Cisdm qqqactive-full

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Cisdm qqqactive-full

  1. 1. An Update of “Loosening Your Collar: Alternative Implementations of QQQ Collars”: Credit Crisis and Out-of-Sample Performance Edward Szado * Thomas Schneeweis ** Original Version: August 2009 Current Update: January 2011*Doctoral Candidate, Isenberg School of Management, University of Massachusetts, Amherst,MA 01003, Director of Research, INGARM, Amherst, MA 01002. INGARM gratefullyacknowledges research support provided by the Options Industry Council. Research results,however, represent those of the authors and do not necessarily represent the views of the OIC.Please address correspondence to Edward Szado, INGARM, 29 S. Pleasant St., Amherst, MA01002, 413-256-0195, or email: eszado@ingarm.org.**Michael and Cheryl Philipp Professor of Finance, Director of CISDM, Isenberg School ofManagement, University of Massachusetts, Amherst. AbstractThis study provides an update to Szado and Schneeweis [2010]. The original study covered theperiod from March 1999 through May 2009. This updated study extends the period of analysisthrough September 2010.The credit crisis and the associated decline in equity markets rekindled new interest in optionbased equity collars and in protective strategies in general. In this paper we consider theperformance of passive and active implementations of the collar strategy on the QQQ ETF aswell as on a sample small cap equity mutual fund. As expected, the results of the analysis showthat a passive collar is most effective (relative to a long underlying position) in declining marketsand less effective in rising markets. This study also considers a more active implementation ofthe collar strategy. Rather than simply applying a set of fixed rules as for the passive collar, inthe active collar adjusted strategy, we apply a set of rules which adapt the collar to varyingeconomic and market conditions. This approach is similar to applying a set of tactical assetallocation rules to a set of investments. There are of course an unlimited number of conditioningfactors that can be used to determine the strategy implementation. In this paper, for purposes ofpresentation, we combine three conditioning factors that have been suggested in academicliterature (momentum, volatility, and a compound macroeconomic factor (unemployment andbusiness cycle)) to generate a dynamic collar adjusted trading strategy. For the period ofanalysis, the active collar adjustment strategy tends to outperform the passive collar both in-sample as well as out-of-sample. Judgments as to the particular benefits of the passive and activecollar strategies are, of course, dependent on the risk tolerance of the individual investor.
  2. 2. Introduction This study provides an update to Szado and Schneeweis [2010]1. The original studycovered the period from March 1999 through May 2009. This updated study extends the periodof analysis through September 2010. In addition to the original analysis, this update includes out-of-sample performance for the active collar strategies based on the trading rules set out in theoriginal paper. The credit crisis and the associated decline in equity markets rekindled new interest inoption based equity collars and in protective strategies in general. In 2008 the QQQ experienceda drawdown of about 50% from peak to trough. Many other asset classes which are generallyconsidered effective equity diversifiers also faced significant losses. This type of contagionacross asset classes suggests that in times of major systematic stress, direct hedges throughprotective option strategies may provide equity portfolios with greater downside risk protectionthan standard multi-asset diversification programs. There are a variety of option strategies whichcan provide capital protection for equity based portfolios. The focus of this paper is one of themore straightforward options based strategies – the collar. A collar is an option basedinvestment strategy that effectively limits (or collars) the returns on an investment in anunderlying asset to fall within a chosen range. An investor who holds a long position in anunderlying asset can convert that position into a collar (collar his position) by purchasing a putoption on the underlying asset and simultaneously selling (writing) a call option on theunderlying asset. The strike price on the call defines the upper bound of the collar and is setabove the strike price for the put (which defines the lower bound of the collar). In a standard1 See “Loosening Your Collar – Alternative Implementations of QQQ Collars,” Edward Szado andThomas Schneeweis, Journal of Trading, Spring 2010, Vol. 5, No. 2, pp. 35-56 2
  3. 3. collar, the call and put have the same expiration dates. The value of a portfolio constructed inthis manner will essentially be restricted to fluctuate within the bounds set by the strike prices ofthe options (adjusted for the net cost of the option positions).2 In this paper, we extend previous research on collar strategies (Schneeweis and Spurgin[2001] and Szado and Kazemi [2009] as well as the original paper this update is based on) byconsidering the performance and risk characteristics of active as well as passive collars. Inaddition, we provide an example of the effectiveness of applying a collar strategy to a sampleequity mutual fund on which options are not available. It is worth noting that this study does notaddress whether these strategies generate “alpha” based on any specific definition of investorrisk aversion. The significance of the results may be interpreted differently by any individualbased on their particular risk aversion. In this study the performance of passively implemented collars on the Powershares QQQETF (ticker: QQQQ) is analyzed. The collars are passive in the sense that they follow a rigid setof rules which do not vary with market conditions. The passive implementations do vary in theirchoice of the initial moneyness and time to expiration of the calls and puts. This study alsoconsiders a more active implementation of the collar strategy. Rather than simply applying a setof fixed rules as for the passive collar, for the active collar adjustment strategy, we apply a set ofrules which adapt the collar to varying economic and market conditions. This approach is similarto applying a set of tactical asset allocation rules to a set of investments. There are of course an2 Collars can be visualized as a combination of covered call and protective put strategies. The collarstrategy essentially adds a long protective put to a covered call strategy. This provides the significantdownside protection which the covered call strategy lacks. The purchase of the long put is financed by thesale of the call. In essence, the collar trades upside participation for downside protection. A tight collarprovides less upside participation and more downside protection than a loose collar. At one extreme, thetightest collar (ATM puts and calls) effectively immunizes the portfolio from market movements. At theother extreme (very far OTM puts and calls), the collar is essentially equivalent to a long index position. 3
  4. 4. unlimited number of conditioning factors that can be used to determine the strategyimplementation. In this paper, for purposes of presentation, we combine three conditioningfactors that have been suggested in academic literature (momentum, volatility, and a compoundmacroeconomic factor (unemployment and business cycle)) to generate a dynamic collaradjusted trading strategy.3 Finally, the study considers the implementation of an active andpassive collar strategy using QQQ options applied to a non-QQQ equity portfolio represented bya small cap equity mutual fund. This provides an additional analysis of the use of the collarstrategy for a wider range of market participants. In the following sections we summarize the methodology and data used in this analysis. Itis important to note that all empirical research may be data and time period dependent. Theoriginal analysis in Szado and Schneeweis [2010] covers the period from the introduction ofoptions on the QQQ (March 19, 1999) through May 31, 2009. This updated analysis covers theperiod from March 19, 1999 through September 30, 2010. This period is broken into various sub-periods to offer a better picture of the benefits and risk of the implemented collar strategies invarious market environments. In the methodology section we describe both the passive andactive collar implementations. In the active collar section we describe how we combine themomentum, volatility and macroeconomic signals to generate a dynamic collar adjustmenttrading strategy process4. In this process, the initial moneyness of the puts and calls isdetermined based on the momentum and macroeconomic signals and the ratio of written calls isdetermined by the volatility signal. The marginal effect of the momentum signal is to widen or3 While these collar implementations are active in the sense that the rules are dependent on managerdecisions, they are implemented systematically with no additional manager discretion.4 While we combine the three signals to generate the strategy, any one of the signals could be used on itsown to generate an active strategy. 4
  5. 5. tighten the collar by increasing or decreasing the amount OTM, respectively. The marginal effectof the macroeconomic signal is to shift the collar up by increasing the amount OTM of the callsand decreasing the amount OTM of the puts, or shift the collar down by moving the strikes in theopposite direction. The marginal effect of the volatility signal is to increase or decrease thenumber of calls written per QQQ and put purchased. Results show that the passive and active collar strategies underperformed the QQQ in thestrong market climb of October 2002 to September 2007. However, in the period around the techbubble and in the credit crisis the passive and active collar strategies provided capital protectionand generated significant returns at relatively low volatility, particularly in the case of the techbubble period. In addition, we provided evidence of the effectiveness of wrapping a passive oractive collar strategy around a portfolio for which no options are available (in this case,represented by a small cap mutual fund). Results for the mutual fund collars are similar to thosereported for the collar strategies on the QQQ. In addition, results show that active collarstrategies on the QQQ and on a small cap mutual fund which use a set of three simple tradingrules to create a dynamic collar adjustment process could provide added benefits over similarpassive collars. Finally, we provide results that indicate that active collars on the QQQ and on asmall cap mutual fund outperform the corresponding passive collars out-of-sample for the periodfrom June 2009 to September 2010.Data and MethodologyData The option price data is provided by Optionmetrics and covers the period from the firstexpiration after the introduction of QQQ options on March 19, 1999 to September 30, 2010. The 5
  6. 6. QQQ, NDX, Treasury bill and VIX data5 is provided by Bloomberg6, while mutual fund data isprovided by Morningstar. Business cycle announcement data are provided by the NationalBureau of Economic Research.Methodology In order to assess the performance of active and passive collar strategies, we constructindices which represent the return streams generated by such strategies. The passive strategiesfollow a fixed set of option selection rules defining the initial moneyness and time to expirationof the calls and puts, regardless of market conditions. In contrast, the active7 collar strategiesbase their option selection rules on a combination of three simple market/economic based signals(momentum, volatility, and a macroeconomic factor) and thus adjust to various marketconditions.Passive Collar Strategy: We generate a daily time series of returns for each of the passivestrategies beginning on March 19, 19998. At the close on this day a 1-month call is written and a1, 3 or 6-month put is purchased. Depending on the particular passive implementation, the initialmoneyness of the calls and puts are set at either 5%, 4%, 3%, 2%, 1% OTM or ATM. At theclose on the Friday prior to the following expiration, we take one of two actions: If 1-month putsare used, the puts and calls are settled at intrinsic value and we roll into new 1-month puts andcalls with the specified moneyness. If a 3- or 6-month put is used, the calls are settled at intrinsic5 NDX, VIX and Initial Unemployment Claims data is collected from March 1998 to ensure sufficient lagtime for signal generation.6 In the original study this data was provided by Datastream.7 It should be noted that while we use the term active to represent these strategies, they are not trulyactively managed. They still follow an established set of selection rules, but the rules include a dynamicelement conditioned on economic variables.8 This is the Friday prior to the first expiration Saturday following the introduction of QQQ options. 6
  7. 7. value and new 1-month calls with the specified moneyness are rolled into, while the longer termput is held for another month. When the new 1-month calls are written, the net proceeds from thesale of the calls and the expiration of the previous calls are fully invested in the strategy and theposition is rebalanced to ensure a 1:1:1 ratio of the underlying, puts and calls. Once the 3- or 6-month put expires, it is settled at intrinsic value and we once again roll into new puts and callswith the specified moneyness and time to expiration. In order to include the impact oftransaction costs, the puts are purchased at the ask price and the calls are written at the bid pricewhen each new put or call position is established. Each trading day in between roll dates, theoptions are priced at the mid-point between the bid and ask prices. In this manner, daily returnsare calculated for each passive strategy implementation. The following example illustrates thisprocess: Passive 2% OTM 1-Month Call 6-Month Put Implementation Date Exdate Quantity Wealth Roll In 3/ 19/ 1999 Purchase QQQ 1.000 @ $ 102.44 $ 108.69 (Initial) Purchase a 6-month 2% OTM put expiring on: 9/17/1999 (Strike price = 100) 1.000 @ $ 9.50 (at ask) Sell a 1-month 2% OTM call expiring on: 4/16/1999 (Strike price = 104) 1.000 @ $ (3.25) (at bid) Roll Out 4/ 16/ 1999 QQQ value 1.000 @ $ 103.94 $ 112.37 Keep the put (now 5-month 4% OTM) expiring on: 9/17/1999 (Strike price = 100) 1.000 @ $ 8.44 (mid of bid/ask) Payout value of previous call at expiration: 4/16/1999 (Strike price = 104) 1.000 @ $ - (intrinsic value) Roll In 4/ 16/ 1999 Purchase QQQ 1.037 @ $ 103.94 $ 112.37 Keep the put (now 5-month 4% OTM) expiring on: 9/17/1999 (Strike price = 100) 1.037 @ $ 8.44 (mid of bid/ask) Sell a 1-month 2% OTM call expiring on: 5/22/1999 (Strike price = 106) 1.037 @ $ (4.00) (at bid) Repeat until put expires Roll Out 9/ 17/ 1999 QQQ value 1.045 @ $ 126.63 $ 123.31 Payout value of the put at expiration: 9/17/1999 (Strike price = 100) 1.045 @ $ - (intrinsic value) Payout value of the call at expiration: 9/17/1999 (Strike price = 118) 1.045 @ $ (8.63) (intrinsic value) Roll In 9/ 17/ 1999 Purchase QQQ 0.924 @ $ 126.63 $ 123.31 Purchase a 6-month 2% OTM put expiring on: 3/18/2000 (Strike price = 124) 0.924 @ $ 10.25 (at ask) Sell a 1-month 2% OTM call expiring on: 10/16/1999 (Strike price = 129) 0.924 @ $ (3.38) (at bid)Active Strategy Market Signals For the active implementations, a series of three market signals determine the choice ofinitial call and put moneyness, as well as the ratio of the number of calls written to the number of 7
  8. 8. puts and QQQ shares purchased, while the initial time to expiration is fixed at one month for thecalls and 6 months for the puts.Active Collar Adjustment Strategy: Three different sets of active market signals are used for thestrategy implementations, differing by their time horizon; short, medium and long-term. Thethree signals are based on momentum, volatility and a compound macroeconomic indicator(unemployment claims and business cycle), respectively. In order to ensure that the strategies areinvestable, all signals use contemporaneously lagged data9.Momentum Signal: The momentum signal is a simple moving average cross-over (SMACO) ofthe NASDAQ-100 index (NDX)10. A SMACO compares a short-term moving average (SMA)and a long-term moving average (LMA) to determine whether an upward or downward trendexists. The rule is defined by the number of days covered by each of the moving averages. Forexample, a 5/150 SMACO rule compares a 5 day SMA with a 150 day LMA. If the SMA isgreater (less) than the LMA, then an upward (downward) trend indicated, suggesting a buy (sell)signal. Our choice of signals is based on Szakmary, Davidson, Schwarz [1999] and Lento[2008]11, which both consider 1/50, 1/150, 5/150, 1/200 and 2/200 SMACO rules on the NDX.Szakmary et al apply NASDAQ index SMACOs as buy/sell signals for individual stocks for theperiod from 1973 to 199112. They find some significant excess returns, although theirsignificance does not survive transactions costs. Similarly, Lento finds some significant9 The signals are designed so that they are based only on data which existed prior to the date on which thesignal would have been generated in practice. For example, a signal for the March 19, 1999 option roll-indate would only use data which existed on March 18, 1999 or earlier.10 The use of the NDX rather than the QQQ provides us with historical data beyond the introduction of theQQQ. In this way, we can generate signals from the beginning of the QQQ data series.11 Additional evidence of the existence of momentum and potential explanations for its existence can befound in Jegadeesh and Titman [2001] and Schneeweis, Kazemi and Spurgin [2008].12 In this paper they do not take short positions. They use the signals as in/out position indicators. 8
  9. 9. forecasting abilities in the same SMACO rules on the NASDAQ at a 10-day lag over the periodof 1995 to 2008. Following their methodology, we use 1/50, 5/150, and 1/200 SMACO rules onthe NDX. This provides us with a short, medium and long-term momentum signal. Each rolldate, we calculate the SMA and LMA for each of the three momentum rules and use them togenerate the momentum signals. All else equal, if the calculation results in a buy signal, thecollar would widen (increasing upside participation with a corresponding reduction in downsideprotection). In contrast, all else equal, the collar would be tightened in response to sell signal(increasing downside protection while reducing upside participation).The following example illustrates the process for the momentum signal calculation: Momentum Signal Calculation for the 3/19/1999 Roll Date 1 Day SMA 5 Day SMA 50 Day SMA 150 Day SMA 200 Day SMA 2102.77 2061.98 1998.76 1629.73 1554.89 Short Term Momentum Signal Calculation: 1 Day SMA = 2102.77 > 50 Day SMA = 1998.76 Since the 1 day SMA is greater than the 50 day SMA, the NDX is trending upwards. This is a bullish signal, so the momentum signal = +1. Holding the macroeconomic signal constant, this would widen the collar (move the put 1% further OTM and the call 1% further OTM). Medium Term Momentum Signal Calculation: 5 Day SMA = 2061.98 > 150 Day SMA = 1629.73 Since the 5 day SMA is greater than the 50 day SMA, the NDX is trending upwards. This is a bullish signal, so the momentum signal = +1. Holding the macroeconomic signal constant, this would widen the collar (move the put 1% further OTM and the call 1% further OTM). Long Term Momentum Signal Calculation: 1 Day SMA = 2102.77 > 200 Day SMA = 1554.89 Since the 1 day SMA is greater than the 200 day SMA, the NDX is trending upwards. This is a bullish signal, so the momentum signal = +1. Holding the macroeconomic signal constant, this would widen the collar (move the put 1% further OTM and the call 1% further OTM). LONG NDX MEDIUM NDX SHORT NDX Momentum Momentum Momentum Signal Signal Signal +1 +1 +1 Note: All moving averages using data up to the prior days close (e.g. 3/18/1999) 9
  10. 10. Volatility Signal: The volatility signal is based on Renicker and Mallick [2005]. Renicker andMallick create an “enhanced” S&P 500 buy-write strategy and back test it over the period from1997 to September 2005.13 They find excess returns to a strategy which writes 0.75 calls to eachlong index position when the markets short-term anxiety level is high (as indicated by a situationin which the 1-month ATM S&P 500 implied volatility is more than 1 standard deviation aboveits current 250-day moving average level), and writes 1.25 calls per index position when theanxiety level is low (when the 1-month implied volatility is more than 1 standard deviationbelow the 250-day average level)14. Their goal in varying the quantity of written calls is to have alonger exposure to the market in times of high anxiety and shorter exposure in times ofcomplacency. We make two minor modifications to their strategy. First, we use the daily VIXclose as an indicator of implied volatility levels. Second, we consider a short, medium and long-term time frame to generate the 3 corresponding signals. In order to match the time frames of ourmomentum signals our short, medium and long-term volatility signals use 50, 150 and 250-daywindows respectively. In keeping with the methodology of Renicker and Mallick, on roll dateswe sell 0.75 (1.25) calls per index position when the previous day’s VIX close is more than 1standard deviation above (below) its current moving average level, otherwise we sell 1 call perindex position as illustrated by the following formula:# of Calls Written per Long Put and Long QQQ Position = 1 + (0.25 * Volatility Signal),where the volatility signal is -1, 0 or +1.13 Note that since the Renicker and Mallick study reported results based on the period used in this study, the use ofthis variable is not independent from the period used to analyze its impact on the collar strategy.14 When the 1-month implied volatility level is within the 1 standard deviation bounds, they follow astandard 1:1 ratio buy-write. 10
  11. 11. Volatility Signal Calculation for the 3/19/1999 Roll Date VIX 50-Day VIX 50-Day VIX 250-Day VIX 250-Day Spot VIX VIX 150-Day Standard Deviation VIX 150-Day Moving Average Standard Moving Standard Deviation Moving Average Deviation Average 24.3 6.5 27.0 5.9 30.4 2.5 27.8 Short Term Volatility 1-Standard Deviation Range Calculation: 1-Standard Deviation Range = VIX 50-Day Moving Average +/- VIX 50-Day Standard Deviation = 27.8 - 2.5 to 27.8 + 2.5 = 25.3 to 30.3 Medium Term Volatility 1-Standard Deviation Range Calculation: 1-Standard Deviation Range = VIX 150-Day Moving Average +/- VIX 150-Day Standard Deviation = 30.4 - 5.9 to 30.4 + 5.9 = 24.6 to 36.3 Long Term Volatility 1-Standard Deviation Range Calculation: 1-Standard Deviation Range = VIX 250-Day Moving Average +/- VIX 250-Day Standard Deviation = 27.0 - 6.5 to 27.0 + 6.5 = 20.5 to 33.5 VIX 50-Day 1 Std. Dev. VIX 150-Day 1 Std. VIX 250-Day 1 Std. Range Dev. Range Dev. Range 25.3 to 30.3 24.6 to 36.3 20.5 to 33.5 Short Term Volatility Signal Calculation: Spot VIX = 24.3 < Lower Bound of the 50-Day 1-Standard Spot VIX is below the lower bound of the 1-standard deviation range around the 50-day Deviation Range = 25.3 moving average of VIX. This indicates a low level of anxiety, suggesting that we should sell more calls. This a bearish signal, so the volatility signal = +1. This signal would result in selling 1.25 calls for each long put and long QQQ position. Medium Term Volatility Signal Calculation: Spot VIX = 24.3 < Lower Bound of the 150-Day 1-Standard Spot VIX is below the lower bound of the 1-standard deviation range around the 150-day Deviation Range = 24.6 moving average of VIX. This indicates a low level of anxiety, suggesting that we should sell more calls. This a bearish signal, so the volatility signal = +1. This signal would result in selling 1.25 calls for each long put and long QQQ position. Long Term Volatility Signal Calculation: Spot VIX = 24.3 is Between the Lower Bound of the 250- Spot VIX is between the lower bound and the upper bound of the 1-standard deviation Day 1-Standard Deviation Range = 20.5 and the the Upper range around the 250-day moving average of VIX. This indicates a medium level of Bound of the 250-Day 1-Standard Deviation Range = 33.5 anxiety, suggesting that we should sell the standard number of calls. This a neutral signal, so the volatility signal = 0. This signal would result in selling 1 call for each long put and long QQQ position. MEDIUM Volatility SHORT Volatility LONG Volatility Signal Signal Signal 0 +1 +1 Note: Spot VIX level and all calculations use data up to the prior days close (e.g. 3/18/1999)It is worth noting that the volatility signal only affects the call writing portion of the strategy,puts are always purchased at a 1:1 ratio with the index15.15 While we could apply these signals to both the put and call positions, we chose to apply them only tothe call writing to be consistent with Renicker and Mallick. 11
  12. 12. Macroeconomic Signal: The final variable used in the active collar adjustment strategy signalprocess is based on the trend of initial unemployment claims and the state of the economy withrespect to the business cycle. Boyd, Hu and Jagannathan [2005] consider the impact ofunemployment rate surprise on the stock market in the period from 1973 to 2000. They find thatin expansionary periods, stocks typically rise on bad unemployment news, while the oppositerelationship holds in contractionary periods16. This is consistent with Veronesi [1999] whichsuggests that bad news in expansionary periods and good news in contractionary periods aretypically correlated with an increase in uncertainty and an increase in the equity risk premium(corresponding to an increase in expected returns and reduction in current prices). We use thesefindings to construct a signal based on initial unemployment claims. The announcements fromthe NBER’s Business Cycle Dating Committee are used to identify the state of the businesscycle. It is worth noting that NBER does not define a recession as two consecutive quarters ofnegative GDP growth. They define it as follows: “A recession is a significant decline ineconomic activity spread across the economy, lasting more than a few months, normally visiblein real GDP, real income, employment, industrial production and wholesale-retail sales”17. Theseannouncements are generally considered the authority on the current state of the business cycle.Since there is often a significant delay in announcement dates, we base the signals onannouncement dates to avoid hindsight biases. For example, the December 2007 peak wasannounced about one year later on December 1, 2008. Our signal would be based on an16 These results are somewhat counter-intuitive in the case of expansionary economies. One might expectrising unemployment to negatively affect stock prices regardless of the business cycle, but the literaturecited above suggests that rising unemployment in expansionary economies causes expected future interestrates to decline, increasing the value of equities, while rising unemployment in contractions indicatesslower future earnings growth rates, reducing the value of equities.17 See http://www.nber.org/cycles.html 12
  13. 13. expansionary economy until December 1, 2008. Since initial unemployment claims are releasedon a weekly basis, we include a one-week lag in the calculations to ensure the investability of ourstrategy. In order to closely match the macroeconomic signal methodology with those of themomentum and volatility signals, we base our short, medium and long-term macroeconomicsignals on 1/10, 1/30 and 1/40 week SMACOs for weekly initial unemployment claims. Sincerising unemployment claims in an expansionary economy is a bullish stock market price andvolatility signal, if the SMA is greater than the LMA, we shift the collar towards the ATM putand OTM call (increasing both strike prices) thereby increasing the portfolio’s exposure toupside moves as well as increasing its vega18. In contractionary periods, rising unemploymentclaims would cause us to shift the strike prices in the opposite direction.18 Since vega is highest for ATM options, moving the short call further OTM and moving the long puttowards the ATM will increase the vega of both option positions. 13
  14. 14. These calculations can be illustrated with the following example: Macroeconomic Signal Calculation for the 3/19/1999 Roll Date NBER Announcements Date Indication 12/22/1992 Trough 11/26/2001 Peak (3/19/1999 is during an expansionary economy) So on 3/19/1999, a downward trend in unemployment is a bearish signal. MEDIUM SHORT 1 W e e k S MA 40 W e e k S MA 30 W e e k S MA 10 W e e k S MA LONG Unemployment Trend Unemploym Unemploym ent Trend ent Trend 308.0 317.1 311.8 311.4 Down Down Down Short Term Macroeconomic Signal Calculation: 1 Week SMA = 308.0 < 10 Week SMA = 311.4 Since the 1 week SMA is less than the 10 week SMA, unemployment is falling. In an expansionary economy this is a bearish signal, so the signal = -1. Holding the momentum signal constant, this would shift the collar down (move the put 1% further OTM and the call 1% less OTM). Medium Term Macroeconomic Signal Calculation: 1 Week SMA = 308.0 < 30 Week SMA = 311.8 Since the 1 week SMA is less than the 30 week SMA, unemployment is falling. In an expansionary economy this is a bearish signal, so the signal = -1. Holding the momentum signal constant, this would shift the collar down (move the put 1% further OTM and the call 1% less OTM). Long Term Macroeconomic Signal Calculation: 1 Week SMA = 308.0 < 40 Week SMA = 317.1 Since the 1 week SMA is less than the 40 week SMA, unemployment is falling. In an expansionary economy this is a bearish signal, so the signal = -1. Holding the momentum signal constant, this would shift the collar down (move the put 1% further OTM and the call 1% less OTM). LONG MEDIUM SHORT Macroeconomic Macroeconomic Macroeconomic Signal Signal Signal -1 -1 -1 Note: All moving averages using data up to the prior weeks close (e.g. 3/12/1999)Trading Rules: We combine the momentum, volatility and macroeconomic signals for each timeframe to generate our short, medium and long-term active strategies. Due to the excessivetransactions costs that would be associated with daily rolling of option positions, changes in thesignals are not incorporated into the strategies on any days except the roll dates19. On each roll19 In the case of strategies where the put and call expirations are not coincident, such as the 1-monthcall/3-month put strategies, the put moneyness will only be reset when it is rolled (in this example, onceevery 3 months), while the call moneyness is reset at each call roll (every month, since we only considerstrategies with 1-month calls). 14
  15. 15. date, the initial moneyness of the puts and calls is determined based on the momentum andmacroeconomic signals and the ratio of written calls is determined by the volatility signal. Ourrules are constructed in such a manner to ensure that the target initial percentage moneyness ofthe options will be an integer which falls between ATM and 5% OTM. The signals adjust theinitial moneyness of the puts and calls from a level near the center of the range at 3% OTM and2% OTM, respectively20. From this central point, the momentum signal will serve to widen ortighten the collar by increasing or decreasing the amount OTM, respectively. Themacroeconomic signal will shift the collar up by increasing the amount OTM of the calls anddecreasing the amount OTM of the puts, or shift the collar down by moving the strikes in theopposite direction. The net effect can be illustrated by the following formulas for the call strikes: Call % OTM = 2 + (Momentum signal + Macroeconomic signal),and for puts: Put % OTM = 3 + (Momentum signal - Macroeconomic signal),where the momentum signal and the macroeconomic signal are +1/-1 binary signals.The following example provides an illustration of the trading signal calculation:20 Puts tend to cost more than calls for a given level of moneyness, so we start the puts further OTM toallow the option component of the strategy to be close to zero cost. 15
  16. 16. Trading Rule Calculation Based on the Three Signals for the 3/19/1999 Roll Date Short Term Trading Rule Calculation: Initial Call Moneyness = 2% OTM + (Momentum signal + Macroeconomic signal) = (2+1-1)% OTM = 2% OTM Initial Put Moneyness = 3% OTM + (Momentum signal - Macroeconomic signal) = (3+1+1)% OTM = 5% OTM Number of Calls per Put and QQQ Position = 1.00 + (0.25 * Volatility Signal) = 1 + (0.25 * 1) = 1.25 Calls SHORT SHORT NDX SHORT QQQ/Put/Call Macroeconomic Momentum Call % OTM Put % OTM Volatility Ratio Signal Signal Signal -1 1 2 % OTM 5 % OTM 1 1/1/1.25 Medium Term Trading Rule Calculation: Initial Call Moneyness = 2% OTM + (Momentum signal + Macroeconomic signal) = (2+1-1)% OTM = 2% OTM Initial Put Moneyness = 3% OTM + (Momentum signal - Macroeconomic signal) = (3+1+1)% OTM = 5% OTM Number of Calls per Put and QQQ Position = 1.00 + (0.25 * Volatility Signal) = 1 + (0.25 * 1) = 1.25 Calls MEDIUM MEDIUM NDX MEDIUM QQQ/Put/Call Macroeconomic Momentum Call % OTM Put % OTM Volatility Ratio Signal Signal Signal -1 1 2 % OTM 5 % OTM 1 1/1/1.25 Long Term Trading Rule Calculation: Initial Call Moneyness = 2% OTM + (Momentum signal + Macroeconomic signal) = (2+1-1)% OTM = 2% OTM Initial Put Moneyness = 3% OTM + (Momentum signal - Macroeconomic signal) = (3+1+1)% OTM = 5% OTM Number of Calls per Put and QQQ Position = 1.00 + (0.25 * Volatility Signal) = 1 + (0.25 * 0) = 1.00 Calls LONG LONG NDX LONG QQQ/Put/Call Macroeconomic Momentum Call % OTM Put % OTM Volatility Ratio Signal Signal Signal -1 1 2 % OTM 5 % OTM 0 1/1/1The trading rules which result from the signals are provided in Exhibit 1. The frequencydistributions of the target strike prices and call writing ratios are provided in Exhibit 2.Exhibit 1: Trading Rules Call %OT M = Put %OT M = NDX Momentum Macroeconomic Call Initial Put Initial 2 + (Momentum Signal + 3 + (Momentum Signal - Signal signal % OT M % OT M Macroeconomic Signal) Macroeconomic Signal) Sce na rio 1 -1 -1 =2-1-1 = 3 - 1 - (-1) 0% 3% Sce na rio 2 +1 -1 =2+1-1 = 3 + 1 - (-1) 2% 5% Sce na rio 3 -1 +1 =2-1+1 = 3 - 1 - (+1) 2% 1% Sce na rio 4 +1 +1 =2+1+1 = 3 + 1 - (+ 1) 4% 3% VIX Signal QQQ/ Call Ratio Sce na rio 1 -1 1.0/ 0.75 Sce na rio 2 0 1.0/ 1.0 Sce na rio 3 1 1.0/ 1.25 16
  17. 17. Exhibit 2: Trading Rule Frequency Distributions Short-Term Signals Medium-Term Signals Long-Term Signals Ca ll Mone yne ss Put Mone yne ss Ca ll Mone yne ss Put Mone yne ss Ca ll Mone yne ss Put Mone yne ss Initia l % OT M Fre que ncy Fre que ncy Fre que ncy Fre que ncy Fre que ncy Fre que ncy 0 20% 0% 15% 0% 14% 0% 1 0% 26% 0% 22% 0% 30% 2 51% 0% 60% 0% 61% 0% 3 0% 35% 0% 48% 0% 31% 4 29% 0% 25% 0% 25% 0% 5 0% 39% 0% 31% 0% 39% Ca lls:U nde rlying Ca ll R a tio Ca ll R a tio Ca ll R a tio R a tio Fre que ncy Fre que ncy Fre que ncy 0.75:1 18% 20% 19% 1.00:1 46% 40% 45% 1.25:1 36% 40% 36% In a later section of the paper we also apply an active and passive collar to a typical smallcap mutual fund. Since the beta of a fund will not necessarily be 1.0 with respect to the QQQ andthe price level of the fund will not match the QQQ underlying price, we scale the optionpositions by the 65-day rolling 1 day lagged beta as well as by the relative price levels of thefund and the QQQ. To adjust for the relative price levels, each day we rebalance our portfolio sothat the ratio of the number of options to the number of shares of the fund is equal to beta timesthe ratio of the mutual fund price over the QQQ price, as given by the following formula21: # of puts or calls = Betamutual fund, QQQ * Pricemutual fund/PriceQQQ21 For active strategies, we also apply the call ratio adjustment based on the volatility signal. 17
  18. 18. This process allows us to maintain the equivalent of a 1:1:1 ratio collar. While the beta isset at each roll date, the relative balance due to price changes is reset each day22. For example, ifthe rolling beta of the mutual fund is 0.75, the price of the mutual fund is $20 and the price of theQQQ is $60 on the roll in date, we write 0.25 calls and purchase 0.25 puts for each long positionin the mutual fund, and rebalance each day (using the 0.75 beta and the current prices) until theexpiration of the options at which time we rebalance using the new rolling beta level as well asthe current prices. The following example provides an illustration of the process by which wegenerate the passive mutual fund collar: Passive 2% OTM 1-Month Call 6-Month Put Mutual Fund Collar Implementation 65-Day Price of Mutual Rolling Price of Mutual Fund:Put: Beta with QQQ Fund Call Ratio Date Exdate Quantity Wealth QQQ Roll In 3/ 19/ 1999 Purchase mutual fund 1.0000 @ $ 99.36 $ 101.76 (Initial) 0.396 99.355 102.437 1:0.38:0.38 Purchase a 6-month 2% OTM QQQ put expiring on: 9/17/1999 (Strike price = 100) 0.3840 @ $ 9.50 (at ask) Sell a 1-month 2% OTM QQQ call expiring on: 4/16/1999 (Strike price = 104) 0.3840 @ $ (3.25) (at bid) Value 3/ 22/ 1999 Value of of mutual fund 1.0000 @ $ 99.17 $ 101.88 Value of of QQQ puts 9/17/1999 (Strike price = 100) 0.3840 @ $ 9.69 (mid of bid/ask) Value of of QQQ calls 4/16/1999 (Strike price = 104) 0.3840 @ $ (2.63) (mid of bid/ask) Rebalance 3/ 22/ 1999 Adjust quantities to maintain the ratio using current prices and the 3/19/1999 beta of 0.396 Adjust quantity of mutual fund 0.9997 @ $ 99.17 $ 101.88 99.171 101.187 1:0.39:0.39 Adjust quantity of QQQ puts 9/17/1999 (Strike price = 100) 0.3880 @ $ 9.69 (mid of bid/ask) Adjust quantity of QQQ calls 4/16/1999 (Strike price = 104) 0.3880 @ $ (2.63) (mid of bid/ask) Roll Out 4/ 16/ 1999 Mutual fund value 0.9988 @ $ 112.34 $ 115.71 112.339 107.062 1:0.42:0.42 Keep the put (now 5-month 4% OTM) expiring on: 9/17/1999 (Strike price = 100) 0.41543 @ $ 8.44 (mid of bid/ask) Payout value of previous call at expiration: 4/16/1999 (Strike price = 104) 0.41543 @ $ - (intrinsic value) Roll In 4/ 16/ 1999 Since this is a roll date, adjust quantities to the new 4/16/1999 beta of 0.340 Keep the mutual fund 1.015 @ $ 112.34 $ 115.71 0.340 112.339 103.937 1:0.37:0.37 Keep the put (now 5-month 4% OTM) expiring on: 9/17/1999 (Strike price = 100) 0.373 @ $ 8.44 (mid of bid/ask) Sell a 1-month 2% OTM QQQ call expiring on: 5/22/1999 (Strike price = 106) 0.373 @ $ (4.00) (at bid) Repeat until put expires, each day between roll dates rebalance quantities to the beta calculated on the previous roll date Roll Out 9/ 17/ 1999 Mutual fund value 0.966 @ $ 146.04 $ 145.61 0.469 146.041 126.625 Payout value of the put at expiration: 9/17/1999 (Strike price = 100) 0.523 @ $ - (intrinsic value) Payout value of the call at expiration: 9/17/1999 (Strike price = 118) 0.523 @ $ 8.63 (intrinsic value) Roll In 9/ 17/ 1999 Keep the mutual fund 0.972 @ $ 146.04 $ 145.61 Purchase a 6-month 2% OTM QQQ put expiring on: 3/18/2000 (Strike price = 124) 0.526 @ $ 10.25 (at ask) Sell a 1-month 2% OTM QQQ call expiring on: 10/16/1999 (Strike price = 129) 0.526 @ $ (3.38) (at bid)22 Beta is reset only on roll dates to closely match the methodology of the passive collar strategies to themethodology of active collar strategies. 18
  19. 19. Trading Rule Calculation For Mutual Fund Collar Short Term Trading Rule Calculation: Initial Call Moneyness = 2% OTM + (Momentum signal + Macroeconomic signal) = (2+1-1)% OTM = 2% OTM Initial Put Moneyness = 3% OTM + (Momentum signal - Macroeconomic signal) = (3+1+1)% OTM = 5% OTM Number of Calls and Puts per Mutual Fund Position before Volatility Signal Impact = Beta Mutual Fund, QQQ * PriceMutual Fund/PriceQQQ Number of Calls and Puts per Mutual Fund Position before Volatility Signal Impact = 0.396 * 99.36 / 102.44 = 0.38 Volatility Signal Impact: Number of Calls per Put = 1.00 + (0.25 * Volatility Signal) = 1 + (0.25 * 1) = 1.25 Calls/Put Number of Puts per Mutual Fund Position = 0.38 Number of Calls per Mutual Fund Position = 1.25 * 0.38 = 0.48 65-Day SHORT SHORT NDX SHORT Price of Rolling Price of Mutual Fund/Put/Call Macroeconomic Momentum Call % OTM Put % OTM Volatility Mutual Beta with QQQ Ratio Signal Signal Signal Fund QQQ -1 +1 2 % OTM 5 % OTM 1 0.396 99.36 102.44 1/0.38/0.48 Medium Term Trading Rule Calculation: Initial Call Moneyness = 2% OTM + (Momentum signal + Macroeconomic signal) = (2+1-1)% OTM = 2% OTM Initial Put Moneyness = 3% OTM + (Momentum signal - Macroeconomic signal) = (3+1+1)% OTM = 5% OTM Number of Calls and Puts per Mutual Fund Position before Volatility Signal Impact = Beta Mutual Fund, QQQ * PriceMutual Fund/PriceQQQ Number of Calls and Puts per Mutual Fund Position before Volatility Signal Impact = 0.396 * 99.36 / 102.44 = 0.38 Volatility Signal Impact: Number of Calls per Put = 1.00 + (0.25 * Volatility Signal) = 1 + (0.25 * 1) = 1.25 Calls/Put Number of Puts per Mutual Fund Position = 0.38 Number of Calls per Mutual Fund Position = 1.25 * 0.38 = 0.48 65-Day MEDIUM MEDIUM NDX MEDIUM Price of Rolling Price of Mutual Fund/Put/Call Macroeconomic Momentum Call % OTM Put % OTM Volatility Mutual Beta with QQQ Ratio Signal Signal Signal Fund QQQ -1 +1 2 % OTM 5 % OTM 1 0.396 99.36 102.44 1/0.38/0.48 Long Term Trading Rule Calculation: Initial Call Moneyness = 2% OTM + (Momentum signal + Macroeconomic signal) = (2+1-1)% OTM = 2% OTM Initial Put Moneyness = 3% OTM + (Momentum signal - Macroeconomic signal) = (3+1+1)% OTM = 5% OTM Number of Calls and Puts per Mutual Fund Position before Volatility Signal Impact = Beta Mutual Fund, QQQ * PriceMutual Fund/PriceQQQ Number of Calls and Puts per Mutual Fund Position before Volatility Signal Impact = 0.396 * 99.36 / 102.44 = 0.38 Volatility Signal Impact: Number of Calls per Put = 1.00 + (0.25 * Volatility Signal) = 1 + (0.25 * 0) = 1.00 Calls/Put Number of Puts per Mutual Fund Position = 0.38 Number of Calls per Mutual Fund Position = 1.00 * 0.38 = 0.38 65-Day LONG LONG NDX LONG Price of Rolling Price of Mutual Fund/Put/Call Macroeconomic Momentum Call % OTM Put % OTM Volatility Mutual Beta with QQQ Ratio Signal Signal Signal Fund QQQ -1 +1 2 % OTM 5 % OTM 0 0.396 99.36 102.44 1/0.38/0.38Results It is worth noting that while the results in this update are fully consistent with the originalpaper, there are slight discrepancies due to changes in data providers, Optionmetrics datacleaning/updating and minor changes to the methodology23. Before reviewing the results of the23 Some minor changes in methodology were made from the September 2010 analysis. The current methodologypicks the closest strike price to the desired strike price whether it is further ITM or OTM. In addition, minor changesin the return streams may have resulted from subsequent data cleaning/updating by OptionMetrics and a change 19
  20. 20. passive and active approach to collar protection, it is perhaps important to briefly discuss threeissues in option based risk management:1) The use of alternative approaches to protecting equity investments,2) the impact of option based strategies on traditional forms of risk comparisons (e.g. SharpeRatio), and3) the necessity for analyzing results over alternative time periods.Alternative Approaches to Option Based Risk Management: There are alternative option basedapproaches to protecting equity based investments. The most obvious choice is typically the useof protective puts. Unfortunately, the use of protective puts tends to be a relatively expensivemethod of capital protection, especially in periods of high volatility. The existence of a negativevolatility risk premium and the resulting excess returns associated with put writing are indicativeof the potential cost of purchasing protective puts24. Another option based approach is the buy-write or covered call strategy. The covered call strategy typically entails the writing of calloptions against a long underlying index position at a one-to-one ratio. A number of studies havesuggested that covered call writing can provide return enhancement as well as a cushion tomitigate losses from market downturns. These include Schneeweis and Spurgin [2001], Whaley[2002] and Hill et al. [2006] which apply the strategy to the S&P 500 and Kapadia and Szadofrom Datastream to Bloomberg for some supplemental data.from those options with full data over the life of theoption. The previous study chose the closest strike nearer the ATM whereas the current methodology picks theclosest strike24 The richness of put prices is not without controversy. While a great deal of literature supports optionrichness (particularly for put options), extensive literature debates its existence (for example, see Ungarand Moran [2009] and Bakshi and Kapadia [2003]). 20
  21. 21. [2007] which applies the buy-write to a broader index, the Russell 2000. Unfortunately, coveredcall writing still leaves an investor exposed to large down moves.Impact of Option Use on Traditional Risk Measures: It should also be noted that we haveincluded Sharpe ratios with our other performance measures for the sake of consistency withprevious literature, but great care should be taken in interpreting the Sharpe ratios. First, anumber of the calculated Sharpe ratios are negative. Negative Sharpe ratios are uninformative.Second, even with positive excess returns, traditional risk-adjusted performance measures suchas the Sharpe ratio and Jensen’s alpha can be misleading. This is particularly true for portfolioswhich include option strategies or other strategies which may result in skewed or kurtotic returndistributions. The Sharpe ratio and Jensen’s alpha assume normally distributed returns25. Inrecognition of the fact that the return distributions generated by our collar strategies may be non-normal, we utilize the Stutzer index and Leland’s alpha as measures of risk adjustedperformance. These measures adjust for the fact that investors which exhibit non-increasingabsolute risk aversion prefer positive skewness26. Therefore positively skewed returndistributions should exhibit lower expected returns than negatively skewed distributions, ceterisparibus.Alternative Time Period Analysis: This paper does not assume any particular model of investorrisk aversion. The significance of the results for any particular investor may therefore bedependent on that investor’s individual risk tolerance. Results should therefore be presented over25 It is also quite possible to manipulate the Sharpe ratio. For example, see Spurgin [2001].26 See Arditti [1967]. 21
  22. 22. various market conditions which provide investors a wider range of results consistent with aparticular risk environment. In order to assess the performance and risk managementcharacteristics of the passive and active collar strategies in different market environments, webreak up our time period into 3 sub-periods. In addition, the performance of the active strategiesis assessed in the out-of-sample period from June 2009 to September 2010. The first sub-period is April 1999 to September 2002. We would expect that this wouldbe a relatively favorable period for the collar strategy, when compared to holding a long indexposition. In this period the QQQ exhibited extremely high realized volatility and experienced astrong run-up followed by a rapid loss of more than ¾ of its value from peak to trough. Whileone would expect that protective strategies would be very beneficial with a drop of thismagnitude, there are two factors that mitigate the benefits of the protective puts. First, putoptions would likely be very expensive in this environment. Secondly, the short call positionwould greatly limit the upside participation of the collar in the incredibly strong run-up of theearly part of the sub-period. This is a particularly interesting sub-period to study, because itcaptures the run-up and collapse of a bubble in the underlying. The second sub-period, which covers October 2002 to September 2007, is less favorablefor the collar strategy. In fact, one might argue that this time period is representative of nearlythe worst environment for the collar (when compared to a long underlying position). In thisperiod, the QQQ exhibits a steady growth rate with relatively low volatility27 and few sharpdownward moves. In this environment, the collar may lose significant revenue on the upside dueto the short calls while it gains very little from the protective puts.27 The 17.5% volatility in this sub-period is quite high, but much smaller than the 30% volatility of theoverall period or the 42% of the early sub-period. 22
  23. 23. The final sub-period covers October 2007 to September 2010. This is another favorableperiod for the collar and covers a major financial crisis which negatively impacted most assetclasses. While this favorable period includes a strong recovery following the collapse due to thefinancial crisis, the recovery is not nearly as strong as the extremely strong run-up of the firstsub-period. Thus we have two relatively favorable sub-periods to consider (one that covers thetech bubble and one that covers the credit crisis) as well as one clearly unfavorable sub-period. Itis worth noting that the first favorable period represents a strong run-up followed by a collapsewhile the last favorable period represents the inverse – a crash followed by a recovery. Before discussing the performance of the collar strategies, it is worth noting that the 1-month/6-month and 1-month/3-month strategies require rebalancing each month in order toreinvest the funds that are collected from the sale of the calls and the funds that are disbursed tocover the cost of calls that expire ITM between put expirations. No adjustment is made for thetransactions costs that would be incurred by these rebalancing activities.Exhibit 3: Growth of $100 in QQQ March 1999 to September 2010 QQQ TR Growth of $100 $250.00 Pe Period 1 : Favorable, Period 3 : Favorable, Tech Bubble Period 2 : Unfavorable Credit Crisis $200.00 Out of Sample Period $150.00 $100.00 $50.00 $- Mar-99 Mar-00 Mar-01 Mar-02 Mar-03 Mar-04 Mar-05 Mar-06 Mar-07 Mar-08 Mar-09 Mar-10 Sep-03 Sep-99 Sep-00 Sep-01 Sep-02 Sep-04 Sep-05 Sep-06 Sep-07 Sep-08 Sep-09 Sep-10 23
  24. 24. Empirical ResultsPassive Collars: We first consider the performance of passive collar strategies. Our discussion iscentered on 1-month call/6-month put collar strategies28. Results comparing the 1-month call/6-month put collars to the 1-month call/1-month put collars are provided in Appendix B.While the exhibits provide statistics for a wide range of collar implementations, our discussion isfocused on the 2% OTM strategies, since they represent a middle ground between the ATM andthe far OTM strategies. Exhibits 4a, 4b, 4c and 4d provide summary statistics for passive 1-month call/6-month put collar strategies utilizing 2% OTM puts with ATM to 5% OTM calls forthe full period as well as the three sub-periods. Similarly, Exhibits 5a, 5b, 5c and 5d providesummary statistics for 2% OTM call collars which use ATM to 5% OTM puts. It is immediatelyapparent when reviewing the exhibits that, while the performance characteristics of the strategyare sensitive to the choice of moneyness for the options, they are far more sensitive to the marketenvironment (rising and/or falling) in which the strategy is implemented. In contrast, the choiceof time to maturity for the calls of 1-month versus 6-month can have a far more significantimpact, as evidenced by the results provided in Appendix B. The summary statistics for the overall period are provided in Exhibits 4a and 5a. Over the138 months of the study, the 2% OTM collar significantly reduces risk and improves realizedreturns. The returns are improved from a -0.3% annualized loss to a 9.6% gain, meanwhilestandard deviation is reduced by about 2/3 from 29.6% to 10.7%. Similarly, the Stutzer indexincreased from 0.05 to 0.67, and the information ratio (relative to the QQQ) for the collar is28 Previous research indicates that these strategies have typically outperformed 1-month call/1-month putstrategies in the recent past. See, for example Szado and Kazemi [2008]. 24
  25. 25. positive at 0.36. Perhaps the most visible impact of implementing the collar strategy is areduction of the maximum drawdown from -81.1% to -17.6% for the 138 month overall period.Exhibit 4a Passive Collars with 2% OTM Puts – April 1999 to September 2010 QQQQ TR QQQQ TR PASSIVE QQQQ TR PASSIVE QQQQ TR PASSIVE QQQQ TR PASSIVE QQQQ TR PASSIVE QQQQ TR PASSIVE COLLARMonthly Data: Apr 1999- COLLAR - 1% OTM, 1 COLLAR - 2% OTM, 1 COLLAR - 3% OTM, 1 COLLAR - 4% OTM, 1 COLLAR - 5% OTM, 1 FUND ONLY - - 0% OTM, 1 Mo Sept 2010 Mo Call.2% OTM. 6 Mo Mo Call.2% OTM. 6 Mo Mo Call.2% OTM. 6 Mo Mo Call.2% OTM. 6 Mo Mo Call.2% OTM. 6 Mo No Options Call.2% OTM. 6 Mo Put. Put. Put. Put. Put. Put. Annualized Return -0.29% 10.13% 9.36% 9.56% 9.76% 10.02% 8.76% Annualized Std Dev 29.55% 9.85% 10.13% 10.66% 11.18% 11.70% 12.14% Sharpe Ratio -0.10 0.76 0.66 0.64 0.63 0.63 0.50 Annual Stutzer Index 0.05 0.77 0.68 0.67 0.66 0.65 0.54 CAPM Beta 1.00 0.07 0.11 0.14 0.18 0.22 0.24 Leland Beta 1.00 0.06 0.10 0.13 0.17 0.21 0.24 Monthly Leland Alpha 0.00% 0.62% 0.56% 0.57% 0.59% 0.61% 0.51% Information Ratio 0.00 0.36 0.34 0.36 0.38 0.41 0.37 Skew -0.25 0.18 0.19 0.15 0.13 0.08 0.01 Kurtosis 0.60 2.77 3.27 3.48 3.54 2.79 2.82 Maximum Drawdown -81.08% -14.06% -16.65% -17.58% -19.17% -19.98% -21.21% Correlation with QQQ 1.00 0.20 0.31 0.38 0.47 0.54 0.59 Min Monthly Return -26.21% -8.63% -8.99% -9.75% -9.89% -10.54% -10.59% Max Monthly Return 23.48% 12.81% 14.09% 15.06% 15.48% 15.37% 15.64% Number of Months 138 138 138 138 138 138 138 % Up Months 54% 65% 64% 64% 67% 64% 61% % Down Months 46% 35% 36% 36% 33% 36% 39% The effectiveness of the collar strategy in the April 1999 to September 2002 sub-period isevident in the results provided in Exhibit 4b and 5b. In the early bubble run-up and collapse, theQQQ experienced an annualized return of -23.3% with a 42.4% volatility. In this volatile market,the 2% OTM passive collar strategy generated an annualized return of 21.6% at a volatility ofonly 13.6%. Thus the collar was able to turn a sizeable loss into a significant gain, while cuttingrisk (as measured by standard deviation) by more than 2/3. Other measures confirm the riskreduction including the minimum monthly return, the percentage of up months, and the Lelandbeta. The capital protection ability of the collar strategy can be illustrated by the maximumdrawdown. The maximum drawdown of the QQQ is reduced significantly from -81.1% to -7.5%over the most severe market move that the QQQ has ever experienced. 25
  26. 26. Exhibit 4b Passive Collars with 2% OTM Puts – April 1999 to September 2002 QQQQ TR QQQQ TR PASSIVE QQQQ TR PASSIVE QQQQ TR PASSIVE QQQQ TR PASSIVE QQQQ TR PASSIVE QQQQ TR PASSIVE COLLARMonthly Data: Apr 1999- COLLAR - 1% OTM, 1 COLLAR - 2% OTM, 1 COLLAR - 3% OTM, 1 COLLAR - 4% OTM, 1 COLLAR - 5% OTM, 1 FUND ONLY - - 0% OTM, 1 Mo Sept 2002 Mo Call.2% OTM. 6 Mo Mo Call.2% OTM. 6 Mo Mo Call.2% OTM. 6 Mo Mo Call.2% OTM. 6 Mo Mo Call.2% OTM. 6 Mo No Options Call.2% OTM. 6 Mo Put. Put. Put. Put. Put. Put. Annualized Return -23.31% 24.22% 22.09% 21.59% 19.86% 18.30% 16.29% Annualized Std Dev 42.44% 13.27% 13.21% 13.63% 14.28% 14.44% 14.85% Sharpe Ratio -0.65 1.52 1.36 1.28 1.10 0.98 0.82 Annual Stutzer Index -0.51 1.42 1.31 1.25 1.09 0.99 0.84 CAPM Beta 1.00 0.03 0.06 0.08 0.11 0.14 0.16 Leland Beta 1.00 0.03 0.06 0.08 0.11 0.14 0.16 Monthly Leland Alpha 0.00% 1.62% 1.52% 1.53% 1.47% 1.40% 1.31% Information Ratio 0.00 1.10 1.09 1.09 1.08 1.07 1.05 Skew 0.14 0.03 0.26 0.39 0.44 0.43 0.41 Kurtosis -0.70 1.15 2.08 2.56 2.86 2.60 2.89 Maximum Drawdown -81.08% -7.54% -7.54% -7.54% -9.16% -9.16% -10.39% Correlation with QQQ 1.00 0.11 0.21 0.26 0.34 0.41 0.47 Min Monthly Return -26.21% -7.54% -7.54% -7.54% -9.16% -9.16% -10.39% Max Monthly Return 23.48% 12.81% 14.09% 15.06% 15.48% 15.37% 15.64% Number of Months 42 42 42 42 42 42 42 % Up Months 40% 79% 74% 74% 74% 67% 64% % Down Months 60% 21% 26% 26% 26% 33% 36%Exhibit 4c Passive Collars with 2% OTM Puts – October 2002 to September 2007 QQQQ TR QQQQ TR PASSIVE QQQQ TR PASSIVE QQQQ TR PASSIVE QQQQ TR PASSIVE QQQQ TR PASSIVE QQQQ TR PASSIVE COLLARMonthly Data: Oct 2002 to COLLAR - 1% OTM, 1 COLLAR - 2% OTM, 1 COLLAR - 3% OTM, 1 COLLAR - 4% OTM, 1 COLLAR - 5% OTM, 1 FUND ONLY - - 0% OTM, 1 Mo Sept 2007 Mo Call.2% OTM. 6 Mo Mo Call.2% OTM. 6 Mo Mo Call.2% OTM. 6 Mo Mo Call.2% OTM. 6 Mo Mo Call.2% OTM. 6 Mo No Options Call.2% OTM. 6 Mo Put. Put. Put. Put. Put. Put. Annualized Return 20.37% 5.43% 4.58% 5.19% 6.89% 7.42% 6.14% Annualized Std Dev 17.54% 6.42% 7.09% 7.93% 8.55% 9.15% 9.75% Sharpe Ratio 1.00 0.40 0.24 0.30 0.47 0.50 0.34 Annual Stutzer Index 1.01 0.42 0.27 0.32 0.49 0.52 0.37 CAPM Beta 1.00 0.19 0.26 0.30 0.38 0.43 0.48 Leland Beta 1.00 0.19 0.28 0.33 0.40 0.44 0.50 Monthly Leland Alpha 0.00% -0.05% -0.24% -0.26% -0.23% -0.24% -0.42% Information Ratio 0.00 -0.98 -1.11 -1.12 -1.10 -1.15 -1.36 Skew 0.34 -0.12 -0.21 -0.23 -0.25 -0.02 -0.20 Kurtosis 1.63 0.18 0.03 0.04 -0.05 -0.06 0.37 Maximum Drawdown -12.36% -11.44% -11.81% -14.02% -12.10% -14.32% -16.44% Correlation with QQQ 1.00 0.51 0.63 0.67 0.77 0.82 0.86 Min Monthly Return -12.09% -4.67% -4.67% -5.49% -5.49% -5.50% -6.90% Max Monthly Return 18.48% 4.47% 4.87% 5.60% 5.90% 6.87% 6.87% Number of Months 60 60 60 60 60 60 60 % Up Months 62% 58% 57% 57% 62% 60% 58% % Down Months 38% 42% 43% 43% 38% 40% 42%Exhibit 4d Passive Collars with 2% OTM Puts – October 2007 to September 2010 QQQQ TR QQQQ TR PASSIVE QQQQ TR PASSIVE QQQQ TR PASSIVE QQQQ TR PASSIVE QQQQ TR PASSIVE QQQQ TR PASSIVE COLLARMonthly Data: Oct 2007 to COLLAR - 1% OTM, 1 COLLAR - 2% OTM, 1 COLLAR - 3% OTM, 1 COLLAR - 4% OTM, 1 COLLAR - 5% OTM, 1 FUND ONLY - - 0% OTM, 1 Mo Sept 2010 Mo Call.2% OTM. 6 Mo Mo Call.2% OTM. 6 Mo Mo Call.2% OTM. 6 Mo Mo Call.2% OTM. 6 Mo Mo Call.2% OTM. 6 Mo No Options Call.2% OTM. 6 Mo Put. Put. Put. Put. Put. Put. Annualized Return -1.03% 2.94% 3.63% 3.84% 3.51% 5.22% 4.76% Annualized Std Dev 26.56% 9.02% 9.70% 10.21% 10.70% 11.93% 12.27% Sharpe Ratio -0.07 0.23 0.29 0.30 0.25 0.37 0.32 Annual Stutzer Index 0.06 0.27 0.33 0.34 0.30 0.41 0.37 CAPM Beta 1.00 0.14 0.19 0.25 0.28 0.34 0.37 Leland Beta 1.00 0.15 0.20 0.25 0.28 0.35 0.37 Monthly Leland Alpha 0.00% 0.19% 0.24% 0.25% 0.23% 0.37% 0.33% Information Ratio 0.00 0.16 0.20 0.23 0.22 0.32 0.31 Skew -0.38 -1.26 -1.25 -1.40 -1.30 -1.05 -1.07 Kurtosis -0.62 2.56 2.40 2.85 2.66 2.10 1.89 Maximum Drawdown -49.74% -14.06% -16.65% -17.58% -19.17% -19.98% -21.21% Correlation with QQQ 1.00 0.41 0.52 0.63 0.68 0.75 0.79 Min Monthly Return -15.58% -8.63% -8.99% -9.75% -9.89% -10.54% -10.59% Max Monthly Return 13.17% 4.44% 4.90% 4.90% 5.73% 6.48% 6.48% Number of Months 36 36 36 36 36 36 36 % Up Months 58% 61% 67% 67% 69% 67% 61% % Down Months 42% 39% 33% 33% 31% 33% 39% 26
  27. 27. To consider these results in a different light, the collar could have earned an investor21.6% per year over the period with a maximum loss of capital of 7.5% regardless of how poorlythe investor timed their entry into the strategy. Clearly in this case, the collar was an effectiveway of capturing a significant return from the bubble run-up without experiencing the magnitudeof losses that came with the collapse. We expected the collar to perform poorly in the next sub-period due to the low volatilityand steady positive returns with very few sharp down moves. The results confirm thisexpectation. Exhibits 4c and 5c provide the evidence. In this steadily climbing, near ideal marketfor the QQQ and poor market for the collar, the collar exhibits a far lower return. The annualizedreturn of the QQQ over the period is 20.4% at relatively moderate volatility of 17.5%. The 2%OTM collar only provides a 5.2% return over this period. It does, however, do so at a far lowervolatility. In this period, the collar provides about ¼ of the returns of the QQQ at less than ½ thevolatility. By most measures, the collar underperforms the QQQ on a risk-adjusted basis in thisperiod. It has a slightly higher maximum drawdown, fewer up-months, a lower Stutzer index, anegative information ratio and a -0.26% monthly Leland alpha. It is interesting to note that thisunderperformance is not nearly as significant as the QQQ’s underperformance in the earlyperiod. The results pertaining to the final sub-period are provided in Exhibits 4d and 5d. This isthe credit crisis period from October 2007 to September 2010. Once again, the collar providessignificant capital protection. The -1.0% annualized loss of the QQQ is improved to a gain of3.8%, while the standard deviation is cut from 26.6% to 10.2%. Therefore, the collar converts aloss to a gain with a return improvement of almost 5% annually while cutting volatility by almost2/3. Other results confirm the collar’s outperformance in this period. The monthly Leland alpha 27

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