March/April 2007Volume 13, Number 3 


JEL classification: G0, G1, G2, G3 




Author: Tobias Adrian Recent high correlations among hedge fund returns could suggest concentrations of risk comparable to those preceding the hedge fund crisis of 1998. A comparison of the current rise in correlations with the elevation before the 1998 event, however, reveals a key difference. The current increase stems mainly from a decline in the volatility of returns, while the earlier rise was driven by high covariances—an alternative measure of comovement in dollar terms. Because volatility and covariances are lower today, the current hedge fund environment differs from the 1998 environment. Hedge funds—private investment partnerships that are not directly regulated—have grown in importance in recent years. Total assets under the management of hedge funds are currently estimated at $1.5 trillion, and the funds contribute more than half of average trading volume in equity and corporate bond markets.1 While the funds are major liquidity providers in normal times, their use of leveraged trading strategies has raised concerns about their liquidity effects in times of market stress. Indeed, the collapse of the hedge fund LongTerm Capital Management (LTCM) in 1998 seemed to confirm fears that heavy losses by hedge funds have the potential to drain significant liquidity from key financial markets (Table 1). These ongoing concerns about hedge fund vulnerability, coupled with the rapid growth of the funds, underscore the importance of understanding risk in this sector. A key determinant of hedge fund risk is the degree of similarity between the trading strategies of different funds. Similar trading strategies can heighten risk when funds have to close out comparable positions in response to a common shock. For example, many funds had to close out positions during the LTCM crisis to meet margin calls and satisfy risk management constraints. There are many ways to assess the similarity of hedge fund strategies. The approach taken in this edition of CurrentIssues is to examine how closely together the funds’ returns move. If the returns of many funds are either high or low at the same time, the funds could record losses simultaneously, with possible adverse consequences for market liquidity and stability. One standard measure of the comovement of hedge fund returns is covariance. The covariance across a group of funds essentially captures the extent to which their returns move together (or apart, in the case of negative covariance) in dollar terms. A high covariance between two funds means that when one earns a largerthannormal amount of money, the other is likely to do the same. However, it matters little if two funds tend to gain or lose at the same time if such joint gains and losses are only a small fraction of the funds’ total returns. Therefore, analysts “normalize” this measure by dividing the covariance of fund returns by the returns’ total variability. This calculation tells us how closely hedge fund returns move together relative to their overall volatility—a different measure of comovement known as correlation. While this measure is frequently used, it has a notable drawback: correlation may change because its numerator (the returns’ covariance) or its denominator (the returns’ volatility) changes. For instance, the correlation of different funds’ returns may rise either because the returns have moved more closely together (their covariance has increased) or because their volatility has fallen. As this article shows, the distinction is more than a mere technicality: the correlation of hedge fund returns rose both in the period prior to the LTCM crisis and in recent times—but for different reasons. An increase in the comovement of dollar returns was the leading cause of rising correlation in the 1990s, but a decline in overall volatility explains the recent rise. Complementing this result is our finding that high correlations of returns generally do not precede increases in volatility in the hedge fund sector, but high covariances among hedge funds do. While the LTCM collapse was preceded by high correlations and high covariances in an environment of increased hedge fund return volatility, the current environment is characterized by only average levels of covariances and low volatility. Therefore, with respect to both volatility and covariance, the current environment differs markedly from the one in the months preceding the LTCM crisis. The final part of our analysis compares hedge fund correlations and volatilities during the LTCM crisis with equity return correlations and volatilities. By the time the LTCM crisis broke in August 1998, hedge fund return correlations had dropped from their peak levels in 1996 and 1997 to a level that was not particularly high. Some hedge fund strategies registered losses while others gained. By contrast, equity return correlations and volatilities increased sharply, a phenomenon known as financial market contagion.2 Thus, this episode provides evidence that while returns on equities and similar financial assets tend to move together during crises, returns on hedge funds tend to react independently, reflecting the differences in hedge fund exposures to various shocks. Hedge Fund Strategies, Returns, and Correlations The data reveal that average returns and standard deviations varied widely across hedge fund strategies during the 19942006 period (Table 2). The Global Macro strategy had a monthly average return of 1.11percent while the return on Dedicated Short Bias was 0.03percent. Standard deviations—a measure of the risk of a particular trading strategy—ranged from 0.84percent, suggesting relatively low risk, to 4.92percent, pointing to greater risk. The distribution of extreme returns also varied widely across strategies. Emerging Markets experienced the largest monthly decline, 23.03percent, while Dedicated Short Bias had the biggest monthly gain, 22.71percent. Significantly, the data also show that correlations among hedge funds were high over the 19942006 period (Table 3). The average correlation of the ten strategies with the Credit Suisse/Tremont Hedge Fund Index was 40percent. Only the Dedicated Short Bias strategy was negatively correlated with the index. Hedge Fund Risk CrossSectional Dispersion of Returns A second advantage of the crosssectional measure is that it captures idiosyncratic risk—the risk unique to an individual asset—as well as systematic risk. This feature is important because shocks that are idiosyncratic in normal times can cause much broader disruptions when intermediaries become financially constrained. For example, an idiosyncratic shock in 1998—the Russian default—became a threat to overall financial stability because of the failure of LTCM. According to our measure, crosssectional volatility of hedge fund returns peaked in August 1998, the month in which the Russian default precipitated the LTCM crisis (Chart 1). Volatility stood at 12.10percent that month, nearly 7 standard deviations above its mean of 2.66percent (Table 4). September and October 1998 also saw high volatility. However, over the next twelve months, a rapid decline occurred. Since 2001, hedge fund return volatility has declined substantially. As Chart 1 shows, average volatility was 3.17percent before that year, but only 2.09percent afterward. The downward trend since 2001 mirrors the pattern of other volatility measures in the financial markets over the same period. Absolute Value of Returns As the chart shows, absolute values of returns were high in the months preceding the LTCM crisis, but many other months in the sample show similarly high or even higher levels of volatility. For instance, the absolute value of the hedge fund index was particularly high in December 1999, the month before the millennium change. Thus, it appears that this measure is not as precise as our crosssectional measure in distinguishing levels of risk. Hedge Fund Return Comovement The spike in crosssectional volatility in August 1998, depicted earlier in Chart 1, was accompanied by a large negative covariance of hedge fund returns (Chart 3). That is to say, some strategies lost money while others profited. The covariance then increased to a positive but not particularly high level in September 1998 before declining to levels close to zero in October and November. This pattern of covariances over time indicates that hedge fund returns diverged significantly as markets reacted to the Russian default. The response by hedge funds was a closing out of positions, leading to the September increase in crosssectional covariance. Thereafter, covariances remained at fairly low levels, reflecting the reduced risk exposures of the funds. Chart 4 presents the crosssectional correlation of hedge fund returns together with the twelvemonth moving average. The moving average was unusually high before the LTCM crisis, and it has been increasing recently. However, a comparison of Chart 4 with Charts 1 and 3 shows that the source of the elevated levels of hedge fund correlations before the LTCM crisis differs from the source in recent months. Whereas the current high level of correlations is associated with an unusually low level of return volatility, the high level of correlations prior to the LTCM crisis is associated with unusually high covariances. Significantly, although the covariance of hedge fund returns has increased in recent months, the most recent twelvemonth average of 0.32 is well below the longrun average of 0.84—suggesting that current covariance levels may not be alarmingly high. Alternative Correlation Measures The chart reveals that the overall pattern of the alternative correlation measures is similar to that of our measure: correlations were high prior to the LTCM crisis, and have been rising recently. However, there are some notable differences. The peak in average correlation prior to the LTCM crisis occurred in July 1998, while our moving average of crosssectional correlations peaked in December 1996. More recently, average correlations have increased since 2003, but crosssectional correlations have risen only since 2005. These differences suggest that the overall evolution of the correlation measures is similar, even though the precise timing varies somewhat. The Temporal Relationship between Hedge Fund Covariances and Risk Table 5 reports the results of our regressions of quarterly hedge fund volatility on lags of itself as well as a combination of lagged values of correlations and covariances. Columns 1 and 3 show no statistical relationship between correlations and future volatilities. Significantly, columns 2 and 3 reveal that elevated covariances do tend to precede increases in volatilities. One can conclude from these results that the increase in covariances—rather than the increase in correlations—was an early indicator of the high volatility that took place during the LTCM crisis. This conclusion is reasonable, because covariances measure hedge fund return comovement in dollar terms while correlations are covariances normalized by volatilities. System risk can occur when returns in the hedge fund sector move significantly in dollar terms; whether such movement is high or low relative to the level of volatilities appears to be less relevant. A further rise in covariances could thus be of some concern, but the current high level of correlations does not appear to be a strong predictor of future volatility. A Comparison with Equity Market Comovement To put our findings in the proper perspective, we compare the behavior of risk and comovement among hedge funds with that of equity market returns. We create indicators of equity market risk by calculating crosssectional equity volatility and plotting equity implied volatility derived from options prices.9 Equity implied volatility peaked in September 1998, the month of the LTCM recapitalization (Chart 6). Crosssectional equity volatility did not spike in either August or September 1998. Equity correlations, however, showed a sharp peak above 60percent in August 1998 (Chart 7). The behavior of equity correlations contrasts strongly with that of hedge fund correlations during the LTCM crisis. As we observed earlier, hedge fund correlations did not spike during either the Russian default or the LTCM event. Taken together, these results suggest that the investment strategies of hedge funds differ substantially from those of marginal equity investors. In particular, the spike in hedge fund crosssectional volatility in August 1998 illustrates the heterogeneity of hedge fund investment strategies. In a related study, Boyson, Stahel, and Stulz (2006) find no evidence of contagion between hedge funds and market indicators—a result consistent with our finding that spikes in correlations and volatilities in the equity market do not coincide with those of hedge fund returns. Conclusion We also find that the evolution of hedge fund risk and comovement during the LongTerm Capital Management crisis differed from the behavior of broad financial market returns. While the correlations of financial assets such as equities spiked at the same time as volatility shot up, hedge fund return correlations were not unusually high at the beginning of the crisis and they declined sharply as it unfolded. This finding reflects the diverse effects of the crisis on the outcomes of different hedge fund strategies: some hedge funds profited during the event while others registered losses.


Notes 
1. Credit Suisse First Boston, “Equity Research Sector Review: Hedge Funds and Investment Banks,” March9,2005. 2. This type of financial market contagion among asset returns is well documented. See, for example, Claessens and Forbes(2001). 3. The strategies are identified in Tables2 and 3. For more details, visit http://www.hedgeindex.com/. 4. From a statistical point of view, this measure of risk is technically not a volatility, but (the square root of) a second moment. However, it captures both the volatility of return innovations and the volatility of expected returns. 5. For example, consider a fund that holds put options on an equity index. When the put is “out of the money,” the sensitivity of the option with respect to the underlying index is small. If the index declines and the value of the put increases, the exposure of the put position to the index rises. The increase in exposure heightens the volatility of the option, even though the decline in the equity index may not be associated with a change in equity market volatility. 6. Intuitively, when volatility decreases, the range of returns narrows, increasing the tendency for correlations to be high. 7. Garbaravicius and Dierick(2005) survey the recent literature on hedge funds and financial stability; to our knowledge, they are the first to report rolling correlations across hedge fund strategies as an indicator of risk. Chanetal.(2005) explore a variety of indicators of systemic risk in the hedge fund sector. McGuire, Remolona, and Tsatsaronis(2005) construct measures of hedge fund leverage using rolling factor exposures of hedge fund returns. 8. The first principal component is the linear combination of returns that best explains the common variation among the returns. 9. We use the equity implied volatility index of the Chicago Board Options Exchange as a measure of equity implied volatility. Crosssectional equity volatility is measured for all traded stocks for each month. 

References 
Boyson, NicoleM., ChristofW.Stahel, and RenéM.Stulz. 2006. “Is There Hedge Fund Contagion?” NBER Working Paper no.12090, March. Chan, Nicholas, MilaGetmansky, ShaneM.Haas, and AndrewW.Lo. 2005. “Systemic Risk and Hedge Funds.” NBER Working Paper no.11200, March. Claessens, Stijn, and KristinJ.Forbes, eds. 2001. International Financial Contagion. Boston: KluwerAcademic. Garbaravicius, Tomas, and FrankDierick. 2005. “Hedge Funds and Their Implications for Financial Stability.” European Central Bank Occasional Paper no.34, August. Kyle, Albert S., and WeiXiong. 2001. “Contagion as a Wealth Effect.” Journal of Finance56, no.4 (August): 140140. McGuire, Patrick, EliRemolona, and KostasTsatsaronis. 2005. “TimeVarying Exposures and Leverage in Hedge Funds.” Bank for International Settlements Quarterly Review, March: 5972. The author thanks Mary Craig and DinaMarchioni for helpful comments. 

About the Author 


Table 1
1998 Timeline of the LongTerm Capital Management (LTCM) Crisis
Date 
Event 

August 17 
Ruble devaluation and moratorium on Russian bonds 
September 2 
LTCM warning to shareholders 
September 22 
Meeting of LTCM with banks at Federal Reserve Bank of New York 
September 23 
LTCM recapitalized by consortium of banks with $3.625 billion 
September 29 
Fed funds rate cut by 25 basis points, to 5.25percent 
October 15 
Fed funds rate cut by 25 basis points, to 5percent 
November 17 
Fed funds rate cut by 25 basis points, to 4.75percent 


Table 2
Summary Statistics for Hedge Fund Index Returns
January 1994 to September 2006
Strategy  Mean  Standard Deviation 
Minimum  Maximum  Months 

Hedge Fund Index  0.87  2.23  7.55  8.53  153 
Convertible Arbitrage  0.73  1.35  4.68  3.57  153 
Dedicated Short Bias  0.03  4.92  8.69  22.71  153 
Emerging Markets  0.81  4.65  23.03  16.42  153 
Equity Market Neutral  0.80  0.84  1.15  3.26  153 
Event Driven  0.92  1.61  11.77  3.68  153 
Fixed Income Arbitrage  0.52  1.07  6.96  2.05  153 
Global Macro  1.11  3.13  11.55  10.60  153 
Long/Short Equity  0.97  2.92  11.44  13.01  153 
Managed Futures  0.54  3.44  9.35  9.95  153 
MultiStrategy  0.77  1.24  4.76  3.61  150 
Source: Author’s calculations, based on data from Credit Suisse/Tremont.
Notes: The table reports summary statistics for returns on Credit Suisse/Tremont hedge fund strategies. The MultiStrategy data begin in April 1994.


Table 3
Correlations of Returns by Hedge Fund Strategy
January 1994 to September 2006
Strategy  Hedge Fund Index 
CA  DSB  EM  EMN  ED  FIA  GM  LSE  MF  MS 
Hedge Fund Index  100  
Convertible Arbitrage (CA)  40  100  
Dedicated Short Bias (DSB)  48  24  100  
Emerging Markets (EM)  66  31  55  100  
Equity Market Neutral (EMN)  32  33  32  24  100  
Event Driven (ED)  68  57  63  66  38  100  
Fixed Income Arbitrage (FIA)  41  53  5  26  11  38  100  
Global Macro (GM)  85  8  12  42  20  38  42  100  
Long/Short Equity (LSE)  79  27  71  60  34  67  18  41  100  
Managed Futures (MF)  7  13  11  7  13  13  5  27  3  100  
MultiStrategy (MS)  22  39  10  2  24  22  30  14  21  4  100 
Source: Author’s calculations, based on data from Credit Suisse/Tremont.
Notes: The table reports correlations across returns on Credit Suisse/Tremont hedge fund strategies. The MultiStrategy data begin in April 1994. Figures are in percent.


Box Measuring Risk in the Hedge Fund Sector 
Our preferred measure of risk is the crosssectional dispersion of returns, defined as the volatility of returns across funds at each point in time. To construct this measure, we let i = 1,..., N index the hedge fund strategies, and we denote the monthly return of strategy i in month t by . We calculate the crosssectional volatility across strategies as the square root of the crosssectional second moment: (1) crosssectional volatility at time t = . Crosssectional covariance is defined as the average of crosssectional moments: (2) crosssectional covariance at time t = . Crosssectional correlation therefore is the ratio of crosssectional covariance and the square of crosssectional volatility. 


Chart 1 



Table 4
Summary Statistics for CrossSectional Moments
April 1994 to September 2006
Summary Statistic  Volatility  Correlation  Covariance 

Mean  2.66  0.11  0.81 
Standard deviation  1.35  0.21  2.40 
Minimum  0.78  0.11  9.74 
Maximum  12.10  0.69  13.19 
Correlation (Percent)  Volatility  Correlation  Covariance 
Volatility  100  
Correlation  4  100  
Covariance  12  67  100 
Source: Author’s calculations, based on data from Credit Suisse/Tremont.
Note: The table reports summary statistics and correlations for the crosssectional volatility, correlation, and covariance of returns on Credit Suisse/Tremont hedge fund strategies.


Chart 2 



Chart 3 


Chart 4 



Chart 5 


Table 5
Dependence of Volatility on Correlation
and Covariance
April 1994 to September 2006
(1)  (2)  (3)  

Volatility  
Lag 1  0.28***  0.33***  0.25* 
Lag 2  0.29**  0.24*  0.21* 
Lag 3  0.05  0.03  0.06 
Correlation  
Lag 1  2.08  1.89  
Lag 2  0.23  1.22  
Lag 3  0.79  0.10  
Covariance  
Lag 1  0.12  0.01  
Lag 2  0.13*  0.19***  
Lag 3  0.06  0.08  
Constant  1.39**  1.18***  1.73** 
Source: Author’s calculations, based on data from Credit Suisse/Tremont.
Notes: The table reports regressions of the crosssectional volatility on lags of crosssectional volatility, correlation, and covariance at a quarterly frequency. Standard errors are adjusted for autocorrelation and heteroskedasticity.
*Statistically significant at the 10 percent level.
**Statistically significant at the 5 percent level.
***Statistically significant at the 1 percent level.

Chart 6 


Chart 7 



Disclaimer  
The views expressed in this article are those of the author and do not necessarily reflect the position of the Federal Reserve Bank of New York or the Federal Reserve System. 
