The document discusses low equity market volatility with the S&P 500 and NASDAQ maintaining under 8% and 16% realized volatility respectively, attributed to low trading volumes during the holiday season. It emphasizes recent weak housing data causing heightened sensitivity among homebuilders to market sentiment, highlighting a significant drop in home sales. The decline in implied volatility presents an opportunity for investors to consider protective positions as uncertainty remains in the housing sector and broader economic indicators.

1. August 29, 2006
Index Volatility Commentary
Ryan Renicker, CFA
1.212.526.9425 • Equity markets traded in an extremely tight range last week and 1-month realized vol remains
ryan.renicker@lehman.com extremely low across indices, at under 8% for the SPX and about 16% for the NDX.
Devapriya Mallick
1.212.526.5429 • This was helped by last week being the lightest week of the year in terms of both cash and
dmallik@lehman.com
derivatives volumes.
• The term structure of large cap vols remains steep with the sell-off in near-dated implied volatility.
• Weak housing data brought the spotlight back on homebuilders last week. This group has
become more sensitive to shifts in market sentiment around monetary policy, and has realized
more volatility than almost any other sub-industry in the S&P 500.
• The recent pullback in implied volatility provides an opportunity to purchase cheap protection in
the space, ahead of expected future volatility.
Lehman Brothers 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 of this report.
Customers of Lehman Brothers in the United States can receive independent, third-party research on the company or companies covered in this report, at no cost to them,
where such research is available. Customers can access this independent research at www.lehmanlive.com or can call 1-800-2LEHMAN to request a copy of this research.
Investors should consider this report as only a single factor in making their investment decision.
PLEASE SEE ANALYST(S) CERTIFICATION AND IMPORTANT DISCLOSURES BEGINNING ON PAGE 5.

2. Equity Derivatives Strategy | Index Volatility Commentary
All Quiet on the Equities Front
Equity markets traded in an extremely tight range last week, with the S&P 500 closing in an average
absolute range of approximately 3 points. 1-month realized vol remains extremely low across indices,
at under 8% for the SPX and about 16% for the NDX.
This has been helped by the lack of activity in markets with investors on vacation. Excluding July 3:
• In terms of equity volumes on the NYSE, the last 6 trading days are among the 7 lightest days
for the year so far.
• Last week, average single stock option volume (for constituents of the S&P 500) was lower
than in any other week of 2006.
Short-dated implied vols have been under pressure and term structures have steepened, especially for
largecaps. Yet investors who bought front month options after the cheapening would not have
managed to compensate for their decay and our long gamma position from two weeks back has taken
a fair amount of pain.
We recommend holding on to the position as sufficient catalysts remain for higher realized vol once
market activity picks up after the holiday season. The relentless beating down of large cap vols also
means that October and December vols still look extremely cheap. 37% of S&P 500 companies (by
weight) are scheduled to report earnings before the October expiration yet SPX ATM Oct implieds
trade around 11%. The December expiration covers an entire earnings cycle and 3 FOMC decisions,
and these are trading at under 12%. Either expiration looks attractive on a hedged basis or as a
means of obtaining downside protection in a market trading at the higher end of its range since May.
Figure 1: Lightest Week of the Year For Cash and Derivatives… Figure 2: … Kept Implied and Realized Vols Subdued
7.0 2.0 30%
Stock Option Volume (Mn Contracts)
6.0
NYSE Equity Volume (Bn Shares
25%
1.5
5.0
20%
4.0
1.0
3.0 15%
2.0
0.5 10%
Stock Option Volume (SPX Constituents)
1.0
Equity Volume (NYSE)
5%
0.0 0.0
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7-
6-
3-
9-
3-
SPX 1m Implied SPX 22d Realized NDX 22d Realized
12
Week Ending NDX 1m Implied IWM 22d Realized IWM 1m Implied
Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers, OptionMetrics, FAME
Homebuilders – More Uncertainty Ahead
The housing market was in the spotlight again last week, with both Existing Home Sales and New
Home Sales recording month on month decreases of over 4%. This was the largest simultaneous drop
in both indices this year and provided further confirmation of a housing slowdown.
Macro indicators paint a gloomy picture for homebuilders. Monthly sales are off 10-20% from their
peaks and unsold homes’ inventory is increasing as home prices begin to flatten (Figure 3).
August 29, 2006 2

3. Equity Derivatives Strategy | Index Volatility Commentary
In a data-dependent environment, shares of homebuilders have been more sensitive to shifts in market
sentiment around monetary policy, as seen by the increasing betas relative to the S&P 500 (Figure 4).
Figure 3: A Gloomy Macro Picture for Homebuilders1… Figure 4: … And Higher Betas2 in a More Rate-Sensitive Market
Last Month of % off % Change 4.0
Indicator
Value Peak/Trough Peak/Trough YoY
Existing Home Sales Total 6.33 Jun-05 -12.9% -11.2%
3.0
Existing Home Sales Months Supply 7.3 Jan-05 97.3% 58.7% Homebuilders - Beta vs SPX
Existing Home Sales Median Price 230 N/A N/A 0.9%
Pending Home Sales 113.9 Aug-05 -11.2% -9.4%
New Home Sales 1072 Jul-05 -21.6% -21.6% 2.0
New Home Sales Months Supply 6.5 Aug-03 85.7% 54.8%
New Home Sales Median Price 230 Apr-06 -10.5% 0.3%
Housing Starts 1795 Jan-06 -20.8% -13.3% 1.0
Homebuyer Affordability Index 103.7 Feb-03 -27.6% -7.8%
Total Residential Construction Spending 650,785 Dec-05 -3.5% -0.6%
Private Residential Construction Spending 641,602 Dec-05 -3.6% -0.8% 0.0
30-year Mortgage Rate 6.38 N/A N/A N/A
6
6
06
6
06
06
6
06
-0
-0
r-0
l-0
MBA Purchase Index 382.2 Jun-05 -27.8% -18.8%
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OFHEO House Price Index 393.78 N/A N/A 8.6%
Source: Lehman Brothers, Bloomberg Source: Lehman Brothers, Bloomberg
Not surprisingly, short term realized volatility for homebuilders has been among the highest across sub-
industries in the S&P 500 (Figure 5). With valuations for the group still some distance from reaching a
floor, we expect names in the space to remain volatile with short-term risks to the downside.
Historically, homebuilders have been particularly sensitive to Fed actions. Since 1989, the group has
outperformed the S&P 500 by an average of 26% (not annualized) during easing cycles and
underperformed by about 26% during tightening cycles (Figure 6). While implied vols for the group
have risen alongside the selloff, the recent pullback provides an opportunity to purchase protection.
Continued uncertainty around any remaining hikes in the current cycle and speculation around any
subsequent eases should keep vols bid in this space.
Figure 5: … Makes Them the Second Most Volatile Sub-Industry Figure 6: Homebuilders Historically Sensitive to Monetary Policy
Realized Realized 10000
S&P 500 GICS Sub-Industry Volatility (22- Volatility (66- Easing
Easing Tightening
-12% -35%
day) day) +51%
Photographic Products 58.5% 41.9%
1000 Tightening
Homebuilding 38.8% 38.3% -39%
Home Entertainment Software 37.2% 32.9%
Easing
Tires & Rubber 37.2% 31.5% +49%
100
Wireless Telecommunication Services 36.7% 26.5% Easing
Electronic Equipment Manufacturers 34.6% 33.4% Easing +5%
Tightening
+38%
Oil & Gas Drilling 33.7% 37.6% -2%
Steel 33.5% 46.5% 10
Specialized Consumer Services 33.5% 23.1%
89
91
93
95
97
99
01
03
05
19
19
19
19
19
19
20
20
20
Internet Retail 33.4% 58.5% Tightening Easing S&P 500 Homebuilding Subindustry S&P 500
Source: Lehman Brothers, Bloomberg Source: Lehman Brothers, Bloomberg
1
We consider troughs for no of months’ supply of new and existing homes. For other indicators, we consider the peak.
2
We caveat that betas calculated using daily returns over a 1-month time frame are not as stable as those using a longer
history. Yet they provide a better picture of recent changes in sensitivity to market returns.
August 29, 2006 3

4. Equity Derivatives Strategy | Index Volatility Commentary
Figure 7: Macro Volatility Summary
S&P 500 Implied and Realized Volatility
20% ETF Rich/Cheap Analysis
XLI
SOX
15%
SMH
XLB
10%
RTH
IBB
5% SPX Implied Vol (3-month)
XLY
SPX Realized Vol (3-month)
XLF
0% XAU
5
6
05
05
5
06
06
6
06
5
6
6
-0
-0
-0
-0
-0
r-0
l-0
OSX
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OIH
Implied Volatility History (NDX, RTY) BKX
30%
PPH
25% IYR
20% BBH
XLU
15%
XLE
10% NDX Implied Vol (3-month)
-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
RTY Implied Vol (3-month)
5% Cheap > > > > > > > > > > > > Rich
Imp Rel Spread (Std Devs from Mean) Imp SPX Spread (Std Devs from Mean)
0%
Note: For each ETF, we calculate the number of standard deviations by which the current 3-month
5
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implied-realized volatility spread differs from its 1-year average. We repeat the calculation for the
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ETF implied vs S&P 500 3-month implied volatility.
S&P 500 Put-Call Skew S&P 500 Skew (1-week Changes)
12% 1.0%
10%
SPX 20-delta Skew (3-month) 0.0%
8% SPX 20-delta Skew (1-month)
6% -1.0%
SPX 1-wk Implied Vol Change (90% Strike)
4%
-2.0% SPX 1-wk Implied Vol Change (100% Strike)
SPX 1-wk Implied Vol Change (110% Strike)
2%
-3.0%
0%
7
7
8
06
6
06
7
08
-0
-0
0
-0
0
5
06
05
05
5
6
06
6
6
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6
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Note: The 20-delta skew is calculated as the difference between the 20-delta put and 20-delta call implied volatililty. Weekly changes of implied volatility at the 90% and 110% strike versus the at-the-money strike are a
measure of richening/cheapening of skew.
Term Structure of ATM Implied Volatility (S&P 500) 3-month Implied and Realized Correlation (S&P 500)
17% 50%
16%
40%
15%
14% 30%
13%
20%
12%
SPX Implied Correlation (3-month)
11%
"Last" 1-wk Back 1-mo Back 10% SPX Realized Correlation (3-month)
10%
9% 0%
5
6
05
05
5
06
06
6
06
5
6
6
7
7
8
06
6
6
7
8
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Source: Lehman Brothers, OptionMetrics, Bloomberg, FAME
August 29, 2006 4

5. Equity Derivatives Strategy | Index Volatility Commentary
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
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August 29, 2006 5