Finding Alpha via Covered Index Writing
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DESCRIPTIONCovered S&P 500 Index call strategies have, on average, outperformed the S&P 500 Index over thepast 15+ years while realizing lower standard deviations of returns. This analysis dissects thestrategy underlying the BuyWrite Monthly Index on the S&P 500. The BXM is the most broadlyquoted benchmark for index callselling strategies. Also discussed are alternative structured S&P500 optionoverwriting strategies, which have even more attractive riskreturn trade-offs than theBXM because they take advantage of the implicit positive risk premium of equities and potentiallyadjust the strike price of the call sold on the basis of the volatility environment.
September/October 2006 www.cfapubs.org 29Financial Analysts JournalVolume 62 Number 52006, Goldman, Sachs & Co.Finding Alpha via Covered Index WritingJoanne M. Hill, Venkatesh Balasubramanian, Krag (Buzz) Gregory, and Ingrid Tierens, CFACovered S&P 500 Index call strategies have, on average, outperformed the S&P 500 Index over thepast 15+ years while realizing lower standard deviations of returns. This analysis dissects thestrategy underlying the BuyWrite Monthly Index on the S&P 500. The BXM is the most broadlyquoted benchmark for index callselling strategies. Also discussed are alternative structured S&P500 optionoverwriting strategies, which have even more attractive riskreturn trade-offs than theBXM because they take advantage of the implicit positive risk premium of equities and potentiallyadjust the strike price of the call sold on the basis of the volatility environment.he new S&P 500 BuyWrite Index (BXM) ofthe Chicago Board Options Exchange(CBOE) has outperformed the S&P 500Index with only two-thirds of its risk.Whats the catch? Well, for one thing, a user of theBXM needs to be willing to accept some underper-formance in spectacularly strong equity marketswhen everyone else is bragging about their hotstock picks. The relatively boring strategy to cap-ture the BXM returns consists of going long S&P 500exposure while shorting at-the-money (ATM) calloptions on the S&P 500. It does best relative to theindex when equity markets are quiet, posting mod-erate or falling returns, and is, therefore, worthstudying further in the current environment.Academics and investment consultants havestudied the BXM in terms of its return and riskcharacteristics both alone and in combination withother asset classes.1 In the period we studied (1January 1990 to 31 October 2005), the BXMs annu-alized return of 11.0 percent was about 60 bps abovethat of the S&P 500, with a standard deviation of lessthan 10 percent (compared with about 14.5 percentfor the S&P 500). Although some of the lower risk interms of standard deviation came from eliminatingupside swings in rising markets, as Figure 1 andFigure 2 show, the track record has been impressivein both bull and bear markets.Some of the best returns of the BXM relative tothe S&P 500 have been in low-volatility periods likethat of the early 1990s and in the bear market of20002002. In some sustained periods, such as19951998, the BXM underperformed the S&P 500by more than 5 percentage points each year.Recently, with investors attracted by the returnand risk characteristics, as well as regular cashflows, of the BXM, several funds and structuredproducts have been created to track the index.2With the recent introduction of options on the S&P500 SPDR (S&P Depositary Receipts) exchange-traded funds (SPY), these strategies can also be usedfor covered call writing on the SPY. The BXM canalso serve as a benchmark for more active or alter-natively structured options strategies designed tooutperform the index.We analyze the strategy underlying the BXMand some alternative structured index optionoverwriting strategies that have even more attrac-tive riskreturn trade-offs than the BXM, includingfixed-strike overwriting strategies and a flexiblestrategy that dynamically adjusts the strike basedon the volatility environment.Factors Driving the Performance of a Covered Call StrategyBefore jumping into the specifics of the BXM andalternative overwriting strategies, we remind read-ers of the factors that drive the performance of thesestrategies. We have identified the following driversof overwriting strategy returns:31. The fair call premium: the premium that wouldgo to the call seller who had perfect volatilityforesight in a world with no trading costs; thatis, the call is priced at the volatility realized overthe life of the option, rather than at impliedvolatility, and there is no bidask spread.Joanne M. Hill is managing director at Goldman, Sachs& Co., New York City. Venkatesh Balasubramanian isan associate at Goldman, Sachs & Co., New York City.Krag (Buzz) Gregory and Ingrid Tierens, CFA, are vicepresidents at Goldman, Sachs & Co., New York City. TFinancial Analysts Journal30 www.cfapubs.org 2006, Goldman, Sachs & Co.Figure 1. Cumulative Total Return on the BXM and S&P 500, 1 January 1990to 31 October 2005Sources: CBOE and Standard & Poors.Figure 2. Annual Total Return on the BXM and S&P 500, 1 January 1990 to 31 October 2005Sources: CBOE and Standard & Poors.31 December 1989 = 100S&P 500BXM5505004504003503002502001501005089 0593 97 01 0391 95 99Annual Return %40302010010203094 98 029690 92 00 04 05S&P 500 BXMFinding Alpha via Covered Index WritingSeptember/October 2006 www.cfapubs.org 312. The volatility premium: the premium that cap-tures the impact of selling options at impliedvolatility instead of at the volatility realizedover the life of the option.3. The exercise cost: the component of the call pre-mium that reflects the market impact of execut-ing the sale. The bidoffer spread is the basisfor this cost unless the transaction size is largeenough to move the price.4. The trading cost: the loss in call premium as aresult of the bidask spread.As we demonstrate later, Items 13 are themost important contributors to performance. Dis-cussions of covered indexselling strategies areusually restricted, however, to Items 1 and 2: theability to collect a steady premium that enhancesperformance and the opportunity to capture aspread of implied volatility over realized volatility,which has been mostly positive at the index level.Because of the general emphasis on these twoissues, we provide more details about them beforewe discuss the significance of the third importantpoint, exercise cost.Call Option Premium Levels. An attractivefeature of call-overwriting strategies is that the callsold generates a monthly cash flow much like inter-est or dividends. However, these cash flows haveimportant differences in regard to how they are col-lected. First, the option premium reflects the proba-bility that the seller will incur a loss through exerciseof the option by the buyer at expiration. Second, taxconsiderations need to be taken into account. In theUnited States, for example, the call premium is tax-able as a capital gain, which for most U.S.-basedinvestors is taxed at a higher rate than dividends.4Figure 3 shows the level of one-month S&P 500call premiums historically for ATM options and foroptions 2 percent and 5 percent out of the money.5The premiums for these options averaged, respec-tively, 2.1 percent, 1.1 percent, and 0.4 percent overthe past 15+ years. The variation over time is pri-marily a result of shifts in volatility reflected inoption prices, but premiums also move higher withthe level of interest rates relative to S&P 500 divi-dend yields. Note that these premiums haverecently been at the lower end of their range becauseboth volatility and short-term interest rates havebeen at lower levels (and with improved corporatecash levels and more favorable dividend tax treat-ment, dividend yields have been shifting higher). The Volatility Connection. Another reasonindex-overwriting strategies have such attractivereturn properties is that they capitalize on inves-tors and traders fears of a financial disaster.Options contain a premium for the volatility envi-ronment expected to prevail during the life of theoption. This premium reflects the risk of having alarge move that would cause a loss to the optionseller. Ever since the crash in October 1987, thevolatility implied in S&P 500 options, especiallyFigure 3. One-Month S&P 500 Call Option Premiums for Various Strikes, 1 January 1990 to 31 October 2005Source: Goldman Sachs.Option Premium (% of spot)53421089 0593 97 01 0391 95 99ATM Call 2% OTM Call 5% OTM CallFinancial Analysts Journal32 www.cfapubs.org 2006, Goldman, Sachs & Co.those with strike prices at or below the index, hascontained a premium for crash or downsidegap riskthe risk that all stocks will fall togetherin jumps so that trading out of positions will bedifficult.Figure 4 shows the implied volatility of ATMone-month S&P 500 index options back to 1990.Only in the highest-volatility regimes has realizedvolatility moved higher than the volatility impliedin option prices. The average spread between one-month implied and realized volatility has been 2.4percentage points for 1990 through October 2005.As Figure 5 shows, however, many times during thebear market conditions of 20002002, the actualmarket risk experienced was higher than that pricedinto the S&P 500 options. The existence of differences between theimplied volatility of S&P 500 options among strikeprices is referred to as the skew. As shown inFigure 4, implied volatility for ATM options is nor-mally higher than realized volatility for the S&P 500.The spread of implied-to-realized volatility, how-ever, is wider for OTM put options than for OTMcall options. For example, over the period January1990 through October 2005, the implied volatility ofthe 2 percent S&P 500 OTM put options averaged3.9 percentage points above realized volatility. Incontrast, the implied volatility of the 2 percent S&P500 OTM call options averaged 1.5 percentagepoints above that of realized one-month volatility.The existence of the skew has two, relatedexplanations that imply higher expected volatilityin declining markets than in rising markets: (1) Mar-kets have a greater tendency to have gap or jumpmoves when they fall than when they rise. Thecause can be a reaction to unexpected negative mac-roeconomic or geopolitical events. (2) Stocks aremore correlated in falling markets than they are inrising markets, or stated differently, good newscomes one stock at a time whereas bad news tendsto affect many companies simultaneously. Theimplication for option-selling strategies is thatinvestors receive higher compensation, in volatilityterms, for committing to buy in a declining marketthan they do for committing to sell in a rising mar-ket. Nevertheless, the spread between implied andrealized volatility for the S&P 500 has remainedpositive, even for 2 percent OTM call options.The Forgotten Factor: Exercise Cost. Thefair call premium positively contributes to the per-formance of overwriting strategies, and the indexvolatility premium usually also adds value, but thereturn lost from calls that expire in the money (ITM)Figure 4. S&P 500 ATM One-Month Option: Implied and Realized Volatility, 1 January 1990 to 31 October 2005Source: Goldman Sachs.Volatility (%)1040302045089 059391 97 0195 99 03Implied VolatilityRealized VolatilityFinding Alpha via Covered Index WritingSeptember/October 2006 www.cfapubs.org 33can easily overwhelm both, especially for callsstruck at the money. In spite of the sizable magni-tude of this cost (it was, on average, close to 2percent a month for ATM calls for 1990 throughOctober 2005), discussions of covered call strategiestoo often ignore this component. The exercise costis by definition negative, and it is capped at zero.The success of a covered call strategy, there-fore, hinges as much on minimizing this exercisecost as on capturing the fair call value and theimplied versus realized volatility premium. If aninvestor expects a positive risk premium associatedwith equities, the investor implicitly expects ATMcalls to expire in the money. If the investor wantsto reduce the expected exercise loss, the investorshould consider OTM strikes and make a trade-offbetween the reduction in expected exercise cost andthe reduction in the call premium associated withmoving from at the money to out of the money. Wepresent empirical evidence that overwriting strate-gies can be significantly enhanced without addingmuch risk by selecting such OTM strategies.BXM Construction Compared with AlternativesThe BXM introduced in 2002 reflects a strategy ofgoing long the S&P 500 and selling (writing) a one-month ATM call option on the S&P 500 on the thirdFriday of each month (the option expiration day).6The BXM methodology assumes that this European-style call option will be sold at a price equal to thevolume-weighted average of the prices of the optionfrom 11:30 a.m. to 12 p.m. EST.7 The option is helduntil expiration one month later, when the strategyrolls and new near-term ATM call options are soldagainst the long S&P 500 holding. The option pre-mium and any dividends on the S&P 500 constitu-ents are assumed to be reinvested in the covered callstrategy (i.e., the BXM is a total-return index).8To study alternative index-overwriting optionstrategies, we carried out strategies that sold a one-month (or three-month where indicated) European-style call on the S&P 500 at the close on the Thursdaybefore monthly (or quarterly) expiration and heldthe position until the close on the Thursday beforethe next monthly (or quarterly) expiration. We usedFigure 5. S&P 500 ATM One-Month Option: Implied vs. Realized VolatilitySpread, 1 January 1990 to 31 October 2005Note: The average spread was 2.4 percentage points; the median, 2.7 percentage points.Source: Goldman Sachs.Volatility Spread (%)1510505101589 0593 97 01 0391 95 99Financial Analysts Journal34 www.cfapubs.org 2006, Goldman, Sachs & Co.a variety of strike prices: ATM, 2 percent OTM, and5 percent OTM for the one-month calls and ATM, 5percent OTM, 7 percent OTM, and 10 percent OTMfor the three-month calls.9 In addition, for the three-month calls, we rolled on a January/April/July/November cycle. We assumed that the bidaskspread was 1 implied volatility point and that theoption premium received was invested at LIBORduring the life of the option.10 Our sample periodwas 18 January 1990 to 17 November 2005 (a total of180 months or 60 quarters).11Of the alternatives we analyzed, the ATM one-month call-overwriting strategy is closest to theBXM approach. Our calculations, however, dif-fered from the BXM return calculation alongbroadly three dimensions:1. We rolled at the close of the Thursday beforeexpiration instead of on expiration Friday.With daily data, this Thursday close is nearestto the time when the BXMs underlying optionwould expire and a new option would be sold.This assumption implies that expiration hap-pens at the close of business and that a new callis sold simultaneously (instead of splittingexpiration day returns into three portions, as isthe case for the BXM).2. We priced exact ATM calls instead of calls that,as is the case for the BXM, are slightly out ofthe money but closest to at the money. In addi-tion, the new BXM strike is influenced bymovements in the S&P 500 during the morningof the expiration Friday, which we did notcapture when we set the new strike at theThursday close.3. We invested the call premium at LIBORinstead of using it as a reduction of the initialcapital required.The impact of this last point was marginalafew basis points, on average, a month. The precisechoice of the strike (a combination of the roll andpricing), however, could be significant. Conse-quently, our ATM strategy is different from theBXM, not a proxy for the BXM, and the results wedescribe should be interpreted in this context.Performance ComparisonWe report in this section the historical return andrisk profiles of the fixed-strike S&P 500 buy-writestrategies over the past 15 years, analyses of indexsensitivity and exercise risk, a performance attribu-tion analysis, and a comparison of one-month andthree-month strategies.Historical Return and Risk Profiles. Thereturn characteristics of the BXM and related S&P500overwriting strategies are attractive, as Table 1shows, over the long history of our study, butTable 2 indicates that these strategies have hadperiods when they underperformed the index. Notethat the periods of underperformance occurred inTable 1. Annualized Performance of BXM and Fixed-Strike S&P 500 Call Overwriting, 18 January 1990 to 17 November 2005Annualized Return Annualized Risk MeasuresStrategy ReturnReturn vs. S&P 500Return vs. Initial DeltaStandard DeviationTracking Errorvs. S&P 50010th PercentileMonthly Return90th PercentileMonthly ReturnS&P 500 10.92% 14.15% 2.72% 5.31%BXM 11.27 0.35% 9.10 7.78% 1.28 2.96ATM 13.25 2.33 5.50% 8.50 8.30 1.00 3.002% OTM 13.42 2.50 4.50 10.43 6.11 1.85 3.685% OTM 12.22 1.30 2.15 12.63 3.32 2.59 5.31Sources: CBOE, Standard & Poors, and Goldman Sachs.Table 2. Returns to BXM and Fixed-Strike S&P Call Overwriting: Subperiod PerformanceJanuary 2000 to November 2005 January 1995 to January 2000 January 1990 to January 1995Strategy ReturnReturn vs. S&P 500 ReturnReturn vs. S&P 500 ReturnReturn vs. S&P 500S&P 500 1.01% 27.71% 10.02% BXM 2.88 3.89% 20.65 7.06% 12.46 2.44%ATM 5.88 6.89 22.10 5.61 13.62 3.602% OTM 4.36 5.37 25.59 2.12 12.87 2.855% OTM 2.58 3.59 26.75 0.95 10.34 0.32Sources: CBOE, Standard & Poors, and Goldman Sachs.Finding Alpha via Covered Index WritingSeptember/October 2006 www.cfapubs.org 35the environment of the 1520 percent U.S. equityreturns of the late 1990s, which few investors expectto be repeated in the next decade.12 The BXM annu-alized return of 11.3 percent for the period 18 Janu-ary 1990 to 17 November 2005 was 35 bps higherthan that of the S&P 500, but the annualized stan-dard deviation of the monthly returns was about 5percentage points lower.13Similarly attractive return and risk characteris-tics (13.3 percent return, 8.5 percent standard devia-tion) came from selling the exact ATM option, whichcan be constructed by weighting option strike pricesthat bracket the index level when each monthlyoption is sold or by selling an OTC option. The riskreduction for the BXM and the ATM strategies camelargely from lower upside return, however, as canbe seen from the 90th percentile returns in Table 1,which are lower than the 90th percentile return ofthe S&P 500. These statistics are based on the fre-quency distribution of monthly returns. Figure 6highlights the lower portion of returns coming fromoption-overwriting strategies in periods of strongindex returns (right tail of the distributions).Table 1 also contains summary return and riskmetrics for OTM S&P 500 callselling strategies.The 2 percent OTM call-selling strategy for one-month options had a somewhat higher return thanthe ATM strategy. This outcome is not surprisingbecause this OTM strategy sells options that aremore likely, given a positive expected return for theS&P 500, to be just slightly out of the money or atthe money at expiration. The risk was not muchhigher than for the ATM option strategy; thegreater risk also comes partly in the favorable formof a higher probability of moderate returns, as Fig-ure 6 shows. This strategy maintains the propertyof higher returns than the S&P 500 (as with theBXM) with only about two-thirds of the risk of theS&P 500. The 5 percent OTM strategy may be themost attractive for investors who wish to use indexoverwriting as a source of alpha. The annualizedrisk (Table 1) is only slightly lower than that of theS&P 500, and the monthly return distribution (Fig-ure 6) is more similar to that of the index in bothrisk and shape.The plot in Figure 7 shows that the farther outof the money the chosen strike is, the more closelythe risk and return profile of the call-selling strat-egy resembles that of the S&P 500. In regard to totalrisktotal return trade-offs, the strategies that areslightly out of the money dominated the ATM strat-egy over the past 15+ years, a time when the S&P500 was appreciating by about 1 percent, on aver-age, a month. Because farther-OTM call-sellingstrategies retain more of the upside returns on theFigure 6. Distribution of Returns from the S&P 500, BXM, and Various Fixed-Strike Strategies, 18 January 1990 to 17 November 2005Sources: CBOE, Standard & Poors, and Goldman Sachs.Percent of Observations50403020100159 615 012 3 63 9 12Monthly Strategy Return (%)ATM BXM 2% OTM5% OTM S&P 500Financial Analysts Journal36 www.cfapubs.org 2006, Goldman, Sachs & Co.S&P 500, they also have lower levels of trackingerror to the S&P 500, as Table 1 shows, than do theBXM or ATM strategies. The 2 percent OTM strat-egy had a tracking error of 6.1 percent a year, andthe 5 percent OTM strategy had a tracking error ofabout half that amount. Keep in mind that, although metrics such astotal risk, tracking error, downside risk, and theexpected loss in upside potential can help an inves-tor assess whether these types of strategies areappropriate, they do not capture all potential risksembedded in overwriting strategies. Unexpectedshifts in volatility, price gaps to the upside, theliquidity in options when the strategy is extended toother indices or to single stocks, bidoffer spreadsthat differ among instruments, and the additionalmonitoring that is required when options are addedto the investment universe are some of the addi-tional factors that need to be taken into account.Year-by-Year Returns. Figure 8 shows thereturn experiences in the period studied for theBXM, the ATM strategy, and the 2 percent OTMone-month call-selling strategy compared with thereturn of the S&P 500, on a year-by-year basis.14 TheBXM outperformed the index in 9 of the 16 yearsafter 1990. The year 1995 was the worst year for thisstrategy; in fact, it was a time when index-overwrit-ing strategies, which had in excess of $10 billion inassets under management at the time, experienceda large outflow as the index gapped higher, largecash payments were due to cover losses, and inves-tors terminated or reduced their commitments.Underperformance compared with the S&P 500was as much as 14.9 percentage points (pps) in1995. Another tough year for the BXM was 2003.Figure 8 also highlights the contrast between per-sistent underperformance of the BXM during thebull market of the late 1990s and strong outperfor-mance in 20002002, when the S&P 500 postednegative results. An S&P 500overwriting strategy centeredaround selling a slightly OTM call (2 percent)exhibited smaller swings than the BXM in annualreturns relative to the S&P 500, especially in the199599 period, because it allowed room for 2 per-cent moves in the index each month that could becaptured by the investor. The outperformance ofthis strategy during the bear market periods wasnot as strong as that of the BXM, but it was quiteconsistent. The more stable and consistent relative-return history under quite varying market condi-tions is one of the primary reasons for potentiallyfavoring the 2 percent OTM strategy over the BXM. Index sensitivity and exercise risk. Table 2and Figure 8 show that the performance of thesecall-selling strategies depends on market direction.When one writes calls against the S&P 500, one isFigure 7. RiskReturn Trade-Off for Call-Selling Strategies and the S&P 500, 18 January 1990 to 17 November 2005Sources: CBOE, Standard & Poors, and Goldman Sachs.Annualized Return (%)ATM1% OTM2% OTM5% OTM10% OTMS&P 50014131211108 15109 11 12 13 14Annualized Risk (%)Finding Alpha via Covered Index WritingSeptember/October 2006 www.cfapubs.org 37effectively decreasing exposure to the market. Thedecrease is measured by the delta of the underlyingcalls. (The delta measures the sensitivity of theoption price to small changes in the index.) Table 3shows a variety of metrics that help in understand-ing the differences among the variations on S&P 500overwriting, including the average delta (from anoption-pricing model). The deltas of the alternativeoverwriting strategies vary quite a bit (finishing ateither 0 or 1 at expiration), as do the frequencies ofexercise, which in cash-settled options reflects theneed to post cash at expiration that represents theITM amount.15 For an ATM strategy, which is similar to theBXM, the investor had a delta and beta close to 0.50in this period. (The beta equals 1 minus the delta,so it measures the exposure to the market; i.e., thedelta of a call is the beta-reduction equivalent.) Thisvalue of 0.50 means the market risk was similar tothat of holding a portfolio 50 percent invested in theS&P 500 and 50 percent invested in one-monthmoney market securities. For an OTM call investor, the market exposureincreased to 66 percent for the 2 percent OTM andto 87 percent for the 5 percent OTM. The OTM callsexpired in the money in 37 percent of the monthsfor the 2 percent OTM strategy (12 percent of themonths for the 5 percent OTM strategy). Thesenumbers are significantly lower than the exercisefrequency of the ATM strategy, which comes closestto the BXM. Note that the delta gives a reasonableestimate of exercise frequency (the percentage ofperiods the options expired in the money).The delta measure can also be used to risk-adjust the return metrics for the index-overwritingstrategies. We used the initial delta () at the timeFigure 8. Year-by-Year Performance of the BXM and Fixed-Strike OTM Call-Overwriting Strategies Compared with the S&P 500, 18 January 1990 to 17 November 2005Sources: CBOE, Standard & Poors, and Goldman Sachs.Return in Excess of S&P 500 (pps)252015105102015525S&P 500 Total Return (%)S&P 500 Total Return (right axis)403010201030204094 98 029690 92 00 0495 99 039791 93 01 050 0BXM (left axis) ATM (left axis) 2% OTM (left axis)Table 3. Delta, Exercise Frequency, and Market Risk of Covered Index Strategies, 18 January 1990 to 17 November 2005StrategyInitial Option EmpiricalBetabMonthsExercisedDelta BetaaS&P 500 1.00 1.00 BXM 0.56 Sell ATM call 0.53 0.47 0.51 61%Sell 2% OTM call 0.34 0.66 0.68 37Sell 5% OTM call 0.13 0.87 0.87 12aThe initial beta is 1 minus the initial delta.bThe empirical beta is estimated from the monthly total returnson the S&P 500 and the monthly strategy returns.Sources: CBOE, Standard & Poors, and Goldman Sachs.Financial Analysts Journal38 www.cfapubs.org 2006, Goldman, Sachs & Co.of the option sale as a basis for constructing a risk-equivalent S&P 500 return consisting of being long1 of the S&P 500 and investing the delta portionat LIBOR during the life of the option. When com-pared with this delta-adjusted S&P 500 returnseries, the ATM strategy outperformed by 5.5 per-centage points, the 2 percent OTM outperformedby 4.5 percentage points, and the 5 percent OTMoutperformed by 2.2 percentage points over the19902005 period (see Table 2). These are solid risk-adjusted alphas. To convert this covered indexstrategy into an alpha-only strategy, one couldsell the call option and buy a delta-equivalentamount of S&P 500 futures, either based on theinitial delta or replicating the shifting delta over thecourse of the month. Performance attribution analysis. The returndecomposition for the ATM, 2 percent OTM, and 5percent OTM call-selling strategies are given in Fig-ure 9. The bars identify how much of the perfor-mance of these strategies in excess of the S&P 500return (the basis points given on the tops of the bars)was a result of the fair call premium, the volatilitypremium, the exercise cost, and the trading cost.16Consistent with prior studies, we found thefollowing: The bulk of the positive performance can beattributed to the fair call premium. The cost of exercise ate away the largest pro-portion of the excess returns. The volatility premium decreased as the strikemoved farther out of the money. Under the assumption that options were sold atone-half a volatility point from midmarket im-plied volatility levels (the basis for generating theoption premiums used in this analysis), tradingcosts subtracted 36 bps a month, on average. One-month vs. three-month strategies. InTable 4, we show the summary return and riskstatistics for S&P 500 three-month option-sellingstrategies and compare them with those of the BXMand S&P 500. In this case, to reflect the higher returnexpectations over quarterly rather than monthlyhorizons, we used higher strike prices for OTMoptions. These OTM strategies all have similarannualized returns over the most recent 15+ yearsof about 10.5 percent, not as high as the strategiesbased on selling the same-strike S&P 500 option ona monthly basis. For three-month calls, the 7 percentOTM strategy has the best risk and return profilewith risk almost 3 percentage points below that ofthe index but a slightly higher return.17Figure 9. Attribution Analysis of One-Month Covered Call Strategies, 18 January 1990 to 17 November 2005Sources: Standard & Poors and Goldman Sachs.Average Return Contribution in Excess of S&P 500 (pps)2.52.01.51.00.501.01.50.52.02.52% OTM 5% OTMATM12 bps15 bps8 bpsVolatility Premium Fair Call Premium Trading Cost Exercise CostFinding Alpha via Covered Index WritingSeptember/October 2006 www.cfapubs.org 39In all cases, the three-month call-selling strate-gies underperformed the strategies selling one-month S&P 500 options. We attribute this result tothe missed opportunity with a three-month strat-egy to reset the strike price monthly in rapidlyrising markets, participate in time decay more fre-quently in highly volatile bear market periods, andcapitalize on a favorable implied-to-realized vola-tility spread with a higher frequency during theyear. In a more active overwriting strategy, wewould suggest that investors shift to writinglonger-term options when implied volatility is atthe high end of its normal range and when S&P 500expected returns are moderate or negative.Dynamic S&P 500 OverwritingAn S&P 500overwriting strategy that is a higherrisk/higher return variation on the BXM shouldappeal to large-capitalization equity investors.Although fixed-strike strategies move in that direc-tion, other, more dynamic ways can also be used toachieve a higher risk and higher return profile. Wepropose a strategy that uses OTM S&P 500 optionswith a higher strike price in more volatile marketconditions and a lower strike price in quieter mar-kets. The strike price of the option is based on atarget probability of exercise, which can be derivedfrom an options implied volatility by using anoption-pricing formula.Because this section no longer refers to strate-gies, like the BXM, that roll on expiration Fridays,we revert to using easier-to-interpret calendarmonths instead of expiration months in our results.What a Dynamic Strike Looks Like. Thestrike prices associated with a 20 percent and a 30percent target probability of exercise are shown inFigure 10. In the early 1990s, when volatility waslow, the strike price associated with the 20 percentprobability was 23 percent out of the moneyasit is today. In the 19972002 period, however, whenvolatility was much higher, the strike price of theoption sold was typically in the 46 percent rangeif the target was 20 percent probability of exercise.Notice how the implied strike price tends to behigher when returns are reversing a great deal. Theone exception that appeared to hurt the strategywas in 2003, when the sharp shift down in volatilitycaused the target strike to compress prior to thestrong market gains in the second part of that year.Characteristics of Dynamic-Strike Strate-gies. The delta, beta, exercise frequency, and riskmetrics for the dynamic overwriting strategies withvarious target exercise probabilities are in Table 5.The 30 percent target probability is comparable tothe 2 percent OTM overwriting strategy (see Table3) in terms of average delta (0.32 versus 0.34) andbeta (0.68 versus 0.66). The 36 percent experiencedexercise frequency is almost identical to that of the2 percent OTM strategy, which was 37 percent. Also,the strategy with the 20 percent target probabilityhas risk characteristics similar to those for selling afixed 4 percent OTM one-month call option.18 As forthe fixed-strike strategies, the initial delta for thedynamic-strike strategies serves as a reasonableproxy for the percentage of months the optionsexpire in the money.Historical Return and Risk. The historicalperformance of the dynamic-strike strategies thatvary the strike price by targeting a probability ofexercise is given in Table 6. In both cases, thedynamic-strike strategies performed in line with thefixed-strike strategies with comparable risk.19 Thestrategy with the 20 percent target probability, forexample, marginally outperformed the strategywith the 4 percent OTM fixed strike with marginallyhigher risk. Figure 11 shows in Panel A the perfor-mance of the 2 percent OTM strategy versus thestrategy based on 30 percent probability of exerciseTable 4. Three-Month Covered Call Strategies vs. S&P 500, 18 January 1990 to 17 November 2005Annualized Return Annualized Risk MeasuresStrategy ReturnReturn vs.S&P 500Standard DeviationTracking Error vs.S&P 50010th Percentile Quarterly Return90th Percentile Quarterly ReturnS&P 500 10.59% 15.60% 6.45% 10.44%BXM 11.20 0.61% 10.30 8.47% 2.61 7.72ATM 10.34 0.25 8.73 9.89 2.20 5.965% OTM 10.48 0.11 11.71 6.67 4.71 8.307% OTM 10.81 0.22 12.82 5.60 5.28 9.1810% OTM 10.65 0.06 14.04 4.16 5.65 11.05Sources: CBOE, Standard & Poors, and Goldman Sachs.Financial Analysts Journal40 www.cfapubs.org 2006, Goldman, Sachs & Co.and in Panel B, the performance of the 4 percentOTM strategy versus the strategy based on 20 per-cent probability of exercise. The scatterplots ofmonthly returns are provided in Figure 12. The strategy with the 20 percent target proba-bility would be attractive for investors seeking analpha strategy with almost full equity market risk.It has delivered an average annualized return morethan 2 percentage points higher than the S&P 500return for the past 15+ years, as shown in thecalendar-year performance chart given in Panel B ofFigure 11 and in the scatterplot in Panel B of Figure12. For investors who want an index-overwritingstrategy with somewhat less total and beta risk, the30 percent target probability might be a better fitwith a beta of 0.7, a standard deviation of 11.3 per-cent (about 3 percentage points less than the S&P500 Index), and a tracking error to the index of 5percent (Table 6). Annualized returns of 12.1 per-cent still show a healthy premium to S&P 500 per-formance, with returns better than the index in 69percent of the months during the period January1990 through October 2005.Panel A in Figure 11 shows that the strategywith the 30 percent probability of exercise by calen-dar year outperformed the S&P 500 in 11 of 16 years.The periods when the dynamic-strike over-writing strategies are superior to the fixed-strikestrategies in terms of return tend to be those withstronger S&P 500 returns. The average strike of 2.4percent of the dynamic-strike strategies provides abit more room for upside than does the fixed-strike2 percent OTM strategy, but the key is how muchthe strike varies with market risk levels. Figure 10. Dynamic Strategies: Strike of Option Sold, 1 January 1990 to31 October 2005Note: The shaded lines denote the average strikes3.8 percent for the 20 percent probability of exerciseand 2.4 percent for the 30 percent probability of exercise.Sources: Standard & Poors and Goldman Sachs.Table 5. Characteristics of Dynamic Strategies, 1 January 1990 to 31 October 2005Prob. of ExerciseAverageStrikeInitial OptionEmpiricalBetaMonths ExercisedAnnualStandard DeviationAnnual Tracking Error vs. S&P 500Delta Beta10% 5.60% 0.10 0.90 0.95 8% 13.80% 1.83%20% 3.81 0.21 0.79 0.87 25 12.76 3.3330% 2.44 0.32 0.68 0.75 36 11.26 5.0140% 1.17 0.42 0.58 0.62 50 9.77 6.74Sources: Standard & Poors and Goldman Sachs.Dynamic Strike Level (% OTM)30% Probability of Exercise20% Probability of Exercise108642089 059391 95 99 0397 01Finding Alpha via Covered Index WritingSeptember/October 2006 www.cfapubs.org 41Implications for Investment StrategiesIndex overwriting can be implemented as a stand-alone strategy or as part of a balanced or assetallocation strategy. The idea of selling upsideequity returns is consistent with the bias of manyasset class strategies to shift out of strongly per-forming asset classes into alternative investmentopportunities. It also fits well into global macro orglobal alpha strategies. Equity indexoverwritingcan also be considered a lower-risk equity enhance-ment strategy that has regularity in its cash flowsfrom the option premiums. This feature makes it apotential alternative to equivalent-risk fixed-income or yield/value-oriented active equity strat-egies. Returns from the BXM or other S&P 500overwriting strategies diversify momentum-basedstrategy returns as well as returns derived fromcurrency or global tactical asset allocation.The BXM provides an easily accessible bench-mark for S&P 500 overwriting, structured prod-ucts, or an index for replication for investorswanting the risk profile of selling ATM options. Forinvestors seeking to retain some upside consistentwith a risk premium for equities or to increasereturns, the BXM can serve as a risk benchmark forevaluating a more aggressive overwriting strategyor variations embedded in structured products.These OTM index optionselling strategies arelikely to have returns that are correlated with theBXM but also have a greater sensitivity to theunderlying index.In most countries with developed index optionmarkets, index options trade at a premium to real-ized index volatility. Against the backdrop of anoutlook for moderate to weak equity market returnsand slowly rising interest rates, the historical trackrecord of overwriting strategies in similar environ-ments is quite compelling. In periods of cyclicallylow interest rates, strategies with a steady cash floware favored. Competitive, liquid markets in short-term index options exist, and investors are comfort-able with using derivatives now that risk systemshave improved. Finally, the quest for diversifiedsources of alpha also argues for choosing indexoverwriting as part of an absolute-return or market-neutral allocation, in which other strategies mayhave alphas more correlated with styles, rising vol-atility, momentum, or other equity market factors.ConclusionThis analysis closely examined the historical returnand risk characteristics of a variety of short-termS&P 500overwriting strategies with both fixedand dynamic strikes. These strategies have veryfavorable performance characteristics at a range ofrisk levels. Because of the presence of an equity riskpremium and the goal of higher returns for equity-based strategies, we would recommend strategiesat least 2 percent out of the money or with a 30percent or less probability of exercise. The lowerexercise frequency also reduces tracking error andoperational issues compared with an ATM strategy,as represented by the BXM. All of the strategiesadapt to changing volatility regimes because theysell one-month options that change in price as vol-atility changes. Investors who hold S&P 500 expo-sure as part of their investment policy and who arelooking for low-risk enhancement strategies maywish to take a close look at the opportunities offeredby the liquid short-term index option markets.We thank Barbara Dunn and Dmitry Novikov for theireditorial and research assistance.This article qualifies for 1 PD credit.Table 6. Return and Risk of Dynamic-Strike Strategies, 1 January 1990 to 31 October 2005Annual Return Annual Risk MeasuresStrategyAverage Strike ReturnReturn vs. S&P 500Standard DeviationTracking Errorvs. S&P 50010th PercentileMonthly Return90th PercentileMonthly ReturnS&P 500 10.40% 14.37% 4.36% 5.98%2% OTM 12.45 2.05% 10.51 5.88% 3.27 3.7430% Prob. exercise 2.44% 12.13 1.73 11.26 5.01 3.52 4.304% OTM 12.35 1.94 12.38 3.69 3.80 4.9320% Prob. exercise 3.81 12.40 2.00 12.76 3.33 4.01 5.28Sources: Standard & Poors and Goldman Sachs.Financial Analysts Journal42 www.cfapubs.org 2006, Goldman, Sachs & Co.Figure 11. Calendar-Year Performance of Fixed-Strike OTM and Dynamic-Strike Call-Overwriting Strategies Compared with the S&P 500, 1 January 1990 to 31 October 2005Sources: Standard & Poors and Goldman Sachs.Return in Excess of S&P 500 (pps)S&P 500 Total Return (right axis)10622610S&P 500 Total Return (%)30402010010203094 98 029690 92 00 0495 99 039791 93 01 05A. 2 percent OTM vs. 30 percent probability of exerciseReturn in Excess of S&P 500 (pps)S&P 500 Total Return (right axis)10622610S&P 500 Total Return (%)30402010010203094 98 029690 92 00 0495 99 039791 93 01 054% OTM (left axis) 20% Probability of Exercise (left axis)2% OTM (left axis) 30% Probability of Exercise (left axis)B. 4 percent OTM vs. 20 percent probability of exerciseFinding Alpha via Covered Index WritingSeptember/October 2006 www.cfapubs.org 43Figure 12. Monthly Performance of Fixed-Strike OTM and Dynamic-Strike Call-Overwriting Strategies Compared with the S&P 500, 1 January 1990 to 31 October 2005Note: The ovals indicate excess returns of the strategy in stronger equity markets.Sources: Standard & Poors and Goldman Sachs.Monthly Excess Return (pps)A. 2 percent OTM vs. 30 percent probability of exercise42246812 1248 0 4 8S&P 500 Return (%)30% Exercise Probability2% OTMMonthly Excess Return (pps)B. 4 percent OTM vs. 20 percent probability of exercise42246812 1248 0 4 8S&P 500 Return (%)20% Exercise Probability4% OTM00Financial Analysts Journal44 www.cfapubs.org 2006, Goldman, Sachs & Co.Appendix A. Calculation of the BXMThe BXM is calculated as follows:where Rt1,t is the total return of the covered callindex portfolio from the close of day t 1 to the closeof day t.The daily return calculation depends onwhether the trading day coincides with expirationor not. On nonexpiration days, return is calculated aswhereSt = the S&P 500 value at the close of day tDt = cash dividends on stocks that went exdividend on day t, expressed in S&P 500index pointsCt = the average of the last bid and ask pricesof the S&P call option reported before4:00 p.m. EST on day tOn expiration days, when the options in the strat-egy are rolled, the return consists of three portions:whereRt1,Settlement = return from the close onday t 1 to the time theSpecial Opening Quotation(SOQ) is determined to set-tle the expiring option (usu-ally before 11:00 a.m. EST)RSettlement,Initiation = return from the SOQ to thetime the new option isdeemed soldRInitiation,t = return from option initia-tion to the close on day tThese three components are defined as follows:andwhereCSettlement = settlement price of the expiring callCVWAP = volume-weighted average of theprices (VWAP) of the new one-month ATM option from 11:30a.m. to 12:00 p.m. ESTSVWAP = VWAP level of the S&P 500 withthe same time and weights as usedin the calculation of CVWAPAppendix B. Calculation of Covered Call Strategy ReturnsIn our analysis, the index calloverwriting strategyreturns were calculated as follows:whereSt = the S&P 500 value at the close of day tDt = cash dividends on stocks that went exdividend on day t, expressed in S&P 500index pointsCt1 = call premium (bid price) received on theThursday before expiration (time t 1)Ct = call premium (ask price) paid on theThursday before the next expiration(time t) to buy back the option = investment horizon (one month or threemonths)Lt1 = continuously compounded annualizedLIBOR at time t 1 for investment hori-zon For the one-month strategy, t 1 to t covers onemonth, from the Thursday before expiration to theThursday before the next expiration; for the three-month strategy, it covers from the Thursday beforethe expiration to three months later.For the dynamic-strike strategies for which weassumed that the rolling of the strategy coincidedwith expiration (both at the close on month-end),the strategy returns can also be written aswhere represents the out-of-the-moneyness ofthe call (0 percent, 2 percent, or 5 percent for one-month calls and 0 percent, 5 percent, 7 percent, or10 percent for three-month calls).BXM BXM Rt t t t= +( ) 1 11 , ,R S D CS Ct tt t tt t=+ 11 1, ,1R R RRt t t Settlement Settlement Initiation = +( ) +( ) +1 11 11, , , IInitiation t, , ( )1RS D CS Ct SettlementSOQ t Settlementt t=+ 11 11, ,R SSSettlement InitiationVWAPSOQ, , = 1R S CS CInitiation tt tVWAP VWAP, , =1R S D SSC eSCSt tt t tttLtttt=+ + 11111 11, , RS D SSC eSS SSt tt t tttLtt ttt=+ +111111110,max , ,Finding Alpha via Covered Index WritingSeptember/October 2006 www.cfapubs.org 45Appendix C. Best and Worst Three-Year Relative PerformanceData for the best and worst three-year periods forselling S&P 500 calls with different strike prices arein Table C1 for both one-month and three-monthoptions. On the positive side, note that the bestperiods for overwriting were during bear marketswith outperformance of 1438 percentage points forthe one-month call-selling strategy or BXM (PanelA) and 1024 percentage points for the three-monthstrategy (Panel B). Defining a year as starting onJanuary expiration and running until the followingyears January expiration, the 19992001 perioddelivered the best relative performance for selling 2percent OTM one-month options; the 200002period provided the best for 5 percent and 7 percentOTM three-month options.As for the worst periods for engaging in over-writing compared with holding the S&P 500, notethat during the 199597 period, S&P 500 overwrit-ing with one-month ATM options was quite costly.Cumulative underperformance was 41 percentagepoints for the BXM and 35 percentage points for theATM option. By selling the 2 percent OTM optioninstead in this time period, the drag was reducedby more than 50 percent to less than only 20percentage points underperformance. Similarresults are visible for the worst 12-quarter periods(Panel B). Selling three-month S&P 500 OTM callsproduced the worst relative underperformancenegative 2946 percentage pointswhich occurredin the 199698 period.These extreme relative returns highlight one ofthe reasons this strategy may be more appealing overthe very long run (10 years): It produces multiple-year returns below the index when equity marketsare in a sustained bullish phase. Few investors, how-ever, expect the market experience of the second halfof the 1990s to be repeated soon, which is a primaryreason overwriting has much appeal today.Table C1. Extreme Cumulative Returns Relative to the S&P 500, 18 January 1990 to 17 September 2005Three Years(January to January) 36-Month PeriodStrategy PeriodExcessReturn vs.S&P 500S&P 500Return PeriodExcessReturn vs.S&P 500S&P 500ReturnA. One-month S&P 500 callselling strategiesBest relative performance BXM 0002 24.0% 34.1% Mar 00Mar 03 26.5% 37.3%ATM call selling 9901 37.7 2.5 Aug 98Aug 01 41.2 12.42% OTM call selling 0002 26.4 34.1 Aug 98Aug 01 30.4 12.45% OTM call selling 0103 14.1 11.9 Oct 01Oct 04 16.0 8.6Worst relative performance BXM 9597 41.1 117.3 Jul 94Jul 97 54.9 120.7ATM call selling 9597 34.7 117.3 Jul 94Jul 97 51.8 120.72% OTM call selling 9698 16.1 110.5 Jul 94Jul 97 27.2 120.75% OTM call selling 9698 8.3 110.5 Nov 95Nov 98 9.8 104.1B. Three-month S&P 500 callselling strategiesThree Years(January to January) 12-Quarter PeriodStrategy PeriodExcessReturn vs.S&P 500S&P 500Return PeriodExcessReturn vs.S&P 500S&P 500ReturnBest relative performance BXM 0002 24.0% 34.1% Apr 00Apr 03 25.4% 35.6%5% OTM call selling 0002 21.8 34.1 Jan 00Jan 03 21.8 34.17% OTM call selling 0002 16.1 34.1 Jan 00Jan 03 16.1 34.110% OTM call selling 9901 10.4 2.5 Jan 99Jan 02 10.4 2.5Worst relative performanceBXM 9597 41.1 117.3 Jul 94Jul 97 54.9 120.75% OTM call selling 9698 45.9 110.5 Apr 95Apr 98 51.0 133.47% OTM call selling 9698 38.8 110.5 Apr 95Apr 98 40.9 133.410% OTM call selling 9698 29.3 110.5 Jan 96Jan 99 29.3 110.5Sources: CBOE, Standard & Poors, and Goldman Sachs.Financial Analysts Journal46 www.cfapubs.org 2006, Goldman, Sachs & Co.Notes1. See, for example, Feldman and Roy (2004) and Whaley(2002). The primary source of information and historicaldata on the BXM and related topics is the CBOE. Seewww.cboe.com/bxm. 2. For example, Rampart Investment Management, ConnorsInvestors Services, Morgan Stanley, and Merrill Lynch usethe BXM as a basis for option-writing products targeted atinstitutional and/or retail clients. Gateway InvestmentAdvisers Gateway Fund, a mutual fund that has existedsince the late 1980s, sells index calls against its S&P 500 stockholdings and buys protective puts. Since mid-2004, morethan 20 closed-end funds have been launched that incorpo-rate option selling in a variety of option strategies, includingstock as well as index options on U.S. and non-U.S. stocksand indices.3. See Balasubramanian and Tierens (2004); Hill and Gregory(2002); Hill, Gregory and Balasubramanian (2003); Hill,Balasubramanian, Gregory, and Tierens (2005); Hill andNovikov (2006); Mussavian and Kassam (2002); Rattray,Gregory, and Balasubramanian (2003); Tierens and Bala-subramanian (2005a, 2005b).4. These gains could be offset by losses on the exercise of theoption, but with ATM or OTM (out-of-the-money) options,only a portion of the options are exercised through time.S&P 500 options are Section 1256 contracts and are, there-fore, marked to market at year-end. Of the realized gains,60 percent are taxed at the long-term capital rate and 40percent are taxed at the short-term capital rate. (Please notethat we are not providing tax, legal, or accounting advice.Readers should consult professional tax, legal, and account-ing advisers for specific information.)5. To be precise, the call premiums in Figure 3 are the sum ofwhat we labeled the fair call premium and the volatilitypremium at the start of this section.6. More precisely, the strike price of the call option is the strikeprice above the prevailing S&P 500 level that is closest to atthe money.7. For details on the methodology and historical data, seewww.cboe.com/bxm. 8. The BXM was set at a value of 100 on 1 June 1988. AppendixA provides details on the calculation of the BXM.9. An index similar to the BXM but selling the listed optionwith a strike closest to (and at least) 2 percent OTM wasintroduced by the CBOE early in 2006, with a return historydating back to 1988. The return and risk profile of this index(ticker BXY) is similar to that of the 2 percent OTM one-month overwriting strategy examined in this article and canbe a useful benchmark for S&P 500 buy-write strategieswith short-term OTM call options.10. The 1 point implied volatility is a conservative estimate thatshould be wide enough to also absorb commission costs.11. Appendix B contains details about how we calculated thereturns on these strategies.12. To fully understand the benefits and risks of this strategy,we also looked at the best and worst relative returns over athree-year window on both a calendar and a 12-quartermoving basis; Appendix C provides the results.13. Because this section defines a month as an expiration monthrather than a calendar month, the annualized risk and returnnumbers differ from the ones quoted in reference to Figure 1.14. A year was defined here as the period starting at the closeof the January expiration Friday and ending at the close ofthe January expiration Friday of the following year. Theseannual periods are not identical, therefore, to calendar years.15. If this strategy were executed via S&P 500 exchange-tradedfunds and ETF options, the SPY ETF could be delivered intothe option exercise.16. We included the reinvestment of the call premium at LIBORin the fair call premium because it was small (a few basispoints a month).17. Note that these measures are based on quarterly rather thanmonthly returns, resulting in BXM and S&P 500 risk mea-surements that are different from those in Table 1.18. These comparisons between dynamic and fixed strikes heldup whether we used calendar month-end or expirationmonth-end.19. To make the results of the fixed- and dynamic-strike strate-gies comparable in Table 6 and the figures, we recalculatedthe fixed-strike strategy results under the assumption ofcalendar-month-end periods instead of expiration-month-end periods. The numbers in Table 6 are, therefore, slightlydifferent from the numbers presented Table 1.ReferencesBalasubramanian, Venkatesh, and Ingrid Tierens. 2004. StockOption Selling Strategies Can Generate Alpha Even in a Flatand Skinny Market. Goldman Sachs Equity Derivatives Strategy(2 November).Feldman, Barry, and Dhruv Roy. 2004. Passive Options-BasedInvestment Strategies: The Case of the CBOE S&P 500 BuyWriteIndex. Ibbotson Associates (28 July).Hill, Joanne M., and Krag (Buzz) Gregory. 2002. Covered IndexStrategies: Appealing Features for Total Return or Income-Oriented Equity Investors. Goldman Sachs Equity DerivativesStrategy (22 October).Hill, Joanne M., and Dmitry Novikov. 2006. Covered IndexStrategies: Revisiting a Source of Enhancement for Equity BetaExposure. Goldman Sachs Equity Derivatives Strategy (28February).Hill, Joanne M., Krag (Buzz) Gregory, and VenkateshBalasubramanian. 2003. Capturing Returns from IndexVolatility Selling Strategies. Goldman Sachs Equity DerivativesStrategy (27 January).Hill, Joanne M., Venkatesh Balasubramanian, Krag (Buzz)Gregory, and Ingrid Tierens. 2005. Finding Alpha in aModerate Return EnvironmentThe BXM and Variations onCovered Index Writing. Goldman Sachs Equity DerivativesStrategy (9 February).Mussavian, Massoud, and Altaf Kassam. 2002. The Impact ofSelling Index Options on Global Equity Portfolios. GoldmanSachs Equity Derivatives Strategy (18 October).Rattray, Sandy, Krag (Buzz) Gregory, and VenkateshBalasubramanian. 2003. Selling Realized VolatilityAnUnfair(ly Profitable) Game? Goldman Sachs Equity DerivativesStrategy (21 January).Tierens, Ingrid, and Venkatesh Balasubramanian. 2005a.Covered Index Call Writing Strategies for EAFE Portfolios.Goldman Sachs Equity Derivatives Strategy (29 July).. 2005b. Options versus Futures: The Long and the Shortof It. Goldman Sachs Equity Derivatives Strategy (24 March).Whaley, Robert E. 2002. On the Return and Risk of the CBOEBuyWrite Monthly Index. Journal of Derivatives, vol. 10(Winter):3542.
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