Volatility: Capitalizing on Fear and Greed

Capital Trading Group One Financial Place 440 S LaSalle Street, Suite 2301 Chicago, IL 60605 Ph: 800.238.2610 Volatility: Capitalizing on Fear and Greed An Overview of Option Premium Capture Strategies Introduction Volatility is one important component of trading that is often overlooked by many participants. While significantly pervasive in all aspects of market dynamics, volatility is often feared rather than comprehended; however, a true understanding of the perceived and realized instability of financial markets can be translated into a trading advantage. A school of thought considers volatility as a pure asset class given its mixture of defining traits i. A classic definition refers to an asset class as a group of like instruments with similar expected risk profiles and return drivers. An asset class should also produce passive long term returns (beta) and such expected returns should not be insignificant in order to justify an allocation in a diversified portfolio. An additional beneficial element should be uncorrelated performance. An array of diverse studies has illustrated that a number of volatility based options strategies produce consistent and significant outperformance indicating the existence of a volatility premium or an options mispricing. The purpose of this paper is to provide an overview of the most relevant studies on the subject, an analysis of the most interesting volatility based strategies and to draw conclusions that may help investors achieve more efficient asset allocations. Volatility Premium The process of understanding option volatility based strategies and whether they truly belong to a modern, diversified portfolio aspiring to improve its efficient frontier revolves around one question: are options in general mispriced? Answering that question requires analytical work on the results of most dedicated strategies but it also requires an analysis of what these options should really price. In other words, are options considered mispriced because the market miscalculates certain risk premia or the models fail to incorporate other potential risks? Before the 2008 financial crisis, there was considerable evidence of outsized returns and significantly high Sharpe Ratios for many volatility selling strategies. Bondarenko (2003) ii, for instance, reports exceptionally large negative returns in long index puts strategies. Negative returns are quoted to be as high as 40% per month for at-the-money (ATM) index puts and negative 95% per month in deep-in-themoney (ITM) index puts. Such return profiles suggest an intrinsic advantage in selling index volatility and either a misprice in options or the presence of a risk premium undetected by traditional models. Broadie-Chernov-Johannes (2008) iii, refute the mispricing explanation by arguing that because options returns are highly non-normal, traditional valuation metrics such as CAPM alphas or Sharpe Ratios are inappropriate tools. They argue that average put returns should be highly negative because of the

leverage imbedded in options and the presence of priced risk. The authors also argue that options returns might be sensitive to volatility as low volatility contributes to reduce expected returns for puts; additionally they also argue that options may be influenced by estimation risk due to options non-linear pay-off and sample uncertainty. Because the risk premium seems to be mostly on the put side - in fact short call index strategies seems to produce negative returns - the presence of priced risk explanation looks appropriate. The 2008 events might have showed how most volatility based strategies must produce very high returns to compensate for the timing of their losses under stress conditions. In other words, while Sharpe Ratios can be very high for long periods of time, the risk premium of the strategy must incorporate the unexpected correlation during major dislocations. This analysis would confirm the intuitive explanation that a crash premium must be offered so that speculators, acting as insurance companies, will be willing to provide such insurance. If this reasoning is accepted and quantified, it opens the door to a viable strategy for the traders that are properly capitalized and better equipped to quantify real risk. It also must be noted that there is consistent difference between index put returns and single stocks put returns. Index put selling seems to be generally much more profitable than single stock put selling; interestingly, out-of-the-money (OTM) short calls strategies with single stocks are again generally profitable. This empirical discovery would indicate not just a simple volatility premium embedded in put options but a) a correlation premium, b) supply/demand imbalances and c) irrational expectations of future market crashes. While the 2008 events seem to have validated the correlation premium, the point on supply and demand was already clearly illustrated by Bollen and Whaley (2004) iv. In their research paper, the authors indicate significant buying pressure on the put side when analyzing S&P 500 index options and when looking at tick data they also record this activity to be largely driven by put buyers especially in OTM strikes. On the other hand, the general profitability of shorting single stock OTM calls reflects an implied volatility premium caused by the speculative nature of investors engaged in these strategies. In this case, investors seem to prefer the lottery ticket profile (positive skeweness) of the trade characterized by a low investment, a predefined maximum loss and a large potential pay-off. Inevitably, investors will overpay and overestimate the probability of a favorable jump in the underlying. Options prices deviations from theoretical expectations can also find explanations in practical limitations to arbitrage. Most theories on market efficiency base their findings on the idea that consistent deviations from rational expectations will be quickly arbitraged away; however, especially in options, market makers and arbitrageurs may find clear limitations to their ability to arb away all the risk. Liquidity issues and jump risk are two elements that make perfect arbitrage rather difficult in this case. Branger-Hansis-Schlag (2010) v provides interesting and supporting analysis to the idea that the structure of risk premia significantly influences options returns. They argue that estimating the proper risk

structure is crucial. Proper modeling should correctly estimate jump intensity risk, jump size risk or jump variance, but admittedly, jumps are rare events which are difficult to estimate. This line of reasoning seems to be in accordance with Broadie-Chernov-Johannes (2008). It is interesting to note that while pure volatility selling strategies remain a niche approach to the markets, most investors are actually engaged in similar strategies such as classic Credit and FX carry strategies, insurance businesses, and certain hedge funds tactics vi. Whether an investor decides to engage in any of these strategies or not, there is still much to be learned from being aware about the dynamics of volatility and its impact on market functionality. Options can unlock much information about market participants positioning and implied volatilities are a direct quantification of market expectations. Outside of the realm of equities and specifically equity indexes, volatility selling strategies have a mixed record. Ilmanen (2011) quotes a 2008 study by Trolle and Schwartz on variance risk premium for energy commodities; the study runs from 1996 to 2006 and shows that averaged implied volatility for oil and gas exceeded average realized volatility by respectively 4% and 3% vii. In other commodities, covered call writing strategies should perform well during upward trends as a result of a mix of beta exposure and volatility premium. Along this line, a non-public proprietary study by Accomazzo and Frankfurter (2009) illustrated positive risk adjusted returns for a simple covered call writing strategy on gold futures. Volatility Based Strategies Ultimately, any successful option strategy designed to capture a volatility beta will rely on the ability to arbitrage a consistent mismatch between the implied volatility embedded in the option prices and the actual volatility realized ex-post by the underlying instrument. Winig-Tongberg-Jones (2011) viii indicate that such premium has been consistent since 1990 in index options; their study reports implied volatility being higher than realized in 86.9% of monthly observations with a mean difference of 4.5%. Covered Call Writing Programs (i.e. BXM, BXY, single stocks): this is most likely the most common option strategy which consists of being long an underlying stock, index or commodity and shorting a call against it. The strategy is a trade-off between upside potential in exchange for certain income (derived from the selling of the call); the success of the strategy is a confluence of directional risk and implied volatility. Ilmanen (2011) reports that between 1994 and 2005 the Implied Volatility-Realized Volatility gap in covered call writing in ATM S&P 500 options was on average 2% ix. The size of potential gains in covered call writing in OTM options would seem to be more dependent on beta exposure and less on volatility arbitrage; in bullish markets OTM calls are therefore preferable. The Chicago Board of Exchange has capitalized over the years on these statistics by offering different covered call indexes and franchising strategies around such benchmarks. BXM and BXY are two examples; BXM is a passive total return index based on being long the S&P 500 index and writing the near term covered all option. This call is held until expiration and cash settled at which point a new onemonth near the money call is sold again. BXY is a similar strategy based on call options 2% out of the

money. For the BXY, the CBOE website x quotes a 9.3% annualized return for the period from January, 31, 1993 to January 31, 2013. These types of volatility selling strategies look particularly interesting from a historical Sharpe Ratio standpoint as they minimize right tail variance and make return distribution more negatively skewed (frequent small gains and few large losses). xi Short Straddles: this strategy is naturally directional agnostic and is strictly a bet on realized volatility resulting to be generally less than implied volatility. A straddle consists of selling simultaneously a put and a call on the same underlying with the same expiration. A trader can implement different degrees of volatility sensitivity by choosing to sell the straddle at the money or at some percentage out of the money (often referred to as a strangle ). One of the most recent studies which includes important data points from 2008 has been produced by Cambridge Associates xii. CA quotes a fully collateralized portfolio of short strangles against a mix of different indexes which achieved slightly higher annualized rates of return than the S&P 500 at a lower volatility level in the period from December 31, 1989 to December 31, 2010. The performance is attractive on a risk adjusted basis but highly correlated to the equity market. Coval-Shumway (2000) xiii show that zero-beta, at-the-money long S&P 500 and S&P 100 straddles produce average losses of approximately 3% per week (meaning 3% positive returns for selling the same straddle) with a 19% volatility and an attractive Sharpe Ratio of 1.2. They also indicate similar losses in zero-beta long straddles in other markets (gains in zero-beta short straddles). Such findings would suggest possible systematic stochastic volatility being priced in options returns (tendency of markets to produce random crashes). Grant-Gregory-Lui (2007) also reports positive performance for different S&P 500 strangles (ATM, 1% OTM and 5% OTM) in the period from January 31, 1996 to September 30, 2007. The risk statistics quoted are not as attractive as in the Coval-Shumway study, however, with Sharpe Ratios varying from 0.67 to 0.72. Short Puts: this strategy is probably the most simple index volatility arbitrage available and it is designed to capture any mispricing of systematic stochastic volatility. This approach can be fully collateralized like the CBOE PUT Index strategy which tracks the performance of selling a sequence of one-month ATM S&P 500 puts and invest the collateral cash at 1 and 3 month T-Bill rates. The CBOE website quotes annualized returns for the PUT index of 9.5% in a twenty year period (1993-2013) versus a 8.4% annualized return for the S&P 500 Index with a Standard Deviation of 10.7% versus the Index Standard Deviation of 15.1%. xiv Variance Swaps: these kinds of swaps are less retail oriented products than traditional puts and calls and don t have a long history. Conceptually, however, they are the perfect tool for arbitraging the implied/realized volatility discrepancy since they carry absolutely no directional bias. However, Ilmanen (2011) notes that while these instruments should be completely delta neutral, they actually show a mild positive market beta due to the classic inverse correlation between market prices and volatility xv. This became quite evident in 2008 when implied volatilities increased during the crash but realized volatilities increased even more significantly.

Grant-Gregory-Lui (2007) report short variance strategies as the highest risk adjusted performers among all the volatility selling strategies xvi VIX futures: a new way of trading volatility has increased in popularity as derivatives on the VIX Index have gained acceptance and liquidity over the last few years. VIX futures are generally used more for directional volatility bets than arbitrage. Gregory-Grant-Stevens (2006) show that in the decade from 1996 to 2006, being short VIX futures would have been on average profitable. They also report an advantage in timing the entry such as following volatility spikes (volatility being mean reverting) or when VIX futures were trading at a substantial premium over spot VIX. xvii Tactical Refinements If one tends to agree with most recent studies and the concept that profitability from selling index volatility comes from a correlation premium and difficulty in estimating jump risk, it becomes manifest that a tactical overlay could help mitigate the correlation risk and make volatility selling a much more mainstream strategy. A value based approach to volatility analysis could be implemented by setting trading rules that prevent selling implied volatility when current ratios are too low by historical standards or by other forecasting tools. Ilmanen (2011) mentions utilizing GARCH forecasting models as a way to predict future volatilities xviii. Following this value based approach, an investor could implement a diversified strategy where forecasted expensive volatilities are sold while forecasted undervalued vols are purchased (at different times or simultaneously in different markets). Tactical refinements could also be implemented with the use of technical analysis. Yang (2011) reports simulations performed using actively managed positions in the S&P 500 index, cash, and covered call or short puts strategies timed by simple crosses such as the 50 day moving average being over/under the 200 day moving average xix. This analysis shows an absolute and risk adjusted outperformance of the actively managed option portfolio over the passive CBOE S&P 500 Monthly Buy-Write (BXM) or the Put- Write (PUT) strategies. Yang also claims an outperformance over the underlying equity index by over 5% in annualized returns with similar risks over a twenty year period (06/01/1988 to 12/31/2010). The idea of using trend following rules to enhance returns (or at least to reduce crash risk) in a volatility selling strategy seems to be intuitive due to the above mentioned correlation risk possibly inherent in this strategy. Another way to mitigate correlation risk would be to utilize spreads and vary delta exposure using market timing tools as described above. This technique would not eliminate correlation risk but it would mitigate its impact on the P&L of the strategy and still allow for a net arbitrage of the Implied/Realized Volatility discrepancy. Portfolio Allocation Decision Recurrent uncertainty in global financial markets has forced sophisticated investors in the past few years toward more complex portfolio diversification strategies in an attempt to mitigate their exposure to risk

produced by traditional asset classes. The material reviewed in this working paper reveals that volatility selling strategies could provide help in this process of diversification. The decision of how much volatility arbitrage exposure an investor should have is naturally the result of many specific variables that are beyond the scope of this study. However, it would seem that as repartitions to alternative strategies become more and more popular, at least small allocations should be beneficial. Driessen-Maenhout (2007) report in their analysis on option pricing anomalies that most investors should have some exposure to these strategies xx. A PIMCO study by Rennison-Pedersen (2012) also highlights the benefits of including a diversified volatility risk premium strategy into a traditional portfolio xxi. Rennison-Pedersen quote statistics on a straddle approach performed on 14 different markets and actively managed (i.e. delta hedged daily) for the period from June 1994 to June 2012. They found volatility strategies to perform relatively well when compared to classic risk premium strategies across different historical periods. They split the testing period in four tranches, pre-crisis (June 1994 June 2007), crisis (July 2007 March 2009), sharp recovery (April 209 March 2010) and sovereign crisis period (April 2010 June 2012); volatility strategies showed good relative performance in all periods and especially in the last two tranches manifesting a tendency to rebound very quickly after drawdowns. Rennison-Pederson also produces a monthly correlation matrix of all volatility strategies with each other and with other risk premia. They conclude that while correlations are generally positive they tend to be fairly low. Conclusions All the studies reviewed in this white paper indicate the existence of a risk premium to be captured via volatility selling strategies. It must be noted that such risk premium is the result of different dynamics and not just pure mispricing. Different option strategies seem to incorporate a mixture of correlation risk, supply-demand imbalances and jump risk estimation; however, they show a recurrent source of risk premium often only mildly correlated to sources of risk in traditional asset classes such as equity or credit. The key to a successful incorporation of these strategies into a traditional portfolio reside in the ability to mitigate correlation risk, in proper diversification and proper weightings. Allocations should be decided based not on passive acceptance of historical statistics but grounded on a dynamic ex-ante framework. Sources Accomazzo, Davide, Frankfurter, Mack, proprietary back-testing for Cervino Capital Management, CTA, 2009 Bollen, Nicholas, Whaley, Robert, 2004, Does Net Buying Pressure Affect the Shape of Implied Volatility Functions, The Journal of Finance, vol. LIX, no 2 Bondarenko, Oleg, 2003, Why Are Put Options So Expensive, Working Paper, University of Illinois, Chicago Branger, Nicole, Hansis, Alexandra, Schlag, Christian, 2010, Expected Options Returns and the Structure of Jump Risk Premia, Working Paper, Annual Meeting of the American Finance Association

Broadie, Mark, Chernov, Mikhail, Johannes, Michael, 2008, Understanding Index Options Returns, Working Paper, Adam Smith Asset Pricing Conference Cambridge Associates, 2011, Highlights From The Benefits of Selling Volatility, Working Paper Coval, Joshua, Shumway, Tyler, 2000, Expected Options Returns, Working Paper, http://ssrn.com/abstract=189840 Driessen, Joost, Maenhout, Pascal, 2007, An Empirical Portfolio Perspective on Option Pricing Anomalies, Review of Finance, 11 (4 Grant, Maria, Gregory, Krag, Stevens, David, 2006, VIX Futures Over the Last Decade, Goldman Sachs, New York Grant, Maria, Gregory, Krag, Lui, Jason 2007, Volatility as an Asset Class, Goldman Sachs, New York Ilmanen, Annti, 2011, Expected Returns, Chichester, UK: John Wiley and Sons LTD Yang, George, 2011, Buy-Write or Put-Write, An Active Portfolio to Strike it Right, Working Paper, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1827363m Rennison, Graham, Pedersen, Niles, (2012), The Volatility Risk Premium, Working Paper for PIMCO Winig, Eric, Tongberg, Kristen, Jones, Alex, 2011, Highlights From the Benefits of Selling Volatility, Clients Report Cambridge Associates LLC i Grant, Maria, Gregory, Krag, Lui, Jason, 2007, Volatility as an Asset Class, Goldman Sachs, New York, page 3 ii Bondarenko, Oleg, 2003, Why Are Put Options So Expensive?, Working Paper, University of Illinois, Chicago iii Broadie, Mark, Chernov, Mikhail, Johannes, Michael, 2008, Understanding Index Options Returns, Working Paper, Adam Smith Asset Pricing Conference iv Bollen, Nicholas, Whaley, Robert, 2004, Does Net Buying Pressure Affect the Shape of Implied Volatility Functions, The Journal of Finance, vol. LIX, no 2 v Branger, Nicole, Hansis, Alexandra, Schlag, Christian, 2010, Expected Options Returns and the Structure of Jump Risk Premia, Working Paper, Annual Meeting of the American Finance Association, pages 22-23 vi Ilmanen, Annti, 2011, Expected Returns, Chichester, UK: John Wiley and Sons LTD, page 308 vii Ilmanen, Annti, 2011, Expected Returns, Chichester, UK: John Wiley and Sons LTD, page 319 viii Winig, Eric, Tongberg, Kristen, Jones, Alex, 2011, Highlights From The Benefits of Selling Volatility, Clients Report Cambridge Associates LLC, page 1 ix Ilmanen, Annti, 2011, Expected Returns, Chichester, UK: John Wiley and Sons LTD, page 311 x www.cboe.com xi Ilmanen, Annti, 2011, Expected Returns, Chichester, UK: John Wiley and Sons LTD, page 311 xii Cambridge Associates, 2011, Highlights From The Benefits of Selling Volatility, Working Paper, pages 1-4 xiii Coval, Joshua, Shumway, Tyler, 2000, Expected Options Returns, Working Paper, http://ssrn.com/abstract=189840, pages 1-34 xiv www.cboe.com xv Ilmanen, Annti, 2011, Expected Returns, Chichester, UK: John Wiley and Sons LTD, page 311 xvi Grant, Maria, Gregory, Krag, Lui, Jason, 2007, Volatility as an Asset Class, Goldman Sachs, New York, page 12 xvii Grant, Maria, Gregory, Krag, Stevens, David, 2006, VIX Futures Over the Last Decade, Goldman Sachs, New York, page 1 xviii Ilmanen, Annti, 2011, Expected Returns, Chichester, UK: John Wiley and Sons LTD, page 315 xix Yang, George,2011, Buy-Write or Put-Write, An Active Portfolio to Strike it Right, Working Paper, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1827363m, pages 1-4

xx Driessen, Joost, Maenhout, Pascal, 2007, An Empirical Portfolio Perspective on Option Pricing Anomalies, Review of Finance, 11 (4), pages 561-603 xxi Rennison, Graham, Pedersen, Niles, (2012), The Volatility Risk Premium, Working Paper for PIMCO, pages 1-10