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VIX as a Companion for Hedge Fund Portfolios

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SRIKANT DASH AND MATTHEW T. MORAN

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MATTHEW T. MORAN

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is a vice president of the Chicago Board Options Exchange. [email protected]

Arbitrage and Distressed Debt are thought to be short volatility. Further, some strategies are expected to benefit from moderate-volatility environments, and others are expected to benefit from high- or low-volatility environments (see, for example, Anson and Ho [2003]). In this article we explore the relationship between VIX and hedge fund returns. Specifically, we explore whether a small allocation to VIX can be constructively used for risk reduction or downside protection in broad-based hedge fund portfolios. While in the past such an exercise would only be of theoretical interest, the availability of exchangetraded VIX futures contracts renders such an exercise practical from an implementation perspective. We use the CSFB/Tremont Hedge Fund Index (HFI) to represent the hedge fund universe. It is important to clarify at the outset that our findings are relevant to users and creators of broad-based hedge fund-of-funds products and broad-based hedge fund index products or those whose hedge fund allocation is broadly diversified across strategies. For purposes of narrow, strategy-based products or allocations, this research can be replicated with ease.

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he CBOE Volatility Index (VIX) is a measure of implied volatility derived from S&P 500 options prices. Although derived from equity index options prices, it is widely regarded to be a broad signal of investor sentiment and market volatility. Whaley [2000] terms it the “investor fear gauge.” It is also believed to be an indicator of investor appetite for risk. The VIX Index is calculated throughout the trading day, and it provides a minute-byminute snapshot of option implied volatility over the next 30 calendar days. In 2003 the methodology for the VIX Index was modified so that it now estimates volatility from the prices of S&P 500 (SPX) index options in a wide range of strike prices (CBOE [2003]). Our study uses the history calculated using the new methodology. Volatility in general, and VIX in particular, is widely thought to influence hedge fund returns. A recent Financial Times article suggested that “when hedge-fund managers lie awake at night worrying about the market, the VIX index is likely to loom large” (Drummond [2005]). On the academic front, there is some empirical evidence suggesting a negative relationship between hedge funds and changes in VIX (see Liew and French [2004]; Kazemi, Schneeweiss, and Martin [2003]; and Amenc, El Bied, and Martellini [2003]). At the individual strategy level, some strategies such as Convertibles are thought to be long volatility, while strategies such as Event-Driven

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is an index strategist at Standard & Poor’s. srikant_dash@ standardandpoors.com

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SRIKANT DASH

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NEGATIVE CORRELATION OF HEDGE FUND RETURNS TO VIX CHANGES

It has been widely documented that VIX is negatively correlated to equity markets and THE JOURNAL OF ALTERNATIVE INVESTMENTS

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EXHIBIT 1 Rolling 30-Month Correlation of HFI with VIX

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0%

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-10% -20%

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-70%

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Jun-04

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Rolling 30-month Correlations of CSFB/Tremont Hedge Fund Index (HFI) with VIX

The Average 30-month Correlation of HFI and VIX was -43%.

EXHIBIT 2

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Returns for VIX in Months Where HFI Losses Were More than 3%

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(J une 1996 - D e c . 2004) . S ourc es : Sta nd ar d & Poor's, C B OE .

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ASYMMETRY IN CORRELATIONS BETWEEN HEDGE FUNDS AND VIX

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Sources: Standard & Poor’s, CBOE.

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that sharp downward moves in the equity market are marked by sharp upward moves in VIX. This inverse relationship occurs with hedge funds as well. Exhibit 1 plots the rolling 30-month correlations of VIX and HFI percent changes. From June 1996 to December 2004, the figure averaged 43%. Exhibit 2 shows the returns for VIX in the nine months between 1995 and 2004 where HFI

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registered a loss of more than 3%. VIX registered a return of more than 35% on seven of those occasions. It registered a loss in 31.5% on one other occasion and had a 10.7% gain on the other.

Although the negative correlations of VIX and HFI shown in Exhibits 1 and 2 do show some promise regarding the prospects of VIX as a risk diversifier or insurance protection for hedge fund portfolios, it is important to explore the relationship in different return environments. Exhibit 3 plots the correlation of VIX and HFI in months where HFI has positive returns and in those months where HFI returns are negative. For the months in which HFI delivered positive returns, the correlation is –5%, whereas for months in which HFI delivered positive returns, it is –44%. This suggests that VIX may provide protection and diversification to broad hedge fund portfolios when they deliver negative returns—that is, when they need it most. This proposition is further strengthened in Exhibit 4, which divides the sample of 120 months into quartiles based on HFI returns and plots the correlations for each period. Clearly, there is an asymmetry of correlations for different return environments

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EXHIBIT 4

Greater Negative Correlation of VIX to Hedge Funds When They Deliver Negative Returns

Greater VIX–Hedge Fund Negative Correlations as Hedge Fund Returns Worsen

-30% -40%

-44% -50% Months with Positive Returns for CSFB/Tremont HFI

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0% -5%

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-20% -30% -40% -50%

-42% 4th Quartile Return Months

3rd Quartile Return Months

2nd Quartile Return Months

1st Quartile Return Months

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Months with Negative Returns for CSFB/Tremont HFI

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Correlation of Monthly CSFB/Tremont Returns to Percent Change in VIX

Correlation of Monthly CSFB/Tremont Returns to Percent Change in VIX

EXHIBIT 3

So ur c e s: S tan d ar d & P oor 's, C B O E.

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12.64% and an annualized risk of 8.13%. With a 5% and 10% allocation, there is a reduction of risk to 7.52% and 7.21% respectively, with a corresponding return reduction to 12.33% and 12.01%. There are no efficient portfolios allocating more than 10% to VIX. This simple mean variance analysis provides us with an initial band in which to allocate VIX to a broad-based hedge fund portfolio. We attempt to refine this allocation further by relying on another property of VIX: mean reversion. Volatility is widely considered to be a mean-reverting process. Rattray and Balasubramanium [2003] and Toikka et al. [2003] document the mean reversion of VIX, especially the property of VIX to swing in the opposite direction when there is a big change. We use this mean reversion property, and the 0% to 10% allocation suggested by mean variance tests, to devise a tactical allocation strategy. If in the past quarter VIX increased by more than 20%, we cut down VIX allocation to 0%. If in the past quarter VIX decreased by more than 20%, we increase VIX allocation to 10%. If VIX changes are between +20% and –20%, we keep the VIX allocation steady at 5%. In essence, if there is a large increase in volatility in the last quarter, we remove our exposure to volatility, since we expect volatility to go down. If there is a large decrease in volatility in the last quarter, we increase our exposure to volatility, since we expect volatility to go up. Both actions are consistent with the negative correlation of VIX and HFI. Exhibit 6 plots cumulative returns of HFI, a static allocation of 5% to a HFI portfolio, and the tactical allocation

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ALLOCATING VIX TO A HEDGE FUND PORTFOLIO

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of hedge funds. When hedge funds are delivering the worst quartile returns, the diversification benefit is best, with a correlation of –42%. Equally interestingly, when the diversification or protection is least needed (in highest quartile months), the correlation is a positive 20%.

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So urc es : S ta nd ar d & P oor 's, C B OE .

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If VIX does possess downside protection or risk reduction opportunities for a broad-based hedge fund portfolio, how much of the portfolio should one allocate to VIX? VIX is merely the second moment of the equity price distribution. Unlike equities, where there is a potential earnings or dividend cash flow stream attached, or bonds, where there is a future coupon and principal cash flow stream attached, or even commodities, where there is scarcity premium or productive use attached, VIX, in theory, has no future cash flows or productive use and in the long run is expected to deliver zero returns. In fact, the VIX return distribution is fairly volatile, with monthly returns of positive or negative 10% fairly common, but the average annualized return for VIX from 1995 to 2004 is 0.07%. Therefore, without even considering any allocation models, a common sense approach would suggest limiting the portfolio exposure to a small amount. To get a basic idea of what percent of VIX to allocate to a broad hedge fund portfolio, we plot a simple efficient frontier in Exhibit 5. This suggests an allocation of 0% to 10%. With no allocation to VIX, the annualized returns are WINTER 2005

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EXHIBIT 5 Efficient Frontier for an HFI+VIX Portfolio

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EXHIBIT 6

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Cumulative Returns of HFI + VIX Portfolios

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HFI + VIX (Tactical Allocation of 0-10%)

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$1.00 Dec-04

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Cumulative Value of $1

$3.72 (tactical)

HFI + VIX (5% Static Allocation)

( D e c . 1 994 - D e c . 2004). So urce s: St and a r d & Po or 's, C BO E .

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VIX AS A COMPANION FOR HEDGE FUND PORTFOLIOS

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Characteristics of HFI + VIX Portfolios

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Sources: Standard & Poor's, CBOE. Based on monthly returns from 1995 to 2004. All deviation figures are annualized. Downside deviation is calculated at a level of minimum acceptable return of 5%, while the Sharpe and Sortino ratios use a risk free rate of 5%.

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usually are settled on the Wednesday morning before the third Friday of the contract month. VIX futures contacts track the level of an “Increased-Value” Index (VBI), which is 10 times the value of VIX, and there also is a futures contract multiplier of $100. Therefore, if the VIX value is 20, VBI is 200, and a single futures contract covers a notional amount of approximately $20,000. If a broadbased hedge fund structure or allocation has $50 million in assets, a 5% overlay allocation would require $2.63 million notional VIX position, which translates to 131 (2,630,000/20,000) contracts to be purchased. Transaction costs would include commissions, fees, bid-ask spread, taxes (if applicable), and market impact costs. If the VIX futures’ bid-ask spread were quoted as a dollar wide and the VBI were at 200, one might say that the bid-ask cost for the investor is half of the spread (from the mid-point of the bid-ask spread), or 25 basis points (0.50/200). Investors should use caution in adding up costs—if investors roll their VIX futures positions several times a year, the total costs can add up. To lessen the total annual roll costs, investors might explore the liquidity of the longer-dated VIX futures. While VIX futures come with the standardization and investor protection features expected from exchangelisted contracts, the current liquidity in VIX futures could pose an implementation hurdle for larger trade sizes. The VIX futures were introduced in 2004 and have not yet achieved the volume and liquidity of the S&P 500 futures and options contacts, which were introduced more than two decades ago. Some investors could explore the use of the over-the-counter (OTC) markets to gain VIX exposure if they are willing to deal with counterparty risk (see, for example, Derman et al. [1999] and Sulima [2001] for a discussion of volatility exposure and the growth of the OTC volatility and variance swaps markets).

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of 0-10% just discussed, over 10 years ending in 2004. Exhibit 7 shows the characteristics of the three portfolios. As can be seen from both exhibits, the tactical allocation portfolio has outperformed the two other portfolios on an absolute return basis as well as on a risk-adjusted return basis. We should note that a t test for differences of means between the portfolio with no VIX and the tactical portfolio gives a p-value of 0.155, suggesting that the outperformance is not significant at the 5% or 10% level. More importantly, our premise of using the mean reversion of VIX and the asymmetry of correlation of VIX to HFI seems to have worked, as seen from the downside risk measures, which show the maximum drawdown, loss deviation, and downside deviation to be better for the tactical allocation portfolio. The tactical allocation example suggested above is a starting point. Alternative rebalancing frequencies and different trigger levels, possibly dynamic triggers, could be experimented with and could possibly generate better risk-return profiles. IMPLEMENTATION ISSUES

How does one implement a broad-based hedge fund strategy with a small allocation to VIX? The most direct way to do so would be using VIX futures. The contracts

CONCLUSIONS

VIX has been termed the “investor fear gauge” and is often considered an indicator of investor appetite for risk. Popular finance as well as academic literature widely considers VIX an influencer of hedge fund returns. Our study shows that VIX is negatively correlated to hedge fund returns and that the correlation profile is asymmetric, with the correlation being more negative in negative months for hedge funds. When hedge funds are delivering the worst quartile returns, the diversification benefit is best. Equally interestingly, when the diversification or protection

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Derman, E., M. Kamal, J. Zou, and K. Demeterfi. “A Guide to Volatility and Variance Swaps.” The Journal of Derivatives, Summer 1999.

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Drummond, James. “Hedge-Fund Managers Lose Sleep over ‘''Investor Fear Gauge.’” Financial Times, June 10, 2005.

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Liew, J., and C. French. “Neutralizing Betas Without Neutralizing Alphas in Funds of Hedge Funds.” Presentation, www.ieor.columbia.edu, November 29, 2004.

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Kazemi, H., T. Schneeweis, and G. Martin. “Understanding Hedge Fund Performance: Research Issues Revisited.” The Journal of Alternative Investments, Spring 2003.

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is least needed, in highest quartile months for the hedge funds, the correlation is positive. This behavior, and the availability of VIX futures and of OTC products that can mimic VIX, opens up interesting possibilities of combining a small allocation to VIX to hedge fund portfolios for risk reduction or downside protection. Whereas standard mean variance measures suggest a static allocation of 0% to 10%, VIX has a range of properties such as mean reversion, and short-term equity market signaling, that can be used to design tactical allocation processes. Our study has focused on broad-based hedge fund portfolios, and the possibility of combining VIX with narrow hedge fund strategies also presents a fertile area for study.

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C Sulima, Cheryl. “Volatility and Variance Swaps.” Capital Market News, Federal Reserve Bank of Chicago, March 2001.

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The authors would like to thank Jay Caauwe, Christian Wind, and Michael Mollet of the CBOE for their valuable suggestions.

Rattray, S., and V. Balasubramanian. “The New VIX as a Market Signal—It Still Works!” Goldman, Sachs & Co. Equity Derivatives Strategy: Options & Volatility, September 5, 2003.

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ENDNOTE

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Amenc, N., S. El Bied, and L. Martellini. “Predictability in Hedge Fund Returns.” Financial Analysts Journal, September/ October 2003.

Toikka, M., E. Tom, S. Chadwick, and M. Bolt-Christmas. “The Volatility Risk Premium: Sell Volatility?” CSFB Equity Derivatives Strategy—Market Commentary, February 26, 2004.

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REFERENCES

Whaley, R.E. “The Investor Fear Gauge.” Journal of Portfolio Management, Spring 2000.

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Anson, M., and H. Ho. “Short Volatility Strategies: Identification, Measurement, and Risk Management.” Journal of Investment Management. Vol. 1, no. 2, pp. 30–43 (2003).

To order reprints of this article, please contact Dewey Palmieri at [email protected] or 212-224-3675.

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CBOE. VIX White Paper, www.cboe.com/vix, 2003.

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