## Abstract

Portfolio managers have long sought the ability to increase diversification and hedge market downturns without sacrificing upside returns. Using volatility as a diversifying asset is an attractive proposition because of volatility’s asymmetric response to underlying price movements. Theoretically, being able to hold the CBOE Volatility Index in a portfolio should provide substantial benefits to a portfolio. The authors find, however, that currently available VIX-related products are costly in their implementation and yield negative abnormal returns. Even so, if investors insist on investing in volatility assets, using VIX futures offers the best Sharpe ratios.

Diversification is one of the first, if not the first, principle one learns in portfolio theory. Diversification can lead to lower portfolio standard deviation without a proportional reduction in portfolio returns. In order for an asset to add diversification benefits to a portfolio, the asset must be less than perfectly positively correlated with the other assets in the portfolio. The less correlated the asset returns, the more diversified the portfolio. In a globalizing market, however, the ability to diversify is becoming increasingly difficult. Different investment classes have been used in the past for their diversification ability, but the correlation between asset classes has been shown to be growing stronger. In addition, financial instruments that are customarily negatively correlated with equity returns may not provide the desired hedge against market downturns because the return correlations become positive in times of distress. For example, during the market collapse in 2008, the value of both equities and commodities fell, even though traditionally, commodities are negative beta assets.^{1} Bond holdings also declined in value during the 2008 crash, as the risk in commercial borrowing increased while liquidity fell. Many hedge funds designed to cushion losses in equity markets actually experienced reversals over the 2007–2009 period. Szado (2009) documented the increased correlation of asset classes returns over the 2007–2008 crisis period, above the levels seen in the 2004–2006 period, meaning that as the need for diversification grew, the ability of many assets to hedge equity holdings shrank, at the most inopportune time.

Such results have led financial experts to search for new assets with diversification properties. One asset class that has come to the forefront is volatility. Volatility is not only negatively correlated with equity returns, but the correlation is strongest when equity returns are negative (e.g., Black 1976; Giot 2005; Daigler and Rossi 2006; Hafner and Wallmeier 2007). The strong negative correlation with equity markets makes volatility very appealing for equity investors. In addition, volatility is a stationary, mean-reverting process that, in theory, would be an excellent diversifier at an average cost of the risk-free rate, as cash earns the risk-free rate and volatility on average earns zero. Thus, having the ability to invest in volatility is of great interest to investors; holding a small amount of volatility provides substantial diversification to the market portfolio, particularly when the market experiences negative returns.

Since its inception in January 1993, the CBOE Volatility Index (VIX) has become a ubiquitous measure of expected equity market volatility.^{2} Therefore, VIX should be considered an ideal asset class for equity investors as its negative correlation is strongest during market downturns, as in the credit crisis of 2007–2008. Hafner and Wallmeier (2007) found log volatility swap returns against log index returns resemble the payoff of a long put position, due to the strong negative correlation in market downturns and near zero correlation in bullish markets.

Black (1976) was the first to discuss that the volatility of stock index returns tends to increase when stock prices drop. The negative correlation between past stock returns and future volatility is commonly referred to as “asymmetric volatility.” Giot (2005), Dennis, Mayhew, and Stivers (2006), and DeLisle, Doran, and Peterson (2011) documented the asymmetric relationship between VIX and the S&P 500 Index and specifically showed that VIX increases and S&P 500 declines are more strongly correlated than VIX decreases and S&P 500 increases. Whaley (2009) documented the mean-reverting nature of VIX and also describes its asymmetric nature such that VIX will react more dramatically to a stock market decline than to a rally. Furthermore, Simon (2003) noted the tendency of traders to overvalue (undervalue) the equity market when volatility levels are unusually low (high). Consistent with Daigler and Rossi (2006), it would appear that investing in VIX when it is low not only provides a hedge against declines in the S&P 500, but it also will not proportionally penalize investors when the S&P 500 increases. Accordingly, Briere, Burgues, and Signora (2010) advocated a sliding approach when hedging. In such a situation, more (fewer) VIX futures contracts are held when VIX levels are notably lower (higher) due to the mean-reverting nature of the index.

To demonstrate the benefit of VIX in an equity portfolio, Panel A of Exhibit 1 provides the average monthly return, standard deviation, and Sharpe ratio for a portfolio consisting of only the S&P 500 and a second portfolio that consists of 90% in the S&P 500 and 10% in the VIX from 1996 to 2016. The average monthly return is 13.5% higher for the portfolio with VIX and the standard deviation is 30.1% lower versus the S&P 500 portfolio, leading to a Sharpe ratio that is improved by 62.5%. These findings are consistent with those of Daigler and Rossi (2006), who showed that adding a long spot VIX position to an S&P 500 portfolio yields a significant diversification benefit.

While this simple and straightforward demonstration displays the diversification benefit that VIX can offer equity investors, it is not as simple as just investing in the VIX in the real world. The VIX is not a traded asset that can be purchased like a stock or bond. Nor is it a typical index like the S&P 500, where investors have the ability to purchase the appropriate weights of each security in the index and replicate its performance (exchange-traded funds execute this strategy for many stock indices). The VIX is the square root of the variance computed from a fictional option on the S&P 500. Although there is a formula to replicate the variance, the replicating portfolio assumes continuous trading, a continuum of listed strike prices, and a listed strike at the money (ATM). In practice, continuous trading is cost prohibitive, strike prices of options are not infinitely available, and ATM options are not always available. Hence, investors cannot simply replicate VIX’s underlying variance portfolio nor invest directly in the VIX.

Nevertheless, since its inception, market makers have been developing strategies to create or closely replicate volatility investment securities due to the ever-increasing demand for investing in such securities. Exchanges have created derivatives on volatility like the VIX futures, volatility swaps, and so on, that are tradable. Equilibrium asset pricing theory suggests that assets should be at least close to fairly priced. Additionally, the negative correlation between VIX and equity returns suggests a negative market beta and thus a negative expected return. This is indeed what we see in practice. For example, Panel B of Exhibit 1 presents the mean monthly return, standard deviation of returns, and the Sharpe ratio for three portfolios: the S&P 500, a mix of 90% S&P 500 and 10% VIX (as if VIX were investable), and a mix of 90% S&P 500 and 10% nearest-term VIX futures (rebalanced monthly). If VIX were investable, the 10% VIX portfolio outperforms the straight S&P 500 portfolio in all dimensions. However, the 10% VIX futures underperforms the S&P 500 portfolio monthly returns and reduces the Sharpe ratio by nearly 90%.

This study examines the use of VIX futures, VIX call options, SPX put options, and SPX option straddles for diversification benefits.^{3} We find evidence that all tradable volatility assets are costly and have negative expected returns. However, VIX futures (and VXX ETNs, which replicate VIX using futures contracts) offer the best Sharpe ratios for their cost. The use of VIX call options, SPX put options, and SPX option straddles are prohibitively expensive and generate negative average portfolio returns, even with only small weights in a portfolio with the S&P 500.

## A BRIEF HISTORY OF VOLATILITY DERIVATIVES

A volatility trade entails investing in a security that offers exposure to volatility without being impacted by the directional changes in the underlying asset. The idea of including volatility into a portfolio is not a new concept. However, the ability to trade such assets is a relatively recent advancement in financial markets.

A variance swap was the first commonly used security to execute a volatility trade. Variance swaps are offered on a variety of equity indexes and are traded over the counter with an initial value of zero. A long position receives the difference between the observed realized variance and the variance swap rate, which is determined at initiation of the contract. Hafner and Wallmeier (2007) analyzed the relationship between variance swap returns with index returns in Europe. They found a pronounced kink at an index return of zero. Similar to findings using data in the United States, they found a strong negative volatility premium, which is defined as the difference between the log realized variance and the log variance swap rate. As a result, selling realized volatility is a more profitable strategy.

The strategy of investing in a straddle, the purchasing of equal numbers of calls and puts, can also be viewed as a volatility trade. However, Brenner, Ou, and Zhang (2006) pointed out that a straddle is inefficient because it insures against volatility changes (i.e., vega) and changes in delta (i.e., gamma). Brenner et al. (2006) introduced an option on a straddle designed to limit exposure to volatility risk. This compound option is sensitive to volatility innovations and thus useful as a hedge. It is important to note, however, that this compound option is theoretical in nature as it is not an exchange-traded asset, thus it is not an implementable strategy.

With the increased popularity and demand for investing in volatility, the CBOE launched trading on VIX futures contracts in March 2004. These contracts have a multiplier of $1,000 and are settled in cash at expiration.^{4} After the success of the VIX futures, the CBOE launched VIX option contracts in February 2006. These options have a multiplier of $100, are European-style options, and when exercised will result in delivery of cash on the business day following expiration.^{5}

Pricing these VIX derivatives can be quite complex. Risk-neutral option pricing models, such as Black and Scholes (1973), depend on the assumption of a no-arbitrage replicating portfolio using the underlying asset and a risk-free asset. For example, with a call option on a stock, Black and Scholes’ insight is that an option equivalent can be constructed by purchasing the stock and borrowing at the risk-free rate. This replicating portfolio creates the exact same payoff as a call option and allows for the call’s valuation. However, risk-neutral pricing is just a valuation tool and does not necessarily propose that the expected return on derivatives is the risk-free rate. Because the capital asset pricing model applies to all assets, the expected return depends on the beta of the call option. So, according to the Black–Scholes model, the expected return depends on the beta of the call: β_{call} = (*S*/*X*)(Δ_{call})(β_{stock}), where *S* is the stock spot price, *X* is the call option’s strike price, Δ_{call} is the delta of the call, and β_{stock} is the beta of the underlying stock. Because market volatility is negatively related to market returns, market volatility and its derivatives have negative betas and, thus, negative expected returns. Additionally, in our case the underlying VIX (market volatility) is not a traded asset, so the replicating portfolio cannot be constructed and thus risk-neutral pricing theory does not apply. Consequently, the shape of the forward curve for volatility products, such as VIX futures, also includes a component related to expected volatility. This differs from S&P 500 futures, which can be priced by no-arbitrage models. Because the pricing of VIX derivatives contain a component related to expected volatility, it is likely the mean-reverting nature of VIX is captured in the price of such derivatives. This may make the derivatives more expensive than they would otherwise be or create tracking error with the underlying VIX.

Szado (2009) noted that exposure to VIX calls and puts as well as VIX futures does not directly mimic holdings in the spot levels of VIX, given that the mean-reverting nature of the underlying are priced into the derivative values. Moran and Dash (2007) showed that the desirable characteristics of VIX are not always reflected in VIX futures and options. Shu and Zhang (2012) demonstrated that VIX futures have some price discovery component but suggested that VIX futures and VIX spot behave in a similar fashion. This lack of deviation is important if VIX futures are going to serve as an adequate proxy for the VIX index. Chen, Chung, and Ho (2011) concluded the addition of VIX futures and VIX-squared portfolios, replicated by SPX call and put options, offer benefits for mean–variance investors. In such arrangements, investors can gain diversification benefits from investing in these VIX-related products and hedge fund managers can use these securities to enhance their equity portfolio performance, as measured by the Sharpe ratio.

Simon and Campasano (2014) examined trading opportunities presented by the VIX futures term structure’s lack of forecast power for subsequent VIX changes. The trading strategy involving shorting (buying) one front VIX futures contract when the VIX futures basis is in contango (backwardation) and the daily roll exceeds 0.10 (−0.10) VIX futures and holding until either the conditions in being in the trade no longer exist or nine business days elapse, producing statistically significant profits. Simon (2017) used a strategy buying VIX call (put) options when the VIX future curve is strongly in backwardation (contango) for five business days, both leading to significantly profitable returns ranging from 7% to 42%. It is worth noting this study assumes trades are entered and exited at the midpoint of the bid–ask spread.

Szado (2009) showed long volatility exposure may result in negative returns in the long run, allowing it to provide a significant protection in downturns, such as the 2008 financial crisis. Alexander and Korovilas (2011) demonstrated that buying VIX futures considerably enhanced equity returns from June 2007 to June 2010, but the analysis was performed ex post and thus is misleading as perfect foresight would seldom justify the purchasing of VIX futures as a long equity diversification tool.

## DATA, SAMPLE, AND METHODOLOGY

The data for comparison of VIX-based hedging strategies are assembled from numerous sources. The actual daily VIX levels used for construction of the theoretical strategy are taken from the CBOE’s historical website.^{6} The methodology for VIX construction was amended in September 2003, although retroactive calculation allows for collection of data beginning in 1990. Historical S&P 500 returns are taken from CRSP in order to calculate the returns of positions that theoretically hedge S&P 500 holdings with the raw VIX level. To adopt actual S&P 500 holdings, we gather price data for the SPY ETF, which mimics the performance of the S&P 500, also from CRSP.

Futures positions are used as one method for creating a VIX-based portfolio. VIX futures began trading on the CBOE futures exchange in March 2004. The daily prices of VIX and S&P 500 futures contracts are collected from Bloomberg, beginning with the arrival of VIX futures. However, VIX futures with two-month expiration dates were not continuously available until the end of 2005. Thus, we limit our analyses of the VIX futures strategy to the time period spanning 2006–2013.

An additional method for assembling a tradable VIX-based portfolio is with the use of VIX options. These options began trading on the CBOE in February 2006, and their daily prices are collected from the OptionMetrics Ivy Database for the 2006–2013 period. Additionally, we collect data on S&P 500 options, SPX, beginning in 1996 and ending in 2013. In addition to examining returns on the puts, SPX options are used to create at-the-money straddles, which are typically employed as strategic plays on volatility. Finally, data for Fama and French’s (1993) MKT, SMB, and HML factors and the Carhart (1997) UMD factor are provided on Kenneth French’s data library website.^{7}

Exhibit 2 presents the summary statistics for S&P 500 and VIX returns. Panel A shows that S&P 500 returns over the entire sample period average 70 basis points (bps) per month, while VIX returns average 130 bps per month. However, the standard deviation of the VIX monthly returns is 18.33%, which is so volatile that the average VIX returns are statistically indistinguishable from zero. Additionally, the median return is negative, highlighting the positively skewed distribution and the mean-reverting nature of volatility.

The correlation between S&P 500 and VIX returns is −0.651, demonstrating a strong negative relationship as should be expected. Panel B of Exhibit 2 limits the sample to months in which S&P 500 returns are positive. Limiting the sample in this manner yields average S&P 500 and VIX returns of 3.22% and −6.52% a month, respectively. The correlation between S&P 500 and VIX returns during these months is −0.283. Panel C, when the sample is limited to months where S&P 500 returns are negative, shows that the average S&P 500 and VIX returns are −3.61% and 14.66% a month, respectively. The return correlation for these months is −0.531. When separating the returns into up and down periods, mean returns for both the S&P 500 and VIX are significantly different from zero, highlighting the importance of differing market conditions. More interestingly, the absolute value of the mean S&P 500 returns is similar for up and down market conditions, while the positive mean VIX returns are twice as large during periods of negative S&P 500 movement as the negative mean VIX returns in periods of positive S&P 500 returns. This result highlights the asymmetric relation between S&P 500 returns and VIX returns and may be indicative of the potential for using volatility as a hedging instrument against S&P 500 losses.

Panel D of Exhibit 2 breaks the sample into months where VIX and the S&P 500 have different monthly signed returns and months where the signed returns are the same. The VIX and S&P 500 have different signed returns in almost 75% of the sample months, with 46% of those occurring when the S&P 500 is up and VIX is down. Just over 17% of the sample has months when both VIX and the S&P 500 are up, which is not unreasonable because large positive movements can result in increases in short-term volatility.^{8} The 8% of observations when volatility falls while the S&P 500 falls is unusual, but it reflects that volatility and returns are not always negatively correlated.

To start our analysis, we first estimate how VIX and the S&P 500 move together. To this end, we estimate the following regression over the entire sample period:

1where *r _{VIX}*

_{,t}is the return of the VIX index on day

*t*,

*r*

_{S&P500}_{,t}is the return of the S&P 500 on day

*t*, α is a constant, and ε

_{t}is the residual on day

*t*. Because it is well documented that the relation between market returns and volatility is asymmetric, we split the sample into positive and negative S&P 500 returns and re-estimate the regression. Exhibit 3 presents the estimations’ results.

When the full sample is used, the relationship between VIX and S&P 500 is highly significant, as a 1% change in the S&P results in a 2.8% change in the VIX. However, consistent with current literature, the relationship is clearly not symmetric when separating the sample into positive and negative S&P 500 returns. When the S&P falls, the magnitude of β is almost twice as large as when the S&P 500 rises (−3.23 versus −1.46, both statistically significant at the 1% level), consistent with Exhibit 2.

## EFFECTIVENESS OF VIX AS A DIVERSIFYING ASSET

### VIX Index as a Theoretical Portfolio Component

Given the asymmetrical relationship between VIX and the S&P 500, we examine whether forming portfolios using the VIX could theoretically result in greater or less volatile returns than simple passive investing in the S&P 500. While it is not possible to directly purchase the VIX index, we nonetheless wish to examine whether theoretical holdings in VIX benefit investors by capturing both the asymmetric relationship between VIX and the S&P 500 as well as the mean reversion in volatility. By doing so, we establish a best-case scenario by which to evaluate the performance of VIX-like assets as a supplement to typical passive investing.

In Exhibit 4, we present mean monthly returns and the CAPM alpha and beta that result from the regression of monthly portfolio returns on the value-weighted monthly market return. We also show the Carhart (1997) four-factor alpha and market beta that result from the regression of monthly returns on the three Fama and French (1993) factors (MKT, SMB, and HML) and Carhart’s (1997) momentum factor (UMD).

All positions presented in Exhibit 4 are long in the S&P 500 but utilize 10% VIX in the portfolio as a potential diversifying asset. In addition to showing the performance of portfolios that constantly invest in VIX, we consider another alternative based on the mean-reverting nature of VIX. The historical mean for the VIX index is roughly 20.2%, which corresponds to the historical average of volatility for market returns of 17.8%. Therefore, consistent with the recommendation of Briere, Burgues, and Signora (2010), a “threshold” strategy of buying the VIX when it drops below its mean may hedge against future decreases in the S&P 500 without the expense of constantly maintaining the hedge. Thus, along with the basic or “no threshold” case, we present results for portfolios that purchase VIX or VIX-like assets only when the VIX is below the threshold of 20.2 at the beginning of a one-month period.

The results in Exhibit 4 show that VIX theoretically serves as an extremely effective hedge to holdings in the S&P 500. In addition to the increase in mean returns and Sharpe ratio (also shown in Panel A of Exhibit 1), the no threshold portfolio that holds 10% VIX has a monthly four-factor alpha of 20 bps that is significant at the 5% level. The mean threshold portfolio has a slightly higher average monthly return than the no threshold portfolio, but its Sharpe ratio and alphas decrease. As might be expected, market betas increase when a threshold for the VIX level is imposed, which highlights the dampening effect of adding VIX to a portfolio. Funds are placed entirely in the S&P 500 on a less frequent basis when a VIX threshold is invoked, and thus while hedging costs may be removed, portfolio betas rise with a threshold.

Unfortunately, it is not possible to directly invest in VIX, and as such, we question whether the performance of VIX-based products will be analogous to the impressive returns offered by the theoretical VIX hedge. It is entirely possible that the pricing and day-to-day management of these assets may erase any theoretical improvements for investors.

### VIX Futures

Since 2006, it has been possible for a portfolio to buy or sell cash-settled VIX futures with expiration dates in each month of the year. Because entering into VIX futures may be a close substitute to theoretical investment in the VIX, we investigate whether investment in the VIX futures actually replicates the payoff of the underlying index. Shu and Zhang (2012) demonstrated that VIX futures have some price discovery component but suggested that VIX futures and VIX spots behave in a similar fashion. This lack of deviation is important if VIX futures are going to serve as an adequate proxy for the VIX. Our futures strategy is to purchase VIX futures contracts at the end of month *t* = 0 that expire in month *t* = 2, sell the contracts at the end of month *t* = 1, and repeat the process (for example, at the end of January we purchase futures expiring in March, sell them at the end of February, and then purchase new contracts that expire in April). This method avoids the roll problem that surfaces when contracts approach expiration.^{9} Exhibit 5 shows the mean returns, Sharpe ratios, and alphas from portfolios that attempt to diversify S&P 500 holdings by purchasing the one-month-ahead VIX futures contracts in various amounts.

The alphas of all the futures-hedged S&P 500 portfolios are statistically significant at the 5% level and are negative (ranging from −29 to −69 bps per month). The Sharpe ratios are also lower for the portfolios that use futures (ranging from −0.063 to 0.077) compared with that of the straight S&P 500 portfolio (0.112). As the percentage of VIX futures in the portfolio is increased, the performance measures deteriorate. The poor performance of the futures may be due to the term structure under which sellers of the futures incorporate a premium for the upside risk in the index futures because, on average, VIX futures have an upward-sloping term structure.

The negative returns from the VIX futures may be representative of the negative volatility risk premium found by Bakshi and Kapadia (2003) and others. More importantly, because VIX itself is not investable, it is impossible to arbitrage the difference in the futures price and the index, always leading to the upward bias in pricing. This is consistent with the findings of Zhang, Shu, and Brenner (2010). Holding VIX futures does impart a reduction to the market beta; however, this reduction in systematic risk comes at a price.

### VIX Options

Unlike the VIX futures contracts, where the only choice is the expiration of the contract, VIX option contracts have both time and strike dimensions. In order to construct portfolios of S&P 500 and VIX calls, at the end of each month, a one-month-ahead VIX call is selected that is closest to at-the-money status and has similar expiration as the futures contracts noted previously (e.g., during the month of February, the portfolio holds options that expire in March). We next compute the monthly return on the call option by purchasing options at the bid price and selling them at the ask price, and then compute the portfolio returns based on VIX call portfolio weights of 5%, 10%, and 15%.

Exhibit 6 shows market betas for the no threshold portfolios that always use VIX calls are not statistically different from zero, but they are all negative. All the alphas for these portfolios are positive, but they are also not statistically significant. The no threshold portfolios have higher mean returns than a straight S&P 500 portfolio, but Sharpe ratios are about half that of the S&P 500 portfolio. The mean threshold strategy has extremely poor performance with negative average returns and alphas ranging from −110 (using a 5% weight on VIX calls) to −291 (using a 15% weight on VIX calls) basis points a month that are statistically significant at the 1% level. These results suggest weighting VIX calls in the portfolio as little as 5% is very expensive.

### SPX Options

Although SPX put options are not considered a volatility asset, their returns are negatively correlated with the S&P 500 when the S&P 500 level falls below the strike price. As such, they may be considered as a similar diversifying asset as a VIX call. Portfolios of S&P 500 holdings hedged with SPX put options are constructed in a similar fashion to the VIX call portfolios. The only difference is that 5% out-of-the-money (OTM) puts are used rather than ATM calls. Exhibit 7 shows the results from the SPX put option strategy.

By all measures, any strategy using OTM SPX put options severely underperforms a straight S&P 500 portfolio. No threshold portfolios have statistically significant mean monthly returns ranging from −160 to −592 bps. Mean threshold portfolio returns average between −77 and −327 bps per month. The portfolio alphas are similar in magnitude and statistical significance. SPX put options are, by far, the most expensive (i.e., generate the poorest performance) asset class we examine in this study.

SPX option straddles (purchasing both ATM call and put options) are considered to be plays on volatility in the S&P 500 (e.g., Broadie, Chernov, and Johannes 2009). With straddles, price movement of the underlying, no matter the direction, generates a payoff to the straddle. Hence, any price volatility moves an ATM straddle into the money. Thus, SPX straddle returns improve the overall portfolio performance. However, Exhibit 8 demonstrates that the transaction costs associated with straddles overcome any diversification benefits of this type of volatility asset.

## CONCLUSION

Our results illustrate the feasibility and effectiveness of attempting to hold volatility as an asset class in order to avoid market shortfalls. Because the current asymmetric relationship between the VIX and the S&P 500 generates the strongest correlations when the market is falling, holding the VIX is a natural candidate for hedging market risk. In fact, our results show that if VIX were directly investable, a portfolio composed of VIX and the S&P 500 would provide returns and risk levels that far outpace the traditional S&P 500 buy-and-hold portfolio. Of course, those initial results are hypothetical and not perfectly replicable via investable VIX derivative products, because such assets price anticipated VIX mean reversion and any mispricing cannot be arbitraged. In summary, it appears that while VIX itself provides an excellent way to add diversification and hedge market downside without significant expense, the investable market products that are available come with negative expected returns. Exhibit 9 presents the buy-and-hold performance of portfolios holding 5% volatility using the volatility assets discussed in this article all in the same time period and starting with $1,000,000. Panel A of Exhibit 9 shows the results of a no threshold strategy that always holds volatility, and Panel B shows the results of holding volatility assets only if the VIX level is below a threshold of 20.2.

The portfolios holding VIX futures or the VXX ETN in combination with the S&P 500 underperforms a straight S&P 500 portfolio but are comparatively the best-performing volatility assets. SPX straddles are the next-best-effective volatility asset. VIX calls and SPX puts, however, appear to be the most expensive and least effective hedge for a straight S&P 500 portfolio. Given the evidence in this study, at this time it appears the most cost-effective method to incorporate a volatility asset into an otherwise diversified portfolio is through the use of VIX futures, or if the investor only has access to equity markets, the VXX ETN, recognizing that the VXX will incur slightly more fees than using futures contracts but does not require a margin account, as do VIX futures. Additionally, we show investors should not place a weight of more than 5% of these assets in their portfolios and, consistent with Briere, Burgues, and Signora (2010), implement a threshold approach to holding these volatility assets.

## ACKNOWLEDGMENT

We would like to thank Hossein Kazemi (the editor) and Gregory W. Brown (guest editor and referee) for their helpful comments.

## ENDNOTES

↵

^{1}Numerous commodity indices also retreated by more than 50% of value during the equity market decline of 2007–2009, as inflation ground to a standstill and consumption of raw materials slowed.↵

^{2}The CBOE Options Exchange continuously calculates the VIX level as 100 times the square root of the expected 30-day variance of the S&P 500 rate of return. The variance is computed as a weighted average of S&P 500 Index options (SPX) prices. Details of the computation are found on the CBOE website at http://cfe.cboe.com/cfe-education/cboe-volatility-index-vx-futures/vix-primer/cboe-futures-exchange-nbsp-nbsp-education.↵

^{3}We also examine the VIX exchange-traded notes (or ETNs; ticker symbol VXX). In 2009, the first broker-traded volatility exchange-traded notes (ETNs) were issued by Barclays Bank in PLC, ticker VXX and VXZ. The VXX tracks the performance of short-term VIX futures index, and VXZ tracks the mid-term VIX futures index. The introduction of these ETNs coincided with the increased liquidity of the futures and options on VIX, the heightened volatility in the market, and investor demand for a product that allowed easy access to volatility. It is important to note the underwriting bank of an ETN promises to pay the returns reflected by the index minus fees. The results associated with VXX are almost identical to those of the VIX futures contracts results. Thus, we omit the analysis from this article, except in Exhibit 9. More detailed results are available upon request.↵

^{4}See http://cfe.cboe.com/cfe-products/vx-cboe-volatility-index-vix-futures/contract-specifications.↵

^{5}See http://www.cboe.com/products/vix-index-volatility/vix-options-and-futures/vix-options/vix-options-specs.↵

^{7}See http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html. We thank Kenneth French for making these data available.↵

^{8}This can happen because it is possible for call options to be bid up, resulting in an implied volatility smile.↵

^{9}As a VIX futures contract approaches expiration, basis risk increases and the divergence between front-month and next-month contracts increases. Additionally, there is no way to hedge the difference between last price and settlement price, which can cause huge variations in returns to the strategy.

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