Actionable trade ideas for stock market investors and traders seeking alpha by overlaying their portfolios with options, other derivatives, ETFs, and disciplined and applied Game Theory for hedge fund managers and other active fund managers worldwide. Ryan Renicker, CFA

1. September 5, 2006
Index Volatility Commentary
Ryan Renicker, CFA
1.212.526.9425 • The end of summer saw yet another lackluster week for equity volatility, with the last two weeks
ryan.renicker@lehman.com being the quietest this year.
Devapriya Mallick
1.212.526.5429 • Last week, the cheapening of front month implied vols was led by smallcaps, which is not
dmallik@lehman.com
surprising in light of their 2.2% outperformance over largecaps.
• The last 3 weeks have seen signs of another smallcap rally after their middle of August troughs,
accompanied by a rally in higher beta industry groups within the S&P 500.
• However, the smallcap vol compression is at odds with the bid for higher quality assets in credit
markets.
• Lehman’s Global Equity strategists have highlighted that largecap valuations look extremely cheap
relative to smallcaps. A bullish long-term stance on largecaps combined with the cheapening in
smallcap vols should increase the marginal propensity to use puts on smallcap indices as a means
of portfolio protection.
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
Largecaps vs Smallcaps - A Closer Look
The end of summer saw yet another lackluster week for equity volatility, with the last two weeks being
the quietest this year for broad market indices. Wednesday and Thursday saw trading in an extremely
tight range (Thursday’s high-low range was the smallest for the year) as investors held back ahead of
Friday’s employment report, and a non-farm payrolls number in line with consensus was not a
significant catalyst at the end of the week.
Consistent with the gamma evaporation, front month vols have cheapened and term structures have
steepened, a trend led initially by largecaps. Last week, the cheapening was led by small cap vols
and IWM1 1-month implied vol finished more than 1% lower while 1-month implied vols for OEX2 were
almost flat (Figure 1).
This is not surprising considering the 2.2% outperformance of the IWM relative to the OEX. A closer
look at regression expectations using weekly returns vs changes in 1-month implied vol since 20033
reveals that last week’s drop in the IWM-OEX ATM implied vol spread is in line with the historical drop
following similar smallcap rallies relative to largecaps (Figure 2).
Figure 1: Smallcap Vols Cheapened Relative to Largecap… Figure 2: … As Expected Given Last Week’s Outperformance
8% 4%
Weekly Change in IWM-OEX Vol Spread
3%
6% Weekly 1m Implied Vol Change (OEX)
Weekly 1m Implied Vol Change (IWM) 2%
4% 1%
2% 0%
-1%
0%
-2%
-2% y = -0.4284x + 0.0015
-3%
R2 = 0.2719
-4% -4%
-5%
-6%
-6%
ul
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03 n
un
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26 y
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17 r
31 r
13 r
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12 r
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-6% -4% -2% 0% 2% 4% 6%
-J
-J
-M
-M
-M
-M
-M
-A
-A
-S
-J
-J
-J
-J
-F
-F
-A
-A
07
21
06
20
09
23
03
28
01
18
Relative 1Wk Return (IWM vs OEX)
Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers, OptionMetrics
2006 has been a year when getting the largecap vs smallcap call correct has been more important
than the average year. Since the selloff in October 2005, the RTY outperformed the OEX by almost
15% over a 6-month period. Almost all of this outperformance was reversed over the subsequent 3
months (Figure 3).
The last 3 weeks have seen signs of another reversal, with the smallcap rally being accompanied by
greater demand for other riskier assets. This can be seen by the outperformance of higher beta industry
groups within the S&P 500 over the same period (Figure 4).
1
We consider IWM implied volatility as a proxy for the RTY because of greater option liquidity.
2
Using OEX returns and implied vols permits us to isolate the behavior of the larger cap names within the S&P 500.
3
Note that while the regression between vol spreads and relative returns of two indices is not as strong as that between
weekly returns and weekly vol changes for a single index, it still results in a reasonable fit.
September 5, 2006 2

3. Equity Derivatives Strategy | Index Volatility Commentary
Figure 3: Signs of the Oct-May Smallcap Rally… Figure 4: …Consistent With Recent Bid For Higher Beta Sectors…
Beta vs Return Return ( Return
130
GICS Industry Group SPX (04- (3Jan - 5May - (11Aug-
Smallcaps outperformed by OEX
125 about 15% till early May
05) 5May) 11Aug) 1Sep)
RTY
S&P 500 Industry Groups With Lowest Betas (2004-2005)
120 Food, Beverage & Tobacco 0.66 3.5% 5.2% 3.3%
Household & Personal Products 0.71 -1.5% 4.6% 2.9%
115 Utilities 0.77 -0.1% 5.3% 2.4%
Food & Staples Retailing 0.80 2.6% -0.6% 2.7%
110
Pharmaceuticals & Biotechnology 0.82 -0.7% 3.0% 4.2%
105 S&P 500 Industry Groups With Highest Betas (2004-2005)
Semiconductors & Semiconductor Equipment 1.50 -3.7% -18.3% 11.3%
100 Reversed almost Technology Hardware & Equipment 1.27 9.2% -15.9% 10.7%
all of it by mid Aug Automobiles & Components 1.25 2.0% 5.5% 4.2%
95 Materials 1.22 11.9% -11.3% 4.6%
Retailing 1.21 5.3% -11.4% 2.3%
06
6
06
06
5
5
06
6
5
06
06
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Source: Lehman Brothers, Bloomberg Source: Lehman Brothers, Bloomberg
However, the small cap vol compression relative to large cap vols is at odds with the bid on higher
quality assets in credit markets. Figure 5 plots the spread between the Lehman US Credit Index OAS
and the Lehman Corporate High Yield OAS, against the 3-month implied vol spread between the
IWM and the OEX. Historically, these two spreads have not been very strongly correlated but they
have moved together during the flight to quality over the last few months. The recent break-down of the
relationship could be a sign of equity markets pricing in a more conducive investment regime for riskier
assets than credit markets.
Lehman’s Global Equity strategists have highlighted that largecap valuations based on median forward
P/Es are currently at extremely cheap levels relative to smallcaps4 (Figure 6). While such a valuation
premium for smallcaps can persist for several years (as in the early 90s), a bullish long-term stance on
largecaps combined with the cheapening in smallcap vols should increase the marginal propensity to
use puts on smallcap indices as a means of portfolio protection.
Figure 5: … But At Odds With Continued Flight to Quality in Credit Figure 6: Valuation Argument Remains Compelling for Largecaps
2.8 14% 3
13%
Lehman HY OAS - Lehman US Credit OAS Median Fw d PE
2.5
3m Imp Vol Spread (IWM-OEX)
2.6 IWM-OEX Imp Vol Spread (3m) 12% (Largecap vs Smallcap)
11% 2
OAS Difference
2.4
10%
1.5
9%
2.2
8% 1
Spreads highly correlated 7%
2.0
during period of anxiety 0.5
6%
1.8 5% 0
06
6
06
06
5
06
06
06
06
l-0
89
90
91
92
93
94
95
96
97
98
99
00
01
02
03
04
05
-0
-
n-
n-
b-
-
g-
r-
ec
ay
ar
Ju
19
19
19
19
19
19
19
19
19
19
19
20
20
20
20
20
20
Ja
Ju
Fe
Ap
Au
M
D
M
Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers Equity Strategy
4
Please see Large-Cap Outperformance, Global Strategy Weekly, August 14, 2006.
September 5, 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%
BKX
IBB
5% SPX Implied Vol (3-month)
XLF
SPX Realized Vol (3-month)
XLY
0% RTH
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6
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06
5
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6
-0
-0
-0
-0
-0
r-0
l-0
XAU
p-
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OSX
Implied Volatility History (NDX, RTY) OIH
30%
IYR
25% PPH
20% BBH
XLE
15%
XLU
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
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implied-realized volatility spread differs from its 1-year average. We repeat the calculation for the
Ju
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Se
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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%
SPX 1-wk Implied Vol Change (90% Strike)
10% SPX 1-wk Implied Vol Change (100% Strike)
SPX 20-delta Skew (3-month)
SPX 1-wk Implied Vol Change (110% Strike)
8% SPX 20-delta Skew (1-month)
6% 0.0%
4%
2%
-1.0%
0%
7
7
8
06
6
06
7
08
-0
-0
0
-0
0
5
06
05
5
6
06
6
6
06
5
6
6
p-
c-
n-
n-
c-
-0
-0
-0
-0
0
r-0
0
l-0
ar
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ct
-
p-
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b-
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De
De
Se
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ay
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ar
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O
M
Ju
Ap
D
Fe
Se
Ja
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Au
O
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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
06
06
6
06
06
5
6
6
7
7
8
06
6
6
7
8
-0
-0
-0
-0
r-0
l-0
-0
-0
0
-0
0
-0
-0
p-
c-
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b-
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p-
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Ju
ar
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Ap
De
Fe
Se
Ja
Ju
Au
O
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Se
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N
O
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D
D
D
Source: Lehman Brothers, OptionMetrics, Bloomberg, FAME
September 5, 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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accurately reflect the firm's quantitative research model (2) no part of the firm's compensation was, is or will be directly or indirectly related to the specific
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September 5, 2006 5