1. Global Horizons
February 2016
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3. Global Horizons comprises part of the Global Series of publications
at Standard Life Investments. It allows us to publish some of our
more detailed work on topics ranging across asset classes, markets
and methodologies.
In this edition, we look at the topic of diversification measurement.
Without so much as a basic measure of diversification agreed within
the investment management industry, it is difficult for investors to
evaluate the portfolio construction methodologies available to them and
to make improvements to existing strategies. We introduce a measure
of diversification that we term the Effective Portfolio Dimensionality
(EPD). We believe EPD to be an original way to assess the number of
independent dimensions of portfolio risk in a way that is consistent
with standard risk models.
A key element of the measure is to introduce a distinction between
diversification and volatility impact. For example, we propose that
negatively correlated strategies, traditionally viewed as useful
diversifiers, can be most helpfully deconstructed into a perfectly
negatively correlated hedge that simply reduces volatility and a
perfectly uncorrelated component that provides diversification benefit.
We assess a number of traditional portfolio construction methodologies
such as Risk Parity and examine the variation in dimensionality of a
typical UK pension plan over the last decade. Results appear to match
intuition and prompt us to look at some initial results for a Maximum
EPD portfolio. These are encouraging and suggest continuing research
in this area may prove to be quite fruitful.
Brian Fleming
Head of Multi-Asset Risk
and Structuring
Jens Kroeske
Quantitative Investment Manager
Global Horizons 2
4. Dimensions of Diversification
3 Global Horizons
Chart 1
Factor snakes and ladders
0
1
2
3
4
5
6
7
8
9
10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Dimensionality/bets
Correlation
Effective portfolio dimensionality
Source: Standard Life Investments (as of November 2015)
Effective number of bets Minimum torsion bets
Diversification is a surprisingly elusive concept given how often it is discussed
in the investment management industry. Primarily this is because, in contrast to
another common term - volatility, there is no agreed way to quantify it. This in turn
limits our ability to easily monitor and then improve the diversification achieved
within portfolios. Diversification means different things to different investors, from
spreading of capital and risk across investments, to portfolio robustness under
stress testing and scenario analysis. However, the assessment is not trivial even in a
basic mean-variance setting due to the nuanced interpretation of myriad volatilities
and correlations between investments. Strong positive correlations are generally
considered to be bad, but anything short of perfect correlation should improve
diversification; negative correlations are generally considered to be good, however,
a correlation close to minus one looks akin to hedging, which theoretically negates
all risk and return; correlations close to zero are perhaps most desirable but are of
limited use if the volatility of one investment dominates.
There is a significant related challenge for investors in terms of
their ability to evaluate the efficacy of various methodologies
that are available to construct better diversified portfolios. One
such popular approach is Risk Parity. While Risk Parity by name
and ambition is designed to achieve a balanced exposure
to diverse risks, associated calculations produce an asset
allocation rather than an explicit assessment of diversification.
Choosing between different portfolios based on a preference
for greater diversification is therefore not possible. For this
reason we believe it would be instructive to have a single
number that represents a portfolio’s diversification and fits
within a standard risk modelling framework. While caution
towards all models and their outputs is warranted, without
such a number investors must resign themselves to heavier
reliance on qualitative judgement to evaluate the diversity of
risks in a portfolio.
Intuitively, many investors believe that being diversified
involves holding a balanced collection of investments
whose returns behave dissimilarly. This naturally points to
looking at measures such as the average correlation between
investments. However, correlation alone is not sufficient to
understand total portfolio risk. Dissimilar return profiles also
hint at volatility reduction as a measure of diversification;
the price fluctuations of individual investments are always
expected to negate each other to some extent at the portfolio
level. However, we argue that portfolios which achieve
significant volatility reduction through combined holdings
are not necessarily better diversified (see case study -
Misdirection from volatility reduction).
In this article, we introduce a diversification measure that
we term Effective Portfolio Dimensionality (EPD). This is
complementary to volatility and hence represents a new
measure of risk. In accordance with more recent strategies for
quantifying diversification [1,2], our initial aim in this area
of research is to deconstruct the volatility and correlation
structure of a portfolio to evaluate the effective number
of independent investments, which we have termed the
Dimensionality. This facilitates direct comparison of different
asset allocations and allows us to specifically target better
diversified portfolios. In the following we also use the EPD to
compare well-known portfolio construction techniques such
as Risk Parity and Minimum Variancea
and demonstrate that
this measure produces intuitive results for real world data.
5. Global Horizons 4
Chart 2
A tour through Flatland
0
20
40
60
80
100
1/N (Equally weighted) Volatility parity Risk parity Most diversified Minimum variance
Hedge fundsPortfolio allocation to:
Source: Bloomberg, Standard Life Investments (as of Novermber 2015)
Real estate UK credit Index-Linked gilts Gilts Global equities UK equities
%
1/N Volatility Parity Risk Parity Most Diversified Minimum Variance
Volatility (%) 6.7 4.2 4.0 3.6 2.6
EPD 1.6 2.2 2.6 2.4 1.7
Misdirection from volatility reduction
An example commonly used to demonstrate the
beneficial effect of diversification is to examine an
equally weighted portfolio of n uncorrelated assets
of equal variance i.e. = , i = 1,…,n.a
The portfolio
variance is then given by = so that 0
as n ∞, leading to the observation that
increasing diversification through the addition of
uncorrelated investments significantly reduces
portfolio variance. However, if we consider a
second portfolio of two assets of equal variance
that have a correlation of ρ1,2
= –1, then we can
achieve a portfolio of zero variance by allocating
capital to them equally. This two asset portfolio will
therefore always achieve a greater proportionate
reduction in variance at the portfolio level, being
100%, when compared to a portfolio containing an
arbitrary large and finite number of uncorrelated
assets. In fact, we do not require the correlation to
be as strong as perfectly negative for this type of
argument to hold.
Although the two asset portfolio does achieve
complete negation of volatility, we believe most
investors would view it as an example of hedging
and the uncorrelated portfolio of investments as
being more diversified. Volatility reduction does
not therefore seem to be a broad enough measure
of diversification. Of course, well diversified
portfolios may exhibit attractive levels of volatility
reduction as a result of having many uncorrelated
parts, but those that achieve the greatest reduction
can often be very concentrated in terms of capital
allocation to different holdings. Using real data and
constructing Minimum Variance portfolios we shall
see that this can also be true in the situation where
correlations are not extremely negative.
Portfolios with extra dimensions
We have built upon a highly innovative procedure introduced
by Meucci et al. [1,2] that led to the introduction of two
new ways to quantify diversification: the Effective Number
of Bets and Minimum Torsion Bets. The procedure uses
statistical factors to decompose the variance of a portfolio of
n investments into n uncorrelated components. The natural
idea is that if the portfolio variance is concentrated in one
component then there is minimal diversification and if the
variance is evenly spread over all n uncorrelated components,
then this represents maximal diversification. It is a direct
mathematical translation of the desire to have balanced
exposure to a diverse set of risks, which here are constructed
to be perfectly uncorrelated.
The Effective Number of Bets and Minimum Torsion Bets are,
respectively, single numbers that vary smoothly between
1 and n depending on the statistical factors used and the
balance of exposures that the portfolio has to those factors.
However, Meucci et al. [2] have also highlighted certain
pathological cases where the Effective Number of Bets and
Minimum Torsion bets produce less intuitive answers. It is
these cases that we address as part of a new framework
through the EPD. We report on the technical details of the
EPD elsewhere [3] but here review some underlying concepts
and properties:
Concepts
¬ Within the linear framework where portfolio volatility is
the primary measure of risk, only zero correlation between
investments should be viewed as pure diversification.b
¬ Perfect negative correlation between investments should
be viewed as hedging. Hedging can be seen as being
beneficial from a volatility reduction perspective, but does
not contribute towards diversification.
¬ Using statistical (or named) factors in the assessment of
diversification can cause ambiguity. This is most easily
seen in considering an individual security. Any security
in any risk model will typically have significant exposure
to multiple factors which, in and of itself, suggests
6. 5 Global Horizons
Chart 3
Escape from Flatland
Source: Bloomberg, Standard Life Investments (as of Novermber 2015)
0
10
20
30
40
50
60
70
80
90
100
%
Volatility parity Risk parity Max EPD Most diversfied Minimum variance1/N (Equally weighted)
Hedge fundsPortfolio allocation to: Real estate UK credit Index-Linked gilts Gilts Global equities UK equities
1/N Volatility Parity Risk Parity Maximum EPD Most Diversified Minimum variance
Volatility (%) 6.7 4.2 4.0 3.8 3.6 2.6
EPD 1.6 2.2 2.6 3.3 2.4 1.7
some diversification through exposure to different risks.
However, no two models are identical so the assessment
will never be the same. For this reason we do not use
factors in our approach and consider the investments
themselves as fundamental building blocks.
The EPD essentially divides imperfect and non-zero
correlations between investments into perfect positive
correlation, perfect negative correlation and zero correlation.
The first two parts are more concerned with the magnitude of
individual asset volatility and the third with diversification,
but all are required to compute the EPD. Additionally, the
EPD is independent of the level of portfolio volatility and so
remains unaffected by a linear scaling of positions, including
through the use of leverage.
We later provide examples of the trade-off between volatility
and diversification. We also note that rejecting a factor based
approach does not preclude the EPD from being consistent
with traditional risk modelling approaches, but rather guides
us to a choice of yardstick that is independent of any chosen
set of factors. This is one property that the EPD has and we
list further properties below.
Properties
¬ For a portfolio containing n investments, the EPD can only
have a value between 1 and n. This number can be, and
typically is, fractional.
¬ The EPD has a value of 1 if all investments are perfectly
correlated and an EPD of 1 is also produced in the trivial
instance of a portfolio containing only one investment.
¬ The EPD can take a maximum value of n if and only if the
investments are uncorrelated and of equal variance i.e.
all investments are uncorrelated with each other and the
standalone volatilities of each investment are equal. This
is, of course, uncommon in practice and the EPD is often
much less than n.
The properties described above are intuitive in that a
portfolio of perfectly correlated assets has only one effective
dimension of risk, and a portfolio will only appear maximally
diversified with n risk dimensions if it is constructed from a
perfect balance of uncorrelated investments.
To demonstrate the behaviour of the EPD we consider an
equally weighted portfolio of n investments of equal volatility
and constant correlation i.e. ρi,j
= ρ for all pairs of investments.
We choose an arbitrary value of n=10 and recalculate the
EPD as we vary the correlation ρ smoothly between 0 and 1.
This is depicted in Chart 1 where we observe, as desired, a
correspondingly smooth transition in the EPD between 10
and 1.
We also overlay the lines for the Effective Number of Bets and
Minimum Torsion Bets, which are horizontal. Meucci et al.
[2] demonstrate that, for such a homogeneous portfolio both
quantities are, surprisingly, independent of ρ and equal to 1
and n respectively.
Balance it and they will come
We now compare the following portfolio construction
techniques using the EPD to illustrate the efficacy of
our framework:
¬ 1/N (equally weighted)
¬ Volatility Parity
¬ Risk Parity
¬ Most Diversified Portfolio™
¬ Minimum Variance
While the Minimum Variance approach specifically targets
variance and not diversification, the resultant portfolios
have interesting properties that are helpful to include in
our analysis. We focus on asset categories that are broadly
representative of the holdings of UK pension schemes: UK
Equities, Global Equities, Gilts, Index-Linked Gilts, UK Credit,
Real Estate, Hedge Funds. Given that there are seven asset
categories, the EPD has a maximum possible value of 7.
7. Global Horizons 6
Chart 4
The cusp of good hope
1.0
1.5
2.0
2.5
3.0
3.5
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0
EPD
Volatility (%)
EPD vs Volatility
Source: Bloomberg, Standard Life Investments (as of November 2015)
1/
N
Volatility parity
Risk parity
Max EPD
Most diversified
Minimum variance
Chart 5
Weighing it all up
0
10
20
30
40
50
60
70
80
90
100
%
UK pension scheme 1/N
Source: Pension Protection Fund, Standard Life Investments (as of November 2015)
Hedge fundsPortfolio allocation to: Real estate UK credit
Index-Linked gilts Gilts Global equities UK equities
Each of the techniques and the time series used for the asset
categories are described in the Appendix.
Using several years of recent data, we calculated the asset
allocations produced using each strategy, which are plotted
in Chart 2 along with the associated portfolio volatility and
dimensionality numbers. The ordering reflects a decreasing
trend in volatility as we move from 1/N through to Minimum
Variance, but such a monotonic trend is not evident in the
dimensionality.
In Chart 2, we see that 1/N has the highest volatility (6.7%)
and the lowest dimensionality (1.6) in comparison to the
others. However, this ranking is somewhat arbitrary as 1/N,
being an equally weighted portfolio, does not use any risk
information (volatility or correlation) in the calculation of
its asset allocation. As volatility information is introduced
in Volatility Parity, both risk characteristics improve,
with a decrease in volatility (4.2%) and an increase in
dimensionality (2.2). Both risk characteristics improve again
with the use of correlation information to construct the Risk
Parity portfolio (4.0%, 2.6). The Most Diversified Portfolio™,
using the same inputs as Risk Parity, produces a further
reduction in portfolio volatility (3.6%). However, it is striking
that in the Most Diversified portfolio there is a shift to a high
concentration of capital within one asset category (gilts)
and an intuitive associated fall in dimensionality (2.4). We
therefore see a divergence in terms of volatility improving
and diversification deteriorating slightly compared with Risk
Parity. This is data set specific, but is generally due to the
stronger negative correlation between gilts and the other
assets being exploited within the Most Diversified Portfolio™,
which blends volatility reduction with diversification in its
assessment. Separating these two components using the EPD
allows us to understand this.
An exaggeration of this impact can be seen if we ignore
diversification as a goal and simply minimise variance, the
effect of which we also see in Chart 2. Here the assets end up
concentrated in only two categories (gilts and hedge fundsc
)
and display a significantly lower volatility relative to all other
approaches. This comes at the cost of a significantly worse
dimensionality (1.7), which is almost a round-trip to that of
the 1/N portfolio (1.6).
With a diversification measure at hand we are now in a
position to directly target a more diversified portfolio. In Chart
3 we have added an EPD optimised solution (Max EPD) to
our series of allocations, with the asset weightings inserted
in between Risk Parity and the Most Diversified Portfolio to
maintain the decreasing trend of volatility.
For this particular data set we observe that the Max EPD
portfolio has a slightly lower volatility (3.8%) than Risk
Parity and a notably higher dimensionality (3.3). The Most
Diversified Portfolio in turn has a slightly lower volatility
again but the higher dimensionality is lost. The appeal of the
Max EPD portfolio can be seen by plotting the relationship
between dimensionality and volatility for this series of
asset allocations as we have done in Chart 4. This hints at
an extended efficient-frontier framework that incorporates
diversification; for example, as we move away from the
minimum variance portfolio for a given level of target return,
diversification and the EPD provide a further attribute and
associated measure with which to assess the relative merits
of different allocations. The idea of extending the mean-
variance efficient frontier to a mean-variance-diversification
efficient surface has previously been proposed by Meucci [1].
To sum up, the Max EPD portfolio looks balanced from a
capital allocation perspective, and offers noticeably higher
dimensionality and a competitive volatility when viewed
against Risk Parity and the Most Diversified Portfolio™.
As discussed in the case study, the volatility aspect is
particularly pleasing as one would hope that a well-diversified
portfolio would exhibit attractive volatility levels due to its
focus on combining uncorrelated components.
EPD in practice
In this section we look at the EPD of a typical asset portfolio
over time to illustrate the performance of our new approach.
8. 7 Global Horizons
Chart 6
Dimension is not momentum
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Mar-05 Aug-06 Dec-07 May-09 Sep-10 Feb-12 Jun-13 Oct-14
FTSE All Share (R.H. Scale) EPD
Dimensionality Index level
Source: Bloomberg, Standard Life Investments (as of 21 October 2015)
Using the same asset categories as earlier we examine the
dimensionality of the average asset allocation of UK pension
schemes taken from the Purple Book published by the UK
Pension Protection Fund [4]. This publication reviews the
asset allocations of around 6,000 UK private sector defined
benefit pension schemes. For comparison purposes we do
not incorporate any scheme liabilities into the analysis. This
implies that the portfolio analytics are absolute in nature.
Chart 5 presents the average asset allocation, normalised
to remove cash positions. In terms of similarity to other
techniques, the weightings are closest to 1/N, which are
also shown. Interestingly, we observe that in comparison
to the previous analysis, the two allocations have the same
dimensionality when rounded to one decimal place, although
the average UK pension scheme has lower volatility.
The variation of the EPD for this portfolio over time is depicted
in Chart 6 with the FTSE All Share index shown to provide
market context (for details and calculations see Appendix). As
one might expect, the EPD moves broadly up and down with
equity market movements but it does not simply follow price
levels. The values remain in a relatively low and tight range
of between 1 and 2.5 and it seems appropriate that it finds
its lowest values around the financial and Eurozone crises in
2008/09 and 2011, reaching a minimum of 1.3 in December
2011. We see that the dimensionality increased substantially
through 2005 before declining very sharply in 2006; it then
oscillated around a low level of 1.5 going into the financial
crisis in 2008. Surprisingly, the EPD then failed to rediscover
levels above 2 until 2014, despite the earlier rally in asset
prices. More recently we have seen a notable fall in the
dimensionality, reflecting concerns about global growth.
This recent loss of diversification potential has also been
seen across equity markets, suggesting continued systemic
fragility. Overall, the dimensionality of a typical UK pension
scheme may seem surprisingly low, but we believe this level
to be reasonable when one considers the correlation and
concentration of typical pension scheme assets.
Conclusions
We have proposed a new way to measure diversification
that we term the Effective Portfolio Dimensionality. This
allows us to assess individual portfolios and compare
different portfolio construction methodologies. The EPD
produces intuitive results and its properties show the EPD to
be a risk quantity that is complementary to portfolio volatility.
This enables us to extend traditional portfolio construction
techniques to explicitly include it for the purposes of
monitoring and improvement.
Initial results suggest a maximum diversification portfolio
(Max EPD) is relatively attractive: in our example the Max
EPD portfolio showed both lower volatility and higher
dimensionality than a Risk Parity approach. Future work will
examine the longer-term performance of Max EPD portfolios
in terms of return, volatility, fat tails and turnover. To do
this, extensive work will be required in the area of portfolio
optimisation, although initial results calculating simple
out-of-sample drawdown properties for higher dimensional
portfolios do look promising. In relation to this, we believe
there is a demonstrable mathematical link between a higher
EPD and reduced drawdowns. We are currently exploring this
and plan to publish results soon.
One reason the EPD is attractive is because it is compatible
with a standard linear risk-modelling framework; however,
this means that it is subject to all of the known limitations of
such a structure. As in our day to day use of risk models, we
believe the resultant analysis can be highly informative as
long as we remain aware of the underlying assumptions. This
awareness continues to point us toward the importance of
scenario analysis to test the robustness of any portfolio.
9. Global Horizons 8
References
[1] A. Meucci. Managing Diversification. Risk 22, 74-79 (May 2009).
[2] A. Meucci, A. Santangelo, and R. Deguest. Measuring Portfolio Diversification Based on Optimized Uncorrelated Factors
(July 2013). Available at: http://www.symmys.com/node/599
[3] B. Fleming and J. Kroeske. An Introduction to Effective Portfolio Dimensionality as a Measure of Diversification.
In preparation.
[4] Pension Protection Fund. The Purple Book (2014). Available at PPF: http://www.pensionprotectionfund.org.uk/
DocumentLibrary/Documents/purple_book_2014.pdf
[5] Y. Choueifaty and Y. Coignard. Toward Maximum Diversification. Journal of Portfolio Management 34(4), 40-51 (2008).
Footnotes
a While it is common to discuss the volatility of a portfolio, the mathematics of risk is often more easily demonstrated using
portfolio variance i.e. = . This is because the variances (and covariances) of investments can simply be added
together to arrive at the portfolio variance, whereas the same linear relationship does not hold for volatilities. We shall
switch between volatility and variance throughout this article as appropriate; however, higher and lower volatility do equate
to higher and lower variance so, for example, minimum variance and minimum volatility portfolios are identical.
b Note that the non-linear extension of this would be full statistical independence of return distributions, which includes
higher order cross terms than covariance.
c It is important to note that while our analysis reflects the correct overall expected behaviour, it should not be taken at face
value as an evaluation of the relative merits of different asset categories. Hedge fund data in particular is subject to many
flattering biases, while the representation of Real Estate using REITs produces a high correlation with equities. Due to their
high correlations, UK Equities, Global Equities and Real Estate behave as close substitutes in this analysis.
*
10. 9 Global Horizons
Appendix
Portfolio construction methodologies
For a portfolio of n assets we denote the weighting of each asset as w > 0, for i = 1,…,n, such that ∑w =1. The volatilities
of each asset and the portfolio are given by σ and σ respectively, with the asset standalone risk calculated as wσ. The
correlation between an asset and the total portfolio is denoted ρ,p. We define each of the portfolio construction methodologies
by the following.
¬ 1/N: equal allocation of capital across assets such that w =
1
⁄n.
¬ Volatility Parity: equal standalone risk such that wσ = w σ for all i and j.
¬ Risk Parity: equal asset beta to the total portfolio such that w ρ,p = w ρ ,p .
¬ Most Diversified Portfolio™ [5]: weights are chosen to maximise the Diversification Ratio™ (DR), which is defined as
(∑wσ)⁄σ . Notice that the DR is improved by increasing the sum of the asset standalone risks relative to the portfolio
volatility. When applied to the examples in our case study, one can see that the DR of the two asset portfolio is only a
function of the correlation between the two assets. As ρ1,2
–1, σ 0 and DR ∞, so we can always find a two asset
portfolio correlation that has a better DR than a broadly balanced portfolio of uncorrelated investments.
¬ Minimum Variance: weights are chosen to minimise σ = ∑i,j
wi
wj
σi
σj
ρi, j
.
Data sets and window lengths
All data for the asset categories used in the main text is sourced from Bloomberg for the period 01/04/2003 - 21/10/2015.
The descriptions and index codes are shown in Table 1:
Table 1
Category Index Description Index Code
UK Equities FTSE All-Share ASX
UK Equities FTSE All-Share Total Return (TR) FTPTTALL
Global Equities MSCI World TR Gross USD (to GBP) GDDUWI
Gilts FTSE UK Conventional Gilts All Stocks FTFIBGT
Index-Linked gilts FTSE UK Index Linked Gilts All Stocks FTFIILA
UK Credit BAML Sterling Non-Gilt UN00
Real Estate FTSE EPRA UK Total Return GBP RLUK
Hedge Funds HFRX Global Hedge Fund Index HFRXGL
Charts 2-5 use data based on an equally weighted 180-week window over the period 31/03/2012 – 30/01/2015. Weekly
logarithmic returns are calculated Wednesday to Wednesday, which is typical of many risk models to reduce the impact of time
zones and holidays. Specific dates aside, this structure is chosen to match that of our 3rd-party multi-asset risk model.
Chart 6 is calculated using daily data over the period 01/04/2003 - 21/10/2015 and an exponentially weighted rolling window
of 104 weeks with a half-life of 52 weeks. The asset category weights are held constant on a weekly basis. The FTSE All Share
(Price) Index (ASX) is used only in this chart as the background comparator.
σ
σ
σ
σ
11. Contact Details
For further information on Standard Life Investments’ research on longer-term
investment themes, please contact:
Frances Hudson
Global Thematic Strategist
frances_hudson@standardlife.com
Telephone: +44 (0)131 245 2787
Visit www.standardlifeinvestments.com or contact us at one of the following offices.
Europe
Standard Life Investments
1 George Street
Edinburgh
United Kingdom
EH2 2LL
Telephone: +44 (0)131 225 2345
Standard Life Investments
90 St. Stephen’s Green
Dublin 2
Ireland
Telephone: +353(0) 1 639 7000
Standard Life Investments
31st Floor
30 St Mary Axe
London
EC3A 8BF
Telephone: +44 (0)207 868 5700
Standard Life Investments
21 Rue Balzac
75008 Paris
France
Telephone: +33 158 05 22 70
Standard Life Investments
Taunusanlage II
60329 Frankfurt am Main
Germany
Telephone: +49 (0) 69 66572 1764
North America
Standard Life Investments (USA) Ltd
One Beacon Street
34th Floor
Boston
MA 02108-3106
Telephone: +1 617 720 7900
Australia
Standard Life Investments Limited
Level 33 Chifley Tower
2 Chifley Square
Sydney NSW 2000
Australia
Telephone: +61 2 9947 1500
Asia Pacific
Standard Life Investments (Hong Kong) Ltd
30th Floor LHT Tower
31 Queen’s Road Central
Hong Kong
Telephone: +852 3589 3188
Standard Life Investments Limited
Beijing Representative Office
Room A902-A903, 9th Floor,
New Poly Plaza
No.1 Chaoyangmen Beidajie
Dongcheng District,
Beijing 100010
People’s Republic of China
Telephone: +86 10 8419 3400
Standard Life Investments (Hong Kong) Ltd
Korea Representative Office
21/F Seoul Finance Center
84 Taepyungro 1-ka, Chung-ku
Seoul, 100-101
Korea
Telephone: +82 2 3782 4760
Global Horizons 10
Dr Brian Fleming
Head of Multi-Asset Risk and Structuring
Multi-Asset Investing
brian_fleming@standardlife.com
Telephone: +44 (0)131 245 8505
Dr Jens Kroeske
Quantitative Investment Manager
Multi-Asset Investing
jens_kroeske@standardlife.com
Telephone: +44 (0)131 245 0057
