012) for a continuoustime model), although the building
blocks that would be involved in the
utility-maximising portfolio rule are the
(2.5)
For P = PSP,LHP, we have:
(2.6)
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Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
2. The Investment Model
and the covariance term is:
This proposition shows that although the
objective of the LHP is to hedge liability
risk and that of the PSP is to deliver a high
risk-adjusted performance, the welfare is
increasing in the Sharpe ratio of the LHP
and in the correlation of the PSP with
liabilities. Indeed, the partial derivatives
of the quadratic utility with respect to
ρPSP,L and λLHP are:
These equalities have straightforward
interpretations. The derivative of IW
with respect to LHP is: (i) increasing in
the allocation to the LHP (the properties
of the LHP matter more when this block
represents a substantial fraction of the
global allocation); (ii) increasing in the
volatility of the LHP (a large volatility
tends to make the surplus more uncertain,
which negatively impacts the utility,
unless it is compensated by a high Sharpe
ratio). Similarly, the derivative of IW with
respect to ρPSP,L is: (i) increasing in x; (ii)
increasing in the risk aversion (highly
risk-averse investors are more concerned
with the variance of the surplus); (iii)
increasing in the volatility of the PSP (the
impact of a high volatility on the variance
of the surplus needs to be compensated
by a greater correlation with liabilities);
(iv) increasing in the volatility of liabilities
(hedging liability risk is more important
when liabilities are particularly risky).
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An EDHEC-Risk Institute Publication
2.2 Comparing Strategies
The quadratic utility serves as a criterion
to compare different portfolio strategies:
a strategy will be preferred to another if it
yields higher utility. An interesting special
case is that of two strategies that lead to the
same surplus variance. Then, the difference
between utilities reduces to the difference
between expected terminal wealths:
(2.7)
where 1 and 2 refer to the two strategies.
This situation is of particular interest
because the difference between utilities
does not depend on the risk aversion,
which is hard to specify given that it is
unobservable. Hence, a recurrent question
in the empirical section of this paper
will be to find a “variance-matching
allocation” x2 given a LDI strategy (PSP1,
LHP1; x1). Denoting with Vi(xi) the variance
of the surplus under the ith strategy,
we have to solve the equation V2(x2) =
V1(x1) (note that the variance is indexed
by i because it depends on the building
blocks, not only on xi). Proposition 1
shows that this equation is quadratic in
x2. As a consequence, it may have either
one solution, two solutions or no solution
at all (in the field of real numbers). The
following proposition gives the conditions
under which at least one solution exists, as
well as the expressions for the solutions.
Proposition 2 (Variance-Matching
Allocations) Consider two LDI strategies
characterised by the triplets (PSP1,LHP1;
x1) and (PSP2,LHP2; x2). Let:
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
2. The Investment Model
If a > 0 and b2 ≥ ac, then the allocations
x2 that satisfy V2(x2) = V1(x1) are given by:
They are equal if b2 = ac.
5 - In the absence of a riskfree asset, the Global Minimum
Variance portfolio would
replace the risk-free asset
in the optimal strategy.
Proof. See Appendix A.
Note that these allocations do not
necessarily lie between 0 and 1. Whether
this condition is satisfied or not depends
on other parameter values, and must
be checked on a case-by-case basis. A
special case where these allocations take
a particularly simple form is when both
strategies make use of a perfect LHP.
Then, the surpluses
for i =
1, 2 are zero, so that:
One of these allocations is clearly
negative, and is thus of limited practical
interest. The other one is proportional to
the ratio of the volatilities of the surpluses
achieved by investing in PSP1 and PSP2,
respectively. If PSP2 is a better hedge
for liabilities, the surplus
has lower volatility than the surplus
, so that x1 is greater than
x2. This result is natural: by improving the
hedging properties of the PSP, one can
allocate less to the LHP (that is, more to
the PSP), without increasing the variance
of the surplus under the LDI strategy.
Because the PSP has generally higher
expected return than the LHP, shifting
the allocation towards the PSP allows
the performance of the portfolio to be
increased. In Section 3, we will quantify
both the increase in allocation and the
gain in expected return for realistic
parameter values.
2.3 Fund Interaction Theorems
The fund interaction theorems of Deguest
et al. (2012) are derived in a continuoustime setting, with a Constant Relative
Risk Aversion utility function. In this
section, we derive similar results in our
two-period setting. Even if they are not
directly used in the empirical section of
the paper (Section 3), they give another
justification for the alignment of the
performance and hedging motives.
The first step is to derive the optimal
strategy. For the simplicity of exposure, it
is convenient to assume that there exists
a risk-free asset, that is a security whose
rate of return Rƒ over [0, T] is known as of
date 0. This asset is thus a zero-coupon
that redeems its principal at date T. We
emphasise that it will not be used in the
empirical analysis and is introduced here
only to simplify the expression of the
optimal strategy.5 Mathematically, the
optimisation program reads:
(2.8)
Proposition 3 (Optimal Strategy Two-Fund Separation)
The weights that solve Program (2.8) are:
where the “optimal PSP” is the maximum
Sharpe ratio portfolio and the “optimal
LHP” is the portfolio that has the highest
squared correlation with liabilities:
λPSP* and σPSP*are the Sharpe ratio and
the volatility of the PSP, and βL/LHP*
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Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
2. The Investment Model
is the beta of liabilities with respect to the
LHP.
Proof. See Appendix B.
The first block, denoted as PSP, is the
maximum Sharpe ratio (MSR) portfolio
computed over the investment universe.
The optimal allocation to this fund is
decreasing in the risk aversion. When γ
grows to infinity, the optimal strategy is to
allocate the weight βL/LHP*to the LHP, and
the remainder to the risk-free asset. This
ensures that the variance of the surplus is
minimised. For a general risk aversion, the
form of the optimal vector of weights is
slightly different from that of the optimal
policy in the continuous-time setting with
CRRA preferences of Martellini and Milhau
(2012). Indeed, the allocation to the LHP is
independent from the risk aversion, while
it is proportional to (1 − 1 / γ) in their
paper. This dissimilarity arises because of
the differences between the two models:
in the one-period framework, portfolios
cannot be rebalanced; and preferences
are represented here by a quadratic utility,
as opposed to a power utility function.
It is worth noting that the optimal
allocation to the PSP depends only on its
Sharpe ratio and volatility, in addition to
the risk aversion. The correlation between
the PSP and liabilities does not impact
the decision to invest more or less in this
block. Similarly, the optimal portfolio rule
does not depend on any performance
indicator of the LHP: the only parameter
of the LHP that matters is the beta of
liabilities with respect to this portfolio.
Overall, it may seem from Proposition 3
that the hedging properties of the PSP
and the performance properties of the
LHP are irrelevant to the investor. This
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An EDHEC-Risk Institute Publication
view is, however, incomplete: while it is
the case that these characteristics do not
enter the optimal rule, it makes intuitive
sense that they will eventually impact the
welfare. For instance, if it happens that the
investor holds a large long position in the
PSP because this fund has a particularly
nice Sharpe ratio, but the PSP is strongly
negatively correlated with liabilities,
this should increase the variance of the
surplus, and, in turn, decrease expected
utility. In the same way, if the LHP turns
out to be a very good hedge of liabilities,
with a beta close to 1, it will be desirable
to invest a substantial fraction of wealth
in it, but if it also has a very poor Sharpe
ratio, this will tend to deteriorate
the performance of the LDI strategy.
The second fund interaction theorem
(Theorem 2) gives a formal justification
to these intuitions. Before we state it, we
provide below a first interaction result,
that gives a relationship between the
parameters of the optimal PSP and those
of the optimal LHP. It has the same form
as the interaction equalities between the
parameters of the PSP and those of the
hedging portfolios derived in Deguest et
al. (2012).
Theorem 1 (1st Fund Interaction
Theorem)
The parameters of the optimal building
blocks defined in Proposition 3 satisfy:
Proof. See Appendix C.
It should be noted that this equality holds
only for the building blocks defined in
Proposition 3, that explicitly maximise
a criterion. It does not hold, in general,
for the heuristic PSP and LHP that appear
in (2.3). In words, this equality means
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
2. The Investment Model
that the relative domination of the PSP
over the LHP in terms of Sharpe ratio
(a domination that can be measured
by the ratio of absolute Sharpe ratios,
|λPSP*|/|λLHP*|, which is greater than 1 by
definition of the two portfolios) is equal
to the relative domination of the LHP
in terms of correlation (which can be
measured by the ratio |ρLHP*,L|/|ρPSP*,L|,
also greater than 1). This result is useful
to interpret the second fund interaction
theorem, which we state now.
Theorem 2 (2nd Fund Interaction
Theorem)
The maximum expected quadratic utility
in (2.8) is:
Proof. See Appendix C.
Four contributions to welfare can be
identified. The term
is a
contribution from the performance
motive, since it depends only on the Sharpe
ratio of the PSP. The term
is a
contribution from the hedging motive: the
coefficient γ in this contribution reflects
the fact that more risk averse investors
attach more importance to hedging
liability risk. The third term, ρPSP*, LλPSP*
σL is a cross-contribution of performance
and hedging motives, since it involves one
performance parameter (the PSP Sharpe
ratio) and one hedging parameter (the
correlation of the PSP with liabilities).
By Theorem 1, it can equivalently be
rewritten in terms of the LHP Sharpe ratio
and the correlation of LHP with liabilities.
Finally, the fourth contribution, equal to
, does not depend on the
strategy: it reflects investor’s aversion
for a high expected terminal value of
liabilities (large μL) and a high uncertainty
in this value (large σL).
Among the first three terms, only the
cross-contribution may be negative.
The interpretation for its sign is as in
Deguest et al. (2012). A positive crossterm means that the PSP is positively
correlated with liabilities (at least to the
extent that it has a positive Sharpe ratio).
Hence, the long position in the PSP that
is taken for performance considerations
also contributes to reduce the surplus
variance. The performance and the
hedging motives are thus in line with each
other, which results in a higher welfare.
The magnitude of this increase in utility
is itself increasing in the correlation of
the PSP with liabilities. On the other
hand, if the PSP covaries negatively with
liabilities, the two motives compete with
each other: the positive Sharpe ratio calls
for a long position in the PSP, regardless
of the correlation, but as a side effect, the
negative correlation magnifies the surplus
variance. This competition negatively
impacts the welfare.
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Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
2. The Investment Model
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3. Empirical Results
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Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
3. Empirical Results
The purpose of this section is to assess
in a quantitative way the benefits of
introducing corporate bonds in the PSP
and/or in the LHP. The general idea is to
compare portfolios that include these
bonds to portfolios that exclude them,
by reasoning with strategies that yield
the same surplus variance. This is thus an
empirical application of the methodology
described in Section 2.2.
3.1 Dataset and Parameter Values
In order to compute quadratic utilities and
variance-matching strategies, we need the
covariance matrix and the expected excess
returns of the assets, and , as well as
the vector of covariances between assets
and liabilities. We calibrate these parameters
to market data. Specifically, we consider
an investment universe that contains one
broad stock index, one sovereign bond
index and one corporate bond index. The
stock is represented by the CRSP valueweighted index of the S&P 500 universe,
the sovereign index by the Barclays US
Treasury bond index and the corporate index
by the Barclays US Corporate Investment
Grade index. All these indices are taken
to be total return indices, that is, with
dividends and coupons reinvested. The two
bond indices are available from Datastream
at the monthly frequency over the period
of February 1973-January 2013, and the
stock index is taken from CRSP. Figure 1
shows the values of $1 invested in each
index on February 28, 1973, and held until
December 31, 2012.
Table 1 reports descriptive statistics on the
three series, obtained from simple monthly
returns. The stock turns out to have the
highest volatility, of 17.2% per year. The
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An EDHEC-Risk Institute Publication
least volatile asset is the nominal bond,
with a standard deviation of 5.7% per year,
and the corporate bond lies between the
other two assets. The correlation between
the two bond indices is as high as 82.1%,
which suggests the presence of a set of
common factors in their returns.
The sample mean returns (not shown in the
table) are respectively 11.27% per year for
the stock, 8.08% for the sovereign bond
and 8.63% for the corporate bond. These
values should be taken cautiously, because
it is well-known (see e.g. Merton (1980))
that sample means are poor estimators of
expected returns. In particular, the expected
return on sovereign bonds seems overstated:
as pointed by Dimson et al. (2008), US
bonds performed well between 1981 and
2000, with average nominal return close
to 12% per year, but the period from 1946
to 1981 saw a bear market, with nominal
returns around 2% per year and negative
real returns due to the high inflation rates
recorded in those years. Hence, a value of
7% for Treasuries seems more in line with
the examination of long-term series. It still
appears to be an optimistic forecast in view
of the low current level of interest rates:
indeed, the presence of mean reversion in
rates makes it more likely for bond prices to
go downwards than upwards in the future.
It is expected that corporate bonds earn a
higher return than sovereigns, due to the
default risk premium that they embed. But
precisely because they are subject to the
default risk of the issuer, the higher return
that they promise can be offset by the
loss of value in case of default or credit
events such as downgrading. As a matter
of fact, Dimson et al. (2008) find that the
differential annualised return between
US nominal and corporate bonds is about
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
3. Empirical Results
50 basis points per year between 1900
and 2000, while the difference in yields,
which measures the premium that investors
require to bear the default and credit risks,
is about twice as high. The 50 basis points
value roughly corresponds to the difference
[8.63%−8.08%] in our dataset. Nevertheless,
the average duration of the corporate index
is 6.7 years, while that of the Treasury index is
4.7 years. Hence, the expected return on the
former should include a maturity premium
in addition to the default premium. We
account for this by assuming an expected
return of 8.4% for corporate bonds.
6 - A broad stock index such
as the S&P 500 has poor
inflation-hedging properties,
but some sectors such as
Oil & Gas and Technology have
higher betas with inflation
(Ang et al., 2012).
Finally, equities are the most risky asset class
of the three, and as a consequence, should
have the highest expected return. This effect
is already present in the data, since the
mean return is 11.27%. But Dimson et al.
(2008) find a premium of 5% over long
bonds. Since we have assumed that nominal
bonds have an expected return of 7% per
year, we thus round the sample value to
12%. To compute the Sharpe ratios of the
asset classes, we take the risk-free rate to
be the average over the period 1973-2012
of the secondary market rate on 3-month
Treasury bills, a series that we obtain from
the website of the Federal Reserve of St.
Louis. This average rate is 5.29%, which
implies the Sharpe ratios 0.39 for stocks,
0.30 for sovereigns and 0.40 for corporates.
3.2.1 Building Blocks
The LDI strategy requires a PSP and an LHP.
In what follows, we consider three different
versions of the PSP with an increasing
fraction of wealth allocated to corporate
bonds: the benchmark PSP, also referred
to as PSP 1, contains 80% of equities, the
remainder being invested in Treasuries. The
other two PSPs respectively contain 15%
and 30% of corporates. In order to fix the
degree of freedom, we impose that the
ratio of stock weight to sovereign weight
be the same in all three PSPs. This leads to:
These PSPs are all dominated by equities,
since it is the asset class that is typically
used to seek performance. But none of
them is meant to be an MSR portfolio. In
the same way, we consider three different
versions of the LHP: the benchmark LHP,
also referred to as LHP 1, is invested in
sovereign bonds only, and the other two
LHPs contain respectively 25% and 100%
of corporate bonds.
3.2 Introducing Corporate Bonds in
PSP or LHP
To illustrate the benefits of introducing
corporate bonds in the portfolio, we assume
that the investor follows a LDI strategy of
the form (2.3). The investment universe
consists of the stock, the sovereign bond
and the corporate bond.
All these portfolios are invested in bonds
only. Since LHPs are most often dominated
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Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
3. Empirical Results
by nominal bonds, the LHP 1 is an acceptable
stylised representation of the typical LHP
held by a pension fund.
6 - A broad stock index such
as the S&P 500 has poor
inflation-hedging properties,
but some sectors such as
Oil & Gas and Technology
have higher betas with
inflation (Ang et al., 2012).
7 - Of course, nominal bonds
are not good hedges for
inflation-indexed liabilities
with a short duration, because
realised inflation risk becomes
the dominant source of risk
when the maturity shortens.
8 - Campbell et al. (2009)
show that the 10-year
breakeven rate in the US was
relatively stable between 2004
and 2008, but collapsed at the
end of 2008, which highlights
the fact that nominal and real
rates are not perfectly
correlated.
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An EDHEC-Risk Institute Publication
In general, the optimal LHP (LHP in
Proposition 3) may contain stocks,
depending on the risk factors to hedge.
For instance, if stocks are good at hedging
inflation risk, then they can be useful for
hedging inflation-linked liabilities.6 In our
model, liability payments are not indexed
on inflation, so the value of liabilities is only
impacted by the discount rate. It is natural
to seek to hedge this risk with nominal
bonds. That is not to say that stocks
do not have any interest-rate hedging
properties, but their duration is more
difficult to evaluate than that of bonds. For
instance, Leibowitz et al. (1989) argue that
the traditional Dividend Discount Model
overstates the duration of equities, and
Reilly et al. (2007) show that the empirical
duration of the S&P 500 exhibits large
fluctuations over time. In contrast, a bond
index, which has a built-in exposure to
interest rate risk, has a much less volatile
duration.
Were liabilities indexed on inflation, one
could also use the obvious option to
introduce inflation-linked bonds in the LHP.
Nevertheless, nominal bonds are in general
dominant in LHPs. This predominance can be
explained by practical reasons: the supply
of nominal bonds still exceeds that of
inflation-linked bonds, although indexed
debt represents a growing fraction of
the outstanding debt of large developed
countries, so these bonds are more liquid.
One can also give theoretical arguments
that justify to some extent the use of
nominal bonds in the LHP. Indeed, interest
rate risk is the dominant source of risk in
liabilities, because the sensitivity of liabilities
to the discount rate is increasing in their
duration, which is typically long. Even for
inflation-indexed liabilities, interest rate risk
dwarfs realised inflation risk, at least when
liabilities have a long maturity (Martellini
and Milhau, 2013).7 As argued by Campbell
et al. (2009), nominal bonds are in fact
perfect substitutes for inflation-linked
bonds if breakeveninflation rates, defined
as the differences between nominal rates
and real rates of the same maturity, are
constant.8
Table 2 gives descriptive statistics for the six
building blocks. For comparison purposes, it
also provides the same statistics for the
stock (the figures for the sovereign bond
and for the corporate bond are read in
columns LHP 1 and LHP 3, respectively). All
these figures have been obtained from the
descriptive statistics for the asset classes
shown in Table 1. In detail, we compute the
expected excess return on a portfolio with
weights as
, so the annualised
expected excess return can be derived from
those of the constituents as:
where T is the investment horizon. The
variance of the portfolio is
,
where
is the covariance matrix of the
assets: its coefficients are given by σij = σi
σj ρij, where ρij is the correlation between
the assets and σi is the volatility of asset i at
horizon T, which can be computed from the
annualised volatility and expected return as:
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
3. Empirical Results
The annualised volatility of the portfolio is
then computed as:
For portfolios invested in a single asset,
these definitions lead to
and
, as expected, but for portfolios
invested in multiple asset classes,
and
depend on the horizon T. We set T to
10 years.
9 - We note that the
portfolios respect the
condition on Sharpe ratios
and correlations with
liabilities (see (2.2)).
Unsurprisingly, introducing corporates in
the LHP has a positive effect on expected
returns, which is a direct consequence of the
outperformance of these bonds over their
sovereign counterparts. It also increases the
volatility, but given the assumed risk-free
interest rate (5.28%, which is the sample
average of the 3-month T-bill rate), it has
also a positive effect on the Sharpe ratio.
For the PSP, however, including corporates
comes at the cost of a lower allocation
to stocks. Because stocks have a higher
expected return, the PSPs that include
corporates have lower expected returns
than the PSP invested only in stocks and
sovereign bonds (PSP1).
We assess the liability-hedging properties
of the various portfolios with respect to two
liability processes. First, we consider liabilities
discounted at the “risk-free” rate: they are
proxied by the sovereign bond index itself.
The second liability value is obtained by
adding a spread to the risk-free rate. This is
motivated by the international accounting
standards SFAS 87.44 and IAS19.78, which
recommend that pension obligations be
valued on the basis of a discount rate equal
to the market yield on AA corporate bonds.
For simplicity, we refer to this rate as the
“risky rate” in what follows. It should be
noted, however, that the “risk-free” rate is
also risky in the sense that it varies over
time. Thus, the name “risky” simply implies
that the AA rate proxies the discount rate
that applies to a defaultable corporate bond
rated as investment grade. We represent
this second liability process by the value
of the corporate bond index. In addition
to the correlations between the various
portfolios and the two liability values, we
also report a related indicator, which is the
volatility of the final surplus, computed as
the square root of:
where ρPL is the correlation between the
portfolio and liabilities. This variance
depends on the initial wealth, A0, and the
initial value for liabilities, L0. We assume
that both these values are equal (initial
funding ratio of 1), and we normalise them
to 1.
Correlations and the surplus volatilities are
also reported in Table 2.9 A first observation
is that all three PSPs are more correlated
with liabilities discounted at the risky rate
than with those discounted at the risk-free
rate. This is due to the dominance of stocks
and corporate bonds over Treasuries in the
PSP: by definition of the liability process,
corporates are a perfect hedge for liabilities
discounted at the risky rate, and as shown
by Table 1, stocks have a correlation of
35.6% with this process, versus 8.50% only
with liabilities discounted at the risk-free
rate. In spite of this higher correlation,
the surpluses computed with respect to
liabilities discounted at the risky rate are
more volatile, which comes from the higher
volatility of these liabilities. It also appears
that introducing corporates in the PSP leads
to higher correlations with both liability
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Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
3. Empirical Results
processes: for instance, when the risky rate
is used, the benchmark PSP (PSP 1) has a
correlation of 39.7% with liabilities, while
the PSP that contains 30% of corporates
(PSP 3) has a correlation of 52.9%. This
comes as no surprise, since corporates are by
definition a perfect hedge for liabilities, but
we also see that the correlation increases
when the risk-free rate is chosen: indeed,
PSP 1 is largely dominated by stocks, that
have little hedging capacity with respect to
nominal interest rate risk, so adding bonds
can only enhance its hedging properties. But
this improvement is paid by a decrease in
expected return, from 11.2% for PSP 1 to
10.4% for PSP 3. This is a consequence of
the decrease in the allocation to equities,
which are the best-performing asset class
in our model. Overall, introducing corporate
bonds in the PSP gives rise to a tradeoff between performance (measured by
expected return) and correlation.
The situation is different for the LHP. The
benchmark LHP is entirely invested in the
asset class with the lowest expected return
(7.0%), so that increasing the allocation
to corporate bonds gives access to higher
performance. When liabilities are discounted
at the risk-free rate, this even generates a
higher correlation with liabilities: indeed,
the correlation between these liabilities and
the LHP invested only in corporate bonds is
perfect, by construction. Hence, in that case,
there is no trade-off between performance
and hedging: using corporate bonds leads
to an improvement on both fronts.
3.2.2 Benefits of Introducing
Corporate Bonds in PSP
As argued previously, the introduction
of corporate bonds in the PSP improves
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An EDHEC-Risk Institute Publication
its correlation with liabilities, but lowers
its performance compared to an equitydominated portfolio. It remains to assess
the net impact of such a modification in the
context of an ALM strategy. The intuition
is as explained in Section 2.2: by choosing
a portfolio that has better correlation with
liabilities, one can decrease the allocation to
the LHP, without increasing the risk of the
global portfolio. In other words, one can
afford investing more in the PSP with
improved hedging properties, while staying
within a fixed risk budget, which is equal
to the volatility of the LDI strategy that
uses the benchmark portfolio. Even if this
higher weight is applied to a portfolio
that has lower expected return (see Table
2), it is expected that the final effect on
the expected return of the strategy will
be positive. In order to verify whether this
intuition is true, we consider a “benchmark”
LDI strategy, invested in the benchmark PSP
(denoted with PSP 1 in Table 2), and in the
LHP that only contains Treasuries (denoted
with LHP 1 in Table 2), and an “improved”
LDI strategy, invested in the same LHP and
an improved PSP, either PSP 2 or PSP 3. For
each allocation x1 to the benchmark PSP, we
seek the variance-matching allocations to
the improved PSPs that contain corporate
bonds. We then compute the difference
between the expected terminal wealths
attained with the benchmark LDI strategy
and with the “improved” LDI strategies. Since
we have normalised the initial asset value
to $1, this difference can be interpreted as
a difference between expected arithmetic
returns. But because returns are usually
expressed in annual terms, we instead
report the difference between annualised
arithmetic returns, that is, if
is the
wealth attained at date T with the
benchmark LDI strategy and
is the
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
3. Empirical Results
wealth attained with the improved one
(i = 2 or 3, depending on the PSP used):
Note that this quantity is different from
the change in quadratic utility (see (2.7)),
which is
, but it is more
interpretable, since it represents a gain (or
a loss, depending on the sign) in annual
expected return. Besides, it has the same
sign as IWi − IW1.
As pointed in Section 2.2, there are in fact
two variance-matching allocations xi for
each value of x1. Let us denote with and
these two values, which are defined in
Proposition 2. Since distinct values of xi lead
to different values for , we have to decide
which one to pick. A meaningful criterion
is the sign of xi and that of 1−xi: for the
LDI strategy (2.3) to involve long positions
in the PSP and the LHP, xi must be between
0 and 1. Thus, a natural criterion would be
to retain the root of the variance-matching
equation that lies within these bounds. This
raises the question whether there exists
exactly one nonnegative solution.
This is the case if the conditions of
Proposition 2 are met, and the quantity
is negative.
The sign of c depends in general on
parameter values, but it is likely to be
positive: indeed, the variance of the surplus
achieved by investing only in LHP 2 will be
in general “small”, at least smaller than the
variance achieved with the LDI strategy.
Thus, one can reasonably expect to have
exactly one positive solution, which is the
higher of the two roots: thus, we retain
as the variance-matching allocation
to the improved PSP. With our parameter
values, it turns out that
is always the
unique positive solution. Nevertheless, it
can be larger than 1, which would yield
short positions in the LHP. Thus, we only
report the value of ∆ for those values of
x1 that imply a long position in the LHP.
Figure 2 shows the variance-matching
allocation and the increase in expected
return, for x1 ranging from 10% to 80%.
It appears that
is larger than x1 for all
tested parameter values, which justifies
the aforementioned intuition: for a given
risk budget, one can invest more in a PSP
with improved liability-hedging ability. The
increase in weight is also larger with the PSP
that contains 30% of corporates (PSP 3)
than with the one that contains only 15%
of these bonds (PSP 2). For instance, using
the risk-free rate plus the spread to discount
liabilities, and assuming an allocation
x1 = 40% to the benchmark PSP, one can
invest 47.5% in PSP 2, and 58.0% in PSP
3. Lower values would be obtained with
liabilities discounted at the risk-free rate:
respectively, 46.2% in PSP 2, and 54.4%
in PSP 3. This makes sense: by introducing
corporate bonds in the PSP, one improves
primarily its correlation with the liability
process whose discount rate includes a
credit spread component, so the increase in
the PSP weight should be higher than for
liabilities discounted without this spread.
A related observation is that the increase
in annual expected return is larger for the
former liability process: still focusing on
the case x1 = 40%, one achieves modest
increases of 5.5 and 12.6 basis points per
year respectively, by investing in PSP 2
and PSP 3 under the valuation rule at the
risk-free rate, and these values grow to
10.5 and 24.6 annual basis points if the
spread is added.
One may be puzzled by the observation
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Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
3. Empirical Results
that the gains in performance do not
converge to zero as x1 approaches zero.
Indeed, if one does not invest in the PSP,
then one should be indifferent to a change
in its composition. But this statement is
incomplete: allocating nothing to the
benchmark PSP does not imply that one
does not invest at all in the improved PSP.
To see this, let us consider the variancematching condition written for the same
pair of building blocks: it reads V1(xi) =
V1(x1), and is of course satisfied for xi = x1.
But because it is a quadratic equation in
xi, it has in general two roots,
and .
For x1 = 0, the expressions of Proposition
2 imply that:
so
is zero if, and only if,
is
nonnegative. Given our parameter values,
b is actually negative, so x+i is positive
(the zero root is
, which is the dropped
solution). This explains why it is possible to
enjoy an increase in expected return even if
one invests nothing in the benchmark PSP.
In order to provide a visual representation
of the changes in the properties of the
strategies, Figure 3 shows the distributions
of the surplus under the three LDI strategies
that are being compared, for an allocation
x1 = 50% to the benchmark PSP: the two
improved strategies are invested in the same
LHP, and in PSP 2 and PSP 3 respectively,
and they satisfy the variance-matching
conditions V2(x2) = V1(x1) and V3(x3) =
V1(x1). Because our theoretical model does
not assume a particular distribution for
asset returns, we need to specify one at
this stage in order to simulate values for
the surplus. We postulate a log-normal
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An EDHEC-Risk Institute Publication
distribution for returns, and we estimate the
moments (vector of expected returns and
covariance matrix)of this distribution as the
sample moments of logarithmic returns of
the stock and the two bond indices. Thus,
these moments are slightly different from
those given in Table 1. We thensimulate
50,000 values for the surplus attained
with each LDI strategy after ten years. By
construction, all three strategies imply the
same surplus volatility (57.5%), but the
expected surpluses are higher with the
strategies that allow for corporate bonds
(20.7% and 24.1% of A0 respectively) than
with the benchmark strategy (18.2% of A0).
The simulated distribution also enables
to estimate the probability of a negative
surplus after ten years: it appears that this
probability is decreasing in the weight of
the corporate bonds in the PSP.
3.2.3 Benefits of Introducing
Corporate Bonds in LHP
We now conduct a similar but dual analysis
in order to measure the gains of introducing
corporate bonds in the LHP. The primary
objective pursued by adding corporate
bonds to nominal bonds in the LHP is
not an improvement in correlation with
liabilities (as for the PSP), but a performance
gain. This, of course, does not rule out the
possibility of enjoying a better correlation:
Table 2 shows that with the valuation rule
at the risky rate, the LHPs that contain
corporates have both greater expected
return and larger correlation.
Thus, the mechanism at work here is
different than the one in Section 3.2.2:
by increasing the performance potential
of the LHP, one can allocate more to the
LHP without lowering the expected return
of the LDI strategy. This higher weight in
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
3. Empirical Results
the LHP should lead to a lower risk for the
strategy. If liabilities are discounted at the
risk-free rate, a trade-off between the two
effects arises, because the LHP with
corporates has lower correlation than the
benchmark LHP invested in sovereign bonds
only. On the other hand, if the discount
rate includes a spread, there is no tradeoff since introducing corporates in the LHP
also enables its correlation to increase.
In order to have a quantitative measure
of the reduction in risk, we take the
following approach: for a given allocation
y1 = 1 − x1to the benchmark LHP, we search
for the allocation yi = 1 − xi to the improved
LHP, which can be either LHP2 = (0, 0.75,
0.25) or LHP3 = (0, 0, 1), that leaves the
expected terminal wealth unchanged.
Denoting with Ei (xi) the expected terminal
surplus in Proposition 1, with i = 2 or 3
depending on the LHP used, we can write
this expectation-matching condition as
Ei(xi) = E1(x1). This equation is linear in xi,
so it has at most one solution, which is
given by:
(there may be no solution in the very special
case where
, but this
equality is unlikely to hold true, because
the PSP has in general higher expected
return than the LHP; at least Table 2 shows
that this condition is verified with our
parameter values). We then compute the
relative change in the volatility of the final
surplus, that is the ratio:
where
is the final wealth achieved with
the LDI strategy invested in PSP 1 and LHP
1 and
is the wealth attained with the
LDI strategy invested in PSP 1 and LHP 2
or LHP 3.
Results are shown in Figure 4. First, it appears
that the use of corporate bonds in the LHP
allows the allocation to this building block
to be increased without adversely impacting
the expected return of the strategy. This
follows from the outperformance of
corporate bonds with respect to sovereign
bonds. Second, this modification of the
composition also leads to a lower surplus
volatility. Since the increase in the LHP
weight is more important for the LHP
invested in corporate bonds only, the
reduction is risk is more substantial with
this LHP. This reduction is also larger when
liabilities are discounted at the risk-free
rate plus spread, which is natural given
that corporate bonds are a perfect hedge
for this liability process. Overall, the relative
decrease in standard deviation can be very
significant. For instance, focusing on the
case where liabilities are discounted at the
risky rate and an allocation 60% to the
benchmark LHP, one decreases the volatility
by 12.6% by investing in LHP 2, and by
64% if one chooses the LHP fully invested
in corporate bonds.
Following the same protocol as in Section
3.2.2, we then simulate the distributions of
surpluses achieved with three LDI strategies,
invested respectively in (PSP 1, LHP 1), (PSP
1, LHP 2) and (PSP 1, LHP 3). The weight
allocated to LHP 1 in the benchmark
strategy is 50%, and the allocations to LHP
2 and LHP 3 are computed in such a way
as to keep the expected terminal wealth
unchanged, or equivalently, the expected
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Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
3. Empirical Results
terminal surplus fixed (at 18.2% of A0). Thus,
what is gained by introducing corporate
bonds is a reduction in the volatility of
the surplus, from 57.5% of A0 with the
benchmark strategy, to only 33.6% with
the strategy that uses corporate bonds as
the unique hedging instrument for liability
risk. The probability of underfunding is also
reduced.
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Conclusion
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Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
Conclusion
This paper provides an empirical analysis
of the sources of added-value of corporate
bonds for institutional investors. For
reasonable parameter values, we have
found corporate bonds to be attractive
additions to investors’ portfolios. On
the one hand, introducing them in
performance-seeking portfolios (PSPs)
typically generates positive benefits
from an asset-liability management
perspective since it will lead to substantial
improvements in hedging benefits,
which come at the cost of a less-thanproportional reduction in performance
compared to equity-dominated portfolios.
Introducing corporate bonds in liabilityhedging portfolios (LHPs) is also found to
generate a positive impact on investor
welfare since it leads to improvements
in both hedging and performance
benefits, especially for investors facing
liabilities discounted using a credit spread
adjustment. In this context, one may want
to assess whether a particular proportion
of corporate bonds in each portfolio would
lead to the highest level of welfare gains.
The answer to this question is of course
that the optimal allocation to corporate
bonds should maximise the Sharpe
ratio within the PSP, and the (squared)
correlation with the liabilities within the
LHP. In fact, the fund interaction theorem
and the fund separation theorem are
not mutually inconsistent; the fund
interaction theorem complements the
fund separation theorem by emphasising
the benefits of having, if and when
possible, an alignment, as opposed to a
conflict, between the performance and
hedging motives.
Our analysis can be extended in many
possible directions. First of all, it would
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An EDHEC-Risk Institute Publication
be useful to draw a distinction between
investment grade bonds and high yield
bonds, given that the risk, return as well
as factor exposure characteristics of these
two segments of the corporate bond
market are clearly distinct. Also, one could
consider corporate bond benchmarks with
various numbers of constituents so
as to assess the impact of credit risk
diversification on the results in the paper.
Finally, the interaction analysis in this
paper could usefully be extended to other
types of securities, including, for example,
equities. In particular, a large crosssectional variation exists in the interest
rate exposure of various segments of the
equity markets, and some sectors (e.g.,
utilities), or types of stocks (e.g., high
dividend stocks), have been found to have
a duration that is substantially higher
than the duration of a well-diversified
equity portfolio (see for example Reilly et
al. (2007)). If an equity benchmark can be
constructed with a substantially enhanced
interest rate risk exposure, without a
significant cost in terms of Sharpe ratio,
then the analysis in this paper suggests
that using this benchmark as opposed to
a standard market index may lead to
improvement in welfare for an investor
facing liabilities.
More generally, there are at least two
reasons why investors would find it
optimal to invest in any asset class.
First, the asset class under consideration
can be useful if it provides access to
excess performance with respect to cash
(speculative demand for risky assets that
generate an exposure to rewarded sources
of risk). Secondly, it can also be useful if it
provides hedging benefits (intertemporal
hedging demands for risky assets that
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
Conclusion
can be used to immunise wealth levels
with respect to risk factors that impact the
value of liabilities and the opportunity set).
Clearly, these motives are not mutually
exclusive; for example, bonds are useful
ingredients in the speculative component
of investors’ portfolios, where they bring
excess performance with respect to cash
and diversification benefits with respect
to equities, and they are also useful in
the hedging component of liability-driven
long-term investors’ portfolios, where they
allow for protection against unexpected
changes in interest rates. The analysis in
our paper suggests that not only are the
two motives not mutually exclusive, but
also that these two motives interact, and
their interaction is a key driver of the
ability for investors to achieve attractive
funding objectives from an asset-liability
management perspective.
An EDHEC-Risk Institute Publication
29
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
Conclusion
30
An EDHEC-Risk Institute Publication
Appendix
An EDHEC-Risk Institute Publication
31
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
Appendix
Figure 1: Time series of bond indices.
This figure shows the values of $1 invested in the S&P 500 Composite, the Barclays US Treasury bond index and the Barclays US
Corporate Investment Grade index respectively.
Table 1: Descriptive statistics on state variables.
In panel (a), off-diagonal elements are correlations, and diagonal elements are annualised standard deviations. These statistics
are based on arithmetic monthly returns over the period February 1973 - January 2013. In panel (b), expected returns are set to
fixed values.
Table 2: Statistics for building blocks (in %).
This table contains the annualised (arithmetic) expected returns, volatilities and Sharpe ratios of the stock (S) and the six building
blocks, as well as their correlations with liabilities and the variances of the terminal surpluses, assuming an initial funding ratio of
1. Liabilities are either discounted at the risk-free rate (“Rf”) or at the risk-free rate plus the AA spread (“Rf+sp.”). The risk-free rate
used to compute the Sharpe ratios is the average 3-month rate over the period considered (5.28%). The compositions are as follows
(stocks, sovereign bonds, corporate bonds): PSP1 = (0.80, 0.20, 0); PSP2 = (0.68, 0.17, 0.15); PSP3 = (0.56, 0.14, 0.30); LHP1 =
(0, 1, 0);
LHP2 = (0, 0.75, 0.25);
LHP3 = (0, 0, 1).
32
An EDHEC-Risk Institute Publication
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
Appendix
Figure 2: Introduction of corporate bonds in the PSP – Increase in annual expected return and in PSP allocation.
Each panel in this figure compares two LDI strategies. The first one (“benchmark”) is invested in the benchmark PSP PSP1 = (0.80,
0.20, 0), and in the LHP
LHP1 = (0, 1, 0) (stocks, sovereign bonds, corporate bonds). The second one (“improved”) is invested in
an improved PSP,
PSP2 = (0.68, 0.17, 0.15) or
PSP3 = (0.56, 0.14, 0.30), and in the same LHP as the benchmark one. For each
allocation to the benchmark PSP, the weight to invest in the improved PSP is chosen so as to keep the variance of the surplus
unchanged. The outperformance of the improved LDI strategy is measured as the gain in annual expected return after ten years,
expressed in basis points. The circled reference lines relate to the benchmark strategy invested in PSP 1 and LHP 1. Panels (a) and
(b) differ through the liability process: liabilities are discounted at the risk-free rate in Panel (a), and at the risk-free rate plus the
spread in Panel (b).
An EDHEC-Risk Institute Publication
33
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
Appendix
Figure 3: Simulated distribution of surplus attained with three LDI strategies that differ through the PSP.
Each panel shows the distribution of the surplus after ten years with a LDI strategy invested either in (PSP 1, LHP 1), (PSP 2, LHP 1)
or (PSP 3, LHP 1). The allocation to PSP 1 in the benchmark strategy is 50%, and the allocations to the other two PSPs are adjusted
so as to keep the expected terminal wealth unchanged. These distributions have been obtained by generating 50,000 values for
the surplus, assuming a log-normal distribution for the three asset classes (stocks, sovereign bonds, corporate bonds). The vertical
red line represents the reference situation of a zero surplus. Also reported are the mean of the surplus (μ), its standard deviation
(s), and the probability of a negative surplus (“Prob.”). Liabilities are discounted at the risk-free rate plus the spread, and the initial
values are A0 = L0 = $1.
34
An EDHEC-Risk Institute Publication
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
Appendix
Figure 4: Introduction of corporate bonds in the LHP – Decrease in surplus volatility and increase in LHP allocation.
Each panel in this figure compares two LDI strategies. The first one (“benchmark”) is invested in the PSP PSP1 = (0.80, 0.20, 0), and
in the benchmark LHP
LHP1 = (0, 1, 0) (stocks, sovereign bonds, corporate bonds). The second one (“improved”) is invested in the
same PSP, and an improved LHP, LHP2 = (0, 0.75, 0.25) or LHP3 = (0, 0, 1). For each allocation to the benchmark LHP, the weight
to invest in the improved LHP is chosen so as to keep the expected terminal wealth unchanged. The reduction in risk is measured
as the relative decrease in the volatility of the surplus after ten years. The circled reference lines relate to the benchmark strategy
invested in PSP 1 and LHP 1. Panels (a) and (b) differ through the liability process: liabilities are discounted at the risk-free rate in
Panel (a), and at the risk-free rate plus the spread in Panel (b).
An EDHEC-Risk Institute Publication
35
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
Appendix
Figure 5: Simulated distribution of surplus attained with three LDI strategies that differ through the LHP.
Each panel shows the distribution of the surplus after ten years with a LDI strategy invested either in (PSP 1, LHP 1), (PSP 1, LHP 2)
or (PSP 1, LHP 3). The allocation to LHP 1 in the benchmark strategy is 50%, and the allocations to the other two LHPs are adjusted
so as to keep the expected terminal wealth unchanged. The distributions have been obtained by generating 50,000 values for the
surplus, assuming a log-normal distribution for the three asset classes (stocks, sovereign bonds, corporate bonds). The vertical red
line represents the reference situation of a zero surplus. Also reported are the mean of the surplus (μ), its standard deviation (s),
and the probability of a negative surplus (“Prob.”). Liabilities are discounted at the risk-free rate plus the spread, and the initial
values are A0 = L0 = $1.
A. Proof of Proposition 2
Rearranging terms in the expression of V2(x2) (see Proposition 1), we can rewrite the
condition V2(x2) = V1(x1) as:
or, equivalently:
The result follows from the textbook conditions for the existence of real solutions to a
quadratic equation and the textbook expressions for these solutions.
36
An EDHEC-Risk Institute Publication
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
Appendix
B. Proof of Proposition 3
The objective function in (2.8) is a quadratic function of
:
the maximum of which is attained for:
(B.1)
Defining the building blocks as in the proposition, we obtain that the expected (excess)
return of the PSP and the covariance of the LHP with liabilities are:
(B.2)
while their variances are:
(B.3)
Hence:
Substituting these expressions back into (B.1), we obtain the expression for
in the proposition.
*
written
C. Proof of Theorems 1 and 2
First, the covariance between the PSP and liabilities is:
so that the product of correlation by Sharpe ratio for the PSP is:
(C.1)
Second, the expected return on the LHP is:
An EDHEC-Risk Institute Publication
37
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
Appendix
hence the product of correlation by
Sharpe ratio is:
Finally,
we
,
obtain
as
claimed in Theorem 2.
For the second interaction theorem, we
note that the maximum of the quadratic
utility is:
(C.2)
We have
by (C.1). Moreover, (B.2) and (B.3) imply
that:
Substituting these expressions in (C.2), we
obtain the decomposition of IW* written
in Theorem 2.
38
An EDHEC-Risk Institute Publication
References
An EDHEC-Risk Institute Publication
39
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
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interaction theorems. Working Paper. EDHEC-Risk Institute.
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• Martellini, L. and V. Milhau (2013). An empirical analysis of the benefits of inflation-linked
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40
An EDHEC-Risk Institute Publication
About Rothschild & Cie
An EDHEC-Risk Institute Publication
41
Analyzing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
About Rothschild & Cie
Rothschild is one of the world’s largest
independent financial advisory groups,
employing approximately 2,800 people in
40 countries around the world. It provides
strategic, M&A, wealth management
and fundraising advice and services to
governments, companies and individuals
worldwide. There are four main arms to the
Group - Global Financial Advisory, Wealth
Management & Trust, Institutional Asset
Management and Merchant Banking - as
well as specialist financial businesses.
Rothschild is family-controlled and
independent and has been at the centre
of the world’s financial markets for over 200
years. From its historical roots in Europe,
the Group has developed a unique global
footprint. Today it has full-scale advisory
businesses across the world, including
locally staffed offices in China, Brazil, India,
the United States of America, the Middle
East and Asia Pacific.
Rothschild’s Global Financial Advisory
business provides impartial, expert advisory
and execution services to corporations,
governments, institutions and individuals.
It delivers the highest quality advice with
discretion, integrity and insight, in the
areas of M&A and strategic advisory and
financing advisory.
Headquartered in Paris, Rothschild & Cie
Gestion provides asset management services
to French and European institutional clients,
external distributors and Independent
Financial Advisors. Rothschild & Cie Gestion
is one of the major players in convictionbased management in France.
42
An EDHEC-Risk Institute Publication
Its subsidiary, Rothschild HDF Investment
Solutions, is an investment management
company offering open architecture
investment solutions in all asset classes.
The firm packages investments to meet
the specific needs of investors, including
commingled or dedicated funds, mandates
and portfolios of managed accounts.
About EDHEC-Risk Institute
An EDHEC-Risk Institute Publication
43
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
About EDHEC-Risk Institute
Founded in 1906, EDHEC is one
of the foremost international
business schools. Accredited by
the three main international
academic organisations,
EQUIS, AACSB, and Association
of MBAs, EDHEC has for a
number of years been pursuing
a strategy of international
excellence that led it to set up
EDHEC-Risk Institute in 2001.
This institute now boasts a team
of 90 permanent professors,
engineers and support staff, as
well as 48 research associates
from the financial industry and
affiliate professors.
The Choice of Asset Allocation
and Risk Management
EDHEC-Risk structures all of its research
work around asset allocation and risk
management. This strategic choice is
applied to all of the Institute's research
programmes, whether they involve
proposing new methods of strategic
allocation, which integrate the alternative
class; taking extreme risks into account
in portfolio construction; studying the
usefulness of derivatives in implementing
asset-liability management approaches;
or orienting the concept of dynamic
“core-satellite” investment management
in the framework of absolute return or
target-date funds.
Academic Excellence
and Industry Relevance
In an attempt to ensure that the research
it carries out is truly applicable, EDHEC has
implemented a dual validation system for
the work of EDHEC-Risk. All research work
must be part of a research programme,
the relevance and goals of which have
been validated from both an academic
and a business viewpoint by the Institute's
advisory board. This board is made up of
internationally recognised researchers,
the Institute's business partners, and
representatives of major international
institutional investors. Management of the
research programmes respects a rigorous
validation process, which guarantees the
scientific quality and the operational
usefulness of the programmes.
44
An EDHEC-Risk Institute Publication
Six research programmes have been
conducted by the centre to date:
• Asset allocation and alternative
diversification
• Performance and risk reporting
• Indices and benchmarking
• Non-financial risks, regulation and
innovations
• Asset allocation and derivative
instruments
• ALM and asset allocation solutions
These programmes receive the support of
a large number of financial companies.
The results of the research programmes
are disseminated through the EDHECRisk locations in Singapore, which was
established at the invitation of the
Monetary Authority of Singapore (MAS);
the City of London in the United Kingdom;
Nice and Paris in France; and New York in
the United States.
EDHEC-Risk has developed a close
partnership with a small number of
sponsors within the framework of
research chairs or major research projects:
• Core-Satellite and ETF Investment, in
partnership with Amundi ETF
• Regulation and Institutional
Investment, in partnership with AXA
Investment Managers
• Asset-Liability Management and
Institutional Investment Management,
in partnership with BNP Paribas
Investment Partners
• Risk and Regulation in the European
Fund Management Industry, in
partnership with CACEIS
• Exploring the Commodity Futures
Risk Premium: Implications for
Asset Allocation and Regulation, in
partnership with CME Group
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
About EDHEC-Risk Institute
• Asset-Liability Management in Private
Wealth Management, in partnership
with Coutts & Co.
• Asset-Liability Management
Techniques for Sovereign Wealth Fund
Management, in partnership with
Deutsche Bank
• The Benefits of Volatility Derivatives
in Equity Portfolio Management, in
partnership with Eurex
• Structured Products and Derivative
Instruments, sponsored by the French
Banking Federation (FBF)
• Optimising Bond Portfolios, in
partnership with the French Central
Bank (BDF Gestion)
• Asset Allocation Solutions, in
partnership with Lyxor Asset
Management
• Infrastructure Equity Investment
Management and Benchmarking,
in partnership with Meridiam and
Campbell Lutyens
• Investment and Governance
Characteristics of Infrastructure Debt
Investments, in partnership with Natixis
• Advanced Modelling for Alternative
Investments, in partnership with
Newedge Prime Brokerage
• Advanced Investment Solutions for
Liability Hedging for Inflation Risk,
in partnership with Ontario Teachers’
Pension Plan
• The Case for Inflation-Linked
Corporate Bonds: Issuers’ and Investors’
Perspectives, in partnership with
Rothschild & Cie
• Solvency II, in partnership with Russell
Investments
• Structured Equity Investment
Strategies for Long-Term Asian Investors,
in partnership with Société Générale
Corporate & Investment Banking
The philosophy of the Institute is to
validate its work by publication in
international academic journals, as well as
to make it available to the sector through
its position papers, published studies, and
conferences.
Each year, EDHEC-Risk organises three
conferences for professionals in order to
present the results of its research, one in
London (EDHEC-Risk Days Europe), one
in Singapore (EDHEC-Risk Days Asia), and
one in New York (EDHEC-Risk Days North
America) attracting more than 2,500
professional delegates.
EDHEC also provides professionals with
access to its website, www.edhec-risk.com,
which is entirely devoted to international
asset management research. The website,
which has more than 58,000 regular
visitors, is aimed at professionals who
wish to benefit from EDHEC’s analysis and
expertise in the area of applied portfolio
management research. Its monthly
newsletter is distributed to more than 1.5
million readers.
EDHEC-Risk Institute:
Key Figures, 2011-2012
Nbr of permanent staff
90
Nbr of research associates
20
Nbr of affiliate professors
28
Overall budget
€13,000,000
External financing
€7,550,000
Nbr of conference delegates
Nbr of participants at research
seminars and executive education
seminars
1,860
868
An EDHEC-Risk Institute Publication
45
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
About EDHEC-Risk Institute
The EDHEC-Risk Institute
PhD in Finance
The EDHEC-Risk Institute PhD in Finance
is designed for professionals who aspire
to higher intellectual levels and aim to
redefine the investment banking and asset
management industries. It is offered in two
tracks: a residential track for high-potential
graduate students, who hold part-time
positions at EDHEC, and an executive track
for practitioners who keep their full-time
jobs. Drawing its faculty from the world’s
best universities, such as Princeton,
Wharton, Oxford, Chicago and CalTech,
and enjoying the support of the research
centre with the greatest impact on the
financial industry, the EDHEC-Risk Institute
PhD in Finance creates an extraordinary
platform for professional development and
industry innovation.
Research for Business
The Institute’s activities have also given
rise to executive education and research
service offshoots. EDHEC-Risk's executive
education programmes help investment
professionals to upgrade their skills with
advanced risk and asset management
training across traditional and alternative
classes. In partnership with CFA Institute,
it has developed advanced seminars based
on its research which are available to CFA
charterholders and have been taking
place since 2008 in New York, Singapore
and London.
In 2012, EDHEC-Risk Institute signed two
strategic partnership agreements with
the Operations Research and Financial
Engineering department of Princeton
University to set up a joint research
programme in the area of risk and
46
An EDHEC-Risk Institute Publication
investment management, and with Yale
School of Management to set up joint
certified executive training courses in
North America and Europe in the area of
investment management.
As part of its policy of transferring knowhow to the industry, in 2013 EDHEC-Risk
Institute has also set up ERI Scientific Beta.
ERI Scientific Beta is an original initiative
which aims to favour the adoption of the
latest advances in smart beta design and
implementation by the whole investment
industry. Its academic origin provides the
foundation for its strategy: offer, in the
best economic conditions possible, the
smart beta solutions that are most proven
scientifically with full transparency in
both the methods and the associated
risks.
EDHEC-Risk Institute
Publications and Position Papers
(2010-2013)
An EDHEC-Risk Institute Publication
47
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
EDHEC-Risk Institute Publications
(2010-2013)
2013
• Deguest, R., L. Martellini, and A. Meucci. Risk parity and beyond - from asset allocation
to risk allocation decisions (June).
• Blanc-Brude, F. and O.R.H. Ismail. Who is afraid of construction risk? (March)
• Lixia, L., L. Martellini, and S. Stoyanov. The relevance of country- and sector-specific
model-free volatility indicators (March).
• Calamia, A., L. Deville, and F. Riva. Liquidity in european equity ETFs: What really
matters? (March).
• Deguest, R., L. Martellini, and V. Milhau.. The benefits of sovereign, municipal and
corporate inflation-linked bonds in long-term investment decisions (February).
• Deguest, R., L. Martellini, and V. Milhau. Hedging versus insurance: Long-horizon
investing with short-term constraints (February).
• Amenc, N., F. Goltz, N. Gonzalez, N. Shah, E. Shirbini and N. Tessaromatis. The EDHEC
european ETF survey 2012 (February).
• Padmanaban, N., M. Mukai, L . Tang, and V. Le Sourd. Assessing the quality of asian
stock market indices (February).
• Goltz, F., V. Le Sourd, M. Mukai, and F. Rachidy. Reactions to “A review of corporate
bond indices: Construction principles, return heterogeneity, and fluctuations in risk
exposures” (January).
• Joenväärä, J., and R. Kosowski. An analysis of the convergence between mainstream
and alternative asset management (January).
• Cocquemas, F. Towards better consideration of pension liabilities in european union
countries (January).
• Blanc-Brude, F. Towards efficient benchmarks for infrastructure equity investments
(January).
2012
• Arias, L., P. Foulquier and A. Le Maistre. Les impacts de Solvabilité II sur la gestion
obligataire (December).
• Arias, L., P. Foulquier and A. Le Maistre. The Impact of Solvency II on Bond Management
(December).
• Amenc, N., and F. Ducoulombier. Proposals for better management of non-financial risks
within the european fund management industry (December).
• Cocquemas, F. Improving Risk Management in DC and Hybrid Pension Plans (November).
• Amenc, N., F. Cocquemas, L. Martellini, and S. Sender. Response to the european
commission white paper "An agenda for adequate, safe and sustainable pensions"
(October).
• La gestion indicielle dans l'immobilier et l'indice EDHEC IEIF Immobilier d'Entreprise
France (September).
48
An EDHEC-Risk Institute Publication
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
EDHEC-Risk Institute Publications
(2010-2013)
• Real estate indexing and the EDHEC IEIF commercial property (France) index (September).
• Goltz, F., S. Stoyanov. The risks of volatility ETNs: A recent incident and underlying
issues (September).
• Almeida, C., and R. Garcia. Robust assessment of hedge fund performance through
nonparametric discounting (June).
• Amenc, N., F. Goltz, V. Milhau, and M. Mukai. Reactions to the EDHEC study “Optimal
design of corporate market debt programmes in the presence of interest-rate and
inflation risks” (May).
• Goltz, F., L. Martellini, and S. Stoyanov. EDHEC-Risk equity volatility index: Methodology
(May).
• Amenc, N., F. Goltz, M. Masayoshi, P. Narasimhan and L. Tang. EDHEC-Risk Asian index
survey 2011 (May).
• Guobuzaite, R., and L. Martellini. The benefits of volatility derivatives in equity portfolio
management (April).
• Amenc, N., F. Goltz, L. Tang, and V. Vaidyanathan. EDHEC-Risk North American index
survey 2011 (March).
• Amenc, N., F. Cocquemas, R. Deguest, P. Foulquier, L. Martellini, and S. Sender. Introducing
the EDHEC-Risk Solvency II Benchmarks – maximising the benefits of equity investments
for insurance companies facing Solvency II constraints - Summary - (March).
• Schoeffler, P. Optimal market estimates of French office property performance (March).
• Le Sourd, V. Performance of socially responsible investment funds against an efficient
SRI Index: The impact of benchmark choice when evaluating active managers – an update
(March).
• Martellini, L., V. Milhau, and A.Tarelli. Dynamic investment strategies for corporate
pension funds in the presence of sponsor risk (March).
• Goltz, F., and L. Tang. The EDHEC European ETF survey 2011 (March).
• Sender, S. Shifting towards hybrid pension systems: A European perspective (March).
• Blanc-Brude, F. Pension fund investment in social infrastructure (February).
• Ducoulombier, F., Lixia, L., and S. Stoyanov. What asset-liability management strategy
for sovereign wealth funds? (February).
• Amenc, N., Cocquemas, F., and S. Sender. Shedding light on non-financial risks – a
European survey (January).
• Amenc, N., F. Cocquemas, R. Deguest, P. Foulquier, Martellini, L., and S. Sender. Ground
Rules for the EDHEC-Risk Solvency II Benchmarks. (January).
• Amenc, N., F. Cocquemas, R. Deguest, P. Foulquier, Martellini, L., and S. Sender. Introducing
the EDHEC-Risk Solvency Benchmarks – Maximising the Benefits of Equity Investments
for Insurance Companies facing Solvency II Constraints - Synthesis -. (January).
An EDHEC-Risk Institute Publication
49
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
EDHEC-Risk Institute Publications
(2010-2013)
• Amenc, N., F. Cocquemas, R. Deguest, P. Foulquier, Martellini, L., and S. Sender. Introducing
the EDHEC-Risk Solvency Benchmarks – Maximising the Benefits of Equity Investments
for Insurance Companies facing Solvency II Constraints (January).
• Schoeffler.P. Les estimateurs de marché optimaux de la performance de l’immobilier
de bureaux en France (January).
2011
• Amenc, N., F. Goltz, Martellini, L., and D. Sahoo. A long horizon perspective on the
cross-sectional risk-return relationship in equity markets (December 2011).
• Amenc, N., F. Goltz, and L. Tang. EDHEC-Risk European index survey 2011 (October).
• Deguest,R., Martellini, L., and V. Milhau. Life-cycle investing in private wealth
management (October).
• Amenc, N., F. Goltz, Martellini, L., and L. Tang. Improved beta? A comparison of indexweighting schemes (September).
• Le Sourd, V. Performance of socially responsible investment funds against an
Efficient SRI Index: The Impact of Benchmark Choice when Evaluating Active Managers
(September).
• Charbit, E., Giraud J. R., F. Goltz, and L. Tang Capturing the market, value, or momentum
premium with downside Risk Control: Dynamic Allocation strategies with exchange-traded
funds (July).
• Scherer, B. An integrated approach to sovereign wealth risk management (June).
• Campani, C. H., and F. Goltz. A review of corporate bond indices: Construction principles,
return heterogeneity, and fluctuations in risk exposures (June).
• Martellini, L., and V. Milhau. Capital structure choices, pension fund allocation decisions,
and the rational pricing of liability streams (June).
• Amenc, N., F. Goltz, and S. Stoyanov. A post-crisis perspective on diversification for risk
management (May).
• Amenc, N., F. Goltz, Martellini, L., and L. Tang. Improved beta? A comparison of indexweighting schemes (April).
• Amenc, N., F. Goltz, Martellini, L., and D. Sahoo. Is there a risk/return tradeoff across
stocks? An answer from a long-horizon perspective (April).
• Sender, S. The elephant in the room: Accounting and sponsor risks in corporate pension
plans (March).
• Martellini, L., and V. Milhau. Optimal design of corporate market debt programmes in
the presence of interest-rate and inflation risks (February).
2010
• Amenc, N., and S. Sender. The European fund management industry needs a better
grasp of non-financial risks (December).
50
An EDHEC-Risk Institute Publication
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
EDHEC-Risk Institute Publications
(2010-2013)
• Amenc, N., S, Focardi, F. Goltz, D. Schröder, and L. Tang. EDHEC-Risk European private
wealth management survey (November).
• Amenc, N., F. Goltz, and L. Tang. Adoption of green investing by institutional investors:
A European survey (November).
• Martellini, L., and V. Milhau. An integrated approach to asset-liability management:
Capital structure choices, pension fund allocation decisions and the rational pricing of
liability streams (November).
• Hitaj, A., L. Martellini, and G. Zambruno. Optimal hedge fund allocation with improved
estimates for coskewness and cokurtosis parameters (October).
• Amenc, N., F. Goltz, L. Martellini, and V. Milhau. New frontiers in benchmarking and
liability-driven investing (September).
• Martellini, L., and V. Milhau. From deterministic to stochastic life-cycle investing:
Implications for the design of improved forms of target date funds (September).
• Martellini, L., and V. Milhau. Capital structure choices, pension fund allocation decisions
and the rational pricing of liability streams (July).
• Sender, S. EDHEC survey of the asset and liability management practices of European
pension funds (June).
• Goltz, F., A. Grigoriu, and L. Tang. The EDHEC European ETF survey 2010 (May).
• Martellini, L., and V. Milhau. Asset-liability management decisions for sovereign wealth
funds (May).
• Amenc, N., and S. Sender. Are hedge-fund UCITS the cure-all? (March).
• Amenc, N., F. Goltz, and A. Grigoriu. Risk control through dynamic core-satellite portfolios
of ETFs: Applications to absolute return funds and tactical asset allocation (January).
• Amenc, N., F. Goltz, and P. Retkowsky. Efficient indexation: An alternative to cap-weighted
indices (January).
• Goltz, F., and V. Le Sourd. Does finance theory make the case for capitalisation-weighted
indexing? (January).
An EDHEC-Risk Institute Publication
51
Analysing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
EDHEC-Risk Institute Position Papers
(2010-2013)
2012
• Till, H. Who sank the boat? (June).
• Uppal, R. Financial Regulation (April).
• Amenc, N., F. Ducoulombier, F. Goltz, and L. Tang. What are the risks of European ETFs?
(January).
2011
• Amenc, N., and S. Sender. Response to ESMA consultation paper to implementing
measures for the AIFMD (September).
• Uppal, R. A Short note on the Tobin Tax: The costs and benefits of a tax on financial
transactions (July).
• Till, H. A review of the G20 meeting on agriculture: Addressing price volatility in the
food markets (July).
2010
• Amenc, N., and V. Le Sourd. The performance of socially responsible investment and
sustainable development in France: An update after the financial crisis (September).
• Amenc, N., A. Chéron, S. Gregoir, and L. Martellini. Il faut préserver le Fonds de Réserve
pour les Retraites (July).
• Amenc, N., P. Schoefler, and P. Lasserre. Organisation optimale de la liquidité des fonds
d’investissement (March).
• Lioui, A. Spillover effects of counter-cyclical market regulation: Evidence from the 2008
ban on short sales (March).
52
An EDHEC-Risk Institute Publication
Analyzing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
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An EDHEC-Risk Institute Publication
53
Analyzing and Decomposing the Sources of Added-Value of Corporate Bonds Within Institutional Investors’ Portfolios - August 2013
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An EDHEC-Risk Institute Publication
For more information, please contact:
Carolyn Essid on +33 493 187 824
or by e-mail to: [email protected]
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