Research & Analytics. Low and Minimum Volatility Indices

(1)

Low and Minimum Volatility Indices

Research & Analytics

(2)

Page 2

Contents

1. Introduction

2. Alternative Approaches 3. Risk Weighted Indices 4. Low Volatility Indices

5. FTSE’s Approach to Minimum Variance

6. Methodology - Overview of Objective and Constraints 7. Small Scale FTSE USA Minimum Variance Index

8. FTSE Developed Minimum Variance Index 9. Regional Results

10. Summary and Conclusions 11. Appendix

• Mathematical details

• Additional regional results

Low & Minimum Volatility Indices

(3)

Page 3

Japan (%) 1980s 2000s

Real GDP 4-5 +1

Inflation 3 -1

Nominal GDP 8 0-1

Nominal Bond Yield 8 1

(now 0.7)

-8%

-6%

-4%

-2%

0%

2%

4%

6%

8%

10%

Jan-90 Jan-92 Jan-94 Jan-96 Jan-98 Jan-00 Jan-02 Jan-04 Jan-06 Jan-08 Jan-10 Jan-12 Japan Nominal GDP growth Y/Y GJGB10 Index

07/02/2013

Japan 10 yr BY vs. Nominal GDP y/y% US10 yr BY vs. Nominal GDP y/y%

?

From 8% to 1%

US (%) 1995-

2000 2013

Real GDP 3-4 2

Inflation 3 1.5-2

Nominal GDP 7 3-4

Nominal Bond Yield 7 2

(heading 3)

1. Introduction

Macro Environment & Volatility

(4)

Page 4

Joined up thinking:

• Dimson, Marsh & Staunton (LBS) 2013 study concluded that:

‘low real interest rates lead to a period of low equity returns’

they project c 3-3.5%

• The US CBO has cut US potential GDP growth to:

2.2% for 2013-23 period vs. 3.3% for 1950-2012

The decline in Nominal and Real Yields

Decline in trend GDP growth expectations

Decline in Equity return projections

Persistently higher volatility?

1. Introduction

Macro Environment & Volatility

(5)

Page 5

2. Alternative Approaches

• Implementation of minimum volatility portfolio requires constraints.

• Max stock, sector country and turnover constraints are typical.

• Minimum Volatility subject to constraints is a low volatility approach.

• Examine simpler approaches and compare to an investable minimum volatility outcome.

Approaches

• Risk or inverse variance weight stocks

• Correlations are ignored.

• Screen universe for a low volatility subset of stocks

• Capture systematic return associated with factor.

• Volatility reduction is incidental.

• Within industry screens to control tracking error

• Apply market cap or risk weight schemes.

• ‘Min Volatility’ Portfolio

• Small scale problem using empirical covariance matrix.

• Large scale problem requires factor model.

• Assess rebalance frequency, concentration and liquidity.

Low and Minimum Volatility Indices

(6)

Page 6

• Re-weight ALL stocks by inverse of realised variance.

• No optimisation required.

• Closed form solution of Minimum Variance Portfolio when correlation is ignored (cross- correlations are zero).

• Variance of daily USD returns over two years.

Performance Summary

• Smaller volatility reduction compared to Min Variance – cross-correlation is important.

• Relatively low tracking error and turnover a consequence of reweighting the entire universe.

Results September 2001 to December 2011: All figures are USD total returns, except FTSE Developed Europe (Euro)

3. Risk Weighted Indices

Risk Wgt Underlying Risk Wgt Underlying Risk Wgt Underlying Risk Wgt Underlying

G. Mean (%p.a.) 5.6 3.7 10.4 6.2 7.9 4.4 9.7 5.4

Volatility (%p.a.) 17.4 21.4 17.0 21.1 19.6 21.4 14.4 18.1

Sharpe Ratio 0.32 0.17 0.61 0.29 0.40 0.20 0.67 0.30

Volatility Reduction(%) -18.9 -19.4 -8.7 -20.7

DD (%) -58.4 -54.2 -45.1 -55.3 -52.6 -54.7 -52.3 -57.4

2 Way Turnover (%p.a.) 67 61 57 60

Excess (% p.a.) 2.0 4.2 3.5 4.2

Tracking Error(%p.a.) 6.7 6.2 4.2 6.7

Information Ratio 0.29 0.68 0.83 0.63

Alpha (% p.a.) 2.39 4.92 3.61 5.08

Alpha t Stat 1.62 3.85 3.27 3.41

Beta 0.78 0.78 0.90 0.75

World Developed Developed Europe Developed Asia Pac FTSE USA

(7)

Page 7

Results September 2001 to December 2011: All figures are USD total returns, except FTSE Developed Europe (Euro)

Risk Weighted Indices: Regional & Global

-50 -40 -30 -20 -10 0 10

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

Volatility Reduction(%) Risk Weight - Full Universe: Reduction in 252 Day Rolling Volatility

AWDEURS AWDPAC WIUSA AWD

80 100 120 140 160

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

Relative Performance

Risk Weight - Full Universe: Relative Performance

AWDEURS AWDPAC WIUSA AWD

(8)

Page 8

• Similar concentration levels to Min Variance at the large cap end of the spectrum.

• Re-weighting of entire universe leads to less concentrated outcomes within small caps.

• Substantially more diversified outcomes than underlying cap weight index.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0% 20% 40% 60% 80% 100%

% Weight

% Stocks

FTSE Developed Concentration / Lorenz Curves

FTSE AWD Min Var Underlying FTSE AWD FTSE AWD Risk Weight

0% 5% 10% 15% 20% 25%

Oil & Gas Basic Materials Industrials Consumer Goods Health Care Consumer Services Telecommunications Utilities Financials Technology

Industry Weight(%) Industry Weights : Dec 2011 Rebalance

AWD WIUSA AWDPAC AWDEURS

(9)

Page 9

4. Low Volatility Indices: FTSE Developed

• Target the return characteristics of low volatility stocks.

• Volatility used to select stocks.

• Low volatility outcome is incidental - there is no specific volatility target.

• Apply cap and risk weights to selected universe.

Factors and Construction

• Factors

• Annualised daily volatility over 2 years in USD.

• Selection

• Selection universe – FTSE Developed.

• Lowest volatility encompassing 50% of market cap.

• Within industry - lowest volatility encompassing 50% of market cap.

• Construction

• Capitalisation or risk weight.

• Rebalance quarterly in March, June, September & December.

• Period

• September 2001 to December 2011.

(10)

Page 10

Low Volatility FTSE Developed: Universe & Within Industry Selection – Cap & Risk Weight

• Application of risk weights to low volatility universe - similar volatility reduction to Min Var

• Cap weighted versions result in relatively small volatility reductions

• Risk weights lead to a consequent increase in tracking error and turnover

• Intra-industry selection reduces tracking error

• Risk weighting applied to intra-industry selection substantially increases levels of diversification

• Volatility differences are relatively small - inverse variance weighting is closer to equal weight

Results September 2001 to December 2011: All figures are USD total returns

Low Volatility Indices: FTSE Developed

Performance Summary

Cap Wgt Risk Wgt Cap Wgt Risk Wgt Underlying

G. Mean (%p.a.) 6.7 10.2 5.5 9.5 5.4

Volatility (%p.a.) 15.3 12.4 16.1 12.9 18.1

Sharpe Ratio 0.44 0.82 0.34 0.74 0.30

Volatility Reduction(%) -15.8 -31.5 -11.3 -28.8

DD (%) -47.6 -43.9 -51.7 -47.4 -57.4

2 Way Turnover (%p.a.) 58 93 62 100

Excess (% p.a.) 1.3 4.7 0.1 4.1

Tracking Error(%p.a.) 5.3 8.1 3.9 7.7

Information Ratio 0.23 0.59 0.02 0.53

Alpha (% p.a.) 2.01 6.06 0.61 5.31

Alpha t Stat 1.60 4.22 0.63 3.68

Beta 0.81 0.63 0.87 0.66

Universe Intra-Ind

50% By Cap 50% By Cap

0% 10% 20% 30%

Industry Weight(%) Industry Weights : Dec 2011

Rebalance

Low 50% By Cap:Intra-Ind:Risk Wgt Low 50% By Cap:Intra-Ind

Low 50% By Cap: Risk Wgt Low 50% By Cap

(11)

Page 11

Low Volatility FTSE Developed: Universe & Within Industry Selection By Cap – Cap & Risk Weight

Low Volatility Factor Indices: FTSE Developed

-60 -50 -40 -30 -20 -10 0 10

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

Volatility Reduction(%)

Risk & Cap Weight: Reduction in 252 Day Rolling Volatility

Low 50% By Cap Low 50% By Cap: Risk Wgt

Low 50% By Cap:Intra-Ind Low 50% By Cap:Intra-Ind:Risk Wgt

(12)

Page 12

5. FTSE’s Approach to Minimum Variance

Overall aims

• Volatility reduction rather than performance – 20-30% average volatility reduction.

• Broad, diversified and investable portfolios – 60% p.a. two way turnover.

• Straightforward, intuitive methodology – no turnover constraint.

• Robust outcomes – consistent reduction in volatility.

Factor exposures - Style

• Primarily low beta, low residual volatility and to a lesser extent small cap.

Turnover – limited through a semi-annual rebalance

• Volatility reduction not affected by rebalance frequency.

• 60% two way p.a. on average.

FTSE Minimum Variance Indices

(13)

Page 13

FTSE’s Approach to Minimum Variance

Constraints and Diversification – some constraints are useful

• Constraints act as insurance against over concentration in any particular stock, sector or country.

• No explicit turnover constraint. Such a constraint leads to a path dependency of resulting portfolios.

• Diversification constraint – regularises covariance matrix.

Factor or Risk Model – facilitates finding a solution, but does not determine outcomes

• If risk model is important, why constrain factor exposures?

• Equally, why impose country or industry constraints? The sophistication of factor model is not key.

Data Frequency and Window

• Results are robust to data frequency or data window selected.

(14)

Page 14

6. Methodology - Overview of Objective and Constraints

Objective

• Minimise the expected index volatility or variance – the marginal risk contribution of all stocks is equal.

• Methodology requires only historic volatility and correlations – expected returns play no role.

• Two years of daily observations used for correlations and volatility, with semi-annual rebalancing.

• Principal Component Analysis (PCA) factor model used to construct the covariance matrix.

• Factor Model overcomes degeneracy / dimensionality problem and facilitates solution.

• Underlying index: FTSE All-World Developed Index Series.

(15)

Page 15

Methodology – Constraints

Constraints

• Stock Weight: maximum weight to avoid concentration in any particular stock.

• Industry Weight: maximum weight to ensure diversification.

• Diversification Target: ensures a minimum number of stocks in the index.

• Capacity Constraint: maximum weight of a constituent relative to the underlying index to promote capacity / avoid illiquidity issues.

• Effective Zero Weight: excludes constituents with a weight of less than 1 basis point.

• Constraint summary:

FTSE Minimum Variance Indices Upper Stock Weight Limit Capacity Constraint

Upper ICB Industry Weight Limit Diversification Target

Effective Zero Weight

20%

1.0% 1.5% 1.5% 1.5%

World Developed Developed Asia Pacific USA

1bp 1bp 1bp 1bp

Developed Europe

20% 20%

1000 400 300 250

20x 20x 20x 20x

20%

(16)

Page 16

Methodology - Constraints

• Country Weight: for a given country weight in the underlying, the minimum and maximum country weights in the minimum variance portfolio lie between upper and lower bounds:

FTSE Minimum Variance Indices 0 10 20 30 40 50 60 70 80 90 100

0 20 40 60 80 100

Country Weight (%)

Underlying Country Weight (%) Underlying Minimum Maximum

(17)

Page 17

7. Small Scale FTSE USA Minimum Variance Index

• Minimise the expected index volatility – the marginal risk contribution of all stocks is equal.

• Construction requires only volatility and correlations – expected return plays no role.

• 2 years of daily observations and quarterly rebalancing.

• Intuitively the Norm constraint ensures a minimum holding.

• Covariance matrix with and without a factor model.

Objective & Constraints

(18)

Page 18

FTSE USA results September 2001 to December 2011: All figures are USD total returns.

• Factor model facilitates solving the problem

• No material difference in outcomes

• Volatility reduction in the order of 17%; 2 way turnover of 80% p.a.

• Broadly diversified outcome across industry groups

• Min Variance portfolio significantly more diversified than underlying FTSE USA Minimum Variance: With & Without Factor Model

FTSE USA Minimum Variance: With & Without Factor Model

0% 5% 10% 15% 20%

Industry Weight(%) Industry Weights : Dec 2011

Rebalance

No Factor Model Factor Model

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0% 20% 40% 60% 80% 100%

% Weight

% Stocks

Min Variance & Underlying: Lorenz Curves

FTSE USA Min Var Underlying FTSE USA

Factor Model Underlying No Factor Model Underlying

G. Mean (%p.a.) 8.17 4.4 8.18 4.4

Volatility (%p.a.) 17.77 21.4 17.76 21.4

Sharpe Ratio 0.46 0.20 0.46 0.20

Volatility Reduction(%) -17.12 -17.14

DD (%) -49.24 -54.7 -49.22 -54.7

2 Way Turnover (%p.a.) 78.43 78.16

Excess (% p.a.) 3.80 3.80

Tracking Error(%p.a.) 5.74 5.75

Information Ratio 0.66 0.66

Alpha (% p.a.) 4.12 4.13

Alpha t Stat 3.35 3.35

Beta 0.81 0.81

FTSE USA FTSE USA

(19)

Page 19

8. FTSE Developed Minimum Variance Index

• Factor model does not drive outcomes, but for larger problems is necessary

• Constraints are necessary to achieve investable outcome

• Volatility reduction is greatest during periods of high volatility

0%

5%

10%

15%

20%

25%

30%

35%

0 5 10 15 20 25 30 35 40

Volatility Reduction

252 Day Rolling Volatility (%)

Underlying Minimum Variance Volatility Reduction

252-day Rolling Volatility of FTSE Developed Index vs. FTSE Developed Minimum Variance Index

11/09/02– 15/06/12, Total Return (USD)

(20)

Page 20

FTSE Developed Minimum Variance Index - Performance

• Consistent out performance through entire period, but particularly noticeable when significant falls occur in the underlying.

50 100 150 200 250 300 350

Performance

Underlying Minimum Variance Relative

Absolute and Relative Performance of FTSE Developed Minimum Variance Index vs. FTSE Developed Index

21/09/01 – 15/06/12, Total Return (USD)

(21)

Page 21

FTSE Developed Minimum Variance Index – Comparative Statistics

• A semi-annual rebalance (March and September) yields comparable results to the quarterly rebalance, but at markedly lower levels of turnover.

• Volatility reduction of 28%.

• Significantly lower draw down.

• Diversification – minimum variance index holds approximately two-thirds of underlying stocks.

All statistics are on an annual basis 21/09/01– 15/06/12, Total Return (USD)

Semi-Annual Quarterly

Geometric Mean (%) 5.82 11.00 10.70

Volatlility (%) 17.91 12.91 12.94

Volatlility Reduction (%) 27.92 27.77

Sharpe Ratio 0.32 0.85 0.83

DD (%) -57.37 -46.30 -47.19

Mean Number of Stocks 1955 1321 1321

Two Way Turnover (%) 62.65 79.47

Excess (%) 4.90 4.61

Tracking Error (%) 6.56 6.52

Information Ratio 0.75 0.71

Alpha (%) 6.24 5.96

Alpha T-Stat 5.83 5.60

Beta 0.69 0.69

MINIMUM VARIANCE UNDERLYING

(22)

Page 22

FTSE Developed Minimum Variance Index – Country and Sector Weights

0 5 10 15 20 25

Industry Weight (%) Minimum Variance Underlying

-10 -5 0 5 10

Australia Belgium Canada Denmark Finland France Germany Greece Hong Kong Ireland Israel Italy Japan Korea Netherlands Norway New Zealand Austria Portugal Singapore Spain Sweden Switzerland UK USA

Active Country Weight (%) All data as at March 2012 rebalance

(23)

Page 23

FTSE Developed Minimum Variance Index – Concentration

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0% 20% 40% 60% 80% 100%

% of Weight

% of Stocks Underlying Min Variance

• Lorenz curves for March 2012

rebalance indicate that the minimum variance portfolio is substantially less concentrated than the underlying cap weighted index.

FTSE Minimum Variance Indices All data as at March 2012 rebalance

(24)

Page 24

FTSE Developed Minimum Variance Index – Liquidity

Liquidity considerations: assumed US$1bn portfolio size at March 2012 rebalance

• 79% (97%) of the minimum variance portfolio can be implemented at less than 10% (50%) of average daily traded volume (ADTV).

• 82% (96%) of the minimum variance portfolio can be rebalanced at 2%(8%) of ADTV.

• Cap weighted indices typically offer substantial implementation advantages.

0 10 20 30 40 50 60 70 80 90 100

0 2 4 6 8 10

% Rebalanced

% Share of ADTV Underlying Min Variance 0

20 40 60 80 100

0 10 20 30 40 50

% Implemented

% Share of ADTV Underlying Min Variance

(25)

Page 25

9. Regional Results – Volatility Reduction

• Volatility reductions of the order of 20-30% on average are achieved for all regions.

252-day Rolling Volatility Reduction of Regional Minimum Variance Index vs. Cap Weighted Index

11/09/02 – 15/06/12, Total Return (USD) except Total Return (EUR) for Europe 0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

Volatility Reduction

World Developed Asia Pacific USA Europe

(26)

Page 26

Regional Results – Performance

• Although performance is not specifically targeted, all regions outperform their cap weighted counterparts

Relative Performance of Regional Minimum Variance Index vs. Cap Weighted Index

21/09/01 – 15/06/12, Total Return (USD) except Total Return (EUR) for Europe 90

100 110 120 130 140 150 160 170 180

Relative Performance

World Developed Asia Pacific USA Europe

(27)

Page 27

Regional Results – Comparative Statistics

• Volatility reduction is consistent across all regions.

• Draw down is also substantially reduced.

• Diversification – minimum variance index represents around two-thirds of underlying across regions.

World, Asia Pacific and Europe rebalanced March and September. USA rebalanced June and December.

All statistics are on an annual basis

21/09/01 – 15/06/12, Total Return (USD) except Total Return (EUR) for Developed Europe

Underlying Min Var Underlying Min Var Underlying Min Var Underlying Min Var

Geometric Mean (%) 5.82 11.00 6.10 10.83 5.17 9.31 3.53 7.90

Volatlility (%) 17.91 12.91 20.86 15.17 21.11 16.61 21.40 14.61

Volatlility Reduction (%) 27.92 27.26 21.30 31.72

Sharpe Ratio 0.32 0.85 0.29 0.71 0.25 0.56 0.16 0.54

DD (%) -57.37 -46.30 -55.32 -41.67 -54.73 -46.38 -58.15 -50.86

Mean Number of Stocks 1955 1321 734 529 623 405 515 341

Two Way Turnover (%) 11.25 62.65 12.89 61.66 10.92 64.08 10.65 60.06

Excess (%) 4.90 4.46 3.93 4.22

Tracking Error (%) 6.56 7.79 6.29 8.32

Information Ratio 0.75 0.57 0.63 0.51

Alpha (%) 6.24 5.81 4.72 4.89

Alpha T-Stat 5.83 4.31 4.05 4.13

Beta 0.69 0.69 0.77 0.66

World Developed Developed Asia Pacific USA Developed Europe

(28)

Page 28

Regional Results – Factor Exposures

• Sub market beta and small cap tilt. Value tilt outside Europe.

• Significant alpha over period after style, size and market adjustment – except Japan.

Factor loadings from monthly regression spanning Jan 2003 to June 2012 -0.1 0.1 0.3 0.5 0.7 0.9

AWD AWDPAC AWDPACXJ WIUSA AWDEURS AWDEXUKS AWEBLOCS WIJPN

Value-Growth Small-Large Market

0.0 2.0 4.0 6.0 8.0 AWD

AWDPAC AWDPACXJ WIUSA AWDEURS AWDEXUKS AWEBLOCS WIJPN

Annualised Alpha Alpha t stat

Factor Loadings By Region Alpha by Region

(29)

Page 29 Rebalance from June 2011 to December 2011; implementation as of December 2011

0 10 20 30 40 50 60 70 80 90 100

0 10 20 30 40 50

% Implemeted

% Share of ADTV

FTSE Developed Implementation: Proportion of Index Implemented By Share of ADTV

Min Var Risk Wgt

Low 50% By Cap Intra-Ind: Cap Wgt Low 50% By Cap Intra-Ind: Risk Wgt

0 10 20 30 40 50 60 70 80 90 100

0 10 20 30 40 50

% Rebalanced

% Share of ADTV

FTSE Developed Rebalance: Proportion Rebalanced By Share of ADTV

Min Var Risk Wgt

Low 50% By Cap Intra-Ind: Cap Wgt Low 50% By Cap Intra-Ind: Risk Wgt

Liquidity Considerations: Assumed 1Bn USD Portfolio Size

• 75% (95%) of the Min Variance portfolio can be implemented at < 10% (50%) of ADTV

• Cap weighted indices typically offer substantial implementation advantages

• Screened risk weighted indices typically exhibit liquidity issues & high turnover

(30)

Page 30

Correlation With Alternatively Weighted Indices

• Minimum variance is relatively uncorrelated with other indices

• Twenty-four month rolling correlation of excess returns (USD TRI)

FTSE Minimum Variance Indices -80%

-60%

-40%

-20%

0%

20%

40%

60%

80%

100%

2003/08 2004/08 2005/08 2006/08 2007/08 2008/08 2009/08 2010/08 2011/08

24 Month Correlation

DBI Developed EDHEC Developed RAFI Developed 1000 RAFI All World 3000

(31)

Page 31

10. Summary and Conclusions

• Pure risk weighted outcomes and cap weighted volatility screens yield smaller volatility reductions

• Where optimisation is to be avoided and volatility reduction is the only objective

• Risk Weight the 50% by Cap of stocks with the lowest volatility

• Where optimisation is to be avoided and tracking error is a concern

• Cap weight the 50% by Cap of stocks with the lowest volatility within industries

• Min Variance and risk weighted volatility screens achieve similar large reductions in volatility

• Similar tracking error and comparable levels of diversification

• Min Variance has lower turnover

• Liquidity profiles of risk weighted volatility screens are inferior

• Screening cut-offs are arbitrary

• Min Variance approach is the preferred and most direct route to volatility reduction

(32)

Page 32

FTSE Global Minimum Variance Index Series

• FTSE Developed Minimum Variance

• FTSE USA Minimum Variance

• FTSE Japan Minimum Variance

• FTSE Developed Europe Minimum Variance

• FTSE Developed Europe ex UK Minimum Variance

• FTSE Developed Eurobloc Minimum Variance

• FTSE Developed Asia Pacific Minimum Variance

• FTSE Developed Asia Pacific ex Japan Minimum Variance

All indices are calculated on a total return basis

(33)

Page 33 FTSE Minimum Indices

Appendix

(34)

Page 34

Minimum Variance: Mathematical details

Objective and Constraints

Objective: Minimise portfolio variance, 𝛔^𝟐= ^𝐍_𝐢=𝟏 ^𝐍_𝐣=𝟏𝐰_𝐢𝐂_𝐢𝐣𝐰_𝐣

where 𝑤_𝑖 is the weight of the 𝑖^𝑡ℎ stock and C_𝑖𝑗 is the covariance matrix constructed using the following Principle Component Analysis (PCA) of an 𝑁 × 𝑁 empirical correlation matrix derived from two years of daily total returns (containing 𝑇 business days).

Let 𝜆₁, . . , 𝜆_𝐾 be the 𝐾 eigenvalues of the empirical correlation matrix that are bigger than 1 + 𝑁/𝑇 + 2 𝑁/𝑇 and let 𝛬 1, … , 𝛬 _𝐾 be their associated eigenvectors each with 𝑁 elements.

Let 𝐷_𝑛𝑚 be the 𝐾 × 𝐾 diagonal matrix with 𝐷_𝑛𝑛 = 𝜆_𝑛 and 𝑃_𝑛𝑗 be the 𝐾 × 𝑁 matrix whose 𝑛^𝑡ℎ row is given by 𝛬 _𝑛. One then constructs the 𝑁 × 𝑁 PCA correlation matrix as 𝜙 = 𝑃𝐷𝑃^𝑇. The diagonal elements of 𝜙 are additionally constrained to be equal to one.

The PCA covariance matrix is then defined by: C_𝑖𝑗 = 𝛿_𝑖 𝛿_𝑗𝜙_𝑖𝑗 where 𝛿_𝑖 is the standard deviation or volatility of the 𝑖^𝑡ℎ stock.

Constraints:

Long Only Constraint: 𝑤_𝑖 ≥ 0 ∀_𝑖 Fully Invested: ^𝑁_𝑖=1𝑤_𝑖 = 1 Upper Stock Limit: 𝑤_𝑖 ≤ 𝑤_𝑚𝑎𝑥 ∀_𝑖

Country Constraint: Bounded by 𝑀𝑎𝑥[ 0.9 ∗ 𝑋 − 5.0, 0.0] and 𝑀𝑖𝑛[1.1 ∗ 𝑋 + 5.0, 100.0] where X is the country weight in the underlying.

Industry Constraint: Maximum weight contribution of a particular Industrial Group is less than or equal to 20%.

Diversification Target: ^𝑁_𝑖=1𝑤_𝑖²= 1/𝐻.

Maximum Weight Multiple: The maximum weight multiple of the underlying market capitalisation weight in the Minimum Variance Index is 20 times.

Effective Zero Weight Threshold: Any optimised stock weight that is less than 1 basis point is treated as having a zero weight.

(35)

Page 35

FTSE Developed Asia Pacific Minimum Variance Index – Country and Sector Weights

-10 -5 0 5 10

Australia Hong Kong Japan Korea New Zealand Singapore

Active Country Weight (%)

0 10 20 30

All data as at March 2012 rebalance

(36)

Page 36

FTSE Developed Asia Pacific Minimum Variance Index - Concentration and Liquidity

• Assumption: US$1 bn portfolio

FTSE Minimum Variance Indices 0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0% 20% 40% 60% 80% 100%

% of Weight

0 20 40 60 80 100

0 10 20 30 40 50

% Rebalanced

(37)

Page 37

FTSE Developed USA Minimum Variance Index – Sector Weights

0 5 10 15 20

Industry Weight (%) Minimum Variance Underlying All data as at June 2012 rebalance

(38)

Page 38

FTSE Developed USA Minimum Variance Index – Concentration and Liquidity

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0% 20% 40% 60% 80% 100%

% of Weight

% of Stocks Underlying Min Variance All data as at June 2012 rebalance

0 20 40 60 80 100

0 1 2 3 4 5

% Rebalanced

(39)

Page 39

FTSE Developed Europe Minimum Variance Index - Country and Sector Weights

-6 -4 -2 0 2 4

Belgium Denmark Finland France Germany Greece Ireland Italy Netherlands Norway Austria Portugal Spain Sweden UK

Active Country Weight (%)

0 5 10 15 20 25

(40)

Page 40

FTSE Developed Europe Minimum Variance Index – Concentration and Liquidity

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0% 20% 40% 60% 80% 100%

% of Weight

0 20 40 60 80 100

0 5 10 15 20 25 30

% Rebalanced

(41)

Page 41

Contact details

Andrew Dougan

Associate Director, Research & Analytics Email: [email protected] Tel no: 0207 866 1975

Disclaimer

This presentation does not constitute an offer or invitation to buy or sell any investment or participate in any investment activity, nor any advice concerning the acquisition or disposal of securities. This presentation has not been approved by a person authorised under the Financial Services and Markets Act 2000 (“FSMA”) for the purposes of section 21 of FSMA.

Accordingly this presentation and the information contained within it is only made to, and for the use of, persons whom FTSE believes to be investment professionals within the meaning of article 19(5) of the Financial Services and Markets Act 2000 (Financial Promotion) Order 2005 or U.S. institutional investors and major U.S. institutional investors, as provided by Rule 15a-6 under the U.S. Securities Exchange Act of 1934. These slides should not be relied upon by anyone else. If you have not received this presentation directly from FTSE, do not use or rely on it or forward it to anyone else.

All information is provided for information purposes only and is derived from historical data and information deemed to be reliable and generally available to the public in its primary form. Nothing in this presentation constitutes financial or investment advice, nor any advice concerning the acquisition or disposal of securities. You should exercise your discretion in your use of the FTSE Global Minimum Variance Index Series (the “Index”) and if you do not have the relevant professional expertise in relation to investments of the kind the Index relates to, before using the Index you should consult an investment professional who does for advice. FTSE makes no claim, prediction, warranty or representation whatsoever, expressly or impliedly, either as to the results to be obtained from the use of the Index or the fitness or suitability of the Index for any particular purpose to which it might be put. No responsibility or liability can be accepted by FTSE for any errors or for any loss from the use of this presentation.

All figures and graphical representations in these slides refer to past performance and are sourced by FTSE. Past performance is not a reliable indicator of future results.

All rights in the Index vest in FTSE. “FTSE®” is a trade mark of the London Stock Exchange Group companies and is used by FTSE under licence.

This publication is not intended for dissemination to the public or distribution by subscription and recipients of this publication shall not disseminate or distribute it in any way. No part of this publication may be reproduced, stored in a retrieval system or transmitted by any other form or means whether electronic,

mechanical, photocopying, recording or otherwise without the prior permission of FTSE.

. FTSE Minimum Variance Indices

Peter Gunthorp

Managing Director, Research & Analytics Email: [email protected] Tel no: 0207 866 1962

(42)

Page 42

LONDON NEW YORK HONG KONG TOKYO BEIJING DUBAI MILAN MUMBAI PARIS SAN FRANCISCO SHANGHAI SYDNEY