Options Strategy Monthly - 2006 - Low Volatility in the 7th Inning? Housing Market, Credit Markets Say "NO"!
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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 ...

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

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Options Strategy Monthly - 2006 - Low Volatility in the 7th Inning? Housing Market, Credit Markets Say "NO"! Document Transcript

  • 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 ofinterest 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 SSource: 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 MSource: 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 FeSource: 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
  • 10. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning? equity volatility (Figure 14), it should be noted that a portion of the elevated volatility in these instances was driven by macroeconomic factors such as the Russian crisis in 1998 and the domestic stock market bubble in 1999 and 2000.Figure 14: Equity Volatility Following Yield Curve Inversions 1998 2000 0.7% 50 0.4% 40 0.6% 10yr-2yr Yield 0.3% 10yr-2yr Yield VIX Index (RHS) 0.2% VIX Index (RHS) 0.5% 40 0.1% 10yr-2yr Spread 10yr-2yr Spread 0.4% 30 0.0% VIX Index VIX Index 0.3% 30 -0.1% 0.2% -0.2% 0.1% 20 -0.3% 0.0% 20 -0.4% -0.1% -0.5% -0.2% 10 -0.6% 10 8 8 0 98 8 8 8 8 98 98 0 00 0 98 0 0 0 7 98 00 00 0 00 0 -9 -9 -0 r-9 -9 -0 -9 r-0 -0 l-9 -0 -0 l-0 -9 -0 b- g- n- n- g- p- n- n- ay p- ar ay ar ct ov ct ov b ec ec Ju Ap Ju Ap Au Ja Ju Au Fe Se Ja Ju Fe Se O M O M M M N N D DSource: Lehman Brothers, Bloomberg Housing Market Weakness Strength in the domestic housing market has in large part supported consumption expenditure, with increasing levels of home equity extraction by home owners. Lehman Brothers economists forecast a cooling off in the housing market, with home prices remaining flat nationally and decreasing about 10% in nearly one third of the real estate market over 20063. A potential negative impact on economic growth could flow through to the stock market and cause options market participants to bid up implied volatility. Energy Prices Although crude oil prices declined after their post-Katrina peak of nearly $70 per barrel, and fell to about $56 in mid-November, they have since rallied back above $60 at year end. While the economy has proven more resilient to this oil shock relative to expectations and consumer sentiment has not suffered significantly, persistently higher energy prices and their pass-through effects to core inflation and discretionary spending could factor in negatively toward the economy and corporate valuations. Volatility Risk We highlighted above how the ongoing systematic sale of volatility has been a less profitable strategy in 2005 than it had been in prior years. If realized volatility increases in 2006, the premium for taking on volatility risk could revert from its current lows and implied volatility would likely rise. Event Risks In addition to the factors above, several near-term events could serve as catalysts for heightened equity risk expectations and, thus, higher implied volatility for U.S. equity markets. These include another active hurricane season, uncertainty surrounding the outcome of the 2006 U.S. Congressional midterm elections, geopolitical concerns, avian flu, etc. 3 Please see “Outlook 2006: Plain Sailing – For Now”, Lehman Brothers Global Economics, December 12, 2005 for additional details. January 10, 2006 10
  • 11. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning? Low Volatility Regime to Continue in 2006? Of course, there are several factors that could enable the current low volatility regime to persist into 2006. For example, if energy prices indeed stabilize or even trend downward - consumers’ financial condition and disposable income would likely improve aggregate sales figures and employment, which combined with the possible strength in corporate earnings, could result in lower risk expectations for the U.S. economy and the equity market in general. If anxiety surrounding a prolonged period of interest rate hikes dissipates, the current low implied volatility regime might remain intact. Lehman’s Equity Strategy team has a 12-month price target of 1400 for the S&P 500, driven by expectations of a benign macroeconomic environment and more than $900 billion to be returned to investors in the form of cash. The 1400 price target implies a 12% gain in the S&P 500 Index for 2006. In addition, the strategy team anticipates multiple expansion in 2006, which would support equity market appreciation. Such a scenario would likely lead to a muted volatility environment.4 On balance however, it is our belief that the catalysts in favor of higher equity market volatility are likely to overweigh the events that would favor a continuation of the current low-volatility regime which began in earnest in the spring of 2003. Thus, we believe both implied and realized volatility for the equity market should trade, on average, a few points higher in 2006 versus 2005. 4 Please see “2006 – A Positive Year for the S&P 500”, Lehman Brothers U.S. Strategy, December 12, 2005 for further details. January 10, 2006 11
  • 12. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning? Earnings Impact on Implied and Realized Volatility Participants in volatility markets tend to focus on earnings events as significant catalysts for realized as well as implied volatility. In this study we explore volatility changes on and around earnings dates and discuss how investors can position themselves for these changes using option strategies. Higher Realized Volatility When Earnings Are Reported Since earnings day can be a potentially significant event for a company’s merits as an investment candidate, on average one would expect stocks to display a relatively higher degree of price variability when earnings figures are released than on other days. To test this hypothesis, we compare the distribution of close-to-close share price returns immediately following earnings announcements with the return distribution for other days. Our universe includes the constituents of the S&P 500 Index over the last two years. Our sample period begins in January 2004 and ends in December 2005. We analyze press releases for each company in the S&P 500 on each quarterly earnings announcement for the past 8 quarters to determine the exact earnings report date and, more importantly, the release time. Thus, if a firm reported before the open or intra-day, the price impact was calculated using stock prices from the close of the day prior to the earnings report date to the close of trading on the earnings report date itself. On the other hand, if a company reported earnings after the close, we calculate the stock’s earnings reaction as the return from the close on the report date to the close of trading the on the following day. As Figure 15 and Figure 16 illustrate, stock prices do, indeed, tend to exhibit relatively larger price moves following earnings announcements than they typically do on non-earnings-report days. The return distribution on earnings days has a relatively high standard deviation and lower predictability, along with the appearance of “fat tails” (Figure 15). On the other hand, stocks’ return distribution on non-earnings days tends to resemble a normal distribution, which has a relatively high concentration of returns centered at zero and a lack of fat tails.Figure 15: 1-Day Return Distribution on Earnings Report Dates Figure 16: 1-Day Return Distribution on Non-Earnings Report Dates 40 5,000 4,000 30 3,000 20 2,000 10 1,000 0 0 0% 1% 2% 3% 4% % % % % % 0% 1% 2% 3% 4% % % % % % -5 -4 -3 -2 -1 -5 -4 -3 -2 -1Source: Lehman Brothers, Bloomberg Source: Lehman Brothers, Bloomberg This observation is also apparent in Figure 17, which plots the equal-weighted-average absolute 1-day price return for each constituent in the S&P 500 Index, before and after each earnings event included in our study. While stocks tend to move roughly 1% up or down on an average day, the magnitude of the change immediately following an earnings release is greater than 3%. January 10, 2006 12
  • 13. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning? Figure 17: Absolute 1-Day Price Returns Around Earnings 3.5% 1-Day Re turn s pike s Avg Absolute 1-day Return 3.0% afte r earnings announce m ent Day t corre sponds to first 2.5% day after e arnings announcem e nt 2.0% 1.5% 1.0% 0.5% 0.0% 10 15 20 5 0 5 0 t-5 t t+ t-2 t-1 t-1 t+ t+ t+ Source: Source: Lehman Brothers, Bloomberg Note: “t” represents the day when the market reacts to an earnings announcement. “t-2” is two days prior to the event, “t+2” is two days following the earnings reaction, and so on. It is also interesting to note that there tends to be excess movement in stocks on the day after companies have reported earnings. We find that on the day after the initial reaction, stocks move about 1.5% in either direction. The magnitude of absolute price moves should be of interest to investors who have taken long gamma positions ahead of the earnings event, and would hope to realize a high level of 1-day volatility to compensate them for the theta decay. Elevated Risk Expectations as Earnings Date Approaches As an earnings date approaches, investors express their views on the expected price move in stocks by trading near-month contracts. Hence, we would expect short-term implied volatility to rise ahead of earnings. In Figure 18, we illustrate how one-month implied volatility5 changes as an earnings announcement approaches. We find that option market participants tend to bid up implied volatility more than two weeks ahead of the report date. However, after the event passes the option’s implied volatility declines, and then tends to stabilize at relatively low levels. Figure 18: 1-month Implied Volatility Leading up to, and Following Earnings Announcements 29% Im plieds drop sharply 28% once catalyst has Im plied Volatility picks passed 27% Avg Implied Vol up steadily as earnings 26% approaches 25% 24% 23% Average Implied Vol 22% 10 15 20 5 0 5 0 t t- 5 t+ t- 2 t- 1 t- 1 t+ t+ t+ Working Days Source: Lehman Brothers, Bloomberg, OptionMetrics 5 For ease of calculation, we use the one-month constant-maturity implied volatility instead of the implied volatility corresponding to the traded constant-expiration contract. As the earnings date approaches, the increase in one-month implied volatility tends to be less than the increase in the volatility of the front-month contract. Thus, the change in one- month implied volatility likely understates the actual change experienced by investors through their contracts. January 10, 2006 13
  • 14. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning? Since implied volatility tends to drift higher prior to earnings announcements, and the underlying stocks generally do not realize abnormally high volatility (except following the announcement), one possible way for investors to position for this would be to purchase ratio calendar spreads with net zero gamma and a positive vega. This position involves selling one shorter-dated option and buying a larger number of longer-dated options, and would benefit from a rise in implied volatility for the longer-dated option. Since the trade is constructed gamma neutral, it should remain relatively immune to changes in realized volatility, particularly if it is unwound shortly prior to the earnings date. On the day prior to the earnings release, a potentially profitable strategy could be to sell delta-hedged calendar spreads with net positive gamma and negative vega exposure, and unwind the position two days later. This trade would benefit from the abnormally high volatility realized owing to the event (long gamma), and from the reversion in implied volatility once the catalyst has passed (short vega). Investors should note that the volatility patterns above are merely averages of a large sample of stocks, and idiosyncratic factors should be taken into account prior to initiating trades such as these. In addition, the success of the trade also depends on the relative impact of changing implied volatility on the two contracts having different maturities. Moreover, the expected profit potential can be negatively impacted by the options’ bid/ask spreads. Expected Stock Price Reaction to Earnings Announcements Having compared changes in implied and realized volatility leading up to an earnings event, we now discuss the earnings-related change in the one-day price move implied by the options market. As earnings season approaches, a stock’s front-month implied volatility tends to be higher than longer dated implied volatility. We can infer from this that the option market anticipates a potentially larger price move following the earnings announcement than what the stock typically realizes. (In this example, the expiration dates for both options fall after the next earnings date). We extract an option’s forward volatility from the 1-month and 2-month implied volatilities and use it to estimate of the “fair value” of non-event implied volatility. The 1-month volatility is considered to be comprised of the fair value volatility and an event volatility component. Once the embedded 1-day event volatility has been calculated, we can use it to estimate the expected value of the stock’s absolute return priced in by options market. Please see Appendix I: Forward Implied Volatility and 1-Day Expected Price Move. In Figure 19, we examine how the 1-day event volatility behaves, on average, as an earnings date approaches. As the diagram illustrates, option market participants tend to begin pricing in a higher price move about two weeks prior to the event date. The 1-day forward volatility estimation steadily increases to its peak immediately prior to the earnings announcement. This pattern is similar to how one-month implied volatility changes ahead of earnings events. Figure 19: Average Change in Options’ Implied 1-Day “Event Volatility” Ahead of Earnings 5% Market prices in highest 4% 1-day event volatility on earnings date Avg Implied Vol 3% 2% 1% Avg 1-Day Event Vol 0% 0 5 0 t-5 t t- 2 t- 1 t- 1 Working Days Source: Lehman Brothers, Bloomberg, OptionMetrics January 10, 2006 14
  • 15. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning? Next, we empirically examine the effectiveness of using event volatilities by plotting the 1-day event volatility implied by the options market against the actual price move realized following the earnings announcement. If options markets are indeed efficient, one would expect stocks that have historically exhibited relatively large reactions to earnings announcements and other potentially significant catalysts would exhibit high 1-day event volatility as well. On the other hand, one would expect stocks that have historically had relatively muted reactions to earnings announcements and other events are likely to have low 1-day event volatility. In Figure 20, we empirically demonstrate that this hypothesis appears to be validated. The 1-day price move immediately following earnings announcement tends to be higher in cases when options market participants were implying a relatively high degree of 1-day event volatility ahead of earnings. Likewise, stocks that tend to exhibit minimal impact due to earnings announcements have had a relatively low degree of 1-day event volatility priced into their options immediately prior to the earnings report. Figure 20: 1-Day Event Volatility Versus Absolute Return on Earnings 10% 9% Absolute Price Move on Earnings 8% Absolute Return on Earnings 7% 6% 5% 4% 3% 2% 1% 0% % % % % 1% 2% 3% 4% 5% 6% 7% 8% 9% 10 11 12 13 1-Day Event Volatility Source: Lehman Brothers, Bloomberg, OptionMetrics Thus, identifying instances when event volatility is incorrectly priced would require one to analyze the behavior of a specific security during its earnings announcement period. This illustrates the difficulty in constructing systematically-based strategies by buying or selling a portfolio of options prior to earnings season. Several idiosyncratic variables, such as a stock’s implied volatility surface, existence or lack of recent earnings pre-announcements, as well as atypical fundamental catalysts highlight the need to examine event volatility estimates on a case-by-case basis. Event Volatility Predicts Announcement Across Sectors In Figure 21, we find that the volatility market’s prediction of a company’s expected absolute price move ahead of an event is relatively reliable, regardless of the sector to which the stock belongs. We find that stocks in the Information Technology, Consumer Discretionary and Industrials sectors tend to exhibit the largest returns (positive or negative) on their earnings announcement date. For these sectors, investors also price in the highest expected moves before the event. On the other hand, Telecommunication Services, Utilities, and Financials tend to exhibit relatively mild reactions to earnings events, and have lower event volatility priced in on average, ahead of their announcements. January 10, 2006 15
  • 16. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning?Figure 21: Predictability of Earnings Impact Across GICS Sector Avg 1-Day Event Absolute Return on 7% Sector Volatility EarningsInformation Technology 6.29% 5.12% 6% Absolute Return on EarningsConsumer Discretionary 4.54% 3.23% 5% InformationIndustrials 3.40% 3.15% TechnologyHealth Care 4.29% 3.10% 4% Consumer Industrials DiscretionaryConsumer Staples 2.84% 2.73% 3% Consumer Staples Health CareMaterials 3.76% 2.51% MaterialsEnergy 3.46% 2.05% 2% Financials Energy UtilitiesFinancials 2.55% 2.04% Telecommunication 1%Utilities 2.77% 1.61% ServicesTelecommunication Services 2.90% 1.49% 0% 0% 1% 2% 3% 4% 5% 6% 7% 1-Day Im plied Event VolatilitySource: Lehman Brothers, Bloomberg, OptionMetrics Predictability of Earnings Impact by Quarter The option market does not appear to price in event risk across quarters in as uniform a manner (Figure 22). While changes in realized and implied volatility in response to Q4 earnings tended be lower than in other quarters, earnings announcements during the Q3 earnings season tend to price in the highest level of event risk. The stock price reaction to Q2 earnings, on the other hand, was the greatest across quarters, even though option market participants likely anticipated lower risk expectations in response to Q2 earnings relative to the Q3 earnings season. Figure 22: Predictability of Earnings Impact by Quarter Avg 1-Day Event Absolute Return on Quarter Volatility Annoucement Q1 3.90% 3.21% Q2 3.92% 3.44% Q3 4.48% 2.99% Q4 3.85% 2.84% Source: Lehman Brothers, Bloomberg, OptionMetrics Conclusion We examined how implied and realized volatility change heading into earnings announcements for constituents within the S&P 500 during the eight quarters since Q1 2004. While stocks tend to exhibit average absolute returns of over 3% following earnings announcements, their average price moves in the days leading up to the announcement were not significantly different from what they exhibited during periods void of significant catalysts. On the other hand, stocks’ implied volatility tends to exhibit a gradual rise during the week or two leading up to a company’s earnings announcement date. In addition, we found that options tend to display significantly lower implied volatility following earnings announcements. We observed a similar pattern for the 1-day price move implied by the options market. We also found investors tend to effectively price in earnings event risk, as stocks that have tended to experience sharp price moves following prior earnings announcements tended to display relatively high earnings-specific implied volatility estimates. On the other hand, firms that typically incur relatively minor stock price reactions following earnings announcements generally display relatively low earnings-driven implied volatility expectations heading in to their announcements. Our study found that these relationships tend to be consistent across all sectors since Q1 2004. January 10, 2006 16
  • 17. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning? Appendix I: Forward Implied Volatility and 1-Day Expected Price Move We describe the methodology used for calculating an option’s forward volatility and the corresponding expected price move on its earnings announcement day. Theoretically, investors should price in the same event volatility using options having 1-month or 2-month expiration terms. However, the 1-month forward volatility between the first month and second month expirations6 does not include the embedded “earnings event risk”, and can be used to estimate the “fair value”, or non-event volatility (Figure 23). Note that the 1-month forward volatility in 1 month’s time following the earnings announcement is only one possible estimate of base volatility and choosing an alternate metric would likely result in a different estimate of the expected stock price move. In addition, investors should consider stock-specific characteristics, and other potentially non-earnings-related catalysts during an options term, prior to selecting the term used to calculate the option’s base volatility. Figure 23: Calculation of Forward Implied Volatility Earnings Announcement One Month Two Month Maturity Maturity One Month Implied Volatility (IV1m), T1 Two Month Implied Volatility (IV2m), T2 Forward Implied Volatility (IVf) Source: Lehman Brothers Formally, using the fact that variances are additive, Variance1m + Varianceforward = Variance2m, or 2 2 2 (IV1m) * T1 + (IVf) * (T2-T1) = (IV2m) * T2, where IV1m, IV2m and IVf are respectively the 1-month, 2-month and forward volatilities. T1 and T2 are the number of days to the 1-month and 2-month maturities respectively. Using the forward volatility as a base volatility and decomposing the 1-month variance into a base variance and an additional variance on account of the event, 2 2 2 (IVf) * (T1-1) + (IVevent) * 1 = (IV1m) * T1, where IVevent is the annualized event volatility. The annualized volatility is converted to a 1-day event volatility for estimating the absolute value of the expected stock price movement. 6 The constant-maturity implied volatilities we consider do not correspond to an actual expiration on a traded contract. However, the process for calculating forward volatility would be similar when using implied volatility with constant expiration dates. January 10, 2006 17
  • 18. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning? Assuming stock returns are normally distributed, the expected absolute return can be described by a half-normal distribution, which is similar to a normal distribution, although the negative half of the density function is overlapped onto the positive half (Figure 25).Figure 24: Theoretical Distribution of Price Returns (Normal) Figure 25: Theoretical Distribution of Absolute Returns (Half-Normal) 1.0 1.0 0.8 0.8 Probability Density Probability Density 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 Standard Deviations Standard DeviationsSource: Lehman Brothers Source: Lehman Brothers Hence, the probability density function of a half-normal distribution is,  − x2  2 1  2  P(x) = exp   , for x >= 0 π IV1− day  (IV1− day ) 2    where x is the absolute 1-day return and IV1-day is the event implied 1-day volatility. The expected value of this distribution is, ∞  − x2  2 1  2 dx E(x) = π IV1−day ∫ x exp (IV1−day )2    0    − x2   2  , we have − (IV1−day ) exp 2  (IV1−day )  Since the quantity within the integral is the differential of 2    0  − x2  2 1  2  * (IV1−day ) exp 2  (IV1−day )  E(x) = 2  π IV1−day  ∞ Therefore, the expected absolute 1-day return implied by the market is 2 E(absolute 1-day return) = IV1−day π January 10, 2006 18
  • 19. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning? Appendix II: Sector Volatility Snapshots In this section, we introduce our Sector Volatility Snapshots. These snapshots allow investors to quickly assess aggregate volatility information for each GICS sector in the S&P 500 Index. The average volatility (implied or realized) for a GICS sector is calculated as the weighted- average- volatility of each of their respective index constituents, weighted by market capitalization. The weighted-average volatility for a GICS industry group is obtained similarly. ETFs having options are mapped to one GICS sector each, although the mapping is not perfect since stocks in an ETF could be classified into multiple sectors as per the GICS sector classification methodology. However, they closely reflect the performance and volatility characteristics of the sectors and industries they represent. • We display the weighted-average implied and realized volatility at the sector level for a one year period. For each industry group within the sector and each ETF that closely resembles the respective industry or sector, we provide the number of standard deviations the current level of the implied-realized volatility spread is trading above or below to its one-year historical mean. A highly negative standard deviation could indicate that options are trading cheap, whereas a highly positive standard deviation possibly implies such options are relatively rich. (Note that there usually do not exist actively traded options at the industry group level and the relative richness/cheapness indicators for these industry groupings should only be used only as a starting point for identifying single-stock volatility trades within that industry group. Furthermore, while options on ETFs exist, their liquidity should be taken into account before executing a trade, since many are currently thinly traded as well.) • The “Largest Implied Volatility Increases” and “Largest Implied Volatility Decreases” denote the stocks within the sectors that have experienced the highest and lowest absolute changes in implied volatility, over one-week and one-month periods. • The Put-Call Skew is calculated as the difference between the 3-month put-implied volatility and the 3-month call-implied volatility for 20 delta puts and 20 delta calls, divided by the 3- month at-the-money implied volatility. The weighted-average skew at the sector and industry group level are calculated similarly, except the volatility used is the market-cap weighted- average implied volatility. If the current skew level is trading a relatively high number of standard deviations above its one-year average, this could indicate the option market is pricing in increasing risk expectations for the underlying stock, since the put–call implied volatility differential implies that option traders have been bidding up put protection, rather than upside participation via long call positions. • We show the history of the slope of the volatility term structure as measured by the difference between 12-month and 3-month at-the-money implied volatilities. Since longer term implied volatility tends to be more stable than implied volatility on shorter-dated options, a lower term structure spread relative to its historical pattern could indicate 3-month options are trading richer than they typically have in the past. Alternatively, if the slope of the term structure is relatively steep, one might infer near term options are trading at a relative discount to longer dated options. January 10, 2006 19
  • 20. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning?Figure 26: Energy Sector Volatility Snapshot (as of January 6, 2006) Implied Volatility vs Realized Volatility Implied-Realized Spread (by Industry Groups/ETF) # of Standard Deviations from 1-year Average 40% XOI 35% IYE 30% OSX XNG 25% XLE 20% OIH 15% Energy 5 5 05 05 5 05 05 05 5 5 5 5 -0 -0 -0 r-0 l-0 -0 -0 n- b- n- g- p- -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 ay ov ec ar ct Ju Ap Ja Fe Ju Au Se O M N M D Cheap > > > > > > > > > > > > Rich Wgt Avg Implied Vol Wgt Avg Realized VolNote: We calculate each sectors average implied volatility by weighting the 3-month at-the-money implied volatility of its constituents by market capitalization.Investors should consider liquidity of options of a stock or ETF before entering an options position since, although options on ETFs exist, many are thinly traded. Largest Implied Volatility Increases Largest Implied Volatility Decreases 1-week Increase 1-month Increase 1-week Decrease 1-month Decrease Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol OXY 32% 2% 39% WFT 32% 2% 35% WMB 33% -3% 39% BR 16% -21% 46% WFT 32% 1% 35% OXY 32% 1% 39% XTO 37% -2% 44% COP 26% -5% 38% BJS 32% 1% 34% HAL 35% 1% 43% COP 26% -1% 38% WMB 33% -4% 39% NBR 32% 1% 36% NBR 32% 1% 36% BHI 29% -1% 34% VLO 38% -4% 44% AHC 36% 1% 42% BJS 32% 1% 34% DVN 33% -1% 42% EP 31% -3% 31% 3-Month Put-Call Skew (20 Delta) Relative Skews (by Industry Groups/ETF) 25% # of Standard Deviations from 1-year Average OSX 20% XLE 15% OIH Energy 10% IYE 5% XOI 0% XNG 5 5 05 5 5 05 5 05 05 5 5 5 -0 -0 -0 -0 r-0 -0 -0 l-0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 n- n- g- p- ay ov ec ar b ct Ju Ap Ja Ju Fe Au Se O M N M D Cheap > > > > > > > > > > > > Rich Wgt Avg 20 Delta Skew (3m) Avg + 1 Stdev Avg - 1 Stdev Note: The put-call skew is calculated by taking the difference between the 20-Delta put-implied volatility and 20-Delta call-implied volatility, divided by the 3-month ATM implied volatility. Sector level volatilities are the market cap weighted implied volatilty for each constituent. A high skew is generally associated with a relatively high demand for downside protection. 12-Month - 3-Month Term Spread Relative Term Spreads (by Industry Groups/ETF) 2% # of Standard Deviations from 1-year Average XOI 1% Energy 0% -1% OSX -2% XLE -3% IYE -4% OIH -5% XNG 5 5 5 5 5 5 05 05 5 5 5 5 -0 -0 0 0 -0 0 r-0 l-0 -0 -0 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 n- b- n- g- p- ay ov ec ar ct Ju Ap Ja Fe Ju Au Se O M M N D Cheap > > > > > > > > > > > > Rich Wgt Avg 12m-3m Term Avg + 1 Stdev Avg - 1 Stdev Note: The term structure spread is calculated by taking the difference between the 12-month ATM implied volatility and the 3-month ATM implied volatility. Sector level term spread is calculated from the market cap weighted implied volatilities of the constituents. A steep term structure indicates shorter-dated implied volatility could be cheap relative to longer-dated implied volatility.Source: Lehman Brothers, OptionMetrics January 10, 2006 20
  • 21. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning?Figure 27: Materials Sector Volatility Snapshot (as of January 6, 2006) Implied Volatility vs Realized Volatility Implied-Realized Spread (by Industry Groups/ETF) # of Standard Deviations from 1-year Average 30% IYM 25% Materials 20% XAU 15% XLB 5 5 05 05 5 05 05 05 5 5 5 5 -0 -0 -0 r-0 l-0 -0 -0 n- b- n- g- p- -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 ay ov ec ar ct Ju Ap Ja Fe Ju Au Se O M N M D Cheap > > > > > > > > > > > > Rich Wgt Avg Implied Vol Wgt Avg Realized VolNote: We calculate each sectors average implied volatility by weighting the 3-month at-the-money implied volatility of its constituents by market capitalization.Investors should consider liquidity of options of a stock or ETF before entering an options position since, although options on ETFs exist, many are thinly traded. Largest Implied Volatility Increases Largest Implied Volatility Decreases 1-week Increase 1-month Increase 1-week Decrease 1-month Decrease Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol ATI 40% 3% 37% ATI 40% 3% 37% EC 15% -7% 48% LPX 28% -5% 22% NEM 35% 3% 34% ROH 23% 3% 24% X 39% -3% 39% PTV 22% -5% 38% AA 26% 1% 18% FCX 35% 3% 35% EMN 24% -2% 25% MON 30% -4% 30% FCX 35% 1% 35% ECL 19% 2% 16% MON 30% -2% 30% TIN 25% -4% 24% HPC 31% 1% 31% NEM 35% 2% 34% LPX 28% -2% 22% X 39% -4% 39% 3-Month Put-Call Skew (20 Delta) Relative Skews (by Industry Groups/ETF) 20% # of Standard Deviations from 1-year Average 18% IYM 16% 14% 12% XAU 10% 8% 6% XLB 4% 2% Materials 0% 5 5 05 5 5 05 5 5 5 5 5 5 -0 -0 -0 -0 r-0 0 0 -0 -0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 l-0 n- n- g- p- ay ov ar b ec ct Ju Ap Ja Fe Ju Au Se O M M N D Cheap > > > > > > > > > > > > Rich Wgt Avg 20 Delta Skew (3m) Avg + 1 Stdev Avg - 1 Stdev Note: The put-call skew is calculated by taking the difference between the 20-Delta put-implied volatility and 20-Delta call-implied volatility, divided by the 3-month ATM implied volatility. Sector level volatilities are the market cap weighted implied volatilty for each constituent. A high skew is generally associated with a relatively high demand for downside protection. Relative Term Spreads (by Industry Groups/ETF) 12-Month - 3-Month Term Spread # of Standard Deviations from 1-year Average 1% 1% XLB 0% Materials -1% -1% XAU -2% IYM -2% 5 5 5 5 5 5 05 05 5 5 5 5 -0 -0 0 0 -0 0 r-0 l-0 -0 -0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 n- b- n- g- p- ay ov ec ar ct Ju Ap Ja Fe Ju Au Se O M M N D Cheap > > > > > > > > > > > > Rich Wgt Avg 12m-3m Term Avg + 1 Stdev Avg - 1 Stdev Note: The term structure spread is calculated by taking the difference between the 12-month ATM implied volatility and the 3-month ATM implied volatility. Sector level term spread is calculated from the market cap weighted implied volatilities of the constituents. A steep term structure indicates shorter-dated implied volatility could be cheap relative to longer-dated implied volatility.Source: Lehman Brothers, OptionMetrics January 10, 2006 21
  • 22. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning?Figure 28: Industrials Sector Volatility Snapshot (as of January 6, 2006) Implied Volatility vs Realized Volatility Implied-Realized Spread (by Industry Groups/ETF) # of Standard Deviations from 1-year Average 25% Transportation XLI Capital Goods 20% XAL CYC 15% Commercial Services & Supplies 5 5 05 05 5 05 05 05 5 5 5 5 -0 -0 -0 r-0 l-0 -0 -0 n- b- n- g- p- -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 ay ov ec ar ct Ju Ap Ja Fe Ju Au Se O M N M D Cheap > > > > > > > > > > > > Rich Wgt Avg Implied Vol Wgt Avg Realized VolNote: We calculate each sectors average implied volatility by weighting the 3-month at-the-money implied volatility of its constituents by market capitalization.Investors should consider liquidity of options of a stock or ETF before entering an options position since, although options on ETFs exist, many are thinly traded. Largest Implied Volatility Increases Largest Implied Volatility Decreases 1-week Increase 1-month Increase 1-week Decrease 1-month Decrease Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol AW 36% 3% 26% ITT 24% 3% 31% DOV 19% -1% 18% NAV 35% -4% 34% MAS 24% 2% 24% CTAS 21% 2% 19% ROK 24% -1% 19% R 29% -2% 30% LUV 29% 1% 25% LUV 29% 2% 25% APCC 33% -1% 29% PBI 16% -2% 15% TYC 25% 1% 21% AW 36% 2% 26% HON 21% -1% 21% HON 21% -2% 21% FDX 22% 1% 20% UTX 18% 1% 17% R 29% -1% 30% PCAR 24% -2% 20% 3-Month Put-Call Skew (20 Delta) Relative Skews (by Industry Groups/ETF) 30% # of Standard Deviations from 1-year Average XLI 25% Transportation 20% XAL 15% Capital Goods 10% Commercial 5% Services & Supplies 0% CYC 5 5 05 5 5 05 5 5 5 5 5 5 -0 -0 -0 -0 r-0 0 0 -0 -0 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 l-0 n- n- g- p- ay ov ar b ec ct Ju Ap Ja Fe Ju Au Se O M M N D Cheap > > > > > > > > > > > > Rich Wgt Avg 20 Delta Skew (3m) Avg + 1 Stdev Avg - 1 Stdev Note: The put-call skew is calculated by taking the difference between the 20-Delta put-implied volatility and 20-Delta call-implied volatility, divided by the 3-month ATM implied volatility. Sector level volatilities are the market cap weighted implied volatilty for each constituent. A high skew is generally associated with a relatively high demand for downside protection. 12-Month - 3-Month Term Spread Relative Term Spreads (by Industry Groups/ETF) # of Standard Deviations from 1-year Average 3% CYC 2% XAL 2% Capital Goods 1% XLI 1% Commercial 0% Services & Supplies -1% Transportation 5 5 5 5 5 5 05 05 5 5 5 5 -0 -0 0 0 -0 0 r-0 l-0 -0 -0 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 n- b- n- g- p- ay ov ec ar ct Ju Ap Ja Fe Ju Au Se O M M N D Cheap > > > > > > > > > > > > Rich Wgt Avg 12m-3m Term Avg + 1 Stdev Avg - 1 Stdev Note: The term structure spread is calculated by taking the difference between the 12-month ATM implied volatility and the 3-month ATM implied volatility. Sector level term spread is calculated from the market cap weighted implied volatilities of the constituents. A steep term structure indicates shorter-dated implied volatility could be cheap relative to longer-dated implied volatility.Source: Lehman Brothers, OptionMetrics January 10, 2006 22
  • 23. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning?Figure 29: Consumer Discretionary Sector Volatility Snapshot (as of January 6, 2006) Implied Volatility vs Realized Volatility Implied-Realized Spread (by Industry Groups/ETF) # of Standard Deviations from 1-year Average 30% Automobiles & Components Media 25% Retailing HHH 20% RTH XLY Consumer Durables & Apparel 15% Consumer Services 5 5 5 05 5 05 5 05 05 5 5 5 -0 -0 0 r-0 l-0 -0 -0 -0 b- g- p- n- n- ay ar ov ec ct -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 Ju Ap Ja Ju Fe Au Se O M M N D Cheap > > > > > > > > > > > > Rich Wgt Avg Implied Vol Wgt Avg Realized VolNote: We calculate each sectors average implied volatility by weighting the 3-month at-the-money implied volatility of its constituents by market capitalization.Investors should consider liquidity of options of a stock or ETF before entering an options position since, although options on ETFs exist, many are thinly traded. Largest Implied Volatility Increases Largest Implied Volatility Decreases 1-week Increase 1-month Increase 1-week Decrease 1-month Decrease Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol MYG 38% 5% 23% DG 26% 4% 22% DCN 55% -12% 96% DCN 55% -14% 96% DG 26% 2% 22% MAT 27% 2% 20% GM 74% -10% 55% BBY 31% -9% 43% SHW 23% 2% 24% AN 22% 2% 16% VC 61% -9% 67% IPG 28% -8% 24% COH 32% 2% 31% IGT 26% 1% 21% OMX 32% -4% 40% SHLD 38% -7% 32% HLT 26% 2% 34% KRI 24% 1% 26% RBK 4% -4% 5% RBK 4% -7% 5% 3-Month Put-Call Skew (20 Delta) Relative Skews (by Industry Groups/ETF) # of Standard Deviations from 1-year Average 25% Automobiles & Components 20% HHH Consumer Durables & Apparel 15% Media 10% Consumer Services XLY 5% Retailing 0% RTH 5 5 05 5 5 05 5 05 05 5 5 5 -0 -0 -0 -0 r-0 -0 -0 l-0 -1.5 -1.0 -0.5 0.0 0.5 n- n- g- p- ay ov ec ar b ct Ju Ap Ja Ju Fe Au Se O M N M D Cheap > > > > > > > > > > > > Rich Wgt Avg 20 Delta Skew (3m) Avg + 1 Stdev Avg - 1 Stdev Note: The put-call skew is calculated by taking the difference between the 20-Delta put-implied volatility and 20-Delta call-implied volatility, divided by the 3-month ATM implied volatility. Sector level volatilities are the market cap weighted implied volatilty for each constituent. A high skew is generally associated with a relatively high demand for downside protection. Relative Term Spreads (by Industry Groups/ETF) 12-Month - 3-Month Term Spread # of Standard Deviations from 1-year Average 2% RTH 1% XLY 1% Automobiles & Components 0% Consumer Durables & Apparel -1% -1% Consumer Services -2% Retailing -2% Media -3% HHH 5 5 5 5 5 5 05 05 5 5 5 5 -0 -0 0 0 -0 0 r-0 l-0 -0 -0 2.0 1.5 1.0 0.5 0.0 -0.5 n- b- n- g- p- ay ov ec ar ct Ju Ap Ja Fe Ju Au Se O M M N D Cheap > > > > > > > > > > > > Rich Wgt Avg 12m-3m Term Avg + 1 Stdev Avg - 1 Stdev Note: The term structure spread is calculated by taking the difference between the 12-month ATM implied volatility and the 3-month ATM implied volatility. Sector level term spread is calculated from the market cap weighted implied volatilities of the constituents. A steep term structure indicates shorter-dated implied volatility could be cheap relative to longer-dated implied volatility.Source: Lehman Brothers, OptionMetrics January 10, 2006 23
  • 24. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning?Figure 30: Consumer Staples Sector Volatility Snapshot (as of January 6, 2006) Implied Volatility vs Realized Volatility Implied-Realized Spread (by Industry Groups/ETF) # of Standard Deviations from 1-year Average 25% Household & Personal Products 20% XLP 15% Food & Staples Retailing Food, Beverage & 10% Tobacco 5 5 05 05 5 05 05 05 5 5 5 5 -0 -0 -0 r-0 l-0 -0 -0 n- b- n- g- p- -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 ay ov ec ar ct Ju Ap Ja Fe Ju Au Se O M N M D Cheap > > > > > > > > > > > > Rich Wgt Avg Implied Vol Wgt Avg Realized VolNote: We calculate each sectors average implied volatility by weighting the 3-month at-the-money implied volatility of its constituents by market capitalization.Investors should consider liquidity of options of a stock or ETF before entering an options position since, although options on ETFs exist, many are thinly traded. Largest Implied Volatility Increases Largest Implied Volatility Decreases 1-week Increase 1-month Increase 1-week Decrease 1-month Decrease Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol RAI 25% 2% 22% CL 17% 1% 12% ABS 31% -3% 34% CVS 26% -3% 30% TSN 28% 2% 28% RAI 25% 1% 22% WAG 20% -2% 21% ADM 27% -2% 27% KR 24% 1% 18% ACV 23% 1% 17% STZ 27% -1% 31% STZ 27% -2% 31% WMT 19% 1% 17% CCE 22% 0% 17% CVS 26% -1% 30% MO 23% -2% 22% UST 24% 1% 24% SWY 27% 0% 24% PG 16% -1% 14% WMT 19% -2% 17% 3-Month Put-Call Skew (20 Delta) Relative Skews (by Industry Groups/ETF) 25% # of Standard Deviations from 1-year Average Food, Beverage & 20% Tobacco 15% XLP 10% Household & Personal Products 5% Food & Staples 0% Retailing 5 5 05 5 5 05 5 5 5 5 5 5 -0 -0 -0 -0 r-0 0 0 -0 -0 -1.0 -0.5 0.0 0.5 1.0 1.5 l-0 n- n- g- p- ay ov ar b ec ct Ju Ap Ja Fe Ju Au Se O M M N D Cheap > > > > > > > > > > > > Rich Wgt Avg 20 Delta Skew (3m) Avg + 1 Stdev Avg - 1 Stdev Note: The put-call skew is calculated by taking the difference between the 20-Delta put-implied volatility and 20-Delta call-implied volatility, divided by the 3-month ATM implied volatility. Sector level volatilities are the market cap weighted implied volatilty for each constituent. A high skew is generally associated with a relatively high demand for downside protection. Relative Term Spreads (by Industry Groups/ETF) 12-Month - 3-Month Term Spread # of Standard Deviations from 1-year Average 2% Food, Beverage & 2% Tobacco 1% Household & Personal Products 1% 0% XLP -1% Food & Staples -1% Retailing 5 5 5 5 5 5 05 05 5 5 5 5 -0 -0 0 0 -0 0 r-0 l-0 -0 -0 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 n- b- n- g- p- ay ov ec ar ct Ju Ap Ja Fe Ju Au Se O M M N D Cheap > > > > > > > > > > > > Rich Wgt Avg 12m-3m Term Avg + 1 Stdev Avg - 1 Stdev Note: The term structure spread is calculated by taking the difference between the 12-month ATM implied volatility and the 3-month ATM implied volatility. Sector level term spread is calculated from the market cap weighted implied volatilities of the constituents. A steep term structure indicates shorter-dated implied volatility could be cheap relative to longer-dated implied volatility.Source: Lehman Brothers, OptionMetrics January 10, 2006 24
  • 25. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning?Figure 31: Health Care Sector Volatility Snapshot (as of January 6, 2006) Implied Volatility vs Realized Volatility Implied-Realized Spread (by Industry Groups/ETF) # of Standard Deviations from 1-year Average 40% BBH 35% IYH 30% XLV PPH 25% Health Care Equipment & Services 20% IBB 15% Pharmaceuticals & Biotechnology 5 5 05 05 5 05 05 05 5 5 5 5 -0 -0 -0 r-0 l-0 -0 -0 n- b- n- g- p- -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 ay ov ec ar ct Ju Ap Ja Fe Ju Au Se O M N M D Cheap > > > > > > > > > > > > Rich Wgt Avg Implied Vol Wgt Avg Realized VolNote: We calculate each sectors average implied volatility by weighting the 3-month at-the-money implied volatility of its constituents by market capitalization.Investors should consider liquidity of options of a stock or ETF before entering an options position since, although options on ETFs exist, many are thinly traded. Largest Implied Volatility Increases Largest Implied Volatility Decreases 1-week Increase 1-month Increase 1-week Decrease 1-month Decrease Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol UNH 25% 1% 24% BOL 31% 6% 31% GDT 18% -6% 41% BSX 33% -11% 25% HUM 32% 1% 39% BCR 24% 3% 18% WYE 18% -3% 20% PFE 21% -10% 32% SGP 25% 1% 23% HSP 25% 3% 23% PFE 21% -2% 32% SGP 25% -6% 23% AGN 25% 1% 24% UNH 25% 3% 24% BDX 19% -2% 22% BMET 29% -5% 23% WLP 25% 1% 25% BAX 21% 2% 18% STJ 27% -2% 25% MEDI 35% -5% 26% Relative Skews (by Industry Groups/ETF) 3-Month Put-Call Skew (20 Delta) # of Standard Deviations from 1-year Average 30% BBH 25% IYH 20% IBB 15% PPH 10% Health Care Equipment & Services 5% XLV 0% Pharmaceuticals & Biotechnology 5 5 05 5 5 05 5 5 5 5 5 5 -0 -0 -0 -0 r-0 0 0 -0 -0 -2.0 -1.5 -1.0 -0.5 0.0 0.5 l-0 n- n- g- p- ay ov ar b ec ct Ju Ap Ja Fe Ju Au Se O M M N D Cheap > > > > > > > > > > > > Rich Wgt Avg 20 Delta Skew (3m) Avg + 1 Stdev Avg - 1 Stdev Note: The put-call skew is calculated by taking the difference between the 20-Delta put-implied volatility and 20-Delta call-implied volatility, divided by the 3-month ATM implied volatility. Sector level volatilities are the market cap weighted implied volatilty for each constituent. A high skew is generally associated with a relatively high demand for downside protection. Relative Term Spreads (by Industry Groups/ETF) 12-Month - 3-Month Term Spread # of Standard Deviations from 1-year Average 2% 2% XLV 1% PPH 1% IYH 0% -1% IBB -1% Pharmaceuticals & Biotechnology -2% BBH -2% -3% Health Care Equipment & Services 5 5 5 5 5 5 05 05 5 5 5 5 -0 -0 0 0 -0 0 r-0 l-0 -0 -0 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 n- b- n- g- p- ay ov ec ar ct Ju Ap Ja Fe Ju Au Se O M M N D Cheap > > > > > > > > > > > > Rich Wgt Avg 12m-3m Term Avg + 1 Stdev Avg - 1 Stdev Note: The term structure spread is calculated by taking the difference between the 12-month ATM implied volatility and the 3-month ATM implied volatility. Sector level term spread is calculated from the market cap weighted implied volatilities of the constituents. A steep term structure indicates shorter-dated implied volatility could be cheap relative to longer-dated implied volatility.Source: Lehman Brothers, OptionMetrics January 10, 2006 25
  • 26. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning?Figure 32: Financials Sector Volatility Snapshot (as of January 6, 2006) Implied Volatility vs Realized Volatility Implied-Realized Spread (by Industry Groups/ETF) # of Standard Deviations from 1-year Average 25% Insurance Diversified Financials RKH 20% BKX Banks Real Estate 15% XBD XLF IYF ICF 10% IYR 5 5 05 05 5 05 05 05 5 5 5 5 -0 -0 -0 r-0 l-0 -0 -0 n- b- n- g- p- -1.5 -1.0 -0.5 0.0 0.5 1.0 ay ov ec ar ct Ju Ap Ja Fe Ju Au Se O M N M D Cheap > > > > > > > > > > > > Rich Wgt Avg Implied Vol Wgt Avg Realized VolNote: We calculate each sectors average implied volatility by weighting the 3-month at-the-money implied volatility of its constituents by market capitalization.Investors should consider liquidity of options of a stock or ETF before entering an options position since, although options on ETFs exist, many are thinly traded. Largest Implied Volatility Increases Largest Implied Volatility Decreases 1-week Increase 1-month Increase 1-week Decrease 1-month Decrease Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol FNM 31% 2% 27% JP 19% 4% 16% ET 32% -3% 29% ET 32% -6% 29% AIV 21% 2% 23% FNM 31% 4% 27% ASN 20% -3% 18% MCO 21% -4% 17% AOC 31% 2% 20% WM 24% 3% 21% SPG 23% -2% 21% FITB 23% -3% 21% UNM 27% 1% 23% UNM 27% 2% 23% SNV 20% -2% 17% VNO 19% -3% 18% FII 21% 1% 16% AOC 31% 2% 20% FRE 21% -2% 19% NFB 20% -3% 17% 3-Month Put-Call Skew (20 Delta) Relative Skews (by Industry Groups/ETF) # of Standard Deviations from 1-year Average 35% ICF 30% RKH IYR 25% XBD 20% Real Estate XLF 15% BKX 10% Insurance 5% Banks IYF 0% Diversified Financials 5 5 05 5 5 05 5 5 5 5 5 5 -0 -0 -0 -0 r-0 0 0 -0 -0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 l-0 n- n- g- p- ay ov ar b ec ct Ju Ap Ja Fe Ju Au Se O M M N D Cheap > > > > > > > > > > > > Rich Wgt Avg 20 Delta Skew (3m) Avg + 1 Stdev Avg - 1 Stdev Note: The put-call skew is calculated by taking the difference between the 20-Delta put-implied volatility and 20-Delta call-implied volatility, divided by the 3-month ATM implied volatility. Sector level volatilities are the market cap weighted implied volatilty for each constituent. A high skew is generally associated with a relatively high demand for downside protection. 12-Month - 3-Month Term Spread Relative Term Spreads (by Industry Groups/ETF) # of Standard Deviations from 1-year Average 3% IYF 2% XBD IYR 2% XLF 1% BKX Real Estate 1% Diversified Financials 0% Insurance -1% Banks ICF -1% RKH 5 5 5 5 5 5 05 05 5 5 5 5 -0 -0 0 0 -0 0 r-0 l-0 -0 -0 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 n- b- n- g- p- ay ov ec ar ct Ju Ap Ja Fe Ju Au Se O M M N D Cheap > > > > > > > > > > > > Rich Wgt Avg 12m-3m Term Avg + 1 Stdev Avg - 1 Stdev Note: The term structure spread is calculated by taking the difference between the 12-month ATM implied volatility and the 3-month ATM implied volatility. Sector level term spread is calculated from the market cap weighted implied volatilities of the constituents. A steep term structure indicates shorter-dated implied volatility could be cheap relative to longer-dated implied volatility.Source: Lehman Brothers, OptionMetrics January 10, 2006 26
  • 27. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning?Figure 33: Information Technology Sector Volatility Snapshot (as of January 6, 2006) Implied-Realized Spread (by Industry Groups/ETF) Implied Volatility vs Realized Volatility # of Standard Deviations from 1-year Average 35% IAH Technology Hardware & Equipment TXX WMH 30% SWH IGV SOX XCI 25% XLK IYW IGN SMH 20% IGW Software & Services MSH 15% Semiconductors & Semiconductor Equipment IGM BDH 5 5 05 05 5 05 05 05 5 5 5 5 -0 -0 -0 r-0 l-0 -0 -0 n- b- n- g- p- ay ov ec ar ct Ju Ap Ja Fe Ju Au Se O M -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 N M D Wgt Avg Implied Vol Wgt Avg Realized Vol Cheap > > > > > > > > > > > > RichNote: We calculate each sectors average implied volatility by weighting the 3-month at-the-money implied volatility of its constituents by market capitalization.Investors should consider liquidity of options of a stock or ETF before entering an options position since, although options on ETFs exist, many are thinly traded. Largest Implied Volatility Increases Largest Implied Volatility Decreases 1-week Increase 1-month Increase 1-week Decrease 1-month Decrease Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol SUNW 46% 7% 33% SEBL 17% 5% 5% PMTC 38% -9% 31% PMTC 38% -11% 31% BMC 35% 6% 34% BMC 35% 4% 34% LU 36% -8% 34% MU 34% -9% 31% GTW 57% 5% 50% UIS 50% 4% 61% CIEN 57% -6% 53% ERTS 33% -5% 31% NVDA 43% 4% 34% GTW 57% 3% 50% JDSU 49% -4% 55% AV 38% -5% 30% HPQ 29% 1% 23% MOLX 27% 3% 20% ANDW 34% -3% 24% LU 36% -5% 34% Relative Skews (by Industry Groups/ETF) 3-Month Put-Call Skew (20 Delta) # of Standard Deviations from 1-year Average 30% XLK BDH 25% IGM SOX IGW 20% IGN MSH Technology Hardware & Equipment 15% IGV IYW Software & Services 10% SMH WMH 5% SWH Semiconductors & Semiconductor Equipment TXX 0% IAH XCI 5 5 05 5 5 05 5 5 5 5 5 5 -0 -0 -0 -0 r-0 0 0 -0 -0 l-0 n- n- g- p- -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 ay ov ar b ec ct Ju Ap Ja Fe Ju Au Se O M M N D Wgt Avg 20 Delta Skew (3m) Avg + 1 Stdev Avg - 1 Stdev Cheap > > > > > > > > > > > > Rich Note: The put-call skew is calculated by taking the difference between the 20-Delta put-implied volatility and 20-Delta call-implied volatility, divided by the 3-month ATM implied volatility. Sector level volatilities are the market cap weighted implied volatilty for each constituent. A high skew is generally associated with a relatively high demand for downside protection. Relative Term Spreads (by Industry Groups/ETF) 12-Month - 3-Month Term Spread # of Standard Deviations from 1-year Average 2% XLK MSH 1% BDH IGM 1% Software & Services SOX 0% TXX SWH -1% Technology Hardware & Equipment IGN -1% Semiconductors & Semiconductor Equipment IGV -2% IYW SMH -2% IGW XCI -3% IAH WMH 5 5 5 5 5 5 05 05 5 5 5 5 -0 -0 0 0 -0 0 r-0 l-0 -0 -0 4.0 3.0 2.0 1.0 0.0 -1.0 -2.0 n- b- n- g- p- ay ov ec ar ct Ju Ap Ja Fe Ju Au Se O M M N D Cheap > > > > > > > > > > > > Rich Wgt Avg 12m-3m Term Avg + 1 Stdev Avg - 1 Stdev Note: The term structure spread is calculated by taking the difference between the 12-month ATM implied volatility and the 3-month ATM implied volatility. Sector level term spread is calculated from the market cap weighted implied volatilities of the constituents. A steep term structure indicates shorter-dated implied volatility could be cheap relative to longer-dated implied volatility.Source: Lehman Brothers, OptionMetrics January 10, 2006 27
  • 28. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning?Figure 34: Telecommunication Services Sector Volatility Snapshot (as of January 6, 2006) Implied Volatility vs Realized Volatility Implied-Realized Spread (by Industry Groups/ETF) # of Standard Deviations from 1-year Average 30% TTH 25% 20% Telecommunication Services 15% IYZ 10% 5 5 05 05 5 05 05 05 5 5 5 5 -0 -0 -0 r-0 l-0 -0 -0 n- b- n- g- p- -0.4 -0.3 -0.2 -0.1 0.0 0.1 ay ov ec ar ct Ju Ap Ja Fe Ju Au Se O M N M D Cheap > > > > > > > > > > > > Rich Wgt Avg Implied Vol Wgt Avg Realized VolNote: We calculate each sectors average implied volatility by weighting the 3-month at-the-money implied volatility of its constituents by market capitalization.Investors should consider liquidity of options of a stock or ETF before entering an options position since, although options on ETFs exist, many are thinly traded. Largest Implied Volatility Increases Largest Implied Volatility Decreases 1-week Increase 1-month Increase 1-week Decrease 1-month Decrease Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol S 28% 2% 23% S 28% 3% 23% CZN 18% -1% 17% CTL 19% -2% 19% BLS 18% 1% 15% Q 39% 2% 32% T 14% -1% 13% T 14% -1% 13% Q 39% 0% 32% VZ 19% 1% 15% CTL 19% -1% 19% CZN 18% -1% 17% VZ 19% 0% 15% BLS 18% 1% 15% AT 19% 0% 18% AT 19% 0% 18% AT 19% 0% 18% AT 19% 0% 18% VZ 19% 0% 15% BLS 18% 1% 15% 3-Month Put-Call Skew (20 Delta) Relative Skews (by Industry Groups/ETF) 25% # of Standard Deviations from 1-year Average 20% TTH 15% 10% IYZ 5% 0% Telecommunication Services -5% 5 5 05 5 5 05 5 5 5 5 5 5 -0 -0 -0 -0 r-0 0 0 -0 -0 -1.0 -0.5 0.0 0.5 1.0 1.5 l-0 n- n- g- p- ay ov ar b ec ct Ju Ap Ja Fe Ju Au Se O M M N D Cheap > > > > > > > > > > > > Rich Wgt Avg 20 Delta Skew (3m) Avg + 1 Stdev Avg - 1 Stdev Note: The put-call skew is calculated by taking the difference between the 20-Delta put-implied volatility and 20-Delta call-implied volatility, divided by the 3-month ATM implied volatility. Sector level volatilities are the market cap weighted implied volatilty for each constituent. A high skew is generally associated with a relatively high demand for downside protection. Relative Term Spreads (by Industry Groups/ETF) 12-Month - 3-Month Term Spread # of Standard Deviations from 1-year Average 5% 4% 3% TTH 2% 1% 0% IYZ -1% -2% -3% Telecommunication -4% Services -5% 5 5 5 5 5 5 05 05 5 5 5 5 -0 -0 0 0 -0 0 r-0 l-0 -0 -0 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 n- b- n- g- p- ay ov ec ar ct Ju Ap Ja Fe Ju Au Se O M M N D Cheap > > > > > > > > > > > > Rich Wgt Avg 12m-3m Term Avg + 1 Stdev Avg - 1 Stdev Note: The term structure spread is calculated by taking the difference between the 12-month ATM implied volatility and the 3-month ATM implied volatility. Sector level term spread is calculated from the market cap weighted implied volatilities of the constituents. A steep term structure indicates shorter-dated implied volatility could be cheap relative to longer-dated implied volatility.Source: Lehman Brothers, OptionMetrics January 10, 2006 28
  • 29. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning? Implied-Realized Spread (by Industry Groups/ETF) Implied Volatility vs Realized Volatility # of Standard Deviations from 1-year Average 30% IDU 25% UTY 20% Utilities 15% XLU 10% UTH 5 5 05 05 5 05 05 05 5 5 5 5 -0 -0 -0 r-0 l-0 -0 -0 n- b- n- g- p- -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 ay ov ec ar ct Ju Ap Ja Fe Ju Au Se O M N M D Cheap > > > > > > > > > > > > Rich Wgt Avg Implied Vol Wgt Avg Realized VolNote: We calculate each sectors average implied volatility by weighting the 3-month at-the-money implied volatility of its constituents by market capitalization.Investors should consider liquidity of options of a stock or ETF before entering an options position since, although options on ETFs exist, many are thinly traded. Largest Implied Volatility Increases Largest Implied Volatility Decreases 1-week Increase 1-month Increase 1-week Decrease 1-month Decrease Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol ED 18% 1% 15% ED 18% 2% 15% PCG 18% -3% 20% AES 26% -6% 28% CNP 24% 1% 23% DYN 46% 2% 38% XEL 17% -2% 17% D 18% -4% 22% PGN 14% 1% 14% PPL 20% 1% 24% PNW 13% -2% 19% CEG 21% -4% 32% TXU 32% 1% 44% SO 16% 1% 14% EXC 24% -1% 25% PCG 18% -3% 20% KSE 16% 0% 17% NI 22% 1% 21% AYE 26% -1% 26% AEE 15% -3% 16% 3-Month Put-Call Skew (20 Delta) Relative Skews (by Industry Groups/ETF) 25% # of Standard Deviations from 1-year Average Utilities 20% XLU 15% IDU 10% UTY 5% UTH 0% 5 5 05 5 5 05 5 5 5 5 5 5 -0 -0 -0 -0 r-0 0 0 -0 -0 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 l-0 n- n- g- p- ay ov ar b ec ct Ju Ap Ja Fe Ju Au Se O M M N D Cheap > > > > > > > > > > > > Rich Wgt Avg 20 Delta Skew (3m) Avg + 1 Stdev Avg - 1 Stdev Note: The put-call skew is calculated by taking the difference between the 20-Delta put-implied volatility and 20-Delta call-implied volatility, divided by the 3-month ATM implied volatility. Sector level volatilities are the market cap weighted implied volatilty for each constituent. A high skew is generally associated with a relatively high demand for downside protection. Relative Term Spreads (by Industry Groups/ETF) 12-Month - 3-Month Term Spread # of Standard Deviations from 1-year Average 2% 2% UTY 1% 1% UTH 0% -1% IDU -1% -2% Utilities -2% -3% XLU 5 5 5 5 5 5 05 05 5 5 5 5 -0 -0 0 0 -0 0 r-0 l-0 -0 -0 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 n- b- n- g- p- ay ov ec ar ct Ju Ap Ja Fe Ju Au Se O M M N D Cheap > > > > > > > > > > > > Rich Wgt Avg 12m-3m Term Avg + 1 Stdev Avg - 1 Stdev Note: The term structure spread is calculated by taking the difference between the 12-month ATM implied volatility and the 3-month ATM implied volatility. Sector level term spread is calculated from the market cap weighted implied volatilities of the constituents. A steep term structure indicates shorter-dated implied volatility could be cheap relative to longer-dated implied volatility.Source: Lehman Brothers, OptionMetrics January 10, 2006 29
  • 30. Equity Derivatives Strategy | Options Strategy Monthly: Low Volatility in the 7th Inning?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 orissuers 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 expressedin this email.Options are not suitable for all investors and the risks of option trading should be weighed against the potential rewards.Supporting documents that form the basis of the recommendations are available on request. Please note that the trade ideas withinthis report in no way relate to the fundamental ratings applied to European stocks by Lehman Brothers Equity Research.FOR CURRENT IMPORTANT DISCLOSURES REGARDING COMPANIES THAT ARE THE SUBJECT OF THIS RESEARCH REPORT, PLEASE SEND AWRITTEN REQUEST TO: Lehman Brothers Control Room, 745 Seventh Avenue, 19th floor, New York, NY 10019 or refer to the firms disclosurewebsite at www.lehman.com/disclosuresImportant DisclosuresThe analysts responsible for preparing this report have received compensation based upon various factors including the Firm’s total revenues, a portion of which isgenerated by investment banking activities.This material has been prepared and/or issued by Lehman Brothers Inc., member SIPC, and/or one of its affiliates (“Lehman Brothers”) and has been approved byLehman Brothers International (Europe), authorized and regulated by the Financial Services Authority, in connection with its distribution in the European EconomicArea. 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If aproduct is income producing, part of the capital invested may be used to pay that income. © 2005 Lehman Brothers. All rights reserved. Additional information isavailable on request. Please contact a Lehman Brothers entity in your home jurisdiction.Lehman Brothers policy for managing conflicts of interest in connection with investment research is available at www.lehman.com/researchconflictspolicy. Ratings,earnings per share forecasts and price targets contained in the Firms equity research reports covering U.S. companies are available atwww.lehman.com/disclosures.Complete disclosure information on companies covered by Lehman Brothers Equity Research is available at www.lehman.com/disclosures. January 10, 2006 30