Enhanced Call Overwriting - Groundbreaking Study Published in 2005
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- Lehman Brothers provides research on companies it also does business with, so its research may not be entirely objective. Investors should consider this and other factors when making investment decisions. - The document discusses strategies for overwriting index call options, such as the S&P 500, to potentially enhance returns. It finds that enhanced strategies that adjust the level of overwriting based on implied volatility can further improve risk-adjusted returns compared to static overwriting strategies. - Specifically, an enhanced strategy that overwrites with fewer calls when implied volatility is high, and more calls when implied volatility is low, performed best in backtests, outperforming simple overwriting strategies and the underlying indices on an absolute and risk-adjusted basis.
Enhanced Call Overwriting - Groundbreaking Study Published in 2005
- 1. 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. Enhanced Call Overwriting Superior risk-adjusted returns for at-the-money overwriting vs. long only. 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. 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. November 17, 2005 Ryan Renicker, CFA 1.212.526.9425 ryan.renicker@lehman.com Devapriya Mallick 1.212.526.5429 dmallik@lehman.com
- 2. Equity Derivatives Strategy | Enhanced Call Overwriting November 17, 2005 2 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 managers to buy-write investment products 1 . 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% -8% -4% 0% 4% 8% 12% M ar-96 S ep -96 M ar-97 S ep -97 M ar-98 S ep -98 M ar-99 S ep -99 M ar-00 S ep -00 M ar-01 S ep -01 M ar-02 S ep -02 M ar-03 S ep -03 M ar-04 S ep -04 M ar-05 S ep -05 BXM-SPTRPerformance BXM Outperforms BXM Underperforms 50 100 150 200 250 300 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 BXM (Scaled) S&P 500 TR Index (Scaled) 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 0% 5% 10% 15% 20% 25% 30% 35% 40% 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 90-DayRealizedVolatility BXM S&P 500 TR Index - 100 200 300 400 500 600 700 800 900 1,000 -7.50% -7.00% -6.50% -6.00% -5.50% -5.00% -4.50% -4.00% -3.50% -3.00% -2.50% -2.00% -1.50% -1.00% -0.50% 0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 4.50% 5.00% 5.50% Daily Return Frequency BXM Index S&P 500 Total Return Index Source: Lehman Brothers, Bloomberg Source: Lehman Brothers, Bloomberg 1 Growing Interest in BuyWrite Strategies, CBOE, September 2005.
- 3. Equity Derivatives Strategy | Enhanced Call Overwriting November 17, 2005 3 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 77% of the variability in BXM’s returns could be explained by the SPTR (R 2 = 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 (Rebalanced at expiration.) Figure 6: BXM vs. SPTR Relative Return Comparison (Rebalanced between expirations.) -12% -8% -4% 0% 4% 8% 12% -20% -16% -12% -8% -4% 0% 4% 8% 12% 16% 20% S&P 500 Total Return BXM-S&P500TotalReturnSpread -12% -8% -4% 0% 4% 8% 12% -20% -16% -12% -8% -4% 0% 4% 8% 12% 16% 20% S&P 500 Total Return BXM-S&P500TotalReturnSpread 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.
- 4. Equity Derivatives Strategy | Enhanced Call Overwriting November 17, 2005 4 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 study incorporates data from February 1996 to September 2005 2 . 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 - 50 100 150 200 250 Feb-96 Feb-97 Feb-98 Feb-99 Feb-00 Feb-01 Feb-02 Feb-03 Feb-04 Feb-05 CumulativePerformance Overw rite Portfolio (Scaled) S&P500 (Scaled) S&P 500 Return -15% -10% -5% 0% 5% 10% 15% -20% -15% -10% -5% 0% 5% 10% 15% 20% Overwrite-S&P500Return 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 explained by SPX returns (R 2 = 0.77). Figure 9: Base Case vs. S&P 500 Risk / Reward Characteristics Base Case Overwrite SPX Base Case - 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.
- 5. Equity Derivatives Strategy | Enhanced Call Overwriting November 17, 2005 5 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% -8% -6% -4% -2% 0% 2% 4% 6% 8% 10% AverageMonthlyReturn Base Case (ATM ) 2%OTM 5%OTM 8%OTM S&P 500 Index M arket Rallies M arket Downturns 0 .3 0 0 .2 4 0 .2 4 0 .19 0 .16 - 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Base Case (ATM ) 2%OTM 5%OTM 8%OTM S&P 500 Index SharpeRatio 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 (ATM) 2% OTM 5% OTM 8% OTM S&P 500 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
- 6. Equity Derivatives Strategy | Enhanced Call Overwriting November 17, 2005 6 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 beginning of the initial trade as of the end of the 2 nd 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) - 50 100 150 200 250 M ar-96S ep -96M ar-97S ep -97M ar-98S ep -98M ar-99S ep -99M ar-00S ep -00M ar-01S ep -01M ar-02S ep -02M ar-03S ep -03M ar-04S ep -04M ar-05S ep -05 CumulativePerformance 1M onth 3 M ont h 6 M ont h S&P 500 (1M onth) -2.0% -1.5% -1.0% -0.5% 0.0% 0.5% 1.0% 1.5% 2.0% %OTMonWrittenCall Average % OTM = 0.41% 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.
- 7. Equity Derivatives Strategy | Enhanced Call Overwriting November 17, 2005 7 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. During our sample period 3 (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% -15% -10% -5% 0% 5% 10% 15% 20% -5 -4 -3 -2 -1 0 1 2 3 4 5 Implied Vol. Z-Score S&P500NextMonthReturn Low Risk Expectations High Risk Expectations -30% -20% -10% 0% 10% 20% 30% -5 -4 -3 -2 -1 0 1 2 3 4 5 Implied Vol. Z-Score Nasdaq100NextMonthReturn Low Risk Expectations High Risk Expectations Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers, OptionMetrics
- 8. Equity Derivatives Strategy | Enhanced Call Overwriting November 17, 2005 8 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 absolute and risk-adjusted returns versus the base case overwriting portfolio 3 . 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 - 50 100 150 200 250 Jan-9 7 Jul-97 Jan-9 8 Jul-98 Jan-9 9 Jul-99 Jan-0 0 Jul-00 Jan-0 1 Jul-01 Jan-0 2 Jul-02 Jan-0 3 Jul-03 Jan-0 4 Jul-04 Jan-0 5 Jul-05 CumulativePerformance Dynamic Overw rite (Scaled) S&P 500 (Scaled) Base Case Overw rite (Scaled) 100 150 200 250 300 350 400 450 500 Jan-9 7 Jul-97 Jan-9 8 Jul-98 Jan-9 9 Jul-99 Jan-0 0 Jul-00 Jan-0 1 Jul-01 Jan-0 2 Jul-02 Jan-0 3 Jul-03 Jan-0 4 Jul-04 Jan-0 5 Jul-05 CumulativePerformance Dynamic Overw rite NDX NDX Base Case Overw rite Tech "Bubble" 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 Enhanced Overwrite SPX Base Case Overwrite SPX NDX Enhanced Overwrite NDX Base Case Overwrite NDX 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.
- 9. Equity Derivatives Strategy | Enhanced Call Overwriting November 17, 2005 9 Appendix I: Call Overwriting, in a Nutshell A call overwriting strategy combines a short call position with an existing long position in the underlying stock. The strike price chosen for the written call corresponds with the desired level of market participation that the investor wishes to obtain. For example, investors believing that an underlying security is likely to trade flat, with a low probability of a rally, might choose to write at-the- money calls. On the other hand, if investors believe a 10% rally in the underlying is possible, they might choose to sell 10% out-of-the-money calls. This reduces the yield enhancement benefits of the overwriting strategy, but allows for greater participation in an upward move in the underlying. Of course, the premium received from writing the out-of-the-money calls will be less than what would have been obtained from an at-the-money sale, other factors held constant. Formally, the annualized maximum upside gain (market participation cap) for a written call at expiration is equal to 1 1 − + t S CK Where K denotes the strike price, C is the call premium collected, S is the stock price as of the trade initiation date and t is the time to option expiration in years. For example, consider an investor who purchases 100 shares of ABC at $50 per share and writes a 3-month call with a $55 strike. Further assume that the premium received (per share) equals $5. At expiration, the investor participates in the underlying up to the strike price. He / she is also entitled to any dividends, provided that the stock is not called away prior to expiration. In this example, the investor receives up to $10 (20% return) during the life of the option: $5 from the stock’s appreciation up to the strike ($55 - $50) plus $5 from the premium received. At expiration, the covered call position would lose money if the stock price closes below $45 on expiry ($50 initial stock price - $5 premium received), although the total loss would be less than a pure long-only position in ABC. In addition, the overwriting strategy would underperform a long-only position in ABC if the stock rallies above $55 as of expiration (opportunity cost versus a long-only strategy above $55) (Figure 20 and Figure 21) Figure 20: Overwrite vs. Long-Only Payoff Diagram Example Figure 21: Payoff Details (Breakeven & Max Upside Highlighted) $(40) $(30) $(20) $(10) $- $10 $20 $30 $40 $20 $25 $30 $35 $40 $45 $50 $55 $60 $65 $70 $75 $80 $85 Stock Price at Expiration PayoffatExpiration Stock P&L Overwrite P&L Stock Price Premium Strike Stock P&L Overwrite P&L Stock Return Overwrite Return $20 $5 $55 -$30 -$25 -60% -50% $25 $5 $55 -$25 -$20 -50% -40% $30 $5 $55 -$20 -$15 -40% -30% $35 $5 $55 -$15 -$10 -30% -20% $40 $5 $55 -$10 -$5 -20% -10% $45 $5 $55 -$5 $0 -10% 0% $50 $5 $55 $0 $5 0% 10% $55 $5 $55 $5 $10 10% 20% $60 $5 $55 $10 $10 20% 20% $65 $5 $55 $15 $10 30% 20% $70 $5 $55 $20 $10 40% 20% $75 $5 $55 $25 $10 50% 20% $80 $5 $55 $30 $10 60% 20% $85 $5 $55 $35 $10 70% 20% Source: Lehman Brothers Source: Lehman Brothers
- 10. Equity Derivatives Strategy | Enhanced Call Overwriting November 17, 2005 10 Motivations for Call Overwriting Yield Enhancement If the stock/portfolio is expected to be range-bound, the premium received will function as yield enhancement. Express Price Target If an investor believes the stock/portfolio is unlikely to trade beyond a price target over a specified period of time, they can write calls against their underlying position with a strike price equal to the target price. This way, the investor receives incremental premium, while enforcing discipline with respect to the specific target selling price. Partial Downside Hedge Since investors receive the call premium when the overwrite is initiated, a downward move in the underlying between the trade initiation date and expiration will be partially offset by the amount of the premium received via the call sale. Reduce Volatility By writing calls against the long stock position, investors are effectively reducing the downside and upside variability relative to a long-only position.
- 11. Equity Derivatives Strategy | Enhanced Call Overwriting November 17, 2005 11 Appendix II: Description of the BXM Index Summary Information Announced by the Chicago Board Options Exchange (CBOE) in April 2002 Time series history: June 1988 – present. Initial value: 100 Rebalanced: monthly Priced: daily Index Description Position: long S&P 500 Index portfolio, short near-term S&P 500 call. Short call position held to expiration, generally the 3 rd Friday of each month. Call option is settled against the Special Opening Quotation (SOQ) of the S&P 500 Index. SOQ: special calculation of the S&P 500 Index derived by using the opening prices of each constituent in the S&P 500 Index. SOQ determined before 11 AM EST, after all S&P 500 constituents have opened for trading. Final settlement price of the call at maturity is the greater of 0 and (SOQ – strike price). Dividends paid on the underlying S&P 500 Index + dollar value of option premium received functionally re-invested in the covered S&P 500 Index portfolio. Subsequent to settlement of expiring call option, a new at-the-money call expiring in the next month is written. Strike price of new call is the S&P 500 Index call listed on the CBOE having the closest strike above the last value of the S&P 500 Index reported before 11 AM EST on expiration. New call option assumed sold at VWAP of its prices during the first ½ hour period beginning at 11:30 AM EST on expiration. BXM Index Level: BXMt = BXMt-1 (1+Rt ) where Rt = daily rate of return for covered portfolio. Gross Daily Return (excluding roll dates): 1 + Rt = (St + Divt – Ct ) / (St-1 – Ct -1) where St = closing value of S&P 500 Index at t, Divt = ordinary cash dividends payable on component stocks underlying S&P 500 Index that trade “ex-dividend” at date t expressed in S&P 500 Index points, and Ct = arithmetic average of last bid and ask prices of the call option reported before 4:00 PM EST on preceding trading day (t-1). Source: Description of the CBOE S&P 500 BuyWrite Index (BXM), October 12, 2004. www.cboe.com/bxm
- 12. Equity Derivatives Strategy | Enhanced Call Overwriting November 17, 2005 12 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. 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. 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