correlation and dispersion in a portfolio context - cboe · why and how dispersion plays a...

For Financial Professionals. Not for Public Distribution. PROPRIETARY. Permission to reprint or distribute any content from this presentation requires the written approval of S&P Dow Jones Indices. 1

Why and how dispersion plays a fundamental role in portfolio, active and index returns.

CORRELATION AND DISPERSION IN A PORTFOLIO CONTEXT

For Financial Professionals. Not for Public Distribution. PROPRIETARY. Permission to reprint or distribute any content from this presentation requires the written approval of S&P Dow Jones Indices.

80%

85%

90%

95%

100%

105%

110%

115%

120%

125%

130%

28

-Se

p-0

1

02

-Oct

-01

06

-Oct

-01

10

-Oct

-01

14

-Oct

-01

18

-Oct

-01

22

-Oct

-01

26

-Oct

-01

30

-Oct

-01

Pri

ce R

etu

rn

Dow Jones Industrial Average -October 2001

2

Source: S&P Dow Jones Indices. Past performance is no guarantee of future results.

DJIA Individual Components

T

WHAT DOES DISPERSION LOOK LIKE?

MCD

INTC

MSFT

MSFT MCD

INTC

T

CAT

CAT

+3% DJIA

+3% DJIA

Dow Jones Industrial Average

Dispersion measures the spread of performances among components of an index (or portfolio)

80%

85%

90%

95%

100%

105%

110%

115%

120%

125%

130%

29

-No

v-1

3

03

-De

c-1

3

07

-De

c-1

3

11

-De

c-1

3

15

-De

c-1

3

19

-De

c-1

3

23

-De

c-1

3

27

-De

c-1

3

31

-De

c-1

3

... and December 2013


KEY CONCEPT: “SPREAD” OF RETURNS

80%

85%

90%

95%

100%

105%

110%

115%

120%

125%

130%

29

-No

v-1

3

03

-De

c-1

3

07

-De

c-1

3

11

-De

c-1

3

15

-De

c-1

3

19

-De

c-1

3

23

-De

c-1

3

27

-De

c-1

3

31

-De

c-1

3

December 2013

80%

85%

90%

95%

100%

105%

110%

115%

120%

125%

130%

28

-Se

p-

01

02

-Oct

-01

06

-Oct

-01

10

-Oct

-01

14

-Oct

-01

18

-Oct

-01

22

-Oct

-01

26

-Oct

-01

30

-Oct

-01

Pri

ce R

etu

rn

October 2001

-21% -15% -9% -3% 3% 9% 15% 21%

V

XOM

AXP

MMM

KO

HD

UNH

TRV

VZ

JNJ

-21% -15% -9% -3% 3% 9% 15% 21%

INTC

C

HPQ

AA

JPM

PG

XOM

CAT

MTLQQ

MRK



0% 6% 12% 18% 24% 30% 36% 42%

INTC

MSFT

HD

HPQ

JNJ

EK

JPM

KO

AXP

XOM

IBM

HON

MTLQQ

MCD

T

Difference from Index (%)

-21% -15% -9% -3% 3% 9% 15% 21%

INTC

MSFT

HD

HPQ

JNJ

EK

JPM

KO

AXP

XOM

IBM

HON

MTLQQ

MCD

T

Change (%)

HOW IS DISPERSION DEFINED?

4

Standard-deviation style calculation: “square-root of average of squared difference to mean”

It = 𝑤𝑖𝑅𝑖,𝑡𝑖

Weighted average return =It Payoff on straddles, struck at It

𝑅𝑖,𝑡 − 𝐼𝑡2 𝑅𝑖,𝑡

𝑤𝑖 𝑅𝑖,𝑡 − 𝐼𝑡2

𝑛

𝑖=1

Dispersion

= 8%


Example: October 2001, DJIA


DISPERSION - SUMMARY

5

The outperformance potential for active management

The magnitude of diversification benefit achieved

An instantaneous measure of correlation

A component of the returns from portfolio rebalancing

A tradable aspect of capital markets

Conceptually

Computationally

The statistical “spread” of returns among securities

= 𝑤𝑖 𝑅𝑖,𝑡 − 𝐼𝑡2

𝑛

𝑖=1

Practically


EXAMPLE: S&P 500® MONTHLY DISPERSION 1989-2014

6

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0%

5%

10%

15%

20%

25%

30%O

ct-

89

Oct-

90

Oct-

91

Oct-

92

Oct-

93

Oct-

94

Oct-

95

Oct-

96

Oct-

97

Oct-

98

Oct-

99

Oct-

00

Oct-

01

Oct-

02

Oct-

03

Oct-

04

Oct-

05

Oct-

06

Oct-

07

Oct-

08

Oct-

09

Oct-

10

Oct-

11

Oct-

12

Oct-

13

S&

P 5

00

Mo

nth

ly S

&P

500 D

isp

ers

ion

Dispersion

S&P 500®



0

15

30

45

60

75

0%

5%

10%

15%

20%

25%Jan

-90

Jan

-91

Jan

-92

Jan

-93

Jan

-94

Jan

-95

Jan-9

6

Jan

-97

Jan

-98

Jan

-99

Jan

-00

Jan

-01

Jan

-02

Jan

-03

Jan

-04

Jan

-05

Jan

-06

Jan

-07

Jan

-08

Jan

-09

Jan

-10

Jan

-11

Jan

-12

Jan-1

3

Jan

-14

VIX

Mo

nth

ly S

&P

500 D

isp

ers

ion

7

Dispersion

VIX®

DISPERSION IS DIFFERENT - BUT CORRELATED - TO VOLATILITY



Dispersion is similar to volatility in several respects:

Both measures of standard deviation in price changes, capturing the degree of movement within a market over a specified time period or periods

Volatile, and highly correlated to each other

Historically persistent in the short term

Historically mean-reverting in the long term

But with a few, potentially important differences

High volatility and lower dispersion: for example in the macro-led markets of August 2011

High dispersion and lower volatility: for example during the formation and collapse of the tech-bubble during 1998-2001

Volatility requires a time series for measurement and speaks to a single security or portfolio, whereas dispersion is a cross-sectional measure, over a single period, for multiple securities

(As we shall see) Dispersion is ultimately a particular combination of volatility and correlation

A FEW OBSERVATIONS FROM HISTORY


SECTION 2: APPLICATIONS OF DISPERSION

• Opportunity set for active management

• Measure of portfolio diversification

• Instantaneous approximation to correlation, completing an analytical ‘recipe’ for volatility

• Factor in determining the rebalancing ‘bonus’


THE OPPORTUNITY SET FOR ACTIVE RETURNS (1)

10

Dispersion is a measure of “idiosyncratic” risk that quantifies the impact of security selection

The phrase “stock-picker’s market” is frequently heard, typically without precise definition.

Low correlation is equated with the opportunities for active managers, but in our view incorrectly

• e.g. 2013-2014 developed equities: no correlation, yet indifferent alpha opportunities.

Return available from security selection and weighting is more naturally associated with dispersion

When dispersion is high, decisions have a greater impact

• Measure of importance e.g. country versus sector importance in international markets.

When dispersion is low, the stakes at the table are lower (operational costs / fees may not be similarly reduced)

c = -1.00

c = +1.00

Source: S&P Dow Jones Indices. See Edwards & Lazzara ; “Dispersion: Measuring Market Opportunity” (2013) for more details and additional references. Past performance is

no guarantee of future results.


EXHIBIT: U.S. EQUITY MANAGERS & DISPERSION

Source: S&P Dow Jones Indices’ SPIVA scorecards (“S&P Index Versus Active”). Data for 2007 are to March end; all other years are full calendar years. Charts are provided for

illustrative purposes. Past performance is no guarantee of future results.

Annual Interquartile Range of U.S. Large-Cap Active Funds vs. S&P 500 Average Monthly Dispersion

“Good” managers performed better in relative terms when dispersion was high

0%

2%

4%

6%

8%

10%

12%

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

Per

cen

t

Performance Spread: top quartile to bottom quartile funds S&P 500 average monthly dispersion


EXHIBIT: OUTPERFORMING FUND LIKELIHOOD AND DISPERSION

12

Percentage of Active Funds outperforming the market versus S&P 500 Average Monthly Dispersion (Selected years highlighted)

High (or low) dispersion did not seem to influence the probability of the average manager outperforming

0%

10%

20%

30%

40%

50%

60%

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

Per

cen

t

Percentage of managers outperforming the S&P 500 S&P 500 average monthly dispersion (previous scale)

Source: S&P Dow Jones Indices’ SPIVA scorecards (“S&P Index Versus Active”). Data for 2007 are to March end; all other years are full calendar years. Charts are provided for

illustrative purposes. Past performance is no guarantee of future results.


THE OPPORTUNITY SET FOR ACTIVE RETURNS (2)

13

Evidence suggests that opportunities might be presented subsequent to periods of high dispersion

Intuitive expectation that high dispersion creates arbitrage opportunities:

• In periods of large and widespread price dislocations (high dispersion), professional investors identify “mispricings”; and subsequently benefit at “return to normality” (lower dispersion).

Various studies have identified that subsequent to periods of high dispersion, certain common strategies

are more likely to outperform; similarly for certain hedge fund styles.

Stivers et al ; Cross-sectional Return Dispersion and the Payoffs of Momentum, Longer-run Contrarian, and Book-to-Market Strategies (2008)

• Value and contrarian strategies perform well subsequent to high dispersion periods, poorly subsequent to low dispersion periods.

• Momentum and growth strategies conversely.

Connors & Li ; Market Dispersion and the Profitability of Hedge Funds (2009)

• One of several studies identifying and positively correlating the excess performance achieved by hedge fund strategies coincident (and subsequent to) changes in dispersion regimes.


EXHIBIT: EQUAL-WEIGHT U.S. EQUITIES RELATIVE PERFORMANCE

Even equally-weighted indices showed an improved performance subsequent to periods extreme dispersion

S&P 500 Dispersion and outperformance of the S&P 500 Equal Weight Index vs S&P 500 (1990 – 2014)

-30%

-20%

-10%

0%

10%

20%

30%

40%

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

2013

0%

2%

4%

6%

8%

10%

12%

14%

16%

Eq

ual

Wei

gh

t O

utp

erfo

rman

ce o

f S

&P

500

Ave

rag

e la

st 6

mo

nts

S&

P50

0 d

isp

ersi

on

Equal Weight Outperformance (next 12 months)

S&P 500 Monthly Dispersion (previous 6 months)

Source: S&P Dow Jones Indices. Index performance shown is relative total return in USD. Past performance is no guarantee of future results.


0%

10%

20%

30%

40%

50%

Dec-9

6

Dec-9

7

Dec-9

8

Dec-9

9

Dec-0

0

De

c-0

1

Dec-0

2

Dec-0

3

Dec-0

4

De

c-0

5

Dec-0

6

Dec-0

7

Dec-0

8

Dec-0

9

Dec-1

0

Dec-1

1

Dec-1

2

Dec-1

3

DJIA volatility

Average Component Volatility

DISPERSION AND DIVERSIFICATION

15

Dispersion is naturally connected to the degree of “diversification” achieved by a portfolio

The dispersion calculation aggregates and averages all the absolute movements in securities that are cancelled out in the portfolio return: suggestive of a diversification measure.

In fact the relationship is empirically direct, once the single-period measure of dispersion is suitably averaged over time (to be compared to the multi-period measure of variance)

Diversification

benefit


0.0%

0.2%

0.4%

0.6%

0.8%

1.0%

1.2%

1.4%

Dec-9

6

Dec-9

7

Dec-9

8

Dec-9

9

Dec-0

0

Dec-0

1

Dec-0

2

Dec-0

3

Dec-0

4

Dec-0

5

Dec-0

6

Dec-0

7

Dec-0

8

Dec-0

9

Dec-1

0

Dec-1

1

Dec-1

2

Dec-1

3

Average Component Variance

𝒗𝟐 + 𝒅𝟐


0.00

0.20

0.40

0.60

0.80

1.00

Jan-

04

Jan-

05

Jan-

06

Jan-

07

Jan-

08

Jan-

09

Jan-

10

Jan-

11

Jan-

12

Jan-

13

Average Monthly S&P 500 Pairwise Correlation

DISPERSION, VOLATILITY AND CORRELATION

16

Pairwise they are related, as a triple they are strictly defined in combinations

𝑣2

𝑣2+𝑑2

v = portfolio volatility

F = (weighted) component volatility

c = (weighted) average correlation

d2 = average of period dispersion2

Familiar concept: average correlation is the proportion of total risk accounted for by portfolio risk, or approximately:

𝑐 ≈ 𝑣2 𝐹2

and since 𝐹2 ≈ 𝑣2 + 𝑑2, correlation is:

𝑣2

𝑣2+𝑑2

NOTE: 𝑣 and 𝑑 are simple to calculate with instantaneous interpretations in (e.g.) VIX and dispersion!

Source: S&P Dow Jones Indices. See Edwards & Lazzara ; “At the Intersection of Diversification, Volatility and Correlation” (2014) for more details and additional references.

Past performance is no guarantee of future results.

𝑐 ≈


0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Val

ue

of

Co

rrel

atio

n M

ult

iplie

r

Correlation

CONSEQUENCES OF THE DISPERSION RELATION

17

Nuanced perspectives on volatility are provided by the relationship to dispersion and correlation

The equation can be also be re-arranged with (market) volatility as the subject:

𝑣2 ≈ 𝑑2 × 𝑐1−𝑐

Conceptually: market volatility is driven by dispersion, amplified or diluted by correlations

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Co

rrel

atio

n

Dispersion

10% vol

20% vol

30% vol

40% vol

50% vol

60% vol

70% vol

80% vol

90% vol

100% vol

𝑐

1 − 𝑐

Source: S&P Dow Jones Indices. Formulae and charts represent models of securities behavior only, actual performance may differ significantly.


DISPERSION AND PORTFOLIO REBALANCING

18

The benefit (or detriment) to frequent portfolio balancing relates to long and short-term dispersion

Sources: S&P Dow Jones Indices ; Bernstein and Wilkinson, “Diversification, Rebalancing and the Geometric Mean Frontier” Research Manuscript (1997) ; Monnier and Rulik,

“Can The Rebalancing Bonus Enhance Beta Return?” Journal of Indices (2013). Formulae represent models of securities behavior only, actual performance may differ

significantly.

The effect on returns of portfolio rebalancing over multiple periods is a balance between:

The long-term benefit from diversification (recall the effect of volatility on geometric returns), which can be derived from the period dispersions.

The long-term cost of de-allocating from the most positive performer (in the long term, any un-rebalanced portfolio is dominated by the best-performing asset).

Formally, the return from rebalancing can be expressed as:

𝑹𝒆𝒕𝒖𝒓𝒏 𝒇𝒓𝒐𝒎 𝒓𝒆𝒃𝒂𝒍𝒂𝒏𝒄𝒊𝒏𝒈 ≈ 𝒅𝟐 − ∅

Where d2 = average of period dispersion2 and ∅ is a function of the spread of longer term returns.

In equal weight portfolios, the additional return from rebalancing is well approximated by full-period dispersion:

𝑬𝑸𝑾 𝑹𝒆𝒕𝒖𝒓𝒏 𝒇𝒓𝒐𝒎 𝒓𝒆𝒃𝒂𝒍𝒂𝒏𝒄𝒊𝒏𝒈 ≈ 𝒅𝟐 − (𝑵 − 𝟏)

𝟐𝒆𝟐

Where 𝒆 is the dispersion of average annual returns among components and 𝑵 is the number of periods.


CURRENT DISPERSION ENVIRONMENT (JULY 2014)

19

Currently in an environment of relatively low dispersion; higher (as usual) in EM and small caps

Source: S&P Dow Jones Indices as of July 2014. Past performance is no guarantee of future results. The Multi-Asset Portfolio comprises equal weights in each of: the S&P 500,

S&P Europe 350, S&P Emerging Market BMI, S&P GSCI®, S&P TOPIX 150, Barclays Aggregate U.S. Corporate High Yield, Barclays Aggregate U.S. Bond and S&P / Citigroup

International Treasury Bond Ex-US Indices. All returns are total returns in USD unhedged.

4.9%

6.3%7.4%

5.2%5.7%

8.2%

2.4%0%

2%

4%

6%

8%

10%

12%

14%

16%

S&P 500S&P MidCap

400S&P SmallCap

600S&P Europe

350

S&P DevelopedEx-U.S.

LargeMidCapS&P Emerging

Market BMI Multi-Asset

Mo

nth

ly D

isp

ersi

on

Quartile Range 90th Percentile Jul-14 Min


DISPERSION AND IDIOSYNCRATIC RISK

20

Can periods of high dispersion support the identification of bubbles?

-7%

-5%

-3%

-1%

1%

3%

5%

7%

9%

Jan

19

91

Oct

19

91

Jul 1

992

Ap

r 19

93

Jan

19

94

Oct

19

94

Jul 1

995

Ap

r 19

96

Jan

19

97

Oct

19

97

Jul 1

998

Ap

r 19

99

Jan

20

00

Oct

20

00

Jul 2

001

Ap

r 20

02

Jan

20

03

Oct

20

03

Jul 2

004

Ap

r 20

05

Jan

20

06

Oct

20

06

Jul 2

007

Ap

r 20

08

Jan

20

09

Oct

20

09

Jul 2

010

Ap

r 20

11

Jan

20

12

Oct

20

12

Jul 2

013

Excess Dispersion mean 1 std above mean 1 std below mean 2 std above mean 2 std below mean

Monthly Dispersion Relative to VIX: Jan 1991 - Jan 2014

tech 'bubble' end Aug 2000

Exce

ss

Dis

per

sio

n

market low end Sep 2002

Market peak end Oct 2007

market low end Feb 2009

equ

ity cau

tion

equ

ity co

nfid

ence

Source: S&P Dow Jones Indices, CBOE, U.K. National Employment Savings Trust and Birmingham University. Past performance is no guarantee of future results.

(With acknowledgements to Paul Cox of NEST) S&P 500 monthly dispersion strongly in excess of implied volatility (VIX) has historically pre-empted severe market stresses


PERFORMANCE DISCLOSURE

21

The S&P 500 Equal Weight Index (the “Index”) was launched on Jan. 9, 2003. All information presented prior to the launch date is back-tested. Back-tested performance is not

actual performance, but is hypothetical. The back-test calculations are based on the same methodology that was in effect when the index was officially launched. Complete index

methodology details are available at www.spdji.com. It is not possible to invest directly in an index.

S&P Dow Jones Indices defines various dates to assist our clients in providing transparency on their products. The First Value Date is the first day for which there is a calculated

value (either live or back-tested) for a given index. The Base Date is the date at which the Index is set at a fixed value for calculation purposes. The Launch Date designates the

date upon which the values of an index are first considered live: index values provided for any date or time period prior to the index’s Launch Date are considered back-tested. S&P

Dow Jones Indices defines the Launch Date as the date by which the values of an index are known to have been released to the public, for example via the company’s public

website or its datafeed to external parties. For Dow Jones-branded indicates introduced prior to May 31, 2013, the Launch Date (which prior to May 31, 2013, was termed “Date of

introduction”) is set at a date upon which no further changes were permitted to be made to the index methodology, but that may have been prior to the Index’s public release date.

Past performance of the Index is not an indication of future results. Prospective application of the methodology used to construct the Index may not result in performance

commensurate with the back-test returns shown. The back-test period does not necessarily correspond to the entire available history of the Index. Please refer to the methodology

paper for the Index, available at www.spdji.com for more details about the index, including the manner in which it is rebalanced, the timing of such rebalancing, criteria for additions

and deletions, as well as all index calculations.

Another limitation of using back-tested information is that the back-tested calculation is generally prepared with the benefit of hindsight. Back-tested information reflects the

application of the index methodology and selection of index constituents in hindsight. No hypothetical record can completely account for the impact of financial risk in actual trading.

For example, there are numerous factors related to the equities, fixed income, or commodities markets in general which cannot be, and have not been accounted for in the

preparation of the index information set forth, all of which can affect actual performance.

The Index returns shown do not represent the results of actual trading of investable assets/securities. S&P Dow Jones Indices LLC maintains the Index and calculates the Index

levels and performance shown or discussed, but does not manage actual assets. Index returns do not reflect payment of any sales charges or fees an investor may pay to

purchase the securities underlying the Index or investment funds that are intended to track the performance of the Index. The imposition of these fees and charges would cause

actual and back-tested performance of the securities/fund to be lower than the Index performance shown. As a simple example, if an index returned 10% on a US $100,000

investment for a 12-month period (or US $10,000) and an actual asset-based fee of 1.5% was imposed at the end of the period on the investment plus accrued interest (or US

$1,650), the net return would be 8.35% (or US $8,350) for the year. Over a three year period, an annual 1.5% fee taken at year end with an assumed 10% return per year would

result in a cumulative gross return of 33.10%, a total fee of US $5,375, and a cumulative net return of 27.2% (or US $27,200).


GENERAL DISCLAIMER

22

Copyright © 2014 by S&P Dow Jones Indices LLC, a part of McGraw Hill Financial. All rights reserved. S&P, S&P 500, S&P MidCap 400, S&P SmallCap 600, S&P GSCI, S&P Europe 350, S&P

Composite1500 and STANDARD & POOR’S are registered trademarks of Standard & Poor’s Financial Services LLC (“S&P”), a subsidiary of McGraw Hill Financial, Inc. Dow Jones is a registered

trademark of Dow Jones Trademark Holdings LLC (“Dow Jones”). Trademarks have been licensed to S&P Dow Jones Indices LLC. Redistribution, reproduction and/or photocopying in whole or in

part are prohibited without written permission. This document does not constitute an offer of services in jurisdictions where S&P Dow Jones Indices LLC, Dow Jones, S&P or their respective affiliates

(collectively “S&P Dow Jones Indices”) do not have the necessary licenses. All information provided by S&P Dow Jones Indices is impersonal and not tailored to the needs of any person, entity or

group of persons. S&P Dow Jones Indices receives compensation in connection with licensing its indices to third parties. Past performance of an index is not a guarantee of future results.

It is not possible to invest directly in an index. Exposure to an asset class represented by an index is available through investable instruments based on that index. S&P Dow Jones Indices does not

sponsor, endorse, sell, promote or manage any investment fund or other investment vehicle that is offered by third parties and that seeks to provide an investment return based on the performance of

any index. S&P Dow Jones Indices makes no assurance that investment products based on the index will accurately track index performance or provide positive investment returns. S&P Dow Jones

Indices LLC is not an investment advisor, and S&P Dow Jones Indices makes no representation regarding the advisability of investing in any such investment fund or other investment vehicle. A

decision to invest in any such investment fund or other investment vehicle should not be made in reliance on any of the statements set forth in this document. Prospective investors are advised to

make an investment in any such fund or other vehicle only after carefully considering the risks associated with investing in such funds, as detailed in an offering memorandum or similar document

that is prepared by or on behalf of the issuer of the investment fund or other vehicle. Inclusion of a security within an index is not a recommendation by S&P Dow Jones Indices to buy, sell, or hold

such security, nor is it considered to be investment advice. Closing prices for S&P US benchmark indices and Dow Jones US benchmark indices are calculated by S&P Dow Jones Indices based on

the closing price of the individual constituents of the index as set by their primary exchange. Closing prices are received by S&P Dow Jones Indices from one of its third party vendors and verified by

comparing them with prices from an alternative vendor. The vendors receive the closing price from the primary exchanges.

These materials have been prepared solely for informational purposes based upon information generally available to the public and from sources believed to be reliable. No content contained in

these materials (including index data, ratings, credit-related analyses and data, research, valuations, model, software or other application or output therefrom) or any part thereof (Content) may be

modified, reverse-engineered, reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of S&P Dow Jones Indices. The

Content shall not be used for any unlawful or unauthorized purposes. S&P Dow Jones Indices and its third-party data providers and licensors (collectively “S&P Dow Jones Indices Parties”) do not

guarantee the accuracy, completeness, timeliness or availability of the Content. S&P Dow Jones Indices Parties are not responsible for any errors or omissions, regardless of the cause, for the

results obtained from the use of the Content. THE CONTENT IS PROVIDED ON AN “AS IS” BASIS. S&P DOW JONES INDICES PARTIES DISCLAIM ANY AND ALL EXPRESS OR IMPLIED

WARRANTIES, INCLUDING, BUT NOT LIMITED TO, ANY WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE OR USE, FREEDOM FROM BUGS, SOFTWARE

ERRORS OR DEFECTS, THAT THE CONTENT’S FUNCTIONING WILL BE UNINTERRUPTED OR THAT THE CONTENT WILL OPERATE WITH ANY SOFTWARE OR HARDWARE

CONFIGURATION. In no event shall S&P Dow Jones Indices Parties be liable to any party for any direct, indirect, incidental, exemplary, compensatory, punitive, special or consequential damages,

costs, expenses, legal fees, or losses (including, without limitation, lost income or lost profits and opportunity costs) in connection with any use of the Content even if advised of the possibility of such

damages.

S&P Dow Jones Indices keeps certain activities of its business units separate from each other in order to preserve the independence and objectivity of their respective activities. As a result, certain

business units of S&P Dow Jones Indices may have information that is not available to other business units. S&P Dow Jones Indices has established policies and procedures to maintain the

confidentiality of certain non-public information received in connection with each analytical process.

In addition, S&P Dow Jones Indices provides a wide range of services to, or relating to, many organizations, including issuers of securities, investment advisers, broker-dealers, investment banks,

other financial institutions and financial intermediaries, and accordingly may receive fees or other economic benefits from those organizations, including organizations whose securities or services

they may recommend, rate, include in model portfolios, evaluate or otherwise address.

CBOE, CBOE Volatility Index and VIX are registered trademarks of Chicago Board Options Exchange, Incorporated (CBOE). CBOE has granted S&P Dow Jones Indices a license to use the VIX

methodology to create a variety of volatility indices.


THANK YOU

Tim Edwards

[email protected]

mailto:[email protected]

correlation and dispersion in a portfolio context - cboe · why and how dispersion plays a...

Documents