Pinning of Stock Prices on Expiration Date - Equity Options

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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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Pinning of Stock Prices on Expiration Date - Equity Options

  1. 1. February 10, 2006 Options Strategy Monthly: February 2006 Ryan Renicker, CFA Q4 Earnings and Volatility Patterns. We find that the average absolute price reaction 1.212.526.9425 immediately following earnings announcements this season has been slightly higher than theryan.renicker@lehman.com average during the past two years. On the other hand, the average change in stocks’ implied Devapriya Mallick volatility heading into the announcement date has been similar to the historical average. We also 1.212.526.5429 find that Retailing stocks had the highest average absolute price reaction relative to what was dmallik@lehman.com priced in by options market. However, Semiconductors & Semiconductor Equipment stocks had the lowest average absolute price reaction relative to what the options market had priced in prior to their earnings announcements. Rapid Growth in ETF Option Volumes. The growth rate of volume in ETF options has outpaced that of single stock options since 2004. Volume in options on Energy ETFs has grown at an even faster pace, and currently accounts for about half of the total volume in all Sector-based ETF options. “Pinning” of Stock Prices on Expiration Date. We find that for stocks closing within 1% of a strike on the day prior to expiration, the return distribution on the expiration date exhibits slightly greater clustering around zero in comparison to the average distribution of equity price returns over the past two years. For stocks with higher open interest of outstanding contracts as a proportion of the stock’s volume, there appears to be a greater dampening of price returns, possibly a consequence of delta-hedging activity by long gamma traders. Sector Volatility Snapshots. Our Sector Volatility Snapshots allow investors to quickly assess aggregate volatility information for each S&P 500 GICS sector. The snapshots 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.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 23.
  2. 2. Equity Derivatives Strategy | Options Strategy Monthly: February 2006 Table of Contents Fourth Quarter Earnings Related Volatility............................................................................. 3 Volatility Trading Environment ............................................................................................. 6 Rapid Growth in ETF Option Volumes ................................................................................. 6 Recent Developments in the Options Market......................................................................... 7 Impact of Option Expiration on Underlying Price Changes..................................................... 8 Price Returns in Expiration Week versus Other Weeks ............................................................ 8 Stock Return Distribution on Expiration Dates......................................................................... 9 Impact of Open Interest on Return Distribution ..................................................................... 10 Conclusion .................................................................................................................. 11 Appendix I: Sector Volatility Snapshots .............................................................................. 12 February 10, 2006 2
  3. 3. Equity Derivatives Strategy | Options Strategy Monthly: February 2006 Fourth Quarter Earnings Related Volatility This January, a majority of companies in the S&P 500 reported fourth quarter results. As of February 7, 2006, 367 S&P 500 constituents have reported 4Q earnings (including December 2005), of which 266 (72%) reported in January. Approximately 59% reported positive EPS surprises, outnumbering companies having negative surprises by a ratio of about 3.31. In this section, we examine how average implied and realized volatility changed during the 20 trading days leading up to each earnings announcement. Our sample universe includes companies in the S&P 500 that reported results from 12/1/05 to 2/7/06. Figure 1 illustrates the average absolute daily percent price change2 for S&P 500 companies that have already reported their results, during the 20 trading days leading up to and immediately following each company’s earnings announcement. We find the average absolute return immediately following earnings announcements (“absolute earnings reaction”) this season has been about 3.5%, slightly higher than the average post-earnings reaction S&P 500 companies experienced in the last two years.3 We believe this year’s slightly higher absolute earnings reaction could be influenced by the relatively large price reactions a select number of companies (such as INTC and YHOO) had in January. We also note that one month implied volatility began rising roughly three weeks before the date of announcement (Figure 2). This is similar to the historical behavior in implied volatility before the earnings announcement.Figure 1: Average Absolute EPS Reaction Ahead of Q4 Earnings Figure 2: Average 1-Month Implied Volatility Ahead of Q4 Earnings 4.0% 30% Average 1-Month Implied Volatility 3.5% Absolute Earnings Reaction 28% Average Absolute Return 3.0% 2.5% 26% 2.0% 24% 1.5% 1.0% 22% Average 1-Month Implied Volatility 0.5% 0.0% 20% t 0 8 6 4 2 0 t-8 t-6 t-4 t-2 0 8 6 4 2 0 t-8 t-6 t-4 t-2 t t-2 t-1 t-1 t-1 t-1 t-1 t- 2 t- 1 t- 1 t- 1 t- 1 t- 1 Days to Earnings Announcem ent Days to Earnings AnnouncementSource: Lehman Brothers, MarketQA Source: Lehman Brothers, OptionMetrics 1 Please see Inside the Earnings Season, U.S. Strategy for additional details. 2 From a volatility trading perspective, absolute returns (the absolute value of actual returns) are more relevant than actual returns. This is because pure volatility traders would delta-hedge option positions to minimize their exposure to directional moves in the underlying stock itself. 3 Please see our report Earnings Impact on Implied and Realized, Options Strategy Monthly, January 10, 2006 for a historical analysis of changes in volatility heading into earnings announcement dates. February 10, 2006 3
  4. 4. Equity Derivatives Strategy | Options Strategy Monthly: February 2006 Next, we examine the degree to which actual absolute earnings reactions thus far in Q4 ‘05 have differed from expected absolute earnings reactions the options market was pricing the day prior to each company’s earnings release. As Figure 3 illustrates, stocks within the Retailing industry group have had the highest average absolute earnings reaction versus what had been priced in by the options market. In other words, it appears that the options market has underestimated the magnitude of the absolute earnings reaction for stocks within the Retailing industry group. However, this average figure is likely skewed by a few companies (such as BBBY, BBY and AMZN) that had large downside surprises, and thus large absolute price returns (ten companies within this industry group have reported earnings so far). On the other hand, stocks within the Semiconductors & Semiconductor Equipment industry group have exhibited relatively low average absolute price returns versus what had been priced in by the options market. We believe one of the primary factors causing this relates to how risk expectations for a relatively high proportion of stocks within an industry group can change in response to one or two company-specific events. For example, we found that option market participants began pricing in higher expected price moves for the majority of Semiconductor stocks that had yet to report in the later half of January, following the large negative reaction to INTC’s earnings announcement. Figure 3: Difference in Implied and Actual Earnings Reaction by Industry Group 3% Implied - Actual Absolute Reaction 2% # Companies Reported 1% 0% Comml Svc & Suppl Tech Hard & Equip House & Pers Prod Semi & Semi Equip H Care Equip & Svc Food & Stpls Retail Food Bev & Tobacco Pharma & Biotech Real Estate Divers Financ Consumer Services Capital Goods Telecom Svc Cons Dur & Apparel Retailing Transportation Media Insurance Banks Auto & Components Energy Materials Utilities Software & Services -1% -2% -3% 31 27 28 24 26 23 19 21 14 16 20 17 17 11 13 10 6 6 10 8 5 5 4 5 -4% Source: Lehman Brothers, OptionMetrics, Bloomberg, MarketQA We have found that immediately following earnings events, 1-month implied volatility tends to decline by about 3 vol points, on average, for stocks within the S&P 500. In this section we examine how 1- month implied volatility changed following earnings announcement this season for companies having extremely positive (> 10%) or negative (< -10%) returns, to test whether changes in implied volatility following an earnings announcement can be dependent upon the direction of a stock’s return. February 10, 2006 4
  5. 5. Equity Derivatives Strategy | Options Strategy Monthly: February 2006 Figure 4: Implied Volatility Change in Stocks Having Large Earnings Reactions Stocks with Stocks with Large Positive Large Negative Reactions Reactions Number of Stocks 15 10 Average Return after Announcement 12.6% -12.3% Average Implied Vol Before Earnings 39% 40% Average Implied Vol After Earnings 31% 35% Average Change in Implied Vol -9% -6% Number of Implied Vol Decreases 15 7 % of Implied Vol Decreases 100% 70% Source: Lehman Brothers, Bloomberg As Figure 4 highlights, only 10 (15) of the companies that have reported earnings thus far have had large negative (positive) reactions following their earnings announcement. Among the 10 companies having large negative reactions, 3 experienced an increase in 1-month implied volatility the day after their earnings were released. On the other hand, for the 15 companies having the large positive stock price reactions, none had an increase in 1-month implied volatility after their earnings were released. In addition, all of these companies’ 1-month implied volatility declined the subsequent day. February 10, 2006 5
  6. 6. Equity Derivatives Strategy | Options Strategy Monthly: February 2006 Volatility Trading Environment Rapid Growth in ETF Option Volumes As we reported in last month’s edition of the Options Strategy Monthly, the total volume for options on single stocks4 increased dramatically during 2005. This general trend has continued in 2006, during which a couple of total daily volume records were set across exchanges. On the other hand, volume on the underlying stocks remains relatively flat. ETF Option Volume Rising Faster than Single Stock Option Volume We analyze how volume of options on Exchange Traded Funds (ETFs) has changed relative to option volume on single stocks. Our universe includes all listed ETFs based on U.S. indices and sectors that currently have options; the single stock universe includes the current constituents of the S&P 500. The sample period is from January 1, 2004 to January 31, 2006. We find that since January 2004, although the absolute 1-month average daily trading volume of single stock options remains high vs. options on ETFs5, the rate of increase in ETF options volume has continued to outpace growth in single stock option volume (Figure 5). We believe one of the primary reasons for this is the increase in the total number of ETFs introduced during the past two years. The total trading volume on these as well as ETFs introduced prior to 2004 has increased, leading to increasing option volumes on ETFs (Figure 6).Figure 5: Option Volume on ETFs Outpacing that of Single Stocks Figure 6: Volume on ETFs and Options on ETFs Rising 200 30 8,000 ETF Option Volume (Scaled) ETF Option Volume (MM contracts) Single-Stk. Option Volume (Scaled) ETF Volume (MM) 25 6,000 Option Avg. Volume (Scaled) 150 20 4,000 100 15 2,000 10 0 4 5 4 5 4 5 4 5 4 5 6 04 05 50 -0 -0 -0 -0 -0 -0 l-0 l-0 0 0 0 n- n- n- p- p- ay ay ar ar ov ov Ju Ju Ja Ja Ja Se Se M M M M N N 4 5 4 4 5 5 4 5 4 5 4 5 r-0 -0 r-0 -0 -0 0 -0 0 0 0 -0 -0 g- g- n- n- ct ct b b ec ec Ap Ap Au Au Ju Ju Fe Fe O O D DSource: Lehman Brothers, OptionMetrics. Source: Lehman Brothers, OptionMetrics, Bloomberg. ETF Option Volume versus Single Stock Option Volume: Macro Risk Matters We find the total volume of options on all U.S. ETFs tends to increase relative to options on stocks during periods of high macro risk expectations for equities, inferred by abnormally high S&P 500 implied volatility (Figure 7). It has been well established that abnormally high “macro fear” tends to result from market shocks, during which single stock performance becomes more dependent on the movement of the market/event itself, rather than company-specific factors such as earnings surprises. In other words, stocks tend to become more positively correlated with one another during periods of 4 Our sample universe includes constituents of the S&P 500 Index. 5 For example, during January 2006, the 1-month average daily option volume at the single-stock level was about 3.8 million contracts versus about 1.0 million for that of ETFs. February 10, 2006 6
  7. 7. Equity Derivatives Strategy | Options Strategy Monthly: February 2006 heightened macro risk expectations, particularly if the abnormally high level of implied volatility coincides with unanticipated events such as terrorist attacks, versus anticipated events such as earnings season, even if the index is realizing relatively lower volatility. Thus, one would expect investors trying to hedge their positions during periods of heightened macro uncertainty to use more “macro-related” instruments such as options on ETFs.Figure 7: Macro Fear: ETF vs. Single Stock Option Total Volume Figure 8: Energy ETF/Total Sector-Based ETF Option Volume Ratio 0.42 60% 70 Option Volume Ratio (Energy/Sector ETFs) 17% GM Credit, IBM Results, 0.40 Energy ETF/Sector ETF Options Volume Ratio ETF vs. Single Stock Option Volume Ratio Poor Econ. Data, SPX Selloff 50% Average Monthly Crude Price Avg Monthly Crude Oil Prices 0.38 Avg. SPX 3-Month Implied Vol. 16% 60 0.36 40% 15% 0.34 0.32 30% 50 14% 0.30 20% 13% 0.28 40 0.26 10% 12% Oil Spikes, Market Fears Rise 0.24 Q3 EPS Anxiety 0% 30 11% 0.22 4 5 4 5 4 5 4 5 4 5 6 04 05 -0 -0 -0 -0 -0 -0 l-0 l-0 0 0 0 n- n- n- p- p- 4 5 ay ay 4 5 ar ar 4 5 4 5 04 05 06 ov ov 04 05 Ju Ju -0 -0 -0 -0 -0 -0 l-0 l-0 Ja Ja Ja Se Se M M M M n- n- n- N N p- p- ay ay ar ar ov ov Ju Ju Ja Ja Ja Se Se M M M M N NSource: Lehman Brothers, OptionMetrics. Source: Lehman Brothers, OptionMetric, Bloomberg We also observe that the recent growth in volume of options on sector-based ETFs is largely driven by the increasing popularity of Energy sector ETFs (e.g. XLE, OIH). As Figure 8 illustrates, the average option volume in Energy ETFs has outpaced volume in other sectors. In addition, the total number of Energy ETF contracts currently trading represents about half of the total volume of options on all sector ETFs. This has occurred concurrently with the rally in crude oil prices and the Energy sector. Recent Developments in the Options Market Options on the VIX On February 24, options on the VIX index will commence trading, presenting an instrument for trading “volatility of volatility”. These options will have contracts expiring on the two near months apart from one additional expiration month on the February quarterly cycle. Investors who wish to insure their portfolios against a large market shock could use calls on the VIX as an alternative to purchasing S&P 500 index puts. However, the VIX index has historically experienced high realized volatility (22-day realized currently trades above 90%) and upside moves in the VIX could be magnified in the event of a large negative market catalyst. The asymmetry of changes in the VIX can be illustrated by the fact that since 1990, there have been 16 instances when it experienced an upside move of more than 20%, compared with 3 cases when the index fell by more than 20%. This should imply that writers of calls on the VIX would demand a higher premium, raising the cost of insurance using calls on the VIX. Change in Options Trading Hours U.S. option exchanges have announced a change in market trading hours for options on stocks and sector-based indexes or ETFs. Beginning February 13, the new trading hours will be from 9:30 AM ET to 4:00 PM ET, instead of the present closing time of 4:02 PM ET. Options on market indexes and ETFs on such indexes will continue to trade until 4:15 PM ET. February 10, 2006 7
  8. 8. Equity Derivatives Strategy | Options Strategy Monthly: February 2006 Impact of Option Expiration on Underlying Price Changes Equity options expire on the Saturday following the third Friday of each month, although the Friday of expiration (or Thursday if the Friday is an exchange holiday) is the last trading date for the expiring contracts. We have found that average contract volume traded in options on stocks and indexes increases as expiration week progresses and reaches a peak on the last trading day of the week6. Several studies have attempted to explore whether the introduction of options impacts the returns of their underlying stocks and indexes. In this study, we examine the effect option hedging activity has on the price movements in the stocks themselves as option expiration approaches. Market makers in option contracts tend to delta-hedge their positions to eliminate exposure to directional changes in the underlying price. This delta-hedging activity becomes more critical as option expiration approaches and the gamma for at-the-money options increases sharply. If the number of shares represented by the outstanding contracts is a significant proportion of the average daily volume in the stock, returns in the cash market can be affected by this delta hedging activity. Delta hedging by traders who have purchased options (long gamma positions) tend to dampen stock price moves, since they tend to hedge by buying the underlying stock when it declines, and sell shares when prices rise. For example, a volatility trader having a long call position would maintain a short position in the underlying stock to hedge against downside directional risk in the underlying. If the stock price increases, the call moves in the money and more shares are needed to be sold in order to maintain the delta-neutral position. The opposite holds if the price decreases, in which case the underlying shares would be repurchased to remain delta-neutral. Thus, if a large proportion of hedgers are long gamma, price changes in the underlying shares would tend to be dampened. On the other hand, delta-hedgers having a net short position in options tend to exacerbate moves in the underlying, since they tend to buy more shares of the underlying as its price increases and sell more when the shares decline. The extent to which stocks remain “pinned” to strikes having relatively high open interest depends on whether the majority of the delta-hedgers have a net long or short option position. Please note that the outstanding open interest at a given strike price is only an approximate measure of the anticipated hedging activity since option market makers can hedge their positions using other option contracts rather than the underlying stock itself. The universe we use in this study includes constituents of the S&P 500 Index. The time period used is from January 2004 to December 2005. Price Returns in Expiration Week versus Other Weeks We compare the average returns on days leading up to expiration Fridays with returns leading up to Fridays on non-expiration weeks. Figure 9 shows that the average return for S&P 500 stocks remains almost constant as the week progresses in non-expiration weeks. However, price variability has tended to be relatively lower toward the end of expiration weeks. 6 Please see Equity Volatility Snapshot, January 24, 2006 for additional details. February 10, 2006 8
  9. 9. Equity Derivatives Strategy | Options Strategy Monthly: February 2006 Figure 9: Comparative Returns in Expiration Week and Other Weeks 0.3% 1.7% 0.2% Absolute Daily Returns 1.6% Daily Returns 0.1% -0.1% t-2 t-1 t 1.5% -0.2% -0.3% 1.4% Expiration Week Returns Returns in Other Weeks Expiration Week Absolute Returns (RHS) Source: Lehman Brothers, OptionMetrics Stock Return Distribution on Expiration Dates Since the mean of the returns is distorted by extreme moves, we compare the return distribution of stocks from the close on the day before expiration to the close on expiration with the average return distribution for all companies in the universe during the last two years. We shortlist stocks whose price could potentially be impacted by hedging activity, by including stocks which close within 1% of a contract strike on the day prior to expiration. Options with such strikes are closer to their at-the-money level and hence are likely to experience wide fluctuations in their delta close to expiration. Figure 10 illustrates the distribution of expiration date returns for the shortlisted stocks. We standardize their returns by dividing their close-to-close return on expiration by their rolling 3-month realized volatility (we do this since a large price move is a more common in stocks having relatively high standard deviations of their returns). Thus, expressing stocks’ return distribution in terms of standard deviation levels adjusts the effect of stocks having higher volatility tending to experience large percentage moves with greater frequency. Figure 10: Distribution of Returns on Expiration Date versus Average Distribution 5% Average Distribution 4% Distribution on Expiration Probability 3% 2% 1% 0% 1 2 3 .3 .2 .1 0. 0. 0. -0 -0 -0 Standard Deviation of Returns Source: Lehman Brothers, MarketQA February 10, 2006 9
  10. 10. Equity Derivatives Strategy | Options Strategy Monthly: February 2006 We find that there is a slightly higher probability of returns remaining closer to zero versus the non- expiration-date return distribution when stocks have a closing price before expiration within 1% of a traded strike, although the effect is not very pronounced on an aggregate basis. This could be a consequence of the hedging activity of long option holders. We also find that the probability of large negative returns tends to be higher than that of the average distribution. However the probability of very large positive returns does not appear to be significantly different from the average distribution on non-expiration dates. The higher peak and fatter tail (representing a more leptokurtic7 distribution) are consistent with the expected delta-hedging activity, which tends to increase the frequency of very high or very low price returns at expiration. Impact of Open Interest on Return Distribution Having examined the return distribution when stocks close near a strike before expiration, we now analyze whether a large open interest of contracts outstanding at that strike has a tendency to cause a greater degree of ”pinning”. We can use the kurtosis of the return distribution as a “pin factor” or a rough proxy for measuring the impact of hedging activity. A higher pin factor would indicate a relatively larger number of returns clustered close to zero and a distribution having fatter tails. (Note that such a measure would be more stable in a distribution having a higher number of data points. Thus, this study only provides an approximate guide to the extent of the “pinning effect”. The open interest outstanding at each strike (calls plus puts) allows us to gauge the stock’s demand or supply if all option holders and writers were dynamically delta hedging their option positions. Thus, we divide the open interest by the stock’s volume to account for its liquidity. We divide the distribution into quartiles on the basis of this open interest to volume ratio, with Quartile 1 representing the group with the highest ratio. Figure 11 demonstrates that the two largest quartiles (according to this metric) exhibit relatively more leptokurtosis, whereas the extent of pinning appears to be much lower for the other two quartiles. However, the probability of extreme returns (more than 0.2 standard deviations) in either direction does not appear to depend very strongly upon the quartile of the open interest to volume ratio. Our study also indicates that high open interest as a proportion of stock volume results in a lower average absolute return for the stock on the day of expiration (Figure 12). This could imply that, on average, the delta-hedging activity of option traders who are net long options appears to have been more pronounced than the hedging activity of short gamma traders. 7 Kurtosis is the fourth moment of a distribution and is a measure of the “peakedness” or “fat-tailedness”. A leptokurtic distribution is one with a higher peak and fatter tails than the normal distribution. A platykurtic distribution has smaller tails and a flatter top than the normal distribution. February 10, 2006 10

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