options on the vix and mean reversion in implied volatility skews

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PLEASE SEE ANALYST(S) CERTIFICATION AND IMPORTANT DISCLOSURES BEGINNING ON PAGE 22.

Volatility Monthly: Low Volatility Marches On

Complacency in the Options Market? Most of the risk indicators we follow suggest we are living in a period of market complacency. However, we believe equity risk expectations are unreasonably low, particularly in light of a host of possible market-moving catalysts that could increase investor uncertainty.

Options on the VIX. Open interest has increased steadily since VIX options began trading slightly more than a week ago. Although implied volatility data and the information content inferred from the various strike levels and expiration terms in VIX options are likely to become more reliable as liquidity in these contracts increases, we believe the current shape of the curve provides insights into the extent of complacency in the marketplace.

Mean Reversion in Implied Volatility Skews. We find that implied volatility skew displays a tendency to revert to its longer term mean. Higher levels of skew, measured by percentile ranking relative to their 1-year history, tend to be followed by lower skew levels in the future with increasing probability. This is found to be true for put skews as well as call skews.

Sector Volatility Snapshots. Our Sector Volatility Snapshots allow investors to quickly assess aggregate volatility information for each S&P 500 GICS sector. The snapshots include implied and realized volatility for each sector and sector-based ETF, along with other useful metrics such as sector put-call skews, sector term structure trends, and notable volatility increases and decreases for stocks within each of the 10 GICS sectors.

March 6, 2006

Ryan Renicker, CFA

1.212.526.9425 [email protected]

Devapriya Mallick 1.212.526.5429

[email protected]

Equity Derivatives Strategy | Volatility Monthly: Low Volatility Marches On

March 6, 2006 2

Table of Contents

Equity Volatility Overview ...........................................................................................3 Complacency Unwarranted?............................................................................................. 3

Volatility Trading Environment ......................................................................................5 VIX Options ................................................................................................................... 5

Mean Reversion in Implied Volatility Skews.....................................................................6 Introduction.................................................................................................................... 6

Volatility Skew as a Measure of Market “Fear” ..................................................................... 6

Mean Reversion in Volatility Skew ...................................................................................... 7

Put Skews vs Call Skews .................................................................................................. 8

Conclusion .................................................................................................................... 9

Appendix I: Sector Volatility Snapshots ........................................................................10 Sector Highlights........................................................................................................... 11


March 6, 2006 3

Equity Volatility Overview Most of the risk indicators we follow suggest we are living in a period of market complacency. First, short-term equity risk expectations remain near multi-year lows. In fact, as Figure 1 illustrates, S&P 500 3-month implied and 66-day realized volatility are again approaching levels not observed since the end of 1996.

Second, longer-term risk expectations (3-month forward volatility in 9 months’ time) are hovering near multi-year lows, and have continued to decline this year, as the S&P 500 rallied since Q4 2005 and is approaching 5-year highs (Figure 2).

In addition, the 3-month S&P 500 skew continues its decline, suggesting investors continue to place incrementally smaller bids for downside protection against market downturns. This measure is closely related to the level of implied volatility itself, and we explore index volatility skew more closely later in this report.

Credit spreads also continue to trade near historically low levels and the high-yield spread relative to the spread on investment grade debt is also near its all-time lows. This might be a signal that investors’ tolerance for risk has increased and expanded across asset classes.

Figure 1: SPX Implied Volatility Remains Ominously Low

Figure 2: Long Term Risk Expectations Continue to Decline

5%

10%

15%

20%

25%

30%

35%

40%

45%

Jan-9

6

Dec-9

6

Nov-9

7

Oct-98

Sep-9

9

Aug-0

0Ju

l-01

Jun-0

2

May-03

Apr-04

Mar-05

Feb-

06

S&P

500

Vol

atili

ty

-

200

400

600

800

1,000

1,200

1,400

1,600

1,800

S&P

500

Inde

x

Implied VolRealized VolS&P 500

1,050

1,100

1,150

1,200

1,250

1,300

1,350

Jan-0

4

Mar-04

May-04

Jul-0

4

Sep-0

4

Nov-0

4

Jan-0

5

Mar-05

May-05

Jul-0

5

Sep-0

5

Nov-0

5

Jan-0

6

Mar-06

S&

P 5

00 In

dex

12%

13%

14%

15%

16%

17%

18%

19%

20%

Forw

ard

Impl

ied

Vol

S&P 5009m-12m Forward Vol

Source: Lehman Brothers, OptionMetrics, Bloomberg Source: Lehman Brothers, OptionMetrics, Bloomberg

Complacency Unwarranted?

We believe equity risk expectations are unreasonably low, particularly in light of a host of possible market-moving catalysts that could be forthcoming and are likely to spill over into a more volatile equity market.

For example, there still remains uncertainty regarding when the Fed is likely to stop raising rates (Lehman’s forecast is continued hiking until the August or September FOMC meeting, with the Fed Funds rate peaking at 5.5%). If the Fed continues to raise rates, there runs the risk that the consumer will begin to cut back on spending and the housing market could weaken, thereby reducing home equity extraction. Moreover, since the Fed is expected to become more dependent on economic data releases, we expect the market to become more “unsettled” prior to such releases. For instance, the average absolute daily return of the S&P 500 in response to releases of non-farm payrolls decreased over the “measured” rate hike period and was the lowest in 2005 (Figure 3). The market’s reaction has been larger thus far in 2006; if this persists going forward, option market participants could begin to price in larger moves as well, resulting in elevated levels of implied volatility.


March 6, 2006 4

Figure 3: Lowest Average Reaction to Non-Farm Payrolls in 2005

0.0%

0.5%

1.0%

1.5%

2.0%

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

Avg

. Abs

olut

e R

eact

ion

to P

ayro

lls

0.0

0.5

1.0

1.5

2.0

Cha

nge

in V

IX a

fter

Pay

rolls

Reaction to Non Farm PayrollsAbsolute Change in VIX Higher Absolute Reaction

Expected in 2006

Source: Lehman Brothers, Bloomberg.

In addition, we believe concern over rising energy prices (potential geopolitical risks in key oil-producing nations, active hurricane season, rising demand during summer months, etc.) and this year’s mid-term congressional elections could contribute to higher market anxiety. Event risks such as an avian flu outbreak could also be a catalyst for greater uncertainty.


March 6, 2006 5

Volatility Trading Environment

VIX Options

Options on the VIX index have been widely awaited by investors and commenced trading on February 24. In a little more than a week since these options started trading, open interest has increased steadily (Figure 4) and the popularity of VIX options can be expected to rise as a larger proportion of long-only fund managers begin using them as a “catastrophe hedge”.

Figure 4: Increasing Interest VIX Options

Figure 5: VIX Implied Volatility Surface (as of March 3)

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

24-Feb 27-Feb 28-Feb 01-Mar 02-Mar 03-Mar

VIX Option Volume

VIX Option Open Interest

0

20

40

60

80

100

120

140

160

180

10 12.5 15 17.5 20

Strike

Impl

ied

Vola

tility

Mar-06

Apr-06

May-06

Source: Lehman Brothers, Bloomberg Source: Lehman Brothers, Bloomberg

The implied volatility surface of VIX options exhibits the expected premium for writing out-of-the-money calls (Figure 5). While implied volatility data and the information content inferred from the various strike levels and expiration terms are likely to become more reliable as liquidity in these contracts increases, we believe the current shape of the curve provides insights into the extent of complacency in the marketplace. Thus, one might expect the higher strikes for the April and May maturities to trade at a significant premium to the at-the-money strike, yet the skew is essentially flat at present. Although there are currently not enough data points to draw statistically meaningful conclusions, we believe a persistence of this pattern could indicate unreasonably low levels of “fear” in the market.


March 6, 2006 6

Mean Reversion in Implied Volatility Skews

Introduction

According to the Black-Scholes option valuation model, implied volatility is assumed to be constant across all strikes and expirations. However, in practice, option contracts trade with different implied volatilities, depending on their maturity as well as the distance of the strike from the underlying stock price.

The tendency for lower strikes in index options to trade at higher levels of implied volatility has been observed since the stock market crash of 1987. Since then, writers of out-of-the-money puts have tended to demand a premium to compensate for the insurance they provide. In addition, demand/supply technicals explain the sustained existence of a volatility skew in index options. Equity investors, in aggregate, have a net long exposure to equity markets and are a natural source of demand for purchasing out-of-the-money puts, thus raising the implied volatility for lower strikes. On the other hand, they tend to supply volatility at higher strikes by selling out-of-the-money calls as part of systematic overwriting strategies, thus suppressing implied volatility at higher strikes.

Another perspective that helps explain skew in the volatility surface is the return distribution of equities. If the Black-Scholes theoretical assumption of stocks’ lognormal distribution was valid, implied volatility would be expected to be flat across strikes. However, the actual return distribution over an extended period of time indicates that equity returns exhibit negative skewness, with fatter downside tails. This supports the notion that investors bid up protection for options having very low strike prices, resulting in higher implied volatility for contracts at these strikes.

Volatility Skew as a Measure of Market “Fear”

Implied volatility is frequently used as a risk indicator in the equity market since there is a well established negative correlation between spot prices and implied volatility. We find that SPX skew, as measured by the difference in implied volatility for the 20-delta puts and calls, moves closely with the level of implied volatility, and can be considered an alternate metric of market “fear” (Figure 6). We also find that daily changes in implied volatility are strongly correlated with daily changes in skew levels (Figure 7).

Figure 6: Skew a Measure of Market Fear

Figure 7: Index Implied Volatility Correlated to Skew

0%

10%

20%

30%

40%

50%

Jan-9

6

Jan-9

7

Jan-9

8

Jan-9

9

Jan-0

0

Jan-0

1

Jan-0

2

Jan-0

3

Jan-0

4

Jan-0

5

Jan-0

6

ATM

Impl

ied

Vol (

3-m

onth

)

0%

5%

10%

15%

20%

80 D

elta

-20

Del

ta S

kew

(3-m

onth

)3-month Implied Vol

3-month 80-20 Delta Skew

R2 = 0.3274

-6%

-4%

-2%

0%

2%

4%

6%

-6% -4% -2% 0% 2% 4% 6%

Daily Change in Implied Vol

Dai

ly C

hang

e in

Ske

w

Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers, OptionMetrics


March 6, 2006 7

However, at the single-stock level, implied volatility changes do not appear to be a strong predictor of changes in skew (Figure 8).

Figure 8: Correlations of Single-Stock Skew Changes With Implied Volatility Changes

1-month Vols 3-month Vols20 Delta 1.7% 3.9%30 Delta 1.8% 3.9%40 Delta 1.3% 2.7%

Source: Lehman Brothers, OptionMetrics

Mean Reversion in Volatility Skew

We have found that the spread of implied relative to realized volatility displays a tendency to revert to its longer term mean1. We now test whether a similar reversion exists for volatility skews. We consider the 20 delta put – 20 delta call skew on 3-month S&P 500 options since 1996. We categorize skew as being “rich” if it is trading at a high percentile relative to where it had traded during the prior year. On the other hand, if it stands at a lower percentile relative to its 1-year history, we label it as “cheap”. If volatility skew indeed exhibits mean reversion, we would expect periods of high skew percentiles to be followed by lower skew in 3 months’ time, and vice versa.

Figure 9 demonstrates that such mean reversion does tend to occur, as successively higher percentiles of skew tend to precede greater declines in skew. For example, on average, when skew was initially labeled as being very “rich” (skew level at a percentile greater than 95%), the skew stood at a lower value in 3 months in 91% of cases and the median drop in skew in these instances was over 2.7%.

On the other hand, when skew was trading at a low percentile relative to its history (“cheap”), its subsequent change tended to be positive, though at a lower degree of magnitude than that of “rich” skew. We believe this reflects the fact that during the sample period of the study, skew on index options has, on average, been in a declining trend. (Thus, the likelihood of “rich” skew being followed by lower skew has been greater than the probability of “cheap” skew being a predictor of elevated skew in future.)

1 Please refer to Identifying Rich and Cheap Implied Volatility, December 20, 2005 for additional details.


March 6, 2006 8

Figure 9: More Extreme Values of Skew Tend to Revert With Higher Probability

"Rich" Skew

Percentile of Skew Relative to 1yr History #

# With Subsequent

Skew Decrease

% Correct

Avg 3-month Change in

Skew

Median 3-month

Change in Skew

Std Dev of Skew Change

70% 644 498 77% -1.23% -1.55% 2.67%80% 412 344 83% -1.68% -1.85% 2.48%90% 241 212 88% -2.23% -2.39% 2.34%95% 144 131 91% -2.68% -2.74% 2.16%

"Cheap" Skew

Percentile of Skew Relative to 1yr History #

# With Subsequent

Skew Increase

% Correct

Avg 3-month Change in

Skew

Median 3-month

Change in Skew

Std Dev of Skew Change

30% 882 473 54% 0.57% 0.29% 2.12%20% 645 349 54% 0.50% 0.27% 1.83%10% 382 231 60% 0.73% 0.48% 1.60%5% 237 156 66% 0.96% 0.85% 1.53%


Put Skews vs Call Skews

Having established the mean reverting characteristics of volatility skew, we now examine the components of skew more closely. Specifically, rather than analyzing the total difference in put and call implied volatility, we now analyze mean reversion in the put skew (OTM put implied vol – ATM implied vol) and call skew (ATM implied vol – OTM call implied vol) separately.

As Figure 10 and Figure 11 illustrate, put skews and call skews have displayed a tendency to revert to their medium-term averages. The effect is stronger for “rich” skew than for “cheap” skew, similar to the observation for put-call skews.

Figure 10: Mean Reversion in Put Skew

Figure 11: Mean Reversion in Call Skew

-2.0%

-1.5%

-1.0%

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Avg Change in Put Skew ("Rich") Avg Change in Put Skew ("Cheap")

< 30th Percentile

< 20th Percentile

< 10th Percentile

< 5th Percentile

> 70th Percentile

> 80th Percentile

> 90th Percentile > 95th

Percentile

-1.5%

-1.0%

-0.5%

0.0%

0.5%

Avg Change in Call Skew ("Rich") Avg Change in Call Skew ("Cheap")

< 30th Percentile

< 20th Percentile

< 10th Percentile

< 5th Percentile

> 70th Percentile

> 80th Percentile

> 90th Percentile

> 95th Percentile



March 6, 2006 9

Conclusion

Possible strategies for taking advantage of the mean reversion characteristics in skew include buying or selling delta-hedged spreads. For example, an investor who believes the put skew is trading at very low levels and expects it to increase, can sell put spreads by buying out-of-the-money puts and writing at-the-money puts. Although hedging the net delta of the spread can theoretically eliminate this position’s exposure to the changes in the underlying index, we note that the position would have some exposure to time decay (theta), which can be partly mitigated by selecting longer term options. Moreover, the success of any strategy attempting to exploit the change in skew would depend on the bid-ask spreads involved. For illiquid out-of-the-money contracts, total transaction costs could overwhelm the profit from the expected movement in skew.


March 6, 2006 10

Appendix I: Sector Volatility Snapshots

In this section, we show our Sector Volatility Snapshots. These snapshots allow investors to quickly assess aggregate volatility information for each GICS sector in the S&P 500 Index.

The average volatility (implied or realized) for a GICS sector is calculated as the weighted- average-volatility of each of their respective index constituents, weighted by market capitalization. The weighted-average volatility for a GICS industry group is obtained similarly. ETFs having options are mapped to one GICS sector each, although the mapping is not perfect since stocks in an ETF could be classified into multiple sectors as per the GICS sector classification methodology. However, they closely reflect the performance and volatility characteristics of the sectors and industries they represent.

• We display the weighted-average implied and realized volatility at the sector level for a one year period. For each industry group within the sector and each ETF that closely resembles the respective industry or sector, we provide the number of standard deviations the current level of the implied-realized volatility spread is trading above or below to its one-year historical mean. A highly negative standard deviation could indicate that options are trading cheap, whereas a highly positive standard deviation possibly implies such options are relatively rich. (Note that there usually do not exist actively traded options at the industry group level and the relative richness/cheapness indicators for these industry groupings should only be used only as a starting point for identifying single-stock volatility trades within that industry group. Furthermore, while options on ETFs exist, their liquidity should be taken into account before executing a trade, since many are currently thinly traded as well.)

• The “Largest Implied Volatility Increases” and “Largest Implied Volatility Decreases” denote the stocks within the sectors that have experienced the highest and lowest absolute changes in implied volatility, over one-week and one-month periods.

• The Put-Call Skew is calculated as the difference between the 3-month put-implied volatility and the 3-month call-implied volatility for 20 delta puts and 20 delta calls, divided by the 3-month at-the-money implied volatility. The weighted-average skew at the sector and industry group level are calculated similarly, except the volatility used is the market-cap weighted-average implied volatility. If the current skew level is trading a relatively high number of standard deviations above its one-year average, this could indicate the option market is pricing in increasing risk expectations for the underlying stock, since the put–call implied volatility differential implies that option traders have been bidding up put protection, rather than upside participation via long call positions.

• We show the history of the slope of the volatility term structure as measured by the difference between 12-month and 3-month at-the-money implied volatilities. Since longer term implied volatility tends to be more stable than implied volatility on shorter-dated options, a lower term structure spread relative to its historical pattern could indicate 3-month options are trading richer than they typically have in the past. Alternatively, if the slope of the term structure is relatively steep, one might infer near term options are trading at a relative discount to longer dated options.


March 6, 2006 11

Sector Highlights

Lehman’s U.S. Equity Strategy team has raised its weighting of the Telecommunication Services sector to Overweight from Market-Weight on the back of improved conditions in end markets, realization of consolidation benefits and strong wireless revenue trends.

Implied volatility for the Telecom sector on a market-cap weighted-average basis has lagged realized volatility, and its current 3-month implied-realized spread stands more than one standard deviation below its 1-year average. We observe that the Telecom HOLDRS Trust (TTH) ETF has had increasing interest among investors, with the total number of contracts traded in February increasing more than two-fold relative to that of January. We recommend investors looking to implement a bullish view on the Telecom sector consider purchasing relatively inexpensive calls on TTH (Figure 12) or some of its largest constituents.

Figure 12: TTH Implied vs Realized Volatility

Figure 13: PPH Implied vs Realized Volatility

8%

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TTH 66-day Realized Vol

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PPH 3-month Implied Vol

PPH 66-day Realized Vol


3-month implied volatility for the S&P 500 Health Care sector steadily declined through February, and currently trades at a discount to 66-day realized volatility. This has been true for both U.S. Major Pharmaceuticals as well as Health Care Equipment stocks. Lehman Brothers' Pharmaceuticals analyst Anthony Butler and Medical Supplies analyst Bob Hopkins currently have positive ratings on their respective sectors. We believe investors wishing to implement a bullish directional view for the Health Care sector should consider purchasing relatively cheap calls on the Pharmaceutical HOLDRS Trust (PPH) ETF (Figure 13).


March 6, 2006 12

Figure 14: Energy Sector Volatility Snapshot (as of March 3, 2006)

Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized VolEP 32% 1% 29% NOV 42% 2% 44% WMB 30% -2% 28% WMB 30% -5% 28%SLB 33% 1% 37% EOG 42% 2% 41% NBR 36% -2% 35% HAL 33% -3% 36%NOV 42% 0% 44% NE 38% 1% 40% EOG 42% -2% 41% RIG 36% -3% 39%BR 14% 0% 24% SUN 38% 1% 40% AHC 32% -2% 33% XTO 35% -3% 34%

CVX 22% 0% 21% BJS 36% 1% 40% XTO 35% -1% 34% XOM 20% -2% 20%

Largest Implied Volatility Increases Largest Implied Volatility Decreases1-week Increase 1-month Increase 1-week Decrease 1-month Decrease

Implied Volatility vs Realized Volatility

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Wgt Avg Implied Vol Wgt Avg Realized Vol

3-Month Put-Call Skew (20 Delta)

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Wgt Avg 20 Delta Skew (3m) Avg + 1 Stdev Avg - 1 Stdev

Implied-Realized Spread (by Industry Groups/ETF)# of Standard Deviations from 1-year Average

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0

OIH

OSX

XOI

XLE

Energy

IYE

XNG

Cheap > > > > > > > > > > > > Rich

Relative Skews (by Industry Groups/ETF)# of Standard Deviations from 1-year Average

-1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

XLE

XOI

Energy

OSX

XNG

IYE

OIH

Cheap > > > > > > > > > > > > Rich

12-Month - 3-Month Term Spread

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Wgt Avg 12m-3m Term Avg + 1 Stdev Avg - 1 Stdev

Relative Term Spreads (by Industry Groups/ETF)# of Standard Deviations from 1-year Average

0.00.51.01.52.02.53.03.5

OSX

IYE

XLE

OIH

XNG

Energy

XOI

Cheap > > > > > > > > > > > > Rich

Note: The put-call skew is calculated by taking the difference between the 20-Delta put-implied volatility and 20-Delta call-implied volatility, divided by the 3-month ATM implied volatility. Sector level volatilities are the market cap weighted implied volatilty for each constituent. A high skew is generally associated with a relatively high demand for downside protection.

Note: The term structure spread is calculated by taking the difference between the 12-month ATM implied volatility and the 3-month ATM implied volatility. Sector level term spread is calculated from the market cap weighted implied volatilities of the constituents. A steep term structure indicates shorter-dated implied volatility could be cheap relative to longer-dated implied volatility.

Note: We calculate each sector's average implied volatility by weighting the 3-month at-the-money implied volatility of its constituents by market capitalization. Investors should consider liquidity of options of a stock or ETF before entering an options position since, although options on ETFs exist, many are thinly traded.



March 6, 2006 13

Figure 15: Materials Sector Volatility Snapshot (as of March 3, 2006)

Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized VolMWV 24% 4% 15% MWV 24% 6% 15% HPC 28% -2% 27% NUE 36% -4% 36%LPX 29% 2% 22% VMC 29% 3% 33% NUE 36% -2% 36% NEM 34% -3% 36%VMC 29% 1% 33% FCX 40% 2% 45% IFF 17% -2% 13% IFF 17% -3% 13%WY 19% 1% 16% HPC 28% 2% 27% EC 13% -1% 47% SEE 19% -2% 15%SIAL 16% 0% 10% PTV 26% 1% 23% AA 27% -1% 25% X 44% -2% 44%



15%

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-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8

XLB

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XAU

IYM

Cheap > > > > > > > > > > > > Rich


-2.0 -1.5 -1.0 -0.5 0.0 0.5

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Cheap > > > > > > > > > > > > Rich


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0.00.10.20.30.40.50.60.70.80.9

Materials

IYM

XAU

XLB

Cheap > > > > > > > > > > > > Rich






March 6, 2006 14

Figure 16: Industrials Sector Volatility Snapshot (as of March 3, 2006)

Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized VolPBI 18% 2% 13% BNI 24% 2% 24% GR 25% -1% 24% RHI 28% -5% 28%NAV 34% 1% 29% HON 21% 2% 22% CD 28% -1% 32% NAV 34% -4% 29%CMI 26% 1% 25% PBI 18% 1% 13% LUV 25% -1% 23% LUV 25% -4% 23%CSX 22% 1% 21% CTAS 20% 1% 17% NSC 23% 0% 24% PLL 20% -3% 16%ETN 21% 1% 17% CD 28% 1% 32% CAT 25% 0% 23% MNST 35% -3% 38%



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Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



-0.4 -0.2 0.0 0.2 0.4 0.6

CYC

Commercial Services & Supplies

XLI

Capital Goods

Transportation

XAL

Cheap > > > > > > > > > > > > Rich


-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

XLI

CommercialServices & Supplies

Capital Goods

CYC

Transportation

XAL

Cheap > > > > > > > > > > > > Rich


-1%

0%

1%

1%

2%

2%

3%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



-1.0-0.50.00.51.0

Commercial Services & Supplies

XLI

CYC

Capital Goods

Transportation

XAL

Cheap > > > > > > > > > > > > Rich






March 6, 2006 15

Figure 17: Consumer Discretionary Sector Volatility Snapshot (as of March 3, 2006)

Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized VolAPOL 34% 4% 42% GM 69% 9% 47% SHW 29% -10% 46% UVN 23% -7% 28%CTB 36% 4% 28% SHW 29% 5% 46% KRI 20% -6% 16% KRI 20% -7% 16%GT 37% 4% 45% RSH 33% 3% 30% LOW 22% -2% 20% MYG 50% -5% 26%LTD 25% 2% 20% BBY 33% 1% 38% SPLS 23% -2% 24% SNA 18% -5% 16%CCL 23% 2% 20% CBS 23% 1% 179% AZO 24% -2% 22% F 41% -4% 29%



15%

20%

25%

30%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



10%

12%

14%

16%

18%

20%

22%

24%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

Media

Consumer Services

HHH

Automobiles & Components

XLY

Retailing

Consumer Durables & Apparel

RTH

Cheap > > > > > > > > > > > > Rich


-2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0

RTH

Retailing

Consumer Services


HHH

XLY

Media


Cheap > > > > > > > > > > > > Rich


-3%

-2%

-2%

-1%

-1%

0%

1%

1%

2%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



0.00.51.01.52.0


HHH

Consumer Services

Retailing

RTH

Media


XLY

Cheap > > > > > > > > > > > > Rich






March 6, 2006 16

Figure 18: Consumer Staples Sector Volatility Snapshot (as of March 3, 2006)

Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized VolTSN 37% 7% 24% TSN 37% 8% 24% HNZ 17% -3% 12% CVS 22% -4% 20%MO 28% 2% 15% ACV 23% 2% 19% CVS 22% -1% 20% AVP 24% -4% 19%KO 13% 1% 11% MO 28% 2% 15% UST 21% 0% 22% HSY 18% -3% 18%

CAG 18% 1% 16% HNZ 17% 1% 12% ABS 12% 0% 32% SLE 17% -2% 15%PEP 13% 1% 10% EL 25% 0% 22% SLE 17% 0% 15% KR 20% -2% 16%



10%

15%

20%

25%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



0%

5%

10%

15%

20%

25%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Food & StaplesRetailing

XLP

Household &Personal Products

Food, Beverage &Tobacco

Cheap > > > > > > > > > > > > Rich


-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2


XLP



Cheap > > > > > > > > > > > > Rich


-1%

-1%

0%

1%

1%

2%

2%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



0.00.20.40.60.81.0



XLP


Cheap > > > > > > > > > > > > Rich






March 6, 2006 17

Figure 19: Health Care Sector Volatility Snapshot (as of March 3, 2006)

Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized VolHSP 31% 8% 37% HSP 31% 6% 37% MHS 26% -2% 24% BSX 32% -16% 35%CHIR 12% 3% 6% THC 46% 3% 33% BMY 22% -2% 19% CHIR 12% -12% 6%SGP 25% 2% 20% SYK 26% 2% 34% BCR 20% -1% 23% ESRX 28% -6% 26%

PDCO 24% 2% 17% LH 19% 2% 17% WPI 23% -1% 20% GDT 19% -5% 27%AET 26% 2% 25% PKI 28% 1% 24% HCA 21% -1% 19% BOL 28% -4% 30%



15%

20%

25%

30%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



10%

12%

14%

16%

18%

20%

22%

24%

26%

28%

30%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

PPH

Pharmaceuticals & Biotechnology

Health Care Equipment & Services

IYH

XLV

BBH

IBB

Cheap > > > > > > > > > > > > Rich


-2.0 -1.5 -1.0 -0.5 0.0 0.5



BBH

IBB

IYH

XLV

PPH

Cheap > > > > > > > > > > > > Rich


-3%

-2%

-2%

-1%

-1%

0%

1%

1%

2%

2%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



-0.8-0.6-0.4-0.20.00.20.40.60.81.01.2

IBB

XLV

PPH

BBH

IYH



Cheap > > > > > > > > > > > > Rich






March 6, 2006 18

Figure 20: Financials Sector Volatility Snapshot (as of March 3, 2006)

Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized VolCFC 29% 3% 24% GDW 25% 2% 21% JP 20% -8% 13% AOC 25% -5% 25%ASN 21% 2% 16% LEH 22% 1% 19% GNW 19% -1% 18% ALL 16% -5% 15%KEY 18% 2% 15% KEY 18% 1% 15% VNO 18% -1% 15% UNM 26% -4% 37%GDW 25% 2% 21% MS 21% 1% 16% BK 19% -1% 14% FNM 27% -3% 29%

C 15% 2% 15% RF 16% 1% 15% SOV 22% -1% 17% PNC 19% -3% 19%



10%

15%

20%

25%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



10%

15%

20%

25%

30%

35%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



-0.5 0.0 0.5 1.0 1.5 2.0

Diversified FinancialsXLFBanksIYFBKXInsuranceRKHIYRXBDICFReal Estate

Cheap > > > > > > > > > > > > Rich


-2.0 -1.5 -1.0 -0.5 0.0 0.5

IYF

InsuranceXLFDiversified Financials

RKHBKXBanks

IYR

XBDReal EstateICF

Cheap > > > > > > > > > > > > Rich


-1%

-1%

0%

1%

1%

2%

2%

3%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



-2.0-1.5-1.0-0.50.00.51.01.5

BKXRKHIYRICFDiversified FinancialsBanksReal EstateXLFXBDIYFInsurance

Cheap > > > > > > > > > > > > Rich






March 6, 2006 19

Figure 21: Information Technology Sector Volatility Snapshot (as of March 3, 2006)

Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized VolJDSU 58% 10% 55% GTW 59% 7% 51% AMCC 47% -6% 42% AMD 47% -5% 47%SYMC 33% 5% 30% SLR 45% 5% 34% ADCT 42% -5% 37% SANM 44% -4% 38%GLW 38% 2% 40% PMCS 45% 3% 47% CIEN 57% -3% 52% AV 34% -4% 35%

CSCO 22% 2% 24% VRSN 32% 2% 24% AV 34% -3% 35% TER 37% -4% 40%YHOO 33% 2% 36% BRCM 42% 2% 48% CTXS 27% -3% 26% ERTS 29% -4% 25%



15%

20%

25%

30%

35%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



-5%

0%

5%

10%

15%

20%

25%

30%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Semiconductors & Semiconductor EquipmentSOXSMHIGMIGWBDHMSHSWHIGNWMHSoftware & ServicesXLKTXXIAHTechnology Hardware & EquipmentIYWXCIIGV

Cheap > > > > > > > > > > > > Rich


-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0

SWHXCIMSHSMHIGMSemiconductors & Semiconductor EquipmentIGWIAHTXXXLKSoftware & ServicesIGVTechnology Hardware & EquipmentIGNIYWWMHSOXBDH

Cheap > > > > > > > > > > > > Rich


-3%

-2%

-2%

-1%

-1%

0%

1%

1%

2%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



-1.5-1.0-0.50.00.51.01.52.0

SMHIAHIGNIGWMSHWMHTechnology Hardware & EquipmentSemiconductors & Semiconductor EquipmentTXXSOXIGVXLKIYWIGMBDHSWHSoftware & ServicesXCI

Cheap > > > > > > > > > > > > Rich






March 6, 2006 20

Figure 22: Telecommunication Services Sector Volatility Snapshot (as of March 3, 2006)

Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized VolS 26% 2% 22% T 15% 1% 14% Q 35% -2% 30% Q 35% -6% 30%

CZN 16% 1% 16% S 26% 1% 22% CTL 19% -1% 20% CZN 16% 0% 16%T 15% 0% 14% VZ 16% 0% 16% AT 20% 0% 15% AT 20% 0% 15%

BLS 17% 0% 17% CTL 19% 0% 20% VZ 16% 0% 16% BLS 17% 0% 17%VZ 16% 0% 16% BLS 17% 0% 17% BLS 17% 0% 17% CTL 19% 0% 20%



10%

15%

20%

25%

30%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



0%

5%

10%

15%

20%

25%

30%

35%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



-4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0

IYZ

TTH

TelecommunicationServices

Cheap > > > > > > > > > > > > Rich


-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0


IYZ

TTH

Cheap > > > > > > > > > > > > Rich


-1%-1%0%1%1%2%2%3%3%4%4%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



-1.0-0.50.00.51.01.52.02.53.03.54.0


TTH

IYZ

Cheap > > > > > > > > > > > > Rich






March 6, 2006 21

Figure 23: Utilities Sector Volatility Snapshot (as of March 3, 2006)

Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized VolDYN 47% 4% 39% XEL 15% 1% 13% KSE 8% -3% 27% KSE 8% -9% 27%GAS 18% 1% 15% PNW 15% 1% 14% CNP 21% -2% 17% AES 25% -5% 23%XEL 15% 1% 13% DUK 17% 0% 14% PNW 15% -1% 14% TXU 29% -5% 24%TE 17% 1% 14% CEG 21% 0% 26% TXU 29% -1% 24% PCG 15% -4% 15%

ETR 17% 1% 13% PGL 19% 0% 16% FPL 17% -1% 15% NI 19% -4% 14%



10%

15%

20%

25%

30%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



0%

5%

10%

15%

20%

25%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



0.0 0.5 1.0 1.5 2.0 2.5

Utilities

IDU

UTH

UTY

XLU

Cheap > > > > > > > > > > > > Rich


-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

UTY

UTH

Utilities

IDU

XLU

Cheap > > > > > > > > > > > > Rich


-3%

-2%

-2%

-1%

-1%

0%

1%

1%

2%

2%

Mar-05

Apr-05

May-05

Jun-0

5Ju

l-05

Aug-05

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06



0.00.51.01.52.0

XLU

IDU

Utilities

UTY

UTH

Cheap > > > > > > > > > > > > Rich






March 6, 2006 22

Analyst Certification: I, Ryan Renicker, hereby certify (1) that the views expressed in this research email accurately reflect my personal views about any or all of the subject securities or issuers referred to in this email and (2) no part of my compensation was, is or will be directly or indirectly related to the specific recommendations or views expressed in this email.

Options are not suitable for all investors and the risks of option trading should be weighed against the potential rewards. Supporting documents that form the basis of the recommendations are available on request. Please note that the trade ideas within this report in no way relate to the fundamental ratings applied to European stocks by Lehman Brothers' Equity Research.

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options on the vix and mean reversion in implied volatility skews

Economy & Finance