Correlation, Correlation everywhere, but not a drop to sell…

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EQUITY RESEARCH

Barclays Capital does and seeks to do business with companies covered in its research reports. As a result,investors should be aware that the firm may have a conflict of interest that could affect the objectivity ofthis report.

Investors should consider this report as only a single factor in making their investment decision.

PLEASE SEE ANALYST(S) CERTIFICATION(S) AND IMPORTANT DISCLOSURES BEGINNING ON PAGE 11

Equity Linked Strategies | U.S. Derivatives Strategy | July 26, 20

INDEX VOLATILITY WEEKLY

Correlation, Correlation everywhere, butnot a drop to sell

Maneesh Deshpande

+1 212 526 2953

[email protected]

BCI, New York

Rohit Bhatia

+1 212 526 0367

[email protected]

BCI, New York

Link to US VolCenter

Vol Center is a premier Equity Derivativesapplication providing Market Data, AnalyMarket Insight and Research

Volatility View: VIX Grinds Lower

VIX continues to trend lower and is now trading at its cheapest since the first week

of May 2010. VIX has historically been the best predictor of where shorter dated VIX

futures settle. There is enough macro uncertainty to keep a floor on how low

implied volatility can go and we find buying VIX Sep10 22.5-20 1x2 put spreads for

~$0.25 an attractive trade.

XLB (VolCenter Link) is trading cheap relative to its realized volatility and SPX and

appears to be the most attractive volatility buy amongst sector ETFs, in our view.

Gold (VolCenter Link) is trading with cheap volatility and rich skew and investors

who believe there will be renewed bearish sentiments regarding Europe sovereign

debt can buy GLD OTM calls

GDX (VolCenter Link) is trading cheap relative to GLD and SPX implied volatility and

GDX options are a good buy to take a delta view or volatility view in the case of

hedged options.

Correlation, Correlation everywhere, but not a drop to sell

Equity correlation is close or higher than its high levels scaled during the credit

crisis. This has profound implications even for non-derivatives investors in that it

indicates that stock-picking skills are less useful in the current environment.

While much of the variation in equity correlation is driven by equity volatility, from a

long term perspective it appears to have had a secular increase in value.

Since 2005, equity correlation has had a close relationship with the increased ETF

volumes relative to the volumes in the underlying stocks.

Option implied correlation, which has traditionally traded at a premium to realized,

is currently trading at a discount which would indicate that the option market is

loathe to believe that the current high correlation is likely to persist. However, the

fact that long dated implied correlation is also equally high and almost equal to its

short dated version appears to provide a conflicting signal.
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Barclays Capital | U.S. Derivatives Strategy: Index Volatility Weekly

July 26, 2010 2

VOLATILITY VIEW

VIX Grinds Lower

VIX continues to trend lower and is now trading at its cheapest since the first week of May

2010. In our previous Index Volatility Weekly, we had commented about how the currentsteep upward sloping term structure of VIX futures (Figure 1

Figure 1:VIX Futures term structure remains steep

) makes selling VXX and buying

VXZ an attractive trade. On a similar theme, VIX has historically been the best predictor of

where shorter dated VIX futures settle, which makes buying VIX puts an attractive trade in

such environments. VIX option implied volatility has moderated from triple digit levels in

May but is still trading close to 80%. While VIX has shown some sharp downside moves

over the past month, we feel VIX will struggle to go too much below the 20 handle at least

over the next few months. There is enough macro uncertainty to keep a floor on how low

implied volatility can go and we find buying VIX Sep10 22.5-20 1x2 put spreads an

attractive trade. The spread costs ~$0.25 and the trade makes money if VIX settles in the

range 22.25-17.75 as of Sep 15, 2010.

22

24

26

28

30

32

34

VIX Aug10 Sep10 Oct10 Nov10 Dec10 Jan11 Feb11 Mar11

VIX Futures

Source: Barclays Capital, OptionMetrics, Bloomberg

Basic Materials appears to be the Cheapest Sector to Buy Volatility

Implied volatility spiked much more than the corresponding realized volatility in May, and

for most of May and June 2010, implied volati lity for most indices and ETFs was trading at a

premium to realized volatility. With the moderation in implied volatility, the situation has

changed, and many sector implied volatilities are now trading at a discount to their realized

volatility. Energy and Health care are the only two sectors where 3-month implied volatility

is at a premium to realized volatility, which is not surprising considering the continuingcatalysts for these sectors.

In our view, comparison of sector implied volatilities with SPX implied volatility can give a

better idea of the relative cheapness of sector implied volatilities in the current environment.

As shown in Figure 2, XLB implied volatility looks cheap relative to both its trailing realized

volatility and SPX implied volatility. In Figure 3 we show the spread of XLB 3-month implied

volatility relative to SPX implied volatility going back a few years. As we can see, the

spreading is trading close to the lowest it has ever traded.
http://www.google.com/http://www.google.com/


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July 26, 2010 3

Investors looking for long volatility exposure can buy XLB straddles. With XLB skew trading

the richest amongst sectors (relative to their history), XLB Sep10 27-30 put spread for $0.45

is a cheap hedge to protect against a pullback in equity markets.

Figure 2: XLB Implied volatility appears cheap relative to its

realized volatility as well as SPX implied volatility

Figure 3: XLB SPX 3-Month implied volatility spread has

cheapened recently

Ticker

3 Month

Implied

Vol

1 Month

Realized

Vol

3 Month

Realized

Vol

Skew

percentile

(2Y

history)

3M Implied vs

AdjRealized

Spread :

Percentile 2Y

3M Implied

vs SPX

Spread :

Percentile

2Y

SPX 23% 24% 27% 92% 4% 50%

XLB 29% 32% 34% 99% 1% 6%

XLE 27% 26% 33% 92% 8% 1%

XLF 31% 33% 36% 85% 16% 16%

XLI 27% 29% 33% 84% 1% 55%

XLK 24% 26% 27% 93% 2% 59%

XLP 17% 16% 18% 87% 1% 70%

XLU 20% 19% 22% 92% 1% 37%

XLV 21% 15% 19% 86% 12% 85%

XLY 27% 30% 31% 88% 1% 27%

3%

5%

7%

9%

11%

13%

15%

17%

19%

21%

Jan-08 Jun-08 Dec-08 Jun-09 Nov-09 May-10

XLB - SPX 3 Month Implied Volatil ity

Source: Barclays Capital, OptionMetrics Source: Barclays Capital, OptionMetrics

Volatility Trades in the Gold Space

Gold has continued to be negatively correlated to movements in EURO and has lost 6% over

the past month as Euro rebounded from trading below1.2 to almost touch 1.3. Gold skew1

has been richening for a while now and currently trades at its richest ever since the launch

of options on GLD (Figure 4). GLD implied volatility is trading in line with its realized

volatility, while historically it has traded at a significant premium to its realized volatility

(Figure 5). Investors who believe that the there will be renewed bearish sentiments

regarding Europe sovereign debt can buy GLD OTM calls which look cheap due to the rich

skew and the cheap implied volatility. We recommend buying GLD Oct10 120 call for $2.45.

The spread can be made cheaper by selling $108 put to go short GLD Oct10 108 120 riskreversal for a cost of $0.9.

1 Skew is defined as the difference between the implied volatility of 25 delta put option and 25 delta call option dividedby 50 delta implied vol


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July 26, 2010 4

Figure 4: GLD skew is trading at its richest ever Figure 5: While GLD implied volatility is at a lower premium

to realized volatility compared to history

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

Aug-08 Feb-09 Aug-09 Feb-10

GLD 3 Month Skew

10%

15%

20%

25%

30%

35%

40%

45%

50%

55%

6/10/08 12/10/08 6/10/09 12/10/09 6/10/10

3 Month GLD Implied Volatility

3 Month GLD Realized Volatility

Source: Barclays Capital, OptionMetrics Source: Barclays Capital, OptionMetrics

Implied volatility of GDX, which is an ETF tracking gold miner stocks has historically had a

close relationship with implied volatility of gold options and implied volatility of SPX options.

GDX options have been cheapening relative to gold options and SPX options and currently

trade close to 2 standard deviations cheap over a 1-year history as shown in . They

also have a rich skew similar to gold options. While not as direct a play as gold on

continuing sovereign debt difficulties in Europe since it is also affected by equity markets,

OTM call options look cheap and can be used to either take a directional view or delta

hedged to take a volatility view.

Figure 6

Figure 6: GDX implied volatility is trading cheap relative to SPX and Gold

-10

-8

-6

-4

-2

0

2

4

6

8

1012

Jul-09 Sep-09 Oct-09 Dec-09 Jan-10 Mar-10 Apr-10 May-10 Jul-10

GDX 3M Vol ~ SPX 3M Volatilit y + GLD 3M Vol Residual (Volatil ity Points)



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July 26, 2010 5

SPOTLIGHT

Correlation, Correlation everywhere, but not a drop to sell

One of the striking features of the current equity derivatives landscape is the high value of

realized and implied correlations. Indeed, while equity volatility is nowhere close to its highsset at the peak of the credit crises, correlation is close or higher than its high levels scaled

during that period. This obviously has profound implications even for non-derivatives

investors in that it indicates that stock-picking skills are less useful in the current

environment.

In this section, we take a close look at this phenomenon. We show that while much of the

variation in equity correlation is driven by equity volatility, from a long-term perspective it

appears to have had a secular increase in value. We hypothesize that this is perhaps driven

by the corresponding increase in popularity of index funds and ETFs. In order to quantify

this we construct a new metric to measure the excess volume in ETFs. We call this the

normalized ETF volume and it is simply the ratio of the total value traded in an ETF over a

period of time and the value traded in each of its constituent stocks. Our calculations showthat while this measure increased steadily until 2005, after that it has moved in tandem with

equity correlation.

We next try to glean some insight from the option market. Option implied correlation, which

has traditionally traded at a premium to realized, is currently trading at a discount which

would indicate that the option market is loathe to believe that the current high correlation is

likely to persist. However, the fact that long dated implied correlation is also equally high

and almost equal to its short dated version appears to provide a conflicting signal.

A (very, very) long-term perspective

In this section, we take a long-term perspective of stock correlation using proprietary dataprovided by Barclays Quantitative Portfolio Strategy team (U.S. Equity Quantitative

Strategies: Market Commentary & Portfolio Rebalance). Obviously, the correlation between

different stocks is not equal and hence several different ways of defining the average

stock correlation are possible. In Appendix A, we detail the standard definition of stock

correlation used in the equity derivatives market. Figure 7 plots the realized correlation for

Russell 1000 index constituents and compares it to monthly SPX realized volatility. Note

that these calculations are completely based on stock returns and hence the term realized.

Several interesting conclusions can be drawn from this graph:

In general the stock correlation is highly correlated (pun not intended) with stock

volatility. This makes sense intuitively since a high volatility environment is by and large

also a top-down macro (as opposed to bottoms-up fundamentals) driven environment.

Indeed a formal regression (in log space) results in an r-square of ~56%

However, this relationship does not always hold. A case in point is the technology

bubble period (1998 20002) when volatility rose but correlation stayed low. This is of

course because the overall volatility was concentrated in technology stocks whose

movement to a large extent was decoupled from other sectors.
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July 26, 2010 6

Figure 7: Stock correlation and volatility: A long-term perspective

0%

10%

20%

30%

40%

50%

60%

70%

Jul-50 Jul-55 Jul-60 Jul-65 Jul-70 Jul-75 Jul-80 Jul-85 Jul-90 Jul-95 Jul-00 Jul-05 Jul-10

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

R1000 Monthly Realized Corr Log SPX Monthly Realized Vol (RHS)

Source: Barclays Capital Quantitative Portfolio Strategy, Bloomberg

After the bursting of the tech-bubble and during the telecom subsequent recession,

correlation again rose and then dropped again during the rally during 2003-2007. Note

that while equity volatility dropped to the same levels as during the early 90s,

correlation did not and appears to have been reset to a new level. As we will discuss in

more detail below, in our opinion this is driven by the increasing popularity of passive

index indexing and (broad market) ETFs.

During the credit crises, correlation (along with volatility) spiked to levels not seen

during over the past decades.

During the subsequent rally in 2009, it dropped back but once again not to the pre-

crises levels.

With the onset of the European debt crises, correlation has spiked again but this time to

levels even higher than during the credit crises. This is also in the context that volatility

did not reach the levels seen during the crises.

The picture that thus emerges from the above analysis is that of a steadily ratchet up of

equity correlation which is not fully explained by a concurrent increase in equity volatility.

An important structural shift in the equity markets over the past few decades has been the

advent of index funds as an alternative to actively managed mandates Figure 8. The

remarkable rise in (broad market based) ETFs over the past decade is of course another

manifestation of the same phenomena. Since the dominance of this kind of index-based

component in the equity fund flows should logically lead to an increase in equity correlation,it is tempting to theorize that the secular shift in equity correlation documented above is

driven by this effect.


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July 26, 2010 7

Figure 8: Assets under management indexed to S&P 500

0

200

400

600

800

1000

1200

1400

1600

1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009

S&P 500 Indexed Assets ($Bn)

Source: Standard & Poors

Given the paucity of data around high frequency equity index fund flows, we choose to rely

on ETF traded volumes as a proxy. We are of course not concerned with the normal ebbsand flows in traded volumes. In order to capture the excess ETF volume, we calculate the

ratio of the value traded in the SPY ETF relative to the value traded in all the constituents of

the SPX index. To the extent that investors are more inclined to trade the market as a whole,

this measure of normalised volume should be higher. As shown in Figure 9

Figure 9: SPX Realized Correlation in recent times has been tightly linked to the volume

trade in SPY relative to SPX constituents

, this metric

steadily increased since 1998 as SPY volume steadily increased. However, since 2005 its

variation appears to be very tightly linked to equity correlation.

0%

10%

20%

30%

40%

50%

60%

70%

80%

April-98 April-00 April-02 April-04 April-06 April-08 April-10

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

SPX 3 Month Realized Correlation (LHS) Normalized SPY Volume (RHS)

Source: Barclays Capital, OptionMetrics, Bloomberg.

Mixed signals from Option markets

As discussed in Appendix A, one can use the same formula used to calculate realized

correlation to back out the correlation assumption imbedded in option prices (the so called

implied correlation). In fact, by using option volatilities for different expirations one can

calculate an implied correlation for different maturities to estimate the option markets

opinion on correlation over different future time horizons.


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July 26, 2010 8

In Figure 10

Figure 10: Implied Correlation trades at premium to Realized

, we chart the trailing 3M realized correlations and compare it to the 3M and

12M implied correlations.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Ja n-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10

Realized Corr 3M Implied Corr 3M Implied Corr 12M


While, implied correlations trend together with realized correlations, it clear that on average,

implied correlations are higher than realized correlations. During crises periods when

realized correlation spikes, while implied correlation does increase it does not do so to the

same extent since the option market does not expect the correlation to stay high for

extended period of time (Figure 11

Figure 11: Implied Realized premium is correlated with the Implied term structure premium

). To some extent, this dynamic is similar to that for

implied volatility. Thus while implied volatility trades at a premium to realized volatility,

when a risk flare happens and realized volatility spikes, implied volatility does not follow

suite to the same extent and trades at a discount to realized volatility.

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Jan-96 Feb-97 Apr-98 Jun-99 Aug-00 Oct-01 Dec-02 Feb-04 Apr-05 May-06 Jul-07 Sep-08 Nov-09

Implied Corr 3M - Implied Corr 12M Implied Corr 3M - Realized Corr 12M


This behaviour has held true even during in the past few months, with the premium

between implied and realized correlation has compressed. In short, a comparison of short

dated implied correlation with trailing realized correlation indicates that the option market

does not expect the current high correlation to persist.


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July 26, 2010 9

However, long dated implied correlation appears to provide a conflicting signal. As

highlighted in Figure 11, during the rare occasions when implied correlation has traded at a

discount to realised, the implied correlated term structure inverts (goes into backwardation)

similar to what happens to implied volatilities. In this context, it is interesting to note that

currently, the long dated correlations are trading almost flat to shorter dated ones. Clearly,

the option market believes that the current state of high realized correlation will persist for

an extended period of time.

Conclusion

To summarize, in our opinion, while equity correlation continues to be highly dependent on

volatility, the rise in indexation has led to a permanent increase in its base level. Thus

while we do believe that the current high levels of realized and implied correlations are

unsustainable, the eventual drop is not likely to be as high as some market participants

might expect.


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July 26, 2010 10

Appendix A

The return of a basket of stocks is simply the total weighted average return of its

constituents. However, the volatility of an index is a function of the volatility of member as

well as how they are correlated to each other. Calculating an implied or realized correlation

number is a process of backing out the average correlation input that gets the individual

stock volatilities to aggregate to the index volatility.

The volatility of a portfolio p can be expressed in terms of the volatilities of its

components i and their weights .iw

+=i j

ijjiji

i

iipwww

222

Here ij is the pairwise correlation between all possible combinations of constituents.

Replacing the pair-wise correlations with a weighted average correlation , we can write:

+=i j

jiji

i

iip www 222

We also know

+=

i j

jiji

i

ii

i

ii wwww 22

2

Hence, index variance is given by

+=

i

ii

i

ii

i

iip www22

2

222

Thus the correlation (implied or realized) is given by

=

i

ii

i

ii

i

iip

ww

w

22

2

222

or2

2

i

ii

p

w

The approximation works because the second term in the numerator and denominator is

quite small as compared to the first terms.


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July 26, 2010 11

Analyst Certification

We, Maneesh S. Deshpande and Rohit Bhatia, hereby certify (1) that the views expressed in this research report accurately reflect our personal viewsabout any or all of the subject securities or issuers referred to in this research report and (2) no part of our compensation was, is or will be directly orindirectly related to the specific recommendations or views expressed in this report.

Important DisclosuresBarclays Capital does and seeks to do business with companies covered in its research reports. As a result, investors should be aware that the firm mayhave a conflict of interest that could affect the objectivity of this report.

Investors should consider this communication as only a single factor in making their investment decision.

The analysts responsible for preparing this report have received compensation based upon various factors including the Firm's total revenues, a portion ofwhich is generated by investment banking activities.

For current important disclosures regarding companies that are the subject of this research report, please send a written request to: BarclaysCapital Research Compliance, 745 Seventh Avenue, 17th Floor, New York, NY 10019 or refer to https://ecommerce.barcap.com/research/cgi-bin/all/disclosuresSearch.plor call 212-526-1072.

On September 20, 2008, Barclays Capital acquired Lehman Brothers' North American investment banking, capital markets, and private investmentmanagement businesses. All ratings and price targets prior to this date relate to coverage under Lehman Brothers Inc. Barclays Capital produces a varietyof research products including, but not limited to, fundamental analysis, equity-linked analysis, quantitative analysis, and trade ideas. Recommendations

contained in one type of research product may differ from recommendations contained in other types of research products, whether as a result ofdiffering time horizons, methodologies, or otherwise.

Risk Disclosure(s):Options are not suitable for all investors. Please note that the trade ideas within this report do not necessarily relate to, and may directly conflict with, thefundamental ratings applied to Barclays Capital Equity Research. The risks of options trading should be weighed against the potential rewards.Risks Call or put purchasing: The risk of purchasing a call/put is that investors will lose the entire premium paid.Uncovered call writing: The risk of selling an uncovered call is unlimited and may result in losses significantly greater than the premium received.Uncovered put writing: The risk of selling an uncovered put is significant and may result in losses significantly greater than the premium received.Call or put vertical spread purchasing (same expiration month for both options): The basic risk of effecting a long spread transaction is limited to thepremium paid when the position is established.Call or put vertical spread writing/writing calls or puts (usually referred to as uncovered writing, combinations or straddles (same expiration monthfor both options): The basic risk of effecting a short spread transaction is limited to the difference between the strike prices less the amount receivedin premiums.Call or put calendar spread purchasing (different expiration months & short must expire prior to the long): The basic risk of effecting a long calendarspread transaction is limited to the premium paid when the position is established.

Because of the importance of tax considerations to many options transactions, the investor considering options should consult with his/her tax advisor asto how taxes affect the outcome of contemplated options transactions.Supporting documents that form the basis of our recommendations are available on request.The Options Clearing Corporation's publication, "Characteristics and Risks of Standardized Options", is available athttp://www.theocc.com/publications/risks/riskchap1.jsp

Barclays Capital offices involved in the production of Equity Research:

LondonBarclays Capital, the investment banking division of Barclays Bank PLC (Barclays Capital, London)New YorkBarclays Capital Inc. (BCI, New York)Tokyo

Barclays Capital Japan Limited (BCJL, Tokyo)So PauloBanco Barclays S.A. (BBSA, So Paulo)Hong KongBarclays Bank PLC, Hong Kong branch (BB, Hong Kong)TorontoBarclays Capital Canada Inc. (BCC, Toronto)

JohannesburgAbsa Capital, a division of Absa Bank Limited (Absa Capital, Johannesburg)

This publication has been prepared by Barclays Capital; the investment banking division of Barclays Bank PLC, and/or one or more of its affiliates asprovided below. This publication is provided to you for information purposes only. Prices shown in this publication are indicative and Barclays Capital isnot offering to buy or sell or soliciting offers to buy or sell any financial instrument. Other than disclosures relating to Barclays Capital, the information
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