Collar Strategies - Not Hedged - Profitable but Also Risky

Lehman Brothers does and seeks to do business with companies covered in its research reports. As a result, investors should be aware that the firm may have a conflict of interest that could affect the objectivity of this report.

Customers of Lehman Brothers in the United States can receive independent, third-party research on the company or companies covered in this report, at no cost to them, where such research is available. Customers can access this independent research at www.lehmanlive.com or can call 1-800-2LEHMAN to request a copy of this research.

Investors should consider this report as only a single factor in making their investment decision.

PLEASE SEE ANALYST(S) CERTIFICATION AND IMPORTANT DISCLOSURES BEGINNING ON PAGE 7.

Index Volatility Commentary

• Systematic strategies that short index volatility have been popular in a period of historically low realized volatility.

• Unhedged put and call writing using OTM SPX options have been profitable strategies over the 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.

September 26, 2006

Ryan Renicker, CFA 1.212.526.9425

[email protected]

Devapriya Mallick 1.212.526.5429

[email protected]

Equity Derivatives Strategy | Index Volatility Commentary

September 26, 2006 2

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

-80

-70-60

-50

-40-30-20

-100

10

20

Jan-9

6

Jan-9

7

Jan-9

8

Jan-9

9

Jan-0

0

Jan-0

1

Jan-0

2

Jan-0

3

Jan-0

4

Jan-0

5

Jan-0

6

Payoff perShort SPX Put

0

100

200

300

Jan-9

6

Jan-9

7

Jan-9

8

Jan-9

9

Jan-0

0

Jan-0

1

Jan-0

2

Jan-0

3

Jan-0

4

Jan-0

5

Jan-0

6

Cumulative Payoff(Short SPX Puts)

Source: 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

-120

-100

-80

-60

-40

-20

0

20

Jan-9

6

Jan-9

7

Jan-9

8

Jan-9

9

Jan-0

0

Jan-0

1

Jan-0

2

Jan-0

3

Jan-0

4

Jan-0

5

Jan-0

6

Payoff per ShortSPX Call

0

20

40

60

80

100

120

140

160

Jan-9

6

Jan-9

7

Jan-9

8

Jan-9

9

Jan-0

0

Jan-0

1

Jan-0

2

Jan-0

3

Jan-0

4

Jan-0

5

Jan-0

6

Cumulative Payoff(Short SPX Calls)

Source: Lehman Brothers, OptionMetrics, Bloomberg Source: Lehman Brothers, OptionMetrics, Bloomberg



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

-1,500

-1,000

-500

0

500

1,000

1,500

2,000

24Mar0

5

03Ju

n05

12Aug

05

21Oct0

5

30Dec

05

10Mar0

6

19May

06

28Ju

l06

Week Ending

Wee

kly

P/L

(per

Mn

Vega

)

Weekly P/L - Short SPXVariance Swap

-3,000

-2,500-2,000

-1,500

-1,000

-5000

500

1,000

1,5002,000

2,500

24Mar0

5

03Ju

n05

12Aug

05

21Oct0

5

30Dec

05

10Mar0

6

19May

06

28Ju

l06

Week Ending

Wee

kly

P/L

(per

Mn

Vega

)

Weekly P/L - Short NDXVariance Swap

Source: 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.



Figure 7: S&P 500 Index Volatility Summary

S&P 500 Put-Call Skew

0%

1%

2%

3%

4%

5%

6%

7%

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06

Mar-06

Apr-06

May-06

Jun-0

6Ju

l-06

Aug-06

SPX 30-delta Skew (3-month)SPX 30-delta Skew (1-month)

S&P 500 Implied and Realized Volatility

5%

10%

15%

20%

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06

Mar-06

Apr-06

May-06

Jun-0

6Ju

l-06

Aug-06

SPX Implied Vol (3-month) SPX Realized Vol (3-month)SPX Implied Vol (1-month) SPX Realized Vol (1-month)

S&P 500 Skew (1-week Changes)

-2.0%

-1.0%

0.0%

1.0%

2.0%

3.0%

Oct-06

Nov-06

Dec-06

Mar-07

Jun-0

7

Dec-07

Jun-0

8

Dec-08

SPX 1w Imp Vol Chg (95%) SPX 1w Imp Vol Chg (100%) SPX 1w Imp Vol Chg (105%)

Term Structure of ATM Implied Volatility (S&P 500)

9%

10%

11%

12%

13%

14%

15%

16%

17%

18%

Oct-06

Nov-06

Dec-06

Mar-07

Jun-0

7

Dec-07

Jun-0

8

Dec-08

Last 1-wk Back 1-mo Back

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.

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

Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers

Source: Lehman Brothers, OptionMetrics

S&P 500 Weekly Returns vs Vol Changes

-4%

-3%

-2%

-1%

0%

1%

2%

3%

4%

Jan-0

6

Feb-06

Mar-06

Mar-06

Apr-06

May-06

Jun-0

6Ju

l-06

Aug-06

Sep-06

SPX Weekly Return SPX Weekly Change in Implied Vol (1m)

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.

History of S&P 500 Term Spread

-3%

-2%

-1%

0%

1%

2%

3%

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06

Mar-06

Apr-06

May-06

Jun-0

6Ju

l-06

Aug-06

SPX 12M-3M Term SpreadSPX 3M-1M Term Spread

Source: Lehman Brothers, OptionMetrics, Bloomberg, FAME



Figure 8: Nasdaq 100 Index Volatility Summary

Nasdaq 100 Put-Call Skew

-1%

0%

1%

2%

3%

4%

5%

6%

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06

Mar-06

Apr-06

May-06

Jun-0

6Ju

l-06

Aug-06

NDX 30-delta Skew (3-month)NDX 30-delta Skew (1-month)

Nasdaq 100 Implied and Realized Volatility

10%

15%

20%

25%

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06

Mar-06

Apr-06

May-06

Jun-0

6Ju

l-06

Aug-06

NDX Implied Vol (3-month) NDX Realized Vol (3-month)NDX Implied Vol (1-month) NDX Realized Vol (1-month)

Nasdaq 100 Skew (1-week Changes)

-2.0%

-1.0%

0.0%

Oct-06

Nov-06

Dec-06

Mar-07

Jun-0

7

Dec-07

NDX 1w Imp Vol Chg (95%) NDX 1w Imp Vol Chg (100%) NDX 1w Imp Vol Chg (105%)

Term Structure of ATM Implied Volatility (Nasdaq 100)

15%

16%

17%

18%

19%

20%

21%

Oct-06

Nov-06

Dec-06

Mar-07

Jun-0

7

Dec-07




Source: Lehman Brothers



Nasdaq 100 Weekly Returns vs Vol Changes

-6%

-4%

-2%

0%

2%

4%

6%

8%

Jan-0

6

Feb-06

Mar-06

Mar-06

Apr-06

May-06

Jun-0

6Ju

l-06

Aug-06

Sep-06

NDX Weekly Return NDX Weekly Change in Implied Vol (1m)



History of Nasdaq 100 Term Spread

-2%

-1%

0%

1%

2%

3%

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06

Mar-06

Apr-06

May-06

Jun-0

6Ju

l-06

Aug-06

NDX 12M-3M Term Spread

NDX 3M-1M Term Spread




Figure 9: Russell 2000 Index Volatility Summary

IWM Put-Call Skew

0%

1%

2%

3%

4%

5%

6%

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06

Mar-06

Apr-06

May-06

Jun-0

6Ju

l-06

Aug-06

IWM 30-delta Skew (3-month)IWM 30-delta Skew (1-month)

IWM Implied and Realized Volatility

10%

15%

20%

25%

30%

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06

Mar-06

Apr-06

May-06

Jun-0

6Ju

l-06

Aug-06

IWM Implied Vol (3-month) IWM Realized Vol (3-month)IWM Implied Vol (1-month) IWM Realized Vol (1-month)

IWM Skew (1-week Changes)

-1.0%

0.0%

1.0%

Oct-06

Nov-06

Dec-06

Mar-07

Jun-0

7

Dec-07

Jan-0

8

Jan-0

9

IWM 1w Imp Vol Chg (95%) IWM 1w Imp Vol Chg (100%) IWM 1w Imp Vol Chg (105%)

Term Structure of ATM Implied Volatility (IWM)

19%

20%

21%

22%

23%

Oct-06

Nov-06

Dec-06

Mar-07

Jun-0

7

Dec-07

Jan-0

8

Jan-0

9




Source: Lehman Brothers Source: Lehman Brothers, OptionMetrics, FAME



IWM Weekly Returns vs Vol Changes

-6%

-4%

-2%

0%

2%

4%

6%

8%

Jan-0

6

Feb-06

Mar-06

Mar-06

Apr-06

May-06

Jun-0

6Ju

l-06

Aug-06

Sep-06

IWM Weekly Return IWM Weekly Change in Implied Vol (1m)



History of IWM Term Spread

-6%

-5%

-4%

-3%

-2%

-1%

0%

1%

2%

3%

4%

Sep-05

Oct-05

Nov-05

Dec-05

Jan-0

6

Feb-06

Mar-06

Apr-06

May-06

Jun-0

6Ju

l-06

Aug-06

IWM 12M-3M Term Spread

IWM 3M-1M Term Spread




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 or issuers 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 expressed in 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 email accurately reflect the firm's quantitative research model (2) no part of the firm's compensation was, is or will be directly or indirectly related to the specific recommendations or views expressed in this research report. Important Disclosures Lehman Brothers does and seeks to do business with companies covered in its research reports. As a result, investors should be aware that the firm may have a conflict of interest that could affect the objectivity of this 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 to them, 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 of this 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 Firm’s total revenues, a portion of which is generated 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/disclosures

And may also be obtained by sending a written request to: LEHMAN BROTHERS CONTROL ROOM , 745 SEVENTH AVENUE, 19TH FLOOR NEW YORK, NY 10019

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 within this 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 by Lehman Brothers International (Europe), authorized and regulated by the Financial Services Authority, in connection with its distribution in the European Economic Area. 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 Australia by Lehman Brothers Australia Pty Limited, and in Singapore by Lehman Brothers Inc., Singapore Branch. (“LBIS”). Where this material is distributed by LBIS, please note that it is intended for general circulation only and the recommendations contained herein does not take into account the specific investment objectives, financial situation or particular needs of any particular person. An investor should consult his Lehman Brothers’ representative regarding the suitability of the product and take into account his specific investment objectives, financial situation or particular needs before he makes a commitment to purchase the investment product. This material is distributed in Korea by Lehman Brothers International (Europe) Seoul Branch. This document is for information purposes only and it should not be regarded as an offer to sell or as a solicitation of an offer to buy the securities or other instruments mentioned in it. No part of this document may be reproduced in any manner without the written permission of Lehman Brothers. With the exception of disclosures relating to Lehman Brothers, this research report is based on current public information that Lehman Brothers considers reliable, but we make no representation that it is accurate or complete, and it should not be relied on as such. In the case of any disclosure to the effect that Lehman Brothers Inc. or its affiliates beneficially own 1% or more of any class of common equity securities of the subject company, the computation of beneficial ownership of securities is based upon the methodology used to compute ownership under Section 13(d) of the United States' Securities Exchange Act of 1934. In the case of any disclosure to the effect that Lehman Brothers Inc. and/or its affiliates hold a short position of at least 1% of the outstanding share capital of a particular company, such disclosure relates solely to the ordinary share capital of the company. Accordingly, while such calculation represents Lehman Brothers’ holdings net of any long position in the ordinary share capital of the company, such calculation excludes any rights or obligations that Lehman Brothers may otherwise have, or which may accrue in the future, with respect to such ordinary share capital. Similarly such calculation does not include any shares held or owned by Lehman Brothers where such shares are held under a wider agreement or arrangement (be it with a client or a counterparty) concerning the shares of such company (e.g. prime broking and/or stock lending activity). Any such disclosure represents the position of Lehman Brothers as of the last business day of the calendar month preceding the date of this report.

This material is provided with the understanding that Lehman Brothers is not acting in a fiduciary capacity. Opinions expressed herein reflect the opinion of Lehman Brothers and are subject to change without notice. The products mentioned in this document may not be eligible for sale in some states or countries, and they may not be suitable for all types of investors. If an investor has any doubts about product suitability, he should consult his Lehman Brothers representative. The value of and the income produced by products may fluctuate, so that an investor may get back less than he invested. Value and income may be adversely affected by exchange rates, interest rates, or other factors. Past performance is not necessarily indicative of future results. If a product is income producing, part of the capital invested may be used to pay that income. © 2006 Lehman Brothers. All rights reserved. Additional information is available 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 Firm's equity research reports covering U.S. companies are available at www.lehman.com/disclosures.

Complete disclosure information on companies covered by Lehman Brothers Equity Research is available at www.lehman.com/disclosures.

Collar Strategies - Not Hedged - Profitable but Also Risky

Economy & Finance

Transcript of Collar Strategies - Not Hedged - Profitable but Also Risky