Download The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk

An EDHEC-Risk Institute Publication
The Impact of Risk Controls
and Strategy-Specific Risk
Diversification on
Extreme Risk
August 2014
Institute
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Printed in France, August 2014. Copyright EDHEC 2014.
The opinions expressed in this study are those of the authors and do not necessarily reflect those of EDHEC Business School.
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
Table of Contents
Executive Summary.................................................................................................. 5
1. Introduction.............................................................................................................9
2. Risk Control Schemes...................................................................................... 13
3. A Conditional EVT Model..................................................................................17
4. Empirical Analysis..............................................................................................25
Conclusion................................................................................................................35
References................................................................................................................37
About EDHEC-Risk Institute.................................................................................41
EDHEC-Risk Institute Publications and Position Papers (2011-2014).........45
An EDHEC-Risk Institute Publication
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The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
About the Authors
Lixia Loh is a senior research engineer at EDHEC-Risk Institute–Asia. Prior to
joining EDHEC Business School, she was a Research Fellow at the Centre for
Global Finance at Bristol Business School (University of the West of England).
Her research interests include empirical finance, financial markets risk, and
monetary economics. She has published in several academic journals, including
the Asia-Pacific Development Journal and Macroeconomic Dynamics, and is
the author of a book, Sovereign Wealth Funds: States Buying the World (Global
Professional Publishing, 2010). She holds an M.Sc. in international economics,
banking and finance from Cardiff University and a Ph.D. in finance from the
University of Nottingham.
Stoyan Stoyanov is professor of finance at EDHEC Business School and head of
research at EDHEC Risk Institute–Asia. He has ten years of experience in the field
of risk and investment management. Prior to joining EDHEC Business School,
he worked for over six years as head of quantitative research for FinAnalytica.
He has designed and implemented investment and risk management models
for financial institutions, co-developed a patented system for portfolio
optimisation in the presence of non-normality, and led a team of engineers
designing and planning the implementation of advanced models for major
financial institutions. His research focuses on probability theory, extreme
risk modelling, and optimal portfolio theory. He has published over thirty
articles in leading academic and practitioner-oriented scientific journals such
as Annals of Operations Research, Journal of Banking and Finance, and the
Journal of Portfolio Management, contributed to many professional handbooks
and co-authored three books on probability and stochastics, financial risk
assessment and portfolio optimisation. He holds a master in science in applied
probability and statistics from Sofia University and a PhD in finance from the
University of Karlsruhe.
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An EDHEC-Risk Institute Publication
Executive Summary
An EDHEC-Risk Institute Publication
5
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
Executive Summary
Empirical studies have demonstrated that
cap-weighted indices do not represent
efficient portfolios. The main reasons are
that cap-weighting results in significant
concentration, ignores correlations between
stocks and, finally, cap-weighted indices
do not exhibit an efficient exposure to
rewarded risk factors Amenc et al. (2014b).
In recent years, the industry has tried to
respond by developing the so-called smart
beta framework, which attempts to address
the three drawbacks.
To construct smart beta indices, traditional
index providers usually employ a set of
methodology choices for stock selection
and weighting, packaged together in a
single index without allowing the investor
the flexibility of making separate choices.
Amenc and Goltz (2013) suggest the ERI
Smart Beta 2.0 approach, which represents a
substantial improvement over the traditional
methods. It separates the two main steps in
the index construction process, allowing the
investor to make an informed decision both
about the factor tilt and the diversification
method. The diversification method deals
with the over-concentration issue and the
factor tilt method leads to an exposure to
better rewarded factors. In contrast to the
very often opaque description of industry
methodologies, the ERI Smart Beta 2.0
approach is fully transparent.
Although deviating away from the
cap-weighted index leads to significant
risk-adjusted performance benefits, it also
exposes investors to additional risks. Firstly,
the alternative weighting scheme may lead
to an over-weighting or under-weighting of
certain sectors or countries relative to the
corresponding cap-weighted index which
may result in temporary underperformance.
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An EDHEC-Risk Institute Publication
It has been shown empirically that sector
and country risks are not priced in and it
would therefore make sense for investors to
try to avoid them. For an empirical analysis,
see for example Cappiello et al. (2008).
Secondly, and more generally, improved
relative performance necessarily comes
at the cost of tracking error (TE) risk.
This risk is of course related to relative
country/sector risk and arises in recognising
that cap-weighted indices, although
representing inefficient portfolios, will
continue to be used as a reference point.
Therefore, from an investor perspective,
tracking error risk needs to be managed. For
additional discussions, see for example Rudd
(1980), Roll (1992) and Chan et al. (1999).
Finally, deviating from a cap-weighted index
implies also departing from the objective of
representing the market. Smart beta
indices require setting a specific objective
which often takes the form of a goal in
an optimisation problem. Solving the
problem requires provision of parameters
that need to be estimated from data. This
exposes the optimal solution to the noise
in the observed stock returns which is also
known as sample risk and it can be relatively
bigger or smaller depending on how many
parameters need to be estimated and of
what type. From an investor perspective,
however, it makes sense to try to diversify
away this risk as much as possible by
combining different smart beta strategies
into one multi-strategy index. The academic
literature confirms this intuition — in the
face of parameter uncertainty, Kan and
Zhou (2007) argue that an investor should
hold a combination of the global minimum
variance portfolio, the maximum Sharpe
ratio portfolio, and a risk-free asset.
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
Executive Summary
Apart from the sample risk diversification,
combining smart beta indices into a multistrategy index could be appealing because
of other benefits including smoothing
conditional performance, see Amenc et
al. (2014a,c).
The goal of this paper is to check empirically
if controlling the exposure to some risks
such as country, sector, tracking error, or
sample risk does not increase the exposure
to other types of risk, such as tail risk, that
may remain unaccounted for by the index
construction process. The analysis in this
paper complements Loh and Stoyanov
(2014b) where we study the tail risk of
smart beta strategies without imposing any
risk controls. For the purposes of this paper,
we use the data for the risk-controlled
strategies available on the Scientific Beta
platform at http://www.scientificbeta.com.
which provides a consistent index
construction framework that can combine
different risk control methods with popular
weighting schemes subject to practical
constraints guaranteeing investable
indices.
The methodology follows the one developed
by Loh and Stoyanov (2014b). We measure
tail risk in terms of conditional Value-atRisk (CVaR) through a time series model
based on a GARCH filter and Extreme Value
Theory (EVT) as a probabilistic model for
the tail. The model allows CVaR to be
decomposed into a volatility component
and a residual tail risk component. From a
risk management perspective, it is important
to segregate the two components because
the dynamics of volatility contributes to the
unconditional tail thickness phenomenon.
Generally, the GARCH part is responsible for
capturing the dynamics of volatility while
EVT provides a model for the behaviour of
the extreme tail of the distribution.
To carry out the analysis on tail risk of
risk-controlled portfolios, we calculate
annualised averages of several statistics.
We provide annualised averages of volatility,
constant scale tail risk (CVaR with constant
volatility of 17% for absolute returns and
constant tracking error of 3% for relative
returns), and the total tail risk computed
through the GARCH-based model (total
CVaR) for the risk-controlled portfolios. The
decomposition provides insight into what
underlies the differences in total CVaR
across portfolios constructed using different
strategies and risk-controlled schemes:
whether it is the average volatility (or TE)
or whether it is the residual tail risk having
explained away the clustering of volatility
effect.
First, we examine the effect of adding a
country or sector neutrality constraint.
The following weighting schemes are
considered: Maximum Deconcentration,
Maximum Decorrelation, Efficient Minimum
Volatility, and Efficient Maximum Sharpe
Ratio. We look at both absolute and relative
returns where relative return is defined
as the portfolio excess return over the
corresponding cap-weighted market index
return.
As a next step, we consider the effect of TE
control on tail risk. Because of the use of
the core-satellite technique to achieve TE
control, we would expect the risk profile
of the TE-controlled index to increasingly
resemble that of the cap-weighted index as
the TE target is reduced. Finally, we compare
diversification benefits of multi-strategy
indices with respect to total CVaR.
An EDHEC-Risk Institute Publication
7
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
Executive Summary
Our main findings in the paper can be
summarised as follows. Firstly, we found
no evidence that controlling for country or
sector risk increases the tail risk of absolute
or relative returns of smart beta strategies.
Furthermore, as expected, tracking error
controls reduce the total tail risk of relative
returns but this is mainly through the
reduction of tracking error itself with no
additional benefits. For example, in the case
of the Developed World universe imposing
a TE of 2%, the minimum volatility portfolio
results in the average TE falling from 3.56%
to 1.02% and the total CVaR falling from
10.79% to 3.02%. The constant TE CVaR,
however, hardly changes from 9.08% to
8.89%, which is statistically insignificant.
Finally, building a multi-strategy portfolio
diversifies the total tail risk of relative
returns; but again, the most significant
factor is the diversification of the tracking
error. For the Developed World universe
for instance, the constant TE CVaR ranges
from 8.71% to 9.71% for the five different
weighting schemes while the constant TE
CVaR for the multi-strategy equals 9.60%
which indicates practically no diversification
benefits. On the other hand, the average
TE for the five different weighting schemes
ranges from 1.92% to 3.56% while the
average TE for the multi-strategy equals
2.15% which is close to the lowest TE of
the multi-strategy constituents. The results
show that the main source of tail risk
diversification is indeed the tracking error
rather than the residual tail risk.
Generally, our results show that adopting
risk control schemes in portfolio
optimisation does not deteriorate tail risk.
From a practical perspective, managing
volatility and tracking error is sufficient
for managing total tail risk in the context
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An EDHEC-Risk Institute Publication
of the different smart beta strategies and
different risk control schemes considered
in the paper.
1. Introduction
An EDHEC-Risk Institute Publication
9
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
1. Introduction
1 - See Amenc et al. (2012a) and
the references therein.
Empirical studies have demonstrated that
cap-weighted indices do not represent
efficient portfolios. Three main reasons for
this have been identified: (i) cap-weighting
results in significant concentration; (ii)
from a portfolio construction perspective,
cap-weighting
ignores
correlations
between stocks; and (iii) cap-weighted
indices are not exposed to well-rewarded
factors. In the recent years, the industry
has tried to respond by developing the
so-called smart beta framework that
attempts to resolve the three drawbacks.
Smart beta portfolios employ weighting
schemes that deviate from cap-weighting
addressing issues (i) and (ii) and they have
been demonstrated to lead to superior
risk-adjusted returns, addressing possibly
to some extent issue (iii).1
Traditional index providers usually employ
a set of methodology choices for stock
selection and weighting packaged together
in a single index without allowing the
investor the flexibility of making separate
choices. Amenc and Goltz (2013) suggest
the ERI Smart Beta 2.0 approach which
represents a substantial improvement over
the traditional methods. It separates the
two main steps in the index construction
process, allowing the investor to make an
informed decision both about the factor
tilt and the diversification method. The
diversification method deals with the
over-concentration issue and the factor
tilt method leads to an exposure to better
rewarded factors.
Although deviating away from the capweighted index leads to significant
risk-adjusted performance benefits,
it also exposes investors to additional
risks. Firstly, the alternative weighting
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An EDHEC-Risk Institute Publication
scheme may lead to an over-weighting
or under-weighting of certain sectors or
countries relative to the corresponding
cap-weighted index, which may result
in temporary underperformance. It has
been shown empirically that sector and
country risks are not priced in and it would
therefore make sense for investors to try
to avoid them. For an empirical analysis,
see for example Cappiello et al. (2008).
Secondly, and more generally, improved
relative performance necessarily comes at
the cost of tracking error risk. This risk is of
course related to relative country/sector
risk and arises in recognising that capweighted indices, although representing
inefficient portfolios, will continue to be
used as a reference point. Therefore, from
an investor perspective, tracking error
risk needs to be managed. For additional
discussions, see for example Rudd (1980),
Roll (1992) and Chan et al. (1999).
Finally, deviating from a cap-weighted
index implies also departing from the
objective of representing the market.
Smart beta indices require setting a
specific objective which often takes the
form of a goal in an optimisation problem.
Solving the problem requires provision of
parameters that need to be estimated
from data. This exposes the optimal
solution to the noise in the observed stock
returns which is also known as sample risk
and it can be relatively bigger or smaller
depending on how many parameters need
to be estimated and of what type. From
an investor perspective, however, it makes
sense to try to diversify away this risk as
much as possible by combining different
smart beta strategies into one multistrategy index. The academic literature
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
1. Introduction
confirms this intuition — in the face of
parameter uncertainty, Kan and Zhou
(2007) argue that an investor should hold
a combination of the global minimum
variance portfolio, the maximum Sharpe
ratio portfolio, and a risk-free asset.
Apart from the sample risk diversification,
combining smart beta indices into a multistrategy index could be appealing because
of other benefits including smoothing
conditional performance, see Amenc et al.
(2014a,c).
The goal of this paper is to check empirically
if controlling the exposure to some risks
such as country, sector, tracking error, or
sample risk does not increase the exposure
to other types of risk, such as tail risk, that
may remain unaccounted for by the index
construction process. The analysis in this
paper complements Loh and Stoyanov
(2014b) where we study the tail risk of
smart beta strategies without imposing
any risk controls. For the purposes of
this paper, we use the data for the riskcontrolled strategies available on the
Scientific Beta platform at http://www.
scientificbeta.com which provides
a
consistent
index
construction
framework that can combine different risk
control methods with popular weighting
schemes subject to practical constraints
guaranteeing investable indices.
The methodology in this paper follows
the one in Loh and Stoyanov (2014b). We
measure tail risk in terms of conditional
Value-at-Risk (CVaR) through a time
series model based on a GARCH filter
and Extreme Value Theory (EVT) as a
probabilistic model for the tail. The model
allows CVaR to be decomposed into a
volatility component and a residual tail
risk component. From a risk management
perspective, it is important to segregate the
two components because the dynamics of
volatility contributes to the unconditional
tail thickness phenomenon. Generally, the
GARCH part is responsible for capturing
the dynamics of volatility while EVT
provides a model for the behaviour of the
extreme tail of the distribution.
To carry out the analysis on tail risk of
risk-controlled portfolios, we calculate
annualised averages of several statistics.
We provide annualised averages of
volatility, constant scale tail risk (CVaR with
constant volatility of 17% for absolute
returns and constant tracking error of
3% for relative returns), and the total
tail risk computed through the GARCHbased model (total CVaR) for the riskcontrolled portfolios. The decomposition
provides insight into what underlies the
differences in total CVaR across portfolios
constructed using different strategies and
risk-controlled schemes: whether it is the
average volatility (or TE) or whether it
is the residual tail risk having explained
away the clustering of volatility effect.
First, we examine the effect of adding a
country or sector neutrality constraint.
The following weighting schemes are
considered: Maximum Deconcentration,
Maximum
Decorrelation,
Efficient
Minimum Volatility, and Efficient
Maximum Sharpe Ratio. We look at both
absolute and relative returns where
relative return is defined as the portfolio
excess return over the corresponding capweighted market index return. We found
that country and sector neutrality do not
have a material effect on tail risk for both
absolute and relative returns.
An EDHEC-Risk Institute Publication
11
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
1. Introduction
As a next step, we consider the effect of TE
control on tail risk. Because of the use of
the core-satellite technique to achieve TE
control, we would expect the risk profile
of the TE-controlled index to increasingly
resemble that of the cap-weighted index
as the TE target is reduced. Finally, we
compare diversification benefits of multistrategy indices with respect to total
CVaR.
Our main findings in the paper are that
there is no evidence that controlling
for country or sector risk increases
tail risk both in terms of absolute
and relative returns. Furthermore, as
expected, tracking error controls reduce
the total tail risk of relative returns but
this is mainly through the reduction of
tracking error itself with no additional
benefits. Finally, building a multi-strategy
portfolio diversifies the total tail risk of
relative returns; but again, the most
significant factor is the diversification of
the tracking error. Our results show that
adopting risk control schemes in portfolio
optimisation does not deteriorate tail risk.
From a practical perspective, managing
volatility and tracking error is sufficient
for managing total tail risk in the context
of the different smart beta strategies and
different risk control schemes considered
in the paper.
The paper is organised in the following
way. Section 2 briefly explains the
different types of risk-controlled schemes
used in the construction of the smart beta
strategies. Section 3 discusses extreme
value theory and its application for tail risk
measurement. Section 4 briefly discusses
the data and provides an analysis of the
results and, finally, Section 5 concludes.
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An EDHEC-Risk Institute Publication
2. Risk Control Schemes
An EDHEC-Risk Institute Publication
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The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
2. Risk Control Schemes
This section briefly discusses four types of
risk control schemes which are quite
common in the industry. They include
country risk control, sector risk control,
tracking error control, and diversifying
strategy specific risk through multi-strategy
indices. The risk-controlled strategies
used in the study are essentially smart
beta portfolios following a particular
weighting scheme with
additional
constrains implementing the corresponding
risk control. All strategies studied in the
paper are implemented with quarterly
rebalancing subject to a threshold constraint
which aims at minimising turnover.
Further details are available at http://www.
scientificbeta.com.
maintaining country-level economic
representation.
As implementing alternative weighting
schemes may result in different levels of
country allocation relative to a reference
index, country neutral versions allow
pursuit of the strategy while suppressing
any deviations from the reference index's
country exposure. Country risk has long
been recognised as a prominent risk factor
impacting equity returns (Erb et al., 1995).
Country neutral weighting allows for a
customised pursuit of a strategy while
refraining from making any implicit country
bets.
2.2. Sector Risk
2.1. Country Risk
Country neutral investment strategies
have grown in importance along with
the increasingly international scope of
investments and with the expanding use
of alternative weighting schemes which
can produce significant deviations from the
reference index if country-neutrality is not
imposed. The imposition of country
neutrality is in effect region-based tracking
error control, which aims at managing
relative risk with respect to countries.
Typically, country neutrality is achieved
by imposing constraints which match the
country weights of the strategy index to
the reference index, while constituents
within each country may be re-weighted.
Upon re-balancing, weights are restored to
their country-based targets. If one assumes
that the cap-weighted reference index is
an accurate reflection of the market, the
alignment of country weights eliminates
the risk of making implicit country bets;
that is, a strategy can be employed while
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An EDHEC-Risk Institute Publication
Sector neutral investment strategies have
been popular among active managers who
attempt to employ their stock picking skills
within sectors. Sector neutrality is a risk
control scheme that attempts to maintain
a sector exposure which is neutral to that
of the corresponding benchmark while
pursuing a non-cap weighted strategy.
For example, in recent years some index
providers have begun to offer indices
which pursue a growth or value strategy,
while maintaining sector neutrality. Like
country neutrality, the imposition of sector
neutrality is in effect sector-based tracking
error control, which aims to manage relative
risk with respect to sectors. If one assumes
that the cap-weighted reference index is an
accurate reflection of the market, aligning
sector weights of a strategy to the reference
index eliminates the risk of making implicit
sector bets; that is, a strategy can be
employed while maintaining sector-level
economic representation.
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
2. Risk Control Schemes
As implementing alternative weighting
schemes may result in drastically different
sector exposures from a reference index,
sector neutral versions of the index allow
the pursuit of the strategy while suppressing
any relative sector tilts. Typically, constraints
are imposed which match the sector
weights of the strategy index to the
reference index, while constituents within
each sector may be re-weighted according
to the strategy.
2.3. Tracking Error
2 - For additional details, see
http://www.scientificbeta.com
Relative risk controls are methods used
to limit the deviation of a strategy index
relative to its cap-weighted reference index.
Relative risk controls are thus essentially
strategies that attempt to respect an explicit
tracking error constraint (e.g. tracking error
limits of 3%, 4%, or 5%, etc.). Effective
tracking error methods draw on hedging
approaches, such as combining the strategy
index (satellite) with a cap-weighted core
and aligning the factor exposures within
the satellite portfolio to be close to those
of the reference index. A variety of methods
to achieve such goals have been developed
in recent years, ranging from the use of
simple weight constraints on segments or
stocks to the use of implicit factor models
to impose factor exposure constraints on
the optimised portfolio (Amenc et al.,
2012b).
Amenc et al. (2012b) introduce a method for
relative risk control which recognises that
only hedging that aligns the factor exposure
of the performance-seeking (strategy)
portfolio with that of the cap-weighted
benchmark, can enable proper management
of extreme relative risk. The hedging
approach combines an optimised portfolio
(strategy index) with a suitably-designed,
time-varying, quantity of the cap-weighted
reference portfolio so as to ensure that
relative risk is kept within budgeted limits
("core-satellite approach"). Since the
optimised portfolio is originally endowed
with an ill-behaved tracking error process,
(i.e. a tracking error that may ex-post
deviate substantially from the average
tracking error level), the approach also
makes sure that ex-ante, the optimised
portfolio risk exposures are sufficiently
well-aligned with the cap-weighted
reference index risk exposures, through
the use of explicit tracking error constraints
in the optimisation procedure as well as
constraints on factor exposures relative to
the cap-weighted reference index.
The relative risk control methods used
for the construction of Scientific Beta
indices employ an explicit tracking error
target which is set at 5%. To achieve this,
the exposure of the strategy to implicit
risk factors is aligned with the reference
portfolio. This leads to a satellite portfolio
with reliable target tracking error level at
5%. Tracking error is further reduced to 2%
or 3% by using a core satellite approach.
2.4. Diversifying Strategy-Specific Risk
Ever since cap-weighting has been proved
to be mean-variance inefficient, several
alternative weighting schemes have been
proposed. These strategies differ from each
other in the assumptions they make and
the objectives they aim to achieve. In this
paper, we use the following weighting
schemes: Efficient Minimum Volatility,
Efficient Maximum Sharpe Ratio, Maximum
Deconcentration, Maximum Decorrelation,
and Diversified Risk Weighted.2
An EDHEC-Risk Institute Publication
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The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
2. Risk Control Schemes
Their objectives are as follows: the Efficient
Minimum Volatility portfolio has minimal
volatility, the objective of the Maximum
Sharpe Ratio is to maximise the Sharpe ratio
of the portfolio, Maximum Deconcentration
is an implementation of the equally
weighted scheme, Maximum Decorrelation
has the objective to build a portfolio of
the least correlated stocks, and finally
the constituents of the Diversified Risk
Weighted portfolio have equal risk
contributions under the assumption of
equal correlations among stocks.
3 - Additional details are
available at http://www.
scientificbeta.com.
Depending on which parameters need to be
estimated to construct the corresponding
portfolio, different features of the input
sample would be critical for the weighting
scheme. For example, Efficient Minimum
Volatility relies on the covariance matrix
only while the Efficient Maximum Sharpe
Ratio relies on both the covariance matrix
and the vector of expected returns. One
aspect of strategy-specific risk is exactly
the sample risk to which a given strategy
is exposed.
The combination of these different
strategies allows the diversification of
the risks that are specific to each strategy
by exploiting the imperfect correlation
between the different strategies' parameter
estimation errors and the differences in
their underlying optimality assumptions.
Kan and Zhou (2007) argue that in the
presence of parameter uncertainty, an
investor should hold a combination of the
Minimum Variance and Maximum Sharpe
Ratio strategies, along with a risk-free
asset. The idea of diversifying across the
two different strategies stems from the
fact that the parameter estimation errors
are not perfectly correlated and can hence
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An EDHEC-Risk Institute Publication
be diversified away. Moreover, as the
single strategy's performance will show
different profiles of dependence on market
conditions, a multi-strategy approach
can help investors smooth the overall
performance across market conditions.
Scientific Beta's Diversified Multi-Strategy
is a combination five different weighting
strategies — Maximum Deconcentration,
Maximum Decorrelation, Efficient Minimum
Volatility, Efficient Maximum Sharpe Ratio
and the Diversified Risk Weighted strategy.
All the portfolio construction steps are
applied separately to each of those five
strategies, which results in five sets of
weights. Only then, the Diversified MultiStrategy is made of the equal-weighted
combination of the resulting sets. In the
Diversified Multi-Strategy weighting
scheme, five Scientific Beta strategies
are combined in order to diversify away
individual strategies' specific risks and to
mix strategies with different sensitivities
to market conditions.3
Badaoui and Lodh (2014) demonstrate the
potential for diversification of the Scientific
Beta Diversified Multi-Strategy index by
showing that it presents a good trade-off
between return and relative risk as the
strategy has a return that corresponds to the
average return of its five components and
a tracking error level that is lower than the
average tracking error of its constituents.
In this paper, our focus is on tail risk.
3. A Conditional EVT Model
An EDHEC-Risk Institute Publication
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The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
3. A Conditional EVT Model
distribution denoted by xF, the conditional
tail
converges to the tail of the GPD
which is defined by,
In finance, EVT has been traditionally
applied to estimate probabilities of extreme
losses or loss thresholds such that losses
beyond it occur with a predefined small
probability, which are also known as high
quantiles of the portfolio loss distribution.
In fact, EVT provides a model for the
extreme tail of the distribution which turns
out to have a relatively simple structure
described through the corresponding
limit distributions such as the Generalised
Extreme Value (GEV) distribution or the
Generalised Pareto Distribution (GPD).
where 1 + ξx > 0 and β > 0 is a scale
parameter. The limit results is (Embrechts
et al., 1997, Chapter 3)
3.1. The Peak-over-Threshold Method
The limit result in (3.4) can be used to
construct an approximation for the tail of
the losses exceeding a high threshold u. If
we denote by y = u + x and express x in
terms of y in (3.2), we obtain
(3.5)
after substituting the limit law
for
For a fixed threshold u, note that
a constant and the tail (y) for y > u
determined entirely by the GPD tail
(3.1)
where x > 0. Because we are interested in
the extreme losses, we need to gain insight
into the probability that the excesses beyond
u, X − u, can exceed a certain loss level.
Thus, (3.1) is re-stated in terms of the tail
(3.2)
There is a celebrated limit result in EVT
which states that as u increases towards
the right endpoint of the support of the loss
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An EDHEC-Risk Institute Publication
(3.4)
where β(u) is a scaling depending on the
selected threshold u.
The approach in this paper is based on the
peak-over-threshold method (POT), see Loh
and Stoyanov (2014a) and the references
therein. Suppose that we have selected a
high loss threshold u and we are interested
in the conditional probability distribution
of the excess losses beyond u. We denote
this distribution by Fu(x) which is expressed
through the unconditional distribution in
the following way,
(3.3)
.
is
is
.
It is possible to define sets of portfolio
loss distributions also known as maximum
domains of attraction (MDA) such that
the limit relation in (3.4) leads to a GPD
with one and the same tail parameter ξ.
Since EVT is used to study rare events,
characteristic of the tail behaviour of the
portfolio loss distribution turns out to be
the important feature; other features of F
are not relevant. We distinguish between
three different classes of portfolio loss
distributions.
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
3. A Conditional EVT Model
The Fréchet MDA, ξ > 0
A loss distribution belongs to this domain
of attraction if and only if X has a tail
decay dominated by a power function in
the following sense,
The link between α and ξ is ξ = 1/α. It
is possible to demonstrate that this MDA
consists of fat-tailed distributions F
that have unbounded moments of order
higher than α, i.e. E|X|k < ∞ if k < α. For
applications in finance, it is safe to assume
that volatility is finite which implies α > 2
and ξ < 1/2, respectively. For further detail,
see (Embrechts et al., 1997, Section 3.3.1).
4 - An approach based on
adaptive calibration of the
threshold is adopted by some
authors. Gonzalo and
Olmo (2004) describe a
method based on minimising
the distance between the
(x) and the tail
empirical
of the GPD with parameters
estimated through the
maximum likelihood method.
The suggested distance is the
Kolmogorov-Smirnov
statistic.
The Gumbel MDA, ξ = 0 This MDA is much
more diverse. A portfolio loss distribution
belongs to the MDA of the Gumbel law if
and only if
in which β(u) is a scaling function and
can be chosen to be equal to the average
excess loss provided that the loss exceeds
the threshold x,
(3.6)
This choice of β(u) is also known as
the mean excess function. This MDA is
characterised in terms of excess losses that
exhibit an asymptotic exponential decay
and consists of distributions with a diverse
tail behaviour: from moderately heavytailed such as the log-normal to light-tailed
distributions such as the Gaussian or even
distributions with bounded support having
an exponential behaviour near the upper
end of the support xF. For further detail,
see (Embrechts et al., 1997, Section 3.3.3).
The Weibull MDA, ξ < 0 This MDA consists
entirely of distributions with bounded
support and is, therefore, not interesting
for modelling the behaviour of risk drivers.
Distributions that belong to this MDA
include for example the uniform and the
beta distribution. For further detail, see
(Embrechts et al., 1997, Section 3.3.2).
Finally, we should note that one distribution
can be in only one MDA. There are examples
of distributions that are not in any of the
three MDAs but they are, however, rather
artificial.
To apply (3.5) in practice, we need to choose
a high threshold u and also to estimate the
probability F(u). In addition, we also need
estimates of ξ and β(u). Regarding the
choice of u, different strategies have been
adopted in the academic literature. One
general recommendation is to set it so
that a given percentage of the sample are
excesses. Chavez-Demoulin and Embrechts
(2004) report that a 10% threshold provides
a good trade-off between the bias and
variability of the estimator of the important
shape parameter ξ when the sample size
is of about 1,000 observations. A similar
guideline is provided by McNeil and Frey
(2000).4 If the threshold is allowed to vary,
then the probability
can be estimated
through the empirical c.d.f. as suggested
for example in McNeil and Frey (2000).
For instance, suppose that X1, X2, . . . ,Xn
is a sample of i.i.d. portfolio losses. If u is
chosen such that exactly m observations
are excesses, then the approximation in
(3.5) becomes
, (3.7)
where s = 1 − m/n and Xs,n is the s-th
observation in the sample sorted in
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3. A Conditional EVT Model
increasing order and and
of ξ and β, respectively.
are estimates
Regarding estimation, a variety of
estimators can be employed to estimate
ξ and β. We use the maximum likelihood
estimator (MLE) which is rationalised by the
uniform convergence in (3.4). For additional
details, see Loh and Stoyanov (2014a) and
the references therein.
3.2. A GARCH-EVT Model for Tail
Risk Estimation
5 - See the related comments
in Loh and Stoyanov (2014a).
6 - The GARCH(1,1) model
turns out to be quite
robust in cases of model
mis-specification, see the
related comments and
additional references in Loh
and Stoyanov (2014a).
Instead of applying the POT method to the
time series directly, we prefer to build a
model for the time-varying characteristics
and apply EVT to the residuals of the model
having explained away, at least partly, the
temporal structure of the time series.5
In line with McNeil and Frey (2000) we
estimate a GARCH model to explain away
the time structure of volatility. To make
things simple, we fit a GARCH(1,1) model to
the portfolio return time series as a general
GARCH filter.6
Denote the time series of portfolio losses
by Xt. The GARCH(1,1) model is given by:
(3.8)
where
, the innovations Zt are
i.i.d. random variables with zero mean,
unit variance and marginal distribution
function FZ(x) and K, a, and b are the
positive parameters with a+b < 1. The
model in (3.8) is fitted to the data and
then the standardised residual is derived.
If we assume that the data is generated by
the model in (3.8), then the standardised
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An EDHEC-Risk Institute Publication
residual is a sample from the distribution
FZ. EVT is applied by fitting the GPD to the
residual using an approximate MLE.
Apart from the probabilistic model, the
other key component of a risk model is the
measure of risk. We use two measures of
risk: VaR and CVaR at the tail probability of
1%. In this section, we provide definitions
and explicitly state the risk forecasts built
through the probabilistic model.
The discussion below assumes that the
random variable X describes portfolio losses
and VaR and CVaR are defined for the right
tail of the loss distribution which translates
into the left tail of the portfolio return
distribution. The same quantities for the
right tail of the return distribution (left tail
of the loss distribution) are obtained from
the definitions below by considering −X
instead of X; that is, the downside of a short
position is the upside of the corresponding
long position. The risk functionals are,
however, multiplied by −1 to preserve the
interpretation that negative risk means a
potential for profit.
Value-at-Risk
The VaR of a random variable X describing
portfolio losses at a tail probability p,
VaRp(X), is implicitly defined as a loss
threshold such that over a given time
horizon losses higher than it occur with
a probability p. By construction, VaR is
the negative of the p-th quantile of
the portfolio return distribution or the
(1 − p)-th quantile of the portfolio loss
distribution. In the industry, VaR is often
defined in terms of a confidence level but
we prefer to reserve the term confidence
level for the context of statistical testing
which we need in Section 4.
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
3. A Conditional EVT Model
Thus, to map the terms properly, in the
industry we talk about VaR at 95% and
99% confidence level which corresponds
to VaR at 5% and 1% tail probability.
Formally, if we suppose that X describes
portfolio losses, then VaR at tail probability
p is defined as
(3.9)
where F -1 denotes the inverse of the c.d.f.
FX(x) = P(X ≤ x) which is also known as the
quantile function of X.
GPD. In the implementation, we set m/n =
0.1 and, thus, in terms of quantiles the 99%
quantile (
) equals the 90%
quantile (X(0,9xn)) plus the corresponding
correction term.7
As mentioned before, we assume that the
portfolio loss distribution is dynamic and
follows the GARCH(1,1) process. Under this
assumption, the conditional VaR model is
given by
7 - The correction term
is obtained from the GPD
and could make sense
for very small values of p
as well; values that may
extend beyond the available
observations in the sample.
For example, suppose that
the sample contains 100
portfolio losses, n = 100, and
set p = 0.001 which is the
VaR corresponding to the
99.9% quantile. Then, X0.9n,n
is the 90th observation in
the sorted sample and the
empirical approximation to
would be the
largest observation in the
sample. As a consequence,
the correction term in (3.11)
allows us to go beyond
the available data points in
the sample which emphasises
a key advantage of EVT to the
historical method.
As explained earlier, we employ EVT
to estimate high quantiles of the loss
distribution. To this end, we adopt the
approximation of the tail in (3.5). Solving
for the value of y yielding a tail probability
of p, we get
(3.10)
The estimator is derived from (3.7) in the
same way. Suppose that X1,n ≤ X1,n ≤ . . .
≤ Xn,n denote the order statistics, then
following (3.7) we get
(3.11)
where s = 1−m/n and m denotes the
number of observations that are considered
excesses. The approximation in (3.11) is
usually interpreted in the following way:
the estimate of VaR equals the empirical
quantile Xs,n, which is such that p < m/n,
plus a correction term obtained through the
(3.12)
where It denotes the information available
at time t,
is given in (3.11) and
is calculated from the sample of the
standardised residuals.
Conditional Value-at-Risk
An important criticism of VaR in the academic
literature is that it is uninformative about
the extreme losses beyond it. Indeed, the
only information provided is the probability
of losing more than VaR which is equal to
the tail probability level p but should any
such loss occur, there is no information
about its possible magnitude. Conditional
value-at-risk is constructed to overcome
this deficiency: CVaR at tail probability p,
CVaRp(X), equals the average loss provided
that the loss exceeds VaRp(X).
CVaR is formally defined as an average of
VaRs,
(3.13)
and if we assume that the portfolio loss
distribution has a continuous c.d.f. then
CVaR can be expressed as a conditional
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3. A Conditional EVT Model
expectation,
(3.14)
In the academic literature, CVaR is also
known as average value-at-risk or expected
shortfall. Average value-at-risk corresponds
directly to the quantity in (3.13) while
expected shortfall is the quantity in (3.14).
Although (3.13) is more general and average
value-at-risk seems to be a better name
for the quantity, we stick to the widely
accepted CVaR; see for example Pflug and
Römisch (2007) for further discussion.
Since CVaR integrates the entire tail, an
asymptotic model for the tail in areas where
no data points are available is even more
important than for VaR. Assuming that
ξ < 1, the expectation in (3.14) can be
calculated explicitly through the GPD,
where
.
Plugging in
from (3.11) and the
corresponding estimates, we get
(3.15)
For derivations and further detail, see
(McNeil et al., 2005, Section 7.2.3).
Under the assumption of a GARCH(1,1)
process for the portfolio loss distribution,
the counterpart of (3.12) for CVaR equals
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An EDHEC-Risk Institute Publication
(3.16)
where
is given in (3.15)
and is estimated from the sample of the
standardised residuals.
3.3. Comparing the Tail Risk of
Different Strategies
Equations (3.12) and (3.16) indicate that
regardless of the adopted risk measure,
the conditional tail risk depends linearly
on the conditional volatility. Therefore,
the objective to compare the tail risk of
different strategies makes sense only for
a given point in time t and a given risk
horizon (e.g. one time step ahead, t + 1).
Then, the problem reduces to comparing
the two forecasts produced by equation
(3.12) or (3.16). If it turns out that the
tail risk of strategy X is bigger than that
of strategy Y, then this may be because
(i) X is more volatile and they have equal
residual tail risk; (ii) X has a higher residual
tail risk and their volatilities are equal; or
(iii) a combined effect which cannot be
decomposed into a volatility and a residual
tail effect.
If the comparison involves a time period,
then we face a bigger problem because
we need to compare a sequence of risk
forecasts. To resolve this issue, we adopt
the following approach. Instead of looking
at an out-of-sample comparison which
would involve calibration and forecasting
in a rolling time-window, we employ an
in-sample approach. That is, we fit the
GARCH model to the selected time period,
extract the residual, and apply the described
methodology to it. Tail risk is calculated
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
3. A Conditional EVT Model
through (3.12) or (3.16) but instead of using
forecasted volatility, we use the estimated
through the GARCH model. For CVaR,
for example, the corresponding formula is
8 - The GLR measure is
defined as the ratio of the
portfolio variance to the
weighted variance of its
constituents.
9 - We use VDR instead of
the standard GLR measure
because the scale of CVaR is
defined in terms of volatility
rather than variance.
To compare tail risk in-sample, we consider
the following three aggregated quantities:
(a) total CVaR over the period, which is the
average of
over the sample
period; (b) the average estimated volatility,
i.e. the average of ; and (c) constant
volatility CVaR, which equals + σ0 ×
where σ0 is one and the same
number across all strategies.
The rationale is as follows. Since for daily
returns is very close to zero, a comparison
of the constant volatility CVaR across
strategies is essentially a comparison of the
residual tail risks. The term σ0 is supposed
to scale the quantity into a meaningful risk
number. Furthermore, combining (a) with (b)
and (c) we are able to tell if the differences
in total CVaR are primarily caused by
differences in the average volatility or the
residual tail risk. Loh and Stoyanov (2014b)
test the validity of the in-sample approach
for this data set using an out-of-sample
back-testing for VaR and CVaR at 1% tail
probability and conclude that the risk model
is realistic. A more detailed back-testing
only for cap-weighted indices supporting
the same conclusion is available in Loh and
Stoyanov (2014a).
3.4. Measuring the Effects of
Diversification
The different weighting schemes considered
in the paper are exposed to different sample
risk depending on the input parameters
they rely on. Combining the five strategies
into one multi-strategy index is supposed
to diversify away some of the sample risk
because the estimators of the different
parameters are not perfectly correlated.
From a tail risk perspective, sample risk in
this context can materialise either as higher
volatility, a fatter tail, or as both together.
Although it would be interesting to develop
a measure of sample risk and check the
diversification benefits of the multistrategy index, this is not simple because
sample risk would need to be isolated. In
this paper, our objective is to measure the
diversification of the total tail risk only one
component of which is sample risk.
CVaR, like any other risk measure, is supposed
to be able to identify diversification
opportunities if they exist; that is, the
CVaR of any portfolio must not exceed
the weighted average of the stand-alone
CVaRs of the constituents. Thus, to explore
the effect of the Diversified Multi-Strategy
Index on tail risk, we calculate a Tail-risk
Diversification Ratio (TDR) similar to the
GLR measure for variance:8
(3.17)
in which CVaRp(r) denotes the portfolio
total CVaR at tail probability p, CVaRp(ri)
denotes the stand-alone total CVaR of the
portfolio constituents (the sub-indices) and
wi denote the weights of the constituents,
. In this case, the portfolio
is the Diversified Multi-Strategy Index, the
constituents are the five sub-indices, and
the weights are equal by construction. Since
volatility is a component in tail risk, we
compare TDR to the Volatility Diversification
Ratio (VDR)9:
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The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
3. A Conditional EVT Model
(3.18)
where σ denotes volatility. By the
sub-additivity property of CVaR and
volatility, it follows that both ratios cannot
exceed 1 and the lower they are, the bigger
the diversification effect. Comparing the
two to one another is useful because if the
main driver of diversification is the volatility
component of CVaR, then the two measures
take similar values. By the sub-additivity
property of CVaR, the following inequality
holds for any portfolio
10 - This is a consequence
of the positive homogeneity
property of CVaR, CV aRp(aX)
= aCV aRp(X), a > 0
where X denotes a random
variable and a is a positive
multiplier. The interpretation
of this property is that if
we double the portfolio
positions, then the risk should
also double.
The inequality can be rested equivalently
in terms of the constant volatility CVaRs,10
If the constant volatility CVaRs are roughly
the same, then those terms cancel and we
get the same inequality expressed in terms
of volatility only,
In other words, if TDR is similar to VDR then
the main effect of diversification is in the
reduction of volatility.
In theory, apart from the volatility
parameter GPD implies that there are two
other parameters that determine tail risk:
the tail index (ξ) and the dispersion of
extremes (β). Results in probability theory
suggest that diversification may influence
the β parameter but has no influence on ξ.
In the case of independent risks, Maddipatla
et al. (2011) prove that the tail behaviour
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An EDHEC-Risk Institute Publication
of the sum of the risks is dominated by the
heaviest tail of the stand-alone risks. We
reproduce the result for the Fréchet MDA
only; results for the other MDAs and further
examples are provided by Maddipatla et
al. (2011).
Theorem 3.1. For independent random
variables r1 and r2, if both of them belong
to the MDA of the Fréchet distribution with
tail indices ξ1 > ξ2 > 0 respectively, then
the sum r1 + r2 belongs to the same MDA
with a tail index equal to ξ1.
As a consequence, combining different
indices in a multi-index diversifies away
volatility but may or may not change the
constant volatility CVaR depending on the
interplay between the parameters ξ and
β. As far as tail thickness alone goes, in
theory the tail index of the multi-index
equals the tail index of the heaviest tail
of the sub-indices even assuming that
the sub-indices are independent which,
although highly unrealistic, represents
a condition in which diversification is
supposed to work best.
4. Empirical Analysis
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The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
4. Empirical Analysis
In this section, we look at differences in tail
risk across various portfolios which have
adopted different risk-controlled schemes
for both absolute and relative returns.
The relative returns are computed as the
difference between the returns of the index
and the cap-weighted index corresponding
to the same geographical region.
11 - Details on the index
construction methodologies
are available at http://www.
scientificbeta.com.
To compare the tail risk across different riskcontrolled schemes, we calculate annualised
averages of several statistics. We provide
annualised averages of volatility, constant
scale tail risk (CVaR with a constant volatility
of 17% for absolute returns and a constant
tracking error of 3% for relative returns)
and the total tail risk computed through the
GARCH-based model (Total CVaR) for the
diversified portfolios. This decomposition
provides insight into what underlies the
differences in total CVaR across portfolios
with different risk-controlled schemes
whether it is the average volatility (or
tracking error) or whether it is the residual
tail risk having explained away the clustering
of volatility effect. CVaR is computed at 1%
tail probability and is interpreted as the
average loss provided that the loss exceeds
VaR at 1% tail probability.
In the sections below, we first describe the
data and then we proceed to the empirical
results.
4.1. Data
To provide an analysis of downside risk for
different types of portfolios, we use data
from the Scientific Beta platform which
provides indices constructed from stocks
from different geographical regions using
different strategies and stock-selection
criteria. The daily sample covers the period
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An EDHEC-Risk Institute Publication
from June 2003 to December 2013. To
carry out the tests, we express all data in
returns. We consider both the absolute and
relative returns, where relative return is
defined as the portfolio excess return over
the corresponding cap-weighted market
index return.
The geographies include the United States,
Eurozone, the United Kingdom, Japan,
Developed Asia-Pacific ex Japan and World
Developed. The strategies are Efficient
Minimum Volatility (MVol), Efficient
Maximum Sharpe Ratio (MSR), Maximum
Deconcentration (MDecon), Maximum
Decorrelation (MDecor)and Diversified Risk
Weighted (DRW). In addition to the these
five strategies, we include Diversified MultiStrategy which combines the five in equal
proportions.11
4.2. Impact of Country and Sector
Risk Control on Tail Risk
To examine the difference in tail risk
for country risk-controlled, sector
risk-controlled and non risk-controlled
portfolios, we considered the four strategies
for which these controls are available on
the Scientific Beta platform. The strategies
are Maximum Deconcentration, Maximum
Decorrelation, Efficient Minimum Volatility
and Efficient Maximum Sharpe Ratio. The
universes studied are Eurozone, Asia-Pacific
ex-Japan, and World Developed. The first
two universes were selected because they
cover different broad geographic regions
and the last one was selected because it
includes all countries. We looked at both
absolute and relative returns where relative
return is defined as the portfolio excess
return over the corresponding cap-weighted
market index return.
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
4. Empirical Analysis
Table 1 shows the impact of country
neutrality on tail risk of absolute and
relative returns across different strategies
and regions. The average volatility and
constant volatility CVaR for both the country
neutral and the non-neutral indices are
very similar. Likewise, in the case of relative
returns, the average TE and the constant
TE CVaR for the country neutral and the
non-neutral indices are also very similar. As
a consequence, the differences in Total CVaR
between country neutral indices and non
country-neutral indices are insignificant.
Generally, controlling country risk does not
have a material effect on the tail risk for
both absolute and relative returns.
Table 1: Annualised risk and return statistics of country neutral indices and indices without the country neutrality constraint for
different strategies and regions. The time period is from June 2003 to December 2013.
Country
Neutral
NonNeutrality
Country
Neutral
0.1769
0.1782
0.5957
0.5953
0.6199
0.6242
0.0667
0.1564
0.1571
0.5992
0.6007
0.5513
0.5552
Efficient Minimum Volatility
0.0773
0.0776
0.1385
0.1413
0.6109
0.6116
0.4978
0.5083
Efficient Maximum Sharpe Ratio
0.0744
0.0672
0.1532
0.1528
0.6048
0.6058
0.5450
0.5446
Maximum Deconcentration
0.1495
0.1450
0.1926
0.1944
0.5897
0.5866
0.6682
0.6709
Maximum Decorrelation
0.1645
0.1548
0.1813
0.1855
0.5932
0.5905
0.6325
0.6442
Efficient Minimum Volatility
0.1736
0.1718
0.1551
0.1692
0.6029
0.5891
0.5502
0.5862
Efficient Maximum Sharpe Ratio
0.1622
0.1708
0.1723
0.1810
0.5963
0.5899
0.6043
0.6280
Maximum Deconcentration
0.1028
0.1027
0.1524
0.1524
0.5640
0.5649
0.5058
0.5065
Maximum Decorrelation
0.1039
0.1024
0.1424
0.1428
0.5677
0.5679
0.4754
0.4770
Country
Neutral
NonNeutrality
0.0685
0.0724
Efficient Minimum Volatility
0.1097
0.1094
0.1229
0.1241
0.5732
0.5734
0.4143
0.4188
Efficient Maximum Sharpe Ratio
0.1054
0.1053
0.1365
0.1371
0.5716
0.5715
0.4589
0.4610
Country
Neutral
0.0127
0.0149
0.0424
0.0402
0.0903
0.0916
0.1276
0.1228
0.0186
0.0132
0.0560
0.0536
0.0914
0.0931
0.1704
0.1663
Efficient Minimum Volatility
0.0233
0.0236
0.0698
0.0662
0.0890
0.0923
0.2071
0.2037
Efficient Maximum Sharpe Ratio
0.0205
0.0137
0.0583
0.0567
0.0905
0.0932
0.1760
0.1762
Country
Neutral
NonNeutrality
Total CVaR
Maximum Deconcentration
Country
Neutral
NonNeutrality
CVaR constant TE
at 3%
Maximum Decorrelation
Country
Neutral
NonNeutrality
Average TE
NonNeutrality
SciBeta
Eurozone
SciBeta
Developed AsiaPacific ex-Japan
SciBeta
Developed
NonNeutrality
Country
Neutral
0.0662
Relative returns
SciBeta
Eurozone
Total CVaR
Maximum Decorrelation
Realised Return
SciBeta
Developed AsiaPacific ex-Japan
CVaR constant
vol at 17%
Maximum Deconcentration
Absolute returns
SciBeta
Developed
Average Volatility
NonNeutrality
Realised Return
Maximum Deconcentration
0.0280
0.0240
0.0483
0.0434
0.0913
0.0945
0.1470
0.1368
Maximum Decorrelation
0.0414
0.0327
0.0583
0.0558
0.0878
0.0909
0.1706
0.1689
Efficient Minimum Volatility
0.0495
0.0480
0.0688
0.0588
0.0817
0.0861
0.1873
0.1688
Efficient Maximum Sharpe Ratio
0.0394
0.0470
0.0604
0.0530
0.0844
0.0869
0.1697
0.1534
Maximum Deconcentration
0.0171
0.0169
0.0204
0.0201
0.0871
0.0884
0.0591
0.0592
Maximum Decorrelation
0.0181
0.0167
0.0231
0.0228
0.0939
0.0935
0.0723
0.0711
Efficient Minimum Volatility
0.0234
0.0232
0.0356
0.0346
0.0908
0.0920
0.1079
0.1061
Efficient Maximum Sharpe Ratio
0.0195
0.0194
0.0243
0.0239
0.0971
0.0974
0.0787
0.0776
An EDHEC-Risk Institute Publication
27
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
4. Empirical Analysis
Table 2 shows the impact of sector neutrality
on tail risk of absolute and relative returns
across different strategies and region. The
conclusions are similar: the differences in
Total CVaR between sector neutral indices
and the non-neutral indices are insignificant.
Our finding is that controlling sector risk
does not have a material effect on tail risk
for both absolute and relative returns.
Table 2: Annualised risk and return statistics of sector neutral indices and indices without the sector neutrality constraint for
different strategies and regions. The time period is from June 2003 to December 2013.
0.1739
0.1051
0.1049
0.6199
0.6080
0.1564
0.1599
0.1057
0.1053
0.5513
0.5615
Efficient Minimum Volatility
0.0773
0.0722
0.1385
0.1458
0.1078
0.1070
0.4978
0.5199
Efficient Maximum Sharpe Ratio
0.0744
0.0708
0.1532
0.1568
0.1067
0.1054
0.5450
0.5508
Maximum Deconcentration
0.1495
0.1464
0.1926
0.1940
0.1041
0.1039
0.6682
0.6717
Maximum Decorrelation
0.1645
0.1548
0.1813
0.1863
0.1047
0.1047
0.6325
0.6504
Sector
Neutral
NonNeutrality
Sector
Neutral
0.1769
0.0697
Sector
Neutral
NonNeutrality
0.0643
0.0724
Efficient Minimum Volatility
0.1736
0.1574
0.1551
0.1653
0.1064
0.1052
0.5502
0.5795
Efficient Maximum Sharpe Ratio
0.1622
0.1583
0.1723
0.1776
0.1052
0.1049
0.6043
0.6211
Maximum Deconcentration
0.1028
0.1026
0.1524
0.1512
0.0995
0.0995
0.5058
0.5018
Maximum Decorrelation
0.1039
0.1021
0.1424
0.1451
0.1002
0.1002
0.4754
0.4843
Efficient Minimum Volatility
0.1097
0.1028
0.1229
0.1298
0.1011
0.1001
0.4143
0.4332
Efficient Maximum Sharpe Ratio
0.1054
0.1033
0.1365
0.1398
0.1009
0.1005
0.4589
0.4685
NonNeutrality
0.0127
0.0109
0.0424
0.0411
0.0903
0.0905
0.1276
0.1238
0.0186
0.0161
0.0560
0.0545
0.0914
0.0903
0.1704
0.1639
Efficient Minimum Volatility
0.0233
0.0184
0.0698
0.0627
0.0890
0.0886
0.2071
0.1853
Efficient Maximum Sharpe Ratio
0.0205
0.0171
0.0583
0.0559
0.0905
0.0915
0.1760
0.1704
Sector
Sector
Neutral
Total CVaR
Maximum Decorrelation
Sector
Neutral
NonNeutrality
CVaR constant TE
at 3%
Maximum Deconcentration
Sector
Neutral
NonNeutrality
Average TE
NonNeutrality
SciBeta
Eurozone
SciBeta
Developed AsiaPacific ex-Japan
SciBeta
Developed
SciBeta
Eurozone
SciBeta
Developed AsiaPacific ex-Japan
NonNeutrality
Sector
Neutral
0.0662
Relative returns
SciBeta
Developed
Total CVaR
Maximum Decorrelation
Realised Return
An EDHEC-Risk Institute Publication
CVaR constant
vol at 17%
Maximum Deconcentration
Absolute returns
28
Average Volatility
NonNeutrality
Realised Return
Maximum Deconcentration
0.0280
0.0252
0.0483
0.0463
0.0913
0.0905
0.1470
0.1397
Maximum Decorrelation
0.0414
0.0328
0.0583
0.0565
0.0878
0.0903
0.1706
0.1700
Efficient Minimum Volatility
0.0495
0.0351
0.0688
0.0590
0.0817
0.0826
0.1873
0.1623
Efficient Maximum Sharpe Ratio
0.0394
0.0359
0.0604
0.0562
0.0844
0.0843
0.1697
0.1579
Maximum Deconcentration
0.0171
0.0169
0.0204
0.0190
0.0871
0.0876
0.0591
0.0555
Maximum Decorrelation
0.0181
0.0165
0.0231
0.0222
0.0939
0.0879
0.0723
0.0651
Efficient Minimum Volatility
0.0234
0.0170
0.0356
0.0278
0.0908
0.0921
0.1079
0.0853
Efficient Maximum Sharpe Ratio
0.0195
0.0176
0.0243
0.0226
0.0971
0.0944
0.0787
0.0711
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
4. Empirical Analysis
4.3. Impact of Tracking Error Control
on Tail Risk
With the use of the core-satellite technique to
achieve TE control, we would expect the risk
profile of the TE-controlled index to resemble
more and more that of the cap-weighted
index as the TE target is reduced from 5%
to 2%. To examine the impact of controlling
tracking error on tail risk, we consider the
relative returns of the four strategies across
the six universes: the United States, Eurozone,
the United Kingdom, Japan, Developed
Asia-Pacific ex Japan, and World Developed.
The TE targets are as follows: uncontrolled,
5%, 3%, and 2%.
The results are provided in Table 3. As
expected, the total CVaR decreases with the
decrease of the TE target. However, there are
no significant differences in the constant
TE CVaR. For example, in the case of the
Developed World universe, imposing a TE
of 2% in the minimum volatility portfolio
results in the average TE falling from 3.56%
to 1.02% and the total CVaR falling from
10.79% to 3.02%. The constant TE CVaR,
however, hardly changes from 9.08% to
8.89%, which is statistically insignificant.
As a result, it follows that the decrease in
total CVaR is driven by the decrease in the
average TE. In other words, reducing the
TE target leads to lower TE which in turn
leads to a lower total CVaR. Controlling for
TE risk does not impact the tail thickness
of the relative returns.
The case of absolute returns is very similar
in that the Total CVaR of the TE-controlled
strategy converges to the Total CVaR of
the cap-weighted index which is driven
by the convergence of the corresponding
volatility. The same effects are present in
the other single-market or broader regional
indices; the conclusion is not specific to a
given universe. Overall, controlling for TE
risk does not impact the tail thickness of
the absolute returns.
These conclusions are supported by the
analysis by Loh and Stoyanov (2014b) that
empirically the weighting scheme does not
change the tail thickness. The parameter
which is most affected is the volatility.
4.4. The Impact of Strategy Specific
Risk Diversification on Tail Risk
To see the effect of combining the five
strategies in multi-strategy index, we
calculate the average volatility, the constant
volatility CVaR, and the total CVaR for the
five strategies and the multi-strategy. We
also calculate the TDR and the VDR ratios
for the multi-strategy portfolio defined in
(3.17) and (3.18), respectively.
Table 4 provides the averaged relative
return risk statistics and the two ratios
computed for the six geographical regions.
Regardless of region, the TDR is below 1
which indicates that the total CVaR of the
Diversified Multi-Strategy is always smaller
than the average of the standalone Total
CVaRs; i.e. there are diversification benefits
for tail risk. All TDRs are, however, very
similar to the corresponding VDRs which,
together with the fact that the constant
scale CVaRs of the Multi-Strategy and the
constituents are very similar, indicates that
the main source of the diversification is in
fact the tracking error.
Table 5 provides the same information for
the case of absolute returns which turns
out to be very similar — the main source
of diversification is the volatility.
An EDHEC-Risk Institute Publication
29
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
4. Empirical Analysis
Table 3: Annualised risk and return statistics of indices with tracking error control for different strategies and regions. The tracking
error target is provided in brackets and equals: no target, 5%, 3%, and 2%. The time period is from June 2003 to December 2013.
0.0780
MDecon (5% TE)
0.0163 0.0364 0.1011 0.1227
0.0919
0.0481
MDecon (3% TE)
0.0102 0.0224 0.1009 0 . 07 5 2
0.0108
0.0924
0.0332
MDecon (2% TE)
0.0071 0.0152 0.1013 0 . 0 51 3
0.0160
0.0309
0.0968
0.0996
MDecor
0.0171 0.0506 0.0894 0 . 1 510
0.0173
0.0280
0.0958
0.0894
MDecor (5% TE)
0.0094 0.0411 0.0928 0.1272
MDecor (3% TE)
0.0105
0.0175
0.0960
0.0559
MDecor (3% TE)
0.0065 0.0255 0.0959 0 . 0 81 7
MDecor (2% TE)
0.0070
0.0120
0.0962
0.0384
MDecor (2% TE)
0.0046 0.0175 0.0975 0.0569
MVol
0.0209
0.0388
0.0917
0.1184
MVol
0.0222 0.0738 0.0872 0 . 21 4 5
MVol (5% TE)
0.0127
0.0278
0.0917
0.0850
MVol (5% TE)
0.0138 0.0419 0.0877 0.1226
MVol (3% TE)
0.0081
0.0178
0.0936
0.0555
MVol (3% TE)
0.0093 0.0265 0.0901 0 . 07 9 5
MVol (2% TE)
0.0057
0.0123
0.0955
0.0391
MVol (2% TE)
0.0068 0.0184 0.0911 0.0560
MSR
0.0166
0.0290
0.0963
0.0930
MSR
0.0197 0.0539 0.0887 0.1595
MSR (5% TE)
0.0130
0.0254
0.0907
0.0768
MSR (5% TE)
0.0079 0.0404 0.0906 0 . 1 21 9
MSR (3% TE)
0.0075
0.0157
0.0896
0.0468
MSR (3% TE)
0.0049 0.0251 0.0939 0 . 07 8 6
MSR (2% TE)
0.0050
0.0108
0.0899
0.0324
MSR (2% TE)
0.0033 0.0172 0.0956 0.0549
MDecon
0.0127
0.0424
0.0903
0.1276
MDecon
0.0280 0.0483 0.0913 0 . 1 4 70
MDecon (5% TE)
0.0091
0.0361
0.0951
0.1145
MDecon (5% TE)
0.0253 0.0429 0.0906 0.1295
MDecon (3% TE)
0.0051
0.0223
0.0964
0.0717
MDecon (3% TE)
0.0159 0.0266 0.0895 0 . 07 9 4
MDecon (2% TE)
0.0029
0.0153
0.0973
0.0497
MDecon (2% TE)
0.0114 0.0188 0.0896 0.0560
MDecor
0.0186
0.0560
0.0914
0.1704
MDecor
0.0414 0.0583 0.0878 0 . 1 70 6
MDecor (5% TE)
0.0089
0.0408
0.0925
0.1258
MDecor (5% TE)
0.0262 0.0474 0.0877 0.1385
MDecor (3% TE)
0.0042
0.0255
0.0918
0.0779
MDecor (3% TE)
0.0170 0.0293 0.0885 0.0865
MDecor (2% TE)
0.0126 0.0208 0.0889 0 . 0 61 7
MVol
0.0495 0.0688 0.0817 0.1873
MVol (5% TE)
0.0155 0.0371 0.0800 0 . 0 9 91
MVol (3% TE)
0.0100 0.0240 0.0831 0.0664
0.0257
0.0088
0.0157
MDecon (2% TE)
0.0061
MDecor
MDecor (5% TE)
SciBeta Japan
0.0145
MDecon (3% TE)
SciBeta Asia-Pacific ex Japan
MDecon (5% TE)
Total CVaR
0.0912
Average
TE
SciBeta United States
SciBeta Eurozone
An EDHEC-Risk Institute Publication
CVaR
Constant TE at 3%
0.0196 0.0409 0.0968 0 . 1 31 8
Average
TE
MDecon
0.0299
MDecon
Strategy
Realised
Returns
Total CVaR
0.0897
Realised
Returns
0.0901
0.0170
Strategy
30
Relative Returns
CVaR
Constant TE at 3%
Relative Returns
MDecor (2% TE)
0.0021
0.0176
0.0909
0.0532
MVol
0.0233
0.0698
0.0890
0.2071
MVol (5% TE)
0.0090
0.0353
0.0868
0.1021
MVol (3% TE)
0.0057
0.0225
0.0879
0.0658
MVol (2% TE)
0.0034
0.0154
0.0895
0.0459
MVol (2% TE)
0.0075 0.0170 0.0871 0.0495
MSR
0.0205
0.0583
0.0905
0.1760
MSR
0.0394 0.0604 0.0844 0.1697
MSR (5% TE)
-0.0024
0.0402
0.0981
0.1314
MSR (5% TE)
0.0301 0.0450 0.0903 0.1354
MSR (3% TE)
-0.0031
0.0253
0.0978
0.0824
MSR (3% TE)
0.0190 0.0279 0.0914 0 . 0 8 51
MSR (2% TE)
-0.0033
0.0174
0.0978
0.0568
MSR (2% TE)
0.0139 0.0199 0.0927 0 . 0 61 5
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
4. Empirical Analysis
Table 3: Annualised risk and return statistics of indices with tracking error control for different strategies and regions. The tracking error
target is provided in brackets and equals: no target, 5%, 3%, and 2%. The time period is from June 2003 to December 2013 (Continued).
CVaR
Constant TE at 3%
MDecon
0.0171 0.0204 0.0871 0 . 0 5 91
0.1306
MDecon (5% TE)
0.0140 0.0172 0.0929 0.0534
MDecon (3% TE)
0.0127
0.0258
0.0924
0.0794
MDecon (3% TE)
0.0086 0.0106 0.0933 0.0330
MDecon (2% TE)
0.0087
0.0177
0.0927
0.0546
MDecon (2% TE)
0.0059 0.0074 0.0933 0 . 02 31
MDecor
0.0179
0.0483
0.0912
0.1469
MDecor
0.0181 0.0231 0.0939 0 . 07 2 3
MDecor (5% TE)
0.0205
0.0368
0.0933
0.1143
MDecor (5% TE)
0.0149 0.0193 0.0966 0.0622
MDecor (3% TE)
0.0127
0.0227
0.0931
0.0706
MDecor (3% TE)
0.0089 0.0120 0.0965 0.0387
MDecor (2% TE)
0.0085
0.0156
0.0932
0.0484
MDecor (2% TE)
0.0060 0.0084 0.0956 0.0268
MVol
0.0273
0.0621
0.0892
0.1848
MVol
0.0234 0.0356 0.0908 0 . 107 9
MVol (5% TE)
0.0141
0.0377
0.0923
0.1160
MVol (5% TE)
0.0122 0.0232 0.0890 0.0689
MVol (3% TE)
0.0085
0.0236
0.0942
0.0741
MVol (3% TE)
0.0077 0.0147 0.0898 0.0440
MVol (2% TE)
0.0057
0.0163
0.0971
0.0528
MVol (2% TE)
0.0054 0.0102 0.0889 0.0302
MSR
0.0275
0.0481
0.0907
0.1454
MSR
0.0195 0.0243 0.0971 0 . 07 8 7
MSR (5% TE)
0.0104
0.0340
0.0887
0.1006
MSR (5% TE)
0.0102 0.0178 0.0917 0.0545
MSR (3% TE)
0.0062
0.0213
0.0922
0.0656
MSR (3% TE)
0.0057 0.0111 0.0905 0.0333
MSR (2% TE)
0.0044
0.0148
0.0934
0.0461
MSR (2% TE)
0.0038 0.0077 0.0894 0 . 02 31
It is curious that the constant scale CVaR
does not seem to change significantly in the
Multi-Strategy index. This result is
consistent with the finding reported by
Loh and Stoyanov (2014b) that within a
given universe, the constant scale CVaR
is not sensitive to the weighting scheme.
Thus, diversifying risk by building a multistrategy index results in a reduction in
the total CVaR but the main reason is the
diversification of either TE or the volatility
of the portfolios depending on whether we
consider absolute or relative returns.
In view of the theoretical discussion in
Section 3.4 and the empirical analysis by
Loh and Stoyanov (2014a,b), the multistrategy index can be viewed as another
portfolio composed of the same stocks
as the underlying sub-indices. Different
SciBeta Developed
Total CVaR
0.1491
0.0928
Average
TE
0.0945
0.0422
Strategy
Realised
Returns
0.0473
0.0194
Total CVaR
CVaR
Constant TE at 3%
0.0196
MDecon (5% TE)
Realised
Returns
MDecon
Strategy
SciBeta United Kingdom
Relative Returns
Average
TE
Relative Returns
weights are applied to the same stocks,
which has an impact on the volatility of
the portfolio but has no effect on the tail
index.
The tail thickness of the sub-indices
should be similar to the tail thickness of
the multi-strategy and also to that of the
cap-weighted index.
The dispersion of extremes on the other
hand may be affected by the weighting
scheme but in this case it seems that the
constant volatility CVaRs of the sub-indices
are quite similar to the constant volatility
CVaR of the multi-strategy, implying that
the effect is minimal.
An EDHEC-Risk Institute Publication
31
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
4. Empirical Analysis
Table 4: Annualised risk and return statistics of the relative returns of multi-strategy indices across different regions and the
corresponding sub-indices. TDR and VDR stand for tail diversification ratio and volatility diversification ratio and are defined in
(3.17) and (3.18), respectively. The time period is from June 2003 to December 2013.
Relative Returns
SciBeta Developed
SciBeta Developed AsiaPacific ex-Japan
SciBeta Japan
SciBeta United Kingdom
SciBeta Eurozone
SciBeta United States
Strategy
32
An EDHEC-Risk Institute Publication
Realised
Returns
Average
TE
CVaR
Constant
TE at 3%
Total
CVaR
Maximum Deconcentration
0.0170
0.0299
0.0901
0.0897
Maximum Decorrelation
0.0160
0.0309
0.0968
0.0996
Efficient Minimum Volatility
0.0209
0.0388
0.0917
0.1184
Efficient Maximum Sharpe Ratio
0.0166
0.0290
0.0963
0.0930
Diversified Risk Weighted
0.0177
0.0258
0.0881
0.0759
Diversified Multi-Strategy
0.0178
0.0262
0.0931
0.0813
Maximum Deconcentration
0.0127
0.0424
0.0903
0.1276
Maximum Decorrelation
0.0186
0.0560
0.0914
0.1704
Efficient Minimum Volatility
0.0233
0.0698
0.0890
0.2071
Efficient Maximum Sharpe Ratio
0.0205
0.0583
0.0905
0.1760
Diversified Risk Weighted
0.0165
0.0443
0.0910
0.1343
Diversified Multi-Strategy
0.0186
0.0518
0.0901
0.1555
Maximum Deconcentration
0.0196
0.0473
0.0945
0.1491
Maximum Decorrelation
0.0179
0.0483
0.0912
0.1469
Efficient Minimum Volatility
0.0273
0.0621
0.0892
0.1848
Efficient Maximum Sharpe Ratio
0.0275
0.0481
0.0907
0.1454
Diversified Risk Weighted
0.0200
0.0465
0.0942
0.1459
Diversified Multi-Strategy
0.0227
0.0463
0.0925
0.1427
Maximum Deconcentration
0.0196
0.0409
0.0968
0.1318
Maximum Decorrelation
0.0171
0.0506
0.0894
0.1510
Efficient Minimum Volatility
0.0222
0.0738
0.0872
0.2145
Efficient Maximum Sharpe Ratio
0.0197
0.0539
0.0887
0.1595
Diversified Risk Weighted
0.0216
0.0446
0.0920
0.1370
Diversified Multi-Strategy
0.0203
0.0504
0.0881
0.1480
Maximum Deconcentration
0.0280
0.0483
0.0913
0.1470
Maximum Decorrelation
0.0414
0.0583
0.0878
0.1706
Efficient Minimum Volatility
0.0495
0.0688
0.0817
0.1873
Efficient Maximum Sharpe Ratio
0.0394
0.0604
0.0844
0.1697
Diversified Risk Weighted
0.0311
0.0478
0.0860
0.1370
Diversified Multi-Strategy
0.0381
0.0536
0.0847
0.1513
Maximum Deconcentration
0.0171
0.0204
0.0871
0.0591
Maximum Decorrelation
0.0181
0.0231
0.0939
0.0723
Efficient Minimum Volatility
0.0234
0.0356
0.0908
0.1079
Efficient Maximum Sharpe Ratio
0.0195
0.0243
0.0971
0.0787
Diversified Risk Weighted
0.0185
0.0192
0.0895
0.0572
Diversified Multi-Strategy
0.0195
0.0215
0.0960
0.0688
TDR
VDR
0.8531
0.8495
0.9535
0.9565
0.9239
0.9165
0.9322
0.9547
0.9320
0.9446
0.9164
0.8767
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
4. Empirical Analysis
Table 5: Annualised risk and return statistics of the absolute returns of multi-strategy indices across different regions and the
corresponding sub-indices. TDR and VDR stand for tail diversification ratio and volatility diversification ratio and are defined in
(3.17) and (3.18), respectively. The time period is from June 2003 to December 2013.
Absolute Returns
SciBeta Developed
SciBeta Developed AsiaPacific ex-Japan
SciBeta Japan
SciBeta United Kingdom
SciBeta Eurozone
SciBeta United States
Strategy
Realised
Returns
Average
Volatility
CVaR
Constant
Volatility at 17%
Total
CVaR
Maximum Deconcentration
0.0987
0.1845
0.5669
0.6152
Maximum Decorrelation
0.0976
0.1748
0.5640
0.5798
Efficient Minimum Volatility
0.1029
0.1503
0.5697
0.5038
Efficient Maximum Sharpe Ratio
0.0983
0.1662
0.5675
0.5549
Diversified Risk Weighted
0.0995
0.1741
0.5694
0.5832
Diversified Multi-Strategy
0.0996
0.1696
0.5676
0.5662
Maximum Deconcentration
0.0662
0.1769
0.5957
0.6199
Maximum Decorrelation
0.0724
0.1564
0.5992
0.5513
Efficient Minimum Volatility
0.0773
0.1385
0.6109
0.4978
Efficient Maximum Sharpe Ratio
0.0744
0.1532
0.6048
0.5450
Diversified Risk Weighted
0.0701
0.1686
0.5972
0.5922
Diversified Multi-Strategy
0.0724
0.1583
0.6024
0.5609
Maximum Deconcentration
0.0979
0.1768
0.5528
0.5748
Maximum Decorrelation
0.0961
0.1668
0.5568
0.5462
Efficient Minimum Volatility
0.1062
0.1426
0.5606
0.4703
Efficient Maximum Sharpe Ratio
0.1065
0.1625
0.5611
0.5364
Diversified Risk Weighted
0.0984
0.1669
0.5569
0.5469
Diversified Multi-Strategy
0.1013
0.1622
0.5583
0.5326
Maximum Deconcentration
0.0620
0.1970
0.5971
0.6920
Maximum Decorrelation
0.0594
0.1809
0.6067
0.6456
Efficient Minimum Volatility
0.0648
0.1577
0.6215
0.5766
Efficient Maximum Sharpe Ratio
0.0621
0.1741
0.6112
0.6257
Diversified Risk Weighted
0.0641
0.1880
0.6040
0.6679
Diversified Multi-Strategy
0.0628
0.1789
0.6094
0.6413
Maximum Deconcentration
0.1495
0.1926
0.5897
0.6682
Maximum Decorrelation
0.1645
0.1813
0.5932
0.6325
Efficient Minimum Volatility
0.1736
0.1551
0.6029
0.5502
Efficient Maximum Sharpe Ratio
0.1622
0.1723
0.5963
0.6043
Diversified Risk Weighted
0.1530
0.1811
0.5933
0.6321
Diversified Multi-Strategy
0.1608
0.1758
0.5956
0.6158
Maximum Deconcentration
0.1028
0.1524
0.5640
0.5058
Maximum Decorrelation
0.1039
0.1424
0.5677
0.4754
Efficient Minimum Volatility
0.1097
0.1229
0.5732
0.4143
Efficient Maximum Sharpe Ratio
0.1054
0.1365
0.5716
0.4589
Diversified Risk Weighted
0.1044
0.1444
0.5660
0.4807
Diversified Multi-Strategy
0.1054
0.1394
0.5685
0.4661
TDR
VDR
0.9979
0.9976
0.9995
0.9974
0.9956
0.9942
0.9995
0.9964
0.9973
0.9959
0.9979
0.9975
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The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
4. Empirical Analysis
34
An EDHEC-Risk Institute Publication
Conclusion
An EDHEC-Risk Institute Publication
35
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
Conclusion
To overcome the deficiencies of
cap-weighted indices, smart beta strategies
have been proposed. They employ weighting
schemes that deviate from cap-weighting,
deal with the problem of concentration
and allow for a flexible index construction
process in which the index can be tilted to
better rewarded factors.
Along with the better risk-adjusted
performance, however, investors in smart
beta strategies are exposed to additional
risks. The weighting scheme may lead to
a temporary over-weighting or underweighting of a given sector or country
relative to the corresponding cap-weighted
benchmark which may lead to periodic
underperformance. Also, the better
risk-adjusted performance necessarily
comes at the cost of some tracking error
to the respective cap-weighted benchmark.
Both aspects recognise that cap-weighted
indices, albeit inefficient portfolios, will
continue to be a reference point and
therefore those relative risks need to be
managed.
Finally, any departure from cap-weighting
is a departure from the goal of representing
the market and should therefore be based
on some other objective, which often
takes the form of a goal in an optimisation
problem. The various parameter inputs
required to solve the problem expose the
weighting scheme to sample risk which
differs from one strategy to another. It
makes sense to consider combining various
strategies into a multi-strategy index in
order to diversify away sample risk, but
also to enjoy better risk-adjusted returns
that come from smoothing the conditional
performance.
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An EDHEC-Risk Institute Publication
Country or sector risk can be avoided
through standard techniques. Tracking error
risk can be managed efficiently through
the classical core-satellite method and
sample risk can be diversified away through
a multi-strategy index. From a practical
perspective, however, it is important to
verify whether by diversifying some aspects
of risk we are not magnifying others, such
as tail risk.
Our main findings in the paper are that
there is no evidence that controlling for
country or sector risk increases tail risk,
both in terms of absolute and relative
returns. Furthermore, as expected, tracking
error controls reduce the total tail risk of
relative returns but this is mainly through
the reduction of tracking error itself with
no additional benefits. Finally, building a
multi-strategy portfolio diversifies the total
tail risk of relative returns; but again, the
most significant factor is the diversification
of the tracking error.
In summary, our results show that
adopting risk control schemes in portfolio
optimisation does not deteriorate tail risk.
From a practical perspective, managing
volatility and tracking error is sufficient
for managing total tail risk in the context
of the different smart beta strategies and
different risk control schemes considered
in the paper.
References
An EDHEC-Risk Institute Publication
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The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
References
• Amenc, N. and F. Goltz. 2013. Smart beta 2.0. Journal of Index Investing 4(3): 15-23.
• Amenc, N., F. Goltz and A. Lodh. 2012a. Choose your betas: Benchmarking Alternative
Equity Strategies. Journal of Portfolio Management 39(1): 88-111.
• Amenc, N., F. Goltz, A. Lodh and L. Martellini. 2012b. Diversifying the Diversifiers and
Tracking the Tracking Error: Outperforming Cap-Weighted Indices with Limited Risk of
Underperformance. Journal of Portfolio Management 38(3): 72-88.
• Amenc, N., F. Goltz, A. Lodh and L. Martellini. 2014a. Scientific Beta Multi-Strategy
Factor Indices: Combining Factor Tilts and Improved Diversification. ERI Scientific Beta
Publication (May).
• Amenc, N., F. Goltz, A. Lodh and L. Martellini. 2014b. Towards Smart Equity Factor
Indices: Harvesting Risk Premia without Taking Unrewarded Risks. Forthcoming in Journal
of Portfolio Management.
• Amenc, N., F. Goltz and A. Thabault. 2014c. Scientific Beta Multi-Beta Multi-Strategy
Indices: Implementing Multi-Factor Equity Portfolios with Smart Factor Indices. ERI
Scientific Beta Publication (May).
• Badaoui, S. and A. Lodh. 2014. Scientific Beta Diversified Multi-Strategy Index. ERI
Scientific Beta Publication (March).
• Cappiello, L., M. L. Duca and A. Maddaloni. 2008. Country and Industry Equity Risk
Premia in the Euro Area - An Intertemporal Approach. European Central Bank Working
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• Chan, L., J. Karceski and J. Lakonishok. 1999. On Portfolio Optimization: Forecasting
Covariances and Choosing the Risk Model. Review of Financial Studies 12: 937-974.
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of Portfolio Management 21(2): 74-83.
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Financial Econometrics 2(3): 349-369.
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of Financial and Quantitative Analysis 42(3): 621-656.
• Loh, L. and S. Stoyanov. 2014a. Tail Risk of Equity Market Indices: An Extreme Value
Theory Approach. EDHEC-Risk Institute Publication (February).
• Loh, L. and S. Stoyanov. 2014b. Tail Risk of Smart Beta Portfolios: An Extreme Value
Theory Approach. EDHEC-Risk Institute Publication (July).
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An EDHEC-Risk Institute Publication
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
References
• Maddipatla, S., R. Sreenivasan and V. Rasbagh. 2011. On Sums of Independent Random
Variables whose Distributions belong to the Max Domain of Attraction of Max Stable
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• McNeil, A. and R. Frey. 2000. Estimation of Tail-Related Risk Measures for Heteroskedastic
Financial Time Series: An Extreme Value Approach. Journal of Empirical Finance 7(3-4):
271-300.
• McNeil, A., R. Frey and P. Embrechts. 2005. Quantitative Risk Management. Princeton.
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An EDHEC-Risk Institute Publication
39
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
References
40
An EDHEC-Risk Institute Publication
About EDHEC-Risk Institute
An EDHEC-Risk Institute Publication
41
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
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 over 95 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.
42
An EDHEC-Risk Institute Publication
Six research programmes have been
conducted by the centre to date:
• Asset allocation and alternative
diversification
• Style and performance analysis
• Indices and benchmarking
• Operational risks and performance
• Asset allocation and derivative
instruments
• ALM and asset management
These programmes receive the support of
a large number of financial companies.
The results of the research programmes
are disseminated through the EDHEC-Risk
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
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
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 65,000 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
€5,250,000
Nbr of conference delegates
1,860
Nbr of participants
at research seminars
640
Nbr of participants at EDHEC-Risk
Institute Executive Education seminars
182
An EDHEC-Risk Institute Publication
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The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
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
investment management, and with Yale
44
An EDHEC-Risk Institute Publication
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, 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
(2011-2014)
An EDHEC-Risk Institute Publication
45
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
EDHEC-Risk Institute Publications
(2011-2014)
2014
• Loh, L., and S. Stoyanov. Tail Risk of Smart Beta Portfolios: An Extreme Value Theory
Approach (July).
• Foulquier, P. M. Arouri and A. Le Maistre. P. A Proposal for an Interest Rate Dampener
for Solvency II to Manage Pro-Cyclical Effects and Improve Asset-Liability Management
(June).
• Amenc, N., R. Deguest, F. Goltz, A. Lodh, L. Martellini and E.Schirbini. Risk Allocation,
Factor Investing and Smart Beta: Reconciling Innovations in Equity Portfolio Construction
(June).
• Martellini, L., V. Milhau and A. Tarelli. Towards Conditional Risk Parity — Improving Risk
Budgeting Techniques in Changing Economic Environments (April).
• Amenc, N., and F. Ducoulombier. Index Transparency – A Survey of European Investors
Perceptions, Needs and Expectations (March).
• Ducoulombier, F., F. Goltz, V. Le Sourd, and A. Lodh. The EDHEC European ETF Survey
2013 (March).
• Badaoui, S., Deguest, R., L. Martellini and V. Milhau. Dynamic Liability-Driven Investing
Strategies: The Emergence of a New Investment Paradigm for Pension Funds? (February).
• Deguest, R., and L. Martellini. Improved Risk Reporting with Factor-Based Diversification
Measures (February).
• Loh, L., and S. Stoyanov. Tail Risk of Equity Market Indices: An Extreme Value Theory
Approach (February).
2013
• Lixia, L., and S. Stoyanov. Tail Risk of Asian Markets: An Extreme Value Theory Approach
(August).
• Goltz, F., L. Martellini, and S. Stoyanov. Analysing statistical robustness of crosssectional volatility. (August).
• Lixia, L., L. Martellini, and S. Stoyanov. The local volatility factor for asian stock markets.
(August).
• Martellini, L., and V. Milhau. Analysing and decomposing the sources of added-value
of corporate bonds within institutional investors’ portfolios (August).
• Deguest, R., L. Martellini, and A. Meucci. Risk parity and beyond - From asset allocation
to risk allocation decisions (June).
• Blanc-Brude, F., Cocquemas, F., Georgieva, A. Investment Solutions for East Asia's
Pension Savings - Financing lifecycle deficits today and tomorrow (May)
• 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).
46
An EDHEC-Risk Institute Publication
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
EDHEC-Risk Institute Publications
(2011-2014)
• 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. Towar¬ds 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).
• 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).
An EDHEC-Risk Institute Publication
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The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
EDHEC-Risk Institute Publications
(2011-2014)
• 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).
• 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).
48
An EDHEC-Risk Institute Publication
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
EDHEC-Risk Institute Publications
(2011-2014)
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).
An EDHEC-Risk Institute Publication
49
The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk — August 2014
EDHEC-Risk Institute Position Papers
(2011-2014)
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).
50
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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