Research. RVX futures as a hedge for small cap specific risk

Transcription

1 Research RVX futures as a hedge for small cap specific risk ftserussell.com June 2015

2 Executive summary: Volatility products can be used to hedge downside risk in equity portfolios RVX SM futures provides a U.S. small cap equity focused alternative to CBOE Volatility Index (VIX Index) futures RVX futures hedges can potentially be more effective when the risk is specific to small cap stocks Summary RVX volatility futures (CBOE Russell 2000 Volatility Index Futures Contracts) track the implied volatility expectations of the U.S. small cap equity market and can be a particularly effective hedge for the risk inherent in the small cap asset class. The potential usefulness of RVX futures in hedging small cap-specific risk is illustrated in this paper with results of a simulation case study that includes two hedging examples based on market movements in spring and summer One example shows that a simulated small cap portfolio could have been better hedged with RVX futures than with VIX futures during the period examined. This paper starts with a brief introduction to volatility products and the concept of small cap-specific risk. It then presents the case study results, starting with a review of market conditions leading up to the small cap market correction in 2014 and continuing through to a comparative estimation of the results of a particular hedging strategy implemented with both RVX and VIX volatility futures. RVX trades are conservatively modeled. A methodology appendix provides details of how the hedges are constructed and valued. It also includes an examination of the differences between volatility indexes and the prices of volatility futures based on those indexes, basic details of the construction of the futures hedges, and the approach used here to estimate the prices used in implementing and rolling RVX and VIX hedges. FTSE Russell RVX futures as a hedge for small cap specific risk 1

3 Introduction VIX-based volatility products have expanded over the last 10 years - from futures contracts, to volatility options, and to increasingly sophisticated ETFs (e.g., VXX and XIV). VIX, the CBOE Volatility Index, is a measure of the implied volatility of the U.S. large cap asset class as represented by the S&P The implied volatility of a security is determined by the prices of options on the security and is an estimate of the market-implied expected volatility over the remaining life of the options. 2 RVX is the implied volatility index for the U.S. small cap asset class as represented by the Russell 2000 Index. 3 Small cap-specific risk, which is driven by factors associated with small cap stocks, is a type of asset class-specific risk. Many risk factors affect all asset classes. The asset class-specific risk examined in this case study is the market perception that small cap stocks might be overpriced relative to the market as a whole. The greater liquidity of the VIX contract has made it a frequent choice for managers seeking to hedge small cap stocks against market-wide risks. Yet the examples developed here show that hedging with VIX may not be the best strategy for small cap-specific risks. Our baseline assumption is that an investor wants to use volatility futures to hedge a small cap portfolio. (Options offer another tool for hedging portfolio risk, but will not be studied here. 4 ) VIX positions are modeled with entry and exit trading at the contract daily settlement price. RVX entry/exit trades are modeled more conservatively by taking the observed bid/ask spread into account, with purchases at the daily settlement price plus one-half the daily quote spread and sales at the daily settlement price minus one-half the daily quote spread. Thus simulated RVX purchases are at the ask price, and simulated sales are at the bid price. The primary cost of maintaining a volatility futures hedge is typically the cost of rolling the contracts, which is when contracts nearing expiration are sold and replaced with longer-dated contracts. VIX contracts are rolled at average time-matched trade prices for both contracts. RVX contracts are rolled conservatively, based on the average time-matched bid price for the expiring contract and ask price for the next-month contract. The methodology appendix provides further details. 1 VIX information may be found at cfe.cboe.com/products/products_vix.aspx. CBOE, Chicago Board Options Exchange, CFE, CBOE Volatility Index, and VIX are registered trademarks of Chicago Board Options Exchange, Incorporated (CBOE). RVX is a service mark of CBOE. The Russell 2000 Index is a registered trademark of FTSE Russell Indexes, used under license. CBOE data is believed to be correct but CBOE does not guarantee the accuracy of the data and will not be held liable for consequences of its use. 2 During the period of this study, both VIX implied volatility and RVX implied volatility are based on the prices of the two nearest-to-expiration monthly options contracts. Contracts at all strike prices are included in the calculation. The prices of these contracts are weighted so as to create a constant 30-day forward expected volatility horizon. Starting fourth quarter 2014, the VIX methodology changed; it now uses the nearest expiring weekly SPX options. 3 RVX futures were recently relaunched. RVX trading was discontinued in the spring of 2009 and reintroduced in the fall of RVX trading still displays limited depth and liquidity. During 2009, RVX trading dwindled, due to a combination of factors that included the financial crisis of the time and technical issues around contract expiration. CBOE information on RVX futures can be found at cfe.cboe.com/products/ Products_VU.aspx. Further information about RVX volatility futures contracts can be found in Russell 2000 Volatility Futures, Barry Feldman, Russell Research, October The interested reader can find a comparison of the relative merits of index options, volatility futures, variance swaps and options on volatility futures in The Art of Hedging, QDS Vega Times, Morgan Stanley, June 14, FTSE Russell RVX futures as a hedge for small cap specific risk 2

4 Hedging the 2014 small cap correction The spring of 2014 was a time of increasing investor uncertainty about U.S. small cap equity prices. Many believed small cap was overvalued. On February 6, 2014, for example, a Bloomberg article noted that implied volatility on ishares Russell 2000 ETF options had spiked and that strategists were seeing a downturn coming for small cap prices. 5 This uncertainly was reflected in RVX values. Figure 1 shows the RVX Index from July 1, 2013, to February 6, A spike in small cap implied volatility can plainly be seen to have started on January 24, A peak can be seen on February 3, followed by a small decline to February 6, as highlighted in red. Figure 1. RVX Index values July 1, 2013 to February 6, RVX /1/2013 7/15/2013 7/29/2013 8/12/2013 8/26/2013 9/9/2013 9/23/ /7/ /21/ /4/ /18/ /2/ /16/ /30/2013 1/13/2014 1/27/2014 Source: CBOE. February 6, 2014 highlighted. Figure 2 displays the RVX premium relative to VIX. The RVX premium is defined as RVX Index values as a percentage relative to VIX Index values. A zero premium corresponds to RVX and VIX indexes having the same value. The RVX premium is a representation of the market perception of the magnitude of small cap risk relative to large cap risk. An increase in expected small cap-specific risk should be reflected in an increase in the RVX premium. Looking at the period January 1, 2014 through August 31, 2014, it can be seen in Figure 2 that there is also a spike in the RVX premium starting on January 24. The RVX premium value of 40.9% on February 6 is highlighted in red, both to provide orientation for the different time periods shown in Figures 1 and 2 and to show that the RVX premium continues to spike on this date, even though the RVX values in Figure 1 decline. This indicates that VIX values declined faster than RVX values from February 3 to February 6. Figure 2 displays the RVX premium until August 31, After February 6, the premium first reverts back into the range in which it had been trending and then trends unevenly upward through at least the beginning of June. One interpretation of this upward trend is that full risk of an expected small cap 5 See Small-Cap Bears at Highest Since 12 Selloff: Options, February 6, 2014, at Bloomberg Online, bloomberg.com/news/ / small-cap-bears-at-highest-since-12-on-selloff-options.html. FTSE Russell RVX futures as a hedge for small cap specific risk 3

5 correction was not immediately reflected in options prices and volatility indexes as of February 6. It can also be seen that the RVX premium declines sharply at the end of July, suggesting a potential end to the period of small cap-specific risk. Figure 2. RVX premium, defined as RVX/VIX-1 January 1, 2014 to August 31, % 70% 60% RVX Premium 50% 40% 30% 20% 10% 0% 1/2/2014 1/16/2014 1/30/2014 2/13/2014 2/27/2014 3/13/2014 3/27/2014 4/10/2014 4/24/2014 5/8/2014 5/22/2014 6/5/2014 6/19/2014 7/3/2014 7/17/2014 7/31/2014 8/14/2014 8/28/2014 Source: CBOE. February 6, 2014 highlighted. The simulation case study is based on the time period January 1, 2014 to August 31, 2014, depicted in Figure 2. This is obviously a retrospective study. The selection of the times to hedge was based on the benefit of a hindsight-based timing ability that is not available to investors. The dates that define the first hedge were selected according to the idea that they might have been chosen by an investor with moderate timing ability. So, for example, the small cap volatility spike starting on January 24, which has already been discussed, is not used as a hedging example. It seems unlikely that an investor with moderate timing ability would have been able to predict this volatility spike with sufficient accuracy. 6 The first hedge is implemented on February 24, about two weeks after the end of the volatility spike and publication of the Bloomberg article. This gives our hypothetical investor time after the February 6 spike to do an assessment of the small cap market and to design and implement a hedge. The second hedge is started on June 30 and ends on August 6. The primary purpose of this second hedge is to compare RVX and VIX hedge performance in a changing market environment, wherein small cap-specific risk is not as prominent. The dates for ending the hedges are not crucial. A change of a few days does not affect the qualitative results. Figure 3 shows the effects of hedging Russell 2000 Index performance over the two periods just described. The cumulative total return of the Russell 2000 is shown, along with cumulative performance when the Russell 2000 is hedged using RVX futures or 6 However, an investor with superior timing ability could have entered a RVX or VIX volatility hedge at the January 22 settlement price and sold at the February 5 settlement price to realize a return of 43.2% for an RVX position and 38.3% for a VIX position, not taking the minimal costs of establishing and liquidating positions into account. FTSE Russell RVX futures as a hedge for small cap specific risk 4

6 VIX futures. The shaded areas indicate the time periods of the hedge examples. The RVX-based hedge outperformed the Russell 2000 and the VIX-based hedge strategy. The VIX-based hedge was initially successful, in the early period of the first hedge, but quickly had increasing periods of underperformance relative to the Russell It is only toward the end of the second hedging window that the VIX-based hedging strategy outperformed the Russell 2000 on a sustained basis. As of August 31, 2014, the RVX-based hedge outperformed the Russell 2000 by 12.95% and outperformed the VIX-based hedge by 7.60%. Figure 3. Russell 2000 Index cumulative total return performance and the performance of two Russell %-hedged strategies, one using RVX and one using VIX futures First hedge period is February 24, 2014 to May 8, Second hedge period is June 30, 2014 to August 6, Data is from Russell Indexes and CBOE. Details of hedge construction are provided in this paper s appendix. Complete time period is January 1, 2014 to August 31, January 1, 2014 = Hedge 1 Hedge 2 1/2/2014 1/16/2014 1/30/2014 2/13/2014 2/27/2014 /2014 3/13/2014 /2014 3/27/2014 /2014 4/10/2014 /2014 4/24/2014 /2014 5/8/2014 /2014 5/22/2014 6/5/2014 6/19/2014 7/3/2014 /2014 7/17/2014 /2014 7/31/2014 /2014 8/14/2014 8/28/2014 Russell 2000 Russell 2000 plus 50% VIX Hedge Russell 2000 plus 50% RVX Hedge Source: CBOE and FTSE Russell. Table 1 presents performance statistics for the complete study history and for the time periods of the two hedges. The results over the complete study history show that the RVX hedge protected investor value with minimal increase in portfolio volatility. The maximum drawdown statistics for the complete history time period show that the RVX hedge reduced maximum drawdown from 9.06% to 7.40% while the VIX hedge had a 17.00% maximum drawdown. The cumulative return of the RVX hedged portfolio was also considerably better. Note that the complete history statistics in Table 1 involve volatility hedges only over the two time periods of the hedging examples. FTSE Russell RVX futures as a hedge for small cap specific risk 5

7 Table 1. Summary performance statistics for the Russell 2000 and RVX-hedged and VIX-hedged Russell 2000 strategies as defined here Results presented for the entire study history and for the two hedge periods: February 24, 2014 to May 8, 2014 and June 30, 2014 to August 6, Time Period Statistic Russell 2000 Complete history: January 1 to August 31, 2014 Hedge 1: February 24 to May 8, 2014 Hedge 2: June 30 to August 6, 2014 Russell 2000 plus 50% RVX Hedge Russell 2000 plus 50% VIX Hedge Average daily return 0.02% 0.10% 0.07% Cumulative return 2.89% 16.21% 10.70% Annualized standard deviation 15.70% 16.55% 20.57% Maximum drawdown 9.06% 7.40% 17.00% Information ratio Daily skew Daily kurtosis Average daily return -0.12% 0.00% -0.17% Cumulative return -6.30% -0.15% -8.96% Annualized standard deviation 16.92% 15.65% 23.30% Maximum drawdown 8.98% 7.18% 16.92% Information ratio Daily skew Daily kurtosis Average daily return -0.24% 0.13% 0.23% Cumulative return -5.58% 3.42% 5.91% Annualized standard deviation 14.96% 22.34% 29.98% Maximum drawdown 7.67% 6.10% 6.29% Information ratio Daily skew Daily kurtosis Source: FTSE Russell and CBOE. Figure 3 shows the RVX functioned successfully as a hedge in the first period, almost completely neutralizing the Russell 2000 Index loss in value. This result was achieved with lower levels of volatility than experienced by the Russell VIX failed as a hedge in the first time period. This failure is visible both in the low returns and the large drawdown reported in Table 1. The results for the second hedge reported in Table 1 show that the RVX hedge performed effectively and provided positive net returns, but was outperformed by the VIX hedge. The performance of the RVX hedge relative to the Russell 2000 index is 9.53%, and that of the VIX hedge is 12.17%. Note, however, that the VIX hedge outperformance is accompanied by considerably higher volatility. As a result of this increase in volatility, the information ratio of the VIX hedge is only marginally higher than that of the RVX hedge. FTSE Russell RVX futures as a hedge for small cap specific risk 6

8 The likely reason for the strong performance of the second VIX-based hedge can be seen in Figure 4. This chart shows a long period of steady declines in VIX values that starts in April and reverses over the month of July, before spiking on July 31 (highlighted in red). This spike occurred on the same day that the Dow Jones industrial average fell 317 points, as a result of investor fears relating to domestic and global concerns. 7 The RVX premium declines sharply at the time of the VIX spike and stabilizes for the first time since the February 6 spike, in a range mostly below that spike. The second hedging period can thus be seen to embody a transition from small cap stock risk being driven primarily by asset class-specific issues to being driven by market-wide factors. Figure 4. RVX premium; RVX and VIX values January 1, 2014 to August 31, % 30 70% 25 RVX premium 60% 50% 40% 30% 20% RVX and VIX Index values 10% 5 0% 0 1/2/2014 1/16/2014 1/30/2014 2/13/2014 2/27/2014 3/13/2014 3/27/2014 4/10/2014 4/24/2014 5/8/2014 5/22/2014 6/5/2014 6/19/2014 7/3/2014 7/17/2014 7/31/2014 8/14/2014 8/28/2014 RVX Premium VIX RVX Source: CBOE. July 31, 2014 highlighted. Conclusion A volatility hedge is utilized to protect against the marketplace volatility under the assessment that the likely benefits outweigh the more certain costs entailed. Because a hedge is costly to maintain, some ability to time implementation and liquidation is important. The effect of the lower liquidity of RVX is modeled in this study by taking positions at ask prices and liquidating positions at bid prices. VIX contracts, in contrast, are modeled to trade at average and settlement prices. These adjustments provide for a more conservative estimate of the performance of RVX hedges relative to VIX hedges. One result of the conservative pricing approach is that the RVX continuous hedge underperformed the VIX continuous hedge over the total study period. In spite of this handicap, the RVX hedge significantly outperformed the VIX hedge in the first 7 See, for example, the CNN Money reporting on that date: money.cnn.com/2014/07/31/investing/stocks-markets. FTSE Russell RVX futures as a hedge for small cap specific risk 7

9 hedging example, which is most directly related to small cap-specific risk. In the second example, where perceived risk is macro in nature, the VIX hedge did better than the RVX hedge, but the RVX hedge still enabled the hypothetical RVX-hedged Russell 2000 portfolio to deliver net positive returns for the time period studied. In conclusion, this case study suggests that when the risk to be hedged is specific to small cap stocks, RVX futures-based hedges may provide for results superior to those of VIX-based hedges. In the appendix below, the method of determining hedged performance is reviewed. Methodology appendix This appendix explains how the examples in the simulation case study were constructed and provides some relevant background information. The methodology used to construct, value and liquidate hedges was designed to enable realistic comparison of RVX-based and VIX-based hedge strategies. A1. Data and futures prices used in this study This study covers the period January 1 to August 31, RVX and VIX index values, contract prices, trade data and RVX quotes are obtained from CBOE, the Chicago Board Options Exchange. 8 Russell 2000 index total return values come from Russell Indexes. The daily value of both RVX and VIX positions is determined by daily settlement prices. VIX entry and exit trades are also based on settlement prices. Prices for VIX trades may be obtained through the trade at settlement (TAS) transaction system available on the CBOE Futures Exchange (CFE ), the trading venue for CBOE volatility futures. The prices assumed for RVX trades and contract rolls are more conservatively estimated, because of the relative thinness of trading. RVX positions are established based on the RVX settlement price but with payment of a premium of one-half the average bid/ask spread quoted that day. This is an estimated ask price. RVX positions are liquidated based on payment of the daily settlement price minus one-half the average bid/ask price quoted that day, representing an estimated bid price. Contract rolls are assumed to take place at the average price ratio between the front-month and second-month contract on the day of the roll. The roll ratio is defined as the price paid for a second-month contract divided by the price at which the first-month contract is sold. Average prices of VIX trades and average RVX bid and ask quotes are determined for each 15-minute block over the study period. VIX roll ratios are based on time-block-matched average front-month and second-month contract trade prices. RVX roll ratios are based on time-block-matched average ask prices for the second-month contract and bid prices for the front-month contract. The average roll ratio on the day of the roll is the average of the ratios defined for each 15-minute block. 8 VIX and RVX contract trading data can be found at cfe.cboe.com/data/historicaldata.aspx. VIX settlement data can also obtained from websites such as Quandl.com. FTSE Russell RVX futures as a hedge for small cap specific risk 8

10 A2. Sizing the hedges A key implementation question the manager faces is how to size the hedge, regardless of whether RVX or VIX contracts are used. For simplicity, we assume that a 50% hedge is implemented. This means that the manager will implement a long volatility contract position that starts off with a value that is 50% of the portfolio assets under management. Given that RVX contract prices are typically higher than VIX contract prices, fewer RVX contracts will be bought to implement similarly sized hedges. The trader view of the size of a volatility futures position is usually in terms of the vega of the position, which is the dollar change in position value with a 1-point change in the price of a volatility contract. 9 Vega can also be considered relative to the portfolio to be hedged. In this case, the vega becomes equal to the hedge ratio (the hedge notional divided by value of the underlying) divided by the contract price. With a hedge ratio of 50% and RVX prices at 20 and VIX at 15, the respective vegas would be 3.33% and 2.50%. This means that a 1-point increase in the VIX would add 3.33% to hedged portfolio value but a 1-point increase in RVX would add only 2.5% to hedged portfolio value. Thus, equal notional sizes of the RVX and VIX sizes will result in VIX providing a somewhat stronger hedge because of its higher vega. Once a volatility contract position is implemented, the effective hedge ratio and vega will vary with the value of the equity and futures positions. A3. Contract prices and volatility index values That hedge strategies must take account of the imperfect relationship between volatility futures prices and spot volatility index values is an important aspect of this study. Volatility futures contract prices are based on the expected value of the associated volatility index at contract expiration. The more time there is until contract expiration, the more the price may change along with the actual change in value of the volatility index. Front-month futures contract prices have the closest relationship with volatility index values. The front-month contract is the contract nearest to expiration. Figure 5 shows front-month contract prices and underlying index values for RVX and VIX contracts over the study period. It can be seen that contract prices are generally close to index values, but that there are systematic differences. Most of the time, the contract prices in Figure 5 are higher than the index values. This is often referred to as contango, a trading term where the more specific meaning is that the contract price is expected to decrease before expiration. On the other hand, it can also be seen that the index value occasionally spikes considerably above the contract price. When the contract price is below the index value, the contract can be said to be in backwardation. This term has the more formal meaning that contract prices are expected to rise before expiration. In volatility futures markets, however, backwardation is not common, and index values tend to decrease more quickly than contract prices, pushing them back into contango before contract expiration. 9 The vega of a single contract is equal to the contract multiplier. Both RVX and VIX contracts are priced at 1,000 times the transaction price, i.e., when a RVX contract is priced at 25, the price of a single contract is $25,000. FTSE Russell RVX futures as a hedge for small cap specific risk 9

11 Figure 5. Contract settlement prices and underlying index values for RVX and VIX near contracts January 1 to August 31, /2/2014 1/16/2014 1/30/2014 2/13/2014 2/27/2014 3/13/2014 3/27/2014 4/10/2014 4/24/2014 5/8/2014 5/22/2014 6/5/2014 6/19/2014 7/3/2014 7/17/2014 7/31/2014 8/14/2014 8/28/2014 VIX RVX VIX front month contract settle RVX front month contract settle Source: CBOE. A4. The RVX contract volatility premium Since it is volatility futures contracts that can be traded, and not the index values themselves, it is important to compare the RVX volatility premium as shown in Figures 2 and 4 with an investable version of this premium based on front-month contract futures prices. A comparison between the index-based premium and that based on front-month contract futures prices is shown in Figure 6. The contract premium rises more slowly and is ultimately lower than the rise in the index premium. It can also be seen that there are sometimes significant variations in the short-term dynamics of the index and futures premia. In general, the index premium can spike more sharply and quickly, while both premia can fall rapidly. FTSE Russell RVX futures as a hedge for small cap specific risk 10

12 Figure 6. Index and front-month contract price ratios for RVX and VIX January 1 to August 31, /2/2014 1/16/2014 1/30/2014 2/13/2014 2/27/2014 3/13/2014 3/27/2014 4/10/2014 4/24/2014 5/8/2014 5/22/2014 6/5/2014 6/19/2014 7/3/2014 7/17/2014 7/31/2014 8/14/2014 8/28/2014 RVX/VIX index ratio RVX/VIX front month contract price ratio Source: CBOE. A5. Settlement prices and average daily contract prices and RVX trade prices VIX average daily trading prices are typically close to settlement prices, which represent the official end-of-day valuations of futures contracts. For VIX, the average difference between average 15-minute block prices and settlement prices was $0.03 over the study period, with a standard deviation of On average, there is little difference between trading and settlement prices. RVX trading was not continuous enough over the study period for meaningful comparison of settlement prices with daily trade prices. Instead, settlement prices may be compared to the average of matched bid and ask quotes. Such implied prices are averaged in 15-minute blocks and then averaged for each trading day. The implied price is the average of the bid and ask. RVX contract implied prices track settlement prices about as well as the prices of VIX contracts, with an average pricing difference of $0.04 and a standard deviation of The average RVX bid/ask spread over the study period is $0.32; its standard deviation is The daily average of this spread is used in the construction of RVX exit and entry prices. A6. Construction of RVX and VIX hedge positions and estimation of their performance A long-lived hedge using futures contracts must be rolled on a periodic basis, due to contract expirations. The CBOE volatility contracts used in this study are issued on, and expire on, a monthly schedule. This roll strategy is based on the two nearest-to-expiration contracts and, as already noted, the contracts are rolled on the last day of trading for the front-month contract. This is the day before contract expiration. CBOE volatility futures contracts settle the morning of contract expiration day. FTSE Russell RVX futures as a hedge for small cap specific risk 11

13 Roll ratios are determined for all contract roll dates as described in the first section of this appendix. If the contracts have the same price, then the roll ratio is 1. If the next month contract is more expensive than the current month, as is common for volatility futures, the new position will have fewer contracts, and the deflator will have to decrease in order to reflect that in calculating the position value, the contract price is now multiplied by a smaller number of contracts. These monthly roll ratios are used to create a roll deflator index series. This index starts out at The value carries forward in time, except that the current value is divided by the roll ratio on every roll date. At the end of August 2014, the values are 0.62 for the RVX roll deflator and 0.70 for VIX roll deflator. These values show that volatility contracts typically trade in contango, and they demonstrate the substantial baseline cost of volatility-based hedging strategies. Indexes for hedge performance are then computed by multiplying front-month contract prices by the hedge deflator on a day-by day basis. This multiplication adjusts the first-month contract price for the effects of contract rolls on position value. The resulting indexes thus can be used to determine the cumulative performance of the RVX-based and VIX-based hedge strategies described here, once they are implemented. Figure 7 shows the performance of these hedges over the study period. Clearly, an investor would have lost money hedging continuously over the entire time period. Over the entire study period, the average daily return to the RVX hedge strategy is -0.20% and the standard deviation is 4.12%, compared to -0.13% and 4.22%, respectively, for the VIX hedge. The relatively poorer overall performance of the RVX continuous hedge is in part the result of basing RVX contract rolls on the ask price for the next month contract and the bid price for the near contract. The superior performance of the RVX hedges in this case study must thus be due to RVX relative performance during the periods hedged, and not to an overall performance advantage. Figure 7. Performance of RVX and VIX continuous hedging indexes January 1, 2014 to August 31, 2014 Hedge value on January 1, 2014 = /2/2014 1/16/2014 1/30/2014 2/13/2014 2/27/2014 3/13/2014 3/27/2014 4/10/2014 4/24/2014 5/8/2014 5/22/2014 6/5/2014 6/19/2014 7/3/2014 7/17/2014 7/31/2014 8/14/2014 8/28/2014 RVX hedge continuous value VIX hedge continuous value Source: Based on data from CBOE. FTSE Russell RVX futures as a hedge for small cap specific risk 12

14 A7. Roll cost Table 2 reports average roll spreads and standard deviations for RVX and VIX futures contracts over the study period. The roll spread is the price difference between the front-month and second-month contracts at the time of contract roll, which is the day before expiration of the front-month contract. The first set of rows reports averages and standard deviations based on settlement prices. The second set of rows reports roll average spreads and standard deviations based on average prices for VIX-based and average quote-based prices for RVX. The quote-based price is based on the average of matched bids and asks for both the front-month and second-month contracts. The third set of rows reports RVX roll spreads based on the quote-based premia and discounts used in this study. Using settlement prices, the average RVX roll cost is about 2.4% of hedge value. Utilizing the quote spread increases the average RVX roll costs to about 5.1% of hedge value. Table 2. Average roll spreads for RVX and VIX volatility contracts January 1, 2014 to August 31, 2014 RVX Settlement price-based Standard deviation Average price or quote based Standard deviation Average bid/ask roll spread 0.96 Standard deviation 0.57 Data Source: CBOE trade data. VIX A8. Performance Accounting Some specific details regarding the construction and rolling of hedges may be helpful in providing for a more intuitive understanding of the results. Entry and exit and daily valuation are treated first, followed by a roll example. Consider that the value of a passive Russell 2000 portfolio is 100 on January 1, 2014, and at market close on February 21, On this latter date, a futures position is established for the first hedging example with a target value of 50% of portfolio value, or The average quote spread is 1.76% for RVX front-month contracts, so the cost of establishing the RVX position is assumed to be 0.88% of the contract value. The returns of the hedge portfolios are based on the continuous value indexes described in Section A6 of this appendix. On February 21, 2014, the settlement price of the RVX front-month contract is On February 24, the settlement price is The value of the position thus declines by 1.03%. The total return on the hedge portfolio at day-end February 24 is thus -1.90% = ( )*(1-.013) - 1. The Russell 2000 closes at on February 24 for a daily total return of 0.85%. The total return of the hedged portfolio is then -0.01% = 0.85% + ½ * (-1.90%); FTSE Russell RVX futures as a hedge for small cap specific risk 13

15 that is, the equity portfolio return plus the return on the hedge portfolio times its starting value relative to the value of the equity portfolio. On subsequent days, the return of the hedge portfolio must be multiplied by the closing value on the previous day of the hedge portfolio as a fraction of the equity portfolio. The cost of exiting an RVX hedge is calculated analogously to the way entry is shown here. For the VIX contract, on February 21, 2014, the settlement price of RVX is On February 24, the settlement value is 15.00, a 1.00% decline in value. As there is no cost to establish the VIX position, the return of the VIX-hedged portfolio for the day is 0.36% = 0.85% + ½ * (-1.00%). Contract rolls involve the exchange of front-month contracts about to expire for next-month contracts. The old futures position is liquidated, and the proceeds are used to establish the new futures position. If the roll ratio is 1.05 for a month and the hedge consists of 100 front-month contracts, the number of contracts after the roll will be = 100 / 1.05, so that the value of the new position will be equal to the value of the old position at the time of trade. It is assumed that the real position sizes are large enough such that fractional contracts do not trade. The daily value of the new position is based on the daily settlement price. The roll deflator properly adjusts portfolio value for the change in the number of contracts in the hedge portfolio. FTSE Russell RVX futures as a hedge for small cap specific risk 14

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