September 26, 2006                                    Index Volatility Commentary      Ryan Renicker, CFA        1.212.526...
Equity Derivatives Strategy | Index Volatility Commentary                                         A Closer Look at Volatil...
Equity Derivatives Strategy | Index Volatility Commentary                                                         Short Va...
Equity Derivatives Strategy | Index Volatility CommentaryFigure 7: S&P 500 Index Volatility Summary                       ...
Equity Derivatives Strategy | Index Volatility CommentaryFigure 8: Nasdaq 100 Index Volatility Summary                    ...
Collar Strategies - Not Hedged - Profitable but Also Risky
Collar Strategies - Not Hedged - Profitable but Also Risky
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Collar Strategies - Not Hedged - Profitable but Also Risky

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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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Collar Strategies - Not Hedged - Profitable but Also Risky

  1. 1. September 26, 2006 Index Volatility Commentary Ryan Renicker, CFA 1.212.526.9425 • Systematic strategies that short index volatility have been popular in a period of historically lowryan.renicker@lehman.com realized volatility. Devapriya Mallick 1.212.526.5429 • Unhedged put and call writing using OTM SPX options have been profitable strategies over the dmallik@lehman.com last decade, but expose the investor to disproportionate downside risks. • Short variance swap strategies on the SPX have remained profitable in spite of vols coming off in recent months. However, sellers of NDX variance have been barely compensated for their short gamma risk.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 7.
  2. 2. Equity Derivatives Strategy | Index Volatility Commentary A Closer Look at Volatility Selling Strategies With the VIX hovering around 12, the performance of systematic volatility selling strategies merits closer scrutiny. Due to the usual implied-realized vol premium, these strategies are popular as a means of yield enhancement, either on a hedged or unhedged basis. Figure 1 shows the monthly P/L of a strategy that sells 5% OTM puts on the S&P 500 as of each monthly expiration date. Over a ten year period, the short puts would have generated a positive yield but would also have exposed the seller to disproportionate downside risks, such as in 2001 and 2002. The cumulative returns from a strategy that shorts 1-month SPX puts on monthly expirations using a $100 margin (Figure 2), while still positive, have been tapering off since 2003. This is not surprising given the low vol environment of the last few years.Figure 1: Monthly P/L from Short 1-Month SPX Puts (5% OTM) Figure 2: Cumulative P/L –1-Month SPX Put Selling Strategy 20 300 10 0 -10 200 -20 -30 -40 100 -50 -60 Payoff per Cumulative Payoff Short SPX Put (Short SPX Puts) -70 -80 0 96 97 98 99 00 01 02 03 04 05 06 96 97 98 99 00 01 02 03 04 05 06 n- n- n- n- n- n- n- n- n- n- n- n- n- n- n- n- n- n- n- n- n- n- Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja JaSource: Lehman Brothers, OptionMetrics, Bloomberg Source: Lehman Brothers, OptionMetrics, Bloomberg A similar observation can be made about a strategy of selling 5% OTM calls on a monthly basis (Figure 3). Here the premium compression trend in the last few years seems to be even more pronounced than for the put-selling strategy. This is partly because the market has rallied steadily over this period, increasing the odds of the written calls finishing in the money. Another factor explaining this is the popularity of index call overwriting that puts downward pressure on OTM call implied vols on index options.Figure 3: Monthly P/L from SPX Call Writing Strategy (5% OTM) Figure 4: Cumulative P/L – Short 1-Month SPX Calls Strategy 20 160 0 140 120 -20 100 -40 80 -60 60 -80 40 Cumulative Payoff (Short SPX Calls) Payoff per Short 20 -100 SPX Call 0 -120 96 97 98 99 00 01 02 03 04 05 06 96 97 98 99 00 01 02 03 04 05 06 n- n- n- n- n- n- n- n- n- n- n- Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja n- n- n- n- n- n- n- n- n- n- n- Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja JaSource: Lehman Brothers, OptionMetrics, Bloomberg Source: Lehman Brothers, OptionMetrics, Bloomberg September 26, 2006 2
  3. 3. Equity Derivatives Strategy | Index Volatility Commentary Short Variance Swaps Systematic call or put selling exposes the investor to directional risk. Thus, even if realized volatility subsequently turns out to be lower than the implied volatility of the written options, the investor could still lose if the market continues upwards or downwards in a steady grind. Delta-hedging on a dynamic basis is one means of mitigating this, but is imperfect due to discontinuous hedging and transaction costs. Variance swaps are instruments that give pure exposure to future realized volatility (gamma) and eliminate the need for dynamic hedging. Figure 5 shows the weekly P/L of a strategy that systematically shorts 1-month variance swaps on the S&P 500. We find that this has largely been a profitable tactic over the past 18 months except for periods of minor market shocks (such as Apr 05, Oct 05 and May/Jun 06). Furthermore, we can make the following observations: • The immediate aftermath of a sell-off is the most attractive time to sell premium, especially if the investor believes the shock to be short-lived. At such times, the bid on implied vols allows the variance seller to pick up a higher premium. • Premiums have been declining over the last two months and for the NDX (Figure 6), are barely at levels where the investor gets sufficiently compensated for the short gamma risk. In spite of SPX variance having cheapened considerably relative to NDX, variance selling has worked better for the SPX only because of abysmally low vols in the latter. • In the last few years, the occasional spike in realized volatility has been milder than in the period ending in 2002. Focusing on a shorter history ignores the disproportionate risks this strategy exposes investors to, in the event of a market crash. At present, tail risks on account of macro factors seem to have receded somewhat, with the inflation picture looking less ominous and last week’s Philadelphia Fed survey causing the market to assign a one-third probability to a Fed ease by year-end. However, with earnings season coming up in a few weeks, and lack of clarity around the effect of slowing growth on corporate profits, we do not believe premium selling strategies offer an attractive risk-reward at this point.Figure 5: Weekly Payoff From Short 1-Month SPX Variance Swaps1 Figure 6: Short Variance Swap Payoff for NDX 2,000 2,500 Weekly P/L - Short SPX 2,000 1,500 Variance Swap 1,500 Weekly P/L (per Mn Vega) Weekly P/L (per Mn Vega) 1,000 1,000 500 500 0 0 -500 -500 -1,000 -1,000 -1,500 -2,000 Weekly P/L - Short NDX -1,500 -2,500 Variance Swap -2,000 -3,000 06 05 06 05 06 05 06 05 06 05 05 05 05 06 05 05 ay ar ar ct ay g n l ar ar ec ct g l n ec Ju Ju Au Ju Au Ju O M M O M M M M D 28 D 28 21 21 24 03 10 24 03 10 12 19 12 19 30 30 Week Ending Week EndingSource: Lehman Brothers, Bloomberg Source: Lehman Brothers, Bloomberg 1 In all cases, we assume mid-market execution and ignore the effect of bid-ask spreads on the respective strategies. September 26, 2006 3
  4. 4. Equity Derivatives Strategy | Index Volatility CommentaryFigure 7: 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 05 5 06 6 06 5 6 6 0 -0 0 -0 0 -0 -0 r-0 l-0 v- p- n- b- n- g- ay ec ar ct Ju Ap No Fe Se Ja Ju Au O M 6 06 06 6 6 06 06 06 6 6 M 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% 3.0% 6% SPX 30-delta Skew (3-month) 2.0% SPX 30-delta Skew (1-month) 5% 1.0% 4% 0.0% 3% 2% -1.0% 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 05 5 05 6 06 6 -0 -0 -0 0 r-0 0 l-0 - p- c- n- b- n- g- ov ay ar ct SPX 1w Imp Vol Chg (95%) SPX 1w Imp Vol Chg (100%) SPX 1w Imp Vol Chg (105%) Ju Ap De Fe Se Ja Ju Au O M M N 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 05 5 5 6 06 6 -0 -0 -0 -0 -0 -0 0 -0 -0 -0 0 r-0 0 l-0 n- n- - v- p- n- b- n- g- ar ov ec ec ec ct ay ec ar ct Ju Ap Ju Ju No Se Ja Fe Ju Au 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 September 26, 2006 4
  5. 5. Equity Derivatives Strategy | Index Volatility CommentaryFigure 8: 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 05 5 06 6 06 5 6 6 0 -0 0 -0 0 -0 -0 r-0 l-0 v- p- n- b- n- g- ay ec ar ct Ju Ap No Fe Se Ja Ju Au O M 6 06 06 6 6 06 06 06 6 6 M 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% 3% -1.0% 2% 1% 0% -2.0% -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 05 5 05 6 06 6 -0 -0 -0 0 r-0 0 l-0 - p- c- n- b- n- g- ov ay ar ct NDX 1w Imp Vol Chg (95%) NDX 1w Imp Vol Chg (100%) NDX 1w Imp Vol Chg (105%) Ju Ap De Fe Se Ja Ju Au O M M N 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% Last 1-wk Back 1-mo Back NDX 12M-3M Term Spread -1% 16% NDX 3M-1M Term Spread 15% -2% 6 6 7 07 7 6 5 06 6 06 6 6 05 5 5 6 06 6 -0 -0 -0 -0 -0 0 -0 -0 -0 0 r-0 0 l-0 n- - v- p- n- b- n- g- ar ov ec ec ct ay ec ar ct Ju Ap Ju No Se Ja Fe Ju Au O O M M N 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 September 26, 2006 5

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