An EDHEC-Risk Institute Publication

The Benefits of Volatility Derivatives in Equity Portfolio Management

May 2012

with the support of

Institute Table of Contents

Executive Summary……………………………………………………………………………… 5

1. Introduction………………………………………………………………………………………15

2. Long-term Analysis Conducted at Index Level …………………………………19

3. Implementing the Analysis with Volatility Futures ……………………………31

4. Short-term Analysis with Volatility Options ……………………………………41

5. Conclusion…………………………………………………………………………………………47

Appendix………………………………………………………………………………………………49

References……………………………………………………………………………………………59

About EDHEC-Risk Institute…………………………………………………………………63

About Eurex Exchange…………………………………………………………………………67

EDHEC-Risk Institute Publications and Position Papers (2009-2012)…… 69

We acknowledge financial support from Eurex for this research project, and would like to thank Stefan Engels, Rex Jones and Lothar Kloster for very useful comments.

Printed in France, May 2012. Copyright© EDHEC 2012. 2 The opinions expressed in this study are those of the authors and do not necessarily reflect those of EDHEC Business School. The authors can be contacted at [email protected]. The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012 Foreword

In 2008, worldwide equity markets collapsed The results we obtain suggest that a long and many assets which conventional volatility position shows a strongly negative investment wisdom until then regarded correlation with respect to the underlying as effective equity diversifiers, such as equity portfolio and that adding a long commodities, also experienced dramatic falls. volatility exposure to an equity portfolio Meanwhile, equity volatility skyrocketed, would result in a substantial improvement causing long positions in equity volatility of the risk-adjusted performance of the to rally. These events, as well as regulatory portfolio. The benefits of the long volatility developments, dashed the exaggerated exposure are found to be the strongest in hopes placed in traditional forms of market downturns, where they are needed diversification and led investors to pay the most. increased attention to the volatility and downside risk of equity holdings, if not The benefits of adding volatility exposure to to question the level of their allocation equity portfolios are also found to be robust to equity altogether. They also prompted with respect to the introduction of trading interest in the possible use of equity volatility costs associated with rolling over volatility derivatives as diversifiers for traditional and derivatives contracts. alternative portfolios in general, and equity positions in particular. We hope that you will find the results of this research both informative and useful. Against this backdrop, the present publication is dedicated to exploring the uses of volatility We would like to express our sincere derivatives by professional investors, with gratitude to our longstanding partners at specific emphasis on their equity portfolio Eurex for supporting this research. management applications.

The research shows how volatility derivatives can be used to optimise access to the equity risk premium in a controlled volatility- Frédéric Ducoulombier risk environment, and to engineer equity Director, EDHEC Risk Institute–Asia portfolios with attractive downside-risk properties.

An EDHEC-Risk Institute Publication 3 The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012 About the Authors

Renata Guobuzaite is a PhD in Finance candidate and research assistant at EDHEC-Risk Institute. Previously, she held the positions of Vice President within Asset Transition Management at J.P. Morgan (London) and a Senior Consultant in Corporate Finance at PricewaterhouseCoopers. She has a Masters degree in Finance from London Business School and an MBA from Washington University in St. Louis. She is also a certified chartered financial analyst (CFA).

Lionel Martellini is Professor of Finance at EDHEC Business School and Scientific Director of EDHEC-Risk Institute. He has graduate degrees in economics, statistics, and mathematics, as well as a PhD in finance from the University of California at Berkeley. Lionel is a member of the editorial board of the Journal of Portfolio Management and the Journal of Alternative Investments. An expert in quantitative asset management and derivatives valuation, his work has been widely published in academic and practitioner journals and has co-authored textbooks on alternative investment strategies and fixed-income securities.

4 An EDHEC-Risk Institute Publication Executive Summary

An EDHEC-Risk Institute Publication 5 The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

Executive Summary

1. Introduction exposure to volatility through trading in Recent market turbulence, coupled with the volatility index futures and/or volatility presence of increasingly strict regulatory index options can be engineered so as to constraints have led institutional investors provide an access to the equity risk premium (pension funds, insurance companies) and while allowing for an explicit management asset managers to monitor the volatility of the volatility risk budget. and downside risk of their equity holdings with increased scrutiny. One approach A number of studies1 suggest that volatility towards the design of equity portfolios in and equity returns tend to move in opposite the presence of tight risk budgets involves directions (i.e. they are strongly negatively building equity portfolio benchmarks with correlated) which allows for significant the lowest possible volatility. Over the diversification benefits from adding a long past few years, this approach has gained volatility position to equity portfolios. In considerable popularity in the industry addition, the negative correlation between and a large number of asset management an implied volatility and underlying equity firms are currently offering global minimum portfolio is found to be strongest in large variance (GMV) portfolios. market downturns. One possible explanation 1 - Szado (2009), Daigler and Rossi (2006), Grant for the negative correlation of equity et al. (2007), Dash and Moran Whether investing in a GMV portfolio volatility to equity market is the “leverage (2007), Alexander and Korovilas (2011). is the most efficient and robust route effect” (Black 1976; Christie 1982; Schwert for managing equity volatility remains, 1989): a decrease (respectively, an increase) however, an open question. From an in equity prices increases (respectively, academic perspective, this approach is not decreases) the company’s leverage, thereby consistent with standard portfolio theory, increasing (respectively, decreasing) the which instead suggests first identifying the risk to equity holders and increasing maximum Sharpe ratio (MSR) portfolio, as (respectively, decreasing) equity volatility. opposed to the GMV portfolio, and then Another alternative explanation (French mixing that portfolio with cash so as to et al. 1987; Bekaert et Wu 2000; Wu achieve the target volatility consistent with 2001; Kim et al. 2004) is the “volatility investors’ risk appetites and budgets. In feedback effect”: assuming that volatility other words, while the GMV is an efficient is incorporated in stock prices, a positive portfolio in the absence of a risk-free asset, volatility shock increases the future it is no longer an efficient portfolio when required return on equity and stock prices a risk-free asset is introduced. are expected to fall simultaneously. The presence of profound economic reasons In this article, we analyse a competing that explain the inverse relationship approach to the design of attractive equity between equity return and volatility is a solutions with managed volatility, based on comforting indication of the robustness mixing well-diversified maximum Sharpe of the diversification benefits to be ratio portfolios with volatility derivatives. expected. It stands in contrast with the Intuitively, one expects that a portfolio well-known lack of robustness of portfolio strategy mixing a well-diversified equity diversification within the equity universe benchmark and a suitably designed long (e.g. international diversification), where

6 An EDHEC-Risk Institute Publication The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

Executive Summary

diversification is known to fail precisely futures contracts, so as to generate the when it is needed the most because of the target level of long volatility exposure. convergence of all correlations to one in We also analyse the benefits of adding periods of high market turbulence. volatility option positions, and found substantial benefits over the sample period, The focus of this paper is to provide a even though the sample size is too limited formal analysis of the benefits of volatility because of data availability for the results derivatives in equity portfolio management to be fully informative. from the perspective of a European investor. Our main contribution is to compare the risk/return characteristic of equity 2. Long-term Analysis Conducted portfolios combined with long volatility at Index Level exposure to those of a GMV equity portfolio The VSTOXX index, based on EURO STOXX – the conventional approach to managing 50 real-time options, is designed to reflect equity volatility. Our paper is in fact the the market expectations of equity price first to provide an explicit comparison of volatility. By definition, the VSTOXX index managed volatility strategies based on is a measure of an expected volatility in the 2 - One additional contribution of the paper is GMV portfolios and managed volatility market which is expected to be strongly to confirm with European strategies based on volatility derivatives. negatively correlated with EURO STOXX 50 data similar results previously obtained with US data. Our results unambiguously suggest that series. As plotted in Figure 1, both series the latter approach is a more efficient way indeed seem to move in opposite directions. to manage equity volatility, especially in To get a first sense of the relationship, we market downturns periods.2 first estimated an unconditional correlation between the VSTOXX and EURO STOXX 50 Our main results can be summarised as index return series based on the full sample follows. Using European data, we first period ranging from January 1999 to April confirm that the correlation between the 2011. Based on the analysis, the results return on volatility indexes and the return confirm a substantial negative correlation on equity indexes is strongly negative, of -0.74 (-0.73 and -0.66, respectively, for with an absolute level of correlation that weekly and monthly data) between two increases in recessions and/or high volatility series for the sample period. regimes compared to the unconditional estimates. We then show that even a In further analysis, we checked whether the relatively modest allocation to volatility results are robust with respect to changes in derivatives, consistent with a reasonable time period and market conditions. In order level of expected performance, can allow to prove that the relationship is consistent an investor to generate equity portfolios over time, we generated 5-year rolling that have more attractive downside risk window correlation estimates between properties compared to GMV portfolios, the two index series returns on the period with a substantial reduction in maximum ranging from January 1999 to April 2011. drawdown levels. These findings are robust The analysis confirmed the correlation level with respect to the introduction of trading to be systematically negative, irrespective costs associated with rolling over volatility of the time period under consideration and

An EDHEC-Risk Institute Publication 7 The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

Executive Summary

Figure 1: Time Evolution of EURO STOXX 50 Index and VSTOXX Indexa

Daily time series for EURO STOXX 50 and VSTOXX indexes. The shaded areas are the NBER recessions. The sample period is January 1999 to April 2011.

increasingly so for more recent time periods. During the recent 2008 crisis, the negative We also analysed whether the negative correlation between VSTOXX and EURO correlation is robust with respect to changes STOXX 50 indexes was particularly strong, in market conditions. In order to distinguish estimated at -0.80 (the highest value so between the periods of high and low far) for the January 2008 to December volatility in the European equity market, 2008 period. These results suggest that the we used a Markov regime-switching model benefits of diversification with volatility (Perlin 2010). Using weekly EURO STOXX 50 indices manifest themselves when they are Index data, we distinguished between the needed the most. states of high, medium and low volatility. The estimated correlation between EURO Next, we analysed the benefits of adding STOXX 50 and VSTOXX index returns is -0.76, a long volatility exposure to the equity -0.73 and -0.62 for the periods of high, portfolio. We use the EURO STOXX 50 medium and low volatility, respectively. index to represent a large cap European stock benchmark. In this section, we only In addition, we used the National Bureau simulated a long volatility position by of Economic Research (NBER) recession/ ‘trading’ in the VSTOXX spot index. Although expansion indicators as a control variable a direct investment in the VSTOXX index is (see Figure 1). The negative correlation not possible in practice, this ‘theoretical’ seems particularly pronounced during approach allowed us to access a longer data the periods indicated as NBER recessions. history (i.e. January 1999 to April 2011) for During NBER recessions the correlation level analysing portfolios’ performances. reached -0.78, which is relatively close to the correlation level (i.e. -0.76) estimated We constructed a number of equity during high volatility periods as defined portfolios with 5% increasing allocations to with the Markov regime-switching model. a long volatility exposure. A long volatility

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Executive Summary

position itself would hardly generate any We then extended the analysis by comparing positive return – 100% investment in the performance between the equity VSTOXX resulted in 0.3% p.a. over the sample portfolio with a long volatility exposure period (additionally, 100% investment in VIX and a GMV portfolio. We used MSCI Europe had a return of -0.7% p.a.) – consistent with Minimum Volatility Index as a proxy GMV the view in current literature that there is portfolio in our study. For this analysis, we a negative risk premium associated with selected the portfolio with long volatility being long volatility.3 However, gradually exposure that had similar volatility to that increasing the equity portfolio’s allocations of a GMV portfolio over the sample period to volatility exposure has a very positive ranging from December 2001 to April 2011. effect on equity portfolio performance. We have illustrated this effect in Figure 2, The results, illustrated in Figure 3, are in an efficient frontier format. clearly in favour of the diversified equity portfolio with a long volatility exposure. The pure equity portfolio is clearly inferior to Both portfolios have relatively similar other investment opportunities, bearing in performances during the periods of low mind the existence of a diversified portfolio volatility and the diversified portfolio with 3 - Bakshi and Kapadia (2003), Carr and Wu (2010). on the efficient frontier that has the same VSTOXX exposure always outperforms standard deviation as the equity portfolio, the GMV portfolio in the periods of high but that offers significantly higher returns. volatility. Although volatilities of both In our sample, the maximum Sharpe ratio portfolios for the sample period are similar, (0.46) is achieved for the portfolio with 30% the returns are significantly improved in the allocation to VSTOXX and 70% allocation diversified portfolio with VSTOXX exposure to EURO STOXX 50. case (i.e. 9.7% compared to a 2.1% return of GMV portfolio).

Figure 2: Impact of Adding Long Volatility Exposure to Equity Portfolio in 5% Increments

The effects of adding VSTOXX index exposure to EURO STOXX 50 portfolio in 5% increments, estimated based on the sample period ranging from January 1999 to April 2011.

An EDHEC-Risk Institute Publication 9 The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

Executive Summary

Figure 3: Performance of Diversified Portfolio with VSTOXX Exposure and Global Minimum Variance (GMV) Portfolio

Daily time series for the diversified portfolio and MSCI Europe Minimum Volatility Index on the sample period ranging from December 2001 to April 2011.

Overall, the results in this section provide size of €1,000 EUR per index point. In our strong evidence of the benefits of adding analysis, we used the data of both currently a long volatility exposure to an equity trading and delisted VSTOXX futures series portfolio. We also demonstrated that to obtain a longer data history (the total adding a volatility exposure to the equity combined sample period ranges from April portfolio not only improves its performance 2008 to April 2011). as compared to a pure equity case, but it can also provide a more efficient method Considering that an individual futures of managing downside volatility exposure contract is traded for limited time only, than the GMV approach. an investor has to roll over the initial VSTOXX investment over the series of consecutive futures contracts for a long 3. Implementing the Analysis with exposure in VSTOXX. We constructed Volatility Futures three separate VIX futures series based on In the previous section a structural volatility different rollover methodologies: 1-month, exposure was represented by a ‘theoretical’ 3-month and longest-traded (LT) series. direct investment in the VSTOXX index. The purpose of this exercise is to analyse However, in practice, the VSTOXX index the costs associated with different rollover is not directly investable, and in order to strategies as a function of the frequency invest in VSTOXX, an investor may take a of rebalancing. We have estimated that position in VSTOXX futures and/or options during the analysed sample period from contracts. Mini-futures on VSTOXX were April 2008 to April 2011, the VSTOXX introduced on the Eurex Exchange in June futures market was approximately 79% in 2009, with a contract value of €100 per contango and 21% in backwardation. As a index point. They replaced previously listed result, a rollover strategy typically induces futures on VSTOXX, which had a contract a negative return.

10 An EDHEC-Risk Institute Publication The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

Executive Summary

A few recent papers4 report that the performing 3-month VSTOXX futures series majority of futures contracts have a lower are presented in Figure 4, in an efficient and less variable carry when rolled over 5 frontier format. It is interesting to note that days prior to maturity, rather than waiting the best performing portfolio is achieved by until maturity. However, this observation is allocating 30% to VSTOXX futures, which specific to the US market and we found no is a similar result to that obtained with evidence that rolling over 5 days prior to VSTOXX index data. maturity significantly improved the results in portfolios with long volatility exposure. In order to access the full impact of Considering this result, we used rollover transaction costs, we incorporated the at maturity in all our further empirical bid-ask spread into the analysis. Including analyses. the bid-ask spread costs significantly affects the performance of VSTOXX futures – the In order to be consistent with our earlier returns decreased by 26%, 12.6% and 8.5% analysis, we again constructed several p.a. for 1-month, 3-month and longest- equity portfolios with increasing allocations term (LT) futures, respectively. to VSTOXX futures positions. As before, 4 - Lee and Lin (2010), Alexander and Korovilas European equity market exposure is We also compared the performance of (2011) approximated by the investment in the the diversified portfolio with a managed EURO STOXX 50 Index. The investment volatility position with VSTOXX futures to in VSTOXX is represented by a fully one of the GMV portfolios. The diversified collateralised VSTOXX futures position. portfolio with VSTOXX futures proves to The analysis starts with the pure equity be a better investment opportunity than portfolio as a benchmark case and adds, in the GMV portfolio. Firstly, it improves 5% increments, a long volatility exposure the standard deviation of returns from to the portfolio. The results for the best 21.6% (for GMV portfolio) to 16.1% p.a.

Figure 4: Impact of Adding Long Volatility Exposure to Equity Portfolio in 5% Increments

The effects of adding VSTOXX Futures (the 3-month series) to a EURO STOXX 50 portfolio in 5% increments, estimated based on the sample period ranging from April 2008 to April 2011.

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Executive Summary

(for diversified portfolio); secondly, it also In order to assess the impact of adding reduces negative returns for the sample VSTOXX options to equity portfolios, we period – from -2.8% (GMV) to -1.0% p.a. constructed a long volatility position (diversified portfolio). In summary, the by rolling over one month to expiration results obtained in this section suggest VSTOXX call options. We use both at-the- that the benefits of adding a long volatility money (ATM) and out-of-the-money (10% exposure to equity portfolios are robust with OTM and 25% OTM) calls for our analysis. respect to the introduction of trading costs Considering that volatility options are much involved in implementation with volatility more sensitive to changes in underlying futures contracts. Careful attention to trade volatility compared to fully collateralised execution is nonetheless required to limit futures contracts, we used 1% increments the negative impact of transaction costs, in volatility exposure rather than 5% negative carry and roll yield on volatility increments used for VSTOXX futures. futures during normal periods. The performance of ATM VSTOXX calls provides very similar results to the VSTOXX 4. Short-term Analysis with futures. While adding a small positive Volatility Options exposure to the volatility index option In this section, we considered a different portfolio slightly improves (1% and 2%) approach based on the use of volatility the performance of the overall portfolio, options for gaining a long exposure further increases provide no additional to volatility. March 2010 witnessed the value. Due to increased sensitivity, the introduction of option contracts on the results achieved with OTM calls is much more VSTOXX index, which provided investors favourable than those achieved with ATM with more flexibility for trading European calls; and, in the case of the 25% OTM calls, volatility. the return improvements are impressive.

Figure 5: Impact of Adding VSTOXX 25% OTM options to Equity Portfolio in 1% Increments

The effects of adding VSTOXX OTM options to EURO STOXX 50 portfolio by 1% increments, estimated based on the sample period ranging from March 2010 to April 2011.

12 An EDHEC-Risk Institute Publication The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

Executive Summary

The performance of the portfolios with However, in both cases, a careful selection increasing allocation to 25% OTM calls is of option strike prices proved to be critical depicted in an efficient frontier form in for portfolio performance. Therefore, it is Figure 5. important to take current market volatility conditions into account when designing and In further analysis, we estimated the impact implementing an option trading strategy. of the bid-ask spread on the performance of the diversified portfolios with VSTOXX However, the data history available for options exposure. In this case, the drag on VSTOXX options is very short (ranging performance amounts to 0.53%, 4.28% and from March 2010 to April 2011). Due 6.21% p.a. for ATM, 10% OTM and 25% OTM to an extremely short data history and calls, respectively. corresponding sample size, it would be difficult to provide a formal analysis of We also considered a classic strategy the marginal benefits to be expected from for managing downside risk in equity using volatility index futures as opposed portfolios – the use of protective puts. In to volatility index options. Therefore, the every financial textbook, protective puts analysis in this section is merely to be are referred to as a direct hedge for the regarded as an example of an alternative price movements in equity portfolios. In way of structuring a long volatility order to test this assertion, we compared exposure. the performance of an equity portfolio with VSTOXX call allocations to that of an equity portfolio mixed with long EURO STOXX 5. Conclusion 50 puts. We find that equity portfolios In this paper, we analyse a novel with EURO STOXX 50 put positions do not approach in the design of attractive perform as well as portfolios mixed with equity solutions with managed volatility, VSTOXX calls. None of the portfolios with based on mixing a well-diversified equity EURO STOXX 50 puts have better ‘adjusted’ portfolio with volatility derivatives, as Sharpe ratios than those of a pure equity opposed to minimising equity volatility portfolio. through minimum variance approaches. The results we obtain suggest that a long Up to this point, we have mostly focused volatility position shows a strongly negative on the diversification properties of volatility correlation with respect to the underlying derivatives. However, an investor can also equity portfolio and that adding a long use VSTOXX options to trade on a specific volatility exposure to an equity portfolio view on the VSTOXX direction or volatility would result in a substantial improvement changes. In this section, we analyse the of the risk-adjusted performance of the performance of two commonly used portfolio. The benefits of the long volatility strategies for generating premium: (i) exposure are found to be strongest in short out-of-the-money VSTOXX puts; market downturns, when they are most and (ii) VSTOXX ratio spread strategy. Both needed. strategies can be used as more innovative ways for equity portfolio management.

An EDHEC-Risk Institute Publication 13 The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

Executive Summary

We also compare the performance of the diversified equity portfolios including volatility derivatives with that of global minimum variance (GMV) portfolios that are commonly used in industry as a benchmark strategy for reducing portfolio risk. We found that the diversified portfolio with long volatility exposure is a more efficient approach for managing risk.

We also consider the challenges related to a practical implementation of this strategy by using derivatives instruments – futures and options – that allow investors direct access to trading volatility. We consider how increasing allocation to volatility derivatives affects the portfolio performance; we also evaluate transaction costs in each case and discuss the advantages and disadvantages of using each type of instrument. The benefits of adding volatility exposure to equity portfolios are found to be robust with respect to the introduction of trading costs associated with rolling over volatility derivatives contracts.

14 An EDHEC-Risk Institute Publication 1. Introduction

An EDHEC-Risk Institute Publication 15 The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

1. Introduction

Recent market turbulence, coupled longer an efficient portfolio when a risk- with the presence of increasingly free asset is introduced. strict regulatory constraints have led institutional investors (pension funds, In this article, we analyse a competing insurance companies) and asset managers approach to the design of attractive equity to monitor the volatility and downside risk solutions with managed volatility, based on of their equity holdings with increased mixing well-diversified maximum Sharpe scrutiny. One approach towards the design ratio portfolios with volatility derivatives. of equity portfolios in the presence of Intuitively, one expects that a portfolio tight risk budgets involves building equity strategy mixing a well-diversified equity portfolio benchmarks with the lowest benchmark and a suitably designed long possible volatility. Over the past few years, exposure to volatility through trading in this approach has gained considerable volatility index futures and/or volatility popularity in the industry, and the non- index options can be engineered so as exhaustive list of firms that are currently to provide an access to the equity risk managing global minimum variance premium while allowing for an explicit (GMV) portfolios includes Acadian Asset management of the volatility risk budget. 5 - Szado (2009), Daigler and Rossi (2006), Grant et al. Management, AXA Rosenberg, Invesco, (2007), Dash and Moran (2007), LGT Capital Management, MSCI Barra, The rapid development of standardised Alexander and Korovilas (2011). SEI, Robeco, State Street Global Advisors products, especially (exchange-traded) and Unigestion, among others. Currently, volatility index futures and (OTC-traded) GMV portfolios are largely promoted variance swaps, has recently provided as pragmatically useful benchmarks for investors with straightforward access to investors or asset managers wishing to a wide range of strategies for gaining benefit from some fraction of the equity structural exposure to volatility. One of risk premium without the full associated main motivations for trading in volatility downside risk. is precisely to diversify equity risk through long implied volatility exposure. A Whether investing in a GMV portfolio number of studies5 suggest that volatility is the most efficient and robust route and equity returns tend to move in for managing equity volatility remains, opposite directions (i.e. they are strongly however, an open question. From an negatively correlated) which allows academic perspective, this approach is for significant diversification benefits not consistent with standard portfolio from adding a long volatility position theory, which instead suggests first to equity portfolios. In addition, the identifying the maximum Sharpe ratio negative correlation between an implied (MSR) portfolio, as opposed to the GMV volatility and underlying equity portfolio portfolio, and then mixing that portfolio is found to be strongest in large market with cash so as to achieve the target downturns. One possible explanation volatility consistent with investors’ risk for the negative correlation of equity appetites and budgets. In other words, volatility to equity market is the “leverage while the GMV is an efficient portfolio in effect” (Black 1976; Christie 1982; the absence of a risk-free asset, it is no Schwert 1989): a decrease (respectively,

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1. Introduction

an increase) in equity prices increases a premium to hold this asset. In a recent (respectively, decreases) the company’s paper, Carr and Wu (2009) find that the leverage, thereby increasing (respectively, negative correlation between stock index decreasing) the risk to equity holders and returns and the return variance generates increasing (respectively, decreasing) equity a strongly negative beta, which would volatility. Another alternative explanation explain a low or even negative expected (French et al. 1987; Bekaert et Wu 2000; return on the long volatility exposure. Wu 2001; Kim et al. 2004) is the “volatility They also find that this negative beta only feedback effect”: assuming that volatility explains a small portion of the negative is incorporated in stock prices, a positive variance risk premiums. Other risk factors volatility shock increases the future identified by the recent literature, such required return on equity and stock prices as size, book-to-market, and momentum are expected to fall simultaneously. The are also unable to explain the strongly presence of profound economic reasons negative variance risk premiums, and they that explain the inverse relationship conclude that the majority of the market between equity return and volatility is a variance risk premium is generated by an comforting indication of the robustness independent variance risk factor. 6 - One additional contribution of the paper is to use European of the diversification benefits to be data to confirm similar results expected. It stands in contrast with the The focus of this paper is to provide previously obtained with US data. well-known lack of robustness of portfolio a formal analysis of the benefits of diversification within the equity universe volatility derivatives in equity portfolio (e.g. international diversification), where management from the perspective diversification is known to fail precisely of a European investor. Our main when it is needed the most because of the contribution is to compare the risk/ convergence of all correlations to one in return characteristic of equity portfolios periods of high market turbulence. combined with long volatility exposure to those of a GMV equity portfolio – The risk diversification benefits of long the conventional approach to managing volatility exposure, however, come at a equity volatility. Our paper is in fact the cost. Recent academic research has found first to provide an explicit comparison of that there is a positive risk premium over managed volatility strategies based on time to being short volatility or conversely, GMV portfolios and managed volatility that there is a negative risk premium strategies based on volatility derivatives. to being long volatility. In equilibrium, Our results unambiguously suggest that because of the negative correlation the latter approach is a more efficient way between market index returns and market to manage equity volatility, especially in index volatility, buyers of options may market downturns periods.6 be willing to pay a premium because a long position in volatility helps hedge More specifically, our main results can be market-wide risk (Bakshi and Kapadia summarised as follows. Using European 2003). In other words, because volatility data, we first confirm that the correlation is negatively correlated with the returns between the return on volatility indexes to equities, investors are willing to pay and the return on equity indexes is

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1. Introduction

strongly negative, with an absolute level of correlation that increases in recessions and/or high volatility regimes compared to the unconditional estimates. We then show that even a relatively modest allocation to volatility derivatives, consistent with a reasonable level of expected performance, can allow an investor to generate equity portfolios that have more attractive downside risk properties compared to GMV portfolios, with a substantial reduction in maximum drawdown levels. These findings are robust with respect to the introduction of trading costs associated with rolling over volatility futures contracts, so as to generate the target level of long volatility exposure. We also analyse the benefits of adding volatility option positions, and found substantial benefits over the sample period, even though the sample size is too limited because of data availability for the results to be fully informative. The remainder of the paper is organised as follows. In Section 2, we analyse the relationship between EURO STOXX 50® and VSTOXX® index series, construct a number of portfolios with varying long volatility exposure and compare their performance with that of a GMV. Section 3 provides a practical insight on how this strategy can be implemented with VSTOXX futures. In Section 4, we discuss an alternative approach for gaining long volatility exposure by using VSTOXX derivatives. Finally, Section 5 concludes.

18 An EDHEC-Risk Institute Publication 2. Long-term Analysis Conducted at Index Level

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2. Long-term Analysis Conducted at Index Level

As discussed in the introduction, a In further analysis, we checked whether the number of academic studies7 discuss the results are robust with respect to changes economic reasons for the existence of a in time period and market conditions. In strong negative correlation between the order to prove that the relationship is equity volatility and underlying equity consistent over time, we generated 5-year markets. In what follows, we will provide rolling window correlation estimates empirical confirmation of this negative between the two index return series on link through a detailed analysis of the the period ranging from January 1999 correlation between VSTOXX® and EURO to April 2011. The analysis confirms the STOXX 50® indexes, and also discuss the correlation level to be systematically portfolio implications of these findings. negative, irrespective of the time period under consideration and increasingly so for more recent time periods (see Figure 2). 2.1. Analysis of the Correlation Between EURO STOXX 50 and We also analysed whether the negative VSTOXX indexes correlation is robust with respect to The VSTOXX index is based on EURO STOXX changes in market conditions. In order to 7 - Black (1976), Christie (1982), Schwert (1989), 50 real-time options and is designed to distinguish between the periods of high French et al. (1987), Wu reflect the market expectations of equity and low volatility in the European equity (2000), Kim et al. (2004). price volatility by measuring the square market, we used a Markov regime-switching root of the implied variance across all model (Perlin 2010). Using weekly EURO options of a given time to expiration. By STOXX 50 Index data, we distinguished definition, the VSTOXX index is a measure between the states of high, medium and of an expected volatility in the market and, low volatility. The estimated correlation therefore, should be strongly negatively between EURO STOXX 50 and VSTOXX correlated with EURO STOXX 50 series index returns is -0.76, -0.73 and -0.62 (Bakshi and Kapadia 2003; Carr and Wu for the periods of high, medium and low 2010; Dash and Moran 2007; Alexander volatility, respectively. This clearly supports and Korovilas 2011). To get a first sense the assumption that negative correlation of the relationship, we first estimated between two series tends to increase with an unconditional correlation between higher volatility in the market. VSTOXX and EURO STOXX 50 index return series based on the full sample period In addition, we used the National Bureau ranging from January 1999 to April 2011 of Economic Research (NBER) recession/ (see Figure 1). We used the daily (as well as expansion indicators as a control variable weekly/monthly) return data for VSTOXX (see Figure 3). The negative correlation and EURO STOXX 50 indexes available seems particularly pronounced during from Datastream. Based on the analysis, the periods indicated as NBER recessions. the results confirm a substantial negative During NBER recessions the correlation correlation of -0.74 (-0.73 and -0.66, level reached -0.78, which is relatively close respectively, for weekly and monthly data) to the correlation level (i.e. -0.76) estimated between two series for the sample period. during high volatility periods as defined with the Markov regime-switching model.

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2. Long-term Analysis Conducted at Index Level

Figure 1: Time Evolution of EURO STOXX 50 Index and VSTOXX Index

Daily time series for EURO STOXX 50 and VSTOXX indexes on the sample period ranging from January 1999 to April 2011.

Figure 2: Correlation of EURO STOXX 50 Index and VSTOXX Index across Time

EURO STOXX 50 index negative correlation with VSTOXX index, based on 5-year daily return rolling window data on the sample period ranging from January 1999 to April 2011.

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Figure 3: Time Evolution of EURO STOXX 50 Index and VSTOXX Index and Recession Periods

Daily time series for EURO STOXX 50 and VSTOXX indexes. The shaded areas are the NBER recessions. The sample period is January 1999 to April 2011.

As an additional robustness check, we We also have estimated the correlation closely analysed the correlation between level in more recent periods starting from VSTOXX and EURO STOXX 50 index returns January 2010 to April 2011 (see Figure during the recent 2008 crisis (see Figure 5). The results show that the negative 4). This period is of a particular interest, correlation between the returns of both because it is a perfect example of both indexes remained strong at -0.81, despite equity market prices and their volatility the fact that the market was much less behaviour during a severe market volatile during this period. This analysis breakdown. Several academic studies (i.e. is consistent with the previous results Szado 2009; Toikka et al. 2004; Lee and using 5-year rolling window correlation Lin 2010; Alexander and Korovilas 2011) estimates (see Figure 2), referring that the suggest that the negative correlation correlation between VSTOXX and EURO between the equity index and its implied STOXX 50 indexes has increased over volatility should be the strongest in large time and is higher in more recent time downward moves. periods.

Indeed, the analysis confirms that the In summary, the correlation level between negative correlation between VSTOXX and EURO STOXX 50 index and VSTOXX index EURO STOXX 50 indexes is particularly series remained negative for all market strong, estimated at -0.80 (the highest conditions (i.e. high/low volatility, growth/ value so far) during the January 2008 to recession) with a significant increase in December 2008 period. The results suggest major downward market moves and, also, that a long position in volatility might higher in more recent time periods. be a particularly effective diversifier in major downward market moves such as the recent crisis.

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Figure 4: EURO STOXX 50 Index and VSTOXX Index Performance in 2008

Daily time series for EURO STOXX 50 and VSTOXX indexes on the sample period ranging from January 2008 to December 2008. 4 - Daigler and Rossi (2006), Dash and Moran (2005, 2007), Grant et al. (2007), Szado Figure 5: EURO STOXX 50 Index and VSTOXX Index Performance in 2010/2011 (2009).

Daily time series for EURO STOXX 50 and VSTOXX indexes on the sample period ranging from January 2010 to April 2011.

2.2. Portfolio analysis and underlying equity portfolio results in In this section, we analyse the benefits significant diversification benefits from of adding a long volatility exposure adding a long volatility position to the to the equity portfolio. A number of equity portfolio, and we want to assess studies4 find that the strong negative whether those benefits can also be found correlation between an implied volatility based on European data.

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We use the EURO STOXX 50 index to – it increases total portfolio returns and represent a large cap European stock decreases standard deviations of returns. benchmark. In this section, we only Then, after a certain point (~25-30% for simulate a long position in the VSTOXX VSTOXX allocations) further allocation to index. Although a direct investment in the long volatility exposure starts increasing VSTOXX index is not possible in practice, the overall portfolio volatility as well. We and while we will focus on investment in have illustrated this effect in Figure 6, VSTOXX derivatives in further sections, this in an efficient frontier format. The pure ‘theoretical’ approach allows us to access a equity portfolio is clearly inferior to other longer data history for analysing portfolios’ investment opportunities, bearing in mind performances. The sample period ranges the existence of a diversified portfolio on from January 1999 to April 2011 and again the efficient frontier that has the same both VSTOXX and EURO STOXX 50 index standard deviation as all equity portfolios, levels are obtained from Datastream. but that offers significantly higher returns. In our sample, the maximum Sharpe For the purpose of this analysis, we ratio (0.46) is achieved for the portfolio constructed a number of equity portfolios with 30% allocation to VSTOXX and 70% with increasing allocations to a long allocation to EURO STOXX 50. volatility exposure. The analysis starts with the pure equity portfolio as a benchmark There is a strong empirical evidence that case and adds (in 5% increments) a long returns on long volatility positions are not volatility exposure to the portfolio. We normal (Carr and Wu 2009; Hafner and use a number of traditional parameters, Wallmeier 2008). We therefore extended including portfolio returns, volatility, our investigation to include the impact of Sharpe ratio, skewness, excess kurtosis, and skewness and kurtosis. The results indicate historical VaR (daily) at 95% threshold, to that equity portfolio returns are usually compare performances of the portfolios. negatively skewed (-0.72 on the sample The results are presented in Table 1. period for EURO STOXX 50), and adding a long volatility exposure has a positive In both cases, the results show that impact on the portfolio skewness. For a long volatility position itself would example, the maximum Sharpe ratio hardly generate any positive return – portfolio (i.e. 30% allocation to VSTOXX and 100% investment in VSTOXX resulted 70% to EURO STOXX 50) has the highest in 0.3% p.a. over the sample period and positive skewness value as well. On the other 100% investment in VIX had a return of hand, adding a long volatility exposure to -0.7% p.a. – consistent with the view in the portfolio also increased the portfolio current literature that there is a negative kurtosis, which indicates higher probability risk premium associated with being long of obtaining an extreme value in the future. volatility (Bakshi and Kapadia 2003; In our sample, introducing an exposure to Carr and Wu 2009). However, gradually volatility risk leads to a relatively substantial increasing the portfolio’s allocations to reduction in the overall portfolio extreme volatility exposure has a very positive downside risk, estimated in terms of the effect on equity portfolio performance portfolio historical VaR.

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Table 1: Summary Statistics for Portfolios with Increasing Allocation to Long Volatility

Jan/1999 – Apr/2011 100% EURO STOXX 50 EURO STOXX 100% 50 + 95% EURO STOXX 5% VSTOXX 50 + 90 % EURO STOXX VSTOXX 10% 50 + 85% EURO STOXX 15% VSTOXX 50 + 80% EURO STOXX 20% VSTOXX 50 + 75% EURO STOXX 25% VSTOXX 50 + EURO STOXX 70% 30% VSTOXX 50 + 65% EURO STOXX 35% VSTOXX 50 + 60% EURO STOXX 40% VSTOXX ... 50 + 5% EURO STOXX 95% VSTOXX VSTOXX 100%

Ann. Return -1.52% 1.40% 4.08% 6.50% 8.64% 10.49% 12.04% 13.27% 14.18% ... 3.00% 0.32% Ann. Std 24.41% 20.20% 16.73% 14.54% 14.23% 15.91% 19.06% 23.09% 27.61% ... 84.95% 90.33% Deviation Sharpe Ratio* -0.19 -0.89 0.05 0.23 0.38 0.46 0.46 0.44 0.40 ... -0.00 -0.03 Skewness -0.72 -0.45 -0.02 0.06 1.23 1.73 1.86 1.63 1.24 ... 0.99 1.04 Excess Kurtosis -0.17 -0.02 0.34 1.12 2.36 3.70 4.34 3.86 2.65 ... 0.54 0.65 Historical VaR -2.40% -1.94% -1.52% -1.25% -1.23% -1.31% -1.54% -1.84% -2.24% ... -7.07% -7.52% (daily) *Note: The resulted negative Sharpe ratios are included only for the completeness of analysis; in general, negative Sharpe ratio would indicate that risk-free asset performs better than the portfolio being analysed and it is difficult to interpret.

Figure 6: Impact of Adding Long Volatility Exposure to Equity Portfolio in 5% Increments

The effects of adding VSTOXX index exposure to EURO STOXX 50 portfolio by 5% increments, estimated based on the sample period ranging from January 1999 to April 2011.

For comparison purposes, we have repeated similar to those obtained with European the same exercise with US market data for data and on a shorter sample period. which a longer data history is available (VIX data is available starting January 1990). We used S&P500 data to represent an investment in equity and VIX - a long position in volatility. The results we obtain, shown in Table 2 below, are qualitatively

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Table 2: Summary Statistics for Portfolios with Increasing Allocation to Long Volatility (US market)

Jan/1990 – Apr/2011 100% S&P500 100% 95% S&P500 + 5% VIX 90 % S&P500 + 10% VIX 85% S&P500 + 15% VIX 80% S&P500 + 20% VIX 75% S&P500 + 25% VIX S&P500 + 30% 70% VIX 65% S&P500 + 35% VIX 60% S&P500 + 40% VIX ... 5% S&P500 + 95% VIX VIX 100%

Ann. Return 8.34% 10.87% 13.12% 15.07% 16.71% 18.02% 19.01% 19.66% 19.96% ... 2.42% -0.72% Ann. Std 18.20% 14.41% 11.99% 11.81% 13.94% 17.57% 21.97% 26.76% 31.76% ... 90.29% 95.70% Deviation Sharpe Ratio* 0.27 0.51 0.80 0.98 0.96 0.83 0.71 0.60 0.52 .. -0.01 -0.04 Skewness -0.78 -0.73 -0.59 -0.33 0.03 0.40 0.70 0.89 1.01 .. 1.06 1.04 Excess Kurtosis 0.35 0.14 -0.29 -0.79 -1.033 -0.73 -0.05 0.63 1.09 .. 0.56 0.46 Historical -1.74% -1.29% -1.02% -0.98% -1.16% -1.47% -1.85% -2.27% -2.69% .. -7.88% -8.32% VaR (daily) *Note: The resulted negative Sharpe ratios are included only for the completeness of analysis; in general, a negative Sharpe ratio would indicate that risk-free asset performs better than the portfolio being analysed and as such is difficult to interpret.

The benefits of adding a long volatility returns and lower volatility over the exposure can be clearly seen when sample period. comparing the performance of diversified portfolios with that of a pure equity However, it should be noted that further portfolio over time (see Figure 7). All allocations of more than 30% to VSTOXX diversified portfolios outperformed the may negatively affect Sharpe ratios for the EURO STOXX 50 portfolio at each point portfolio due to the impact of a negative in time, with the maximum Sharpe ratio risk premium on long equity exposure portfolio (30% in VSTOXX + 70% in EURO that eventually offsets the benefits of the STOXX 50) resulting in significantly higher reduction in risk.

Figure 7: Performance of EURO STOXX 50 Index and Portfolios with VSTOXX Exposure

Daily time series for EURO STOXX 50 Index and diversified portfolios with VSTOXX exposure on the sample period ranging from January 1999 to April 2011.

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2.3. Comparison with a Global For this analysis, we selected the portfolio Minimum Variance Portfolio with long volatility exposure that had We then extend the analysis by comparing similar volatility to that of GMV portfolio the performance between the equity over the sample period ranging from portfolio with a long volatility exposure December 2001 to April 2011. The closest and a GMV portfolio. Global minimum portfolio in term of volatility of returns variance portfolios are commonly used can be approximated by portfolio with in the industry as a practical benchmark 30% allocation to VSTOXX and 70% for an equity portfolio with a managed allocation to EURO STOXX 50 (with downside risk exposure. We used MSCI volatility of 18.4% p.a. versus 16.8% p.a. Europe Minimum Volatility Index as of GMV portfolio). a proxy GMV portfolio in our study. The MSCI Europe Minimum Volatility The results, illustrated in Figure 8, are Index is calculated by optimising an clearly in favour of the diversified equity underlying MSCI Europe Index (that portfolio with a long volatility exposure. covers 16 developed countries including Both portfolios perform relatively similar Austria, Belgium, Denmark, Finland, during the periods of low volatility and the France, Germany, Greece, Ireland, Italy, diversified portfolio with VSTOXX exposure the Netherlands, Norway, Portugal, always outperforms the GMV portfolio in Spain, Sweden, Switzerland and the the periods of high volatility. Although United Kingdom) by using an estimated volatilities of both portfolios for the covariance matrix (based on the BARRA sample period are similar, the returns are model) to produce an index that has the significantly improved in the diversified lowest absolute volatility. The daily data portfolio with VSTOXX exposure case (i.e. on MSCI Europe Minimum Volatility Index 9.7% compared to a 2.1% return of GMV performance is available on Bloomberg portfolio). The estimated Sharpe ratio for starting from December 2001. the diversified portfolio is relatively high

Figure 8: Performance of Diversified Portfolio with VSTOXX Exposure and Global Minimum Variance (GMV) Portfolio

Daily time series for the diversified portfolio and MSCI Europe Minimum Volatility Index on the sample period ranging from December 2001 to April 2011.

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at 0.39 and the Sharpe ratio for the GMV volatility exposure during a more recent portfolio is very close to 0. period starting January 2010 to April 2011 (see Figure 10). Both portfolios follow each The advantages of the diversified equity other closely during this period where portfolio with a long volatility exposure an equity portfolio with long volatility are particularly clear during a recent exposure results in slightly higher return market crisis of 2008. Figure 9 shows the of 9.5% p.a., compared to the 6.8% p.a. performances of both GMV and equity return of the GMV portfolio. However, the portfolios with a long volatility exposure volatility of an equity portfolio with long during this period. Holding the diversified volatility exposure is also higher at 20.1% portfolio with VSTOXX exposure not only p.a., compared to the GMV portfolio’s protects portfolio value, but also results in volatility of 15.3% p.a. a 10% gain during this period, while the GMV portfolio loses 37.2% of its value. An equity portfolio with a long volatility The GMV portfolio also has much higher exposure, again, shows a superior volatility during this period, reaching to performance in May 2010 down market, 28.7% p.a. as compared to 22.1% p.a. for when rising concerns regarding sovereign the diversified equity portfolio with a crises were followed by the “Flash Crash long volatility exposure. of 2:45” on May 6th.

We also compared the performances of Overall, the results in this section provide GMV and equity portfolio with a long strong evidence of the benefits of adding

Figure 9: Performance of Diversified Portfolio with VSTOXX Exposure and Global Minimum Variance (GMV) Portfolio in 2008

Daily time series for the diversified portfolio and MSCI Europe Minimum Volatility Index on the sample period ranging from January 2008 to December 2008.

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Figure 10: Performance of Diversified Portfolio with VSTOXX Exposure and Global Minimum Variance (GMV) Portfolio in 2010/2011

Daily time series for the diversified portfolio and MSCI Europe Minimum Volatility Index on the sample period ranging from January 2010 to April 2011.

a long volatility exposure to an equity portfolio. As it appears, even a small addition of allocation to VSTOXX has a potential to improve portfolio efficiency. We also demonstrate that adding a volatility exposure to the equity portfolio not only improves its performance as compared to a pure equity case, but it can also provide a more efficient method of managing downside volatility exposure than the GMV approach.

However, it should be noted that, so far, we have used a ‘hypothetical’ investment in the VSTOXX index. We will focus on a more practical implementation of this strategy through trading in VSTOXX futures contracts in the next section.

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30 An EDHEC-Risk Institute Publication 3. Implementing the Analysis with Volatility Futures

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In the previous section a structural investment in futures contracts on the volatility exposure was represented by first day of the sample. On the rollover a ‘theoretical’ direct investment in the day the algorithm chooses the next VSTOXX index. However, in practice, the month available contract (in the 1-month VSTOXX index is not directly investable, series) or the next available contract on and in order to invest in VSTOXX, an the quarterly cycle (the 3-month series). investor may take a position in VSTOXX The third series, the longest-traded (LT) futures and/or options contracts. series, always rolls over into the longest maturity contract that is actively traded. The purpose of this exercise is to analyse 3.1. Constructing Time Series with the costs associated to different rollover VSTOXX Futures strategies as a function of the frequency Mini-futures on VSTOXX were introduced of rebalancing. on the Eurex Exchange in June 2009, with a contract value of €100 per index Corresponding VSTOXX futures term point. They replaced previously listed structure curves can have one of two futures on VSTOXX, which had a contract shapes: in contango, the futures prices for size of €1,000 per index point. The data short maturities are less expensive than including bid-ask prices and trading those maturing later; or, in backwardation, volumes on currently traded VSTOXX mini the opposite is true. Figure 11 shows futures as well as delisted VSTOXX futures VSTOXX implied volatility term structure is obtained from the intraday transaction on the 19 May 2010, when market was in records provided by Eurex. In our analysis, backwardation, and Figure 12 indicates we used the data of both currently a contango market observed on the 8 trading and delisted VSTOXX futures series October 2010. The VSTOXX futures market to obtain a longer data history. The total is typically in contango; backwardation combined sample period ranges from April is experienced only during a period of 2008 to April 2011, which is, of course, unusual high volatility. We have estimated substantially smaller than the sample that during the analysed sample period period used in our previous analysis based from April 2008 to April 2011, the VSTOXX on volatility index level data. futures market was approximately 79% in contango and 21% in backwardation. As a Considering that an individual futures result, a rollover strategy typically induces contract is traded for limited time only, a negative return. an investor has to roll over the initial VSTOXX investment over the series of A few recent papers (Lee and Lin 2010; consecutive futures contracts for a long Alexander and Korovilas 2011) report that exposure in VSTOXX. Following Alexander the majority of futures contracts have a and Korovilas (2011), we constructed lower and less variable carry when rolled three separate VIX futures series based over 5 days prior to maturity, rather than on different rollover methodologies: waiting until maturity. However, this 1-month, 3-month and longest-traded observation is specific to the US market (LT) series. All series start with an initial and is, mostly, due to the maturity effect,

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which is exacerbated by the settlement the difference between the VIX futures process for VIX futures. The underlying settlement price and VIX deviated from VIX index is based on average bid and ask zero. This convergence problem leads option prices, but VIX futures are settled on to increased arbitrage trading activity the special opening quotation (SOQ) price. over the last few days prior to maturity, The SOQ is extracted using actual traded causing increased volatility in VIX futures prices of SPX options during the market prices as they approach the last trading open at settlement day. Consequently, day.

Figure 11: VSTOXX Futures Term Structure in Backwardation, the 19thMay, 2010

VSTOXX Futures Term Structure in Backwardation, 19th May, 2010

Figure 12: VSTOXX Futures Term Structure in Contango, 8thOctober, 2010

VSTOXX Futures Term Structure in Contango, 8th October, 2010

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In order to evaluate a potential impact Figure 13 depicts the relative performance of early rollover for VSTOXX futures, we of the VSTOXX Index and all VSTOXX therefore compared the performance of all futures time series (i.e. 1-month, VSTOXX futures time series (i.e. 1-month, 3-month and LT time series) over the 3-month and LT time series) when rolled sample period. As was the case for the over 5 days prior to maturity versus with VSTOXX Index in the previous section, all that when rolled over at maturity. Unlike futures series are negatively correlated VIX futures, the final settlement price of with the EURO STOXX 50 index. The VSTOXX futures contracts is estimated as correlation between EURO STOXX 50 and an average of actual VSTOXX values on the the 1-month, 3-month and LT futures last trading day between 11:30 and 12:00 time series’ returns are -0.69, -0.68 and CET, therefore, reducing the possibility -0.61, respectively. It should be noted that of arbitrage trading. Although rolling the 1-month series exhibits the highest over 5 days prior to maturity slightly negative correlation with EURO STOXX reduced the volatility of futures series, index; however it has the largest drag on we found no evidence that it significantly performance due to higher rollover costs. improved the results in portfolios with In contrast, the longest-traded (LT) series long volatility exposure. Considering this lead to lower trading costs, but also show result, we use rollover at maturity in all a lower negative correlation with the our further empirical analyses. EURO STOXX 50 index. The 3-month series

Figure 13: Performance of EURO STOXX 50 Index and VSTOXX Futures

Daily time series EURO STOXX 50 Index and VSTOXX Futures on the sample period ranging from April 2008 to January 2011.

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exhibit a rather similar correlation with As before, the European equity market EURO STOXX 50 index to that of 1-month exposure will be approximated by the series (i.e. -0.68 vs. -0.69), and has the investment in EURO STOXX 50 Index. best performance over the sample period. The investment in VSTOXX futures is represented by a long position in a fully The performance of a long volatility collateralised VSTOXX futures position. To position implemented with VSTOXX futures create this investment, a long position in differs from a hypothetical situation where the front-month futures contract is fully the ‘theoretical’ investment in volatility is collateralised by holding a full value of assumed to be made by directly investing the contract in a bank deposit paying in VSTOXX Index (as discussed in the EURIBOR interest rate. By the end of previous section). The VSTOXX return is the day, all positions are rebalanced by driven by changes in the level of implied marking-to-market and adjusting the volatilities. In contrast, the returns of the collateral position to reflect the cash VSTOXX futures are driven by changes in inflow or outflow from marking to market. expectations of implied volatilities (Dash Returns for all days between the roll- and Moran 2007; Szado 2009; Alexander in day and maturity date are calculated and Korovilas 2011). The relationship using the mid-point between the bid and is further complicated by the fact that ask prices. The futures position is rolled volatility tends to follow a mean reverting into the next contract at the close on the process. Due to the mean reverting nature day prior to maturity. of volatility, the investment in VSTOXX futures is a priori expected to exhibit a We analyse the carry and rollover costs significantly lower volatility than the of buy-and-hold VIX futures positions ‘theoretical’ direct investment in VSTOXX based on different rollover methodologies Index. This is confirmed in our sample (1-month, 3-month and LT time series). where, for example, the 3-month VSTOXX First, we consider an ‘efficient’ investment Futures series has a very similar return in VSTOXX futures with no associated to the VSTOXX index (-7.78% p.a. vs. bid-ask spread costs – for instance, by -7.76% p.a.) over the sample period with assuming that each contract is rolled over substantially lower volatility (61.1% p.a. as to the next one based on the mid-price compared to 101.3% of VSTOXX Index). defined as the mid-point between the bid and ask prices. As in the previous section, we constructed a number of equity 3.2. Portfolio Analysis portfolios with increasing allocations to In order to be consistent with our earlier VSTOXX futures. The analysis starts with analysis of adding a long volatility the pure equity portfolio as a benchmark exposure to the equity portfolio through case and adds, in 5% increments, a long the VSTOXX index, we again construct volatility exposure to the portfolio. several equity portfolios with a few different allocations to a VSTOXX futures Given that both EURO STOXX 50 and position. VSTOXX futures returns were negative over the sample period, we have adjusted

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the performance measure used to 3-month series showed better results compare the portfolios. Due to negative than longest-traded (LT) series as well - returns, a traditional Sharpe ratio would the maximum ‘adjusted’ performance result in negative values that are difficult measure achieved with 3-month series to interpret. We used a similar measure, totalled to 0.41, as compared to 0.26 with however, instead of calculating excess LT series. returns over a risk-free rate, we estimated them over a specific benchmark, which The results for the best performing in this case was a pure equity portfolio 3-month VSTOXX futures series are EURO STOXX 50 Index return. This presented in Figure 14 in an efficient measure indicates how well each portfolio frontier format. Clearly, adding an performed when comparing to the exposure with 3-month VSTOXX futures benchmark case, adjusted for the riskiness series is beneficial to the portfolio of the portfolio. performance in both return and volatility terms. It is interesting to note that the The summary table with the results of best performing portfolio is achieved by this analysis is presented in Appendix 1. allocating 30% to VSTOXX futures, which The 3-month VSTOXX Futures series were is a similar result to that obtained with a clear winner in this case. All diversified VSTOXX index data (see Figure 5). For portfolios with allocations to 3-month more detailed comparison, the results VSTOXX futures series outperformed a for all VSTOXX Futures series (1-month, pure equity portfolio over the sample 3-month, LT) in efficient frontier form are period. The 3-month series performed included in Appendix 2. significantly better than 1-month series where allocation to volatility exposure managed to reduce portfolio volatility, but failed to improve the returns. In addition,

Figure 14: Impact of Adding Long Volatility Exposure to Equity Portfolio in 5% Increments

The effects of adding VSTOXX Futures (the 3-month series) to the EURO STOXX 50 portfolio in 5% increments, estimated based on the sample period ranging from April 2008 to April 2011.

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3.3. Transaction Costs adding the 1-month series no longer When considering futures as an instrument contributes to improving the performance for a long volatility exposure, we however over the pure equity case. The 3-month also need to take into consideration actual and longest-traded (LT) series still show trading costs (i.e. bid-ask spread) that some potential for improving portfolio are associated with the futures’ rollover diversification; however, the effect strategy. In order to access the full impact is mostly due to reduced volatility of of transaction costs, we incorporated the the overall portfolio with little if any bid-ask spread into the analysis. In this improvement in average performance. case, all long VSTOXX futures positions are rolled into at their ask prices then are In order to simulate the impact of trading closed at bid prices on the day prior to costs over a longer sample period, we maturity. The results of the analysis are applied average costs associated with presented in Appendix 3. Including the trading VSTOXX futures to VSTOXX Index bid-ask spread, costs significantly affect data that is available for the sample the performance of VSTOXX futures. The period ranging from January 1999 to April returns are decreased by 26.6%, 12.6% 2011. We used the maximum Sharpe ratio and 8.5% p.a. for 1-month, 3-month and portfolio that was estimated with VSTOXX longest-term (LT) futures, respectively. Index data in the previous section and After accounting for bid-ask spread costs, adjusted its performance for the costs that would be incurred if VSTOXX futures

Figure 15: Performance of EURO STOXX 50 Index and Diversified Portfolio with VSTOXX Futures Series

Daily time series for EURO STOXX 50 Index and diversified portfolios with VSTOXX Futures series on the sample period ranging from January 1999 to April 2011.

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were to actually be traded. The results are the standard deviation of returns from presented in Figure 15, and confirm the 21.6% (for GMV portfolio) to 16.1% (for benefits of introducing a long volatility diversified portfolio). Secondly, it would exposure even after the presence of also reduce negative returns for the trading costs are accounted for. sample period – from -2.8% (GMV) to -1.0% (diversified portfolio).

3.4. Comparison with a Global We can also take a closer look at both Minimum Variance Portfolio GMV and diversified portfolios with We also compare the performance of VSTOXX futures exposure performance the diversified portfolio with a managed during 2008 financial crisis (see Figure volatility position with VSTOXX futures 17). Both portfolios exhibit rather to one of the GMV portfolio. As in the similar performance until the middle of previous section, MSCI Europe Minimum September 2008, when unprecedented Volatility index is used as a proxy for losses in the market occurred, following the GMV portfolio and the diversified the failure of Lehman Brothers. After portfolio has 70% allocation to EURO that, the performance of GMV portfolio STOXX 50 and 30% allocation to VSTOXX deteriorated sharply resulting to 28.2% loss exposure. We used the best-performing in portfolio value. The diversified portfolio 3-month VSTOXX futures series to create with VSTOXX futures exposure managed an investment in VSTOXX index. to protect the investment value and even gain 7.4% due to significantly increased As indicated in Figure 16, the diversified volatility in the market. The volatility of portfolio with VSTOXX Futures presents the diversified portfolio returns was also a better investment opportunity than lower at 19.3% as compared to 31.0% GMV portfolio. Firstly, it would reduce volatility of GMV portfolio.

Figure 16: Performance of Diversified Portfolio with VSTOXX Futures and Global Minimum Variance (GMV) Portfolio

Daily time series for the diversified portfolio and MSCI Europe Minimum Volatility Index on the sample period ranging from April 2008 to April 2011.

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Figure 17: Performance of Diversified Portfolio with VSTOXX Futures and Global Minimum Variance (GMV) Portfolio in 2008

Daily time series for the diversified portfolio and MSCI Europe Minimum Volatility Index on the sample period ranging from January 2008 to December 2008.

Figure 18: Performance of Diversified Portfolio with VSTOXX Futures and Global Minimum Variance (GMV) Portfolio in 2010/2011

Daily time series for the diversified portfolio and MSCI Europe Minimum Volatility Index on the sample period ranging from January 2010 to December 2011.

In more recent periods, starting from GMV portfolio in bear market that started January 2010, the comparison of in May 2001, however in the following performances of GMV portfolio and less volatile period it decreased in value diversified portfolio with VSTOXX futures more than the GMV portfolio (-6.7% exposure is more complicated (see Figure p.a. vs. 6.8% for the GMV portfolio). This 18). The diversified portfolio with VSTOXX is mainly due to negative carry and roll futures exposure clearly outperformed the yield of VSTOXX futures, considering that

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3. Implementing the Analysis with Volatility Futures

a portfolio with a ‘theoretical’ investment in VSTOXX Index (see Figure 9) would achieve much better results during this period.

In summary, the results obtained in this section suggest that the benefits of adding a long volatility exposure to equity portfolios, which are particularly strong during market downturns, are robust with respect to the introduction of trading costs involved in implementation with volatility futures contracts. Careful attention to trade execution is nonetheless required to limit the negative impact of transaction costs, negative carry and roll yield on volatility futures during normal periods.

40 An EDHEC-Risk Institute Publication 4. Short-term Analysis with Volatility Options

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4. Short-term Analysis with Volatility Options

In this section, we consider a different In order to assess the impact of adding approach based on the use of volatility VSTOXX options to equity portfolios, options for gaining a long exposure to we constructed the portfolio strategy volatility. March 2010 witnessed the by rolling over one month to expiration introduction of option contracts on the VSTOXX call options. We use both at-the- VSTOXX index, which provided investors money (ATM) and out-of-the-money (10% with more flexibility for trading European OTM and 25% OTM) calls for our analysis. volatility. Each month, on the day before expiration, the options are rolled to the next month The data on VSTOXX put/call options is contract and the portfolio is rebalanced collected from the intraday transaction to the target weights. Considering that records provided by Eurex and Bloomberg. volatility options are much more sensitive to changes in underlying volatility compared to fully collateralised futures 4.1. Portfolio Analysis with VSTOXX contracts, we used 1% increments in Calls volatility exposure rather than 5% While futures contracts are the most increments used for VSTOXX futures. straightforward approach to gaining long volatility exposure, using options The results of the analysis are presented might allow investors to gain access to in Appendix 4. The performance of ATM the upside of volatility exposure without VSTOXX calls provides very similar results the associated downside. Empirical results to the VSTOXX futures. While adding a in several recent papers (Grant et al. small positive exposure to the volatility 2007; Szado 2009) actually suggest that index option portfolio (1% and 2%) call options have potential to provide a slightly improves the performance of the particularly effective diversification of overall portfolio, further increases provide equity risk compared to other financial no additional value. Due to increased instruments (e.g. volatility futures or leverage, the results achieved with OTM index puts). calls is much more favourable than those achieved with ATM calls; and in the It should be noted that the data history case of the 25% OTM calls, the return available for VSTOXX options is very short improvements are impressive. (ranging from March 2010 to April 2011). Due to an extremely short data history The performance of the portfolios with and corresponding sample size, it would increasing allocation to 25% OTM calls be difficult to provide a formal analysis of is depicted in an efficient frontier form the marginal benefits to be expected from in Figure 19. The portfolio with the best using volatility index futures as opposed performance (as compared with an all to volatility index options. Therefore, the equity case) is with 2% allocation to OTM analysis in this section is merely to be VSTOXX calls and the rest (98%) allocated regarded as an example of an alternative to equity. It should be noted that the way for structuring a long volatility diversified portfolio with a similar volatility exposure. of returns to that of the equity portfolio

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4. Short-term Analysis with Volatility Options

Figure 19: Impact of Adding VSTOXX 25% OTM options to Equity Portfolio in 1% Increments

The effects of adding VSTOXX OTM options to EURO STOXX 50 portfolio by 1% increments, estimated based on the sample period ranging from March 2010 to April 2011.

6 - We used the data from Eurex Top Level order book (19.4% p.a. vs. 22.8% p.a.) performed However, the benefits of adding OTM for estimating bid/ask significantly better in terms of returns (both 10% and 25%) calls are still clear, prices. However, the benefits of using options in this – while all equity portfolios resulted in even after including transaction costs in case might be somewhat understated; in practice, 0.95% p.a. return, the diversified portfolio the analysis. In both cases, holding a 2% when trades are executed, with OTM call exposure had an extremely allocation to volatility options ex-post led the actual spreads quoted in the market (approx. 0.3-0.5 attractive return of 12.3% p.a. during this to the highest “adjusted” Sharpe ratio. vol points) are lower than pure book quotes used in the period. For comparison, the results of the Compared to pure equity portfolio return analysis. portfolios with allocation to all VSTOXX of 0.95% during this period, the portfolios option series (i.e. ATM, 10% OTM and 25% with 2% allocations to 10% OTM and OTM) are presented in the Appendix 5. 25% OTM calls resulted in 5.2% p.a. and 15.8% p.a. returns respectively. Also, the volatility is even decreased with 10% OTM 4.2. Transaction Costs call allocation equalling to 17.12% as In further analysis, we estimated the compared with 22.8% of equity portfolio. impact of the bid-ask spread on the performance of the diversified portfolios with VSTOXX options exposure. In this 4.3. Protective EURO STOXX 50 puts case VSTOXX options are rolled in at the In this section, we compare the results ask price at the open and rolled out at obtained so far with the results that intrinsic value.6 The results for all series would be generated by a classic strategy are presented in Appendix 6. When bid-ask for managing downside risk in equity spread costs are taken into consideration, portfolios – the use of protective puts. adding ATM calls to the portfolio does In every financial textbook, protective not increase the returns, although, they puts are referred to as a direct hedge still reduce standard deviation of the for the price movements in equity portfolio. portfolios.

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4. Short-term Analysis with Volatility Options

Although, holding a long EURO STOXX 50 Appendix 7. We find that equity portfolios put position is a simple way to eliminate with EURO STOXX 50 put positions do equity portfolio losses in the declining not perform as well as portfolios mixed market, there is empirical evidence (e.g. with VSTOXX calls. None of the portfolios Szado 2009) that the opportunity might with EURO STOXX 50 puts have better be prohibitive because of the smile ‘adjusted’ Sharpe ratios than those of a effect (implied volatility of out-of-the- pure equity portfolio. While the allocation money puts tends to be higher than the to ATM puts helps to reduce volatility implied volatility of in-the-money puts). (although at the expense of decreasing In previous chapters, we proved that returns), allocation to OTM puts mostly the negative correlation between EURO increases volatility and results in losses STOXX 50 and VSTOXX is conditional in for the portfolio. nature and tends to be strongest in the large downward market moves, when it Overall, there seems to be an efficiency is needed the most. Considering these gain on our sample period from using conditions, one might expect that the VSTOXX derivatives or futures for diversification benefits of VSTOXX options downside risk protection on equity may provide a more efficient way to portfolios compared to using EUROSTOXX manage downside risk than EURO STOXX 50 put options. 50 puts.

In order to test this conjecture, we compare 4.4. Using Volatility Derivatives to the performance of an equity portfolio Bet on Volatility Changes with VSTOXX call allocations to that of Up to this point, we have mostly focused an equity portfolio mixed with long EURO on the diversification properties of STOXX 50 puts. For consistent analysis, we volatility derivatives. However, an investor use the same moneyness levels for EURO can also use VSTOXX options to trade on STOXX 50 puts as we used for VSTOXX a specific view on the VSTOXX direction calls (i.e. ATM, 10% OTM and 25% OTM). or volatility changes. In this section, we Each month, at the same rollover day as analyse the performance of two commonly used for VSTOXX calls, EURO STOXX 50 used strategies for generating premium: put positions are rolled over to the next (i) short out-of-the-money VSTOXX puts; month contract. ATM, 10% OTM and 25% and (ii) VSTOXX ratio spread strategy. OTM puts are added to the base equity portfolio using 1% increments. 4.4.1. Shorting out-of-the-money VSTOXX puts The performance of portfolios mixed with In order to implement this strategy, VSTOXX calls was analysed in section 4.1 an investor can sell VSTOXX puts on a and the results presented in Appendix 4. systematic basis if a rise in volatility The summary statistics of the performance levels is expected. If expected volatility of portfolios with EURO STOXX 50 puts is increasing, this position allows for the sample period ranging from premium income to be generated, while March 2010 to April 2011 is presented in also creating a long volatility exposure.

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4. Short-term Analysis with Volatility Options

However, its performance can be poor applying this approach, it turns out that if volatility starts declining after a large all short VSTOXX put positions expire out spike. of the money and a full premium is earned. As a result, it significantly improved the We first test this strategy by estimating the performance of the strategy based on position’s performance of selling the next shorting out-of-the-money VSTOXX put downside puts on each monthly rollover options. A summary statistic for an equity day for the sample period ranging from portfolio with a 1% increasing allocation March 2010 to April 2011. This position is to short VSTOXX puts is presented in then added to the equity portfolio in 1% Appendix 8. A short VSTOXX put positioned increments to evaluate its effectiveness in with carefully selected strikes during the overall portfolio management. The results sample period resulted in a significant (presented in Appendix 8) indicate that profit with each additional 1% of VSTOXX although this strategy slightly reduced put allocation, resulting in over 10% p.a. overall portfolio volatility (from 22.8% return increase (although it was somehow p.a. of equity portfolio to 19.4% p.a. with less effective in reducing volatility). 2% investment in short VSTOXX puts), it did not improve the returns. This is due The improvement in overall portfolio to decreasing VSTOXX levels during this performance driven by using the ‘tiered’ period, as selling downside put strikes approach for selecting short VSTOXX put commonly resulted in a loss. All premium strikes is substantial. For example, a pure income earned was eroded as volatility equity portfolio earns 0.95% p.a. return dropped following May sovereign crisis in with 22.8% p.a. volatility for the sample 2010. period, and the portfolio with 2% short VSTOXX put allocation, that has a similar An alternative way for implementing this 22.8% volatility, results in an impressive strategy includes a more careful selection 24.4% p.a. return over the same period. of put strikes. In this case, out-of-the- money VSTOXX puts are sold on a ‘tiered’ 4.4.2. A ratio call spread strategy basis. We used the following rules for The ratio spread is a strategy that involves selecting out-of-the-money VSTOXX puts. buying a number of options and selling more options of the same underlying This approach allows for picking deeper stock at expiration and at a different out-of-the-money puts when volatility strike price. This strategy is consistent level is high, and it is therefore more likely with the view that the underlying asset to mean-revert back to a lower level. By (in this case, a volatility index) will

Table 3: ‘Tiered’ Approach for Selecting Short VSTOXX Put Strikes VSTOXX Front Month Futures VSTOXX Put Strike with Distance to Future <25 5 25-30 7.5 30-35 10 35-40 15

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4. Short-term Analysis with Volatility Options

experience little volatility in the near 1% increments. The results for both term. Hence, the ratio call spread strategy strategies are presented in Appendix 9. is used to get upside exposure to volatility We can conclude that the first strategy at a reduced premium outlay. While this with a fixed 5 volatility points difference position benefits from ‘modest’ increases between strikes was, somehow, useful in VSTOXX levels, it is, however exposed to in reducing volatility (from 22.8% p.a. the risk of a large volatility spike. of equity portfolio to 16.0% p.a. with 2% investment in short VSTOXX puts), Implied volatility of VSTOXX options is however, it resulted in significant losses typically quite high (at levels of 80%) for the portfolio over the sample period. and, in addition, the call skew can be quite steep. We can capitalise upon this The second ‘tiered’ approach was more by selling two deep out-of-the money successful in improving return, however, at VSTOXX calls and using the proceeds to the expense of increased overall volatility purchase a closer out-of-the-money of the portfolio. For example, the equity call. As in the previous section, we tested portfolio with 2% allocation to the call this strategy with two approaches. First, ratio spread generates a return of 4.2% on each monthly rollover day, two 25% p.a. with 36.4% p.a. volatility over the OTM calls are sold and one closer OTM call sample period. In comparison, an equity with the strike difference of 5 volatility portfolio with 2% allocation to pure 25% points is bought. The second approach OTM VSTOXX call position earns 22.0% tested is a ‘tiered’ approach, where we p.a. return with 30.8% p.a. volatility. still sell two 25% OTM calls, but the strike of a purchased closer OTM call is selected We introduced both short out-of- based on the following rules. the-money VSTOXX puts and ratio call strategies as examples of how By applying a ‘tiered’ approach, we would VSTOXX options can be used in more sell further out-of-the-money calls in innovative ways for the equity portfolio low volatility regime to avoid losing management. In both cases, a careful on the first two short calls if VSTOXX selection of option strike prices proved increases sharply, while, in high volatility to be critical for portfolio performance. regime, the overall increase in volatility of Therefore, it is important to take current volatility would impact the call skew and market volatility conditions into account provide more premium for two sold deep when designing and implementing an out-of-the-money calls. option trading strategy.

In each case, the call ratio spread position was added to the equity portfolio in

Table 4: ‘Tiered’ Approach for Selecting VSTOXX Call Strikes VSTOXX Front Month Futures VSTOXX Call Strike with Distance to Future <25 10 25-35 7.5 >35 5

46 An EDHEC-Risk Institute Publication 5. Conclusion

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5. Conclusion

In this paper, we analyse a novel approach introduction of trading costs associated in the design of attractive equity solutions with rolling over volatility derivatives with managed volatility, based on mixing contracts. a well-diversified equity portfolio with volatility derivatives, as opposed to minimising equity volatility through minimum variance approaches. The results we obtain suggest that a long volatility position shows a strongly negative correlation with respect to the underlying equity portfolio and that adding a long volatility exposure to an equity portfolio would result in a substantial improvement of the risk-adjusted performance of the portfolio. The benefits of the long volatility exposure are found to be strongest in market downturns, when they are most needed.

We also compare the performance of the diversified equity portfolios including volatility derivatives with that of global minimum variance (GMV) portfolios that are commonly used in the industry as a benchmark strategy for reducing portfolio risk. We found that the diversified portfolio with long volatility exposure is a more efficient approach for managing risk.

We also consider the challenges related to a practical implementation of this strategy by using derivatives instruments – futures and options – that allow investors direct access to trading volatility. We consider how increasing allocation to volatility derivatives affects the portfolio performance; we also evaluate transaction costs in each case and discuss the advantages/disadvantages for using each type of instrument. The benefits of adding volatility exposure to equity portfolios are found to be robust with respect to the

48 An EDHEC-Risk Institute Publication Appendix

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Appendix

Appendix1 Summary Statistics for Portfolios with Increasing Allocation to VSTOXX Futures

Jun/2009 – Apr/2011 ... 5% VSTOXX Futures 5% VSTOXX 10% VSTOXX Futures VSTOXX 10% 95% VSTOXX Futures 95% VSTOXX 15% VSTOXX Futures 15% VSTOXX Futures 20% VSTOXX Futures 25% VSTOXX Futures 30% VSTOXX Futures 35% VSTOXX Futures 40% VSTOXX 100% VSTOXXFutures 100% 5% EURO STOXX 50 + 5% EURO STOXX 100% EURO STOXX 50 EURO STOXX 100% 70% EURO STOXX 50 + EURO STOXX 70% 95% EURO STOXX 50 + 95% EURO STOXX 50 + 85% EURO STOXX 50 + 80% EURO STOXX 50 + 75% EURO STOXX 50 + 65% EURO STOXX 50 + 60% EURO STOXX 90 % EURO STOXX 50 + 90 % EURO STOXX

1-Month Futures Time Series : Annualised -7.47% -6.68% -6.25% -6.14% -6.34% -6.84% -7.61% -8.63% -9.88% ... -34.14% -36.82% Return Annualised 29.48% 24.80% 21.18% 18.87% 18.13% 18.95% 21.04% 23.99% 27.47% ... 73.84% 78.11% Std Deviation Adj. Sharpe - 0.03 0.06 0.07 0.06 0.03 -0.01 -0.048 -0.09 ... -0.36 -0.38 Ratio* 3-Month Futures Time Series : Annualised -7.47% -5.87% -4.50% -3.33% -2.35% -1.57% -0.97% -0.53% -0.26% ... -6.51% -7.78% Return Annualised 29.48% 25,01% 21,25% 18,30% 16,36% 15.59% 16.06% 17.56% 19.82% ... 57.34% 61.07% Std Deviation Adj. Sharpe - 0.06 0.14 0.23 0.31 0.38 0.41 0.40 0.36 ... 0.02 -0.01 Ratio* LT Futures Time Series : Annualised -7.47% -6.16% -5.11% -4.29% -3.68% -3.27% -3.05% -3.01% -3.13% ... -13.41% -15.02% Return Annualised 29.48% 25.30% 21.87% 19.25% 17.53% 16.78% 17.01% 18.09% 19.81% ... 51.58% 54.82% Std Deviation Adj. Sharpe - 0.05 0.11 0.17 0.22 0.25 0.26 0.25 0.22 ... -0.12 -0.14 Ratio* *Note: Due to negative returns, a traditional Sharpe ratio would result in negative values that are difficult to interpret. We adjusted the performance measure, where, instead of calculating excess returns over a risk-free rate, we estimated them over a specific benchmark (i.e. EURO STOXX 50 Index return). This measure indicates how well each portfolio performed when compared to all equity portfolio cases, adjusted for the riskiness of the portfolio.

50 An EDHEC-Risk Institute Publication The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

Appendix

Appendix 2 Impact of Adding VSTOXX Index Futures exposure to Equity portfolio in 5% increments

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Appendix

Appendix 3 Summary Statistics for Portfolios with Increasing Allocation to VSTOXX Futures (Including Bid-Ask Spread Costs)

Jun/2009 – Apr/2011 ... 5% VSTOXX Futures 5% VSTOXX 10% VSTOXX Futures VSTOXX 10% 95% VSTOXX Futures 95% VSTOXX 15% VSTOXX Futures 15% VSTOXX Futures 20% VSTOXX Futures 25% VSTOXX Futures 30% VSTOXX Futures 35% VSTOXX Futures 40% VSTOXX 5% EURO STOXX 50 + 5% EURO STOXX 100% VSTOXX Futures VSTOXX 100% 100% EURO STOXX 50 EURO STOXX 100% 70% EURO STOXX 50 + EURO STOXX 70% 95% EURO STOXX 50 + 95% EURO STOXX 50 + 85% EURO STOXX 50 + 80% EURO STOXX 50 + 75% EURO STOXX 50 + 65% EURO STOXX 50 + 60% EURO STOXX 90 % EURO STOXX 50 + 90 % EURO STOXX

1-Month Futures Time Series : Ann. Return -7.47% -9.01% -10.89% -13.06% -15.48% -18.12% -20.93% -23.89% -26.96% ... -61,65% -64.46% Ann. Std 29,48% 24,88% 21,34% 19,09% 18,39% 19,23% 21,32% 24,28% 27,79% ... 75,54% 80,19% Deviation Adj. Sharpe - -0.06 -0.16 -0.29 -0.44 -0.55 -0.63 -0.68 -0.70 ... -0.72 -0.711 Ratio* 3-Month Futures Time Series : Ann. Return -7.47% -6.50% -5.77% -5.26% -4.94% -4.82% -4.88% -5.11% -5.51% ... -18.53% -20.35% Ann. Std 29.48% 25.02% 21.27% 18.31% 16.35% 15.56% 15.99% 17.48% 19.74% ... 58.02% 61.86% Deviation Adj. Sharpe - 0.04 0.08 0.12 0.15 0.17 0.16 0.14 0.10 ... -0.19 -0.21 Ratio* LT Futures Time Series : Ann. Return -7.47% -6.71% -6.19% -5.89% -5.80% -5.89% -6.15% -6.58% -7.17% ... -19.92% -23.54% Ann. Std 29.48% 25.35% 21.95% 19.32% 17.57% 16.77% 16.95% 17.98% 19.68% ... 52.03% 55.43% Deviation Adj. Sharpe - 0.03 0.06 0.08 0.09 0.09 0.08 0.05 0.02 ... -0.24 -0.29 Ratio* *Note: Due to negative returns, a traditional Sharp ratio would result in negative values that are difficult to interpret. We adjusted the performance measure, where, instead of calculating excess returns over a risk-free rate, we estimated them over a specific benchmark (i.e. EURO STOXX 50 Index return). This measure indicates how well each portfolio performed when compared to all equity portfolio cases, adjusted for the riskiness of the portfolio.

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Appendix

Appendix 4 Summary Statistics for Portfolios with Increasing Allocation to VSTOXX Calls

Mar/20010 – Apr/2011 ... VSTOXX Options VSTOXX 1% VSTOXX Options 1% VSTOXX Options 2% VSTOXX Options 3% VSTOXX Options 5% VSTOXX Options 6% VSTOXX Options 7% VSTOXX Options 8% VSTOXX Options 9% VSTOXX 100% EURO STOXX 50 EURO STOXX 100% 100% VSTOXX Options VSTOXX 100% 91% EURO STOXX 50 + EURO STOXX 91% 99% EURO STOXX 50 + 99% EURO STOXX 50 + 97% EURO STOXX 50 + 95% EURO STOXX 50 + 94% EURO STOXX 50 + 93% EURO STOXX 50 + 92% EURO STOXX 98 % EURO STOXX 50 + 98 % EURO STOXX 96% EURO STOX 50 + 4% 96% EURO STOX

ATM Calls : Ann. Return 0.95% 1.29% 0.96% 0.02% -1.46% -3.43% -5.80% -8.53% -11.56% -14.83% ... -100.00% Ann. Std 22.81% 18.03% 16.01% 17.12% 20.48% 24.95% 29.86% 34.92% 39.98% 44.99% ... 777.31% Deviation Adj. Sharpe - 0.02 0.00 -0.05 -0.12 -0.18 -0.23 -0.27 -0.31 -0.35 ... -0.13 Ratio* 10% OTM Calls : Ann. Return 0.95% 5.80% 9.53% 12.19% 13.84% 14.57% 14.44% 13.54% 11.96% 9.78% ... -100% Ann. Std 22.81% 17.29% 18.29% 23.82% 30.93% 38.37% 45.74% 52.89% 59.80% 66.46% ... 758.83% Deviation Adj. Sharpe - 0.28 0.47 0.47 0.42 0.35 0.30 0.24 0.18 0.13 ... -0.13 Ratio* 25% OTM Calls : Ann. Return 0.95% 12.31% 22.03% 30.12% 36.60% 41.54% 45.02% 47.13% 47.97% 47.67% ... -100% Ann. Std 22.81% 19.37% 30.85% 45.24% 59.47% 73.07% 86.02% 98.37% 110.19% 121.48% ... 1012.56% Deviation Adj. Sharpe - 0.59 0.68 0.64 0.60 0.56 0.51 0.47 0.43 0.38 ... -0.10 Ratio* *Note: Due to negative returns, a traditional Sharpe ratio would result in negative values that are difficult to interpret. We adjusted the performance measure, where, instead of calculating excess returns over a risk-free rate, we estimated them over a specific benchmark (i.e. EURO STOXX 50 Index return). This measure indicates how well each portfolio performed when compared to all equity portfolio cases, adjusted for the riskiness of the portfolio.

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Appendix

Appendix 5 Impact of Adding VSTOXX Index Options exposure to Equity portfolio in 1% increments

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Appendix

Appendix 6 Summary Statistics for Portfolios with Increasing Allocation to VSTOXX Calls (With Bid-Ask Spread Costs)

Mar/20010 – Apr/2011 ... VSTOXX Options VSTOXX 1% VSTOXX Options 1% VSTOXX Options 2% VSTOXX Options 3% VSTOXX Options 5% VSTOXX Options 6% VSTOXX Options 7% VSTOXX Options 8% VSTOXX Options 9% VSTOXX 100% VSTOXXOptions 100% 100% EURO STOXX 50 EURO STOXX 100% 91% EURO STOXX 50 + EURO STOXX 91% 99% EURO STOXX 50 + 99% EURO STOXX 50 + 97% EURO STOXX 50 + 95% EURO STOXX 50 + 94% EURO STOXX 50 + 93% EURO STOXX 50 + 92% EURO STOXX 98 % EURO STOXX 50 + 98 % EURO STOXX 96% EURO STOX 50 + 4% 96% EURO STOX

ATM Calls : Ann. Return 0.95% 0.76% -0.04% -1.38% -3.21% -5.46% -8.07% -10.99% -14.16% -17.53% ... -100.00% Ann. Std 22.81% 18.27% 16.00% 16.44% 19.07% 22.92% 27.32% 31.95% 36.64% 41.30% ... 785.92% Deviation Adj. Sharpe - -0.01 -0.06 -0.14 -0.22 -0.28 -0.33 -0.37 -0.41 -0.45 ... -0.13 Ratio* 10% OTM Calls : Ann. Return 0.95% 3.51% 5.15% 5.95% 5.97% 5.29% 3.97% 2.1% -0.27% -3.05% ... -100.00% Ann. Std 22.81% 17.67% 17.10% 20.60% 26.11% 32.30% 38.64% 44.94% 51.11% 57.12% ... 776.10% Deviation Adj. Sharpe - 0.14 0.25 0.24 0.19 0.13 0.08 0.03 -0.02 -0.07 ... -0.13 Ratio* 25% OTM Calls : Ann. Return 0.95% 9.52% 15.82% 20.16% 22.80% 23.97% 23.87% 22.70% 20.62% 17.78% ... -100.00% Ann. Std 22.81% 20.39% 28.20% 39.39% 51.09% 62.59% 73.73% 84.47% 94.84% 104.8% ... 1034.10% Deviation Adj. Sharpe - 0.42 0.53 0.49 0.43 0.37 0.31 0.26 0.21 0.16 ... -0.10 Ratio* *Note: Due to negative returns, a traditional Sharpe ratio would result in negative values that are difficult to interpret. We adjusted the performance measure, where, instead of calculating excess returns over a risk-free rate, we estimated them over a specific benchmark (i.e. EURO STOXX 50 Index return). This measure indicates how well each portfolio performed when compared to all equity portfolio cases, adjusted for the riskiness of the portfolio.

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Appendix

Appendix 7 Summary Statistics for Portfolios with Increasing Allocation to EURO STOXX 50 Puts

Mar/20010 – Apr/2011 ... VSTOXX Options VSTOXX 1% VSTOXX Options 1% VSTOXX Options 2% VSTOXX Options 3% VSTOXX Options 5% VSTOXX Options 6% VSTOXX Options 7% VSTOXX Options 8% VSTOXX Options 9% VSTOXX 100% VSTOXXOptions 100% 100% EURO STOXX 50 EURO STOXX 100% 91% EURO STOXX 50 + EURO STOXX 91% 99% EURO STOXX 50 + 99% EURO STOXX 50 + 97% EURO STOXX 50 + 95% EURO STOXX 50 + 94% EURO STOXX 50 + 93% EURO STOXX 50 + 92% EURO STOXX 98 % EURO STOXX 50 + 98 % EURO STOXX 96% EURO STOX 50 + 4% 96% EURO STOX

ATM Puts : Ann. Return 0.95% 0.33% -0.68% -2.04% -3.71% -5.65% -7.84% -10.24% -12.81% -15.54% ... -100.00% Ann. Std 22.81% 17.77% 13.65% 11.15% 11.12% 13.38% 16.91% 21.00% 25.31% 29.71% ... 537.62% Deviation Adj. Sharpe - -0.03 -0.12 -0.27 -0.42 -0.49 -0.52 -0.53 -0.54 -0.55 ... -0.19 Ratio* 10% OTM Puts : Ann. Return 0.95% -1.50% -4.34% -7.52% -10.95% -14.57% -18.34% -22.20% -26.11% -30.03% ... -100% Ann. Std 22.81% 16.31% 19.50% 27.56% 36.63% 45.68% 54.49% 63.02% 71.28% 79.30% ... 912.51% Deviation Adj. Sharpe - -0.15 -0.27 -0.31 -0.32 -0.34 -0.35 -0.37 -0.38 -0.39 ... -0.11 Ratio* 25% OTM Puts : Ann. Return 0.95% -7.88% -16.02% -23.51% -30.39% -36.72% -42.54% -47.87% -52.75% -57.22% ... -100% Ann. Std 22.81% 19.78% 27.84% 38.93% 50.26% 61.28% 71.89% 82.09% 91.93% 101.43% ... 116.25% Deviation Adj. Sharpe - -0.45 -0.61 -0.63 -0.62 -0.61 -0.60 -0.59 -0.58 -0.57 ... -0.10 Ratio* *Note: Due to negative returns, a traditional Sharpe ratio would result in negative values that are difficult to interpret. We adjusted the performance measure, where, instead of calculating excess returns over a risk-free rate, we estimated them over a specific benchmark (i.e. EURO STOXX 50 Index return). This measure indicates how well each portfolio performed when compared to all equity portfolio cases, adjusted for the riskiness of the portfolio.

56 An EDHEC-Risk Institute Publication The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

Appendix

Appendix 8 Summary Statistics for Portfolios with Increasing Allocation to Short VSTOXX Puts

Mar/20010 – Apr/2011 ... VSTOXX Options VSTOXX 1% VSTOXX Options 1% VSTOXX Options 2% VSTOXX Options 3% VSTOXX Options 5% VSTOXX Options 6% VSTOXX Options 7% VSTOXX Options 8% VSTOXX Options 9% VSTOXX 100% VSTOXXOptions 100% 100% EURO STOXX 50 EURO STOXX 100% 91% EURO STOXX 50 + EURO STOXX 91% 99% EURO STOXX 50 + 99% EURO STOXX 50 + 97% EURO STOXX 50 + 95% EURO STOXX 50 + 94% EURO STOXX 50 + 93% EURO STOXX 50 + 92% EURO STOXX 98 % EURO STOXX 50 + 98 % EURO STOXX 96% EURO STOX 50 + 4% 96% EURO STOX

‘Next Strike Down’ : Ann. Return 0.95% -1.92% -4.85% -7.85% -10.90% -13.99% -17.12% -20.27% -23.45% -26.63% ... n/a Ann. Std 22.81% 21.10% 19.93% 19.41% 19.62% 20.53% 22.08% 24.15% 26.64% 29.45% ... n/a Deviation Adj. Sharpe - -0.14 -0.29 -0.45 -0.60 -0.73 -0.82 -0.88 -0.92 -0.94 ... n/a Ratio* ‘Tiered’ Approach : Ann. Return 0.95% 12.11% 24.39% 37.88% 52.69% 68.94% 86.75% 106.3% 127.61% 150.96% ... n/a Ann. Std 22.81% 21.56% 21.81% 23.61% 26.72% 30.85% 35.72% 41.15% 47.06% 53.37% ... n/a Deviation Adj. Sharpe - 0.52 1.07 1.56 1.94 2.20 2.40 2.56 2.69 2.81 ... n/a Ratio* *Note: Due to negative returns, a traditional Sharpe ratio would result in negative values that are difficult to interpret. We adjusted the performance measure, where, instead of calculating excess returns over a risk-free rate, we estimated them over a specific benchmark (i.e. EURO STOXX 50 Index return). This measure indicates how well each portfolio performed when compared to all equity portfolio cases, adjusted for the riskiness of the portfolio.

An EDHEC-Risk Institute Publication 57 The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

Appendix

Appendix 9 Summary Statistics for Portfolios with Increasing Allocation to Ratio Spread Strategy

Mar/20010 – Apr/2011 ... VSTOXX Options VSTOXX 1% VSTOXX Options 1% VSTOXX Options 2% VSTOXX Options 3% VSTOXX Options 5% VSTOXX Options 6% VSTOXX Options 7% VSTOXX Options 8% VSTOXX Options 9% VSTOXX 100% VSTOXXOptions 100% 100% EURO STOXX 50 EURO STOXX 100% 91% EURO STOXX 50 + EURO STOXX 91% 99% EURO STOXX 50 + 99% EURO STOXX 50 + 97% EURO STOXX 50 + 95% EURO STOXX 50 + 94% EURO STOXX 50 + 93% EURO STOXX 50 + 92% EURO STOXX 98 % EURO STOXX 50 + 98 % EURO STOXX 96% EURO STOX 50 + 4% 96% EURO STOX

Strike Difference - 5 vol points: Ann. Return 0.95% -39.24% -83.81% n/a n/a n/a n/a n/a n/a n/a ... n/a Ann. Std 22.81% 18.03% 16.01% n/a n/a n/a n/a n/a n/a n/a ... n/a Deviation Adj. Sharpe - -0.36 -0.16 n/a n/a n/a n/a n/a n/a n/a ... n/a Ratio* ‘Tiered’ Approach : Ann. Return 0.95% 2.65% 4.18% 5.54% 6.71% 7.67% 8.42% 8.93% 9.20% 9.21% ... n/a Ann. Std 22.81% 28.32% 36.36% 45.59% 55.45% 65.69% 76.25% 87.11% 98.29% 109.83% ... n/a Deviation Adj. Sharpe - 0.06 0.09 0.10 0.10 0.10 0.10 0.09 0.08 0.08 ... n/a Ratio* *Note: Due to negative returns, a traditional Sharpe ratio would result in negative values that are difficult to interpret. We adjusted the performance measure, where, instead of calculating excess returns over a risk-free rate, we estimated them over a specific benchmark (i.e. EURO STOXX 50 Index return). This measure indicates how well each portfolio performed when compared to all equity portfolio cases, adjusted for the riskiness of the portfolio.

58 An EDHEC-Risk Institute Publication References

An EDHEC-Risk Institute Publication 59 The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

References

• Alexander, C., and D.Korovilas (2011), “The Hazards of Volatility Diversification”, working paper. • Bakshi, G., and N. Kapadia (2003), “Delta-Hedged Gains and the Negative Market Volatility Risk Premium”, The Review of Financial Studies, 16, 2, 527-566. • Bekaert, G., and G. Wu (2000), “Asymmetric Volatilities and Risk in Equity Markets”, Review of Financial Studies, 13, 1, 1-42. • Black, F. (1976), “Studies in Stock Price Volatility Changes”, Proceedings of the 1976 Business Meeting of the Business and Economic Statistic Section, American Statistical Association, p 177-181, 22. • Briere, M. A. Burgues and O.Signori (2009), “Volatility as an Asset Class for Long-Term Investors”, working paper. • Carr, P, and L. Wu (2009), “Variance Risk Premiums”, Review of Financial Studies, 22, 3, 1311-1341. • Chen, H., S. Chung, and K. Ho (2010), “The diversification effects of volatility-related assets”, Journal of Banking and Finance. • Christie, A. (1982), “The Stochastic Behavior of Common Stock Variances: Value, Leverage and Interest Rate Effects”, Journal of Financial Economics, 10, p. 407-432. • Cornish E., R. Fisher (1937), “Moments and Cumulants in the Specification of Distributions”, Review of International Statistical Institute, 307-320. • Daigler, R. T. And L. Rossi (2006), “A Portfolio of Stocks and Volatility”, Journal of Investing (Summer) 99-106. • Dash, S. and M.T. Moran (2005), “VIX as a Companion for Hedge Fund Portfolios”, Journal of Alternative Investments (Winter) 75-80. • Dash, S. And M.T. Moran (2007), “VIX Futures and Options: Pricing and Using Volatility Products to Manage Downside Risk and Improve Efficiency in Equity Portfolios”, The Journal of Trading, 2, 3, 96-105. • Favre, L. J. Galeano (2002), “Mean Modified Value-at-Risk Optimisation with Hedge Funds”, Journal of Alternative Investments, 5, 2, 21-25. • French, K., G. Schwert, and R. Stambaugh (1987), “Expected Stock Return and Volatility”, Journal of Financial Economics, 19, 3-30. • Grant, M., K. Gregory and J. Lui (2007), “Considering All Options”, Goldman Sachs Global Investment Research (14 August). • Grant, M., K. Gregory and J. Lui (2007), “Volatility as an Asset”, Goldman Sachs Global Investment Research (15 November). • Hafner, R., and M. Wallmeier (2008), “Optimal Investments in Volatility”, Financial Markets and Portfolio Management, 22, 2, 147-167.

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References

• Kim, C., J. Morley, and C. Nelson (2004), “Is there a Positive Relationship between Stock Market Volatility and the Equity Premium?”, Journal of Money, Credit and Banking, 36, 3, 339-360. • Lee, B. And Y. Lin (2010), “Using Volatility Instruments as Extreme Downside Hedges”, working paper. • Ma, C., J. Mercer, and M. Walker (1992), “Rolling over Futures Contracts: A Note”, Journal of Futures Markets, 12, 2, 203-217. • Martellini, L. And V. Ziemann (2007), “Extending Black-Litterman analysis beyond the mean-variance framework”, The Journal of Portfolio Management, 33, 4, 33-44. • Perlin, M. (2010), “MS_Regress – The MATLAB Package for Markov Regime Switching Models”, available at SSRN: http://ssrn.com/abstract=1714016. • Schwert, G. (1989), “Why Does the Stock Market Volatility Change over Time”, Journal of Finance, 44, 5, 1115-1153. • Szado E. (2009), “VIX Futures and Options – A Case Study of Portfolio Diversification, During the 2008 Financial Crisis”, working paper, University of Amherst. • Toikka, M., E.K. Tom, S. Chadwick, and M. Bolt-Christmas (2004), “Volatility as an Asset?” CSFB Equity and Dervatives Strategy (26 February). • Wu, G. (2001), “The Determinants of Asymmetric Volatility”, Review of Financial Studies, 14, 837-859.

An EDHEC-Risk Institute Publication 61 The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

References

62 An EDHEC-Risk Institute Publication About EDHEC-Risk Institute

An EDHEC-Risk Institute Publication 63 The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012 The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

About EDHEC-Risk Institute

Founded in 1906, EDHEC is The Choice of Asset Allocation and a business viewpoint by the Institute's one of the foremost and Risk Management advisory board. This board is made up of international business schools. EDHEC-Risk structures all of its research work internationally recognised researchers, Accredited by the three main international academic around asset allocation and risk management. the Institute's business partners, and organisations, EQUIS, AACSB, This issue corresponds to a genuine representatives of major international and Association of MBAs, expectation from the market. On the one institutional investors. Management of the EDHEC has for a number of hand, the prevailing stock market situation research programmes respects a rigorous years been pursuing a strategy of international excellence that in recent years has shown the limitations of validation process, which guarantees the led it to set up EDHEC-Risk in diversification alone as a risk management scientific quality and the operational 2001. With eighty professors, technique and the usefulness of approaches usefulness of the programmes. research engineers, and research based on dynamic portfolio allocation. On the associates, EDHEC-Risk has the largest asset management other, the appearance of new asset classes Six research programmes have been research team in Europe. (hedge funds, private equity, real assets), conducted by the centre to date: with risk profiles that are very different • Asset allocation and alternative from those of the traditional investment diversification universe, constitutes a new opportunity • Style and performance analysis and challenge for the implementation of • Indices and benchmarking allocation in an asset management or asset- • Operational risks and performance liability management context. • Asset allocation and derivative instruments This strategic choice is applied to all of the • ALM and asset management Institute's research programmes, whether they involve proposing new methods of These programmes receive the support of strategic allocation, which integrate the a large number of financial companies. alternative class; taking extreme risks into The results of the research programmes account in portfolio construction; studying are disseminated through the EDHEC- the usefulness of derivatives in implementing Risk locations in Singapore, which asset-liability management approaches; was established at the invitation of or orienting the concept of dynamic the Monetary Authority of Singapore “core-satellite” investment management in (MAS), the City of London in the United the framework of absolute return or target- Kingdom, and Nice, France. In addition, it date funds. has a research team located in the United States.

Academic Excellence EDHEC-Risk has developed a close and Industry Relevance partnership with a small number of In an attempt to ensure that the research sponsors within the framework of research it carries out is truly applicable, EDHEC has chairs or major research projects: implemented a dual validation system for • Core-Satellite and ETF Investment, the work of EDHEC-Risk. All research work in partnership with Amundi ETF must be part of a research programme, • Regulation and Institutional the relevance and goals of which have Investment, in partnership with AXA been validated from both an academic Investment Managers

64 An EDHEC-Risk Institute Publication The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

About EDHEC-Risk Institute

• Asset-Liability Management and The philosophy of the Institute is to Institutional Investment Management, validate its work by publication in in partnership with BNP Paribas international academic journals, as well as Investment Partners to make it available to the sector through • Risk and Regulation in the European its position papers, published studies, and Fund Management Industry, conferences. in partnership with CACEIS • Exploring the Commodity Futures Each year, EDHEC-Risk organises two Risk Premium: Implications for Asset conferences for professionals in order to Allocation and Regulation, present the results of its research, one in in partnership with CME Group London (EDHEC-Risk Days – Europe) and • Asset-Liability Management one in Singapore (EDHEC-Risk Days – Asia), Techniques for Sovereign Wealth attracting more than 2,000 professional Fund Management, delegates. in partnership with Deutsche Bank • The Benefits of Volatility Derivatives EDHEC also provides professionals with in Equity Portfolio Management, access to its website, www.edhec-risk.com, in partnership with Eurex which is entirely devoted to international • Structured Products and Derivative asset management research. The website, Instruments, sponsored by the French which has more than 50,000 regular Banking Federation (FBF) visitors, is aimed at professionals who • Advanced Modelling for Alternative wish to benefit from EDHEC’s analysis and Investments, in partnership with expertise in the area of applied portfolio Newedge Prime Brokerage management research. Its monthly • Advanced Investment Solutions for newsletter is distributed to more than Liability Hedging for Inflation Risk, 1,000,000 readers. in partnership with Ontario Teachers’ Pension Plan EDHEC-Risk Institute: • The Case for Inflation-Linked Key Figures, 2010-2011 Corporate Bonds: Issuers’ and Investors’ Nbr of permanent staff 80 Perspectives, Nbr of research associates 19 in partnership with Rothschild & Cie Nbr of affiliate professors 26 • Solvency II Benchmarks, Overall budget €11,200,000 in partnership with Russell Investments External financing €6,215,000 • Structured Equity Investment Nbr of conference delegates 1,850 Strategies for Long-Term Asian Investors, Nbr of participants at EDHEC-Risk 391 in partnership with Société Générale Indices & Benchmarks seminars Nbr of participants at EDHEC-Risk Corporate & Investment Banking 419 Institute Risk Management seminars Nbr of participants at EDHEC-Risk 356 Institute Executive Education seminars

An EDHEC-Risk Institute Publication 65 The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

About EDHEC-Risk Institute

The EDHEC-Risk Institute PhD in indices and benchmarks that provide more Finance efficient or more academic-based solutions The EDHEC-Risk Institute PhD in Finance to investors’ needs than current offers is designed for professionals who aspire available on the market. to higher intellectual levels and aim to redefine the investment banking and asset management industries. It is offered in two tracks: a residential track for high-potential graduate students, who hold part-time positions at EDHEC, and an executive track for practitioners who keep their full-time jobs. Drawing its faculty from the world’s best universities and enjoying the support of the research centre with the greatest impact on the financial industry, the EDHEC- Risk Institute PhD in Finance creates an extraordinary platform for professional development and industry innovation.

Research for Business The Institute’s activities have also given rise to executive education and research service offshoots. EDHEC-Risk's executive education programmes help investment professionals to upgrade their skills with advanced risk and asset management training across traditional and alternative classes. In partnership with CFA Institute, it has developed advanced seminars based on its research which are available to CFA charterholders and have been taking place since 2008 in New York, Singapore and London.

While EDHEC-Risk makes important public contributions to the advancement of applied financial research and the improvement of industry practices, the insights drawn from EDHEC-Risk’s “Indices & Benchmarking”, “ALM and Asset Management” and “Derivatives and Asset Management” research programmes over the past several years have led to a series of

66 An EDHEC-Risk Institute Publication About Eurex Exchange

An EDHEC-Risk Institute Publication 67 The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

Eurex Exchange

Eurex Exchange is one of the world’s leading derivatives exchanges. Our wide range of more than 1,600 products across eleven traditional and alternative asset classes provides our customers a broad diversity and thus greater opportunities.

The product portfolio includes liquid equity- based contracts on indexes, single equities, ETFs and dividends. Furthermore, volatility, weather, property and a growing choice in commodity derivatives complement our broad offering. At Eurex Exchange you can also trade one of the world’s most liquid fixed income markets. And you can enter off-order book trades through our EurexOTC Trade Entry services – giving you opportunity to trade big volume without execution risk.

You will find all this on one single platform – and Eurex Exchange’s innovative and reliable technology provides more than 430 members and about 8,300 traders with access to our products and services.

Eurex Exchange is a member of Eurex Group. Today, the Group comprises six integrated businesses with representative offices in all major financial centers around the world: Eurex Exchange, the International Securities Exchange, the European Energy Exchange, Eurex Clearing, Eurex Bonds and Eurex Repo.

www.eurexchange.com

68 An EDHEC-Risk Institute Publication EDHEC-Risk Institute Publications and Position Papers (2009-2012)

An EDHEC-Risk Institute Publication 69 The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012 The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

EDHEC-Risk Institute Publications (2009-2012)

2012 • Amenc, N., F. Goltz, L. Tang, and V. Vaidyanathan. EDHEC-Risk North American Index Survey 2011 (March). • Amenc, N., F. Cocquemas, R. Deguest, P. Foulquier, L. Martellini, and S. Sender. Introducing the EDHEC-Risk Solvency II Benchmarks – maximising the benefits of equity investments for insurance companies facing Solvency II constraints - Summary - (March). • Schoeffler, P. Optimal market estimates of french office property performance (March). • Le Sourd, V. Performance of socially responsible investment funds against an efficient SRI Index: The impact of benchmark choice when evaluating active managers – an update (March). • Martellini, L., V. Milhau, and A.Tarelli. Dynamic investment strategies for corporate pension funds in the presence of sponsor risk (March). • Goltz, F., and L. Tang. The EDHEC European ETF survey 2011 (March). • Sender, S. Shifting towards hybrid pension systems: A european perspective (March). • Blanc-Brude, F. Pension fund investment in social infrastructure (February). • Ducoulombier, F., L. Lixia, and S. Stoyanov. What asset-liability management strategy for sovereign wealth funds? (February). • Amenc, N., F. Cocquemas, and S. Sender. Shedding light on non-financial risks – a European survey (January). • Amenc, N., F. Cocquemas, R. Deguest, P. Foulquier, L. Martellini, and S. Sender. Ground Rules for the EDHEC-Risk Solvency II Benchmarks. (January). • Amenc, N., F. Cocquemas, R. Deguest, P. Foulquier, L. Martellini, and S. Sender. Introducing the EDHEC-Risk Solvency Benchmarks – Maximising the Benefits of Equity Investments for Insurance Companies facing Solvency II Constraints - Synthesis -. (January). • Amenc, N., F. Cocquemas, R. Deguest, P. Foulquier, L. Martellini, and S. Sender. Introducing the EDHEC-Risk Solvency Benchmarks – Maximising the Benefits of Equity Investments for Insurance Companies facing Solvency II Constraints (January). • Schoeffler.P. Les estimateurs de marché optimaux de la performance de l’immobilier de bureaux en France (January).

2011 • Amenc, N., F. Goltz, Martellini, L., and D. Sahoo. A Long Horizon Perspective on the Cross-Sectional Risk-Return Relationship in Equity Markets (December 2011). • Amenc, N., F. Goltz, and L. Tang. EDHEC-Risk European Index Survey 2011 (October). • Deguest,R., L. Martellini, and V. Milhau. Life-Cycle Investing in Private Wealth Management (October).

70 An EDHEC-Risk Institute Publication The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

EDHEC-Risk Institute Publications (2009-2012)

• Amenc, N., F. Goltz, Martellini, L., and L. Tang. Improved Beta? A Comparison of Index- Weighting Schemes (September). • Le Sourd, V. Performance of Socially Responsible Investment Funds against an Efficient SRI Index: The Impact of Benchmark Choice when Evaluating Active Managers (September). • Charbit, E., J. R. Giraud, F. Goltz, and L.Tang Capturing the Market, Value, or Momentum Premium with Downside Risk Control: Dynamic Allocation Strategies with Exchange-Traded Funds (July). • Scherrer, B. An Integrated Approach to Sovereign Wealth Risk Management (June). • Campani, C.H. and F. Goltz. A Review of corporate bond indices: Construction principles, return heterogeneity, and fluctuations in risk exposures (June). • Martellini, L., and V. Milhau. Capital structure choices, pension fund allocation decisions, and the rational pricing of liability streams (June). • Amenc, N., F. Goltz, and S. Stoyanov. A post-crisis perspective on diversification for risk management (May). • Amenc, N., F. Goltz, L. Martellini, and L. Tang. Improved beta? A comparison of index- weighting schemes (April). • Amenc, N., F. Goltz, L. Martellini, and D. Sahoo. Is there a risk/return tradeoff across stocks? An answer from a long-horizon perspective (April). • Sender, S. The elephant in the room: Accounting and sponsor risks in corporate pension plans (March). • Martellini, L., and V. Milhau. Optimal design of corporate market debt programmes in the presence of interest-rate and inflation risks (February).

2010 • Amenc, N., and S. Sender. The European fund management industry needs a better grasp of non-financial risks (December). • Amenc, N., S, Focardi, F. Goltz, D. Schröder, and L. Tang. EDHEC-Risk European private wealth management survey (November). • Amenc, N., F. Goltz, and L. Tang. Adoption of green investing by institutional investors: A European survey (November). • Martellini, L., and V. Milhau. An integrated approach to asset-liability management: Capital structure choices, pension fund allocation decisions and the rational pricing of liability streams (November). • Hitaj, A., L. Martellini, and G. Zambruno. Optimal Hedge Fund Allocation with Improved Estimates for Coskewness and Cokurtosis Parameters (October). • Amenc, N., F. Goltz, L. Martellini, and V. Milhau. New frontiers in benchmarking and liability-driven investing (September).

An EDHEC-Risk Institute Publication 71 The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

EDHEC-Risk Institute Publications (2009-2012)

• Martellini, L., and V. Milhau. From deterministic to stochastic life-cycle investing: Implications for the design of improved forms of target date funds (September). • Martellini, L., and V. Milhau. Capital structure choices, pension fund allocation decisions and the rational pricing of liability streams (July). • Sender, S. EDHEC survey of the asset and liability management practices of European pension funds (June). • Goltz, F., A. Grigoriu, and L. Tang. The EDHEC European ETF survey 2010 (May). • Martellini, L., and V. Milhau. Asset-liability management decisions for sovereign wealth funds (May). • Amenc, N., and S. Sender. Are hedge-fund UCITS the cure-all? (March). • Amenc, N., F. Goltz, and A. Grigoriu. Risk control through dynamic core-satellite portfolios of ETFs: Applications to absolute return funds and tactical asset allocation (January). • Amenc, N., F. Goltz, and P. Retkowsky. Efficient indexation: An alternative to cap-weighted indices (January). • Goltz, F., and V. Le Sourd. Does finance theory make the case for capitalisation-weighted indexing? (January).

2009 • Sender, S. Reactions to an EDHEC study on the impact of regulatory constraints on the ALM of pension funds (October). • Amenc, N., L. Martellini, V. Milhau, and V. Ziemann. Asset-liability management in private wealth management (September). • Amenc, N., F. Goltz, A. Grigoriu, and D. Schroeder. The EDHEC European ETF survey (May). • Sender, S. The European pension fund industry again beset by deficits (May). • Martellini, L., and V. Milhau. Measuring the benefits of dynamic asset allocation strategies in the presence of liability constraints (March). • Le Sourd, V. Hedge fund performance in 2008 (February). • La gestion indicielle dans l'immobilier et l'indice EDHEC IEIF Immobilier d'Entreprise France (February). • Real estate indexing and the EDHEC IEIF Commercial Property (France) Index (February). • Amenc, N., L. Martellini, and S. Sender. Impact of regulations on the ALM of European pension funds (January). • Goltz, F. A long road ahead for portfolio construction: Practitioners' views of an EDHEC survey. (January).

72 An EDHEC-Risk Institute Publication The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

EDHEC-Risk Institute Position Papers (2009-2012)

2012 • Amenc, N., F. Ducoulombier, F. Goltz and L. Tang. What are the risks of European ETFs? (January).

2011 • Amenc, N., and S. Sender. Response to ESMA consultation paper to implementing measures for the AIFMD (September). • Uppal, R. A Short note on the Tobin Tax: The costs and benefits of a tax on financial transactions (July). • Till, H. A review of the G20 meeting on agriculture: Addressing price volatility in the food markets (July).

2010 • Amenc, N., and V. Le Sourd. The performance of socially responsible investment and sustainable development in France: An update after the financial crisis (September). • Amenc, N., A. Chéron, S. Gregoir, and L. Martellini. Il faut préserver le Fonds de Réserve pour les Retraites (July). • Amenc, N., P. Schoefler, and P. Lasserre. Organisation optimale de la liquidité des fonds d’investissement (March). • Lioui, A. Spillover effects of counter-cyclical market regulation: Evidence from the 2008 ban on short sales (March).

2009 • Till, H. Has there been excessive speculation in the US oil futures markets? (November). • Amenc, N., and S. Sender. A welcome European Commission consultation on the UCITS depositary function, a hastily considered proposal (September). • Sender, S. IAS 19: Penalising changes ahead (September). • Amenc, N. Quelques réflexions sur la régulation de la gestion d'actifs (June). • Giraud, J.-R. MiFID: One year on (May). • Lioui, A. The undesirable effects of banning short sales (April). • Gregoriou, G., and F.-S. Lhabitant. Madoff: A riot of red flags (January).

An EDHEC-Risk Institute Publication 73 The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012

Notes

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74 An EDHEC-Risk Institute Publication The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012 For more information, please contact: Carolyn Essid on +33 493 187 824 or by e-mail to: [email protected]

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