November 17, 2005
                                    Enhanced Call Overwriting
      Ryan Renicker, CFA
        1.212.526...
Equity Derivatives Strategy | Enhanced Call Overwriting




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Equity Derivatives Strategy | Enhanced Call Overwriting


                                                           BXM R...
Equity Derivatives Strategy | Enhanced Call Overwriting


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Equity Derivatives Strategy | Enhanced Call Overwriting




                                                        Alteri...
Equity Derivatives Strategy | Enhanced Call Overwriting




                                 Altering Expiration Dates

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Equity Derivatives Strategy | Enhanced Call Overwriting


                                                          Enhanc...
Equity Derivatives Strategy | Enhanced Call Overwriting


                                         Performance of Enhanced...
Enhanced Call Overwriting (2005)
Enhanced Call Overwriting (2005)
Enhanced Call Overwriting (2005)
Enhanced Call Overwriting (2005)
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Enhanced Call Overwriting (2005)

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Enhanced Call Overwriting*

Systematically overwriting the S&P 500 with 1-month at-the-money calls, rebalanced on a monthly basis at expiration, outperformed the S&P 500 Index during our sample period (1996 – 2005). This “base case” overwriting strategy also generated superior risk-adjusted returns versus the index.

Overwriting portfolios with out-of-the-money calls tends to outperform at-the-money overwriting during market rallies, but provides less protection during market downturns. However, out-of-the money overwriting also results in relatively higher return variability and inferior risk-adjusted performance.

During the sample period, overwriting the S&P 500 with short-dated options, rebalanced more frequently, outperformed overwriting with longer-dated options, rebalanced less frequently. We discuss possible explanations for these performance differences.

We find that going long the market during periods of heightened short-term anxiety, inferred from the presence of relatively high S&P 500 1-month at-the-money implied volatility, has, on average, been a winning strategy. To a slightly lesser extent, having relatively less exposure to the market during periods of complacency – or relatively low implied market implied volatility – was also beneficial.

We create an “enhanced” overwriting strategy – whereby investors systematically overwrite the S&P 500 or Nasdaq 100 with disproportionately fewer (more) calls against the indices when risk expectations are relatively high (low).

Our enhanced overwriting portfolios handily outperformed the base case overwrite portfolios and the respective underlying indices, on an absolute and risk-adjusted basis. For example, the average annual return for the S&P 500 enhanced overwriting portfolio from 1997 – 2005 was 7.9%, versus 6.6% for the base case overwrite portfolio and 5.5% for the S&P 500 Index.

Overwriting with fewer calls when implied volatility is rich, and more calls when implied volatility is cheap, could improve the absolute and risk-adjusted performance of index-oriented overwriting portfolios.

This goes against the conventional tendency for investors to sell calls against their positions when implied volatility is high.

*Renicker, Ryan and Devapriya Mallick., “Enhanced Call Overwriting.”, Lehman,Brothers Global Equity Research Nov 17, 2005.

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Enhanced Call Overwriting (2005)

  1. 1. November 17, 2005 Enhanced Call Overwriting Ryan Renicker, CFA 1.212.526.9425 Superior risk-adjusted returns for at-the-money overwriting vs. long only. Systematically ryan.renicker@lehman.com overwriting the S&P 500 with 1-month at-the-money calls, rebalanced on a monthly basis at expiration, outperformed the S&P 500 Index during our sample period (1996 – 2005). This Devapriya Mallick 1.212.526.5429 “base case” overwriting strategy also generated superior risk-adjusted returns versus the dmallik@lehman.com index. Risk/return profile changes when overwriting with out-of-the-money calls. Overwriting portfolios with out-of-the-money calls tends to outperform at-the-money overwriting during market rallies, but provides less protection during market downturns. However, out-of-the- money overwriting also results in relatively higher return variability and inferior risk-adjusted performance. Short-dated overwriting has outperformed long-dated overwriting. During the sample period, overwriting the S&P 500 with short-dated options, rebalanced more frequently, outperformed overwriting with longer-dated options, rebalanced less frequently. We discuss possible explanations for these performance differences. “Enhanced” Overwriting. We find that going long the market during periods of heightened short-term anxiety, inferred from the presence of relatively high S&P 500 1-month at-the-money implied volatility, has, on average, been a winning strategy. To a slightly lesser extent, having relatively less exposure to the market during periods of complacency – or relatively low implied market implied volatility – was also beneficial. We create an “enhanced” overwriting strategy – whereby investors systematically overwrite the S&P 500 or Nasdaq 100 with disproportionately fewer (more) calls against the indices when risk expectations are relatively high (low). Our Enhanced Overwriting Strategy performed the best. Our enhanced overwriting portfolios handily outperformed the base case overwrite portfolios and the respective underlying indices, on an absolute and risk-adjusted basis. For example, the average annual return for the S&P 500 enhanced overwriting portfolio from 1997 – 2005 was 7.9%, versus 6.6% for the base case overwrite portfolio and 5.5% for the S&P 500 Index. Goes against conventional tendency to overwrite when volatility is rich. Overwriting with fewer calls when implied volatility is rich, and more calls when implied volatility is cheap, could improve the absolute and risk-adjusted performance of index-oriented overwriting portfolios. This goes against the conventional tendency for investors to sell calls against their positions when implied volatility is high. 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 12.
  2. 2. Equity Derivatives Strategy | Enhanced Call Overwriting Call Overwriting and the CBOE S&P 500 BuyWrite Index (BXM) Call overwriting is a trading strategy whereby investors sell call options against their long position in the underlying. Specifically, an overwriting investor sells a stock’s upside potential beyond the strike price in exchange for the initial premium received from the short call transaction. Investors typically overwrite their portfolios when they anticipate range-bound stock prices, wish to hedge against a short-term market retracement, reduce the total volatility of their portfolios or to enhance yield. Please see Appendix I: Call Overwriting in a Nutshell for additional details on the call overwriting strategy. Overwriting has become increasingly popular among equity investors. According to the Chicago Board Options Exchange (CBOE), more than $13 billion has been recently allocated by asset 1 managers to buy-write investment products . This popularity has led the CBOE, in cooperation with Standard & Poor’s, to develop the CBOE S&P 500 BuyWrite Index (BXM), which measures the total return of a “covered call” strategy applied to the S&P 500 Index (SPX). Specifically, the BXM consists of a hypothetical portfolio consisting of a long position in the SPX and a short 1-month at-the-money SPX call, rebalanced on a monthly basis at expiration. See Appendix II: Description of the BXM Index for further details. From January 1996 to September 2005, the BXM had an average annual return of 9.6%, versus 8.6% for the S&P 500 Total Return Index (SPTR). The BXM also had consistently lower realized volatility than the SPTR. Figure 1: BXM – SPTR Relative Performance (Quarterly) Figure 2: BXM vs. SPTR Cumulative Performance 12% 300 8% BXM Outperf orms 250 ance 4% erform 200 0% B M - S TR P 150 P -4% X 100 BXM (Scaled) -8% S&P 500 TR Index (Scaled) BXM Underperf orms 50 -12% 96 97 98 99 00 01 02 03 04 05 6 6 7 7 8 8 9 9 0 0 1 1 2 2 3 3 4 4 5 5 -9 -9 r-9 -9 r-9 -9 r-9 -9 r-0 -0 r-0 -0 r-0 -0 r-0 -0 r-0 -0 r-0 -0 n- n- n- n- n- n- n- n- n- n- ar ep ep Ma ep Ma ep Ma ep Ma ep Ma ep Ma ep Ma ep Ma ep Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja a M S M S S S S S S S S S Source: Lehman Brothers, Bloomberg Source: Lehman Brothers, Bloomberg Figure 3: BXM vs. SPTR Rolling 90-Day Realized Volatility Figure 4: BXM vs. SPTR Daily Return Distribution 1,000 40% 900 BXM 35% S&P 500 TR Index BXM Index 800 0 a e lize o tility 30% 700 9 -D yR a dV la 25% 600 F uny req e c 500 20% 400 15% S&P 500 Total Return Index 300 10% 200 5% 100 0% - 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% % % % % % % % % % % % % 6 7 8 9 0 1 2 3 4 5 00 50 00 50 00 50 00 50 00 50 00 50 9 9 9 9 0 0 0 0 0 0 .5 .0 .5 .0 .5 .0 .5 .0 .5 .0 .5 .0 .5 .0 .5 n- n- n- n- n- n- n- n- n- n- 0. 0. 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. -7 -7 -6 -6 -5 -5 -4 -4 -3 -3 -2 -2 -1 -1 -0 Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Daily Return Source: Lehman Brothers, Bloomberg Source: Lehman Brothers, Bloomberg 1 Growing Interest in BuyWrite Strategies, CBOE, September 2005. November 17, 2005 2
  3. 3. Equity Derivatives Strategy | Enhanced Call Overwriting BXM Risk / Reward Characteristics A comparison of the Sharpe ratios demonstrates that the BXM has had superior risk-adjusted performance relative to a traditional long-only position in the SPTR from January 1996 to September 2005. Over this time period, the BXM had a Sharpe ratio of 0.55, versus 0.31 for the SPTR. Although the BXM outperformed the SPTR on an absolute basis, a substantial contribution to the superior risk- adjusted performance can be attributed to the BXM’s markedly lower volatility. During the study period, the beta of the monthly total returns of the BXM with respect to the SPTR was about 0.62, and about 2 77% of the variability in BXM’s returns could be explained by the SPTR (R = 0.77). However, since the BXM portfolio incorporates a short call position on the underlying index, its relative performance versus the SPX is largely dependent on the market’s direction. In directionless or bear markets, overwritten portfolios are more likely to outperform the SPTR, since the initial cash flow received from the short call position cushions the loss of the long underlying position. The BXM tends to lag SPTR in bull markets, as the overwritten portfolio’s profit potential is capped on the upside. This pattern is even more pronounced if the BXM portfolio returns are calculated strictly between monthly expiration dates (Figure 5). In this case, the relative performance of the BXM versus the SPTR is almost entirely dependent upon the market’s performance for the month leading up to expiration. However, if the overwritten portfolio is rebalanced between expiration dates, the relative performance of the BXM versus the SPTR becomes dependent upon both the direction of the market (“delta effect”) as well as the change in the implied volatility for the short call option (“vega effect”) (Figure 6). Figure 5: BXM vs. SPTR Relative Return Comparison Figure 6: BXM vs. SPTR Relative Return Comparison (Rebalanced at expiration.) (Rebalanced between expirations.) 12% 12% pread & 0 o l e rn p e d 8% 8% B M- S P5 0T ta R tu S r a B M- S P500 Total R turn S 4% 4% e 0% 0% -20% -16% -12% -8% -4% 0% 4% 8% 12% 16% 20% -20% -16% -12% -8% -4% 0% 4% 8% 12% 16% 20% -4% -4% & -8% X -8% X -12% -12% S&P 500 Total Re turn S&P 500 Total Re turn Source: Lehman Brothers Source: Lehman Brothers For example, there are instances when the BXM underperforms the SPTR during market downturns (Figure 6, bottom left quadrant, circles). In these cases, the increase in the value of the written call option attributed to rising implied volatility (“vega”) overwhelmed the drop in its value due to the market’s decline. Thus, investors short the calls would incur a loss at rebalance since they would have to buy back the calls at a higher price than what they had originally sold them for when the trade was initiated. On these 6 occasions, the SPTR was down an average of 3.7%, and the BXM underperformed the SPTR about 1.1%, on average. On the other hand, the BXM occasionally outperforms the SPTR by more than anticipated despite strong market performance (Figure 6, top right quadrant). In these cases, the initial premium received and the decrease in the value of the call option sold attributed to declining implied volatility was greater than the opportunity cost incurred when the market rallied beyond the strike price. November 17, 2005 3
  4. 4. Equity Derivatives Strategy | Enhanced Call Overwriting Overwriting Scenarios Does it then follow that overwriting 1-month at-the-money calls is the optimal covered call strategy? Why not overwrite a position by shorting out-of-the-money calls, or sell longer-dated calls rebalanced less frequently? In this section, we explore some of these overwriting alternatives and examine their risk/reward characteristics. Base Case We analyze the absolute performance and risk/reward profile of systematically overwriting the SPX with 1-month at-the-money calls, rebalanced at each sequential monthly option expiration date. The 2 study incorporates data from February 1996 to September 2005 . The base case overwriting strategy outperformed the SPX in 63% of the 115 months included in our study and outperformed the SPX by about 0.5% per year (Figure 9). In addition, the overwrite portfolio tended to outperform (underperform) the market during market declines (rallies). Figure 7: Base Case Overwrite vs. S&P 500 Index Performance Figure 8: Base Case Relative Performance vs. S&P 500 Index 250 15% 10% Cumulative Performance Overwrite - S&P 500 Return 200 5% 150 0% 100 -5% 50 Overw rite Portfolio (Scaled) -10% S&P 500 (Scaled) -15% - 0% 5% 0% % % % % 0% 5% 10 15 20 -5 -2 -1 -1 96 97 98 99 00 01 02 03 04 05 b- b- b- b- b- b- b- b- b- b- S&P 500 Return Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers, OptionMetrics In addition, the overwrite portfolio fared better than the market on a risk-adjusted basis. Specifically, the overwriting strategy yielded a Sharpe ratio of 0.30 versus 0.16 for the SPX. During the study period, the beta of the monthly total returns of the base case overwrite portfolio with respect to the SPX was about 0.56, and about 77% of the variability in the overwritten portfolio’s returns could be 2 explained by SPX returns (R = 0.77). Figure 9: Base Case vs. S&P 500 Risk / Reward Characteristics Base Case Base Case - SPX Overwrite SPX Average Annual Return 7.5% 7.0% 0.5% Annualized Excess Return 3.3% 2.8% 0.5% Standard Deviation 11.1% 17.3% -6.2% Sharpe Ratio 0.30 0.16 # Months Outperformed 72 43 29 % Months Outperformed 63% 37% 25% Note: Annualized excess return is relative to 1-month LIBOR. Source: Lehman Brothers, OptionMetrics 2 For simplicity, we exclude dividends and transaction costs in the return calculations of both the overwrite portfolio and the S&P 500 Index and assume that all trades are executed at the close on expiration. November 17, 2005 4
  5. 5. Equity Derivatives Strategy | Enhanced Call Overwriting Altering “Moneyness” of Calls In this section, we analyze the tradeoffs associated with overwriting the SPX with 2%, 5% and 8% out- of-the-money calls, rebalanced at each monthly expiration date from January 1996 to September 2005. Since a call option’s delta decreases as the strike price increases, and the underlying portfolio has a delta of 1.0, the overwritten portfolio’s net delta approaches 1.0 as deeper out-of-the-money (OTM) calls are sold against the underlying portfolio. This means that overwriting strategies incorporating out- of-the-money calls tend to outperform at-the-money overwriting during market rallies, but provide less protection during market downturns (Figure 10). This also results in higher return variability and lower risk-adjusted performance (Figure 11). Figure 10: Average Return During Market Rallies, Downturns Figure 11: Altering “Moneyness”: Sharpe Ratio Comparison 10% M arket Rallies 0.35 M arket Downt urns 8% 0 .3 0 0.30 6% Average Monthly Return 0 .2 4 0 .2 4 4% 0.25 Sharpe Ratio 2% 0 .19 0.20 0 .16 0% 0.15 -2% 0.10 -4% -6% 0.05 -8% - -10% Base Case 2%OTM 5%OTM 8%OTM S&P 500 Index Base Case 2%OTM 5%OTM 8%OTM S&P 500 Index (ATM ) (ATM ) Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers, OptionMetrics During our sample period, systematically overwriting the SPX with 5% OTM calls generated the highest average annual return across the “moneyness” scenarios (Figure 12). In the environment we have considered, 5% OTM overwriting allowed investors to participate in monthly market rallies during the bull markets of 1996 – 2000 and 2003 – 2005, while retaining a slight downside hedge during the bear market of late 2000 – early 2003. However, the volatility of portfolios overwritten with out-of-the money calls was relatively high and the risk-adjusted returns of out-of-the-money overwriting became less attractive as further out-of-the-money calls were sold against the underlying portfolio (Figure 11). Figure 12: Base Case, OTM Overwriting vs. S&P 500 Risk / Reward Characteristics (1/96 – 9/05) Base Case S&P 500 2% OTM 5% OTM 8% OTM (ATM) Index Average Annual Return 7.5% 7.2% 8.0% 7.5% 7.0% Annualized Excess Return 3.3% 3.0% 3.8% 3.2% 2.8% Standard Deviation 11.1% 12.6% 15.5% 16.7% 17.3% Sharpe Ratio 0.30 0.24 0.24 0.19 0.16 # Months Overwrite Outperforms S&P 500 72 77 101 107 NA % Months Overwrite Outperforms S&P 500 63% 67% 88% 93% NA Source: Lehman Brothers, OptionMetrics November 17, 2005 5
  6. 6. Equity Derivatives Strategy | Enhanced Call Overwriting Altering Expiration Dates We compare the risk/reward attributes of overwriting the SPX with at-the-money calls expiring in 1, 3 and 6 months, rebalanced at expiration every 1, 3 and 6 months, respectively. The short-dated overwrite portfolios significantly outperformed the 6 month covered call strategy during this time period (Figure 13). Below, we explore possible explanations for these performance differences. “Trending Market” Bias. Portfolios overwritten with longer dated options, rebalanced less frequently, may outperform shorter-dated overwriting strategies if markets are “choppy”. For example, assume investor A overwrites the SPX with 1-month at-the-money calls, rebalanced once, for a combined two month holding period. Investor B overwrites the SPX with 2-month at-the-money calls, and closes out this position when the two-month options expire. If the market has a significant rally between the initial trade date and 1 month from initiation, A realizes a loss and has to sell new, higher-strike calls for the second month of the trade. If the market then reverts back to the level where it was trading at the nd beginning of the initial trade as of the end of the 2 month, the new calls expire worthless and A retains the entire premium on the calls sold at the roll date. Thus, investor A’s total net profit equals the sum of the premiums received on each of the two short call transactions, less the loss incurred due to the market rally during the first month of the trade. Investor B, however, retains the entire premium received from selling the 2-month calls, and does not incur the interim loss one month into the trade. During our sample period, the loss due to rebalancing more frequently did not overwhelm the other factors that contributed to the outperformance of the shorter-dated overwriting. “Out-of-the-Money Rebalance” Bias. At each rebalance date, the new “at-the-money” call written against the SPX is selected by choosing the listed option having the closest strike price above the closing price of the SPX as of the close of trading on that day; for our base case portfolio, the calls shorted were, on average, about 0.41% out-of-the-money (Figure 14). Since this option is typically out- of-the-money at the trade initiation date, the value of the overwritten portfolio partially participates in a rally of the underlying during the trade’s holding period, unlike a pure “at-the-money” overwrite position. Thus, if the market has a series of monthly rallies between each roll date, the cumulative impact of writing slightly out-of-the-money versus at-the-money calls is compounded. Figure 13: One, Three, Six Month Overwrites vs. SPX Figure 14: % OTM for Each Monthly Rebalance (Base Case) 250 2.0% u u tiv e fo m n e C m la eP r r a c 200 1.5% 1.0% % T o W nC ll itte a 150 0.5% 100 OM n r 0.0% 1 M ont h 50 3 M o nt h -0.5% 6 M o nt h Ave r age % OTM = 0.41% S&P 50 0 (1 M ont h) -1.0% - -1.5% S 6 M 6 S 7 M 7 S 8 M 98 S 9 M 9 S 0 M 0 S 1 M 1 S 2 M 02 S 3 M 3 S 4 M 4 S 5 5 -9 -9 -9 -9 -9 -9 -9 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 - - ep ep ep ep ep ep ep ep ep ep ar ar ar ar ar ar ar ar ar ar M -2.0% Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers, OptionMetrics Rate of Time Decay. As an at-the-money option approaches expiration, the rate of time decay (theta) tends to increase at an increasing rate, particularly during the last week or two heading into expiration, other factors held constant. Thus, a relatively large proportion of the total time decay for an at-the-money option occurs close to its expiration (a 6-month option retains a relatively high proportion of its original “time value” even one month prior to expiration). Investors who sell options benefit if the value of the option sold decreases more rapidly with the passage of time. Thus, the expected total premium from selling six consecutive 1-month at-the-money calls (which have yet to undergo rapid time decay) can be higher than that expected from selling one 6-month at-the-money call. This could have contributed to the higher return for the short-dated call overwriting strategy versus overwriting with longer-dated options. November 17, 2005 6
  7. 7. Equity Derivatives Strategy | Enhanced Call Overwriting Enhanced Overwriting Since covered call strategies have a tendency to underperform traditional long-only strategies during market rallies and outperform during market downturns, and since a relatively high proportion of overwriting returns can be explained by movements in the underlying portfolio overwritten, overwriting strategies that are dynamically rebalanced ahead of relatively large market rallies or downturns can naturally enhance the returns generated. Generally speaking, a stock’s near-term implied volatility tends to rise during market retracements and decline as the market rallies. This suggests option market participants alter their short-term forecast of a stock’s future return uncertainty (risk) in response to recent observations in the underlying stock’s movement. 3 During our sample period (1/97 to 9/05), the SPX was up in 55 months, and declined in 49 months. In the month following up months, the market declined 53% of the time. In the month following down months, the market rallied in 59% of the months. Since risk expectations (measured by at-the- money implied volatility) generally rose following these market downturns, the market had a tendency to rally after spikes in implied volatility. In other words, it is likely that investors were already pricing in their worst fears for the market after the market had declined, and tended to be rewarded for going long the market when market fear was excessive. To a lesser extent, investors generally experienced lower returns investing in the market when risk expectations were relatively low (complacency). To illustrate this, we calculate the number of standard deviations (z score) 1-month at-the-money implied volatility stood above or below the average 1-month at-the-money implied volatility for each index during the year prior to each monthly rebalance date. Next, we calculate the return for each respective index for each following month. As Figure 15 demonstrates, the SPX tended to rally during the month following rebalance dates in which the market had relatively high implied volatility levels and, to a lesser extent, decline the month following rebalance dates in which the market had relatively low implied volatility levels. Specifically, when the z score was greater than 1 at the beginning of the monthly rebalance, the SPX was up 80% of the time during the next month; when the z score was less than -1, the SPX declined 61% of the time during the following month. Although less pronounced, this pattern was also evident for the NDX, which was up 58% of the time during the month following periods when the z score was greater than 1. When the z score was less than -1, the NDX declined 56% of the time during the subsequent month (Figure 16). Based on these results, we conclude going long during periods of complacency has, on average, not been a winning strategy during this time period. This phenomenon also tended to occur for the Nasdaq 100 Index (NDX), although to a lesser extent. Figure 15: Implied Vol. Z-Score vs. Next Month SPX Returns Figure 16: Implied Vol. Z-Score vs. Next Month NDX Returns 20% 30% Nasdaq 100 Next Month Return 15% 20% S&P 500 Next Month Return 10% 10% 5% 0% 0% -5% -10% -10% -20% -15% Low Risk Expectations High Risk Expectations Low Risk Expectations High Risk Expectations -20% -30% -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 Im plied Vol. Z-Score Im plied Vol. Z-Score Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers, OptionMetrics November 17, 2005 7
  8. 8. Equity Derivatives Strategy | Enhanced Call Overwriting Performance of Enhanced Overwriting for the S&P 500 and Nasdaq 100 Since the underlying market tended to rally following periods of heightened risk aversion and decline following periods of low implied volatility, we test whether writing disproportionately fewer (more) calls against the indices when risk expectations were high (low) would have generated superior 3 absolute and risk-adjusted returns versus the base case overwriting portfolio . We find that this “enhanced overwriting strategy” handily outperformed the base case and the underlying indices, on an absolute and risk-adjusted basis (Figure 17, Figure 18, Figure 19). Figure 17: SPX Enhanced, Base Case Overwrite Portfolios vs. SPX Figure 18: NDX Enhanced, Base Case Overwrite Portfolios vs. NDX 250 500 Te ch "Bubble " Dynamic Overw rite 450 NDX NDX Base Case Overw rite 200 400 um la e e rm n e um la e e rm n e C u tiv P rfo a c C u tiv P rfo a c 350 150 300 100 250 200 50 Dynamic Overw rite (Scaled) 150 S&P 500 (Scaled) Base Case Overw rite (Scaled) - 100 7 8 9 0 1 2 3 4 5 7 8 9 0 1 2 3 4 5 7 8 9 0 1 2 3 4 5 7 8 9 0 1 2 3 4 5 l-9 l-9 l-9 l-0 l-0 l-0 l-0 l-0 l-0 l-9 l-9 l-9 l-0 l-0 l-0 l-0 l-0 l-0 9 9 9 0 0 0 0 0 0 9 9 9 0 0 0 0 0 0 n- n- n- n- n- n- n- n- n- n- n- n- n- n- n- n- n- n- Ju Ju Ju Ju Ju Ju Ju Ju Ju Ju Ju Ju Ju Ju Ju Ju Ju Ju Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers, OptionMetrics In addition, the SPX enhanced overwriting strategy outperformed the base case SPX overwriting strategy 36% of the time, performed in line 46% of the time and underperformed the base case only 18% of the time. The NDX enhanced overwriting strategy outperformed the base case NDX strategy 38% of the time, performed in line 37% of the time and underperformed the base case only 25% of the time. These results imply that the conventional tendency for investors to sell calls against indices having rich implied volatilities – in order to maximize the premium received – might not have been the optimal strategy during the past 9 years, since the indices tended to rally following periods of heightened implied volatility. Rather, it would have led to higher opportunity costs since overwriting investors – by definition – would have sold away at least some of the underlying portfolio’s upside potential. Figure 19: SPX, NDX Enhanced, Base Case Overwrite, Underlying Index Risk / Reward Comparison SPX SPX Base NDX NDX Base Enhanced Case SPX Enhanced Case NDX Overwrite Overwrite Overwrite Overwrite Average Annual Return 7.9% 6.6% 5.5% 9.8% 8.8% 7.1% Annualized Excess Return 3.8% 2.5% 1.5% 5.7% 4.7% 3.0% Standard Deviation 11.7% 11.5% 18.0% 19.8% 19.4% 32.5% Sharpe Ratio 0.33 0.22 0.08 0.29 0.24 0.09 # Months Outperformed Index 67 67 NA 65 65 NA Source: Lehman Brothers, OptionMetrics 3 In our enhanced overwrite portfolios, we write 0.75 calls against each respective underlying index at each rebalance date if the 1-month at-the-money implied volatility of the index at this rebalance date is more than 1 standard deviation above the average of where the 1-month implied volatility has traded on a daily basis during the prior year (z-score of implied volatility > 1.0). We write 1.25 calls against the index at each rebalance date if the 1-month at-the-money implied volatility of the index at this date is more than 1 standard deviation below the average of where the 1-month implied volatility has traded on a daily basis during the prior year (z-score < -1.0). We write 1.0 calls against the index if the 1-month implied volatility is within + or – 1 standard deviation of where it has traded during the 1 year prior to the rebalance date. Since z-score calculations require 1 year of historical vol data, and our volatility database includes data from 1996 – present, our sample period for the enhanced overwriting strategies begins January 1997. November 17, 2005 8

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