Current Global Equity Market Dynamics and the Use …newyork.qwafafew.org/wp-content/uploads/sites/4/2017/01/2013... · Current Global Equity Market Dynamics and the Use of Factor

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Current Global Equity Market Dynamics and the Use of Factor Portfolios for Hedging Effectiveness Déborah Berebichez, Ph.D.

February 2013

msci.com ©2013. All rights reserved. 2 msci.com

Outline

I. Overview of Barra’s Global Equity Model

II. Is Buying an Index Really a Country bet?

III. Greece Case Study

IV. Hedging out Undesired Exposures with a Factor-Mimicking Portfolio

V. Rebalancing Frequency


I. Overview of our Global Equity Model

msci.com ©2013. All rights reserved.

Barra Global Equity Model (GEM3) – Characteristics

Barra Model Factors represent important drivers of both risk and return in the global equity markets

Common Factors are grouped into World, Country, Industry, Style, and Currency components

Barra Global Equity Model (GEM3) Long & Short Horizons

Coverage of 77 Country Factors and 66 Currencies

74,000+ Assets

Daily Model Updates (Exposures, Covariance Matrix & Specific Risk)

Optimization Bias Adjustment improves risk forecasts for optimized portfolios

Volatility Regime Adjustment calibrates factor volatilities to current levels

Daily model history back to 1997

34 Industry GICS-based and 11 Style Factors

4


GEM3 Regression Methodology

Every stock has unit exposure to World factor

Exposures to countries/industries given by (0,1)

Country and industry returns both net of World factor

Style exposures cap-weighted mean zero

Apply constraints to eliminate two-fold collinearity with World

Regression weighting: square-root of market-cap

Estimation universe: MSCI ACWI IMI

n

s

sns

i

ini

c

cncwn ufXfXfXfr

GEM3 treats country and industry factors symmetrically:

5


Performance of Country Factors

USA has outperformed over sample period

Japan has underperformed, with higher volatility

6

Year

1997 1999 2001 2003 2005 2007 2009 2011

Cu

mu

lati

ve R

etu

rn (

Per

cen

t)

-40

-20

0

20

40 USA

Japan


Performance of Industry Factors

Banking factor fared poorly during Internet Bubble and since 2007

Airlines performed poorly from 1998-2008

7

Year

1997 1999 2001 2003 2005 2007 2009 2011

Cu

mu

lati

ve R

etu

rn (

Per

cen

t)

-80

-60

-40

-20

0

20

40

Airlines

Banks


11 Style Factors in GEM3

8

Beta

Momentum

Size

Earnings Yield

Residual Volatility

Growth

Dividend Yield

Book to Price

Leverage

Liquidity

Non-linear Size


Descriptors of Residual Volatility Factor Residual Volatility

9


Descriptor of Momentum Factor Momentum

10


January 2013 Global Equity Market Watch – Highlights

The World factor continued its positive performance with a 5% percent return in January 2013. This marks eight months of non-negative monthly performance for the World factor

The Value Factor posted a 1.1 percent return in January 2013. This is the highest return among the style factors, both by the absolute value and by z-score

The Japan factor remained the top contributor to cross-sectional volatility for the second month in a row

The Korea and Malaysia factors are among the bottom performers by z-score, and top contributors to cross-sectional volatility

11

msci.com ©2013. All rights reserved. 12

Mean trailing 12-month realized volatilities of country, industry (cap-weighted) and style factors (equal-weighted)

Year

1997 1999 2001 2003 2005 2007 2009 2011 2013

Me

an

Tra

ilin

g 1

2m

Vo

latilit

y

0

5

10

15

20

0

5

10

15

20

Countries

Industries

Styles

Country factors dominated in late 1990s Industries dominated during wake of Internet Bubble

Systemic Financial Crisis


II. Is Buying an Index Really a Country Bet?


Is Buying an Index Really a Country Bet?

14

When you buy/sell an Index such as MSCI Greece IMI to gain (long or short) exposure to the country Greece, you are not only getting exposure to Greece but to many other style and industry factors

You are getting more (or less) than just the country. The returns (or lack thereof) depend on the exposure to multiple underlying factors

A real country bet like a pure Greece exposure can be achieved in two ways:

Constructing a factor-mimicking Greece portfolio (very high exposure to Greece and very low exposure to every other country, style, industry and the world factor)

Or by hedging out the underlying exposure to all other undesired factors


Malaysia Cumulative Returns 12 Months February 2013

MSCI Malaysia IMI Daily Cumulative Returns (blue) (-14%)

Pure Malaysia Market Returns (red) (0.27%)

15

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

20

12

/02

/20

20

12

/02

/29

20

12

/03

/09

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/26

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/12

/27

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13

/01

/07

20

13

/01

/16

20

13

/01

/25

20

13

/02

/05

20

13

/02

/14

Pure Malaysia Mkt Factor

MSCI Malaysia IMI Index


III. Greece Case Study


Greece Cumulative Returns 12 Months February 2013

MSCI Greece IMI Cumulative Returns (blue) (8.5%)

Pure Greece Country Returns (red) (39%)

17

-60.00%

-40.00%

-20.00%

0.00%

20.00%

40.00%

60.00%

20

12

/02

/20

20

12

/02

/29

20

12

/03

/09

20

12

/03

/20

20

12

/03

/29

20

12

/04

/09

20

12

/04

/18

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12

/04

/27

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/05

/08

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/05

/17

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12

/05

/28

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12

/06

/06

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/06

/15

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/06

/26

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12

/07

/05

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12

/07

/16

20

12

/07

/25

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12

/08

/03

20

12

/08

/14

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/08

/23

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/09

/03

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/09

/12

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12

/09

/21

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/10

/02

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12

/10

/11

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/10

/22

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/10

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/11

/09

20

12

/11

/20

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/11

/29

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/12

/10

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/12

/19

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/12

/28

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13

/01

/08

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13

/01

/17

20

13

/01

/28

20

13

/02

/06

20

13

/02

/15

MSCI Greece IMI -Cumulative Returns Pure Greece -Cumulative Returns


MSCI Greece IMI Return Attribution

18

Country is a large positive driver of returns (34.43%)

Risk Styles are a large detractor from returns (-23.88%)

The most negative influence comes from the Residual Volatility factor (-16.39%)

Followed by the Momentum factor (-10.22%)

Large negative specific return (-16.62%) not typical of an Index

Source of Return Contribution to Return

Total Managed 8.48%

Residual 6.16%

Common Factor 22.78%

World 11.88%

Industry 0.35%

Country 34.43%

Risk Indices -23.88%

Beta 2.56%

Book-to-Price 0.04%

Dividend Yield 0.01%

Earnings Yield -0.17%

Growth -0.09%

Leverage 0.13%

Liquidity -0.08%

Momentum -10.22%

Non-Linear Size 0.21%

Residual Volatility -16.39%

Size 0.10%

Specific -16.62%

Currency 2.23%


MSCI Greece IMI Return Attribution

19


MSCI Greece IMI Residual Volatility Contribution to return

Exposure of the Index to Residual Volatility

Cumulative Residual Volatility Returns (blue)

Contribution of Residual Volatility to the Index Returns (-16.39%)

20


MSCI Greece IMI Momentum Contribution

Exposure of the Index to Momentum

Cumulative Momentum Returns (blue)

Contribution of Momentum to the Index Returns (-10.22%)

21


IV. Hedging out Undesired Exposures with a Factor-Mimicking Portfolio


Characteristics of Factor Mimicking Portfolios

23

A pure factor portfolio exactly replicates the payoffs to the factor

A factor-mimicking portfolio strikes a balance between factor tracking and index investability and replicability

Achieves a high level of exposure to a particular factor (the “Target Factor”) and very low exposure to all other styles, industries, countries and the world factor, while minimizing specific risk

Constraints can be number of constituents, monthly turnover, trade limit, shorting cost, etc

Applications:

PASSIVE: To capture alpha as the basis for ETFs for style investing such as value, growth, large-cap, etc

ACTIVE: To hedge out undesired risk


Constructing a Factor-Mimicking Portfolio

24

Barra Aegis Optimizer Settings

Benchmark: Pure Factor Asset

Universe: MSCI ACWI IMI

Trading Constraint: Maintain Exposures Close to the Benchmark

Style Constraints:

Risk Style Exposures = All Zero except for a Target Exposure of 1 to the desired Style

Country Equity Exposures = All Zero Country Equity Exposures

Industries Exposures = All Zero Industry Exposures

World Equity Exposure = Zero World Equity Exposure


Characteristics of Residual Volatility Portfolio

25


Risk Style Exposures for Residual Volatility Portfolio

26

Insignificant Exposures to countries, sectors and the World Equity Factor


V. Rebalancing Frequency

Change in Quality of the Factor-Mimicking Portfolios


Exposure of Initial Portfolio to Residual Volatility Over Time

28

One Year Degradation (no rebalancing)

With monthly rebalancing

Factor mimicking portfolios get degraded over time. This determines the frequency of rebalancing


Exposure of Initial Portfolio to Momentum Over Time

29

One Year Degradation (no rebalancing)

With monthly rebalancing

Factor mimicking portfolios get degraded over time. This determines the frequency of rebalancing


MSCI 24 Hour Global Client Service

Asia Pacific

China North 10800.852.1032 (toll free)

China South 10800.152.1032 (toll free)

Hong Kong +852.2844.9333

Seoul +798.8521.3392 (toll free)

Singapore 800.852.3749 (toll free)

Sydney +61.2.9033.9333

Tokyo +81.3.5226.8222

Europe, Middle East & Africa

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Geneva +41.22.817.9777

London +44.20.7618.2222

Milan +39.02.5849.0415

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Americas 1.888.588.4567 (toll free)

Atlanta +1.404.551.3212

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A Brief Digression: Risk Attribution

Identifies three drivers of time series volatility

Risk contributions are intuitive and fully additive

Aligns risk attribution model with investment process

t m mt

m

R x g Return Attribution, Period t

mx Source Exposure;

,m m m

m

R x g g R Risk Attribution x-sigma-rho formula

mtg Source Return

33


Exact CSV Decomposition

Identifies three drivers of cross-sectional volatility

Volatility contributions are intuitive and fully additive

CSV can be attributed to individual factors!

n n nr u Return Decomposition (factor vs specific)

Explained CS Volatility x-sigma-rho formula

( ) ,k k k

k

f X X

n k nk

k

f X Linear Factor Structure

34


Approximate CSV Decomposition

Collinearity among GEM2 factors is typically small

Reasonable and useful approximation:

Contribution to explained CSV is roughly proportional to the squared factor return and the variance of factor exposures

2

2( )k

k

k

Xf

No-collinearity Approximation

35


Style Factor Selection

Good style factors should:

Significantly increase explanatory power of model

Have high statistical significance

Be stable across time

Not be excessively collinear with other factors

Be intuitive and consistent with investors’ views

Stability Measure:

Collinearity Measure:

1corr ,t t t

k k kX X

2

1+

1nk nl l nk k

l k k

X X b VIFR

Variance Inflation Factor

Factor Stability Coefficient

36


Contribution of Style Factors to Cross-Sectional Volatility

Beta dominated in the aftermath of the Internet bubble

Momentum dominated in late 1990s and in 2009

40

Year

1997 1999 2001 2003 2005 2007 2009 2011

Mon

thly

RM

S Co

ntri

butio

n (%

)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Momentum

Beta


Model Highlights and Overview

Methodology Details

Factor Structure

Explanatory Power

Optimization Bias Adjustment

Volatility Regime Adjustment

New Specific Risk Model

Additional Empirical Results

Summary

Outline

41


Full daily updates of all components of the model

Extended coverage to 22 frontier markets

Enhanced style factors

Methodology Advances:

An innovative Optimization Bias Adjustment methodology designed to provide improved risk forecasts for optimized portfolios by reducing the effects of sampling error

Volatility Regime Adjustment designed to calibrate volatility forecasts to current levels

A new specific risk model based on daily asset-level specific returns with Bayesian adjustment designed to reduce biases due to sampling error

Improved risk forecasts

Model Highlights

42


GEM3 Regression Methodology: Constraints

Cap-weighted country/industry factor returns sum to zero:

i

ii

c

cc fwfw 0;0 Constraints

n

s

sns

i

ini

c

cncwn ufXfXfXfr

n

nknk rf

gives the weight of stock n in pure factor portfolio k

GEM3 Regression:

Factor returns

Interpret fw as the cap-weighted return of the world portfolio

kn

43


Style Factor Selection

Good style factors should:

Significantly increase explanatory power of model

Have high statistical significance

Be stable across time

Not be excessively collinear with other factors

Be intuitive and consistent with investors’ views

Stability Measure:

Collinearity Measure:

1corr ,t t t

k k kX X

2

1+

1nk nl l nk k

l k k

X X b VIFR

Variance Inflation Factor

Factor Stability Coefficient

44


Korea Cumulative Returns 12 Months February 2013

MSCI Korea Daily Cumulative Returns (blue) (1.27%)

Pure Korea Market Returns (red) (-9%)

45

-20.00%

-15.00%

-10.00%

-5.00%

0.00%

5.00%

10.00%

20

12

/02

/20

20

12

/03

/01

20

12

/03

/13

20

12

/03

/23

20

12

/04

/04

20

12

/04

/16

20

12

/04

/26

20

12

/05

/08

20

12

/05

/18

20

12

/05

/30

20

12

/06

/11

20

12

/06

/21

20

12

/07

/02

20

12

/07

/12

20

12

/07

/24

20

12

/08

/03

20

12

/08

/15

20

12

/08

/27

20

12

/09

/06

20

12

/09

/18

20

12

/09

/28

20

12

/10

/10

20

12

/10

/22

20

12

/11

/01

20

12

/11

/13

20

12

/11

/23

20

12

/12

/05

20

12

/12

/17

20

12

/12

/27

20

13

/01

/08

20

13

/01

/18

20

13

/01

/30

20

13

/02

/11

MSCI Korea Daily Returns

Korea Mkt Factor


Optimization Bias Adjustment


Initial Factor Covariance Matrix

Use daily factor returns to estimate factor covariance matrix (FCM)

Use shorter half-life to estimate volatilities (responsiveness)

Use longer half-life for correlations (conditioning)

Account for serial correlations and asynchronicity using the Newey-West method

Factor Newey-West Factor Newey-West Factor

Volatility Volatility Correlation Correlation CSV

Model Half-Life Lags Half-Life Lags Half-Life

GEM3S 84 10 504 3 42

GEM3L 252 10 504 3 168

S-Model designed for most accurate forecasts at one-month horizon

L-Model designed for greater stability in risk forecasts (less responsive)

47


Eigenfactors and Optimization Bias

Traditional risk models tend to underpredict the risk of optimized portfolios

This bias is related to estimation error in the covariance matrix

Eigenfactors represent uncorrelated linear combinations of pure factors

Eigenfactors solve certain classes of minimum variance optimizations

Eigenfactors reliably capture systematic biases in the sample factor covariance matrix (FCM)

The biases can be demonstrated and estimated by simulation

Removing the biases of the eigenfactors is effective at removing the biases of optimized portfolios

Jose Menchero, DJ Orr, and Jun Wang. “Eigen-Adjusted Covariance Matrices,” MSCI Research Insight, May 2011

48


Assume that the sample FCM F0 denotes the “true” FCM

Simulate a set of factor returns fn from F0 (e.g., Cholesky approach)

Compute simulated FCM Fn using same estimator as used for F0

Diagonalize Fn to obtain simulated eigenfactor volatilities

Use F0 to compute the “true” volatilities of simulated eigenfactors

Compute the average bias of simulated eigenfactors by Monte Carlo simulation

Assume F0 suffers from the same biases as the simulated FCM and de-bias the eigenvariances

Transform adjusted FCM back to the original pure basis

Optimization Bias Adjustment Methodology

49


Volatility Regime Adjustment for Factors


Construct factor covariance matrix F using “standard” time-series techniques (e.g., EWMA with serial correlation adjustments)

Use cross-sectional observations (bias statistics) to calibrate factor volatilities to current levels

Volatility Regime Adjustment for Factor Covariance Matrix

k

2

k F k F F FVolatility Regime Adjusted Factor Covariance Matrix

F Factor Volatility Multiplier

2

2 1 ktt

k kt

fB

K

2 2

F t t

t

B

Cross-Sectional Bias Statistic (squared)

(EWMA)

51


Volatility Regime Adjustments for Factor Covariance Matrix

Cross-sectional observations provide an “instantaneous” measure of factor volatility levels

During stable periods, Volatility Regime Adjustment tends to be very small

Adjustments are rapid and intuitive following market shocks

Volatility Regime Adjustment helps “when needed most”

(Factor CSV)

Year

1995 1997 1999 2001 2003 2005 2007 2009 2011

Fact

or

Vo

lati

lity

Mu

ltip

lier

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Fact

or

CSV

(p

erce

nt

dai

ly)

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8FactorVolatilityMultiplier

FactorCSV

Industry and Style Factors

21F

t kt

k

CSV fK

52


Improvement with Volatility Regime Adjustment (Factors)

With Volatility Regime Adjustment, most months the mean bias statistics are closer to the ideal value of 1

Volatility Regime Adjustment reduces the underforecasting bias during crises and the overforecasting bias following crises

Plot mean bias statistics (rolling 12m) of all factors, with and without Volatility Regime Adjustment

Year

1998 2000 2002 2004 2006 2008 2010 2012

Mea

n B

ias

Stat

isti

c

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

With Volatility Regime Adjustment

Unadjusted

Volatility Regime Adjustment (GEM3S)

53

Documents

Current Global Equity Market Dynamics and the Use …newyork.qwafafew.org/wp-content/uploads/sites/4/2017/01/2013... · Current Global Equity Market Dynamics and the Use of Factor