fund data and variance risk proxy used in this chapter. Section 3 presents the em-pirical results, including both the time-series and cross-sectional analysis. Section 4 checks the robustness of the results, with respect to other risk factors and alternative hedge fund data. Section 5 concludes.
2.2 Data and Variance Risk Proxy
2.2.1 Hedge Fund Data
The hedge fund data is obtained from the BarclayHedge data base, which contains 9357 funds in total. I apply net-of-fee hedge fund returns for the sample period from January 1996 to September 2008. The BarclayHedge database provides good qual-ity data with fewer missing observations and better fund-specific information than other widely-used hedge fund databases, such as TASS, HFR, and CISDM/MSCI.
Especially, the database contains both live and dead funds, which avoid survivorship bias (see Fung and Hsieh (2000) and Agarwal and Naik (2004)). According to the strategy classification document released by Hedge Fund Research in 2010, I group all funds to five primary strategies: Equity Hedge (EH), Event Driven (ED), Rel-ative Values (RV), Macro (MAC), and Fund of Funds (FOF). EH has totally 1302 funds and contains strategies of Equity Long, Equity Short, Equity Long/Short, and Equity Index Trading. ED has totally 319 funds and consists of strategies such as Event Driven, Distressed Securities, and Merger Arbitrage. RV has 1722 funds which include Fixed Income Arbitrage and Convertible Arbitrage. MAC has 181 funds and comprises the Systematic Trading and Multi-Strategy funds. The largest group is the fund of funds, which consist of 2635 funds. I first construct a value-weighted index across all funds, where the weight is determined by assets under
2.2. Data and Variance Risk Proxy 41
management. Such index represents the hedge fund industry at an aggregate level.
I then construct strategy-specific index within each investment objectives, which provide perspectives on the heterogeneity of hedge fund strategies. I report the summary statistics in Table 2.1.
2.2.2 Variance Risk Proxy
Considerable evidence shows that variance risk is priced in the cross-section of asset returns. A widely-used proxy to measure variance risk is the difference between the realized return variance and the implied variance. Previous studies usually use a synthetic swap rate which is replicated from option prices (see Bondarenko (2004), Carr and Wu (2008)). In this study, I apply the market quotations of variance swaps on the S&P 500 index. The data is obtained from a major investment bank which has substantial history of active trading on variance swaps. It offers important ad-vantages for the study in hedge fund. First, the quotations reflect pure variance risk, without any estimation bias on variance swap rate. Further, using returns of tradable assets in the factor regression model, I can interpret the intercept as risk-adjusted returns.
To be consistent with the reporting conventions of hedge fund returns, I select the variance swaps with fixed 1-month maturity and obtain the first-day observation at each month within the sample period from January 1996 to September 2008. Table 2.2 presents the existence, the magnitude and the risk characteristics of variance risk premium in the sample. On average, the realized variance is considerably smaller than the variance swap rate. In a formal test, the hypothesis that the two quantities are equal is firmly rejected by the p-value. These evidences indicate a statistically significant negative variance risk premium. I plot the time-series of realized and implied variance in Figure 2.1 Panel A, which provides a visible impression about the spread between the realize and implied variance.
2.2. Data and Variance Risk Proxy 42
Beyond the sample mean, the time series of the variance risk premium show big negative skewness and positive kurtosis. The risk characteristics are different from the market index, as shown in the CAPM regression results. The variance risk premium has extremely small market beta, only 0.02, while a much larger alpha.
This result is consistent with the findings in Carr and Wu (2008), who find that the majority of variance risk premium cannot be explained by market risk, size factor, value factor, or momentum factors.
An important property of variance risk premium is the asymmetric pattern across the states of economy. To illustrate this point, I plot the variance risk premium and S&P 500 index returns in Figure 2.1 Panel B. We can see that the magnitude of variance risk premium is negative over most time of the sample period, while occasionally spikes, indicating months with especially high realized variance. Many spikes occur during market downturns or crisis times. For example, the largest spike in the sample period occurs in February 2002, when the internet bubble bursts and triggers large variations in the stock market. The second largest spike is in October 1997, which coincides with the 1997 Asia Financial Crisis period. Other spikes are observed in September 1998 when LTCM collapse and in July 2007 during the early period of the subprime crisis.
The time-series patterns of variance risk premium is consistent with the literature.
Bollerslev, Tauchen, and Zhou (2008) publish their estimation of variance risk pre-mium3. I find that the correlation between the variance swap quotations and the measure in Bollerslev, Tauchen, and Zhou (2008) is about 0.9, indicating very simi-lar patterns.
Since the variance risk carries a negative premium on average and most hedge fund
3The data can be downloaded from the author’s webpage