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. January 10, 2006
Options Strategy Monthly: Low Volatility in the 7th Inning?
Ryan Renicker, CFA Low Volatility Environment Continued in 2005. In 2005, the S&P 500 was largely range-
1.212.526.9425 bound, resulting in the continuation of the nearly 3-year low volatility regime. Although the 12-
ryan.renicker@lehman.com
month minus 3-month term spread remained positive, the Q4 market rally, accompanied by the
Devapriya Mallick substantial decline in short-dated volatility at the end of the year led the term spread higher. This
1.212.526.5429 relatively steep term spread could be a signal that the options market is pricing in higher short-
dmallik@lehman.com
dated implied volatilities during the following year.
Volatility Trading Environment in 2005. Call overwriting continued to be an increasingly
popular strategy. This year, the BXM performed roughly in-line with the S&P 500 Total Return
Index. Systematically selling volatility was a more difficult strategy in 2005, as implied volatility
continued to decline relative to subsequently realized volatility. In October 2005, the CBOE
launched options with weekly expirations on the SPX and OEX. “Weeklys” allow investors to trade
nearer-term volatility more efficiently than traditional option contracts.
Higher Volatility for 2006? We believe both implied and realized volatility for the S&P 500
and single stocks should trade a few volatility points higher in 2006 relative to 2005. Potential
catalysts include credit concerns, an uncertain interest rate outlook, housing market weakness,
volatile energy prices, reversion in the volatility risk premium, and event risks such as the 2006
U.S. Congressional elections, geopolitical concerns, avian flu, etc.
Low Volatility Regime to Continue in 2006? Potential risks to our forecast arise if energy
prices stabilize, consumers’ financial condition improves, strength in employment continues, fears
of interest rate hikes dissipate, and strong EPS figures and/or multiple expansion allows the S&P
500 to break out of its range.
Forecasting Expected Stock Price Moves For Earnings Announcements . We find stocks
exhibit average absolute returns of over 3% following earnings reports and their implied volatility
gradually rises during the weeks leading up to the announcement. The options market tends to
efficiently price in event risks, with higher implied volatility corresponding to stocks that tend to
realize relatively large moves following earnings. This was found to be consistent across sectors since
the first quarter of 2004.
Introducing the Sector Volatility Snapshots. We introduce our Sector Volatility Snapshots,
which allow investors to quickly assess aggregate volatility information for each S&P 500 GICS
sector. The snapshots will be included in each Options Strategy Monthly, and 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 we analyze.
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 30.

2. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning?
Table of Contents
Volatility Overview: 2005 ..........................................................................................3
Low Volatility Environment Continues: Will the Status Quo Persist? ............................................ 3
Implied Volatility Term Spread and Forward Implied Volatility .................................................. 4
Patterns in Implied Volatility Skew....................................................................................... 5
Volatility Trading Environment in 2005 ..........................................................................6
Call Overwriting Strategies ............................................................................................... 6
Volatility Risk Premium Convergence ................................................................................... 6
Dispersion Trading .......................................................................................................... 7
Options with Weekly Expirations (“Weeklys”)....................................................................... 7
Option Volumes Continue to Accelerate, Currently Stand at Record Levels.................................. 8
Volatility Outlook for 2006 .........................................................................................9
Potential Catalysts for Higher Volatility................................................................................. 9
Low Volatility Regime to Continue in 2006?....................................................................... 11
Earnings Impact on Implied and Realized Volatility .........................................................12
Higher Realized Volatility When Earnings Are Reported ....................................................... 12
Elevated Risk Expectations as Earnings Date Approaches...................................................... 13
Expected Stock Price Reaction to Earnings Announcements ................................................... 14
Event Volatility Predicts Announcement Across Sectors .......................................................... 15
Predictability of Earnings Impact by Quarter ....................................................................... 16
Conclusion .................................................................................................................. 16
Appendix I: Forward Implied Volatility and 1-Day Expected Price Move .............................17
Appendix II: Sector Volatility Snapshots .......................................................................19
January 10, 2006 2

3. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning?
Volatility Overview: 2005
Low Volatility Environment Continues: Will the Status Quo Persist?
Throughout the majority of 2005, the S&P 500 Index traded in a relatively tight range, as investors
weighed micro factors such as consistently strong earnings growth, against macro and geopolitical
concerns, such as rising short-term interest rates and historically high energy prices.
These opposing forces tended to partially offset one another, preventing the market from experiencing
a strong move to either the upside or downside. This, in turn, resulted in relatively low implied volatility
for the S&P 500 for most of the year. In addition, S&P 500 90-day realized volatility averaged a mere
10% for the year. Implied volatility, which tends to trade at a premium to realized, averaged slightly
over 12%. In addition, there were three occasions - February, July, and November - when S&P 500
short-dated implied volatility approached 10-year lows.
However, credit concerns among U.S. automotive manufacturers took center stage in April, leading
(briefly) to widening spreads in credit markets. This credit-driven shock – and accompanying market
sell-off – resulted in a temporary spike in short-dated S&P 500 implied volatility, indicating investors
were becoming increasingly concerned that credit deterioration could negatively impact the aggregate
equity market. This fear quickly subsided, however, and implied volatility retreated from its intra-year
high and the S&P 500 rebounded to its multi-year highs.
We observed a relatively brief increase in equity risk expectations in October, as investors braced for
rd
the economic consequences of Hurricanes Katrina and Rita and 3 quarter earnings reports, and
anxiously evaluated the degree to which rising interest rates would impact the domestic economic
environment. However, heading into November, the market rallied before trading relatively sideways
throughout most of December, and implied volatility once again retraced to its multi-year lows.
Figure 1: Key Developments in 2005 and their Impact on the S&P 500 and 3-Month Implied Volatility
18% 1,300
SPX at 3 1/2 Auto Woes Drive Interest Rate Fears
17% Year High Credit Spreads and Weigh on Market, 1,280
Vol. Higher Vols. Spike
16%
Pre Q3 Earnings 1,260
15%
1,240
Implied Volatility
S&P 500 Index
14%
1,220
13%
1,200
12%
1,180
11%
1,160
10%
Im plied Vol. Approaches Lack of Catalysts Heading into
9% 1,140
All-Tim e Low s Year End
8% 1,120
5
05
05
05
05
05
05
5
5
5
05
05
l-0
-0
-0
-0
p-
-
n-
n-
b-
-
g-
r-
ov
ec
ay
ar
ct
Ju
Ja
Ju
Fe
Ap
Se
Au
O
M
N
D
M
S&P 500 Im plied Volatility (3-m onth) S&P 500
Source: Lehman Brothers, OptionMetrics
January 10, 2006 3

4. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning?
Implied Volatility Term Spread and Forward Implied Volatility
The term structure of implied volatility and the forward volatility interpolated from longer-dated options
can provide insights into how short-dated risk expectations are expected to change in the future. The
volatility term spread, measured by the difference between 12-month and 3-month implied volatility,
typically moves in inversely with near-term volatility, since longer-dated implied volatility tends to be
more stable than shorter-dated implied volatility.
In 2005, the 12-month – 3-month term spread bottomed out in April, as investors bid up shorter-term
protection during the market downturn associated with widening auto credit spreads. The term spread
again narrowed in October as the demand for near-term protection accelerated. Heading into year
end, the term spread steepened as near-term catalysts for equity volatility subsided (Figure 2).
Figure 2: 12-Month – 3-Month Term Spread
3.0% 1,300
read
2.5%
1,250
erm Sp
2.0%
dex
1,200
12 M nth - 3 M nth T
S&P 500 In
1.5%
o
1,150
1.0%
o
1,100
0.5% 12M-3M Term Spread
S&P 500 Index
0.0% 1,050
5
05 05 -0
5
-0
5
-0
5 05 l-0
5
-0
5
-0
5
-0
5
-0
n- b- ar pr ay n- ug ep ct ov
Ja Fe M A M Ju Ju A S O N
Source: Lehman Brothers, OptionMetrics
To glean additional information from the term structure, we compare the expected 3-month implied
volatility level, in 9 months’ time, (3-month forward volatility in 9 months) with the current 3-month at-the-
money implied volatility (Figure 3). While 3-month forward volatility has tended to trade in line with
“current” 3-month implied volatility during the past five years (with the exception from mid 2002 to
early 2003), we have recently observed the spread between the two metrics widening throughout
2005. We believe this likely indicates the options market is pricing in expectations for higher short-
dated implied volatility in the months ahead.
Figure 3: 9-Month, 12-Month Forward Implied Vol. vs. 3-Month at-the-money Implied Volatility
40%
9M, 12M Forw ard Implied Vol.
3M Implied Vol.
35%
30%
Forw ard 3-M onth
Vol. 9-M onths From Now
25% High ve rs us Curre nt
3-Month Vol.
20%
15%
10%
1
2
3
4
5
1
2
3
4
5
l-0
l-0
l-0
l-0
l-0
0
0
0
0
0
n-
n-
n-
n-
n-
Ju
Ju
Ju
Ju
Ju
Ja
Ja
Ja
Ja
Ja
Source: Lehman Brothers, OptionMetrics
January 10, 2006 4

5. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning?
Patterns in Implied Volatility Skew
Examining changes in the absolute level of at-the-money implied volatility for short-dated options tends
to be a common means of estimating risk expectations in the market.
However, we believe another useful metric for estimating the degree of market “fear” or
“complacency” is the change in the put–call skew, which, compares the relative levels of out-of-the-
money implied volatility on 20 delta put contracts with that of 20 delta calls.
In Figure 4, we observe two instances when the implied volatility skew experienced rather dramatic
increases – once in mid April, and again in mid October – similar to what was observed for at-the-
money implied volatility levels. A rise in skew implies investors were likely bidding up downside
protection to hedge their existing long portfolios against a possible market downturn.
We observed a decline in the demand for downside protection, and perhaps an increased demand
for upside exposure in the market during the rally from mid May to the middle of June, as evidenced by
the declining put–call skew. A similar trading pattern also occurred during the November rally, as the
demand for downside protection subsided when the market rebounded from its late October lows.
Figure 4: S&P 500 Index 20 Delta Put – Call Skew (3-Month Constant Maturity Implied Volatility)
7.0% 16%
3-Month 20-Delta Put-Call Skew
6.5% 3-month Implied Vol (RHS)
15%
6.0%
14%
5.5%
5.0% 13%
4.5%
12%
4.0%
11%
3.5%
3.0% 10%
05
5
05
05
05
5
05
5
5
5
05
05
l-0
-0
-0
-0
-0
p-
-
n-
n-
b-
g-
r-
ov
ec
ay
ar
ct
Ju
Ja
Ju
Fe
Ap
Se
Au
O
M
N
D
M
Source: Lehman Brothers, OptionMetrics
January 10, 2006 5

6. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning?
Volatility Trading Environment in 2005
Call Overwriting Strategies
Call overwriting has become an increasingly popular strategy during the past few years, as investors
sought to obtain incremental alpha during the largely range-bound markets of recent years. In an
overwrite strategy, an investor holds a long position in a stock or index portfolio and simultaneously
writes at-the-money or out-of-the-money calls against the long position.
According to the Chicago Board Options Exchange (CBOE), more than $13 billion has recently been
allocated by asset managers to buy-write products, many of which are benchmarked to CBOE S&P
500 BuyWrite Index (BXM).
During the last five years, the BXM has not only generated additional yield over the S&P 500 (Figure
5), but also displayed relatively lower standard deviation. Of course, the effectiveness of any
overwriting strategy largely depends on the direction of the underlying portfolio itself1. Thus, overwriters
did not participate in the November market rally, and if going forward the market breaks out of its
range, the popularity of the strategy could decline.
Figure 5: Performance of Passive Call Overwriting (BXM) vs. S&P 500 Total Return Index
120
110
100
90
80
70
60
Market Rallies, BXM Index
Overw riting Underperforms
50 S&P 500 Total Return
40
01
02
03
04
05
0
1
2
3
4
5
-0
-0
-0
-0
-0
-0
n-
n-
n-
n-
n-
ec
ec
ec
ec
ec
ec
Ju
Ju
Ju
Ju
Ju
D
D
D
D
D
D
Source: Lehman Brothers, Bloomberg, OptionMetrics
Volatility Risk Premium Convergence
From a pure volatility trading perspective, the average spread of 3-month at-the-money implied volatility
over the subsequent three months’ realized volatility (ex-post realized volatility) can be a useful measure
to gauge the premium demanded by option sellers for incurring short volatility risk. This spread traded
lower in 2005 than it had in previous years, partly reflecting the growth of strategies that systematically
implement net short volatility positions (such as call overwriting funds).
1
Please see Renicker, R.N. and Mallick D. (2005) Enhanced Call Overwriting, Lehman Brothers, Equity Derivatives
Strategy, (pages 3, 5 and 9) for further details.
January 10, 2006 6

7. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning?
As Figure 6 and Figure 7 demonstrate, the continued compression of the volatility risk premium was
witnessed both in options on the S&P 500 Index as well as on single stock options.
Figure 6: Volatility Risk Premium (SPX Index Options) Figure 7: Average Implied and Realized Volatility (Equity Options)
Average Premium ( 45%
Year 3-month Implied - Weighted Average Implied Vol
40% Weighted Average Realized Vol
Future Realized)
1996 2.93% 35%
Implied Volatility - Ex-Post Realized Volatility
1997 2.21% Dif f erential Approaching Zerio
1998 3.52% 30%
1999 4.89% 25%
2000 -0.61%
2001 2.02% 20%
2002 -1.84% 15%
2003 5.73%
03
04
05
3
4
5
3
4
03
04
05
l-0
l-0
l-0
-0
-0
n-
n-
n-
2004 4.16%
r-
r-
r-
ct
ct
Ju
Ju
Ju
Ja
Ja
Ja
Ap
Ap
Ap
O
O
2005 1.48%
Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers, OptionMetrics
Dispersion Trading
The last twelve months provided a few attractive opportunities for entering into index dispersion trades
in response to periods of elevated implied correlation relative to realized correlation. The implied-
realized correlation spread first peaked in April (Figure 9), as investors demanded a relatively high
degree of systematic protection to hedge their portfolios from market retracements, such as the credit-
driven downturn in the spring. However, there was an opportunity to profitably unwind the position
shortly thereafter, when the equity market rallied into May and market-related anxiety dissipated.
Figure 8: 3-Month Implied and Realized Correlation (S&P 500) Figure 9: Correlation Spread (3-Month) Versus Index Level
45 20 1300
Possible
Entry Points
40 15
1250
S&P 500 Index Level
35 10
Correlation Spread
1200
Correlation
30 5
1150
25 0
1100
20 -5 Possible
Implied Correlation (3m) Implied Realized Correlation Spread Exit Points
Realized Correlation (66d) S&P 500 Index (RHS)
15 -10 1050
5
5
5
5
5
5
5
5
05
05
5
5
5
5
5
05
5
5
05
05
5
05
5
5
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
l-0
-0
-0
l-0
-0
-0
b-
b-
n-
n-
n-
n-
ay
ay
ar
ug
ar
pr
ug
ov
pr
ct
ep
ov
ct
ep
ec
ec
Ju
Ju
Ja
Ju
Fe
Ja
Ju
Fe
O
O
M
M
A
M
A
M
N
N
A
A
D
D
S
S
Source: Lehman Brothers Source: Lehman Brothers, Bloomberg
There were several other opportunities to enter dispersion trades between August and October, again
driven by elevated systematic anxiety resulting from the uncertain interest rate outlook. However, as the
market recovered in November, reduced demand for market level protection provided an attractive exit
point for dispersion trades, as implied correlation again retreated to levels below what had been
realized.
Options with Weekly Expirations (“Weeklys”)
In October 2005, the CBOE launched index options with weekly expirations on the SPX and the OEX.
Weeklys have similar contract specifications as other options on their respective underlying indexes.
However, they are listed each Friday and expire the following Friday. No Weeklys are listed on the
January 10, 2006 7

8. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning?
Friday before the expiration for standard options. Weekly options on the SPX are European-style with
AM settlement, while those on the OEX are American-style, with PM settlement.
In our opinion, Weeklys allow investors to more efficiently trade nearer-term volatility than traditional
option contracts. Weeklys can provide additional flexibility if one wishes to express directional views
on stocks or indices immediately prior to an upcoming catalyst.
Figure 10: Average Daily Volumes in Weekly Options
SPX Weekly Options Average Daily Volume
Volume in Volume in Standard % Volume in
Weeklys Options Weeklys
November 1,459 344,295 0.42%
December 2,301 278,543 0.83%
OEX Weekly Options Average Daily Volume
Volume in Volume in Standard % Volume in
Weeklys Options Weeklys
November 2,220 69,404 3.20%
December 2,397 52,090 4.60%
Source: CBOE
While the average volume in Weeklys (Figure 10) currently represents a relatively small proportion of
the total volume on standard option contracts (less than 1% market share for S&P 500 index options;
less than 5% market share for S&P 100 options), their popularity might increase in the coming year.
Option Volumes Continue to Accelerate, Currently Stand at Record Levels
In 2005, the use of options as speculative investment vehicles or hedging instruments increased in
popularity as the volume of total option contracts traded, as well as open interest, continued to exhibit
remarkable growth. In fact, as Figure 11 illustrates, the total number of contracts traded on all U.S.
options exchanges (including both calls and puts) increased from 392 million in 2003 to roughly 683
million contracts during 2005, a nearly 75% increase.
Figure 11: Total Monthly Volume for Options on S&P 500 Stocks Versus S&P 500 Constituent Share Volume
80
Total Contracts Traded (Mn)
Option Trading Volume
70 Aggregate Stock Volume (Bn Shares)
has Accelerated
Monthly Trading Volume
60 Stock Trading Volume
has been Rather Muted
50 Average Monthly Average Year End
Contract Volume (MM) Open Interest (MM)
40
30
2003 33 59
2004 44 84
20
2005 57 101
10
0
03
04
05
3
4
5
3
4
5
-0
-0
-0
-0
-0
-0
n-
n-
n-
ay
ay
ay
p
p
p
Ja
Ja
Ja
Se
Se
Se
M
M
M
Source: Lehman Brothers, OptionMetrics
In addition, the total open interest of option contracts at the end of the year increased from roughly 59
million contracts in 2003 to about 101 million at 2005 end, a nearly 72% increase. On the other
hand, total trading volume in shares of S&P 500 constituents generally remained flat over the same
period.
January 10, 2006 8

9. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning?
Volatility Outlook for 2006
Potential Catalysts for Higher Volatility
Below we highlight several potential catalysts could lead to higher equity market volatility for the year
ahead.
Credit Concerns
Although credit spreads have tightened since their recent peak in April 2005, Lehman Brothers Credit
Strategists are forecasting a widening of investment grade spreads by about 10 bps in 2006 on the
back of lingering uncertainty over auto credit and increased LBO activity for the overall market2.
Historically, credit spreads and equity volatility tend to display a positive relationship, since both are
viewed as risk metrics for an underlying security (Figure 12).
Figure 12: High-Grade Credit Spreads vs. Implied Volatility Figure 13: High-Yield Credit Spreads vs. Implied Volatility
50% 3.0 50% 11.0
VIX Index
45% 45% 10.0
US Credit Index OAS (RHS) 9.0
40% 40%
US High Yield Index OAS (%
US Credit Index OAS (%)
35% 8.0
35%
2.0
7.0
30% 30%
VIX Index
VIX Index 6.0
25% 25%
5.0
20% 20%
4.0
1.0
15% 15%
3.0
10% 10% 2.0
VIX Index
5% 5% 1.0
US High Yield Index OAS (RHS)
0% 0.0 0% 0.0
00
01
02
03
04
05
1
2
3
4
5
0
01
02
03
04
05
1
02
3
04
5
-0
-0
-0
-0
-0
0
-0
-0
-0
g-
g-
g-
g-
g-
g-
g-
g-
b-
g-
g-
b-
g-
g-
b
b
b
b
b
b
b
b
Au
Au
Au
Au
Au
Au
Au
Au
Au
Au
Au
Au
Fe
Fe
Fe
Fe
Fe
Fe
Fe
Fe
Fe
Fe
Source: Lehman Brothers, Bloomberg Source: Lehman Brothers, Bloomberg
This relationship has been weaker heading into year end, as credit spreads have continued to widen,
whereas equity implied volatility has drifted lower. To the extent credit spread widening is driven by
company-specific default concerns and event risks, as opposed to shareholder-friendly actions by
management (share buybacks, special dividends etc), it could be a factor supporting the case for
higher equity implied volatility in the year ahead.
Interest Rate Outlook
Historically, the onset of a monetary tightening cycle has been a precursor to elevated equity volatility.
However, during the most recent tightening cycle, the Fed has induced relatively low uncertainty by
consistently raising interest rates at a “measured pace”. As the end of the rate hikes approaches, there
is lack of consensus about the future direction of monetary policy and its ultimate impact on the
economic climate.
Furthermore, the recent yield curve inversion (measured by the 10-year minus 2-year treasury yield
differential) which occurred at the end of 2005, might lead investors to seek greater protection from a
possible economic downturn, since inverted yield curves have historically tended to forecast recessions.
Although the two most recent instances of yield curve inversion (1998 and 2000) coincided with rising
2
Please see “2006 Credit Outlook: Shifting Gears”, Lehman Brothers U.S. Credit Strategy, December 19, 2005 for
further details.
January 10, 2006 9