Option Implied Volatility for Small Cap Stocks

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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 managers and other active fund managers worldwide. Ryan Renicker, CFA

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  • 1. October 10, 2006 Index Volatility Commentary Smallcap Vols Ryan Renicker, CFA 1.212.526.9425 Cheapryan.renicker@lehman.com IWM options have gained in popularity, partly because smallcap beta relative to largecaps is at Devapriya Mallick 1.212.526.5429 multi-year highs. dmallik@lehman.com Smallcaps have recently shown disproportionate participation in any downside moves in the market. The two weeks heading into earnings have tended to be a period of smallcap underperformance; largecap valuations continue to be extremely cheap relative to smallcaps. The IWM-SPX implied vol spread has cheapened to levels last seen in early June. We believe fundamental and seasonal factors make this an opportune time to enter this spread.Lehman Brothers does and seeks to do business with companies covered in its research reports. As a result, investors should be aware that the firm may have a conflict 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 8.
  • 2. Equity Derivatives Strategy | Index Volatility Commentary Smallcap Vols Cheap Smallcap Vols Cheap Relative to Largecap Vols Since the beginning of the year, IWM options have gained in popularity as a punting vehicle. Average listed volume in IWM contracts more than doubled in the month of May in comparison to the previous month. Though volumes have come off in recent months as the demand for downside protection has receded, monthly IWM option volumes remain higher than in early 2006 (Figure 1). An environment where macroeconomic data was deemed more important for determining the path of Fed policy made the Russell 2000 a more attractive instrument for placing leveraged bets. Another explanation for the greater use of IWM options could be the increasing beta of the Russell 2000 relative to the SPX, which is currently at multi year highs (Figure 2). This is largely explained by the extremely serene levels of largecap realized vols (1-month realized volatility for the S&P 500 has been hovering in the 7-8% range).Figure 1: IWMs are the favored punting vehicle in a sell-off Figure 2: RTY beta to SPX at multi year highs 700,000 2.0 600,000 Avg SPX Option Volume RTY Beta vs SPX Avg IWM Option Volume 1.5 (Rolling 3-month) 500,000 400,000 1.0 300,000 200,000 0.5 100,000 0.0 0 5 6 7 8 9 0 1 2 3 4 5 6 06 6 06 06 06 06 06 r-9 -9 r-9 r-9 r-9 r-0 r-0 r-0 r-0 -0 r-0 r-0 06 06 l-0 r r p- - n- n- b- - g- r- Ap Ap Ap Ap Ap Ap Ap Ap Ap Ap Ap Ap ay ar Ju Ja Ju Fe Ap Se Au M MSource: Lehman Brothers, OptionMetrics Source: Lehman Brothers, OptionMetrics, FAME Seasonal effects argue for smallcap underperformance in the short run. The two weeks heading into the start of earnings season have tended to be a period of weakness for the IWM. Out of the 15 such periods since 2003, the IWM has finished lower on 10 occasions. The IWM-SPX implied vol spread for the 1-month maturity has also widened on 9 out of these 15 instances. Lehmans Equity Strategists have highlighted that based on median forward P/E multiples, largecap valuations are historically cheap relative to smallcaps. In keeping with this and the heightened macro risks, smallcap vols kept getting bid up relative to largecap vols till the middle of August. The spread has been reversing for the subsequent two months. Following last weeks outperformance of the Russell 2000, IWM implied vols have cheapened further relative to the SPX. 1-month IWM implied volatility currently trades at an 8 pt premium to SPX options. This is the cheapest the spread has been since early June (Figure 3). October 10, 2006 2
  • 3. Equity Derivatives Strategy | Index Volatility Commentary Smallcap Vols CheapFigure 3: Spread to Largecap Vols Has Cheapened Considerably Figure 4: Risks skewed to the downside 0.8% % 14 0.6% IWM-SPX Implied Vol (1-Month) 0.4% % 12 0.2% 0.0% % 10 -0.2% Avg RTY vs SPX outperformance 8% -0.4% w hen SPX closes higher Avg RTY vs SPX underperformance -0.6% w hen SPX closes low er 6% -0.8% 06 6 06 06 06 06 06 06 06 l-0 p- - n- n- b- - g- n- 4% r- ay ar Ju Ja Ju Fe Ap Se Au 5 5 6 6 5 6 M 05 06 M r-0 -0 r-0 -0 l-0 l-0 n- ct ct Ju Ju Ap Ap Ja Ja O OSource: Lehman Brothers, Bloomberg Source: Lehman Brothers, Bloomberg Further examination of relative performance since the end of the smallcap rally reveals that the Russell 2000 has also exhibited disproportionate participation in any market moves to the downside. In September, the Russell 2000 outperformed the SPX by 18 bps on average when the SPX closed higher. In contrast, on days when the SPX closed lower, RTY underperformance relative to SPX averaged about 56 bps. We believe this is an opportune time to enter the IWM-SPX volatility spread. The spread looks cheaper over a 1-month horizon than it does further out the curve. Fundamental and seasonal factors argue in favor of the IWM realizing more volatility relative to the SPX in the short term, than what is currently implied by the spread. October 10, 2006 3
  • 4. Equity Derivatives Strategy | Index Volatility Commentary Smallcap Vols CheapFigure 5: Macro Volatility Summary Cash and Derivatives Volumes ETF Rich/Cheap Analysis 7.0 2.0 SMH SOX 6.0 Stock Optn Volume (Mn Contracts) XLI NYSE Equity Volume (Bn Shares) 1.5 5.0 OSX XAU 4.0 XLB 1.0 RTH 3.0 XLY IBB 2.0 0.5 OIH Stock Option Volume (SPX Constituents) PPH 1.0 Equity Volume (NYSE) XLE XLF 0.0 0.0 IYR eb ug 29 p ep an 17 b 17 ar pr un 12 pr 4- l 26 ay ay 20 n 31 ar 14 r 23 n 18 g 15 p 21 l u Ju a Fe Au Se e Ja Ju -J M -M -M -A -A -M -M BBH -J -F -J -A -S -S 7- 6- 9- 3- 3- 1- 28 Week Ending BKX XLU Source: Lehman Brothers, OptionMetrics, Bloomberg -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 Note: Stock option volume is the total volume across all contracts for constituents of the S&P 500. Cheap > > > > > > > > > > > > Rich For each ETF, we calculate the number of standard deviations by which the current 3-month implied-realized Imp Rel Spread (Std Devs from Mean) Imp SPX Spread (Std Devs from Mean) volatility spread differs from its 1-year average. We repeat the calculation for the ETF implied vs S&P 500 3-month implied volatility. Source: Lehman Brothers, OptionMetrics, Bloomberg 3-month Implied and Realized Correlation (S&P 500) Term Structure of Implied Correlation (SPY) 50% 50% 45% 40% 40% 30% 35% 30% 20% SPX Implied Correlation (3-month) 25% SPY Implied Correlation 10% SPX Realized Correlation (3-month) 20% 0% 15% 0.0 0.5 1.0 1.5 2.0 2.5 05 6 5 06 06 6 06 06 06 5 6 6 -0 -0 -0 -0 r-0 l-0 v- n- b- n- g- p- ay ec ar ct Ju Ap Years to Maturity No Ja Fe Ju Au Se O M M D Source: Lehman Brothers, OptionMetrics, FAME Source: Lehman Brothers, Bloomberg Source: Lehman Brothers, OptionMetrics, FAME 3-month Implied and Realized Correlation (Nasdaq 100) Term Structure of Implied Correlation (QQQQ) 50% 50% 45% 40% 40% 30% 35% 30% 20% 25% QQQQ Implied Correlation 10% NDX Implied Correlation (3-month) NDX Realized Correlation (3-month) 20% 0% 15% 0.0 0.5 1.0 1.5 2.0 2.5 5 06 6 06 6 6 5 05 6 06 06 6 -0 -0 -0 0 r-0 0 l-0 - c- n- b- n- g- p- ov ay ar ct Ju Ap Years to Maturity De Ja Fe Ju Au Se O M M N Source: Lehman Brothers, OptionMetrics, FAME Note: Implied and realized correlation highlight the relationship between volatility of index options and the volatility of options on constituents within that index. Implied correlation reconciles implied volatility of index options with constituent implied volatility. Realized correlation is computed from the realized volatilities of the index and its constituents.Source: Lehman Brothers, OptionMetrics, Bloomberg, FAME October 10, 2006 4
  • 5. Equity Derivatives Strategy | Index Volatility Commentary Smallcap Vols CheapFigure 6: S&P 500 Index Volatility Summary S&P 500 Implied and Realized Volatility S&P 500 Weekly Returns vs Vol Changes 20% 4% 3% 2% 15% 1% 0% 10% -1% -2% -3% 5% -4% 5 6 6 6 5 06 6 06 06 5 6 6 -0 -0 0 -0 0 -0 -0 r-0 l-0 n- b- n- g- p- ov ay ec ar ct Ju Ap Ja Fe Ju Au Se O M 6 06 06 6 6 06 06 06 6 6 M N D -0 -0 -0 r-0 l-0 n- b- n- g- p- ay ar ar Ju Ap Ja Fe Ju Au Se M M M SPX Implied Vol (3-month) SPX Realized Vol (3-month) SPX Implied Vol (1-month) SPX Realized Vol (1-month) SPX Weekly Return SPX Weekly Change in Implied Vol (1m) Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers, OptionMetrics, Bloomberg Note: 1-month and 3-month implied volatility are interpolated volatilities for rolling maturities. 3-month realized volatility is calculated as the standard deviation of daily log returns over a 66 trading day historical window. 1- month realized volatility uses 22 days. Weekly spot returns in the index are compared with weekly changes in 1-month ATM implied volatility. S&P 500 Put-Call Skew S&P 500 Skew (1-week Changes) 7% 1.0% 6% SPX 30-delta Skew (3-month) SPX 30-delta Skew (1-month) 5% 0.0% 4% 3% -1.0% 2% 1% -2.0% 0% 6 6 7 07 7 08 8 6 -0 -0 -0 -0 -0 -0 n- n- ov ec ar ec c ct De Ju Ju O M N D D 5 06 6 06 6 6 5 5 6 06 06 6 -0 -0 -0 -0 0 r-0 0 l-0 - n- b- n- g- p- ov ay ec ar ct SPX 1w Imp Vol Chg (95%) SPX 1w Imp Vol Chg (100%) SPX 1w Imp Vol Chg (105%) Ju Ap Fe Ja Ju Au Se O M M N D Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers Note: The 30-delta skew is calculated as the difference between the 30-delta put and 30-delta call implied volatililty. Weekly changes of implied volatility at the 95% and 105% strike versus the at-the-money strike provide a measure of richening/cheapening of skew. Term Structure of ATM Implied Volatility (S&P 500) History of S&P 500 Term Spread 18% 3% 17% 2% 16% 15% 1% 14% 0% 13% 12% -1% 11% Last 1-wk Back 1-mo Back SPX 12M-3M Term Spread -2% 10% SPX 3M-1M Term Spread 9% -3% 6 6 7 07 7 08 8 6 5 06 6 06 6 6 5 5 6 06 06 6 -0 -0 -0 -0 -0 -0 0 -0 -0 -0 0 r-0 0 l-0 n- n- - v- n- b- n- g- p- ar ov ec ec ec ct ay ec ar ct Ju Ap Ju Ju No Ja Fe Ju Au Se O O M M N D D D M D Source: Lehman Brothers Note: The volatility term structure shows implied volatility for ATM strike options for each listed expiration. The term spread history plots the implied vol difference between 12-month and 3-month options and that between 3-month and 1-month options for the last 1 year.Source: Lehman Brothers, OptionMetrics, Bloomberg, FAME October 10, 2006 5
  • 6. Equity Derivatives Strategy | Index Volatility Commentary Smallcap Vols CheapFigure 7: Nasdaq 100 Index Volatility Summary Nasdaq 100 Implied and Realized Volatility Nasdaq 100 Weekly Returns vs Vol Changes 25% 8% 6% 20% 4% 2% 0% 15% -2% -4% 10% -6% 5 6 6 6 5 06 6 06 06 5 6 6 -0 -0 0 -0 0 -0 -0 r-0 l-0 n- b- n- g- p- ov ay ec ar ct Ju Ap Ja Fe Ju Au Se O M 6 06 06 6 6 06 06 06 6 6 M N D -0 -0 -0 r-0 l-0 n- b- n- g- p- ay ar ar Ju Ap Ja Fe Ju Au Se M M M NDX Implied Vol (3-month) NDX Realized Vol (3-month) NDX Implied Vol (1-month) NDX Realized Vol (1-month) NDX Weekly Return NDX Weekly Change in Implied Vol (1m) Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers, OptionMetrics, Bloomberg Note: 1-month and 3-month implied volatility are interpolated volatilities for rolling maturities. 3-month realized volatility is calculated as the standard deviation of daily log returns over a 66 trading day historical window. 1- month realized volatility uses 22 days. Weekly spot returns in the index are compared with weekly changes in 1-month ATM implied volatility. Nasdaq 100 Put-Call Skew Nasdaq 100 Skew (1-week Changes) 6% 0.0% NDX 30-delta Skew (3-month) 5% NDX 30-delta Skew (1-month) 4% -1.0% 3% 2% -2.0% 1% 0% -3.0% -1% 6 6 7 07 7 6 -0 -0 -0 -0 -0 n- ov ec ar ec ct Ju O M N D D 5 06 6 06 6 6 5 5 6 06 06 6 -0 -0 -0 -0 0 r-0 0 l-0 - n- b- n- g- p- ov ay ec ar ct NDX 1w Imp Vol Chg (95%) NDX 1w Imp Vol Chg (100%) NDX 1w Imp Vol Chg (105%) Ju Ap Fe Ja Ju Au Se O M M N D Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers Note: The 30-delta skew is calculated as the difference between the 30-delta put and 30-delta call implied volatililty. Weekly changes of implied volatility at the 95% and 105% strike versus the at-the-money strike provide a measure of richening/cheapening of skew. Term Structure of ATM Implied Volatility (Nasdaq 100) History of Nasdaq 100 Term Spread 21% 3% 20% 2% 19% 1% 18% 0% 17% NDX 12M-3M Term Spread -1% 16% Last 1-wk Back 1-mo Back NDX 3M-1M Term Spread 15% -2% 6 6 7 07 7 6 5 06 6 06 6 6 5 5 6 06 06 6 -0 -0 -0 -0 -0 -0 -0 -0 -0 0 r-0 0 l-0 n- - n- b- n- g- p- ar ov ec ec ct ov ay ec ar ct Ju Ap Ju Ja Fe Ju Au Se O O M M N D D M N D Source: Lehman Brothers Note: The volatility term structure shows implied volatility for ATM strike options for each listed expiration. The term spread history plots the implied vol difference between 12-month and 3-month options and that between 3-month and 1-month options for the last 1 year.Source: Lehman Brothers, OptionMetrics, Bloomberg, FAME October 10, 2006 6
  • 7. Equity Derivatives Strategy | Index Volatility Commentary Smallcap Vols CheapFigure 8: Russell 2000 Index Volatility Summary IWM Implied and Realized Volatility IWM Weekly Returns vs Vol Changes 30% 8% 6% 25% 4% 20% 2% 0% 15% -2% -4% 10% -6% 5 6 6 6 5 06 6 06 06 5 6 6 -0 -0 0 -0 0 -0 -0 r-0 l-0 n- b- n- g- p- ov ay ec ar ct Ju Ap Fe Ja Ju Au Se O M 6 06 06 6 6 06 06 06 6 6 M N D -0 -0 -0 r-0 l-0 n- b- n- g- p- ay ar ar Ju Ap Ja Fe Ju Au Se M M M IWM Implied Vol (3-month) IWM Realized Vol (3-month) IWM Implied Vol (1-month) IWM Realized Vol (1-month) IWM Weekly Return IWM Weekly Change in Implied Vol (1m) Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers, OptionMetrics, Bloomberg Note: 1-month and 3-month implied volatility are interpolated volatilities for rolling maturities. 3-month realized volatility is calculated as the standard deviation of daily log returns over a 66 trading day historical window. 1- month realized volatility uses 22 days. Weekly spot returns in the index are compared with weekly changes in 1-month ATM implied volatility. IWM Put-Call Skew IWM Skew (1-week Changes) 6% 0.0% 5% -1.0% 4% -2.0% 3% 2% -3.0% IWM 30-delta Skew (3-month) 1% IWM 30-delta Skew (1-month) -4.0% 0% 6 6 7 07 7 08 09 6 -0 -0 -0 -0 -0 n- n- n- ov ec ar ec ct Ju Ja Ja O M N D D 5 06 6 06 6 6 5 5 6 06 06 6 -0 -0 -0 -0 0 r-0 0 l-0 - n- b- n- g- p- ov ay ec ar ct IWM 1w Imp Vol Chg (95%) IWM 1w Imp Vol Chg (100%) IWM 1w Imp Vol Chg (105%) Ju Ap Fe Ja Ju Au Se O M M N D Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers Note: The 30-delta skew is calculated as the difference between the 30-delta put and 30-delta call implied volatililty. Weekly changes of implied volatility at the 95% and 105% strike versus the at-the-money strike provide a measure of richening/cheapening of skew. Term Structure of ATM Implied Volatility (IWM) History of IWM Term Spread 24% 4% 23% 3% 2% 22% 1% 21% 0% 20% -1% 19% -2% 18% -3% 17% Last 1-wk Back 1-mo Back IWM 12M-3M Term Spread -4% IWM 3M-1M Term Spread 16% -5% 15% -6% 6 6 7 07 7 08 09 6 5 06 5 6 06 6 6 06 06 5 6 6 -0 -0 -0 -0 -0 -0 -0 -0 -0 0 r-0 0 l-0 n- n- n- - n- b- n- g- p- ar ov ec ec ct ov ay ec ar ct Ju Ju Ja Ja Ap Fe Ja Ju Au Se O M O N D D M M N D Source: Lehman Brothers Source: Lehman Brothers, OptionMetrics, FAME Note: The volatility term structure shows implied volatility for ATM strike options for each listed expiration. The term spread history plots the implied vol difference between 12-month and 3-month options and that between 3-month and 1-month options for the last 1 year.Source: Lehman Brothers, OptionMetrics, Bloomberg, FAME October 10, 2006 7
  • 8. Equity Derivatives Strategy | Index Volatility Commentary Smallcap Vols CheapAnalyst 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.To the extent that any of the conclusions are based on a quantitative model, Lehman Brothers hereby certifies (1) that the views expressed in this research emailaccurately reflect the firms quantitative research model (2) no part of the firms compensation was, is or will be directly or indirectly related to the specificrecommendations or views expressed in this research report.Important DisclosuresLehman 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 aconflict of interest that could affect the objectivity of this email communication.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 tothem, where such research is available. Customers can access this independent research at www.lehmanlive.com or can call 1-800-2-LEHMAN to request a copy ofthis research.Investors should consider this communication as only a single factor in making their investment decision.The analysts responsible for preparing this report have received compensation based upon various factors including the Firms total revenues, a portion of which isgenerated by investment banking activities.Stock price and ratings history charts along with other important disclosures are available on our disclosure website at www.lehman.com/disclosuresAnd may also be obtained by sending a written request to: LEHMAN BROTHERS CONTROL ROOM , 745 SEVENTH AVENUE, 19TH FLOOR NEW YORK, NY10019Options 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.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. This material is distributed in Japan by Lehman Brothers Japan Inc., and in Hong Kong by Lehman Brothers Asia Limited. This material is distributed in Australiaby Lehman Brothers Australia Pty Limited, and in Singapore by Lehman Brothers Inc., Singapore Branch. (LBIS). 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