STOXX Minimum Variance Indices
June 2020| Confidential – Not for Redistribution – Copyright © 2019 Qontigo GmbH. Qontigo is part of Deutsche Börse Group.

Content

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Minimum Variance – Overview

STOXX Minimum Variance Indices

Risk and Return Characteristics

Appendix| Confidential – Not for Redistribution – Copyright © 2019 Qontigo GmbH. Qontigo is part of Deutsche Börse Group.

Minimum Variance
Overview

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STOXX is now part of Qontigo…
A new financial intelligence driver, modernizing investment management

3

Index

Analytics

STOXX & DAXWorld-class indices that are licensed tomore than 500 companies, including theworld’s largest financial product issuers,
capital owners and asset managers.

AXIOMA
Best of breed portfolio construction and risk
analytics tools.

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Minimum Variance Portfolio
Based on Markowitz’s Nobel Prize winning Modern Portfolio Theory
Why Minimum Variance▪ The Minimum Variance portfolio (MVP) is an efficient portfolio withminimal risk

Risk-return optimization
Return(Performance)
Efficient frontier▪ The MVP is the only portfolio on the efficient frontier that does not
require a return estimation:▪ Unlike returns, risks can be forecasted relatively accurately
and reduced without harming returns as non-remunerated
market risks are diversified away
▪ Historically, MVP strategies were less impacted by market
downturns▪ MVPs use less risk budget available to investors, giving access tohigher long term returns on a constant risk basis

Minimum
Variance
portfolio

Typical marketcap weighted
index

Risk (Volatility)

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Advantages of Minimum Variance InvestingDistinctively improved risk-return profile▪

Low risk, enables higher allocation to equity with same risk budgeting▪

▪

Low drawdowns, low beta: can be combined with high beta for overall portfolio enhanced risk/return▪

Historically, higher long term performance with temporary underperformance in strong years only▪
▪

▪

Win by losing less!
Active-like returns with stable upward trending returns, avoiding large drawdowns

Outperformance and strong Sharpe ratio driven by behavioral reasons

▪
▪
▪

5

In low interest rate environment especially, ability to reduce fixed income allocation

Behavioral biases: investor psychology, asymmetric (lottery) payout preferences, representativeness, over-confidence
Structural constraints: inability to employ leverage, benchmark relative risk constraints
These promote the outperformance and low risk of Min Var portfolios| Confidential – Not for Redistribution – Copyright © 2019 Qontigo GmbH. Qontigo is part of Deutsche Börse Group.

STOXX Approach – A Robust Factor-based Risk Model Reducing
Computational Complexity and Generating Superior Results
Two primary approaches used in the industry
Historical Covariance Approach▪ Mathematically cumbersome and inefficient▪ Spurious correlations▪ Universe often cut just to enable computation

Factor Model Approach▪ More robust, using more information▪ No spurious correlations▪ Enable full universe utilization

STOXX adopts AXIOMA’s state-of-the-art factor model for its minimum variance indices▪

Fundamental / technical factors that specify systematic risk drivers in regions and single countries. Models designed to forecast
volatility “out of sample”

STOXX Minimum Variance Indices uses best of breed portfolio optimization algorithm▪

Creates more efficient portfolios than competitors with more stable optimization results and constraining the results against
relevant factors, leading to more investable indices

STOXX is the only provider of true Minimum Variance Indices using a Factor Model Approach6| Confidential – Not for Redistribution – Copyright © 2019 Qontigo GmbH. Qontigo is part of Deutsche Börse Group.

STOXX Minimum VarianceIndices
Methodology

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STOXX’s Innovative Minimum Variance Concept
Extends its global smart-beta offering

1 Superior methodology

Flexible dual offering▪ Using Axioma’s superior fundamental risk model to robustly andaccurately forecast and minimize risk
▪ Overpriced securities are not over-weighted▪ Weighting done by optimization, requires fewer components▪ Reduced risk and draw downs, higher returns▪ Superior methodology, superior output compared▪ to low risk weighting

2▪ STOXX Minimum Variance Indices come in two versions:
Constrained and Unconstrained▪ The Constrained Version: Similar exposures to market-cap index
with much lower risk
▪ The Unconstrained Version: first of its kind globally,▪ with complete freedom to fulfill its Minimum VariancemandateSTOXXMinimum▪ Selection universe is a broad index▪ Only extremely liquid stocks considered▪ Model less constrained as a result▪ Turnover and transaction costs are considered in optimization
directly for a holistic optimization

3 Highly liquid and low transaction costs
8

Variance▪ Well-diversified and UCITs compliant▪ Tradable and trackable▪ Constrained version has very low active positions on
countries/sectors/risk factors
Adapted to portfolio constraints| Confidential – Not for Redistribution – Copyright © 2019 Qontigo GmbH. Qontigo is part of Deutsche Börse Group.

4

STOXX’s Minimum Variance Indices Come in Two Versions
Catering to different investor objectives
Unconstrained version

Constrained version▪ Full optimization to minimize risk

▪ Optimization is constrained to limit bias of Minimum
Variance index into a specific industry/country/factor whencompared to the underlying index▪ With only very basic constraints, there is the freedom toprovide increased optimality in resulting portfolio▪ Resulting portfolio might have a bias towards certain
properties (specific factor, geography etc.) as the aim ispurely to Minimize Variance▪ Most factors/attributes are constrained except for variance,
resulting in a very similar index but with reduced risk
▪ Offers an advantage for investors seeking to track abenchmark▪ The freedom is expected to provide lower risk
▪ Caters to an investment in a Minimum Variance portfolio
while not concerned about the underlying benchmark

9▪ Caters to the need of a superior risk return profile over thebenchmark, or a risk minimized benchmark| Confidential – Not for Redistribution – Copyright © 2019 Qontigo GmbH. Qontigo is part of Deutsche Börse Group.

STOXX Minimum Variance Methodology Works Empirically in All Geographies
400

500

STOXX Global 1800 Minimum Variance (USD GR)
STOXX Global 1800 Minimum Variance Unconstrained (USD GR)
STOXX Global 1800 (USD GR)

400

STOXX USA 900 Minimum Variance (USD GR)
STOXX USA 900 Minimum Variance Unconstrained (USD GR)
STOXX USA 900 (USD GR)

300

300
200
200
100

100

0
Jun-10400

Jun-12

Jun-14Jun-16Jun-18Jun-20STOXX Europe 600 Minimum Variance (EUR GR)
STOXX Europe 600 Minimum Variance Unconstrained (EUR GR)
STOXX Europe 600 (EUR GR)

0
Jun-10

400

300

300

200

200

100

100

0
Jun-10 Jun-11

Jun-12 Jun-13 Jun-14 Jun-15

Jun-16 Jun-17 Jun-18 Jun-19 Jun-20

Jun-11

Jun-12

Jun-14Jun-15Jun-16Jun-17

Jun-18Jun-19Jun-20Jun-16 Jun-17 Jun-18 Jun-19

Jun-20STOXX Japan 600 Minimum Variance (JPY GR)STOXX Japan 600 Minimum Variance Unconstrained (JPY GR)STOXX Japan 600 (JPY GR)

0
Jun-10 Jun-11

Jun-12 Jun-13 Jun-14 Jun-15

1) Source: STOXX data from Jun. 30, 2010 to Jun. 30, 202010

Jun-13| Confidential – Not for Redistribution – Copyright © 2019 Qontigo GmbH. Qontigo is part of Deutsche Börse Group.

Risk and Return Characteristics

11| Confidential – Not for Redistribution – Copyright © 2019 Qontigo GmbH. Qontigo is part of Deutsche Börse Group.

STOXX Global Minimum Variance Indices
Return1)

Risk and return characteristics

Perf. overall (annualized)

STOXX Global
STOXX Global
STOXX Global
1800 Min. Var.
1800
1800 Min. Var.
Unconstrained
10.80%
9.12%
10.67%

400

300

Perf. (1Y)

-1.85%-5.07%

3.79%

Perf. (3Y) (annualized)

5.59%

4.08%

7.42%

Perf. (5Y) (annualized)

7.49%

6.17%

7.58%

Vol. overall (annualized)

11.46%

10.64%

15.05%

Volatility (1Y) (annualized)

23.48%

22.41%

27.76%

Volatility (3Y) (annualized)

14.88%

14.19%

18.26%

Volatility (5Y) (annualized)

12.87%

12.36%

16.10%

Sharpe ratio (Overall)

0.89

0.81

0.71

Sharpe ratio (5Y)

0.53

0.45

0.46

Tracking Error (Overall)

7.50%

9.39%

Tracking error (5Y)

6.66%

8.21%

Dividend Yield (Overall)

5.34%

4.84%

4.92%

STOXX Global 1800 Minimum Variance (USD GR)

Maximum drawdown

31.79%

31.67%

33.77%STOXX Global 1800 Minimum Variance Unconstrained (USD GR)

190

225

1801

Constituents

200

100

0
Jun-10Jun-12STOXX Global 1800 (USD GR)

1) Source: STOXX data from Jun. 30, 2010 to Jun. 30, 2020

12

Jun-14| Confidential – Not for Redistribution – Copyright © 2019 Qontigo GmbH. Qontigo is part of Deutsche Börse Group.

Jun-16Jun-18Jun-20STOXX USA Minimum Variance Indices
Return1)

Risk and return characteristics
STOXX USASTOXX USASTOXX USA
900 Min. Var.
900
900 Min. Var.
Unconstrained
Perf. overall (annualized)
Perf. (1Y)
Perf. (3Y) (annualized)
Perf. (5Y) (annualized)
Vol. overall (annualized)
Volatility (1Y) (annualized)
Volatility (3Y) (annualized)
Volatility (5Y) (annualized)
Sharpe ratio (Overall)
Sharpe ratio (5Y)
Tracking Error (Overall)
Tracking error (5Y)
Dividend Yield (Overall)Maximum drawdown
Constituents

13.32%-2.03%
8.30%
10.04%
14.13%
28.27%
18.51%
15.74%
0.91
0.61
6.44%
7.62%
5.99%
29.97%
90

12.50%-4.85%
5.34%
7.89%
12.98%
28.99%
18.48%
15.60%
0.92
0.49
8.91%
9.08%
6.24%
32.66%
95

13.76%
8.09%
11.04%
10.69%
17.59%
33.91%
22.72%
19.55%
0.78
0.56

5.14%
34.55%
900

450
400
350
300
250
200
150
100
50
0
Jun-10Jun-12

Jun-16STOXX USA 900 Minimum Variance (USD GR)
STOXX USA 900 Minimum Variance Unconstrained (USD GR)
STOXX USA 900 (USD GR)

1) Source: STOXX data from Jun. 30, 2010 to Jun. 30, 202013

Jun-14| Confidential – Not for Redistribution – Copyright © 2019 Qontigo GmbH. Qontigo is part of Deutsche Börse Group.

Jun-18Jun-20STOXX Europe Minimum Variance Indices
Return1)

Risk and return characteristics
STOXX Europe
600 Min. Var.

STOXX Europe
600 Min. Var.
Unconstrained

STOXX Europe
600

Perf. overall (annualized)

8.16%

10.03%

7.68%

Perf. (1Y)

-4.82%-1.79%-3.87%

Perf. (3Y) (annualized)

1.80%

3.57%

1.51%

Perf. (5Y) (annualized)

2.86%

6.07%

2.20%

200

Vol. overall (annualized)

13.39%

12.28%

17.27%

150

Volatility (1Y) (annualized)

21.81%

21.13%

26.80%

Volatility (3Y) (annualized)

14.75%

14.41%

18.06%

Volatility (5Y) (annualized)

15.21%

14.41%

18.38%

0.66

0.84

0.52
0.23

Sharpe ratio (Overall)
Sharpe ratio (5Y)

0.29

0.51

Tracking Error (Overall)

6.61%

8.35%

Tracking error (5Y)

6.04%

7.34%

350
300
250

100
50
0
Jun-10Jun-12

Jun-16Jun-18Dividend Yield (Overall)

4.66%

5.40%

4.85%

STOXX Europe 600 Minimum Variance (EUR GR)

Maximum drawdown

29.87%

29.87%

35.34%STOXX Europe 600 Minimum Variance Unconstrained (EUR GR)

160

133

600

ConstituentsSTOXX Europe 600 (EUR GR)

1) Source: STOXX data from Jun. 30, 2010 to Jun. 30, 2020

14

Jun-14| Confidential – Not for Redistribution – Copyright © 2019 Qontigo GmbH. Qontigo is part of Deutsche Börse Group.

Jun-20STOXX Japan Minimum Variance Indices
Return1)

Risk and return characteristics

Perf. overall (annualized)
Perf. (1Y)
Perf. (3Y) (annualized)

STOXX JapanSTOXX JapanSTOXX Japan
600 Min. Var.
600
600 Min. Var.
Unconstrained
10.88%
8.65%
8.31%
0.19%
-6.92%
2.75%
3.39%
0.28%
1.52%

Perf. (5Y) (annualized)

3.47%

0.62%

1.15%

Vol. overall (annualized)

15.50%

14.13%

19.45%

Volatility (1Y) (annualized)

17.27%

18.39%

21.07%

Volatility (3Y) (annualized)

13.25%

13.07%

16.67%

Volatility (5Y) (annualized)

15.55%

14.64%

19.43%

Sharpe ratio (Overall)

0.74

0.66

0.51

Sharpe ratio (5Y)

0.30

0.12

0.16

Tracking Error (Overall)

8.41%

11.30%

Tracking error (5Y)

8.23%

11.22%

Dividend Yield (Overall)

4.42%

3.92%

3.13%

Maximum drawdown

24.25%

28.70%

31.18%

121

104

600

Constituents

400

300

200

100

0
Jun-10Jun-12

Jun-16Jun-18STOXX Japan 600 Minimum Variance (JPY GR)STOXX Japan 600 Minimum Variance Unconstrained (JPY GR)STOXX Japan 600 (JPY GR)

1) Source: STOXX data from Jun. 30, 2010 to Jun. 30, 202015

Jun-14| Confidential – Not for Redistribution – Copyright © 2019 Qontigo GmbH. Qontigo is part of Deutsche Börse Group.

Jun-20Appendix

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STOXX Minimum Variance Indices Come in Two Versions…
Unconstrained version

Constrained version

Capping▪

▪ At least 30% of underlying broad index: 𝐻𝑀𝑖𝑛𝑉𝑎𝑟 ≥ 𝐻𝐵𝑎𝑠𝑒 ∗ 30%

Effective
portfolio size

Rebalancing
and max.
turnover

UCITS compliant: individual components capped at 8%; all individual components with weights ≥4.5% jointly capped at 35% 1)with 𝑤 = component weight; 𝐻 = effective number of assets, and𝐻 =▪
▪

Monthly rebalancing
5% one way turnover constraint 2)▪ Quarterly rebalancing▪ 7.5% one way turnover constraint 2)

Country andindustry
exposure▪

Not applied to unconstrained version▪ Constrained Minimum Variance Index’s exposure bycountry and industry must remain within ±5% of exposureof base index by country and industry

Factor exposure▪

Not applied to unconstrained version▪ Constrained Minimum Variance Index must remain within
a 0.25 standard deviation of the base index’s exposure toeach factor

1) Note that these “4.5/8/35” rule is slightly stricter than required by UCITS constraints which imply “5/10/40” rule2) One-way turnover defines the portion of a portfolio that is sold in order to buy other components

17

1
σ 𝑤2

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…that Cater to Different Investor Needs (I)Version 1: STOXX Minimum Variance Unconstrained Index
Index Characteristics

Index Constraints

Caters to investors trying to capture
the full benefit of a minimum variancestrategy▪ Diversification▪ Most optimal risk-adjusted return▪ Full optimization to minimize risk

- index constituent capping at 8%- sum of index constituent with weight over 4.5% are capped at 35%▪ Turnover- monthly rebalancing- one-way turnover constrained to a maximum of 5%▪ With only very basic constraints, there is the freedom to provide
increased optimality in the resulting portfolio▪ May have relative biases towards certain factors, geographies etc.

▪ Expected to provide lowest risk

18

| Confidential – Not for Redistribution – Copyright © 2019 Qontigo GmbH. Qontigo is part of Deutsche Börse Group.

…that Cater to Different Investor Needs (II)Version 2: STOXX Minimum Variance Constrained Index
Index Characteristics
Caters to investors with high benchmark
sensitivity and tracking error constraints▪ Optimization is constrained to limit biases of Minimum Varianceindex relative to the benchmark▪ Most factors/attributes are constrained except for variance,
resulting in a very similar index but with reduced risk
▪ Improves portfolio risk-return efficiency while tracking benchmark

19

Index Constraints▪ Diversification- index constituent capping at 8%- sum of index constituent with weight over 4.5% are capped at 35%▪ Turnover- quarterly rebalancing- one-way turnover constrained to a maximum of 7.5%

▪ Benchmark Constraints- ICB sector and country weights constrained to +/-5% of theunderlying benchmark index- index is constrained within +/-0,25 standard deviations of theunderlying benchmark index’s factor exposure (excl. volatility, size)| Confidential – Not for Redistribution – Copyright © 2019 Qontigo GmbH. Qontigo is part of Deutsche Börse Group.

Historical Covariance Method Versus the Factor Model Approach
Variance/covariance matrix is superior
Variance/covariance Matrix

Historical covariance▪

Correlation model determines the correlation between the components byusing historical data
Cov ariance matrix

Component A

Component A

1

Component B
Component C etc.

▪

Component B

Component C▪ For each component, the exposure to each factor is determined, and factor
covariances are calculated
Cov ariance matrix component A

Factor 1

Factor 1

1

Factor 2

Factor 2

1
1

Minimizing of variance using the covariance matrix is subject to certain
constraints:▪ Component capping▪ Industry capping▪ Diversification in terms of effective assets

Factor 3 etc

For the constrained version:▪ Apply further constraints:▪ Component capping▪ Diversification in terms of effective assets▪ Rebalancing and max turnover▪ Country and industry exposure▪ Factor exposure
For the unconstrained version:▪ Apply further constraints:▪ Component capping▪ Diversification in terms of effective assets▪ Rebalancing and max turnover

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Factor 3

1
1

The Axioma Optimization Process
Technical methodology
Optimization

Factor constraints▪ Uses a Second Order Cone Optimization (SOCP)▪ With Branch and Bound▪ SOCP to model any quadratic term (in objective or
constraint)▪ Branch and Bound to solve combinatorial constraints▪ Except for the unconstrained versions, all STOXX Minimum
Variance indices will be constrained to have factor exposure similar
to its underlying index, with respect to the factors:▪ Value▪ Growth▪ Medium Term Momentum▪ Short Term Momentum▪ Leverage▪ Liquidity▪ Exchange rate Sensitivity▪ Additional proprietary methods used to improve quality of solution
and speed of optimization▪ Specialized heuristics▪ Fine tuned Branch and Bound algorithm▪ Proprietary reformulation techniques for combinatorialconstrains21▪ Size is not used as the underlying index is a broad index and a size
pre selection has already been made| Confidential – Not for Redistribution – Copyright © 2019 Qontigo GmbH. Qontigo is part of Deutsche Börse Group.

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