1) Realized volatility of the S&P 500 over the past 10 days was around 6%, but the average daily trading range was similar to June/July, indicating greater uncertainty than realized volatility captures. 2) Looking at median monthly realized volatility since 1946, August volatility has typically been in line with other months, weakening the case for an expected "summer volatility crush". 3) The author believes upcoming macroeconomic data releases could increase volatility from the low levels of the past few summers. They recommend purchasing hedged S&P 500 options expiring in September, which recently cheapened more than other maturities.

1. August 15, 2006
Index Volatility Commentary
Ryan Renicker, CFA
1.212.526.9425 • S&P 500 realized volatility for the 10 trading days in August looks fairly low at about 6%; yet the
ryan.renicker@lehman.com average daily high-low range is of the same order as in June/July. This indicates market
Devapriya Mallick
uncertainty is greater than what is captured by the realized volatility calculation.
1.212.526.5429
dmallik@lehman.com
• Since the end of World War II, median monthly realized volatility for August has been in line with
other months, weakening the case for a “summer vol crush”.
• We believe the presence of macroeconomic catalysts could make the late summer more volatile
than the last few years.
• S&P options expiring in September cheapened about 1 vol pt last week, more than any other
maturity. We recommend investors purchase these on a hedged basis to get cheap gamma
exposure.
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
Not Quite a Vol Crush
For the first 10 trading days of August, S&P 500 realized volatility at about 6% looks extremely low.
However, the average daily high-low range in which the S&P 500 has traded – measured as a % of
the day’s close – stands at 1%, which is close to the average for June and July (Figure 1).
This has two important implications for gamma traders:
• Implied vs realized spreads based on very short term realized volatility calculations are likely
to look richer than they really are.
• For long gamma investors, delta-hedging from close to close would have been a suboptimal
strategy over the last 10 days.
We take a closer look at the seasonality of realized volatility over the 60-year post World War II
period from 1946 to 2005. To lessen the effect of outliers, we consider the median for each month
over this period.
• We find that October has tended to be the most volatile month while December has been the
most range-bound.
• S&P 500 realized vol in the summer months has been in line with that of other months (Figure
2), even though August has been a relatively uneventful month over the last 3 years.
This would mitigate the argument for a short gamma positioning at this stage in anticipation of a
“summer vol crush”.
Figure 1: Realized Vol Looks Low Though Uncertainty Persists Figure 2: Seasonality Does Not Justify Selling Gamma
18% 1.4% 13%
Monthly Realized Vol (lhs)
16% Avg Daily High-Low Range (% of Close) (rhs) Median Monthly Realized
1.2%
Vol (1946-2005)
14%
1.0% 12%
12%
10% 0.8%
11%
8% 0.6%
6%
0.4%
4% 10%
0.2%
2%
0% 0.0% 9%
6
06
6
06
b
l
06
6
ar
n
n
v
c
p
ay
06
ct
6
r
Ju
g
l-0
-0
Fe
Ap
No
De
-0
Ja
Ju
Se
r-0
Au
M
O
n-
n-
b-
M
g-
ay
ar
Ju
Ja
Ju
Fe
Ap
Au
M
M
Source: Lehman Brothers, Bloomberg Source: Lehman Brothers, Bloomberg
August 15, 2006 2

3. Equity Derivatives Strategy | Index Volatility Commentary
Economic Releases Continue to be Important
The noteworthy macroeconomic event last week was Tuesday’s Fed pause after 17 consecutive hiking
decisions since June 2004. Investors had been waiting on the sidelines in anticipation of the decision
– last Monday’s NYSE volume was the least in almost a month – and the market rallied about 5
handles following the FOMC meeting, only to reverse within minutes.
We examine select economic releases within the last two months to quantify the immediate market
reaction to each of these (Figure 3). Given concerns about mounting inflation risks, CPI releases have
been relatively important catalysts. For instance, within the first 30 minutes of trading after the July CPI
release, the S&P 500 had moved 1% from its previous close.
Figure 3: Market Reaction to Select Economic Catalysts
SPX Return SPX Return VIX Change VIX Change
Date Time Macro Catalyst
(first 30 mins) (first 60 mins) (first 30 mins) (first 60 mins)
13-Jun 8:30 PPI 0.2% 0.0% -0.4 0.3
14-Jun 8:30 CPI 0.5% 0.5% -0.8 -1.2
29-Jun 14:15 FOMC Meeting 0.8% 1.1% -2.7 -3.4
7-Jul 8:30 Non Farm Payrolls -0.3% -0.1% 0.3 0.1
18-Jul 8:30 PPI 0.3% 0.1% -0.7 -0.4
19-Jul 8:30 CPI 1.0% 1.1% -2.1 -2.5
20-Jul 14:00 FOMC Minutes -0.4% -0.4% 0.4 0.5
28-Jul 8:30 Q2 GDP 0.7% 0.4% -0.8 -0.6
4-Aug 8:30 Non Farm Payrolls 0.6% 0.6% -0.8 -0.7
8-Aug 14:15 FOMC Meeting -0.3% -0.6% 0.0 -0.1
Source: Lehman Brothers, Bloomberg
The economic calendar for this week includes PPI data on Tuesday and CPI on Wednesday. We
expect inflation numbers to continue to be significant drivers of market volatility.
In this backdrop, we view the 1 vol pt cheapening over the last week in SPX Sep options as
unwarranted. ATM implied vol in the Sep line is trading at around 12.8% and has dropped more than
any other maturity. We recommend investors purchase hedged options maturing in September to get
cheap exposure to potential future gamma.
August 15, 2006 3

4. Equity Derivatives Strategy | Index Volatility Commentary
Figure 4: Macro Volatility Summary
S&P 500 Implied and Realized Volatility
20% ETF Rich/Cheap Analysis
SMH
15% SOX
XLB
10% IBB
OIH
5% SPX Implied Vol (3-month)
OSX
SPX Realized Vol (3-month)
XLI
0%
XAU
5
6
05
05
5
06
06
6
06
5
6
6
-0
-0
-0
-0
-0
r-0
l-0
g-
p-
n-
b-
n-
BKX
ov
ay
ec
ar
ct
Ju
Ap
Au
Se
Ja
Fe
Ju
O
M
M
N
D
XLY
Implied Volatility History (NDX, RTY)
30% IYR
XLF
25%
RTH
20%
PPH
15%
XLE
10%
NDX Implied Vol (3-month)
XLU
RTY Implied Vol (3-month)
5%
BBH
0%
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
05
6
05
05
5
06
06
6
06
5
6
6
Cheap > > > > > > > > > > > > Rich
-0
-0
-0
-0
r-0
l-0
v-
g-
p-
n-
b-
n-
ay
ec
ar
ct
Ju
Ap
No
Au
Se
Ja
Fe
Ju
O
M
M
D
Imp Rel Spread (Std Devs from Mean) Imp SPX Spread (Std Devs from Mean)
S&P 500 Put-Call Skew S&P 500 Skew (1-week Changes)
12% 6.0%
5.0% SPX 1-wk Implied Vol Change (90% Strike)
10% SPX 1-wk Implied Vol Change (100% Strike)
SPX 20-delta Skew (3-month) 4.0% SPX 1-wk Implied Vol Change (110% Strike)
SPX 20-delta Skew (1-month)
8% 3.0%
6% 2.0%
1.0%
4%
0.0%
2% -1.0%
0% -2.0%
06
06
6
7
07
7
08
8
6
5
06
05
05
5
6
06
6
6
5
6
6
-0
-0
-0
-0
-0
-0
-0
-0
-0
0
r-0
0
l-0
g-
p-
n-
n-
c
ar
ec
ec
ct
-
g-
p-
n-
b-
n-
ov
ay
ec
ar
ct
De
Au
Se
Ju
Ju
Ju
Ap
O
M
Ja
Fe
Ju
Au
Se
D
D
O
M
M
N
D
Term Structure of Implied Volatility (S&P 500) 3-month Implied and Realized Correlation (S&P 500)
16% 50%
40%
15%
30%
14%
20%
SPX ATM Implied Vol (Aug-14)
SPX Implied Correlation (3-month)
13% SPX ATM Implied Vol (Aug-07) 10% SPX Realized Correlation (3-month)
12% 0%
5
6
05
05
5
06
06
6
06
5
6
6
7
7
8
06
06
6
6
7
8
-0
-0
-0
-0
-0
r-0
l-0
-0
-0
0
-0
0
-0
-0
g-
p-
n-
b-
n-
g-
p-
n-
n-
ov
ay
ec
ar
ct
Ju
ar
ec
ec
ec
ct
Ap
Fe
Au
Se
Ja
Ju
O
Ju
Ju
Au
Se
M
M
N
D
O
M
D
D
D
Source: Lehman Brothers, OptionMetrics, Bloomberg, FAME
August 15, 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
in this email.
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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
recommendations or views expressed in this research report.
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August 15, 2006 5