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. October 10, 2006
Index Volatility Commentary – Smallcap Vols
Ryan Renicker, CFA
1.212.526.9425
Cheap
ryan.renicker@lehman.com
• IWM options have gained in popularity, partly because smallcap beta relative to largecaps is at
Devapriya Mallick
1.212.526.5429 multi-year highs.
dmallik@lehman.com
• Smallcaps have recently shown disproportionate participation in any downside moves in the
market.
• The two weeks heading into earnings have tended to be a period of smallcap underperformance;
largecap valuations continue to be extremely cheap relative to smallcaps.
• The IWM-SPX implied vol spread has cheapened to levels last seen in early June. We believe
fundamental and seasonal factors make this an opportune time to enter this spread.
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 8.

2. Equity Derivatives Strategy | Index Volatility Commentary – Smallcap Vols Cheap
Smallcap Vols Cheap Relative to Largecap Vols
Since the beginning of the year, IWM options have gained in popularity as a punting vehicle.
Average listed volume in IWM contracts more than doubled in the month of May in comparison to the
previous month. Though volumes have come off in recent months as the demand for downside
protection has receded, monthly IWM option volumes remain higher than in early 2006 (Figure 1).
An environment where macroeconomic data was deemed more important for determining the path of
Fed policy made the Russell 2000 a more attractive instrument for placing leveraged bets.
Another explanation for the greater use of IWM options could be the increasing beta of the Russell
2000 relative to the SPX, which is currently at multi year highs (Figure 2). This is largely explained by
the extremely serene levels of largecap realized vols (1-month realized volatility for the S&P 500 has
been hovering in the 7-8% range).
Figure 1: IWMs are the favored punting vehicle in a sell-off Figure 2: RTY beta to SPX at multi year highs
700,000 2.0
600,000 Avg SPX Option Volume
RTY Beta vs SPX
Avg IWM Option Volume 1.5 (Rolling 3-month)
500,000
400,000
1.0
300,000
200,000 0.5
100,000
0.0
0
5
6
7
8
9
0
1
2
3
4
5
6
06
6
06
06
06
06
06
r-9
-9
r-9
r-9
r-9
r-0
r-0
r-0
r-0
-0
r-0
r-0
06
06
l-0
r
r
p-
-
n-
n-
b-
-
g-
r-
Ap
Ap
Ap
Ap
Ap
Ap
Ap
Ap
Ap
Ap
Ap
Ap
ay
ar
Ju
Ja
Ju
Fe
Ap
Se
Au
M
M
Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers, OptionMetrics, FAME
Seasonal effects argue for smallcap underperformance in the short run. The two weeks heading into
the start of earnings season have tended to be a period of weakness for the IWM. Out of the 15 such
periods since 2003, the IWM has finished lower on 10 occasions. The IWM-SPX implied vol spread
for the 1-month maturity has also widened on 9 out of these 15 instances.
Lehman’s Equity Strategists have highlighted that based on median forward P/E multiples, largecap
valuations are historically cheap relative to smallcaps. In keeping with this and the heightened macro
risks, smallcap vols kept getting bid up relative to largecap vols till the middle of August. The spread
has been reversing for the subsequent two months.
Following last week’s outperformance of the Russell 2000, IWM implied vols have cheapened further
relative to the SPX. 1-month IWM implied volatility currently trades at an 8 pt premium to SPX options.
This is the cheapest the spread has been since early June (Figure 3).
October 10, 2006 2

3. Equity Derivatives Strategy | Index Volatility Commentary – Smallcap Vols Cheap
Figure 3: Spread to Largecap Vols Has Cheapened Considerably Figure 4: Risks skewed to the downside
0.8%
%
14
0.6%
IWM-SPX Implied
Vol (1-Month) 0.4%
%
12
0.2%
0.0%
%
10
-0.2%
Avg RTY vs SPX outperformance
8%
-0.4% w hen SPX closes higher
Avg RTY vs SPX underperformance
-0.6% w hen SPX closes low er
6%
-0.8%
06
6
06
06
06
06
06
06
06
l-0
p-
-
n-
n-
b-
-
g-
n- 4%
r-
ay
ar
Ju
Ja
Ju
Fe
Ap
Se
Au
5
5
6
6
5
6
M
05
06
M
r-0
-0
r-0
-0
l-0
l-0
n-
ct
ct
Ju
Ju
Ap
Ap
Ja
Ja
O
O
Source: Lehman Brothers, Bloomberg Source: Lehman Brothers, Bloomberg
Further examination of relative performance since the end of the smallcap rally reveals that the Russell
2000 has also exhibited disproportionate participation in any market moves to the downside. In
September, the Russell 2000 outperformed the SPX by 18 bps on average when the SPX closed
higher. In contrast, on days when the SPX closed lower, RTY underperformance relative to SPX
averaged about 56 bps.
We believe this is an opportune time to enter the IWM-SPX volatility spread. The spread looks cheaper
over a 1-month horizon than it does further out the curve. Fundamental and seasonal factors argue in
favor of the IWM realizing more volatility relative to the SPX in the short term, than what is currently
implied by the spread.
October 10, 2006 3

4. Equity Derivatives Strategy | Index Volatility Commentary – Smallcap Vols Cheap
Figure 5: Macro Volatility Summary
Cash and Derivatives Volumes
ETF Rich/Cheap Analysis
7.0 2.0
SMH
SOX
6.0
Stock Optn Volume (Mn Contracts)
XLI
NYSE Equity Volume (Bn Shares)
1.5
5.0 OSX
XAU
4.0 XLB
1.0 RTH
3.0 XLY
IBB
2.0
0.5 OIH
Stock Option Volume (SPX Constituents) PPH
1.0
Equity Volume (NYSE) XLE
XLF
0.0 0.0
IYR
eb
ug
29 p
ep
an
17 b
17 ar
pr
un
12 pr
4- l
26 ay
ay
20 n
31 ar
14 r
23 n
18 g
15 p
21 l
u
Ju
a
Fe
Au
Se
e
Ja
Ju
-J
M
-M
-M
-A
-A
-M
-M
BBH
-J
-F
-J
-A
-S
-S
7-
6-
9-
3-
3-
1-
28
Week Ending BKX
XLU
Source: Lehman Brothers, OptionMetrics, Bloomberg
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
Note: Stock option volume is the total volume across all contracts for constituents of the S&P 500. Cheap > > > > > > > > > > > > Rich
For each ETF, we calculate the number of standard deviations by which the current 3-month implied-realized Imp Rel Spread (Std Devs from Mean) Imp SPX Spread (Std Devs from Mean)
volatility spread differs from its 1-year average. We repeat the calculation for the ETF implied vs S&P 500 3-month
implied volatility.
Source: Lehman Brothers, OptionMetrics, Bloomberg
3-month Implied and Realized Correlation (S&P 500) Term Structure of Implied Correlation (SPY)
50% 50%
45%
40%
40%
30%
35%
30%
20%
SPX Implied Correlation (3-month) 25% SPY Implied Correlation
10% SPX Realized Correlation (3-month)
20%
0% 15%
0.0 0.5 1.0 1.5 2.0 2.5
05
6
5
06
06
6
06
06
06
5
6
6
-0
-0
-0
-0
r-0
l-0
v-
n-
b-
n-
g-
p-
ay
ec
ar
ct
Ju
Ap
Years to Maturity
No
Ja
Fe
Ju
Au
Se
O
M
M
D
Source: Lehman Brothers, OptionMetrics, FAME Source: Lehman Brothers, Bloomberg
Source: Lehman Brothers, OptionMetrics, FAME
3-month Implied and Realized Correlation (Nasdaq 100) Term Structure of Implied Correlation (QQQQ)
50% 50%
45%
40%
40%
30% 35%
30%
20%
25%
QQQQ Implied Correlation
10% NDX Implied Correlation (3-month)
NDX Realized Correlation (3-month) 20%
0% 15%
0.0 0.5 1.0 1.5 2.0 2.5
5
06
6
06
6
6
5
05
6
06
06
6
-0
-0
-0
0
r-0
0
l-0
-
c-
n-
b-
n-
g-
p-
ov
ay
ar
ct
Ju
Ap
Years to Maturity
De
Ja
Fe
Ju
Au
Se
O
M
M
N
Source: Lehman Brothers, OptionMetrics, FAME
Note: Implied and realized correlation highlight the relationship between volatility of index options and the volatility of options on constituents within that index. Implied correlation reconciles implied volatility of index
options with constituent implied volatility. Realized correlation is computed from the realized volatilities of the index and its constituents.
Source: Lehman Brothers, OptionMetrics, Bloomberg, FAME
October 10, 2006 4

5. Equity Derivatives Strategy | Index Volatility Commentary – Smallcap Vols Cheap
Figure 6: S&P 500 Index Volatility Summary
S&P 500 Implied and Realized Volatility S&P 500 Weekly Returns vs Vol Changes
20% 4%
3%
2%
15%
1%
0%
10% -1%
-2%
-3%
5%
-4%
5
6
6
6
5
06
6
06
06
5
6
6
-0
-0
0
-0
0
-0
-0
r-0
l-0
n-
b-
n-
g-
p-
ov
ay
ec
ar
ct
Ju
Ap
Ja
Fe
Ju
Au
Se
O
M
6
06
06
6
6
06
06
06
6
6
M
N
D
-0
-0
-0
r-0
l-0
n-
b-
n-
g-
p-
ay
ar
ar
Ju
Ap
Ja
Fe
Ju
Au
Se
M
M
M
SPX Implied Vol (3-month) SPX Realized Vol (3-month)
SPX Implied Vol (1-month) SPX Realized Vol (1-month) SPX Weekly Return SPX Weekly Change in Implied Vol (1m)
Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers, OptionMetrics, Bloomberg
Note: 1-month and 3-month implied volatility are interpolated volatilities for rolling maturities. 3-month realized volatility is calculated as the standard deviation of daily log returns over a 66 trading day historical window. 1-
month realized volatility uses 22 days. Weekly spot returns in the index are compared with weekly changes in 1-month ATM implied volatility.
S&P 500 Put-Call Skew S&P 500 Skew (1-week Changes)
7% 1.0%
6% SPX 30-delta Skew (3-month)
SPX 30-delta Skew (1-month)
5% 0.0%
4%
3%
-1.0%
2%
1%
-2.0%
0%
6
6
7
07
7
08
8
6
-0
-0
-0
-0
-0
-0
n-
n-
ov
ec
ar
ec
c
ct
De
Ju
Ju
O
M
N
D
D
5
06
6
06
6
6
5
5
6
06
06
6
-0
-0
-0
-0
0
r-0
0
l-0
-
n-
b-
n-
g-
p-
ov
ay
ec
ar
ct
SPX 1w Imp Vol Chg (95%) SPX 1w Imp Vol Chg (100%) SPX 1w Imp Vol Chg (105%)
Ju
Ap
Fe
Ja
Ju
Au
Se
O
M
M
N
D
Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers
Note: The 30-delta skew is calculated as the difference between the 30-delta put and 30-delta call implied volatililty. Weekly changes of implied volatility at the 95% and 105% strike versus the at-the-money strike
provide a measure of richening/cheapening of skew.
Term Structure of ATM Implied Volatility (S&P 500) History of S&P 500 Term Spread
18% 3%
17%
2%
16%
15% 1%
14%
0%
13%
12% -1%
11% Last 1-wk Back 1-mo Back SPX 12M-3M Term Spread
-2%
10% SPX 3M-1M Term Spread
9% -3%
6
6
7
07
7
08
8
6
5
06
6
06
6
6
5
5
6
06
06
6
-0
-0
-0
-0
-0
-0
0
-0
-0
-0
0
r-0
0
l-0
n-
n-
-
v-
n-
b-
n-
g-
p-
ar
ov
ec
ec
ec
ct
ay
ec
ar
ct
Ju
Ap
Ju
Ju
No
Ja
Fe
Ju
Au
Se
O
O
M
M
N
D
D
D
M
D
Source: Lehman Brothers
Note: The volatility term structure shows implied volatility for ATM strike options for each listed expiration. The term spread history plots the implied vol difference between 12-month and 3-month options and that
between 3-month and 1-month options for the last 1 year.
Source: Lehman Brothers, OptionMetrics, Bloomberg, FAME
October 10, 2006 5