The Benefits Of Volatility Derivatives In Equity Portfolio .

The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012Executive SummaryFigure 1: Time Evolution of EURO STOXX 50 Index and VSTOXX IndexaDaily time series for EURO STOXX 50 and VSTOXX indexes. The shaded areas are the NBER recessions. The sample period is January1999 to April 2011.increasingly so for more recent time periods.We also analysed whether the negativecorrelation is robust with respect to changesin market conditions. In order to distinguishbetween the periods of high and lowvolatility in the European equity market,we used a Markov regime-switching model(Perlin 2010). Using weekly EURO STOXX 50Index data, we distinguished between thestates of high, medium and low volatility.The estimated correlation between EUROSTOXX 50 and VSTOXX index returns is -0.76,-0.73 and -0.62 for the periods of high,medium and low volatility, respectively.In addition, we used the National Bureauof Economic Research (NBER) recession/expansion indicators as a control variable(see Figure 1). The negative correlationseems particularly pronounced duringthe periods indicated as NBER recessions.During NBER recessions the correlation levelreached -0.78, which is relatively close tothe correlation level (i.e. -0.76) estimatedduring high volatility periods as definedwith the Markov regime-switching model.8An EDHEC-Risk Institute PublicationDuring the recent 2008 crisis, the negativecorrelation between VSTOXX and EUROSTOXX 50 indexes was particularly strong,estimated at -0.80 (the highest value sofar) for the January 2008 to December2008 period. These results suggest that thebenefits of diversification with volatilityindices manifest themselves when they areneeded the most.Next, we analysed the benefits of addinga long volatility exposure to the equityportfolio. We use the EURO STOXX 50index to represent a large cap Europeanstock benchmark. In this section, we onlysimulated a long volatility position by‘trading’ in the VSTOXX spot index. Althougha direct investment in the VSTOXX index isnot possible in practice, this ‘theoretical’approach allowed us to access a longer datahistory (i.e. January 1999 to April 2011) foranalysing portfolios’ performances.We constructed a number of equityportfolios with 5% increasing allocations toa long volatility exposure. A long volatility

The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012Executive Summaryposition itself would hardly generate anypositive return – 100% investment inVSTOXX resulted in 0.3% p.a. over the sampleperiod (additionally, 100% investment in VIXhad a return of -0.7% p.a.) – consistent withthe view in current literature that there isa negative risk premium associated withbeing long volatility.3 However, graduallyincreasing the equity portfolio’s allocationsto volatility exposure has a very positiveeffect on equity portfolio performance.We have illustrated this effect in Figure 2,in an efficient frontier format.3 - Bakshi and Kapadia(2003), Carr and Wu (2010).The pure equity portfolio is clearly inferior toother investment opportunities, bearing inmind the existence of a diversified portfolioon the efficient frontier that has the samestandard deviation as the equity portfolio,but that offers significantly higher returns.In our sample, the maximum Sharpe ratio(0.46) is achieved for the portfolio with 30%allocation to VSTOXX and 70% allocationto EURO STOXX 50.We then extended the analysis by comparingthe performance between the equityportfolio with a long volatility exposureand a GMV portfolio. We used MSCI EuropeMinimum Volatility Index as a proxy GMVportfolio in our study. For this analysis, weselected the portfolio with long volatilityexposure that had similar volatility to thatof a GMV portfolio over the sample periodranging from December 2001 to April 2011.The results, illustrated in Figure 3, areclearly in favour of the diversified equityportfolio with a long volatility exposure.Both portfolios have relatively similarperformances during the periods of lowvolatility and the diversified portfolio withVSTOXX exposure always outperformsthe GMV portfolio in the periods of highvolatility. Although volatilities of bothportfolios for the sample period are similar,the returns are significantly improved in thediversified portfolio with VSTOXX exposurecase (i.e. 9.7% compared to a 2.1% returnof GMV portfolio).Figure 2: Impact of Adding Long Volatility Exposure to Equity Portfolio in 5% IncrementsThe effects of adding VSTOXX index exposure to EURO STOXX 50 portfolio in 5% increments, estimated based on the sample periodranging from January 1999 to April 2011.An EDHEC-Risk Institute Publication9

The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012Executive SummaryFigure 3: Performance of Diversified Portfolio with VSTOXX Exposure and Global Minimum Variance (GMV) PortfolioDaily time series for the diversified portfolio and MSCI Europe Minimum Volatility Index on the sample period ranging fromDecember 2001 to April 2011.Overall, the results in this section providestrong evidence of the benefits of addinga long volatility exposure to an equityportfolio. We also demonstrated thatadding a volatility exposure to the equityportfolio not only improves its performanceas compared to a pure equity case, but itcan also provide a more efficient methodof managing downside volatility exposurethan the GMV approach.3. Implementing the Analysis withVolatility FuturesIn the previous section a structural volatilityexposure was represented by a ‘theoretical’direct investment in the VSTOXX index.However, in practice, the VSTOXX indexis not directly investable, and in order toinvest in VSTOXX, an investor may take aposition in VSTOXX futures and/or optionscontracts. Mini-futures on VSTOXX wereintroduced on the Eurex Exchange in June2009, with a contract value of 100 perindex point. They replaced previously listedfutures on VSTOXX, which had a contract10An EDHEC-Risk Institute Publicationsize of 1,000 EUR per index point. In ouranalysis, we used the data of both currentlytrading and delisted VSTOXX futures seriesto obtain a longer data history (the totalcombined sample period ranges from April2008 to April 2011).Considering that an individual futurescontract is traded for limited time only,an investor has to roll over the initialVSTOXX investment over the series ofconsecutive futures contracts for a longexposure in VSTOXX. We constructedthree separate VIX futures series based ondifferent rollover methodologies: 1-month,3-month and longest-traded (LT) series.The purpose of this exercise is to analysethe costs associated with different rolloverstrategies as a function of the frequencyof rebalancing. We have estimated thatduring the analysed sample period fromApril 2008 to April 2011, the VSTOXXfutures market was approximately 79% incontango and 21% in backwardation. As aresult, a rollover strategy typically inducesa negative return.

The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012Executive SummaryA few recent papers4 report that themajority of futures contracts have a lowerand less variable carry when rolled over 5days prior to maturity, rather than waitinguntil maturity. However, this observation isspecific to the US market and we found noevidence that rolling over 5 days prior tomaturity significantly improved the resultsin portfolios with long volatility exposure.Considering this result, we used rolloverat maturity in all our further empiricalanalyses.4 - Lee and Lin (2010),Alexander and Korovilas(2011)In order to be consistent with our earlieranalysis, we again constructed severalequity portfolios with increasing allocationsto VSTOXX futures positions. As before,European equity market exposure isapproximated by the investment in theEURO STOXX 50 Index. The investmentin VSTOXX is represented by a fullycollateralised VSTOXX futures position.The analysis starts with the pure equityportfolio as a benchmark case and adds, in5% increments, a long volatility exposureto the portfolio. The results for the bestperforming 3-month VSTOXX futures seriesare presented in Figure 4, in an efficientfrontier format. It is interesting to note thatthe best performing portfolio is achieved byallocating 30% to VSTOXX futures, whichis a similar result to that obtained withVSTOXX index data.In order to access the full impact oftransaction costs, we incorporated thebid-ask spread into the analysis. Includingthe bid-ask spread costs significantly affectsthe performance of VSTOXX futures – thereturns decreased by 26%, 12.6% and 8.5%p.a. for 1-month, 3-month and longestterm (LT) futures, respectively.We also compared the performance ofthe diversified portfolio with a managedvolatility position with VSTOXX futures toone of the GMV portfolios. The diversifiedportfolio with VSTOXX futures proves tobe a better investment opportunity thanthe GMV portfolio. Firstly, it improvesthe standard deviation of returns from21.6% (for GMV portfolio) to 16.1% p.a.Figure 4: Impact of Adding Long Volatility Exposure to Equity Portfolio in 5% IncrementsThe effects of adding VSTOXX Futures (the 3-month series) to a EURO STOXX 50 portfolio in 5% increments, estimated based on thesample period ranging from April 2008 to April 2011.An EDHEC-Risk Institute Publication11

The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012Executive Summary(for diversified portfolio); secondly, it alsoreduces negative returns for the sampleperiod – from -2.8% (GMV) to -1.0% p.a.(diversified portfolio). In summary, theresults obtained in this section suggestthat the benefits of adding a long volatilityexposure to equity portfolios are robust withrespect to the introduction of trading costsinvolved in implementation with volatilityfutures contracts. Careful attention to tradeexecution is nonetheless required to limitthe negative impact of transaction costs,negative carry and roll yield on volatilityfutures during normal periods.4. Short-term Analysis withVolatility OptionsIn this section, we considered a differentapproach based on the use of volatilityoptions for gaining a long exposureto volatility. March 2010 witnessed theintroduction of option contracts on theVSTOXX index, which provided investorswith more flexibility for trading Europeanvolatility.In order to assess the impact of addingVSTOXX options to equity portfolios, weconstructed a long volatility positionby rolling over one month to expirationVSTOXX call options. We use both at-themoney (ATM) and out-of-the-money (10%OTM and 25% OTM) calls for our analysis.Considering that volatility options are muchmore sensitive to changes in underlyingvolatility compared to fully collateralisedfutures contracts, we used 1% incrementsin volatility exposure rather than 5%increments used for VSTOXX futures.The performance of ATM VSTOXX callsprovides very similar results to the VSTOXXfutures. While adding a small positiveexposure to the volatility index optionportfolio slightly improves (1% and 2%)the performance of the overall portfolio,further increases provide no additionalvalue. Due to increased sensitivity, theresults achieved with OTM calls is much morefavourable than those achieved with ATMcalls; and, in the case of the 25% OTM calls,the return improvements are impressive.Figure 5: Impact of Adding VSTOXX 25% OTM options to Equity Portfolio in 1% IncrementsThe effects of adding VSTOXX OTM options to EURO STOXX 50 portfolio by 1% increments, estimated based on the sample periodranging from March 2010 to April 2011.12An EDHEC-Risk Institute Publication

The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012Executive SummaryThe performance of the portfolios withincreasing allocation to 25% OTM calls isdepicted in an efficient frontier form inFigure 5.In further analysis, we estimated the impactof the bid-ask spread on the performanceof the diversified portfolios with VSTOXXoptions exposure. In this case, the drag onperformance amounts to 0.53%, 4.28% and6.21% p.a. for ATM, 10% OTM and 25% OTMcalls, respectively.We also considered a classic strategyfor managing downside risk in equityportfolios – the use of protective puts. Inevery financial textbook, protective putsare referred to as a direct hedge for theprice movements in equity portfolios. Inorder to test this assertion, we comparedthe performance of an equity portfolio withVSTOXX call allocations to that of an equityportfolio mixed with long EURO STOXX50 puts. We find that equity portfolioswith EURO STOXX 50 put positions do notperform as well as portfolios mixed withVSTOXX calls. None of the portfolios withEURO STOXX 50 puts have better ‘adjusted’Sharpe ratios than those of a pure equityportfolio.Up to this point, we have mostly focusedon the diversification properties of volatilityderivatives. However, an investor can alsouse VSTOXX options to trade on a specificview on the VSTOXX direction or volatilitychanges. In this section, we analyse theperformance of two commonly usedstrategies for generating premium: (i)short out-of-the-money VSTOXX puts;and (ii) VSTOXX ratio spread strategy. Bothstrategies can be used as more innovativeways for equity portfolio management.However, in both cases, a careful selectionof option strike prices proved to be criticalfor portfolio performance. Therefore, it isimportant to take current market volatilityconditions into account when designing andimplementing an option trading strategy.However, the data history available forVSTOXX options is very short (rangingfrom March 2010 to April 2011). Dueto an extremely short data history andcorresponding sample size, it would bedifficult to provide a formal analysis ofthe marginal benefits to be expected fromusing volatility index futures as opposedto volatility index options. Therefore, theanalysis in this section is merely to beregarded as an example of an alternativeway of structuring a long volatilityexposure.5. ConclusionIn this paper, we analyse a novelapproach in the design of attractiveequity solutions with managed volatility,based on mixing a well-diversified equityportfolio with volatility derivatives, asopposed to minimising equity volatilitythrough minimum variance approaches.The results we obtain suggest that a longvolatility position shows a strongly negativecorrelation with respect to the underlyingequity portfolio and that adding a longvolatility exposure to an equity portfoliowould result in a substantial improvementof the risk-adjusted performance of theportfolio. The benefits of the long volatilityexposure are found to be strongest inmarket downturns, when they are mostneeded.An EDHEC-Risk Institute Publication13

The Benefits of Volatility Derivatives in Equity Portfolio Management — May 2012Executive SummaryWe also compare the performance of thediversified equity portfolios includingvolatility derivatives with that of globalminimum variance (GMV) portfolios that arecommonly used in industry as a benchmarkstrategy for reducing portfolio risk. Wefound that the diversified portfolio withlong volatility exposure is a more efficientapproach for managing risk.We also consider the challenges related toa practical implementation of this strategyby using derivatives instruments – futuresand options – that allow investors directaccess to trading volatility. We consider howincreasing allocation to volatility derivativesaffects the portfolio performance; we alsoevaluate transaction costs in each case anddiscuss the advantages and disadvantagesof using each type of instrument. Thebenefits of adding volatility exposure toequity portfolios are found to be robustwith respect to the introduction of tradingcosts associated with rolling over volatilityderivatives contracts.14An EDHEC-Risk Institute Publication

1. IntroductionAn EDHEC-Risk Institute Publication15

The Benefits of Volatility Derivatives in Equity Portfolio Management — May 20121. Introduction5 - Szado (2009), Daiglerand Rossi (2006), Grant et al.(2007), Dash and Moran (2007),Alexander and Korovilas (2011).Recent market turbulence, coupledwith the presence of increasinglystrict regulatory constraints have ledinstitutional investors (pension funds,insurance companies) and asset managersto monitor the volatility and downside riskof their equity holdings with increasedscrutiny. One approach towards the designof equity portfolios in the presence oftight risk budgets involves building equityportfolio benchmarks with the lowestpossible volatility. Over the past few years,this approach has gained considerablepopularity in the industry, and the nonexhaustive list of firms that are currentlymanaging global minimum variance(GMV) portfolios includes Acadian AssetManagement, AXA Rosenberg, Invesco,LGT Capital Management, MSCI Barra,SEI, Robeco, State Street Global Advisorsand Unigestion, among others. Currently,GMV portfolios are largely promotedas pragmatically useful benchmarks forinvestors or asset managers wishing tobenefit from some fraction of the equityrisk premium without the full associateddownside risk.Whether investing in a GMV portfoliois the most efficient and robust routefor managing equity volatility remains,however, an open question. From anacademic perspective, this approach isnot consistent with standard portfoliotheory, which instead suggests firstidentifying the maximum Sharpe ratio(MSR) portfolio, as opposed to the GMVportfolio, and then mixing that portfoliowith cash so as to achieve the targetvolatility consistent with investors’ riskappetites and budgets. In other words,while the GMV is an efficient portfolio inthe absence of a risk-free asset, it is no16An EDHEC-Risk Institute Publicationlonger an efficient portfolio when a riskfree asset is introduced.In this article, we analyse a competingapproach to the design of attractive equitysolutions with managed volatility, based onmixing well-diversified maximum Sharperatio portfolios with volatility derivatives.Intuitively, one expects that a portfoliostrategy mixing a well-diversified equitybenchmark and a suitably designed longexposure to volatility through trading involatility index futures and/or volatilityindex options can be engineered so asto provide an access to the equity riskpremium while allowing f

ratio portfolios with volatility derivatives. Intuitively, one expects that a portfolio strategy mixing a well-diversified equity benchmark and a suitably designed long exposure to volatility through trading in volatility index futures and/or volatility index options can be enginee