# Do Hedge Funds Exploit Rare Disaster Concerns?

Do Hedge Funds Exploit Rare Disaster Concerns?
Gao, George P;Gao, Pengjie;Song, Zhaogang
2018-03-24 00:00:00
Abstract We find hedge funds that have higher return covariation with a disaster concern index, which we develop through out-of-the-money puts on various economic sector indices, earn significantly higher returns in the cross-section. We provide evidence that these funds’ managers are more skilled at exploiting the market’s ex ante rare disaster concerns (SEDs), which may not be associated with disaster risk. In particular, high-SED funds, on average, outperform low-SED funds by 0.96% per month, but have less exposure to disaster risk. They continue to deliver superior future performance when SEDs are estimated using the disaster concern index purged of disaster risk premiums and have leverage-managing and extreme market-timing abilities. Received June 30, 2014; editorial decision August 26, 2017 by Editor Laura Starks. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web Site next to the link to the final published paper online. Prior research on hedge fund performance and disaster risk focuses on the covariance between fund returns and ex post realized disaster shocks. In the time series, a number of hedge fund investment styles, characterized as de facto sellers of put options, incur substantial losses when the market declines (Mitchell and Pulvino 2001; Agarwal and Naik 2004). In the cross-section, individual hedge funds have heterogeneous disaster risk exposure, and funds with greater exposure to disaster risk usually earn higher returns during normal times, but experience losses during stressful times (Agarwal, Bakshi, and Huij 2010; Jiang and Kelly 2012). At face value, the existing evidence suggests that hedge funds, as a whole, are much like conventional assets in an economy with disaster risk: they earn higher returns simply by being more exposed to disaster risk. We hypothesize that certain hedge fund managers possess skills in exploiting ex ante market disaster concerns and thus deliver superior future fund performance while being less exposed to disaster risk. Our empirical evidence lends strong support to this hypothesis. In particular, it has been documented that market participants, including institutional investors, pay a “fear premium” beyond the compensation for disaster risk to insure against disaster shocks (Bollen and Whaley 2004; Driessen and Maenhout 2007; Han 2008; Bollerslev and Todorov 2011). We hypothesize that if hedge fund managers have better skills in exploiting disaster concerns or the fear premium, they could deliver superior future fund performance. In particular, they could do so because they may be better at identifying market fears that do not result in disaster shocks. By supplying disaster insurance to investors with high disaster concerns, some fund managers profit more than others, who do not possess such skills.1 Second, even when some disaster concerns are subsequently realized as disaster shocks, certain fund managers may be better than others at identifying through research whether the fear premium is overpriced, and thus be able to profit from their research skills. Third, “difficulty in inference regarding ... severity of disasters ... can effectively lead to significant disagreements among investors about disaster risk” (Chen, Joslin, and Tran 2012). That is, disaster concerns can have different levels of fear premiums paid by different investors, regardless of whether a disaster shock is ultimately realized or not. Skilled fund managers can profit from investors who pay a high fear premium and avoid those who pay a low fear premium. In sum, fund managers’ skills in exploiting disaster concerns can contribute to higher returns for certain hedge funds, and at the same time do not necessarily make them more exposed to disaster shocks. To test this hypothesis, we develop a measure of a fund’s skill at exploiting rare disaster concerns (SED) using the covariation between fund returns and a disaster concern index that we construct with out-of-the-money put options on various stock sector indices. We argue that this covariance between hedge fund returns and ex ante disaster concerns can identify skillful fund managers.2 Conceptually, when the market’s disaster concern is high, funds with managers more skilled at identifying the value of the fear premium should earn higher contemporaneous returns than others. Consistent with our conjecture that hedge funds exhibit different levels of skills at exploiting disaster concerns, we find substantial heterogeneity of SED across hedge funds as well as significant persistence in SED. Our main tests focus on the relation between the SED measure and future fund performance. In our baseline results, funds in the highest SED decile on average outperform funds in the lowest SED decile by $$0.96\%$$ per month (Newey-West t-statistic of $$2.8$$).3 Moreover, high-SED funds exhibit significant performance persistence. The return spread of the high-minus-low SED deciles ranges from $$0.84\%$$ per month (t-statistic of $$2.6$$) for a three-month holding horizon to $$0.44\%$$ per month (t-statistic of $$1.9$$) for a 12-month holding horizon. We also show that the outperformance of high-SED funds is pervasive across almost all hedge fund investment styles. These results run against the interpretation that these hedge funds earn higher returns on average simply by being more exposed to disaster risk. If this were true, that is, if the covariation between fund returns and the disaster concern index (i.e., the SED measure) measures disaster risk exposure, then the high-SED funds should earn lower returns on average (rather than the higher returns we document) because they are good hedges against disaster risk under this interpretation. We provide several pieces of supporting evidence for our hypothesis that SED captures the skill of some hedge fund managers at exploiting disaster concerns. First, if SED captures fund managers’ skill rather than the disaster risk exposure of hedge funds, high-SED funds should be less exposed to disaster risk. We test this possibility by computing the loadings of SED fund deciles on a large set of macroeconomic variables, market risk factors, volatility risk factors, liquidity factors, and option-based risk measures (Ang, Chen, and Xing 2006; Ang et al. 2006; Pastor and Stambaugh 2003; Acharya and Pedersen 2005; Sadka 2006; Hu, Pan, and Wang 2013; Brunnermeier and Pedersen 2009; Mitchell and Pulvino 2012; Bali, Brown, and Caglayan 2011; Bali, Brown, and Caglayan 2012). We find strong evidence that high-SED funds are actually less risky than low-SED funds, consistent with the interpretation that high-SED fund managers are more skilled at exploiting disaster concerns. If our results are driven by missing risk factors, then these factors would have to be nearly uncorrelated with the large set of known risk factors we employ. Second, recognizing that our $$\mathbb{RIX}$$ measure is the price of a disaster insurance contract that contains compensations for both objective disaster shocks (rational disaster risk premiums) and subjective concerns (or fears) about disaster risk, we purge the disaster risk premium from $$\mathbb{RIX}$$ based on the stochastic disaster risk model of Seo and Wachter (2014), and reestimate funds’ SED. These SED estimates capture the managers’ skill in exploiting the pure concerns about disaster risk more directly. We continue to observe that high-SED funds strongly outperform low-SED funds with these revised SED estimates, further supporting our hypothesis that high-SED funds earn higher returns because of their managers’ superior skills at exploiting rare disaster concerns. Third, if SED captures skills, then we expect high-SED fund managers to be better at managing leverage and at timing extreme market conditions. To test this corollary hypothesis, we calculate the leverage implied by $$\mathbb{RIX}$$ and estimate each fund’s ability to manage leverage. The evidence supports this hypothesis, in that high-SED funds’ managers appear to have superior leverage-managing ability: they reduce their fund’s exposure to market-wide leverage when the market leverage condition worsens. This evidence is consistent with the procyclicality of hedge fund leverage documented by Ang, Gorovyy, and van Inwegen (2011) and Jiang (2014), whereas our innovative evidence reveals the intriguing connection between how hedge fund managers exploit disaster concerns and how they manage fund leverage. Moreover, we estimate each fund’s extreme-market-timing ability and find that high-SED funds, on average, have strong bear-market-timing ability. Both results are consistent with the interpretation of SED as measuring fund managers’ skills, though we note that such evidence is only suggestive, because of the lack of fund-level data on portfolio holdings, investment positions, and balance sheets. We also provide strong empirical evidence against alternative interpretations. First, it could be that the higher average returns the high-SED funds earn over the full sample are just a result of better performance during normal times and (hypothetically) worse performance during stressful times that are short in our sample period of 1996–2010. In other words, the high-SED funds may simply be lucky during our sample period. To test this alternative, we perform a conditional portfolio analysis of SED-sorted funds in normal versus stressful market times, and find that high-SED funds outperform low-SED funds even more in stressful market times, including the severe 2008 financial crisis. Such evidence is inconsistent with the luck interpretation and supports our skill-based explanation of hedge fund performance. Second, as the spikes in the $$\mathbb{RIX}$$ factor often occur when disaster shocks hit the market, it is possible that some of our high-SED funds earn profits by purchasing—rather than selling—disaster insurance before the disaster shock; these funds then realize large positive payoffs when such disastrous outcomes hit the market. Among the credit-style hedge fund sample, we identify a potential set of such funds and find even stronger SED effects on future fund performance after excluding them from our portfolio analysis. Moreover, we explore a general identification condition for the funds purchasing disaster insurance: the time $$t-1$$ returns of these funds, who pay a cost to buy disaster insurance before disastrous events at time $$t$$ should have significant negative loadings on the $$\mathbb{RIX}$$ at time $$t$$ Accordingly, we identify fund managers who purchase disaster insurance by regressing the fund’s monthly excess return at $$t-1$$ on the next-period $$\mathbb{RIX}$$ at $$t$$. We find no significant return difference between low- and high-exposure funds, a finding that contradicts the interpretation that the high-SED funds purchase disaster insurance. These results support our theory that the skills of high-SED fund managers are to identify the existence and magnitude of the fear premium and sell insurance contracts accordingly, rather than to forecast the disaster event and buy disaster insurance beforehand. Third, we investigate whether high-SED funds are those that exploit insurance associated with the intermediate rather than the extreme tails of the market. The answer is unequivocally no. In particular, we capture the intermediate tails of the market using the VIX, given that it is less sensitive to the extreme tail events captured by $$\mathbb{RIX}$$. We find that hedge fund portfolios formed on the covariation between fund excess returns and the VIX (analogous to SED) have no significant return spreads. Moreover, sequential sorts show that the SED well explains cross-sectional hedge fund returns in the presence of potential fund managers’ skill at exploiting intermediate tails, but not vice versa. Collectively, these results suggest that it is fund managers’ skill at exploiting disaster concerns, rather than concerns about intermediate tail events, that explain cross-sectional hedge fund performance. Fourth, and finally, as our paper primarily contributes to the literature about hedge fund managers’ skills and cross-sectional fund performance, we show that the SED measure is distinct from other fund manager skill variables, including the skill of hedging systematic risk (Titman and Tiu 2011), the skill of adopting innovative strategies (Sun, Wang, and Zheng 2012), the skill of timing market liquidity (Cao et al. 2013), and the conditional performance measure based on downside returns (Sun, Wang, and Zheng 2013), using both Fama and MacBeth 1973 regressions and double-sorting portfolios.4 Throughout the paper, we compute risk-adjusted abnormal returns using the Fung and Hsieh (2001) 8-factor model and the 10-factor model recently developed by Namvar et al. (2014) (NPPR, hereafter). The difference in alpha between the high- and low-SED funds remains highly significant: 1.27% and 0.80% per month, with Newey-West t-statistics of 3.8 and 2.8, relative to the Fung-Hsieh and NPPR models, respectively. Our results also survive a battery of robustness checks, including alternative measures of ex ante disaster concerns using 90-day options and S&P 500 index options, different choices of portfolio weight, fund size, fund backfilling bias, delisted fund returns, fund December and non-December returns, different benchmark models, and different hedge fund databases. In addition, we control for a large set of hedge fund characteristics using Frazzini and Pedersen (2014) regressions. 1. The Conceptual Framework and Hypothesis Our main hypothesis is that certain hedge fund managers are more skilled at exploiting disaster concerns, in the sense that they can better reap a high premium in disaster risk insurance. It has been well documented that market participants, including institutional investors, usually pay a high premium over the compensation for disaster risk to insure against disaster risk (Bollen and Whaley 2004; Driessen and Maenhout 2007; Han 2008; Constantinides, Jackwerth, and Perrakis 2009; Bollerslev and Todorov 2011). If certain hedge fund managers are better at exploiting disaster concerns and reaping the overpaid high premium, they could deliver superior future fund performance.5 Our hypothesis is not inconsistent with the prior research showing that hedge funds earn returns simply by taking on exposure to disaster risk on the whole (Mitchell and Pulvino 2001; Agarwal and Naik 2004), but differs by emphasizing that one group of skilled hedge fund managers should be able to take on the high premium in disaster insurance with less disaster risk exposure than others. To identify these skilled fund managers and capture their skill at exploiting disaster concerns, we use the covariation between fund returns and ex ante disaster concerns (SED). When the market’s disaster concern level is high, funds with managers more skilled at identifying the value of the fear premium should earn higher contemporaneous returns than the rest by selling disaster insurance. Therefore, our main hypothesis predicts that high-SED hedge funds should earn higher future returns in the cross-section. This prediction runs directly against the interpretation that these hedge funds earn higher returns simply by being more exposed to disaster risk. If this were true, that is, if the covariation between fund returns and ex ante disaster concerns captures disaster risk exposure, then the high-SED funds should earn lower returns because they are good hedges against disaster risk under this interpretation. We further test several important aspects of our main hypothesis. First, if SED captures fund managers’ skill rather than the fund’s disaster risk exposure, high-SED funds should be less exposed to disaster risk. Second, our hypothesis is that high-SED fund managers are skilled at identifying the existence and magnitude of the fear premium and selling insurance contracts accordingly. As a result, the SED effect is expected to be most significant when we use measures of pure concerns or fears about disaster risk. Third, as both the leverage and the extreme market conditions are integrated parts of any disaster episodes, we expect high-SED fund managers to be better at managing leverage and at timing extreme market conditions, as two specific types of skills. Because of the lack of fund-level data on portfolio holdings, investment positions, and balance sheets, it is unrealistic to prove that the covariation between fund returns and disaster concerns entirely captures fund managers’ skill at exploiting disaster concerns. In consequence, it is important to rule out alternative mechanisms that SED may be related to. The first alternative is that the higher returns earned by high-SED funds over the full sample are just a result of better performance during normal times and (hypothetically) worse performance during stressful times that are short in our sample. In other words, the high-SED funds may simply be lucky during our sample period. Second, it is possible that some high-SED funds earn profits by purchasing—rather than selling—disaster insurance before the disaster shock, because disaster concerns usually spike when disaster shocks hit the market. Third, high-SED funds could be those that exploit insurance associated with the intermediate rather than the extreme tails of the market. 2. Data and Estimation 2.1 Measuring rare disaster concerns In this section, we develop a rare disaster concern index ($$\mathbb{RIX}$$) to estimate the ex ante market expectation regarding future disaster events. We build on the model-free implied volatility measures of Carr and Madan (1998), Britten-Jones and Neuberger (2000), Carr and Wu (2009), and Du and Kapadia (2012). In particular, the value of $$\mathbb{RIX}$$ depends on the price difference between two option-based replication portfolios of variance swap contracts. The first portfolio accounts for mild market volatility shocks, and the second accounts for extreme volatility shocks induced by market jumps associated with rare event risk. By construction, the $$\mathbb{RIX}$$ is equal to the insurance price against extreme downside market movements in the future. Over time, the $$\mathbb{RIX}$$ signals variations in ex ante disaster concerns. 2.1.1 Construction of $$\mathbb{RIX}$$ Consider an underlying asset whose time-$$t$$ price is $$S_{t}$$. We assume for simplicity that the asset does not pay dividends. An investor holding this security is concerned about its price fluctuations over a time period $$[t,T]$$. One way to protect him- or herself against price changes is to buy a contract that delivers payments equal to the extent of price variations over $$[t,T]$$, minus a prearranged price. Such a contract is called a “variance swap contract,” as the price variations are essentially about the stochastic variance of the price process.6 The standard variance swap contract in practice pays \begin{equation*} \left( \ln \frac{S_{t+\Delta }}{S_{t}}\right) ^{2}+\left( \ln \frac{ S_{t+2\Delta }}{S_{t+\Delta }}\right) ^{2}+\cdots +\left( \ln \frac{S_{T}}{ S_{T-\Delta }}\right) ^{2} \end{equation*} minus the prearranged price $$\mathbb{VP}$$. In principle, replication portfolios consisting of out-of-the-money (OTM) options written on $$\left. S_{t}\right.$$ can be used to replicate the time-varying payoff associated with the variance swap contract and, hence, to determine the price $$\left. \mathbb{VP}\right.$$. We now introduce two replication portfolios and their implied prices for the variance swap contract. The first, which underlies the CBOE’s construction of VIX and focuses on the limit of the discrete sum of squared log returns, determines $$\mathbb{VP}$$ as \begin{equation} \mathbb{IV}\equiv \frac{2e^{r\tau }}{\tau }\left\{ \int_{K>S_{t}}\frac{1}{ K^{2}}C(S_{t};K,T)dK+\int_{K<S_{t}}\frac{1}{K^{2}}P(S_{t};K,T)dK\right\} , \label{f:IV} \end{equation} (1) where $$\left. r\right.$$ is the constant risk-free rate, $$\left. \tau \equiv T-t\right.$$ is the time-to-maturity, and $$\left. C(S_{t};K,T)\right.$$ and $$\left. P(S_{t};K,T)\right.$$ are the prices of call and put options with strike $$\left. K\right.$$ and maturity date $$\left. T\right.$$, respectively. As observed in Equation (1), this replication portfolio contains positions in OTM calls and puts with a weight inversely proportional to their squared strikes. The second replication portfolio relies on $$\left. Var_{t}^{\mathbb{Q}}\left( \ln S_{T}/S_{t}\right) \right.$$, which avoids the discrete sum approximation, and determines $$\left. \mathbb{VP}\right.$$ as \begin{align} \mathbb{V} &\equiv \frac{2e^{r\tau }}{\tau }\left\{ \int_{K>S_{t}}\frac{1-\ln\left( K/S_{t}\right)}{K^{2}}C(S_{t};K,T)dK \right. \notag \\ &\quad\left. +\int_{K<S_{t}}\frac{1-\ln\left( K/S_{t}\right) }{K^{2}}P(S_{t};K,T)dK\right\} . \label{f:V} \end{align} (2) This replication portfolio differs from the first in Equation (1) by assigning larger (smaller) weights to more deeply OTM put (call) options. As strike price $$\left. K\right.$$ declines (increases), that is, put (call) options become more out of the money, $$\left. 1-\ln \left( K/S_{t}\right)\right.$$ becomes larger (smaller). Since more deeply OTM options protect investors against larger price changes, it is intuitive that the difference between $$\mathbb{IV}$$ and $$\mathbb{V}$$ captures investors’ expectations about the distribution of large price variations. Our measure of disaster concerns is essentially equal to the difference between $$\mathbb{V}$$ and $$\mathbb{IV}$$, which is due to extreme deviations of $$S_{T}$$ from $$S_{t}$$. However, both upside and downside price jumps contribute to this difference. In view of the many recent studies that indicate that investors are more concerned about downside price swings (Liu, Pan, and Wang 2005; Ang, Chen, and Xing 2006; Barro 2006; Gabaix 2012; Wachter 2013), we focus on downside rare events associated with unlikely, but extremely negative, price jumps. In particular, we consider the downside versions of both $$\mathbb{IV}$$ and $$\mathbb{V}$$: \begin{align} \mathbb{IV}^{-} &\equiv \frac{2e^{r\tau }}{\tau }\int_{K<S_{t}}\frac{1}{ K^{2}}P(S_{t};K,T)dK, \notag \\ \mathbb{V}^{-} &\equiv \frac{2e^{r\tau }}{\tau }\int_{K<S_{t}}\frac{1-\ln \left( K/S_{t}\right) }{K^{2}}P(S_{t};K,T)dK, \label{f:downsideV_IV} \end{align} (3) where only OTM put options that protect investors against negative price jumps are used. We then define our rare disaster concern index ($$\mathbb{RIX}$$) as \begin{equation} \mathbb{RIX}\equiv \mathbb{V}^{-}-\mathbb{IV}^{-}=\frac{2e^{r\tau }}{\tau } \int_{K<S_{t}}\frac{\ln \left( S_{t}/K\right) }{K^{2}}P(S_{t};K,T)dK. \label{f:RIX_portfolio} \end{equation} (4) Assume the price process follows the Merton (1976) jump-diffusion model, with $$dS_{t}/S_{t}=\left( r-\lambda \mu _{J}\right) dt+\sigma dW_{t}+dJ_{t}$$, where $$\left. r\right.$$ is the constant risk-free rate, $$\left. \sigma\right.$$ is the volatility, $$\left. W_{t}\right.$$ is a standard Brownian motion, $$\left. J_{t}\right.$$ is a compound Poisson process with jump intensity $$\left. \lambda \right.$$, and the compensator for the Poisson random measure $$\left. \omega \left[ dx,dt\right] \right.$$ is equal to $$\left. \lambda \frac{1}{\sqrt{2\pi }\sigma _{J}}\exp \left( -\left( x-\mu_{J}\right) ^{2}/2\right) \right.$$. We can show that \begin{equation} \mathbb{RIX}\equiv 2\mathbb{E}_{t}^{\mathbb{Q}}\int_{t}^{T}\int_{R_{0}} \left( 1+x+x^{2}/2-e^{x}\right) \omega ^{-}\left[ dx,dt\right] , \label{f:RIX} \end{equation} (5) where $$\left. \omega ^{-}\left[ dx,dt\right] \right.$$ is the Poisson random measure associated with negative price jumps. Therefore, $$\mathbb{RIX}$$ captures all the high-order ($$\geq 3$$) moments of the jump distribution with negative sizes, given that $$e^{x}-(1+x+x^{2}/2)$$ = $$x^{3}/3+x^{4}/4+\cdots.$$ Motivated by the fact that hedge funds invest in different sectors of the economy, we make one further extension, particularly relevant for analyzing hedge fund performance. Namely, we measure market concerns about future rare disaster events associated with various economic sectors, instead of relying on the S&P 500 index exclusively. In particular, we employ liquid index options on six sectors: the KBW banking sector (BKX), the PHLX semiconductor sector (SOX), the PHLX gold and silver sector (XAU), the PHLX housing sector (HGX), the PHLX oil service sector (OSX), and the PHLX utility sector (UTY). This allows us to avoid the caveat of using options on a single market index under which the perceived disastrous outcome of one economic sector may be offset by a euphoric outlook in another sector. Specifically, we first use OTM puts on each sector index to calculate sector-level disaster concern indices, and then take a simple average across them to obtain a market-level $$\mathbb{RIX}$$. Such a construction is likely to incorporate disaster concerns about various economic sectors, which is particularly important for investigating hedge fund performance. 2.1.2 Option data and empirical estimation We obtain daily data on options from 1996 through 2010 from OptionMetrics. For both European calls and puts on the six sector indices we consider, the dataset includes the daily best closing bid and ask prices, in addition to implied volatility and option Greeks (delta, gamma, vega, and theta). Following the literature, we clean the data as follows: (1) we exclude options with nonstandard expiration dates, missing implied volatility, zero open interest, or either a zero bid price or a negative bid-ask spread; (2) we discard observations with a bid or ask price of less than 0.05 to mitigate the effect of price recording errors; and (3) we remove observations where option prices violate no-arbitrage bounds. Because there is no closing price in OptionMetrics, we use the mid-quote price (i.e., the average of the best bid and ask prices) as the option price.7 Finally, we consider only options with maturities longer than 7 days and shorter than 180 days for liquidity reasons. We focus on a 30-day horizon to illustrate the construction of $$\mathbb{RIX}$$, that is, $$\left. T-t=30\right.$$. On a daily basis, we choose options with exactly 30 days to expiration, if they are available. Otherwise, we choose two contracts with the nearest maturities to 30 days, with one longer and the other one shorter than 30 days. We keep only out-of-the-money put options and exclude days with fewer than two option quotes of different moneyness levels for each chosen maturity. As observed in Equation (4), the computation of $$\mathbb{RIX}$$ relies on a continuum of moneyness levels. Similar to Carr and Wu (2009), we interpolate implied volatilities across the range of observed moneyness levels. For moneyness levels outside the available range, we use the implied volatility of the lowest (highest) moneyness contract for moneyness levels below (above) it. In total, we generate 2,000 implied volatility points equally spaced over a strike range of zero to three times the current spot price for each chosen maturity on each date. We then obtain a 30-day implied volatility curve, either exactly or by interpolating the two implied volatility curves of the two chosen maturities. Finally, we use the generated 30-day implied volatility curve to compute the OTM option prices based on the Black and Scholes (1973) formula and then $$\mathbb{RIX}$$ according to a discretization of Equation (4) for each day. After obtaining those daily estimates, we take the daily average over the month to deliver a monthly time series of $$\mathbb{RIX}$$, extending from January 1996 to June 2010. We further divide $$\mathbb{RIX}$$ by $$\mathbb{V}^{-}$$ as a normalization, to mitigate the effect of different volatility levels across different economy sectors. The sector-level OTM index puts we use are generally liquid, and thus the liquidity effect of these OTM puts on $$\mathbb{RIX}$$ is expected to be small.8 2.1.3 Descriptive statistics Table 1 presents descriptive statistics for the disaster concern indices. Panel A shows the monthly aggregated $$\mathbb{RIX}$$ has a mean of 0.063, with a standard deviation of 0.02. Among sector-level disaster concern indices, the semiconductor sector has the highest mean (0.076) and median (0.070), whereas the utility sector has the lowest mean (0.029) and median (0.027). Interestingly, the banking sector has the highest standard deviation, likely due to the 2007–2008 financial crisis. Figure 1 presents a time-series plot of the aggregated $$\mathbb{RIX}$$ that illustrates how the market’s perception of future disaster events varies over time. We observe that disaster concerns spike not only when disaster shocks hit the market, such as the LTCM collapse, the crash of Nasdaq, and the recent financial crisis, but also during bull markets, such as the peak of Nasdaq and the market rally in October 2011. Figure 1 View largeDownload slide Time series of RIX This figure plots the monthly time series of the rare disaster concern index (RIX) from January 1996 to December 2011. Figure 1 View largeDownload slide Time series of RIX This figure plots the monthly time series of the rare disaster concern index (RIX) from January 1996 to December 2011. Table 1 Descriptive statistics of rare disaster concern indices A. Summary statistics of monthly time series Mean Min P25 Median P75 Max SD N KBW Banking Sector (BKX) 0.057 0.017 0.037 0.054 0.068 0.165 0.029 192 PHLX Semiconductor Sector (SOX) 0.076 0.037 0.055 0.070 0.095 0.143 0.025 192 PHLX Gold Silver Sector (XAU) 0.065 0.036 0.051 0.063 0.073 0.140 0.018 192 PHLX Housing Sector (HGX) 0.063 0.030 0.046 0.054 0.073 0.139 0.023 114 PHLX Oil Service Sector (OSX) 0.072 0.039 0.053 0.066 0.087 0.165 0.025 179 PHLX Utility Sector (UTY) 0.029 0.012 0.023 0.027 0.033 0.071 0.010 165 Aggregated Factor ($$\mathbb{RIX}$$) 0.063 0.034 0.046 0.061 0.074 0.141 0.020 192 A. Summary statistics of monthly time series Mean Min P25 Median P75 Max SD N KBW Banking Sector (BKX) 0.057 0.017 0.037 0.054 0.068 0.165 0.029 192 PHLX Semiconductor Sector (SOX) 0.076 0.037 0.055 0.070 0.095 0.143 0.025 192 PHLX Gold Silver Sector (XAU) 0.065 0.036 0.051 0.063 0.073 0.140 0.018 192 PHLX Housing Sector (HGX) 0.063 0.030 0.046 0.054 0.073 0.139 0.023 114 PHLX Oil Service Sector (OSX) 0.072 0.039 0.053 0.066 0.087 0.165 0.025 179 PHLX Utility Sector (UTY) 0.029 0.012 0.023 0.027 0.033 0.071 0.010 165 Aggregated Factor ($$\mathbb{RIX}$$) 0.063 0.034 0.046 0.061 0.074 0.141 0.020 192 B. Correlations between rare disaster concern indices and other factors $$\mathbb{RIX}$$ BKX SOX XAU HGX OSX UTY MKTRF –0.102 –0.110 –0.013 –0.150 –0.172 –0.067 –0.177 SMB 0.002 –0.019 0.087 –0.019 –0.030 –0.032 –0.051 HML –0.165 –0.109 –0.112 –0.211 –0.209 –0.171 –0.032 UMD –0.121 –0.202 –0.055 0.017 –0.225 –0.020 –0.080 PTFSBD 0.248 0.194 0.259 0.226 0.277 0.239 0.172 PTFSFX 0.051 0.073 –0.024 0.130 0.102 0.009 –0.005 PTFSCOM –0.055 –0.031 –0.112 0.056 0.048 –0.083 –0.154 PTFSIR 0.177 0.242 –0.029 0.163 0.348 0.091 0.069 PTRSSTK –0.026 0.032 –0.114 0.017 0.139 –0.079 –0.015 Liquidity risk: PS –0.193 –0.214 –0.087 –0.226 –0.325 –0.096 –0.242 Liquidity risk: Sadka –0.310 –0.401 –0.130 –0.283 –0.408 –0.195 –0.220 Liquidity risk: Noise –0.009 –0.046 –0.055 0.092 –0.009 0.005 0.010 Change of term spread 0.222 0.251 0.169 0.167 0.280 0.141 0.259 Change of default spread 0.221 0.146 0.123 0.256 0.208 0.241 0.002 Change of VIX –0.094 –0.065 –0.112 –0.025 –0.048 –0.096 –0.057 B. Correlations between rare disaster concern indices and other factors $$\mathbb{RIX}$$ BKX SOX XAU HGX OSX UTY MKTRF –0.102 –0.110 –0.013 –0.150 –0.172 –0.067 –0.177 SMB 0.002 –0.019 0.087 –0.019 –0.030 –0.032 –0.051 HML –0.165 –0.109 –0.112 –0.211 –0.209 –0.171 –0.032 UMD –0.121 –0.202 –0.055 0.017 –0.225 –0.020 –0.080 PTFSBD 0.248 0.194 0.259 0.226 0.277 0.239 0.172 PTFSFX 0.051 0.073 –0.024 0.130 0.102 0.009 –0.005 PTFSCOM –0.055 –0.031 –0.112 0.056 0.048 –0.083 –0.154 PTFSIR 0.177 0.242 –0.029 0.163 0.348 0.091 0.069 PTRSSTK –0.026 0.032 –0.114 0.017 0.139 –0.079 –0.015 Liquidity risk: PS –0.193 –0.214 –0.087 –0.226 –0.325 –0.096 –0.242 Liquidity risk: Sadka –0.310 –0.401 –0.130 –0.283 –0.408 –0.195 –0.220 Liquidity risk: Noise –0.009 –0.046 –0.055 0.092 –0.009 0.005 0.010 Change of term spread 0.222 0.251 0.169 0.167 0.280 0.141 0.259 Change of default spread 0.221 0.146 0.123 0.256 0.208 0.241 0.002 Change of VIX –0.094 –0.065 –0.112 –0.025 –0.048 –0.096 –0.057 Rare disaster concern indices are constructed using the prices of 30-day out-of-the-money put options on 6 different sector indices from 1996 to 2011. The aggregated rare disaster concern index ($$\mathbb{RIX}$$) is a simple average of the 6 sector-level disaster concern indices. Panel A reports summary statistics for their monthly time series, and panel B reports the time-series correlations between one rare disaster concern index and a number of factors, including the Fama-French-Carhart four factors (MKTRF, SMB, HML, and UMD), the Fung-Hsieh 5 trend-following factors (PTFSBD, PTFSFX, PTFSCOM, PTFSIR, and PTFSSTK), the Pastor-Stambaugh (PS) liquidity risk factor, the Sadka liquidity risk factor, the Hu-Pan-Wang liquidity risk factor (Noise), change in term spread, change in default spread, and change in VIX. Table 1 Descriptive statistics of rare disaster concern indices A. Summary statistics of monthly time series Mean Min P25 Median P75 Max SD N KBW Banking Sector (BKX) 0.057 0.017 0.037 0.054 0.068 0.165 0.029 192 PHLX Semiconductor Sector (SOX) 0.076 0.037 0.055 0.070 0.095 0.143 0.025 192 PHLX Gold Silver Sector (XAU) 0.065 0.036 0.051 0.063 0.073 0.140 0.018 192 PHLX Housing Sector (HGX) 0.063 0.030 0.046 0.054 0.073 0.139 0.023 114 PHLX Oil Service Sector (OSX) 0.072 0.039 0.053 0.066 0.087 0.165 0.025 179 PHLX Utility Sector (UTY) 0.029 0.012 0.023 0.027 0.033 0.071 0.010 165 Aggregated Factor ($$\mathbb{RIX}$$) 0.063 0.034 0.046 0.061 0.074 0.141 0.020 192 A. Summary statistics of monthly time series Mean Min P25 Median P75 Max SD N KBW Banking Sector (BKX) 0.057 0.017 0.037 0.054 0.068 0.165 0.029 192 PHLX Semiconductor Sector (SOX) 0.076 0.037 0.055 0.070 0.095 0.143 0.025 192 PHLX Gold Silver Sector (XAU) 0.065 0.036 0.051 0.063 0.073 0.140 0.018 192 PHLX Housing Sector (HGX) 0.063 0.030 0.046 0.054 0.073 0.139 0.023 114 PHLX Oil Service Sector (OSX) 0.072 0.039 0.053 0.066 0.087 0.165 0.025 179 PHLX Utility Sector (UTY) 0.029 0.012 0.023 0.027 0.033 0.071 0.010 165 Aggregated Factor ($$\mathbb{RIX}$$) 0.063 0.034 0.046 0.061 0.074 0.141 0.020 192 B. Correlations between rare disaster concern indices and other factors $$\mathbb{RIX}$$ BKX SOX XAU HGX OSX UTY MKTRF –0.102 –0.110 –0.013 –0.150 –0.172 –0.067 –0.177 SMB 0.002 –0.019 0.087 –0.019 –0.030 –0.032 –0.051 HML –0.165 –0.109 –0.112 –0.211 –0.209 –0.171 –0.032 UMD –0.121 –0.202 –0.055 0.017 –0.225 –0.020 –0.080 PTFSBD 0.248 0.194 0.259 0.226 0.277 0.239 0.172 PTFSFX 0.051 0.073 –0.024 0.130 0.102 0.009 –0.005 PTFSCOM –0.055 –0.031 –0.112 0.056 0.048 –0.083 –0.154 PTFSIR 0.177 0.242 –0.029 0.163 0.348 0.091 0.069 PTRSSTK –0.026 0.032 –0.114 0.017 0.139 –0.079 –0.015 Liquidity risk: PS –0.193 –0.214 –0.087 –0.226 –0.325 –0.096 –0.242 Liquidity risk: Sadka –0.310 –0.401 –0.130 –0.283 –0.408 –0.195 –0.220 Liquidity risk: Noise –0.009 –0.046 –0.055 0.092 –0.009 0.005 0.010 Change of term spread 0.222 0.251 0.169 0.167 0.280 0.141 0.259 Change of default spread 0.221 0.146 0.123 0.256 0.208 0.241 0.002 Change of VIX –0.094 –0.065 –0.112 –0.025 –0.048 –0.096 –0.057 B. Correlations between rare disaster concern indices and other factors $$\mathbb{RIX}$$ BKX SOX XAU HGX OSX UTY MKTRF –0.102 –0.110 –0.013 –0.150 –0.172 –0.067 –0.177 SMB 0.002 –0.019 0.087 –0.019 –0.030 –0.032 –0.051 HML –0.165 –0.109 –0.112 –0.211 –0.209 –0.171 –0.032 UMD –0.121 –0.202 –0.055 0.017 –0.225 –0.020 –0.080 PTFSBD 0.248 0.194 0.259 0.226 0.277 0.239 0.172 PTFSFX 0.051 0.073 –0.024 0.130 0.102 0.009 –0.005 PTFSCOM –0.055 –0.031 –0.112 0.056 0.048 –0.083 –0.154 PTFSIR 0.177 0.242 –0.029 0.163 0.348 0.091 0.069 PTRSSTK –0.026 0.032 –0.114 0.017 0.139 –0.079 –0.015 Liquidity risk: PS –0.193 –0.214 –0.087 –0.226 –0.325 –0.096 –0.242 Liquidity risk: Sadka –0.310 –0.401 –0.130 –0.283 –0.408 –0.195 –0.220 Liquidity risk: Noise –0.009 –0.046 –0.055 0.092 –0.009 0.005 0.010 Change of term spread 0.222 0.251 0.169 0.167 0.280 0.141 0.259 Change of default spread 0.221 0.146 0.123 0.256 0.208 0.241 0.002 Change of VIX –0.094 –0.065 –0.112 –0.025 –0.048 –0.096 –0.057 Rare disaster concern indices are constructed using the prices of 30-day out-of-the-money put options on 6 different sector indices from 1996 to 2011. The aggregated rare disaster concern index ($$\mathbb{RIX}$$) is a simple average of the 6 sector-level disaster concern indices. Panel A reports summary statistics for their monthly time series, and panel B reports the time-series correlations between one rare disaster concern index and a number of factors, including the Fama-French-Carhart four factors (MKTRF, SMB, HML, and UMD), the Fung-Hsieh 5 trend-following factors (PTFSBD, PTFSFX, PTFSCOM, PTFSIR, and PTFSSTK), the Pastor-Stambaugh (PS) liquidity risk factor, the Sadka liquidity risk factor, the Hu-Pan-Wang liquidity risk factor (Noise), change in term spread, change in default spread, and change in VIX. Panel B of Table 1 reports correlations between $$\mathbb{RIX}$$ and a set of factors related to market, size, book-to-market equity, momentum, trend following, market liquidity, funding liquidity, term spread, default spread, and volatility. We find that $$\mathbb{RIX}$$ is only mildly correlated with the usual equity risk factors ($$-$$0.17 and $$-$$0.12 for book-to-market and momentum factors, respectively) and hedge fund risk factors (0.25 and 0.18 for the Fung-Hsieh trend-following factors PTFSBD for bonds, and PTFSIR for short-term interest rates, respectively). More importantly, $$\mathbb{RIX}$$ is weakly correlated with risk factors related to market disaster shocks, for example, between 0.20 and 0.31 with market liquidity (Pastor and Stambaugh 2003; Sadka 2006), around 0.22 with the change of the default spread, and only $$-$$0.10 with the change of VIX for volatility risk. These low correlations further indicate that ex ante disaster concerns are quite distinct from realized disaster shocks ex post, even though they often spike simultaneously. 2.2 Hedge fund data The data on hedge fund monthly returns are obtained from the Lipper TASS database. In addition to the returns, the database also provides fund characteristics, including assets under management (AUM), net asset value (NAV), management fees, and incentive fees, among others.9 Because our measure of rare disaster concerns begins in 1996 when the OptionMetrics data become available, the full sample period of hedge funds we use is from January 1996 through July 2010. We further require funds to report returns net of fees in US dollars, and to have at least 18 months of return history in the TASS database. Moreover, from an institutional investment and market impact perspective, funds with low AUM are of less economic importance; we hence include only funds with at least $${\$}$$10 million AUM at the time of portfolio formation (but not after) in our baseline analysis, following Cao et al. (2013) and Hu, Pan, and Wang (2013). Overall, we exclude 3674 funds from the TASS database, and retain 5864 funds in total over our time period of 01/1996-07/2010. An equal-weight hedge fund portfolio on average earns $$\left. 0.8\%\right.$$ per month with a standard deviation of $$\left. 1.9\%\right.$$; it earned the highest (lowest) mean return of $$\left. 2.2\%\right.$$ ($$\left. -1.4\%\right.$$) per month in 1999 (2008). Table IA-2 of the Internet Appendix provides more detailed descriptive statistics for our hedge fund sample. 2.3 The SED estimates of hedge funds We now explain our measure of hedge fund manager skill at exploiting rare disaster concerns and present various properties of SED-sorted hedge fund portfolios. 2.3.1 The SED estimates We measure hedge fund managers’ skill at exploiting rare disaster concerns through the covariation between fund returns and our measure of ex ante rare disaster concerns ($$\mathbb{RIX}$$). At the end of each month from June 1997 to June 2010, for each hedge fund, we first perform 24-month rolling-window regressions of a fund’s monthly excess return on the CRSP value-weighted market excess return and $$\mathbb{RIX}$$. Then, we measure the fund’s SED using the estimated regression coefficient on $$\mathbb{RIX}$$. To ensure that we have a reasonable number of observations in the estimation, we require funds to have at least 18 months of returns. To understand the cross-sectional variations of hedge fund managers’ skill at exploiting disaster concerns, Table 2 reports panel regressions of the SED estimates on fund characteristics as of June for each year from 1997 to 2010. We find that higher-SED funds tend to have smaller AUM as well as positive return skewness over the past two years. We also observe a strong negative relation between the Fung-Hsieh alpha and SED. This is not surprising because funds with a high Fung-Hsieh alpha behave like they are purchasing disaster insurance by loading highly on the Fung and Hsieh (2001) trend-following factors that are constructed through lookback straddles and hence earn negative mean returns.10 They are consequently less likely to sell disaster insurance and more likely to be low-SED funds. Finally, the variations of SED seem to be more significant across funds than across time. For instance, the adjusted R-squared increases from 3.5% to 21.1% when fund fixed effects are included, while it only increases from 3.5% to 9.2% when year fixed effects are included.11 Table 2 Determinants of hedge fund skills in exploiting rare disaster concerns (SED) (1) (2) (3) (4) (5) (6) (7) (8) Minimal investment (log) 0.029 0.020 0.0187 0.010 (2.25) (1.58) (1.49) (0.80) Management fee (%) $$-$$5.7253 $$-$$3.604 $$-$$5.1803 $$-$$3.146 ($$-$$1.99) ($$-$$1.27) ($$-$$1.82) ($$-$$1.13) Incentive fee (%) 0.0077 $$-$$0.067 $$-$$0.1361 $$-$$0.184 (0.03) ($$-$$0.27) ($$-$$0.56) ($$-$$0.75) Redemption notice 0.0002 0.000 $$-$$0.0002 0.000 $$\quad$$ period (month) (0.40) (0.80) ($$-$$0.38) (0.01) Lockup period (month) $$-$$0.0022 $$-$$0.003 $$-$$0.0011 $$-$$0.002 ($$-$$1.29) ($$-$$1.67) ($$-$$0.63) ($$-$$1.02) High water mark (dummy) 0.0541 0.052 0.0571 0.056 (1.62) (1.58) (1.72) (1.70) Personal capital $$-$$0.0157 $$-$$0.008 $$-$$0.0087 $$-$$0.002 $$\quad$$ invested (dummy) ($$-$$0.51) ($$-$$0.25) ($$-$$0.28) ($$-$$0.05) Leverage (dummy) 0.0509 0.031 0.0476 0.029 (1.85) (1.14) (1.75) (1.07) AUM (log) $$-$$0.0291 $$-$$0.023 $$-$$0.0225 $$-$$0.017 $$-$$0.092 $$-$$0.087 $$-$$0.0514 $$-$$0.049 ($$-$$2.49) ($$-$$2.03) ($$-$$1.99) ($$-$$1.56) ($$-$$3.13) ($$-$$2.87) ($$-$$1.84) ($$-$$1.68) AGE (log) 0.0195 0.015 0.0066 0.005 0.0044 0.007 $$-$$0.0912 $$-$$0.075 (0.64) (0.50) (0.22) (0.17) (0.07) (0.11) ($$-$$0.81) ($$-$$0.68) Fund flow (past 1 year) 0.0164 0.011 0.0059 0.001 $$-$$0.0111 $$-$$0.012 $$-$$0.0368 $$-$$0.037 (1.18) (0.83) (0.40) (0.07) ($$-$$0.23) ($$-$$0.27) ($$-$$0.69) ($$-$$0.73) Return volatility 1.7971 2.737 0.6537 1.541 6.5084 8.006 2.9691 4.251 $$\quad$$ (past 2 years) (0.69) (1.04) (0.25) (0.57) (2.00) (2.58) (0.81) (1.23) Return skewness 0.1032 0.079 0.0791 0.059 0.1703 0.140 0.1358 0.110 $$\quad$$ (past 2 years) (4.66) (3.47) (3.54) (2.57) (6.96) (5.44) (5.22) (4.03) Return kurtosis 0.0206 0.024 0.0069 0.010 0.0043 0.008 $$-$$0.0010 0.003 $$\quad$$ (past 2 years) (2.47) (2.83) (0.81) (1.13) (0.44) (0.86) ($$-$$0.11) (0.31) Alpha (F-H $$-$$11.1859 $$-$$10.656 $$-$$10.2262 $$-$$9.833 $$-$$14.922 $$-$$14.227 $$-$$13.8962 $$-$$13.325 $$\quad$$ factor model) ($$-$$3.95) ($$-$$3.81) ($$-$$3.61) ($$-$$3.50) ($$-$$4.20) ($$-$$4.04) ($$-$$3.85) ($$-$$3.70) R-squared (F-H 0.5228 0.409 0.4406 0.340 0.4021 0.341 0.3107 0.253 $$\quad$$ factor model) (5.67) (4.56) (5.00) (3.94) (3.27) (2.86) (2.73) (2.27) SDI 0.458 0.362 0.3408 0.251 0.3079 0.268 0.2646 0.224 (4.96) (4.05) (3.70) (2.80) (2.28) (2.08) (1.99) (1.75) Downside return 7.2535 7.440 9.451 9.631 4.7459 5.544 6.7865 7.461 (1.93) (1.98) (2.43) (2.50) (1.53) (1.85) (2.13) (2.42) Liquidity timing $$-$$0.0073 $$-$$0.008 $$-$$0.0178 $$-$$0.017 $$-$$0.0122 $$-$$0.013 $$-$$0.0186 $$-$$0.018 ($$-$$0.62) ($$-$$0.73) ($$-$$1.44) ($$-$$1.45) ($$-$$0.76) ($$-$$0.86) ($$-$$1.15) ($$-$$1.18) Volatility timing $$-$$0.2435 0.500 0.0319 0.697 $$-$$0.4652 0.557 $$-$$0.3144 0.628 ($$-$$0.82) (1.30) (0.10) (1.81) ($$-$$1.38) (1.37) ($$-$$0.88) (1.53) Market timing 0.0118 0.0104 0.0116 0.0113 (2.53) (2.24) (1.75) (1.70) Extreme market 0.009 0.010 0.002 0.004 $$\quad$$ timing (Bullish) (2.57) (2.84) (0.52) (0.96) Extreme market 0.027 0.026 0.030 0.029 $$\quad$$ timing (Bearish) (7.21) (6.91) (6.99) (6.93) Constant Included Included Included Included Included Included Included Included Year FEs No No Yes Yes No No Yes Yes Fund FEs No No No No Yes Yes Yes Yes Observations 10,330 10,245 10,330 10,245 10,330 10,313 10,330 10,313 Adjusted R-squared 0.0346 0.079 0.0921 0.134 0.2114 0.246 0.2550 0.286 (1) (2) (3) (4) (5) (6) (7) (8) Minimal investment (log) 0.029 0.020 0.0187 0.010 (2.25) (1.58) (1.49) (0.80) Management fee (%) $$-$$5.7253 $$-$$3.604 $$-$$5.1803 $$-$$3.146 ($$-$$1.99) ($$-$$1.27) ($$-$$1.82) ($$-$$1.13) Incentive fee (%) 0.0077 $$-$$0.067 $$-$$0.1361 $$-$$0.184 (0.03) ($$-$$0.27) ($$-$$0.56) ($$-$$0.75) Redemption notice 0.0002 0.000 $$-$$0.0002 0.000 $$\quad$$ period (month) (0.40) (0.80) ($$-$$0.38) (0.01) Lockup period (month) $$-$$0.0022 $$-$$0.003 $$-$$0.0011 $$-$$0.002 ($$-$$1.29) ($$-$$1.67) ($$-$$0.63) ($$-$$1.02) High water mark (dummy) 0.0541 0.052 0.0571 0.056 (1.62) (1.58) (1.72) (1.70) Personal capital $$-$$0.0157 $$-$$0.008 $$-$$0.0087 $$-$$0.002 $$\quad$$ invested (dummy) ($$-$$0.51) ($$-$$0.25) ($$-$$0.28) ($$-$$0.05) Leverage (dummy) 0.0509 0.031 0.0476 0.029 (1.85) (1.14) (1.75) (1.07) AUM (log) $$-$$0.0291 $$-$$0.023 $$-$$0.0225 $$-$$0.017 $$-$$0.092 $$-$$0.087 $$-$$0.0514 $$-$$0.049 ($$-$$2.49) ($$-$$2.03) ($$-$$1.99) ($$-$$1.56) ($$-$$3.13) ($$-$$2.87) ($$-$$1.84) ($$-$$1.68) AGE (log) 0.0195 0.015 0.0066 0.005 0.0044 0.007 $$-$$0.0912 $$-$$0.075 (0.64) (0.50) (0.22) (0.17) (0.07) (0.11) ($$-$$0.81) ($$-$$0.68) Fund flow (past 1 year) 0.0164 0.011 0.0059 0.001 $$-$$0.0111 $$-$$0.012 $$-$$0.0368 $$-$$0.037 (1.18) (0.83) (0.40) (0.07) ($$-$$0.23) ($$-$$0.27) ($$-$$0.69) ($$-$$0.73) Return volatility 1.7971 2.737 0.6537 1.541 6.5084 8.006 2.9691 4.251 $$\quad$$ (past 2 years) (0.69) (1.04) (0.25) (0.57) (2.00) (2.58) (0.81) (1.23) Return skewness 0.1032 0.079 0.0791 0.059 0.1703 0.140 0.1358 0.110 $$\quad$$ (past 2 years) (4.66) (3.47) (3.54) (2.57) (6.96) (5.44) (5.22) (4.03) Return kurtosis 0.0206 0.024 0.0069 0.010 0.0043 0.008 $$-$$0.0010 0.003 $$\quad$$ (past 2 years) (2.47) (2.83) (0.81) (1.13) (0.44) (0.86) ($$-$$0.11) (0.31) Alpha (F-H $$-$$11.1859 $$-$$10.656 $$-$$10.2262 $$-$$9.833 $$-$$14.922 $$-$$14.227 $$-$$13.8962 $$-$$13.325 $$\quad$$ factor model) ($$-$$3.95) ($$-$$3.81) ($$-$$3.61) ($$-$$3.50) ($$-$$4.20) ($$-$$4.04) ($$-$$3.85) ($$-$$3.70) R-squared (F-H 0.5228 0.409 0.4406 0.340 0.4021 0.341 0.3107 0.253 $$\quad$$ factor model) (5.67) (4.56) (5.00) (3.94) (3.27) (2.86) (2.73) (2.27) SDI 0.458 0.362 0.3408 0.251 0.3079 0.268 0.2646 0.224 (4.96) (4.05) (3.70) (2.80) (2.28) (2.08) (1.99) (1.75) Downside return 7.2535 7.440 9.451 9.631 4.7459 5.544 6.7865 7.461 (1.93) (1.98) (2.43) (2.50) (1.53) (1.85) (2.13) (2.42) Liquidity timing $$-$$0.0073 $$-$$0.008 $$-$$0.0178 $$-$$0.017 $$-$$0.0122 $$-$$0.013 $$-$$0.0186 $$-$$0.018 ($$-$$0.62) ($$-$$0.73) ($$-$$1.44) ($$-$$1.45) ($$-$$0.76) ($$-$$0.86) ($$-$$1.15) ($$-$$1.18) Volatility timing $$-$$0.2435 0.500 0.0319 0.697 $$-$$0.4652 0.557 $$-$$0.3144 0.628 ($$-$$0.82) (1.30) (0.10) (1.81) ($$-$$1.38) (1.37) ($$-$$0.88) (1.53) Market timing 0.0118 0.0104 0.0116 0.0113 (2.53) (2.24) (1.75) (1.70) Extreme market 0.009 0.010 0.002 0.004 $$\quad$$ timing (Bullish) (2.57) (2.84) (0.52) (0.96) Extreme market 0.027 0.026 0.030 0.029 $$\quad$$ timing (Bearish) (7.21) (6.91) (6.99) (6.93) Constant Included Included Included Included Included Included Included Included Year FEs No No Yes Yes No No Yes Yes Fund FEs No No No No Yes Yes Yes Yes Observations 10,330 10,245 10,330 10,245 10,330 10,313 10,330 10,313 Adjusted R-squared 0.0346 0.079 0.0921 0.134 0.2114 0.246 0.2550 0.286 This table reports monthly panel regressions of the SED estimates on the fund characteristics from 1997 to 2010. Columns 1–4 include fund characteristics that are reported in a June snapshot of each year, with no fixed effects in the first two and with year fixed effects in the last two. (We use the June values of the fund characteristics lagged to the SED estimates.) Columns 5–8 include time-varying fund characteristics with fund fixed effects in the first two and with both fund and year fixed effects in the last two. The fund characteristics reported in the annual June snapshots include minimal investment, management fee, incentive fee, redemption notice period, lockup period, high water mark, personal capital invested, and leverage. The time-varying fund characteristics include the AUM, AGE, average monthly fund flow within the past one year, monthly excess return volatility, skewness, and kurtosis over the past two years. We also include the Fung-Hsieh alpha, R-squared, the strategy distinctiveness index (SDI), downside return, and market, liquidity, and volatility timing variables. In addition, we include two extreme market timing variables for a bullish market (Bull) and a bearish market (Bear). We report regression estimates, as well as robust standard errors clustered at the fund level in parentheses. Table 2 Determinants of hedge fund skills in exploiting rare disaster concerns (SED) (1) (2) (3) (4) (5) (6) (7) (8) Minimal investment (log) 0.029 0.020 0.0187 0.010 (2.25) (1.58) (1.49) (0.80) Management fee (%) $$-$$5.7253 $$-$$3.604 $$-$$5.1803 $$-$$3.146 ($$-$$1.99) ($$-$$1.27) ($$-$$1.82) ($$-$$1.13) Incentive fee (%) 0.0077 $$-$$0.067 $$-$$0.1361 $$-$$0.184 (0.03) ($$-$$0.27) ($$-$$0.56) ($$-$$0.75) Redemption notice 0.0002 0.000 $$-$$0.0002 0.000 $$\quad$$ period (month) (0.40) (0.80) ($$-$$0.38) (0.01) Lockup period (month) $$-$$0.0022 $$-$$0.003 $$-$$0.0011 $$-$$0.002 ($$-$$1.29) ($$-$$1.67) ($$-$$0.63) ($$-$$1.02) High water mark (dummy) 0.0541 0.052 0.0571 0.056 (1.62) (1.58) (1.72) (1.70) Personal capital $$-$$0.0157 $$-$$0.008 $$-$$0.0087 $$-$$0.002 $$\quad$$ invested (dummy) ($$-$$0.51) ($$-$$0.25) ($$-$$0.28) ($$-$$0.05) Leverage (dummy) 0.0509 0.031 0.0476 0.029 (1.85) (1.14) (1.75) (1.07) AUM (log) $$-$$0.0291 $$-$$0.023 $$-$$0.0225 $$-$$0.017 $$-$$0.092 $$-$$0.087 $$-$$0.0514 $$-$$0.049 ($$-$$2.49) ($$-$$2.03) ($$-$$1.99) ($$-$$1.56) ($$-$$3.13) ($$-$$2.87) ($$-$$1.84) ($$-$$1.68) AGE (log) 0.0195 0.015 0.0066 0.005 0.0044 0.007 $$-$$0.0912 $$-$$0.075 (0.64) (0.50) (0.22) (0.17) (0.07) (0.11) ($$-$$0.81) ($$-$$0.68) Fund flow (past 1 year) 0.0164 0.011 0.0059 0.001 $$-$$0.0111 $$-$$0.012 $$-$$0.0368 $$-$$0.037 (1.18) (0.83) (0.40) (0.07) ($$-$$0.23) ($$-$$0.27) ($$-$$0.69) ($$-$$0.73) Return volatility 1.7971 2.737 0.6537 1.541 6.5084 8.006 2.9691 4.251 $$\quad$$ (past 2 years) (0.69) (1.04) (0.25) (0.57) (2.00) (2.58) (0.81) (1.23) Return skewness 0.1032 0.079 0.0791 0.059 0.1703 0.140 0.1358 0.110 $$\quad$$ (past 2 years) (4.66) (3.47) (3.54) (2.57) (6.96) (5.44) (5.22) (4.03) Return kurtosis 0.0206 0.024 0.0069 0.010 0.0043 0.008 $$-$$0.0010 0.003 $$\quad$$ (past 2 years) (2.47) (2.83) (0.81) (1.13) (0.44) (0.86) ($$-$$0.11) (0.31) Alpha (F-H $$-$$11.1859 $$-$$10.656 $$-$$10.2262 $$-$$9.833 $$-$$14.922 $$-$$14.227 $$-$$13.8962 $$-$$13.325 $$\quad$$ factor model) ($$-$$3.95) ($$-$$3.81) ($$-$$3.61) ($$-$$3.50) ($$-$$4.20) ($$-$$4.04) ($$-$$3.85) ($$-$$3.70) R-squared (F-H 0.5228 0.409 0.4406 0.340 0.4021 0.341 0.3107 0.253 $$\quad$$ factor model) (5.67) (4.56) (5.00) (3.94) (3.27) (2.86) (2.73) (2.27) SDI 0.458 0.362 0.3408 0.251 0.3079 0.268 0.2646 0.224 (4.96) (4.05) (3.70) (2.80) (2.28) (2.08) (1.99) (1.75) Downside return 7.2535 7.440 9.451 9.631 4.7459 5.544 6.7865 7.461 (1.93) (1.98) (2.43) (2.50) (1.53) (1.85) (2.13) (2.42) Liquidity timing $$-$$0.0073 $$-$$0.008 $$-$$0.0178 $$-$$0.017 $$-$$0.0122 $$-$$0.013 $$-$$0.0186 $$-$$0.018 ($$-$$0.62) ($$-$$0.73) ($$-$$1.44) ($$-$$1.45) ($$-$$0.76) ($$-$$0.86) ($$-$$1.15) ($$-$$1.18) Volatility timing $$-$$0.2435 0.500 0.0319 0.697 $$-$$0.4652 0.557 $$-$$0.3144 0.628 ($$-$$0.82) (1.30) (0.10) (1.81) ($$-$$1.38) (1.37) ($$-$$0.88) (1.53) Market timing 0.0118 0.0104 0.0116 0.0113 (2.53) (2.24) (1.75) (1.70) Extreme market 0.009 0.010 0.002 0.004 $$\quad$$ timing (Bullish) (2.57) (2.84) (0.52) (0.96) Extreme market 0.027 0.026 0.030 0.029 $$\quad$$ timing (Bearish) (7.21) (6.91) (6.99) (6.93) Constant Included Included Included Included Included Included Included Included Year FEs No No Yes Yes No No Yes Yes Fund FEs No No No No Yes Yes Yes Yes Observations 10,330 10,245 10,330 10,245 10,330 10,313 10,330 10,313 Adjusted R-squared 0.0346 0.079 0.0921 0.134 0.2114 0.246 0.2550 0.286 (1) (2) (3) (4) (5) (6) (7) (8) Minimal investment (log) 0.029 0.020 0.0187 0.010 (2.25) (1.58) (1.49) (0.80) Management fee (%) $$-$$5.7253 $$-$$3.604 $$-$$5.1803 $$-$$3.146 ($$-$$1.99) ($$-$$1.27) ($$-$$1.82) ($$-$$1.13) Incentive fee (%) 0.0077 $$-$$0.067 $$-$$0.1361 $$-$$0.184 (0.03) ($$-$$0.27) ($$-$$0.56) ($$-$$0.75) Redemption notice 0.0002 0.000 $$-$$0.0002 0.000 $$\quad$$ period (month) (0.40) (0.80) ($$-$$0.38) (0.01) Lockup period (month) $$-$$0.0022 $$-$$0.003 $$-$$0.0011 $$-$$0.002 ($$-$$1.29) ($$-$$1.67) ($$-$$0.63) ($$-$$1.02) High water mark (dummy) 0.0541 0.052 0.0571 0.056 (1.62) (1.58) (1.72) (1.70) Personal capital $$-$$0.0157 $$-$$0.008 $$-$$0.0087 $$-$$0.002 $$\quad$$ invested (dummy) ($$-$$0.51) ($$-$$0.25) ($$-$$0.28) ($$-$$0.05) Leverage (dummy) 0.0509 0.031 0.0476 0.029 (1.85) (1.14) (1.75) (1.07) AUM (log) $$-$$0.0291 $$-$$0.023 $$-$$0.0225 $$-$$0.017 $$-$$0.092 $$-$$0.087 $$-$$0.0514 $$-$$0.049 ($$-$$2.49) ($$-$$2.03) ($$-$$1.99) ($$-$$1.56) ($$-$$3.13) ($$-$$2.87) ($$-$$1.84) ($$-$$1.68) AGE (log) 0.0195 0.015 0.0066 0.005 0.0044 0.007 $$-$$0.0912 $$-$$0.075 (0.64) (0.50) (0.22) (0.17) (0.07) (0.11) ($$-$$0.81) ($$-$$0.68) Fund flow (past 1 year) 0.0164 0.011 0.0059 0.001 $$-$$0.0111 $$-$$0.012 $$-$$0.0368 $$-$$0.037 (1.18) (0.83) (0.40) (0.07) ($$-$$0.23) ($$-$$0.27) ($$-$$0.69) ($$-$$0.73) Return volatility 1.7971 2.737 0.6537 1.541 6.5084 8.006 2.9691 4.251 $$\quad$$ (past 2 years) (0.69) (1.04) (0.25) (0.57) (2.00) (2.58) (0.81) (1.23) Return skewness 0.1032 0.079 0.0791 0.059 0.1703 0.140 0.1358 0.110 $$\quad$$ (past 2 years) (4.66) (3.47) (3.54) (2.57) (6.96) (5.44) (5.22) (4.03) Return kurtosis 0.0206 0.024 0.0069 0.010 0.0043 0.008 $$-$$0.0010 0.003 $$\quad$$ (past 2 years) (2.47) (2.83) (0.81) (1.13) (0.44) (0.86) ($$-$$0.11) (0.31) Alpha (F-H $$-$$11.1859 $$-$$10.656 $$-$$10.2262 $$-$$9.833 $$-$$14.922 $$-$$14.227 $$-$$13.8962 $$-$$13.325 $$\quad$$ factor model) ($$-$$3.95) ($$-$$3.81) ($$-$$3.61) ($$-$$3.50) ($$-$$4.20) ($$-$$4.04) ($$-$$3.85) ($$-$$3.70) R-squared (F-H 0.5228 0.409 0.4406 0.340 0.4021 0.341 0.3107 0.253 $$\quad$$ factor model) (5.67) (4.56) (5.00) (3.94) (3.27) (2.86) (2.73) (2.27) SDI 0.458 0.362 0.3408 0.251 0.3079 0.268 0.2646 0.224 (4.96) (4.05) (3.70) (2.80) (2.28) (2.08) (1.99) (1.75) Downside return 7.2535 7.440 9.451 9.631 4.7459 5.544 6.7865 7.461 (1.93) (1.98) (2.43) (2.50) (1.53) (1.85) (2.13) (2.42) Liquidity timing $$-$$0.0073 $$-$$0.008 $$-$$0.0178 $$-$$0.017 $$-$$0.0122 $$-$$0.013 $$-$$0.0186 $$-$$0.018 ($$-$$0.62) ($$-$$0.73) ($$-$$1.44) ($$-$$1.45) ($$-$$0.76) ($$-$$0.86) ($$-$$1.15) ($$-$$1.18) Volatility timing $$-$$0.2435 0.500 0.0319 0.697 $$-$$0.4652 0.557 $$-$$0.3144 0.628 ($$-$$0.82) (1.30) (0.10) (1.81) ($$-$$1.38) (1.37) ($$-$$0.88) (1.53) Market timing 0.0118 0.0104 0.0116 0.0113 (2.53) (2.24) (1.75) (1.70) Extreme market 0.009 0.010 0.002 0.004 $$\quad$$ timing (Bullish) (2.57) (2.84) (0.52) (0.96) Extreme market 0.027 0.026 0.030 0.029 $$\quad$$ timing (Bearish) (7.21) (6.91) (6.99) (6.93) Constant Included Included Included Included Included Included Included Included Year FEs No No Yes Yes No No Yes Yes Fund FEs No No No No Yes Yes Yes Yes Observations 10,330 10,245 10,330 10,245 10,330 10,313 10,330 10,313 Adjusted R-squared 0.0346 0.079 0.0921 0.134 0.2114 0.246 0.2550 0.286 This table reports monthly panel regressions of the SED estimates on the fund characteristics from 1997 to 2010. Columns 1–4 include fund characteristics that are reported in a June snapshot of each year, with no fixed effects in the first two and with year fixed effects in the last two. (We use the June values of the fund characteristics lagged to the SED estimates.) Columns 5–8 include time-varying fund characteristics with fund fixed effects in the first two and with both fund and year fixed effects in the last two. The fund characteristics reported in the annual June snapshots include minimal investment, management fee, incentive fee, redemption notice period, lockup period, high water mark, personal capital invested, and leverage. The time-varying fund characteristics include the AUM, AGE, average monthly fund flow within the past one year, monthly excess return volatility, skewness, and kurtosis over the past two years. We also include the Fung-Hsieh alpha, R-squared, the strategy distinctiveness index (SDI), downside return, and market, liquidity, and volatility timing variables. In addition, we include two extreme market timing variables for a bullish market (Bull) and a bearish market (Bear). We report regression estimates, as well as robust standard errors clustered at the fund level in parentheses. 2.3.2 Characteristics of SED-sorted fund portfolios At the end of each month, we sort our sample of hedge funds into SED decile portfolios, and compute a decile’s SED as the cross-sectional average of funds’ SED in that decile. Table 3 presents the characteristics of SED-sorted hedge fund portfolios. Panel A shows that high-SED funds have lower assets under management, a larger fund flow, less liquidation, and a lower nonreporting rate. Furthermore, high-SED funds are better at hedging systematic risk with respect to the Fung and Hsieh (2001) benchmark factors (the R-squared measure used in Titman and Tiu (2011)). They have more innovative strategies, as measured by the strategy distinctiveness index from Sun, Wang, and Zheng (2012), and they tend to be low liquidity timers but high market and volatility timers (Cao et al. 2013). These results are consistent with our hypothesis that managers of high-SED funds have better skills that are associated with superior return performance. Panel B reports the likelihood distribution of different hedge fund investment styles within each SED decile. On average, among funds with the highest SED, the managed futures type is most likely to show up, whereas the fund-of-funds type is least likely. Table 3 Variations of SED A. Characteristics of SED-sorted hedge fund portfolios SED AUM ($${\$}$$M) AGE (months) Fund flow R squared SDI Liquidity timing Market timing Volatility timing Downside return Upside return Liquidation rate (%) Nonreporting Rate (%) 1 - Low skill 172.8 68 0.010 0.533 0.305 0.059 –0.551 –0.007 –0.019 0.036 3.56 3.13 2 187.2 71 0.013 0.557 0.311 0.096 –0.269 –0.005 –0.011 0.024 2.77 2.54 3 186.7 72 0.016 0.559 0.331 0.100 –0.132 –0.008 –0.009 0.019 2.38 2.29 4 203.5 72 0.011 0.555 0.347 0.039 –0.126 –0.005 –0.007 0.016 2.69 1.91 5 193.4 71 0.015 0.546 0.362 0.014 –0.059 –0.005 –0.005 0.015 2.71 2.02 6 199.5 71 0.014 0.532 0.374 –0.012 –0.053 –0.004 –0.004 0.014 2.71 1.92 7 210.7 71 0.016 0.515 0.382 –0.018 0.059 –0.003 –0.004 0.014 2.89 2.39 8 192.3 70 0.044 0.505 0.382 –0.029 0.363 –0.002 –0.003 0.015 2.69 2.36 9 175.4 70 0.018 0.515 0.365 –0.099 0.574 –0.001 –0.004 0.019 2.46 2.33 10 - High skill 151.2 69 0.051 0.524 0.348 –0.600 1.582 0.011 –0.005 0.028 2.13 2.25 High - Low –21.6 1.000 0.041 –0.009 0.043 –0.659 2.133 0.018 0.014 –0.008 –1.40 –0.91 t-stat Sgn rank (–2.25) (0.64) (2.13) (–1.56) (6.80) (–3.43) (3.55) (3.68) (10.99) (–5.22) (–7.50) (–5.85) (p-val) (0.007) (0.972) (0.000) (0.522) (0.000) (0.000) (0.003) (0.016) (0.000) (0.000) (0.000) (0.000) A. Characteristics of SED-sorted hedge fund portfolios SED AUM ($${\$}$$M) AGE (months) Fund flow R squared SDI Liquidity timing Market timing Volatility timing Downside return Upside return Liquidation rate (%) Nonreporting Rate (%) 1 - Low skill 172.8 68 0.010 0.533 0.305 0.059 –0.551 –0.007 –0.019 0.036 3.56 3.13 2 187.2 71 0.013 0.557 0.311 0.096 –0.269 –0.005 –0.011 0.024 2.77 2.54 3 186.7 72 0.016 0.559 0.331 0.100 –0.132 –0.008 –0.009 0.019 2.38 2.29 4 203.5 72 0.011 0.555 0.347 0.039 –0.126 –0.005 –0.007 0.016 2.69 1.91 5 193.4 71 0.015 0.546 0.362 0.014 –0.059 –0.005 –0.005 0.015 2.71 2.02 6 199.5 71 0.014 0.532 0.374 –0.012 –0.053 –0.004 –0.004 0.014 2.71 1.92 7 210.7 71 0.016 0.515 0.382 –0.018 0.059 –0.003 –0.004 0.014 2.89 2.39 8 192.3 70 0.044 0.505 0.382 –0.029 0.363 –0.002 –0.003 0.015 2.69 2.36 9 175.4 70 0.018 0.515 0.365 –0.099 0.574 –0.001 –0.004 0.019 2.46 2.33 10 - High skill 151.2 69 0.051 0.524 0.348 –0.600 1.582 0.011 –0.005 0.028 2.13 2.25 High - Low –21.6 1.000 0.041 –0.009 0.043 –0.659 2.133 0.018 0.014 –0.008 –1.40 –0.91 t-stat Sgn rank (–2.25) (0.64) (2.13) (–1.56) (6.80) (–3.43) (3.55) (3.68) (10.99) (–5.22) (–7.50) (–5.85) (p-val) (0.007) (0.972) (0.000) (0.522) (0.000) (0.000) (0.003) (0.016) (0.000) (0.000) (0.000) (0.000) B. Ratios of hedge fund investment styles within each SED decile portfolio Long/Short equity Equity market Dedicated short Global macro Emerging markets Event driven Fund of funds Fixed income Convertible arbitrage Managed futures Multi strategy Options strategy SED Hedge Neutral Bias Arbitrage 1 - Low skill 11.7% 3.5% 13.0% 11.0% 21.9% 6.3% 4.1% 9.0% 3.8% 8.4% 5.2% 2.1% 2 11.0% 7.4% 10.1% 7.9% 12.2% 8.8% 9.7% 6.6% 4.2% 8.2% 6.8% 7.1% 3 9.9% 9.5% 7.4% 7.7% 8.5% 10.7% 13.6% 9.2% 5.0% 8.2% 7.3% 3.1% 4 7.8% 8.8% 5.2% 7.1% 6.6% 10.8% 14.6% 10.6% 5.2% 6.3% 8.1% 8.7% 5 6.5% 8.0% 4.0% 6.2% 5.9% 10.6% 13.8% 10.5% 7.4% 5.3% 9.6% 12.2% 6 6.3% 10.0% 4.3% 6.8% 5.1% 11.1% 13.2% 10.7% 10.1% 5.6% 10.2% 6.7% 7 6.2% 9.5% 4.5% 7.8% 4.8% 10.0% 9.5% 9.2% 11.9% 5.7% 10.9% 10.0% 8 6.7% 9.5% 6.1% 8.7% 5.0% 8.5% 5.3% 8.5% 12.2% 6.6% 9.8% 13.1% 9 8.7% 9.8% 10.3% 9.7% 6.1% 6.4% 3.2% 6.2% 12.1% 9.8% 8.7% 8.9% 10 - High skill 9.0% 7.1% 15.8% 9.4% 8.7% 2.7% 1.9% 4.7% 8.3% 16.7% 6.6% 9.0% B. Ratios of hedge fund investment styles within each SED decile portfolio Long/Short equity Equity market Dedicated short Global macro Emerging markets Event driven Fund of funds Fixed income Convertible arbitrage Managed futures Multi strategy Options strategy SED Hedge Neutral Bias Arbitrage 1 - Low skill 11.7% 3.5% 13.0% 11.0% 21.9% 6.3% 4.1% 9.0% 3.8% 8.4% 5.2% 2.1% 2 11.0% 7.4% 10.1% 7.9% 12.2% 8.8% 9.7% 6.6% 4.2% 8.2% 6.8% 7.1% 3 9.9% 9.5% 7.4% 7.7% 8.5% 10.7% 13.6% 9.2% 5.0% 8.2% 7.3% 3.1% 4 7.8% 8.8% 5.2% 7.1% 6.6% 10.8% 14.6% 10.6% 5.2% 6.3% 8.1% 8.7% 5 6.5% 8.0% 4.0% 6.2% 5.9% 10.6% 13.8% 10.5% 7.4% 5.3% 9.6% 12.2% 6 6.3% 10.0% 4.3% 6.8% 5.1% 11.1% 13.2% 10.7% 10.1% 5.6% 10.2% 6.7% 7 6.2% 9.5% 4.5% 7.8% 4.8% 10.0% 9.5% 9.2% 11.9% 5.7% 10.9% 10.0% 8 6.7% 9.5% 6.1% 8.7% 5.0% 8.5% 5.3% 8.5% 12.2% 6.6% 9.8% 13.1% 9 8.7% 9.8% 10.3% 9.7% 6.1% 6.4% 3.2% 6.2% 12.1% 9.8% 8.7% 8.9% 10 - High skill 9.0% 7.1% 15.8% 9.4% 8.7% 2.7% 1.9% 4.7% 8.3% 16.7% 6.6% 9.0% Panel A reports summary statistics for the monthly characteristics of SED-sorted hedge fund decile portfolios, including the assets under management (AUM), number of months from a fund’s inception to portfolio formation date (AGE), fund flow in the most recent month, R-squared from Titman and Tiu (2011) Titman and Tiu (2011), strategy distinctiveness index (SDI) from Sun, Wang, and Zheng (2012), liquidity-, market-, and volatility-timing ability measures from Cao et al. (2013), the downside and upside returns from Sun, Wang, and Zheng (2013), and the fund liquidation rate and the nonreporting rate within 1 year of portfolio formation. Within each decile, we first calculate the cross-sectional average of funds’ characteristics and then calculate the time-series average over all portfolio formation months. We report both the t-statistics and p-values of signed rank statistics for high-minus-low SED portfolios. Panel B reports the ratios of each of the 12 hedge fund investment styles in each SED decile. We first compute the ratios of the 12 investment styles for each SED decile in each month and then calculate their respective time-series average. Table 3 Variations of SED A. Characteristics of SED-sorted hedge fund portfolios SED AUM ($${\$}$$M) AGE (months) Fund flow R squared SDI Liquidity timing Market timing Volatility timing Downside return Upside return Liquidation rate (%) Nonreporting Rate (%) 1 - Low skill 172.8 68 0.010 0.533 0.305 0.059 –0.551 –0.007 –0.019 0.036 3.56 3.13 2 187.2 71 0.013 0.557 0.311 0.096 –0.269 –0.005 –0.011 0.024 2.77 2.54 3 186.7 72 0.016 0.559 0.331 0.100 –0.132 –0.008 –0.009 0.019 2.38 2.29 4 203.5 72 0.011 0.555 0.347 0.039 –0.126 –0.005 –0.007 0.016 2.69 1.91 5 193.4 71 0.015 0.546 0.362 0.014 –0.059 –0.005 –0.005 0.015 2.71 2.02 6 199.5 71 0.014 0.532 0.374 –0.012 –0.053 –0.004 –0.004 0.014 2.71 1.92 7 210.7 71 0.016 0.515 0.382 –0.018 0.059 –0.003 –0.004 0.014 2.89 2.39 8 192.3 70 0.044 0.505 0.382 –0.029 0.363 –0.002 –0.003 0.015 2.69 2.36 9 175.4 70 0.018 0.515 0.365 –0.099 0.574 –0.001 –0.004 0.019 2.46 2.33 10 - High skill 151.2 69 0.051 0.524 0.348 –0.600 1.582 0.011 –0.005 0.028 2.13 2.25 High - Low –21.6 1.000 0.041 –0.009 0.043 –0.659 2.133 0.018 0.014 –0.008 –1.40 –0.91 t-stat Sgn rank (–2.25) (0.64) (2.13) (–1.56) (6.80) (–3.43) (3.55) (3.68) (10.99) (–5.22) (–7.50) (–5.85) (p-val) (0.007) (0.972) (0.000) (0.522) (0.000) (0.000) (0.003) (0.016) (0.000) (0.000) (0.000) (0.000) A. Characteristics of SED-sorted hedge fund portfolios SED AUM ($${\$}$$M) AGE (months) Fund flow R squared SDI Liquidity timing Market timing Volatility timing Downside return Upside return Liquidation rate (%) Nonreporting Rate (%) 1 - Low skill 172.8 68 0.010 0.533 0.305 0.059 –0.551 –0.007 –0.019 0.036 3.56 3.13 2 187.2 71 0.013 0.557 0.311 0.096 –0.269 –0.005 –0.011 0.024 2.77 2.54 3 186.7 72 0.016 0.559 0.331 0.100 –0.132 –0.008 –0.009 0.019 2.38 2.29 4 203.5 72 0.011 0.555 0.347 0.039 –0.126 –0.005 –0.007 0.016 2.69 1.91 5 193.4 71 0.015 0.546 0.362 0.014 –0.059 –0.005 –0.005 0.015 2.71 2.02 6 199.5 71 0.014 0.532 0.374 –0.012 –0.053 –0.004 –0.004 0.014 2.71 1.92 7 210.7 71 0.016 0.515 0.382 –0.018 0.059 –0.003 –0.004 0.014 2.89 2.39 8 192.3 70 0.044 0.505 0.382 –0.029 0.363 –0.002 –0.003 0.015 2.69 2.36 9 175.4 70 0.018 0.515 0.365 –0.099 0.574 –0.001 –0.004 0.019 2.46 2.33 10 - High skill 151.2 69 0.051 0.524 0.348 –0.600 1.582 0.011 –0.005 0.028 2.13 2.25 High - Low –21.6 1.000 0.041 –0.009 0.043 –0.659 2.133 0.018 0.014 –0.008 –1.40 –0.91 t-stat Sgn rank (–2.25) (0.64) (2.13) (–1.56) (6.80) (–3.43) (3.55) (3.68) (10.99) (–5.22) (–7.50) (–5.85) (p-val) (0.007) (0.972) (0.000) (0.522) (0.000) (0.000) (0.003) (0.016) (0.000) (0.000) (0.000) (0.000) B. Ratios of hedge fund investment styles within each SED decile portfolio Long/Short equity Equity market Dedicated short Global macro Emerging markets Event driven Fund of funds Fixed income Convertible arbitrage Managed futures Multi strategy Options strategy SED Hedge Neutral Bias Arbitrage 1 - Low skill 11.7% 3.5% 13.0% 11.0% 21.9% 6.3% 4.1% 9.0% 3.8% 8.4% 5.2% 2.1% 2 11.0% 7.4% 10.1% 7.9% 12.2% 8.8% 9.7% 6.6% 4.2% 8.2% 6.8% 7.1% 3 9.9% 9.5% 7.4% 7.7% 8.5% 10.7% 13.6% 9.2% 5.0% 8.2% 7.3% 3.1% 4 7.8% 8.8% 5.2% 7.1% 6.6% 10.8% 14.6% 10.6% 5.2% 6.3% 8.1% 8.7% 5 6.5% 8.0% 4.0% 6.2% 5.9% 10.6% 13.8% 10.5% 7.4% 5.3% 9.6% 12.2% 6 6.3% 10.0% 4.3% 6.8% 5.1% 11.1% 13.2% 10.7% 10.1% 5.6% 10.2% 6.7% 7 6.2% 9.5% 4.5% 7.8% 4.8% 10.0% 9.5% 9.2% 11.9% 5.7% 10.9% 10.0% 8 6.7% 9.5% 6.1% 8.7% 5.0% 8.5% 5.3% 8.5% 12.2% 6.6% 9.8% 13.1% 9 8.7% 9.8% 10.3% 9.7% 6.1% 6.4% 3.2% 6.2% 12.1% 9.8% 8.7% 8.9% 10 - High skill 9.0% 7.1% 15.8% 9.4% 8.7% 2.7% 1.9% 4.7% 8.3% 16.7% 6.6% 9.0% B. Ratios of hedge fund investment styles within each SED decile portfolio Long/Short equity Equity market Dedicated short Global macro Emerging markets Event driven Fund of funds Fixed income Convertible arbitrage Managed futures Multi strategy Options strategy SED Hedge Neutral Bias Arbitrage 1 - Low skill 11.7% 3.5% 13.0% 11.0% 21.9% 6.3% 4.1% 9.0% 3.8% 8.4% 5.2% 2.1% 2 11.0% 7.4% 10.1% 7.9% 12.2% 8.8% 9.7% 6.6% 4.2% 8.2% 6.8% 7.1% 3 9.9% 9.5% 7.4% 7.7% 8.5% 10.7% 13.6% 9.2% 5.0% 8.2% 7.3% 3.1% 4 7.8% 8.8% 5.2% 7.1% 6.6% 10.8% 14.6% 10.6% 5.2% 6.3% 8.1% 8.7% 5 6.5% 8.0% 4.0% 6.2% 5.9% 10.6% 13.8% 10.5% 7.4% 5.3% 9.6% 12.2% 6 6.3% 10.0% 4.3% 6.8% 5.1% 11.1% 13.2% 10.7% 10.1% 5.6% 10.2% 6.7% 7 6.2% 9.5% 4.5% 7.8% 4.8% 10.0% 9.5% 9.2% 11.9% 5.7% 10.9% 10.0% 8 6.7% 9.5% 6.1% 8.7% 5.0% 8.5% 5.3% 8.5% 12.2% 6.6% 9.8% 13.1% 9 8.7% 9.8% 10.3% 9.7% 6.1% 6.4% 3.2% 6.2% 12.1% 9.8% 8.7% 8.9% 10 - High skill 9.0% 7.1% 15.8% 9.4% 8.7% 2.7% 1.9% 4.7% 8.3% 16.7% 6.6% 9.0% Panel A reports summary statistics for the monthly characteristics of SED-sorted hedge fund decile portfolios, including the assets under management (AUM), number of months from a fund’s inception to portfolio formation date (AGE), fund flow in the most recent month, R-squared from Titman and Tiu (2011) Titman and Tiu (2011), strategy distinctiveness index (SDI) from Sun, Wang, and Zheng (2012), liquidity-, market-, and volatility-timing ability measures from Cao et al. (2013), the downside and upside returns from Sun, Wang, and Zheng (2013), and the fund liquidation rate and the nonreporting rate within 1 year of portfolio formation. Within each decile, we first calculate the cross-sectional average of funds’ characteristics and then calculate the time-series average over all portfolio formation months. We report both the t-statistics and p-values of signed rank statistics for high-minus-low SED portfolios. Panel B reports the ratios of each of the 12 hedge fund investment styles in each SED decile. We first compute the ratios of the 12 investment styles for each SED decile in each month and then calculate their respective time-series average. If a hedge fund’s manager is skilled at exploiting the market’s rare disaster concerns, the fund should display a relatively persistent SED over time. We hence compute the average SED for each decile in holding periods of one month, one quarter, and up to three years, subsequent to the portfolio’s formation month. Table 4 presents the time-series means of these average SED measures for each decile portfolio, as well as the difference between their high- and low-SED deciles. We observe that the differences in SED across decile portfolios slowly decrease over time, yet they are still meaningfully different even three years after the portfolio’s formation. For example, the differences in SED between the highest and lowest SED decile portfolios are 3.48, 2.18, and 1.11 at 1-month, 1-year, and 3-year holding horizons, respectively, and all are statistically significant. Table 4 The persistence of SED SED Portfolio formation month Holding horizon 1 mo 3 mo 6 mo 9 mo 12 mo 18 mo 24 mo 36 mo 1 - Low skill –2.255 –2.068 –1.922 –1.715 –1.543 –1.388 –1.121 –0.946 –0.787 2 –0.974 –0.906 –0.855 –0.781 –0.721 –0.669 –0.576 –0.508 –0.439 3 –0.599 –0.568 –0.544 –0.513 –0.485 –0.457 –0.411 –0.373 –0.335 4 –0.389 –0.371 –0.360 –0.346 –0.334 –0.323 –0.304 –0.291 –0.269 5 –0.238 –0.231 –0.231 –0.233 –0.233 –0.232 –0.229 –0.224 –0.210 6 –0.109 –0.114 –0.118 –0.130 –0.137 –0.144 –0.157 –0.162 –0.154 7 0.027 0.013 –0.008 –0.034 –0.052 –0.067 –0.090 –0.102 –0.104 8 0.208 0.175 0.144 0.100 0.064 0.034 –0.013 –0.040 –0.057 9 0.508 0.452 0.392 0.313 0.252 0.198 0.117 0.070 0.024 10 - High skill 1.573 1.407 1.257 1.066 0.916 0.789 0.578 0.447 0.318 High - Low 3.827 3.475 3.179 2.781 2.460 2.177 1.699 1.392 1.106 (23.85) (25.40) (27.01) (29.48) (28.58) (27.01) (24.25) (23.88) (26.50) SED Portfolio formation month Holding horizon 1 mo 3 mo 6 mo 9 mo 12 mo 18 mo 24 mo 36 mo 1 - Low skill –2.255 –2.068 –1.922 –1.715 –1.543 –1.388 –1.121 –0.946 –0.787 2 –0.974 –0.906 –0.855 –0.781 –0.721 –0.669 –0.576 –0.508 –0.439 3 –0.599 –0.568 –0.544 –0.513 –0.485 –0.457 –0.411 –0.373 –0.335 4 –0.389 –0.371 –0.360 –0.346 –0.334 –0.323 –0.304 –0.291 –0.269 5 –0.238 –0.231 –0.231 –0.233 –0.233 –0.232 –0.229 –0.224 –0.210 6 –0.109 –0.114 –0.118 –0.130 –0.137 –0.144 –0.157 –0.162 –0.154 7 0.027 0.013 –0.008 –0.034 –0.052 –0.067 –0.090 –0.102 –0.104 8 0.208 0.175 0.144 0.100 0.064 0.034 –0.013 –0.040 –0.057 9 0.508 0.452 0.392 0.313 0.252 0.198 0.117 0.070 0.024 10 - High skill 1.573 1.407 1.257 1.066 0.916 0.789 0.578 0.447 0.318 High - Low 3.827 3.475 3.179 2.781 2.460 2.177 1.699 1.392 1.106 (23.85) (25.40) (27.01) (29.48) (28.58) (27.01) (24.25) (23.88) (26.50) This table reports the time-series mean of the average SED for each SED-sorted decile portfolio, for the month of portfolio formation and the subsequent portfolio holding periods of up to 36 months. We also report the difference between the high and low SED deciles and the corresponding t-statistics. Table 4 The persistence of SED SED Portfolio formation month Holding horizon 1 mo 3 mo 6 mo 9 mo 12 mo 18 mo 24 mo 36 mo 1 - Low skill –2.255 –2.068 –1.922 –1.715 –1.543 –1.388 –1.121 –0.946 –0.787 2 –0.974 –0.906 –0.855 –0.781 –0.721 –0.669 –0.576 –0.508 –0.439 3 –0.599 –0.568 –0.544 –0.513 –0.485 –0.457 –0.411 –0.373 –0.335 4 –0.389 –0.371 –0.360 –0.346 –0.334 –0.323 –0.304 –0.291 –0.269 5 –0.238 –0.231 –0.231 –0.233 –0.233 –0.232 –0.229 –0.224 –0.210 6 –0.109 –0.114 –0.118 –0.130 –0.137 –0.144 –0.157 –0.162 –0.154 7 0.027 0.013 –0.008 –0.034 –0.052 –0.067 –0.090 –0.102 –0.104 8 0.208 0.175 0.144 0.100 0.064 0.034 –0.013 –0.040 –0.057 9 0.508 0.452 0.392 0.313 0.252 0.198 0.117 0.070 0.024 10 - High skill 1.573 1.407 1.257 1.066 0.916 0.789 0.578 0.447 0.318 High - Low 3.827 3.475 3.179 2.781 2.460 2.177 1.699 1.392 1.106 (23.85) (25.40) (27.01) (29.48) (28.58) (27.01) (24.25) (23.88) (26.50) SED Portfolio formation month Holding horizon 1 mo 3 mo 6 mo 9 mo 12 mo 18 mo 24 mo 36 mo 1 - Low skill –2.255 –2.068 –1.922 –1.715 –1.543 –1.388 –1.121 –0.946 –0.787 2 –0.974 –0.906 –0.855 –0.781 –0.721 –0.669 –0.576 –0.508 –0.439 3 –0.599 –0.568 –0.544 –0.513 –0.485 –0.457 –0.411 –0.373 –0.335 4 –0.389 –0.371 –0.360 –0.346 –0.334 –0.323 –0.304 –0.291 –0.269 5 –0.238 –0.231 –0.231 –0.233 –0.233 –0.232 –0.229 –0.224 –0.210 6 –0.109 –0.114 –0.118 –0.130 –0.137 –0.144 –0.157 –0.162 –0.154 7 0.027 0.013 –0.008 –0.034 –0.052 –0.067 –0.090 –0.102 –0.104 8 0.208 0.175 0.144 0.100 0.064 0.034 –0.013 –0.040 –0.057 9 0.508 0.452 0.392 0.313 0.252 0.198 0.117 0.070 0.024 10 - High skill 1.573 1.407 1.257 1.066 0.916 0.789 0.578 0.447 0.318 High - Low 3.827 3.475 3.179 2.781 2.460 2.177 1.699 1.392 1.106 (23.85) (25.40) (27.01) (29.48) (28.58) (27.01) (24.25) (23.88) (26.50) This table reports the time-series mean of the average SED for each SED-sorted decile portfolio, for the month of portfolio formation and the subsequent portfolio holding periods of up to 36 months. We also report the difference between the high and low SED deciles and the corresponding t-statistics. Overall, the characteristics of SED-sorted hedge fund portfolios are consistent with our main hypothesis that high-SED fund managers are skilled at exploiting disaster concerns and deliver superior fund performance. We now turn to our baseline test of this hypothesis. 3. SED and Hedge Fund Performance In this section, we first present the results of the baseline test of our main hypothesis: high-SED funds deliver better future returns. We then provide corroborative evidence that high-SED funds earn higher returns because of their managers’ superior skill at exploiting disaster concerns. 3.1 Baseline result We rank hedge funds into 10 deciles according to their SED. Decile 1 (10) consists of funds with the lowest (highest) SED, and the high-minus-low SED portfolio goes long on funds in decile 10 and short on funds in decile 1. We hold the portfolios for one month and calculate equal-weighted returns. To measure portfolio-level risk-adjusted abnormal returns (alphas), we consider two benchmark models. The first is the Fung and Hsieh (2001) 8-factor model, including two equity factors, a size factor, three primitive trend-following factors, and two macro-based factors. (We follow Sadka (2010) and use the tradable portfolio returns of the 7- to 10-year Treasury Index and the Corporate Bond Baa Index from Barclays Capital instead of the original proposed term spread and credit spread.) The second is the NPPR 10-factor model, which extracts the first 10 return-based principal components from 251 global assets across different countries and asset classes, applying the method of Pukthuanthong and Roll (2009). Moreover, we adjust the alpha estimates for potential hedge fund return smoothing following the literature (Getmansky, Lo, and Makarov 2004; Titman and Tiu 2011). Specification (1) of Table 5 presents our baseline results for the monthly SED-sorted hedge fund portfolio returns. Each decile has 148 hedge funds on average and is well diversified. We report mean excess returns, Fung-Hsieh 8-factor alphas, and NPPR 10-factor alphas, all in percentages. (Table IA-3 of the Internet Appendix reports the detailed estimates of factor loadings.) We observe a near-monotonically increasing relation between SED and average excess return. High-skill funds outperform low-skill funds by more than 0.96% per month (with a Newey-West t-statistic of 2.8). The Fung-Hsieh 8-factor alpha and NPPR 10-factor alpha of the high-minus-low SED portfolio are 1.27% and 0.80% with t-statistics of 3.8 and 2.8, respectively.12 Furthermore, the excess returns of the bottom two SED deciles are not statistically different from zero, whereas the top two SED deciles earn 0.57% and 0.91% per month and are both at least three standard errors from zero.13 Table 5 Performance of SED-sorted hedge fund portfolios (1) Baseline results (2) No AUM restriction (3) Correct backfilling bias (4) Delisting fund return SED Excess ret F-H alpha NPPR alpha Excess ret F-H alpha NPPR alpha Excess ret F-H alpha NPPR alpha Excess ret F-H alpha NPPR alpha 1 - Low skill –0.058 –0.628 –0.088 0.073 –0.466 0.045 –0.233 –0.900 –0.276 –0.970 –1.560 –0.912 (–0.14) (–2.81) (–0.33) (0.18) (–2.40) (0.19) (–0.52) (–3.40) (–0.90) (–2.04) (–6.02) (–3.03) 2 0.195 –0.117 0.129 0.229 –0.047 0.112 0.016 –0.365 –0.007 –0.613 –0.984 –0.679 (0.81) (–0.93) (0.77) (0.96) (–0.34) (0.63) (0.06) (–2.66) (–0.04) (–2.00) (–5.18) (–3.07) 3 0.294 0.008 0.241 0.292 0.024 0.204 0.229 –0.047 0.177 –0.218 –0.514 –0.219 (1.45) (0.07) (1.59) (1.48) (0.22) (1.33) (1.05) (–0.36) (1.19) (–0.91) (–3.20) (–1.30) 4 0.296 0.044 0.246 0.281 0.031 0.224 0.174 –0.120 0.155 –0.279 –0.517 –0.362 (1.69) (0.37) (2.06) (1.61) (0.30) (1.82) (0.88) (–0.91) (1.23) (–1.22) (–3.54) (–2.48) 5 0.264 –0.001 0.241 0.277 0.057 0.217 0.172 –0.144 0.180 –0.290 –0.567 –0.314 (1.47) (–0.01) (1.98) (1.73) (0.54) (1.91) (0.87) (–0.72) (1.45) (–1.35) (–3.19) (–2.17) 6 0.280 0.090 0.228 0.272 0.073 0.227 0.206 –0.000 0.132 –0.300 –0.445 –0.328 (1.87) (0.84) (2.45) (1.82) (0.70) (2.42) (1.33) (–0.00) (1.23) (–1.62) (–3.15) (–2.49) 7 0.337 0.150 0.270 0.330 0.146 0.277 0.300 0.113 0.227 –0.155 –0.355 –0.227 (2.40) (1.70) (2.85) (2.40) (1.79) (3.11) (2.03) (1.19) (2.26) (–0.79) (–2.73) (–1.79) 8 0.419 0.233 0.332 0.570 0.417 0.514 0.380 0.184 0.286 –0.243 –0.454 –0.305 (3.01) (2.56) (3.35) (2.89) (2.36) (2.43) (2.45) (1.72) (2.69) (–1.23) (–3.37) (–2.26) 9 0.568 0.347 0.465 0.585 0.374 0.478 0.487 0.280 0.411 –0.019 –0.255 –0.125 (3.15) (2.43) (3.19) (3.47) (3.14) (3.62) (2.78) (2.03) (3.19) (–0.08) (–1.64) (–0.75) 10 - High skill 0.905 0.668 0.735 0.967 0.752 0.825 0.724 0.498 0.547 0.334 0.098 0.160 (4.17) (3.44) (3.35) (4.47) (3.97) (3.96) (3.12) (2.51) (2.40) (1.46) (0.52) (0.74) High - Low 0.963 1.267 0.804 0.894 1.184 0.757 0.957 1.372 0.798 1.303 1.619 1.051 (2.76) (3.78) (2.82) (2.70) (3.70) (2.67) (2.66) (3.86) (2.63) (3.12) (4.34) (3.17) (1) Baseline results (2) No AUM restriction (3) Correct backfilling bias (4) Delisting fund return SED Excess ret F-H alpha NPPR alpha Excess ret F-H alpha NPPR alpha Excess ret F-H alpha NPPR alpha Excess ret F-H alpha NPPR alpha 1 - Low skill –0.058 –0.628 –0.088 0.073 –0.466 0.045 –0.233 –0.900 –0.276 –0.970 –1.560 –0.912 (–0.14) (–2.81) (–0.33) (0.18) (–2.40) (0.19) (–0.52) (–3.40) (–0.90) (–2.04) (–6.02) (–3.03) 2 0.195 –0.117 0.129 0.229 –0.047 0.112 0.016 –0.365 –0.007 –0.613 –0.984 –0.679 (0.81) (–0.93) (0.77) (0.96) (–0.34) (0.63) (0.06) (–2.66) (–0.04) (–2.00) (–5.18) (–3.07) 3 0.294 0.008 0.241 0.292 0.024 0.204 0.229 –0.047 0.177 –0.218 –0.514 –0.219 (1.45) (0.07) (1.59) (1.48) (0.22) (1.33) (1.05) (–0.36) (1.19) (–0.91) (–3.20) (–1.30) 4 0.296 0.044 0.246 0.281 0.031 0.224 0.174 –0.120 0.155 –0.279 –0.517 –0.362 (1.69) (0.37) (2.06) (1.61) (0.30) (1.82) (0.88) (–0.91) (1.23) (–1.22) (–3.54) (–2.48) 5 0.264 –0.001 0.241 0.277 0.057 0.217 0.172 –0.144 0.180 –0.290 –0.567 –0.314 (1.47) (–0.01) (1.98) (1.73) (0.54) (1.91) (0.87) (–0.72) (1.45) (–1.35) (–3.19) (–2.17) 6 0.280 0.090 0.228 0.272 0.073 0.227 0.206 –0.000 0.132 –0.300 –0.445 –0.328 (1.87) (0.84) (2.45) (1.82) (0.70) (2.42) (1.33) (–0.00) (1.23) (–1.62) (–3.15) (–2.49) 7 0.337 0.150 0.270 0.330 0.146 0.277 0.300 0.113 0.227 –0.155 –0.355 –0.227 (2.40) (1.70) (2.85) (2.40) (1.79) (3.11) (2.03) (1.19) (2.26) (–0.79) (–2.73) (–1.79) 8 0.419 0.233 0.332 0.570 0.417 0.514 0.380 0.184 0.286 –0.243 –0.454 –0.305 (3.01) (2.56) (3.35) (2.89) (2.36) (2.43) (2.45) (1.72) (2.69) (–1.23) (–3.37) (–2.26) 9 0.568 0.347 0.465 0.585 0.374 0.478 0.487 0.280 0.411 –0.019 –0.255 –0.125 (3.15) (2.43) (3.19) (3.47) (3.14) (3.62) (2.78) (2.03) (3.19) (–0.08) (–1.64) (–0.75) 10 - High skill 0.905 0.668 0.735 0.967 0.752 0.825 0.724 0.498 0.547 0.334 0.098 0.160 (4.17) (3.44) (3.35) (4.47) (3.97) (3.96) (3.12) (2.51) (2.40) (1.46) (0.52) (0.74) High - Low 0.963 1.267 0.804 0.894 1.184 0.757 0.957 1.372 0.798 1.303 1.619 1.051 (2.76) (3.78) (2.82) (2.70) (3.70) (2.67) (2.66) (3.86) (2.63) (3.12) (4.34) (3.17) This table reports the excess returns, the Fung-Hsieh alphas, and the NPPR alphas of the 10 decile portfolios sorted on SED measures. We hold decile portfolios for one month and calculate equally weighted returns and alphas in percentages, with Newey and West (1987) t-statistics reported in parentheses, both for each decile and for the high-minus-low SED portfolio. Four sets of results are presented: (1) the baseline sample of hedge funds with at least $${\$}$$10 million in assets under management (AUM) at the time of portfolio formation; (2) the broad hedge fund sample with no restrictions on fund AUM; (3) the fund returns corrected for backfilling bias using the date when a fund was added into the TASS database; and (4) the returns of delisted funds that enter into the “graveyard” fund sample in the TASS database by being set to -100%. Table 5 Performance of SED-sorted hedge fund portfolios (1) Baseline results (2) No AUM restriction (3) Correct backfilling bias (4) Delisting fund return SED Excess ret F-H alpha NPPR alpha Excess ret F-H alpha NPPR alpha Excess ret F-H alpha NPPR alpha Excess ret F-H alpha NPPR alpha 1 - Low skill –0.058 –0.628 –0.088 0.073 –0.466 0.045 –0.233 –0.900 –0.276 –0.970 –1.560 –0.912 (–0.14) (–2.81) (–0.33) (0.18) (–2.40) (0.19) (–0.52) (–3.40) (–0.90) (–2.04) (–6.02) (–3.03) 2 0.195 –0.117 0.129 0.229 –0.047 0.112 0.016 –0.365 –0.007 –0.613 –0.984 –0.679 (0.81) (–0.93) (0.77) (0.96) (–0.34) (0.63) (0.06) (–2.66) (–0.04) (–2.00) (–5.18) (–3.07) 3 0.294 0.008 0.241 0.292 0.024 0.204 0.229 –0.047 0.177 –0.218 –0.514 –0.219 (1.45) (0.07) (1.59) (1.48) (0.22) (1.33) (1.05) (–0.36) (1.19) (–0.91) (–3.20) (–1.30) 4 0.296 0.044 0.246 0.281 0.031 0.224 0.174 –0.120 0.155 –0.279 –0.517 –0.362 (1.69) (0.37) (2.06) (1.61) (0.30) (1.82) (0.88) (–0.91) (1.23) (–1.22) (–3.54) (–2.48) 5 0.264 –0.001 0.241 0.277 0.057 0.217 0.172 –0.144 0.180 –0.290 –0.567 –0.314 (1.47) (–0.01) (1.98) (1.73) (0.54) (1.91) (0.87) (–0.72) (1.45) (–1.35) (–3.19) (–2.17) 6 0.280 0.090 0.228 0.272 0.073 0.227 0.206 –0.000 0.132 –0.300 –0.445 –0.328 (1.87) (0.84) (2.45) (1.82) (0.70) (2.42) (1.33) (–0.00) (1.23) (–1.62) (–3.15) (–2.49) 7 0.337 0.150 0.270 0.330 0.146 0.277 0.300 0.113 0.227 –0.155 –0.355 –0.227 (2.40) (1.70) (2.85) (2.40) (1.79) (3.11) (2.03) (1.19) (2.26) (–0.79) (–2.73) (–1.79) 8 0.419 0.233 0.332 0.570 0.417 0.514 0.380 0.184 0.286 –0.243 –0.454 –0.305 (3.01) (2.56) (3.35) (2.89) (2.36) (2.43) (2.45) (1.72) (2.69) (–1.23) (–3.37) (–2.26) 9 0.568 0.347 0.465 0.585 0.374 0.478 0.487 0.280 0.411 –0.019 –0.255 –0.125 (3.15) (2.43) (3.19) (3.47) (3.14) (3.62) (2.78) (2.03) (3.19) (–0.08) (–1.64) (–0.75) 10 - High skill 0.905 0.668 0.735 0.967 0.752 0.825 0.724 0.498 0.547 0.334 0.098 0.160 (4.17) (3.44) (3.35) (4.47) (3.97) (3.96) (3.12) (2.51) (2.40) (1.46) (0.52) (0.74) High - Low 0.963 1.267 0.804 0.894 1.184 0.757 0.957 1.372 0.798 1.303 1.619 1.051 (2.76) (3.78) (2.82) (2.70) (3.70) (2.67) (2.66) (3.86) (2.63) (3.12) (4.34) (3.17) (1) Baseline results (2) No AUM restriction (3) Correct backfilling bias (4) Delisting fund return SED Excess ret F-H alpha NPPR alpha Excess ret F-H alpha NPPR alpha Excess ret F-H alpha NPPR alpha Excess ret F-H alpha NPPR alpha 1 - Low skill –0.058 –0.628 –0.088 0.073 –0.466 0.045 –0.233 –0.900 –0.276 –0.970 –1.560 –0.912 (–0.14) (–2.81) (–0.33) (0.18) (–2.40) (0.19) (–0.52) (–3.40) (–0.90) (–2.04) (–6.02) (–3.03) 2 0.195 –0.117 0.129 0.229 –0.047 0.112 0.016 –0.365 –0.007 –0.613 –0.984 –0.679 (0.81) (–0.93) (0.77) (0.96) (–0.34) (0.63) (0.06) (–2.66) (–0.04) (–2.00) (–5.18) (–3.07) 3 0.294 0.008 0.241 0.292 0.024 0.204 0.229 –0.047 0.177 –0.218 –0.514 –0.219 (1.45) (0.07) (1.59) (1.48) (0.22) (1.33) (1.05) (–0.36) (1.19) (–0.91) (–3.20) (–1.30) 4 0.296 0.044 0.246 0.281 0.031 0.224 0.174 –0.120 0.155 –0.279 –0.517 –0.362 (1.69) (0.37) (2.06) (1.61) (0.30) (1.82) (0.88) (–0.91) (1.23) (–1.22) (–3.54) (–2.48) 5 0.264 –0.001 0.241 0.277 0.057 0.217 0.172 –0.144 0.180 –0.290 –0.567 –0.314 (1.47) (–0.01) (1.98) (1.73) (0.54) (1.91) (0.87) (–0.72) (1.45) (–1.35) (–3.19) (–2.17) 6 0.280 0.090 0.228 0.272 0.073 0.227 0.206 –0.000 0.132 –0.300 –0.445 –0.328 (1.87) (0.84) (2.45) (1.82) (0.70) (2.42) (1.33) (–0.00) (1.23) (–1.62) (–3.15) (–2.49) 7 0.337 0.150 0.270 0.330 0.146 0.277 0.300 0.113 0.227 –0.155 –0.355 –0.227 (2.40) (1.70) (2.85) (2.40) (1.79) (3.11) (2.03) (1.19) (2.26) (–0.79) (–2.73) (–1.79) 8 0.419 0.233 0.332 0.570 0.417 0.514 0.380 0.184 0.286 –0.243 –0.454 –0.305 (3.01) (2.56) (3.35) (2.89) (2.36) (2.43) (2.45) (1.72) (2.69) (–1.23) (–3.37) (–2.26) 9 0.568 0.347 0.465 0.585 0.374 0.478 0.487 0.280 0.411 –0.019 –0.255 –0.125 (3.15) (2.43) (3.19) (3.47) (3.14) (3.62) (2.78) (2.03) (3.19) (–0.08) (–1.64) (–0.75) 10 - High skill 0.905 0.668 0.735 0.967 0.752 0.825 0.724 0.498 0.547 0.334 0.098 0.160 (4.17) (3.44) (3.35) (4.47) (3.97) (3.96) (3.12) (2.51) (2.40) (1.46) (0.52) (0.74) High - Low 0.963 1.267 0.804 0.894 1.184 0.757 0.957 1.372 0.798 1.303 1.619 1.051 (2.76) (3.78) (2.82) (2.70) (3.70) (2.67) (2.66) (3.86) (2.63) (3.12) (4.34) (3.17) This table reports the excess returns, the Fung-Hsieh alphas, and the NPPR alphas of the 10 decile portfolios sorted on SED measures. We hold decile portfolios for one month and calculate equally weighted returns and alphas in percentages, with Newey and West (1987) t-statistics reported in parentheses, both for each decile and for the high-minus-low SED portfolio. Four sets of results are presented: (1) the baseline sample of hedge funds with at least $${\$}$$10 million in assets under management (AUM) at the time of portfolio formation; (2) the broad hedge fund sample with no restrictions on fund AUM; (3) the fund returns corrected for backfilling bias using the date when a fund was added into the TASS database; and (4) the returns of delisted funds that enter into the “graveyard” fund sample in the TASS database by being set to -100%. Specification (2) of Table 5 repeats the baseline analysis by including the hedge funds with less than $${\$}$$10 million AUM. We observe that the results are similar to those in specification (1). For example, high-skill funds outperform low-skill funds by 0.89% per month with a t-statistic of 2.7. The Fung-Hsieh 8-factor alpha and the NPPR 10-factor alpha are 1.18% and 0.76% per month, respectively, and both are statistically significant. Specification (3) of Table 5 reports excess returns and alphas for SED-sorted fund portfolios after correcting the upward backfilling bias in hedge fund returns pointed out by Bhardwaj, Gorton, and Rouwenhorst (2013). Following their procedure, we exclude fund returns from the month when a fund was first added to the TASS database. We indeed observe an upward backfilling bias in fund returns. For example, among hedge funds in decile 5, the bias is 0.092% (0.264% $$-$$ 0.172%) per month. Nevertheless, removing this backfilling bias hardly changes our results. High-skill funds continue to outperform low-skill funds by 0.96% per month (t-statistic = 2.7), and monthly alphas are 1.37% (t-statistic = 3.9) and 0.80% (t-statistic = 2.6) based on the Fung-Hsieh 8-factor model and the NPPR 10-factor model, respectively.14 Specification (4) of Table 5 reports portfolio results after accounting for hedge fund “delisting” events due to liquidation, no longer reporting, or unable to contact fund. In particular, the TASS database doesn’t report “delisted” hedge fund returns. We fill in a large negative return of $$-$$100% in the month immediately after a hedge fund exits the database, for which we find SED-sorted fund portfolio returns similar to the baseline results. For instance, the return spread of the high-minus-low SED fund portfolio is 1.3% per month, with a t-statistic of 3.1. Results are also similar when we use different assigned values for hedge fund “delisting” returns, such as $$-$$90%, $$-$$50%, and so on, consistent with Table 3, which shows that high-SED funds have lower liquidation rates.15 Overall, the empirical evidence strongly supports our hypothesis that hedge funds that have managers skilled at exploiting rare disaster concerns earn higher returns in the cross-section. This positive effect of SED on hedge fund performance runs directly against the interpretation that high-SED funds earn higher returns on average simply by being more exposed to disaster risk. If the SED measure, that is, the covariation between fund returns and ex ante disaster concerns, were capturing disaster risk exposure, high-SED funds should earn lower returns because they are good hedges against disaster risk under this interpretation.16 That being said, we provide corroborative evidence that high-SED funds do indeed earn higher returns because of their managers’ superior skill at exploiting disaster concerns, in the following sections. 3.2 Risk exposure If SED captures the managers’ skill rather than the hedge funds’ disaster risk exposure, high-SED funds should be less exposed to disaster risk. We test this possibility by computing the loadings of SED fund deciles on various risk factors. Guided by the macro disaster risk literature (e.g., Barro 2006; Wachter 2013), we include the following set of risk factors: gross domestic product (GDP) growth, inflation, corporate default risk, and the term spread of bond yields. GDP growth is the real per capita growth rate of the GDP, computed quarterly using the real GDP growth rate obtained from Federal Reserve Economic Data (FRED) of the Federal Reserve Bank of St. Louis and the annual population growth obtained from the World Economic Outlook database of the International Monetary Fund. The inflation rate is the monthly year-on-year percentage change of the core consumer price index (CPI). We proxy the corporate default risk using the difference between the Moody’s Aaa and Baa corporate bond yields, obtained from FRED. We also compute the term spread between the 10-year U.S. Treasury yield and the 3-month Treasury-bill rate. We also consider various funding liquidity risk factors, because liquidity crunches are often part of disaster shocks (Brunnermeier, Nagel, and Pedersen 2008). The funding liquidity variables include the Treasury-Eurodollar (TED) spread, equal to the 3-month LIBOR minus the 3-month Treasury-bill rate, the LIBOR-Repo spread, equal to the 3-month LIBOR minus the 3-month General Collateral Treasury repurchase rate, and the Swap-Treasury spread, equal to the 10-year interest rate swap rate minus the 10-year Treasury yield. For market liquidity, we use the on-the-run minus the off-the-run 10-year Treasury yield spread obtained from the Federal Reserve Board, the level of liquidity measure from Pastor and Stambaugh (2003), and the “noise” measure from Hu, Pan, and Wang (2013), associated with the availability of arbitrage capital. We use the first-order difference in each of these monthly series to measure liquidity shocks. (Using the residuals from an AR(1) or AR(2) model, like Korajczyk and Sadka 2008, Moskowitz, Ooi, and Pedersen 2012, and Asness, Moskowitz, and Pedersen 2013, does not change our results.) We define U.S. funding liquidity shocks, U.S. market liquidity shocks, and U.S. all liquidity shocks as the first principal components based on the correlation matrices of the corresponding sets of liquidity factors. Panel A of Table 6 reports the loadings of SED-sorted hedge fund portfolios on macro and liquidity risk factors. We observe that high-SED funds have higher loadings on macro and liquidity risk factors (the loadings on the negative of GDP growth are higher equivalently), implying that when macro and liquidity risks are high, high-SED funds indeed perform better than low-SED funds. The difference in factor loadings is highly significant for all factors, except that it is marginally significant for inflation risk. Table 6 Risk exposure of SED-sorted hedge fund portfolios A. Loadings on macro and liquidity risk factors B. Loadings on option-based factors SED Default risk Term spread Real GDP growth Inflation rate Market liquidity Funding liquidity All liquidity Volatility skew volatility Risk-neutral skewness Risk-neutral kurtosis Risk-neutral spread Option return 1 - Low skill –0.061 –0.008 0.008 –0.013 –0.006 –0.004 –0.005 –0.091 –0.862 –0.004 0.000 –0.328 (–3.88) (–0.95) (3.20) (–2.42) (–3.61) (–3.19) (–4.15) (–1.25) (–4.01) (–0.79) (0.71) (–6.83) 2 –0.044 –0.004 0.003 –0.005 –0.004 –0.003 –0.004 –0.042 –0.543 –0.003 0.000 –0.187 (–4.90) (–0.85) (2.36) (–1.40) (–4.55) (–3.65) (–4.98) (–1.14) (–5.65) (–0.74) (0.61) (–3.63) 3 –0.037 –0.006 0.002 –0.003 –0.003 –0.003 –0.003 –0.036 –0.392 –0.003 0.000 –0.194 (–4.84) (–1.43) (1.96) (–1.19) (–4.08) (–4.58) (–5.47) (–1.13) (–3.50) (–1.16) (1.04) (–6.00) 4 –0.030 –0.005 0.002 –0.002 –0.003 –0.003 –0.003 –0.021 –0.418 –0.003 0.000 –0.181 (–4.40) (–1.41) (2.25) (–0.80) (–4.13) (–4.33) (–5.32) (–0.69) (–5.12) (–1.59) (1.29) (–7.85) 5 –0.029 –0.003 0.002 –0.001 –0.003 –0.003 –0.003 –0.049 –0.497 –0.003 0.000 –0.245 (–3.91) (–0.74) (1.30) (–0.26) (–3.85) (–4.44) (–5.20) (–1.45) (–5.38) (–1.52) (1.12) (–5.11) 6 –0.025 –0.003 0.001 –0.001 –0.003 –0.002 –0.002 –0.021 –0.369 –0.001 0.000 –0.155 (–4.29) (–1.05) (1.25) (–0.36) (–4.19) (–3.81) (–4.91) (–0.79) (–4.30) (–0.75) (0.26) (–7.90) 7 –0.026 –0.004 0.001 –0.000 –0.003 –0.002 –0.003 –0.025 –0.336 –0.000 0.000 –0.128 (–4.55) (–1.43) (1.06) (–0.18) (–4.84) (–4.81) (–6.06) (–1.03) (–4.19) (–0.29) (0.14) (–4.44) 8 –0.020 0.001 0.000 –0.001 –0.002 –0.002 –0.002 0.016 –0.289 –0.001 0.000 –0.115 (–3.46) (0.45) (0.43) (–0.60) (–3.28) (–4.22) (–4.74) (0.58) (–4.08) (–0.80) (0.78) (–6.50) 9 –0.015 –0.002 –0.001 –0.001 –0.001 –0.001 –0.001 0.008 –0.083 –0.000 –0.000 –0.052 (–1.75) (–0.36) (–0.80) (–0.35) (–1.62) (–1.27) (–1.69) (0.19) (–0.52) (–0.09) (–0.16) (–0.97) 10 - High skill –0.003 0.010 –0.003 –0.004 –0.000 –0.001 –0.001 0.095 –0.060 –0.000 0.000 –0.008 (–0.23) (1.52) (–1.31) (–0.84) (–0.27) (–0.77) (–0.70) (1.37) (–0.21) (–0.08) (0.02) (–0.10) High - Low 0.058 0.018 –0.010 0.010 0.006 0.004 0.005 0.186 0.801 0.004 –0.000 0.320 (3.43) (2.03) (–4.07) (1.62) (3.15) (2.37) (3.28) (1.74) (2.13) (0.62) (–0.57) (3.10) A. Loadings on macro and liquidity risk factors B. Loadings on option-based factors SED Default risk Term spread Real GDP growth Inflation rate Market liquidity Funding liquidity All liquidity Volatility skew volatility Risk-neutral skewness Risk-neutral kurtosis Risk-neutral spread Option return 1 - Low skill –0.061 –0.008 0.008 –0.013 –0.006 –0.004 –0.005 –0.091 –0.862 –0.004 0.000 –0.328 (–3.88) (–0.95) (3.20) (–2.42) (–3.61) (–3.19) (–4.15) (–1.25) (–4.01) (–0.79) (0.71) (–6.83) 2 –0.044 –0.004 0.003 –0.005 –0.004 –0.003 –0.004 –0.042 –0.543 –0.003 0.000 –0.187 (–4.90) (–0.85) (2.36) (–1.40) (–4.55) (–3.65) (–4.98) (–1.14) (–5.65) (–0.74) (0.61) (–3.63) 3 –0.037 –0.006 0.002 –0.003 –0.003 –0.003 –0.003 –0.036 –0.392 –0.003 0.000 –0.194 (–4.84) (–1.43) (1.96) (–1.19) (–4.08) (–4.58) (–5.47) (–1.13) (–3.50) (–1.16) (1.04) (–6.00) 4 –0.030 –0.005 0.002 –0.002 –0.003 –0.003 –0.003 –0.021 –0.418 –0.003 0.000 –0.181 (–4.40) (–1.41) (2.25) (–0.80) (–4.13) (–4.33) (–5.32) (–0.69) (–5.12) (–1.59) (1.29) (–7.85) 5 –0.029 –0.003 0.002 –0.001 –0.003 –0.003 –0.003 –0.049 –0.497 –0.003 0.000 –0.245 (–3.91) (–0.74) (1.30) (–0.26) (–3.85) (–4.44) (–5.20) (–1.45) (–5.38) (–1.52) (1.12) (–5.11) 6 –0.025 –0.003 0.001 –0.001 –0.003 –0.002 –0.002 –0.021 –0.369 –0.001 0.000 –0.155 (–4.29) (–1.05) (1.25) (–0.36) (–4.19) (–3.81) (–4.91) (–0.79) (–4.30) (–0.75) (0.26) (–7.90) 7 –0.026 –0.004 0.001 –0.000 –0.003 –0.002 –0.003 –0.025 –0.336 –0.000 0.000 –0.128 (–4.55) (–1.43) (1.06) (–0.18) (–4.84) (–4.81) (–6.06) (–1.03) (–4.19) (–0.29) (0.14) (–4.44) 8 –0.020 0.001 0.000 –0.001 –0.002 –0.002 –0.002 0.016 –0.289 –0.001 0.000 –0.115 (–3.46) (0.45) (0.43) (–0.60) (–3.28) (–4.22) (–4.74) (0.58) (–4.08) (–0.80) (0.78) (–6.50) 9 –0.015 –0.002 –0.001 –0.001 –0.001 –0.001 –0.001 0.008 –0.083 –0.000 –0.000 –0.052 (–1.75) (–0.36) (–0.80) (–0.35) (–1.62) (–1.27) (–1.69) (0.19) (–0.52) (–0.09) (–0.16) (–0.97) 10 - High skill –0.003 0.010 –0.003 –0.004 –0.000 –0.001 –0.001 0.095 –0.060 –0.000 0.000 –0.008 (–0.23) (1.52) (–1.31) (–0.84) (–0.27) (–0.77) (–0.70) (1.37) (–0.21) (–0.08) (0.02) (–0.10) High - Low 0.058 0.018 –0.010 0.010 0.006 0.004 0.005 0.186 0.801 0.004 –0.000 0.320 (3.43) (2.03) (–4.07) (1.62) (3.15) (2.37) (3.28) (1.74) (2.13) (0.62) (–0.57) (3.10) This table reports the portfolio loadings on macro and liquidity risk factors (panel A) and option-based factors (panel B) of the10 SED-sorted hedge fund portfolios. The loadings are estimated using time-series regressions of portfolio returns on one of the factors together with the market excess return. The macro and liquidity factors include (1) default spread, equal to the difference between the Moody’s Aaa and Baa corporate bond yield; (2) term spread, equal to the difference between the 10-year Treasury bond yield and the 3-month Treasury-bill rate; (3) real GDP growth, based on the quarterly growth rate of real per capita GDP; (4) inflation rate, equal to the monthly year-on-year percentage change of the consumer price index; (5) market liquidity, proxied by the first principal component based on the correlation matrix of U.S. market liquidity factors, including the on-the-run-minus-off-the-run 10-year Treasury yield spread, the Pastor and Stambaugh (2003) liquidity factor, and the Hu, Pan, and Wang (2013) noise factor; (6) funding liquidity, proxied by the first principal component based on the correlation matrix of U.S. funding liquidity shocks, including the TED spread, the LIBOR-Repo spread, and the Swap-Treasury spread; and (7) all liquidity, proxied by the first principal component based on the correlation matrix of all market liquidity and funding liquidity shocks. We measure liquidity shocks using the first-order difference in each of the liquidity measures above, and define a liquidity measure such that an increased value means lower liquidity. The option-based factors include (8) the volatility skew, equal to the difference between the S&P 500 index OTM put implied volatility and ATM call implied volatility like in Xing, Zhang, and Zhao (2010); (9) the risk-neutral volatility, skewness, and kurtosis, implied from the S&P 500 index options like in Bakshi, Kapadia, and Madan (2003); and (10) the spread between the S&P 500 index OTM put returns and ATM put returns. Table 6 Risk exposure of SED-sorted hedge fund portfolios A. Loadings on macro and liquidity risk factors B. Loadings on option-based factors SED Default risk Term spread Real GDP growth Inflation rate Market liquidity Funding liquidity All liquidity Volatility skew volatility Risk-neutral skewness Risk-neutral kurtosis Risk-neutral spread Option return 1 - Low skill –0.061 –0.008 0.008 –0.013 –0.006 –0.004 –0.005 –0.091 –0.862 –0.004 0.000 –0.328 (–3.88) (–0.95) (3.20) (–2.42) (–3.61) (–3.19) (–4.15) (–1.25) (–4.01) (–0.79) (0.71) (–6.83) 2 –0.044 –0.004 0.003 –0.005 –0.004 –0.003 –0.004 –0.042 –0.543 –0.003 0.000 –0.187 (–4.90) (–0.85) (2.36) (–1.40) (–4.55) (–3.65) (–4.98) (–1.14) (–5.65) (–0.74) (0.61) (–3.63) 3 –0.037 –0.006 0.002 –0.003 –0.003 –0.003 –0.003 –0.036 –0.392 –0.003 0.000 –0.194 (–4.84) (–1.43) (1.96) (–1.19) (–4.08) (–4.58) (–5.47) (–1.13) (–3.50) (–1.16) (1.04) (–6.00) 4 –0.030 –0.005 0.002 –0.002 –0.003 –0.003 –0.003 –0.021 –0.418 –0.003 0.000 –0.181 (–4.40) (–1.41) (2.25) (–0.80) (–4.13) (–4.33) (–5.32) (–0.69) (–5.12) (–1.59) (1.29) (–7.85) 5 –0.029 –0.003 0.002 –0.001 –0.003 –0.003 –0.003 –0.049 –0.497 –0.003 0.000 –0.245 (–3.91) (–0.74) (1.30) (–0.26) (–3.85) (–4.44) (–5.20) (–1.45) (–5.38) (–1.52) (1.12) (–5.11) 6 –0.025 –0.003 0.001 –0.001 –0.003 –0.002 –0.002 –0.021 –0.369 –0.001 0.000 –0.155 (–4.29) (–1.05) (1.25) (–0.36) (–4.19) (–3.81) (–4.91) (–0.79) (–4.30) (–0.75) (0.26) (–7.90) 7 –0.026 –0.004 0.001 –0.000 –0.003 –0.002 –0.003 –0.025 –0.336 –0.000 0.000 –0.128 (–4.55) (–1.43) (1.06) (–0.18) (–4.84) (–4.81) (–6.06) (–1.03) (–4.19) (–0.29) (0.14) (–4.44) 8 –0.020 0.001 0.000 –0.001 –0.002 –0.002 –0.002 0.016 –0.289 –0.001 0.000 –0.115 (–3.46) (0.45) (0.43) (–0.60) (–3.28) (–4.22) (–4.74) (0.58) (–4.08) (–0.80) (0.78) (–6.50) 9 –0.015 –0.002 –0.001 –0.001 –0.001 –0.001 –0.001 0.008 –0.083 –0.000 –0.000 –0.052 (–1.75) (–0.36) (–0.80) (–0.35) (–1.62) (–1.27) (–1.69) (0.19) (–0.52) (–0.09) (–0.16) (–0.97) 10 - High skill –0.003 0.010 –0.003 –0.004 –0.000 –0.001 –0.001 0.095 –0.060 –0.000 0.000 –0.008 (–0.23) (1.52) (–1.31) (–0.84) (–0.27) (–0.77) (–0.70) (1.37) (–0.21) (–0.08) (0.02) (–0.10) High - Low 0.058 0.018 –0.010 0.010 0.006 0.004 0.005 0.186 0.801 0.004 –0.000 0.320 (3.43) (2.03) (–4.07) (1.62) (3.15) (2.37) (3.28) (1.74) (2.13) (0.62) (–0.57) (3.10) A. Loadings on macro and liquidity risk factors B. Loadings on option-based factors SED Default risk Term spread Real GDP growth Inflation rate Market liquidity Funding liquidity All liquidity Volatility skew volatility Risk-neutral skewness Risk-neutral kurtosis Risk-neutral spread Option return 1 - Low skill –0.061 –0.008 0.008 –0.013 –0.006 –0.004 –0.005 –0.091 –0.862 –0.004 0.000 –0.328 (–3.88) (–0.95) (3.20) (–2.42) (–3.61) (–3.19) (–4.15) (–1.25) (–4.01) (–0.79) (0.71) (–6.83) 2 –0.044 –0.004 0.003 –0.005 –0.004 –0.003 –0.004 –0.042 –0.543 –0.003 0.000 –0.187 (–4.90) (–0.85) (2.36) (–1.40) (–4.55) (–3.65) (–4.98) (–1.14) (–5.65) (–0.74) (0.61) (–3.63) 3 –0.037 –0.006 0.002 –0.003 –0.003 –0.003 –0.003 –0.036 –0.392 –0.003 0.000 –0.194 (–4.84) (–1.43) (1.96) (–1.19) (–4.08) (–4.58) (–5.47) (–1.13) (–3.50) (–1.16) (1.04) (–6.00) 4 –0.030 –0.005 0.002 –0.002 –0.003 –0.003 –0.003 –0.021 –0.418 –0.003 0.000 –0.181 (–4.40) (–1.41) (2.25) (–0.80) (–4.13) (–4.33) (–5.32) (–0.69) (–5.12) (–1.59) (1.29) (–7.85) 5 –0.029 –0.003 0.002 –0.001 –0.003 –0.003 –0.003 –0.049 –0.497 –0.003 0.000 –0.245 (–3.91) (–0.74) (1.30) (–0.26) (–3.85) (–4.44) (–5.20) (–1.45) (–5.38) (–1.52) (1.12) (–5.11) 6 –0.025 –0.003 0.001 –0.001 –0.003 –0.002 –0.002 –0.021 –0.369 –0.001 0.000 –0.155 (–4.29) (–1.05) (1.25) (–0.36) (–4.19) (–3.81) (–4.91) (–0.79) (–4.30) (–0.75) (0.26) (–7.90) 7 –0.026 –0.004 0.001 –0.000 –0.003 –0.002 –0.003 –0.025 –0.336 –0.000 0.000 –0.128 (–4.55) (–1.43) (1.06) (–0.18) (–4.84) (–4.81) (–6.06) (–1.03) (–4.19) (–0.29) (0.14) (–4.44) 8 –0.020 0.001 0.000 –0.001 –0.002 –0.002 –0.002 0.016 –0.289 –0.001 0.000 –0.115 (–3.46) (0.45) (0.43) (–0.60) (–3.28) (–4.22) (–4.74) (0.58) (–4.08) (–0.80) (0.78) (–6.50) 9 –0.015 –0.002 –0.001 –0.001 –0.001 –0.001 –0.001 0.008 –0.083 –0.000 –0.000 –0.052 (–1.75) (–0.36) (–0.80) (–0.35) (–1.62) (–1.27) (–1.69) (0.19) (–0.52) (–0.09) (–0.16) (–0.97) 10 - High skill –0.003 0.010 –0.003 –0.004 –0.000 –0.001 –0.001 0.095 –0.060 –0.000 0.000 –0.008 (–0.23) (1.52) (–1.31) (–0.84) (–0.27) (–0.77) (–0.70) (1.37) (–0.21) (–0.08) (0.02) (–0.10) High - Low 0.058 0.018 –0.010 0.010 0.006 0.004 0.005 0.186 0.801 0.004 –0.000 0.320 (3.43) (2.03) (–4.07) (1.62) (3.15) (2.37) (3.28) (1.74) (2.13) (0.62) (–0.57) (3.10) This table reports the portfolio loadings on macro and liquidity risk factors (panel A) and option-based factors (panel B) of the10 SED-sorted hedge fund portfolios. The loadings are estimated using time-series regressions of portfolio returns on one of the factors together with the market excess return. The macro and liquidity factors include (1) default spread, equal to the difference between the Moody’s Aaa and Baa corporate bond yield; (2) term spread, equal to the difference between the 10-year Treasury bond yield and the 3-month Treasury-bill rate; (3) real GDP growth, based on the quarterly growth rate of real per capita GDP; (4) inflation rate, equal to the monthly year-on-year percentage change of the consumer price index; (5) market liquidity, proxied by the first principal component based on the correlation matrix of U.S. market liquidity factors, including the on-the-run-minus-off-the-run 10-year Treasury yield spread, the Pastor and Stambaugh (2003) liquidity factor, and the Hu, Pan, and Wang (2013) noise factor; (6) funding liquidity, proxied by the first principal component based on the correlation matrix of U.S. funding liquidity shocks, including the TED spread, the LIBOR-Repo spread, and the Swap-Treasury spread; and (7) all liquidity, proxied by the first principal component based on the correlation matrix of all market liquidity and funding liquidity shocks. We measure liquidity shocks using the first-order difference in each of the liquidity measures above, and define a liquidity measure such that an increased value means lower liquidity. The option-based factors include (8) the volatility skew, equal to the difference between the S&P 500 index OTM put implied volatility and ATM call implied volatility like in Xing, Zhang, and Zhao (2010); (9) the risk-neutral volatility, skewness, and kurtosis, implied from the S&P 500 index options like in Bakshi, Kapadia, and Madan (2003); and (10) the spread between the S&P 500 index OTM put returns and ATM put returns. Furthermore, panel B of Table 6 reports the loadings of SED-sorted hedge fund portfolios on alternative risk factors based on option prices, including the volatility skew equal to the S&P 500 index OTM put volatility and ATM call volatility (Xing, Zhang, and Zhao 2010), the risk-neutral volatility, skewness, and kurtosis implied from S&P 500 index options (Bakshi, Kapadia, and Madan 2003), and the spread between the S&P 500 index OTM puts returns and ATM puts returns. Similar to panel A, the loadings on these option-based factors also show that high-SED funds have lower risk exposure than low-SED funds. In addition, the double-sorted fund portfolios reported in Table IA-4 of the Internet Appendix further confirm the robustness of the SED effect to the various risk factors. 3.3 Rare disaster concerns purged of rational disaster risk premiums Our baseline $$\mathbb{RIX}$$ measure is the price of disaster insurance contracts and hence contains a premium for both disaster risk exposure and pure disaster concern or fear. As discussed in Section 2, as our hypothesis is that high-SED fund managers have the skill of reaping the fear premium rather than passively taking disaster risk exposure, we expect the SED effect to be significant if we can construct measures of pure disaster concerns. In this section, we attempt to construct an alternative measure of pure disaster concern by purging the premium for disaster risk exposure from $$\mathbb{RIX}$$. In particular, we deploy the Seo and Wachter (2014) model, which captures the time-varying nature of disaster risk and matches the salient features of the U.S. aggregate market return and volatility. Option prices calculated from this model, being calibrated to consumption and aggregate market data, reflect the compensation that investors seek for bearing their losses when disaster shocks are realized. We calculate a model- implied $$\mathbb{RIX}^{M}$$ via Equation (4) using the OTM put prices from the model, and then subtract it from our original $$\mathbb{RIX}$$. The difference, dubbed $$\mathbb{RIX}^{C}$$, measures the premium of disaster insurance that investors are willing to pay beyond the disaster risk premium. The SED calculated with respect to this $$\mathbb{RIX}^{C}$$ hence directly captures the fund managers’ skill at exploiting pure disaster concerns.17 We reestimate each fund’s SED using the 24-month rolling-window regressions of monthly fund excess returns on the market factor and the $$\mathbb{RIX}^{C}$$ factor. We then form SED decile portfolios each month, hold them for one month, and calculate equal-weighted returns. Table-7 reports the monthly returns and NPPR alphas of these decile portfolios and of the high-minus-low SED portfolio. Specifically, Column 1 is based on $$\mathbb{RIX}^{C}$$, calculated with the size parameter of disaster shock set at 22%, the original calibrated value in Seo and Wachter (2014), and Columns 2 and 3 use additional experimental values of 20% and 10%, respectively. We observe that high-SED funds outperform low-SED funds by about $$\left.1.18-1.21\%\right.$$ per month with t-statistics all larger than $$\left. 3.3\right.$$. The NPPR 10-factor alpha of the high-minus-low SED portfolio ranges from about $$\left. 1.07\%\right.$$ to $$\left. 1.11\%\right.$$ per month, at least four standard errors from zero. Indeed, the positive effect of SED on fund performance using the pure disaster concern measure $$\mathbb{RIX}^{C}$$ is quantitatively stronger than that in our baseline analysis of Table 5 using the original $$\mathbb{RIX}$$ that does not exclude the premium of disaster risk exposure. To the degree that the Seo-Wachter disaster risk model captures the premium for disaster risk, these results provide reaffirming evidence for our main hypothesis that certain fund managers possess superior skills at exploiting pure disaster concerns and so deliver better fund performance than others do. Table 7 Purging disaster risk exposure $$\mathbb{RIX}^{M}$$-based SDR SED based on $$\mathbb{RIX}^{C}$$ (= $$\mathbb{RIX} - \mathbb{RIX}^{M}$$) Jump size=22% following Seo and Wachter 2014 Jump size=20% Jump size=10% Excess return NPPR alpha Excess return NPPR alpha Excess return NPPR alpha 1 - Low skill –0.187 –0.213 –0.188 –0.208 –0.185 –0.199 (–0.46) (–0.94) (–0.46) (–0.91) (–0.44) (–0.84) 2 0.202 0.156 0.219 0.167 0.195 0.148 (0.81) (1.18) (0.86) (1.20) (0.77) (1.09) 3 0.270 0.233 0.292 0.238 0.312 0.239 (1.36) (2.15) (1.49) (2.19) (1.64) (2.22) 4 0.253 0.184 0.249 0.187 0.246 0.192 (1.38) (1.66) (1.38) (1.75) (1.36) (1.91) 5 0.272 0.238 0.274 0.232 0.270 0.222 (1.77) (2.74) (1.72) (2.58) (1.67) (2.22) 6 0.275 0.226 0.287 0.236 0.312 0.262 (1.89) (2.66) (1.97) (2.75) (2.10) (3.08) 7 0.354 0.299 0.344 0.289 0.334 0.285 (2.54) (3.46) (2.46) (3.31) (2.39) (3.37) 8 0.466 0.376 0.467 0.380 0.463 0.382 (3.05) (3.74) (3.07) (3.85) (2.96) (3.74) 9 0.579 0.466 0.605 0.498 0.616 0.507 (3.38) (3.84) (3.44) (4.00) (3.63) (4.16) 10 - High skill 1.023 0.897 1.009 0.889 0.993 0.869 (4.24) (4.61) (4.33) (4.75) (4.22) (4.64) High - Low 1.210 1.110 1.198 1.097 1.178 1.068 (3.51) (4.57) (3.48) (4.58) (3.35) (4.41) $$\mathbb{RIX}^{M}$$-based SDR SED based on $$\mathbb{RIX}^{C}$$ (= $$\mathbb{RIX} - \mathbb{RIX}^{M}$$) Jump size=22% following Seo and Wachter 2014 Jump size=20% Jump size=10% Excess return NPPR alpha Excess return NPPR alpha Excess return NPPR alpha 1 - Low skill –0.187 –0.213 –0.188 –0.208 –0.185 –0.199 (–0.46) (–0.94) (–0.46) (–0.91) (–0.44) (–0.84) 2 0.202 0.156 0.219 0.167 0.195 0.148 (0.81) (1.18) (0.86) (1.20) (0.77) (1.09) 3 0.270 0.233 0.292 0.238 0.312 0.239 (1.36) (2.15) (1.49) (2.19) (1.64) (2.22) 4 0.253 0.184 0.249 0.187 0.246 0.192 (1.38) (1.66) (1.38) (1.75) (1.36) (1.91) 5 0.272 0.238 0.274 0.232 0.270 0.222 (1.77) (2.74) (1.72) (2.58) (1.67) (2.22) 6 0.275 0.226 0.287 0.236 0.312 0.262 (1.89) (2.66) (1.97) (2.75) (2.10) (3.08) 7 0.354 0.299 0.344 0.289 0.334 0.285 (2.54) (3.46) (2.46) (3.31) (2.39) (3.37) 8 0.466 0.376 0.467 0.380 0.463 0.382 (3.05) (3.74) (3.07) (3.85) (2.96) (3.74) 9 0.579 0.466 0.605 0.498 0.616 0.507 (3.38) (3.84) (3.44) (4.00) (3.63) (4.16) 10 - High skill 1.023 0.897 1.009 0.889 0.993 0.869 (4.24) (4.61) (4.33) (4.75) (4.22) (4.64) High - Low 1.210 1.110 1.198 1.097 1.178 1.068 (3.51) (4.57) (3.48) (4.58) (3.35) (4.41) This table reports the monthly excess returns and NPPR alphas of hedge fund portfolios sorted by the SED measure that are estimated using the rare disaster concern index purged of disaster risk exposure. We compute model-implied option prices from the Seo and Wachter (2014) stochastic disaster risk model (SDR), based on which we calculate a disaster-risk-model-implied RIXM that captures the compensation for disaster risk exposure. The purged rare disaster concern index $$\mathbb{RIX}^{C}$$ is the difference between our original $$\mathbb{RIX}$$ and $$\mathbb{RIX}^{M}$$. The results of Column 1 use the original calibrated jump size parameters from Seo and Wachter (2014), and those in Columns 2 and 3 experiment with different values for the jump size parameter, namely 20% and 10%, respectively. The sample period of portfolio returns is from July 1997 to July 2010. Newey-West t-statistics are reported in parentheses. Table 7 Purging disaster risk exposure $$\mathbb{RIX}^{M}$$-based SDR SED based on $$\mathbb{RIX}^{C}$$ (= $$\mathbb{RIX} - \mathbb{RIX}^{M}$$) Jump size=22% following Seo and Wachter 2014 Jump size=20% Jump size=10% Excess return NPPR alpha Excess return NPPR alpha Excess return NPPR alpha 1 - Low skill –0.187 –0.213 –0.188 –0.208 –0.185 –0.199 (–0.46) (–0.94) (–0.46) (–0.91) (–0.44) (–0.84) 2 0.202 0.156 0.219 0.167 0.195 0.148 (0.81) (1.18) (0.86) (1.20) (0.77) (1.09) 3 0.270 0.233 0.292 0.238 0.312 0.239 (1.36) (2.15) (1.49) (2.19) (1.64) (2.22) 4 0.253 0.184 0.249 0.187 0.246 0.192 (1.38) (1.66) (1.38) (1.75) (1.36) (1.91) 5 0.272 0.238 0.274 0.232 0.270 0.222 (1.77) (2.74) (1.72) (2.58) (1.67) (2.22) 6 0.275 0.226 0.287 0.236 0.312 0.262 (1.89) (2.66) (1.97) (2.75) (2.10) (3.08) 7 0.354 0.299 0.344 0.289 0.334 0.285 (2.54) (3.46) (2.46) (3.31) (2.39) (3.37) 8 0.466 0.376 0.467 0.380 0.463 0.382 (3.05) (3.74) (3.07) (3.85) (2.96) (3.74) 9 0.579 0.466 0.605 0.498 0.616 0.507 (3.38) (3.84) (3.44) (4.00) (3.63) (4.16) 10 - High skill 1.023 0.897 1.009 0.889 0.993 0.869 (4.24) (4.61) (4.33) (4.75) (4.22) (4.64) High - Low 1.210 1.110 1.198 1.097 1.178 1.068 (3.51) (4.57) (3.48) (4.58) (3.35) (4.41) $$\mathbb{RIX}^{M}$$-based SDR SED based on $$\mathbb{RIX}^{C}$$ (= $$\mathbb{RIX} - \mathbb{RIX}^{M}$$) Jump size=22% following Seo and Wachter 2014 Jump size=20% Jump size=10% Excess return NPPR alpha Excess return NPPR alpha Excess return NPPR alpha 1 - Low skill –0.187 –0.213 –0.188 –0.208 –0.185 –0.199 (–0.46) (–0.94) (–0.46) (–0.91) (–0.44) (–0.84) 2 0.202 0.156 0.219 0.167 0.195 0.148 (0.81) (1.18) (0.86) (1.20) (0.77) (1.09) 3 0.270 0.233 0.292 0.238 0.312 0.239 (1.36) (2.15) (1.49) (2.19) (1.64) (2.22) 4 0.253 0.184 0.249 0.187 0.246 0.192 (1.38) (1.66) (1.38) (1.75) (1.36) (1.91) 5 0.272 0.238 0.274 0.232 0.270 0.222 (1.77) (2.74) (1.72) (2.58) (1.67) (2.22) 6 0.275 0.226 0.287 0.236 0.312 0.262 (1.89) (2.66) (1.97) (2.75) (2.10) (3.08) 7 0.354 0.299 0.344 0.289 0.334 0.285 (2.54) (3.46) (2.46) (3.31) (2.39) (3.37) 8 0.466 0.376 0.467 0.380 0.463 0.382 (3.05) (3.74) (3.07) (3.85) (2.96) (3.74) 9 0.579 0.466 0.605 0.498 0.616 0.507 (3.38) (3.84) (3.44) (4.00) (3.63) (4.16) 10 - High skill 1.023 0.897 1.009 0.889 0.993 0.869 (4.24) (4.61) (4.33) (4.75) (4.22) (4.64) High - Low 1.210 1.110 1.198 1.097 1.178 1.068 (3.51) (4.57) (3.48) (4.58) (3.35) (4.41) This table reports the monthly excess returns and NPPR alphas of hedge fund portfolios sorted by the SED measure that are estimated using the rare disaster concern index purged of disaster risk exposure. We compute model-implied option prices from the Seo and Wachter (2014) stochastic disaster risk model (SDR), based on which we calculate a disaster-risk-model-implied RIXM that captures the compensation for disaster risk exposure. The purged rare disaster concern index $$\mathbb{RIX}^{C}$$ is the difference between our original $$\mathbb{RIX}$$ and $$\mathbb{RIX}^{M}$$. The results of Column 1 use the original calibrated jump size parameters from Seo and Wachter (2014), and those in Columns 2 and 3 experiment with different values for the jump size parameter, namely 20% and 10%, respectively. The sample period of portfolio returns is from July 1997 to July 2010. Newey-West t-statistics are reported in parentheses. 3.4 Managing leverage and extreme market timing In this section, we provide evidence that sheds light on two potential specific aspects of high-SED fund managers’ skill at exploiting disaster concerns: the skill of managing leverage and the skill of timing extreme market conditions. First, we calculate the $$\mathbb{RIX}$$-implied leverage defined as $${\it \Omega} _{\mathbb{RIX}}=(\partial \mathbb{RIX}/\mathbb{RIX)}/(\partial S/S)=\Delta _{\mathbb{RIX}}\cdot S/(\mathbb{RIX})$$, where $$S$$ is the underlying index level for the corresponding OTM put options and $$\Delta_{\mathbb{RIX}}$$ is the delta of $$\mathbb{RIX}$$. This implied leverage essentially captures the elasticity of the change in the disaster insurance price to the change in the underlying index. Following the $$\mathbb{RIX}$$ estimation procedure, we first obtain the monthly $${\it \Omega} _{\mathbb{RIX}}$$ estimates for each of the six sector indices, then standardize them over the respective full sample, and finally take the average across the sectors to get the aggregated market-level leverage. (The BKW banking index had a 10:1 split on March 22, 2004, and we make adjustments accordingly in the leverage calculation.) The monthly time-series plot in Figure 2 shows that $${\it \Omega} _{\mathbb{RIX}}$$ is countercyclical, consistent with the fact that the sensitivity of disaster insurance payoffs to the change in the underlying index is larger when the market condition worsens. Therefore, high-SED funds selling disaster insurance will suffer large losses when $${\it \Omega} _{\mathbb{RIX}}$$ is high. Accordingly, we study whether high-SED funds’ managers have the skill of managing leverage, in the sense that they reduce exposure to $${\it \Omega} _{\mathbb{RIX}}$$ at the inception of worsening market conditions, based on the following regression: \begin{align} RET_{i,t} &=a_{i}+b_{i}MKT_{t}+c_{i}\cdot {\it \Omega} _{\mathbb{RIX},t}+d_{1i}\cdot \left( {\it \Omega} _{\mathbb{RIX},t}-{\it \Omega} _{\mathbb{RIX},t-1}\right) \notag \\ &\quad +d_{2i}\cdot \max \left\{ 0,-\left( {\it \Omega} _{\mathbb{RIX},t}-{\it \Omega} _{\mathbb{RIX},t-1}\right) \right\} +\epsilon _{i,t}\text{,} \label{f:LeverageSkill} \end{align} (6) where $$RET_{i,t}$$ is the fund’s monthly excess return, and $$MKT_{t}$$ is the market excess return. Note that fund $$i$$’s exposure to leverage shock is equal to $$d_{1i}-d_{2i}$$ when the market worsens, with $${\it \Omega} _{\mathbb{RIX},t}-{\it \Omega} _{\mathbb{RIX},t-1}>0$$, and equal to $$d_{1i}$$ when the market improves, with $${\it \Omega} _{\mathbb{RIX},t}-{\it \Omega} _{\mathbb{RIX},t-1}<0$$. In consequence, we expect $$d_{2i}>0$$ for funds with leverage-managing ability. Figure 2 View largeDownload slide RIX-implied leverage and leverage-managing ability of high- and low-SED funds This figure plots the monthly time series of the RIX-implied leverage (left scale) and of measures of the leverage-managing ability of high-SED and low-SED funds (right scale). Figure 2 View largeDownload slide RIX-implied leverage and leverage-managing ability of high- and low-SED funds This figure plots the monthly time series of the RIX-implied leverage (left scale) and of measures of the leverage-managing ability of high-SED and low-SED funds (right scale). Figure 2 also plots the estimates of $$d_{2i}$$ based on a rolling estimation of (6) for high- and low-SED funds. We observe that the $$d_{2i}$$ estimates are mostly positive for high-SED funds, but negative for low-SED funds, implying that high-SED funds reduce their exposure to option-implied leverage when the market conditions worsen. This is consistent with the procyclicality of hedge fund leverage, documented by Ang, Gorovyy, and van Inwegen (2011) and Jiang (2014). Most importantly, we find that high-SED funds reduce their exposure to $${\it \Omega} _{\mathbb{RIX},t}$$, more than low-SED funds, suggesting a positive dependence of SED on fund managers’ skill at managing leverage. Table 8 further reports panel regressions of the SED on leverage-managing skills, proxied by $$d_{2i}$$. The results, shown in Column 1, confirm that high-SED funds’ managers are better able to manage leverage than low-SED funds’ managers. Moreover, from Columns 2 and 3, we find that this positive relation is significant among funds reporting leverage use in the TASS database, but not among others. Table 8 Leverage-managing skills and SED-sorted fund portfolios Variables (1) All baseline (2) No reporting of leverage (3) Reporting leverage Leverage-managing-skill 0.386 0.352 1.057 0.188 0.148 0.446 0.415 (2.12) (1.88) (4.44) (0.61) (0.47) (2.03) (1.84) Minimal investment 0.019 0.014 0.020 (2.65) (2.23) (1.52) Management fee (%) –5.209 –9.665 –2.943 (–2.17) (–3.31) (–0.95) Incentive fee (%) 0.583 0.769 0.505 (3.31) (4.49) (1.67) Redemption notice period –0.001 0.000 –0.001 (–1.61) (0.53) (–2.16) Lockup period –0.001 –0.004 0.000 (–1.12) (–2.07) (0.28) High water mark 0.047 –0.060 0.119 (1.67) (–1.96) (2.67) Personal capital invested –0.019 –0.014 –0.021 (–0.76) (–0.45) (–0.57) Leverage 0.025 (1.15) AUM –0.047 (–1.65) AGE –0.083 (–0.74) Fund flow (past 1-year) –0.043 (–0.75) Return volatility(past 2-year) 3.294 (0.97) Return skewness(past 2-year) 0.135 (5.26) Return kurtosis(past 2-year) 0.001 (0.16) Alpha (F-H factor model) –11.669 (–3.25) R-squared (F-H factors) 0.319 (2.71) SDI 0.249 (1.86) Downside return 5.433 (1.84) Liquidity timing –0.024 (–1.48) Market timing 0.008 (1.30) Volatility timing –0.277 (–0.80) Year FEs No Yes Yes No Yes No Yes Fund FEs No No Yes No No No No Observations 20,331 20,155 10,326 8,286 8,161 12,045 11,994 Adjusted R-squared 0.002 0.004 0.265 0.000 0.007 0.002 0.005 Variables (1) All baseline (2) No reporting of leverage (3) Reporting leverage Leverage-managing-skill 0.386 0.352 1.057 0.188 0.148 0.446 0.415 (2.12) (1.88) (4.44) (0.61) (0.47) (2.03) (1.84) Minimal investment 0.019 0.014 0.020 (2.65) (2.23) (1.52) Management fee (%) –5.209 –9.665 –2.943 (–2.17) (–3.31) (–0.95) Incentive fee (%) 0.583 0.769 0.505 (3.31) (4.49) (1.67) Redemption notice period –0.001 0.000 –0.001 (–1.61) (0.53) (–2.16) Lockup period –0.001 –0.004 0.000 (–1.12) (–2.07) (0.28) High water mark 0.047 –0.060 0.119 (1.67) (–1.96) (2.67) Personal capital invested –0.019 –0.014 –0.021 (–0.76) (–0.45) (–0.57) Leverage 0.025 (1.15) AUM –0.047 (–1.65) AGE –0.083 (–0.74) Fund flow (past 1-year) –0.043 (–0.75) Return volatility(past 2-year) 3.294 (0.97) Return skewness(past 2-year) 0.135 (5.26) Return kurtosis(past 2-year) 0.001 (0.16) Alpha (F-H factor model) –11.669 (–3.25) R-squared (F-H factors) 0.319 (2.71) SDI 0.249 (1.86) Downside return 5.433 (1.84) Liquidity timing –0.024 (–1.48) Market timing 0.008 (1.30) Volatility timing –0.277 (–0.80) Year FEs No Yes Yes No Yes No Yes Fund FEs No No Yes No No No No Observations 20,331 20,155 10,326 8,286 8,161 12,045 11,994 Adjusted R-squared 0.002 0.004 0.265 0.000 0.007 0.002 0.005 This table reports panel regressions for the SED measure on measures of fund managers’ skills in managing leverage, controlling for the same set of fund characteristics used in Table 2. Column 1 reports results for the whole baseline sample of hedge funds, and Columns 2 and 3 report results for the sample of funds reporting no leverage use and use of leverage, respectively. Different sets of the fund and year fixed effects are considered in different specifications, and robust t-statistics are reported in parentheses. Table 8 Leverage-managing skills and SED-sorted fund portfolios Variables (1) All baseline (2) No reporting of leverage (3) Reporting leverage Leverage-managing-skill 0.386 0.352 1.057 0.188 0.148 0.446 0.415 (2.12) (1.88) (4.44) (0.61) (0.47) (2.03) (1.84) Minimal investment 0.019 0.014 0.020 (2.65) (2.23) (1.52) Management fee (%) –5.209 –9.665 –2.943 (–2.17) (–3.31) (–0.95) Incentive fee (%) 0.583 0.769 0.505 (3.31) (4.49) (1.67) Redemption notice period –0.001 0.000 –0.001 (–1.61) (0.53) (–2.16) Lockup period –0.001 –0.004 0.000 (–1.12) (–2.07) (0.28) High water mark 0.047 –0.060 0.119 (1.67) (–1.96) (2.67) Personal capital invested –0.019 –0.014 –0.021 (–0.76) (–0.45) (–0.57) Leverage 0.025 (1.15) AUM –0.047 (–1.65) AGE –0.083 (–0.74) Fund flow (past 1-year) –0.043 (–0.75) Return volatility(past 2-year) 3.294 (0.97) Return skewness(past 2-year) 0.135 (5.26) Return kurtosis(past 2-year) 0.001 (0.16) Alpha (F-H factor model) –11.669 (–3.25) R-squared (F-H factors) 0.319 (2.71) SDI 0.249 (1.86) Downside return 5.433 (1.84) Liquidity timing –0.024 (–1.48) Market timing 0.008 (1.30) Volatility timing –0.277 (–0.80) Year FEs No Yes Yes No Yes No Yes Fund FEs No No Yes No No No No Observations 20,331 20,155 10,326 8,286 8,161 12,045 11,994 Adjusted R-squared 0.002 0.004 0.265 0.000 0.007 0.002 0.005 Variables (1) All baseline (2) No reporting of leverage (3) Reporting leverage Leverage-managing-skill 0.386 0.352 1.057 0.188 0.148 0.446 0.415 (2.12) (1.88) (4.44) (0.61) (0.47) (2.03) (1.84) Minimal investment 0.019 0.014 0.020 (2.65) (2.23) (1.52) Management fee (%) –5.209 –9.665 –2.943 (–2.17) (–3.31) (–0.95) Incentive fee (%) 0.583 0.769 0.505 (3.31) (4.49) (1.67) Redemption notice period –0.001 0.000 –0.001 (–1.61) (0.53) (–2.16) Lockup period –0.001 –0.004 0.000 (–1.12) (–2.07) (0.28) High water mark 0.047 –0.060 0.119 (1.67) (–1.96) (2.67) Personal capital invested –0.019 –0.014 –0.021 (–0.76) (–0.45) (–0.57) Leverage 0.025 (1.15) AUM –0.047 (–1.65) AGE –0.083 (–0.74) Fund flow (past 1-year) –0.043 (–0.75) Return volatility(past 2-year) 3.294 (0.97) Return skewness(past 2-year) 0.135 (5.26) Return kurtosis(past 2-year) 0.001 (0.16) Alpha (F-H factor model) –11.669 (–3.25) R-squared (F-H factors) 0.319 (2.71) SDI 0.249 (1.86) Downside return 5.433 (1.84) Liquidity timing –0.024 (–1.48) Market timing 0.008 (1.30) Volatility timing –0.277 (–0.80) Year FEs No Yes Yes No Yes No Yes Fund FEs No No Yes No No No No Observations 20,331 20,155 10,326 8,286 8,161 12,045 11,994 Adjusted R-squared 0.002 0.004 0.265 0.000 0.007 0.002 0.005 This table reports panel regressions for the SED measure on measures of fund managers’ skills in managing leverage, controlling for the same set of fund characteristics used in Table 2. Column 1 reports results for the whole baseline sample of hedge funds, and Columns 2 and 3 report results for the sample of funds reporting no leverage use and use of leverage, respectively. Different sets of the fund and year fixed effects are considered in different specifications, and robust t-statistics are reported in parentheses. Second, we examine whether a fund’s SED is related to its extreme-market-timing ability. Specifically, we estimate each fund’s extreme-market-timing ability using the following regression: \begin{align} RET_{i,t}&=a_{i}+b_{i}MKT_{t}+c_{i}\cdot MKT_{i}^{2}\times Bull_{t} \notag \\ &\quad +d_{i}\cdot MKT_{i}^{2}\times Bear_{t}+\epsilon _{i,t}\text{,} \label{f:ExtremeMarketTiming} \end{align} (7) where $$Bull_{t}$$ and $$Bear_{t}$$ are dummy variables for months with market returns ranked into the top and bottom quintiles of the monthly return time series. The coefficients $$c_{i}$$ and $$d_{i}$$ in (7) capture the fund’s exposure to the absolute (square) magnitude of market returns in bull and bear markets, respectively, and hence the manager’s respective timing skills. Panel regressions of the SED on bull and bear market-timing skills, reported in Columns 2, 4, 6, and 8 of Table 2, show that high-SED funds, on average, have significant bear-market timing ability in all specifications, but have bull-market timing ability only when no fund fixed effects are included. 4. Alternative Interpretations In this section, we provide strong evidence against alternative interpretations of the high-SED funds’ superior performance. We consider the possibility that our results are being driven by luck, by funds’ use of disaster insurance, and by funds’ positions on intermediate tails. We also control for various fund managers skills already documented in the literature. 4.1 Luck One alternative interpretation of the superior average performance of high-SED funds over the full sample may be a combination of better performance in normal times and worse performance in stressful times that are short during our sample period. In other words, high-SED funds could be just luckier than low-SED funds. However, the monthly series of high-minus-low SED portfolio returns provided in Figure 3 show that high-SED funds outperform others not only in normal times but also in stressful times, including during the 2008 financial crisis, which is evidence against the luck interpretation. Figure 3 View largeDownload slide Time series of high-minus-low SED portfolio returns This figure plots the monthly time series of the excess returns of the high-minus-low SED portfolios from July 1997 to July 2010. Figure 3 View largeDownload slide Time series of high-minus-low SED portfolio returns This figure plots the monthly time series of the excess returns of the high-minus-low SED portfolios from July 1997 to July 2010. To formally rule out this interpretation, we perform a conditional portfolio analysis of SED-sorted funds in stressful versus normal times. We consider four different definitions of stressful versus normal times: (1) months during which the market excess returns lose more than 10% versus others; (2) months in the lowest quintile versus others when we rank all months into five groups by market excess returns; (3) National Bureau of Economic Research (NBER) recession periods versus others; and (4) months in the lowest versus highest decile when we rank all months into 10 groups by market excess returns. The returns of SED-sorted decile fund portfolios for the four specifications are reported in Columns 1, 2, 3, and 4 of Table 9, respectively. Table 9 SED-sorted fund performance in normal times versus in stressful times (1) Group months by market excess returns (2) Rank months by market excess returns(quintiles) (3) Group months by NBER recessions (4) Rank months by market excess returns(deciles) SED Full sample $$\geq$$ 10% loss Others Lowest quintile Others Stressful times Normal times Lowest Highest 1 - Low skill –0.187 –8.856 0.157 –4.310 0.868 –2.217 0.253 –6.265 2.447 (–0.46) (–2.90) (0.57) (–5.27) (3.18) (–2.34) (0.79) (–4.56) (2.10) 2 0.202 –4.832 0.402 –2.596 0.918 –1.080 0.480 –3.474 1.686 (0.81) (–2.95) (2.26) (–5.59) (5.53) (–1.85) (2.43) (–4.39) (1.40) 3 0.270 –3.434 0.417 –1.927 0.833 –0.978 0.541 –2.671 1.193 (1.36) (–2.95) (2.90) (–5.24) (6.35) (–2.00) (3.67) (–4.36) (2.86) 4 0.253 –3.202 0.390 –1.598 0.726 –0.569 0.431 –2.268 1.304 (1.38) (–2.60) (3.11) (–4.46) (6.22) (–1.33) (3.12) (–3.52) (2.58) 5 0.272 –2.673 0.389 –1.302 0.675 –0.523 0.445 –2.058 1.240 (1.77) (–2.15) (3.68) (–3.82) (7.12) (–1.27) (4.00) (–3.40) (2.67) 6 0.275 –2.309 0.378 –1.261 0.668 –0.479 0.438 –1.810 1.214 (1.89) (–2.08) (3.62) (–4.17) (7.04) (–1.27) (4.01) (–3.38) (2.47) 7 0.354 –1.815 0.440 –1.104 0.727 –0.264 0.488 –1.605 1.389 (2.54) (–1.90) (4.19) (–3.99) (7.51) (–0.73) (4.48) (–3.30) (3.74) 8 0.466 –1.844 0.557 –1.060 0.856 –0.054 0.578 –1.423 1.749 (3.05) (–2.22) (4.62) (–4.22) (7.07) (–0.16) (4.37) (–3.14) (3.49) 9 0.579 –2.032 0.683 –1.289 1.057 0.289 0.642 –1.426 2.025 (3.38) (–1.97) (4.70) (–5.18) (7.03) (1.03) (3.73) (–3.13) (2.38) 10 - High skill 1.023 –1.539 1.124 –0.952 1.528 0.815 1.068 –0.967 2.907 (4.24) (–1.24) (5.05) (–2.43) (6.33) (1.66) (4.28) (–1.50) (2.95) High - Low 1.210 7.317 0.967 3.358 0.660 3.032 0.814 5.298 0.460 (3.51) (2.56) (4.23) (4.12) (2.87) (3.59) (3.29) (3.87) (0.47) (1) Group months by market excess returns (2) Rank months by market excess returns(quintiles) (3) Group months by NBER recessions (4) Rank months by market excess returns(deciles) SED Full sample $$\geq$$ 10% loss Others Lowest quintile Others Stressful times Normal times Lowest Highest 1 - Low skill –0.187 –8.856 0.157 –4.310 0.868 –2.217 0.253 –6.265 2.447 (–0.46) (–2.90) (0.57) (–5.27) (3.18) (–2.34) (0.79) (–4.56) (2.10) 2 0.202 –4.832 0.402 –2.596 0.918 –1.080 0.480 –3.474 1.686 (0.81) (–2.95) (2.26) (–5.59) (5.53) (–1.85) (2.43) (–4.39) (1.40) 3 0.270 –3.434 0.417 –1.927 0.833 –0.978 0.541 –2.671 1.193 (1.36) (–2.95) (2.90) (–5.24) (6.35) (–2.00) (3.67) (–4.36) (2.86) 4 0.253 –3.202 0.390 –1.598 0.726 –0.569 0.431 –2.268 1.304 (1.38) (–2.60) (3.11) (–4.46) (6.22) (–1.33) (3.12) (–3.52) (2.58) 5 0.272 –2.673 0.389 –1.302 0.675 –0.523 0.445 –2.058 1.240 (1.77) (–2.15) (3.68) (–3.82) (7.12) (–1.27) (4.00) (–3.40) (2.67) 6 0.275 –2.309 0.378 –1.261 0.668 –0.479 0.438 –1.810 1.214 (1.89) (–2.08) (3.62) (–4.17) (7.04) (–1.27) (4.01) (–3.38) (2.47) 7 0.354 –1.815 0.440 –1.104 0.727 –0.264 0.488 –1.605 1.389 (2.54) (–1.90) (4.19) (–3.99) (7.51) (–0.73) (4.48) (–3.30) (3.74) 8 0.466 –1.844 0.557 –1.060 0.856 –0.054 0.578 –1.423 1.749 (3.05) (–2.22) (4.62) (–4.22) (7.07) (–0.16) (4.37) (–3.14) (3.49) 9 0.579 –2.032 0.683 –1.289 1.057 0.289 0.642 –1.426 2.025 (3.38) (–1.97) (4.70) (–5.18) (7.03) (1.03) (3.73) (–3.13) (2.38) 10 - High skill 1.023 –1.539 1.124 –0.952 1.528 0.815 1.068 –0.967 2.907 (4.24) (–1.24) (5.05) (–2.43) (6.33) (1.66) (4.28) (–1.50) (2.95) High - Low 1.210 7.317 0.967 3.358 0.660 3.032 0.814 5.298 0.460 (3.51) (2.56) (4.23) (4.12) (2.87) (3.59) (3.29) (3.87) (0.47) This table reports the mean excess returns of SED-sorted decile fund portfolios in stressful versus normal times. We consider four different specifications of stressful versus normal times: (1) months during which the market excess returns lose more than 10% versus others; (2) months in the lowest quintile when we rank all months into five groups of market excess returns versus others; (3) NBER recession periods versus others; and (4) months in the lowest versus highest decile when we rank all months into 10 groups of market excess returns. The first column repeats the performance of SED-sorted fund portfolios over the full sample from Table 5 for comparison. The sample period of portfolio returns is from July 1997 to July 2010. Newey and West (1987) t-statistics are in parentheses. Table 9 SED-sorted fund performance in normal times versus in stressful times (1) Group months by market excess returns (2) Rank months by market excess returns(quintiles) (3) Group months by NBER recessions (4) Rank months by market excess returns(deciles) SED Full sample $$\geq$$ 10% loss Others Lowest quintile Others Stressful times Normal times Lowest Highest 1 - Low skill –0.187 –8.856 0.157 –4.310 0.868 –2.217 0.253 –6.265 2.447 (–0.46) (–2.90) (0.57) (–5.27) (3.18) (–2.34) (0.79) (–4.56) (2.10) 2 0.202 –4.832 0.402 –2.596 0.918 –1.080 0.480 –3.474 1.686 (0.81) (–2.95) (2.26) (–5.59) (5.53) (–1.85) (2.43) (–4.39) (1.40) 3 0.270 –3.434 0.417 –1.927 0.833 –0.978 0.541 –2.671 1.193 (1.36) (–2.95) (2.90) (–5.24) (6.35) (–2.00) (3.67) (–4.36) (2.86) 4 0.253 –3.202 0.390 –1.598 0.726 –0.569 0.431 –2.268 1.304 (1.38) (–2.60) (3.11) (–4.46) (6.22) (–1.33) (3.12) (–3.52) (2.58) 5 0.272 –2.673 0.389 –1.302 0.675 –0.523 0.445 –2.058 1.240 (1.77) (–2.15) (3.68) (–3.82) (7.12) (–1.27) (4.00) (–3.40) (2.67) 6 0.275 –2.309 0.378 –1.261 0.668 –0.479 0.438 –1.810 1.214 (1.89) (–2.08) (3.62) (–4.17) (7.04) (–1.27) (4.01) (–3.38) (2.47) 7 0.354 –1.815 0.440 –1.104 0.727 –0.264 0.488 –1.605 1.389 (2.54) (–1.90) (4.19) (–3.99) (7.51) (–0.73) (4.48) (–3.30) (3.74) 8 0.466 –1.844 0.557 –1.060 0.856 –0.054 0.578 –1.423 1.749 (3.05) (–2.22) (4.62) (–4.22) (7.07) (–0.16) (4.37) (–3.14) (3.49) 9 0.579 –2.032 0.683 –1.289 1.057 0.289 0.642 –1.426 2.025 (3.38) (–1.97) (4.70) (–5.18) (7.03) (1.03) (3.73) (–3.13) (2.38) 10 - High skill 1.023 –1.539 1.124 –0.952 1.528 0.815 1.068 –0.967 2.907 (4.24) (–1.24) (5.05) (–2.43) (6.33) (1.66) (4.28) (–1.50) (2.95) High - Low 1.210 7.317 0.967 3.358 0.660 3.032 0.814 5.298 0.460 (3.51) (2.56) (4.23) (4.12) (2.87) (3.59) (3.29) (3.87) (0.47) (1) Group months by market excess returns (2) Rank months by market excess returns(quintiles) (3) Group months by NBER recessions (4) Rank months by market excess returns(deciles) SED Full sample $$\geq$$ 10% loss Others Lowest quintile Others Stressful times Normal times Lowest Highest 1 - Low skill –0.187 –8.856 0.157 –4.310 0.868 –2.217 0.253 –6.265 2.447 (–0.46) (–2.90) (0.57) (–5.27) (3.18) (–2.34) (0.79) (–4.56) (2.10) 2 0.202 –4.832 0.402 –2.596 0.918 –1.080 0.480 –3.474 1.686 (0.81) (–2.95) (2.26) (–5.59) (5.53) (–1.85) (2.43) (–4.39) (1.40) 3 0.270 –3.434 0.417 –1.927 0.833 –0.978 0.541 –2.671 1.193 (1.36) (–2.95) (2.90) (–5.24) (6.35) (–2.00) (3.67) (–4.36) (2.86) 4 0.253 –3.202 0.390 –1.598 0.726 –0.569 0.431 –2.268 1.304 (1.38) (–2.60) (3.11) (–4.46) (6.22) (–1.33) (3.12) (–3.52) (2.58) 5 0.272 –2.673 0.389 –1.302 0.675 –0.523 0.445 –2.058 1.240 (1.77) (–2.15) (3.68) (–3.82) (7.12) (–1.27) (4.00) (–3.40) (2.67) 6 0.275 –2.309 0.378 –1.261 0.668 –0.479 0.438 –1.810 1.214 (1.89) (–2.08) (3.62) (–4.17) (7.04) (–1.27) (4.01) (–3.38) (2.47) 7 0.354 –1.815 0.440 –1.104 0.727 –0.264 0.488 –1.605 1.389 (2.54) (–1.90) (4.19) (–3.99) (7.51) (–0.73) (4.48) (–3.30) (3.74) 8 0.466 –1.844 0.557 –1.060 0.856 –0.054 0.578 –1.423 1.749 (3.05) (–2.22) (4.62) (–4.22) (7.07) (–0.16) (4.37) (–3.14) (3.49) 9 0.579 –2.032 0.683 –1.289 1.057 0.289 0.642 –1.426 2.025 (3.38) (–1.97) (4.70) (–5.18) (7.03) (1.03) (3.73) (–3.13) (2.38) 10 - High skill 1.023 –1.539 1.124 –0.952 1.528 0.815 1.068 –0.967 2.907 (4.24) (–1.24) (5.05) (–2.43) (6.33) (1.66) (4.28) (–1.50) (2.95) High - Low 1.210 7.317 0.967 3.358 0.660 3.032 0.814 5.298 0.460 (3.51) (2.56) (4.23) (4.12) (2.87) (3.59) (3.29) (3.87) (0.47) This table reports the mean excess returns of SED-sorted decile fund portfolios in stressful versus normal times. We consider four different specifications of stressful versus normal times: (1) months during which the market excess returns lose more than 10% versus others; (2) months in the lowest quintile when we rank all months into five groups of market excess returns versus others; (3) NBER recession periods versus others; and (4) months in the lowest versus highest decile when we rank all months into 10 groups of market excess returns. The first column repeats the performance of SED-sorted fund portfolios over the full sample from Table 5 for comparison. The sample period of portfolio returns is from July 1997 to July 2010. Newey and West (1987) t-statistics are in parentheses. In the stressful times defined in specifications (1)–(4), almost all funds lose, consistent with the literature that hedge funds earn profits overall but incur losses during market downturns.18 However, high-SED funds lose much less and still outperform low-SED funds. For example, in the months when the market loses more than 10%, high-SED funds outperform low-SED funds by 7.32% per month, with a t-statistic of 2.6, although they lost about 1.5% in these months on average. Overall, in specifications (1)–(3), high-SED funds earn higher returns than low-SED funds, ranging between 66–97 basis points per month. All are statistically significant at the 1% level. Furthermore, we expect fund managers’ skill at exploiting disaster concerns to be irrelevant to fund performance when the market disaster concern is low, for example, in a bull market. This is because there is simply not much space for the high-SED fund managers to explore in terms of disaster concerns. In the months in the highest decile when we rank all months into 10 groups by market excess returns in specification (4), we observe that the return difference between high- and low-SED funds is only 0.46% and not significantly different from zero, consistent with our hypothesis. Overall, these empirical findings, especially the pronounced outperformance of high-SED funds in stressful times, including the severe 2008 financial crisis, are inconsistent with the luck interpretation. 4.2 Purchasing versus selling disaster insurance Another alternative interpretation is that the high-SED funds include those that purchase, rather than sell, disaster insurance before a disaster shock and so receive positive payoffs after a disaster shock. This is possible because disaster concerns often spike when a negative shock hits the market. To rule out this possibility, we attempt to identify funds that purchase disaster insurance in this section. A stronger SED effect after eliminating these funds from the portfolio analysis would constitute evidence against this alternative interpretation. A particular type of such funds are the short credit funds, which typically buy credit risk insurance, such as credit default swaps (CDS), before stressful times, and benefit from widening credit spreads afterward.19 However, no hedge fund database identifies short credit funds directly, to the best of our knowledge. We identify short credit funds in a simple and transparent way using the style analysis from Sharpe (1992). We first estimate each fund’s credit exposure using a 24-month rolling regression of its monthly returns on the monthly U.S. credit spread, that is, the yield difference between Moody’s Aaa and Baa corporate bonds. We then define a short credit fund as a fund with positive and significant (at the 10% level or better) exposure. We focus exclusively on the set of credit-style hedge funds from the TASS database, including event-driven, fixed-income arbitrage, and convertible arbitrage, which all have significant exposure to the credit market. Both the identification of short credit funds and the portfolio analyses are conducted within this credit-style fund sample. Columns 1 and 2 of Table 10 present the SED- sorted hedge fund portfolios, for the whole set of credit-style funds and for the sample excluding the short credit funds, respectively. In Column 1, we show that, among all credit-style hedge funds, high-SED funds outperform low-SED funds by about 0.77% per month (t-statistic = 2.6), with Fung-Hsieh and NPPR alphas of similar magnitudes (both three standard errors from zero). In Column 2, we show a greater outperformance of high-SED funds after excluding the short credit funds: the return spread of the high-minus-low SED portfolio is about 0.95% per month (t-statistic = 3.0), with Fung-Hsieh and NPPR alphas from 0.92% to 1.04% per month; both are significant at the 1% level. The last column formally shows that the return difference between the SED portfolios excluding short credit funds and those including short credit funds is highly significant. For example, the return difference between the two high-minus-low SED portfolios is about 18 basis points per month (t-statistic = 2.6).20 Table 10 SED-sorted portfolios within credit hedge funds (1) Includes short credit funds (2) Excludes short credit funds Difference (2) - (1) SED Excess return F-H alpha NPPR alpha Excess return F-H alpha NPPR alpha Excess return F-H alpha NPPR alpha 1 - Low skill 0.044 –0.215 –0.013 –0.020 –0.303 –0.069 –0.064 –0.088 –0.056 (0.12) (–0.98) (–0.06) (–0.05) (–1.36) (–0.29) (–1.82) (–2.57) (–1.60) 2 0.294 0.148 0.210 0.262 0.113 0.181 –0.032 –0.035 –0.029 (1.09) (0.96) (1.11) (0.97) (0.73) (0.96) (–1.84) (–1.78) (–1.76) 3 0.299 0.135 0.206 0.285 0.131 0.180 –0.014 –0.005 –0.026 (1.19) (1.02) (1.25) (1.13) (1.01) (1.08) (–0.76) (–0.18) (–1.61) 4 0.321 0.200 0.217 0.301 0.177 0.199 –0.020 –0.022 –0.018 (1.58) (1.93) (1.53) (1.45) (1.69) (1.37) (–1.75) (–1.93) (–1.38) 5 0.230 0.119 0.194 0.207 0.094 0.178 –0.023 –0.026 –0.017 (1.38) (1.13) (1.70) (1.24) (0.86) (1.54) (–1.73) (–1.67) (–1.51) 6 0.216 0.130 0.161 0.212 0.125 0.164 –0.005 –0.005 0.003 (1.35) (1.35) (1.44) (1.34) (1.29) (1.53) (–0.36) (–0.43) (0.21) 7 0.283 0.207 0.252 0.291 0.215 0.256 0.008 0.008 0.004 (2.01) (2.55) (2.61) (2.03) (2.56) (2.55) (0.76) (0.84) (0.36) 8 0.472 0.360 0.383 0.466 0.345 0.368 –0.006 –0.014 –0.015 (2.96) (4.04) (3.38) (2.90) (3.95) (3.25) (–0.31) (–0.64) (–0.64) 9 0.551 0.447 0.489 0.527 0.419 0.473 –0.024 –0.028 –0.017 (3.96) (4.18) (4.60) (3.74) (3.73) (4.20) (–0.61) (–0.76) (–0.46) 10 - High skill 0.813 0.633 0.731 0.926 0.737 0.855 0.113 0.105 0.124 (3.76) (4.15) (4.40) (3.82) (4.14) (4.54) (1.98) (2.05) (2.20) High - Low 0.769 0.848 0.744 0.946 1.040 0.924 0.177 0.192 0.180 (2.58) (3.12) (3.02) (3.00) (3.58) (3.49) (2.59) (2.99) (2.59) (1) Includes short credit funds (2) Excludes short credit funds Difference (2) - (1) SED Excess return F-H alpha NPPR alpha Excess return F-H alpha NPPR alpha Excess return F-H alpha NPPR alpha 1 - Low skill 0.044 –0.215 –0.013 –0.020 –0.303 –0.069 –0.064 –0.088 –0.056 (0.12) (–0.98) (–0.06) (–0.05) (–1.36) (–0.29) (–1.82) (–2.57) (–1.60) 2 0.294 0.148 0.210 0.262 0.113 0.181 –0.032 –0.035 –0.029 (1.09) (0.96) (1.11) (0.97) (0.73) (0.96) (–1.84) (–1.78) (–1.76) 3 0.299 0.135 0.206 0.285 0.131 0.180 –0.014 –0.005 –0.026 (1.19) (1.02) (1.25) (1.13) (1.01) (1.08) (–0.76) (–0.18) (–1.61) 4 0.321 0.200 0.217 0.301 0.177 0.199 –0.020 –0.022 –0.018 (1.58) (1.93) (1.53) (1.45) (1.69) (1.37) (–1.75) (–1.93) (–1.38) 5 0.230 0.119 0.194 0.207 0.094 0.178 –0.023 –0.026 –0.017 (1.38) (1.13) (1.70) (1.24) (0.86) (1.54) (–1.73) (–1.67) (–1.51) 6 0.216 0.130 0.161 0.212 0.125 0.164 –0.005 –0.005 0.003 (1.35) (1.35) (1.44) (1.34) (1.29) (1.53) (–0.36) (–0.43) (0.21) 7 0.283 0.207 0.252 0.291 0.215 0.256 0.008 0.008 0.004 (2.01) (2.55) (2.61) (2.03) (2.56) (2.55) (0.76) (0.84) (0.36) 8 0.472 0.360 0.383 0.466 0.345 0.368 –0.006 –0.014 –0.015 (2.96) (4.04) (3.38) (2.90) (3.95) (3.25) (–0.31) (–0.64) (–0.64) 9 0.551 0.447 0.489 0.527 0.419 0.473 –0.024 –0.028 –0.017 (3.96) (4.18) (4.60) (3.74) (3.73) (4.20) (–0.61) (–0.76) (–0.46) 10 - High skill 0.813 0.633 0.731 0.926 0.737 0.855 0.113 0.105 0.124 (3.76) (4.15) (4.40) (3.82) (4.14) (4.54) (1.98) (2.05) (2.20) High - Low 0.769 0.848 0.744 0.946 1.040 0.924 0.177 0.192 0.180 (2.58) (3.12) (3.02) (3.00) (3.58) (3.49) (2.59) (2.99) (2.59) This table reports the performance of SED-sorted hedge fund portfolios in the sample of credit hedge funds, including event driven, fixed income arbitrage, and convertible arbitrage funds from the TASS database. Column 1 reports results for all credit funds; Column 2 reports results excluding the set of short credit funds; and Column 3 reports the difference. Following the style analysis of Sharpe (1992), we identify the short-credit funds by estimating each fund’s credit exposure to the U.S. credit spread, that is, the yield difference between Moody’s Aaa and Baa corporate bonds. A short-credit fund is defined as a fund with positive and significant (at a minimum level of 10%) exposure. On average, each SED decile has 35 or 36 funds when short credit funds are included, and 26–32 funds when short credit funds are excluded. We report the monthly mean returns, Fung-Hsieh alphas, and NPPR alphas all in percentages, and Newey and West (1987) t-statistics in parentheses. Table 10 SED-sorted portfolios within credit hedge funds (1) Includes short credit funds (2) Excludes short credit funds Difference (2) - (1) SED Excess return F-H alpha NPPR alpha Excess return F-H alpha NPPR alpha Excess return F-H alpha NPPR alpha 1 - Low skill 0.044 –0.215 –0.013 –0.020 –0.303 –0.069 –0.064 –0.088 –0.056 (0.12) (–0.98) (–0.06) (–0.05) (–1.36) (–0.29) (–1.82) (–2.57) (–1.60) 2 0.294 0.148 0.210 0.262 0.113 0.181 –0.032 –0.035 –0.029 (1.09) (0.96) (1.11) (0.97) (0.73) (0.96) (–1.84) (–1.78) (–1.76) 3 0.299 0.135 0.206 0.285 0.131 0.180 –0.014 –0.005 –0.026 (1.19) (1.02) (1.25) (1.13) (1.01) (1.08) (–0.76) (–0.18) (–1.61) 4 0.321 0.200 0.217 0.301 0.177 0.199 –0.020 –0.022 –0.018 (1.58) (1.93) (1.53) (1.45) (1.69) (1.37) (–1.75) (–1.93) (–1.38) 5 0.230 0.119 0.194 0.207 0.094 0.178 –0.023 –0.026 –0.017 (1.38) (1.13) (1.70) (1.24) (0.86) (1.54) (–1.73) (–1.67) (–1.51) 6 0.216 0.130 0.161 0.212 0.125 0.164 –0.005 –0.005 0.003 (1.35) (1.35) (1.44) (1.34) (1.29) (1.53) (–0.36) (–0.43) (0.21) 7 0.283 0.207 0.252 0.291 0.215 0.256 0.008 0.008 0.004 (2.01) (2.55) (2.61) (2.03) (2.56) (2.55) (0.76) (0.84) (0.36) 8 0.472 0.360 0.383 0.466 0.345 0.368 –0.006 –0.014 –0.015 (2.96) (4.04) (3.38) (2.90) (3.95) (3.25) (–0.31) (–0.64) (–0.64) 9 0.551 0.447 0.489 0.527 0.419 0.473 –0.024 –0.028 –0.017 (3.96) (4.18) (4.60) (3.74) (3.73) (4.20) (–0.61) (–0.76) (–0.46) 10 - High skill 0.813 0.633 0.731 0.926 0.737 0.855 0.113 0.105 0.124 (3.76) (4.15) (4.40) (3.82) (4.14) (4.54) (1.98) (2.05) (2.20) High - Low 0.769 0.848 0.744 0.946 1.040 0.924 0.177 0.192 0.180 (2.58) (3.12) (3.02) (3.00) (3.58) (3.49) (2.59) (2.99) (2.59) (1) Includes short credit funds (2) Excludes short credit funds Difference (2) - (1) SED Excess return F-H alpha NPPR alpha Excess return F-H alpha NPPR alpha Excess return F-H alpha NPPR alpha 1 - Low skill 0.044 –0.215 –0.013 –0.020 –0.303 –0.069 –0.064 –0.088 –0.056 (0.12) (–0.98) (–0.06) (–0.05) (–1.36) (–0.29) (–1.82) (–2.57) (–1.60) 2 0.294 0.148 0.210 0.262 0.113 0.181 –0.032 –0.035 –0.029 (1.09) (0.96) (1.11) (0.97) (0.73) (0.96) (–1.84) (–1.78) (–1.76) 3 0.299 0.135 0.206 0.285 0.131 0.180 –0.014 –0.005 –0.026 (1.19) (1.02) (1.25) (1.13) (1.01) (1.08) (–0.76) (–0.18) (–1.61) 4 0.321 0.200 0.217 0.301 0.177 0.199 –0.020 –0.022 –0.018 (1.58) (1.93) (1.53) (1.45) (1.69) (1.37) (–1.75) (–1.93) (–1.38) 5 0.230 0.119 0.194 0.207 0.094 0.178 –0.023 –0.026 –0.017 (1.38) (1.13) (1.70) (1.24) (0.86) (1.54) (–1.73) (–1.67) (–1.51) 6 0.216 0.130 0.161 0.212 0.125 0.164 –0.005 –0.005 0.003 (1.35) (1.35) (1.44) (1.34) (1.29) (1.53) (–0.36) (–0.43) (0.21) 7 0.283 0.207 0.252 0.291 0.215 0.256 0.008 0.008 0.004 (2.01) (2.55) (2.61) (2.03) (2.56) (2.55) (0.76) (0.84) (0.36) 8 0.472 0.360 0.383 0.466 0.345 0.368 –0.006 –0.014 –0.015 (2.96) (4.04) (3.38) (2.90) (3.95) (3.25) (–0.31) (–0.64) (–0.64) 9 0.551 0.447 0.489 0.527 0.419 0.473 –0.024 –0.028 –0.017 (3.96) (4.18) (4.60) (3.74) (3.73) (4.20) (–0.61) (–0.76) (–0.46) 10 - High skill 0.813 0.633 0.731 0.926 0.737 0.855 0.113 0.105 0.124 (3.76) (4.15) (4.40) (3.82) (4.14) (4.54) (1.98) (2.05) (2.20) High - Low 0.769 0.848 0.744 0.946 1.040 0.924 0.177 0.192 0.180 (2.58) (3.12) (3.02) (3.00) (3.58) (3.49) (2.59) (2.99) (2.59) This table reports the performance of SED-sorted hedge fund portfolios in the sample of credit hedge funds, including event driven, fixed income arbitrage, and convertible arbitrage funds from the TASS database. Column 1 reports results for all credit funds; Column 2 reports results excluding the set of short credit funds; and Column 3 reports the difference. Following the style analysis of Sharpe (1992), we identify the short-credit funds by estimating each fund’s credit exposure to the U.S. credit spread, that is, the yield difference between Moody’s Aaa and Baa corporate bonds. A short-credit fund is defined as a fund with positive and significant (at a minimum level of 10%) exposure. On average, each SED decile has 35 or 36 funds when short credit funds are included, and 26–32 funds when short credit funds are excluded. We report the monthly mean returns, Fung-Hsieh alphas, and NPPR alphas all in percentages, and Newey and West (1987) t-statistics in parentheses. Furthermore, we explore a general identification scheme for hedge funds purchasing disaster insurance prior to an escalated $$\mathbb{RIX}$$: these fund managers purchase insurance at t$$-$$1 and profit from market distress at t, with an escalated $$\mathbb{RIX}$$ at t. Therefore, the t$$-$$1 return of funds that purchase disaster insurance should have negative loadings on $$\mathbb{RIX}_{t}$$, and should earn higher future returns in the cross-section. Accordingly, we measure the skill of hedge funds at purchasing disaster insurance using the regression coefficient of funds’ monthly excess return at t$$-$$1 on the next-period $$\mathbb{RIX}$$ at t.21 In Tables IA-6 and IA-7 of the Internet Appendix, we show portfolio results similar to those in Table 10: (1) funds that are low-skilled (high-skilled) at purchasing disaster insurance do not earn positive (negative) returns; (2) there is no significant return difference between low- and high-skill funds; and (3) after we exclude the funds that are likely to purchase disaster insurance, the SED effect is similar to or stronger than our baseline results. In sum, we find strong empirical evidence against the alternative interpretation that high-SED funds are simply purchasing disaster insurance in one way or another. 4.3 Intermediate versus extreme tails A further alternative interpretation is that the superior outperformance of high-SED funds is due to their skill at exploiting insurance against mild market shocks or intermediate tail events, given that disaster shocks are rare by definition. To rule out this possibility, we need a measure of the market’s intermediate tail concerns in order to capture fund managers’ skill at exploiting concerns about mild market shocks. In this regard, the measure $$\mathbb{IV}$$ in (1) of Section 2.1, which underlies the construction of the CBOE’s VIX, is less sensitive to the extreme tail events captured by $$\mathbb{RIX}$$, as seen from (5). Thus, we use VIX as a measure of intermediate tail events, and the covariation between the fund returns and VIX to capture fund managers’ skill at exploiting concerns about intermediate tails, which we denote as skill at exploiting volatility concerns (SEV). We perform two sets of sequential sorts and rank hedge funds into 25 portfolios according to the SEV and SED measures. In panel A of Table 11, we first sort all funds into quintiles based on each fund’s SEV, and then sort funds within each SEV quintile into five portfolios based on each fund’s SED. We observe that high-SED funds outperform low-SED funds within each quintile of SEV. The return spreads of the high-minus-low SED portfolios range from $$0.43\%$$ to $$1.1\%$$ per month, all statistically significant at the $$\left. 1\%\right.$$ level. The Fung-Hsieh and NPPR alphas are similar in magnitude and statistical significance. However, when we first sort all funds into quintiles based on each fund’s SED and then sort funds within each SED quintile into five SEV portfolios, the results, reported in panel B, show that SEV has no power to explain hedge fund returns within any SED quintile. On average, the return difference between high-SEV and low-SEV funds is $$\left. 0.11\%\right.$$ and less than one standard error from zero.22 Table 11 Hedge fund portfolios sorted on SED and SEV A. Sequential sorting, first on SEV and then on SED 1 Low SED 2 3 4 5 High SED 5-1 F-H alpha NPPR alpha 1 - Low SEV 0.111 0.330 0.505 0.941 1.183 1.073 1.158 0.892 (0.36) (1.47) (2.32) (3.58) (3.36) (4.30) (4.41) (3.52) 2 0.067 0.277 0.259 0.479 0.639 0.572 0.729 0.528 (0.29) (2.06) (1.77) (3.59) (3.19) (3.40) (4.56) (3.17) 3 0.103 0.194 0.297 0.359 0.629 0.526 0.586 0.509 (0.58) (1.54) (2.79) (3.69) (4.35) (3.71) (4.21) (3.67) 4 0.137 0.279 0.242 0.260 0.566 0.429 0.556 0.364 (0.72) (2.23) (2.19) (2.45) (4.82) (3.19) (4.67) (3.10) 5 - High SEV –0.092 0.032 0.107 0.286 0.524 0.616 0.818 0.648 (–0.30) (0.17) (0.61) (2.02) (3.29) (2.47) (3.65) (2.73) Average 0.065 0.223 0.282 0.465 0.708 0.643 0.770 0.588 (0.30) (1.56) (2.06) (3.50) (4.14) (4.44) (5.65) (4.29) A. Sequential sorting, first on SEV and then on SED 1 Low SED 2 3 4 5 High SED 5-1 F-H alpha NPPR alpha 1 - Low SEV 0.111 0.330 0.505 0.941 1.183 1.073 1.158 0.892 (0.36) (1.47) (2.32) (3.58) (3.36) (4.30) (4.41) (3.52) 2 0.067 0.277 0.259 0.479 0.639 0.572 0.729 0.528 (0.29) (2.06) (1.77) (3.59) (3.19) (3.40) (4.56) (3.17) 3 0.103 0.194 0.297 0.359 0.629 0.526 0.586 0.509 (0.58) (1.54) (2.79) (3.69) (4.35) (3.71) (4.21) (3.67) 4 0.137 0.279 0.242 0.260 0.566 0.429 0.556 0.364 (0.72) (2.23) (2.19) (2.45) (4.82) (3.19) (4.67) (3.10) 5 - High SEV –0.092 0.032 0.107 0.286 0.524 0.616 0.818 0.648 (–0.30) (0.17) (0.61) (2.02) (3.29) (2.47) (3.65) (2.73) Average 0.065 0.223 0.282 0.465 0.708 0.643 0.770 0.588 (0.30) (1.56) (2.06) (3.50) (4.14) (4.44) (5.65) (4.29) B. Sequential sorting, first on SED and then on SEV 1 Low SEV 2 3 4 5 High SEV 5-1 F-H Alpha NPPR Alpha 1 - Low SED –0.260 0.137 0.125 0.003 0.017 0.277 0.312 0.208 (–0.83) (0.65) (0.69) (0.01) (0.06) (0.97) (1.13) (0.73) 2 0.116 0.287 0.213 0.308 0.334 0.218 0.262 0.232 (0.57) (2.09) (1.74) (2.65) (2.65) (1.36) (1.70) (1.55) 3 0.201 0.245 0.264 0.320 0.419 0.218 0.276 0.240 (1.04) (1.94) (2.45) (3.34) (3.92) (1.65) (2.48) (2.34) 4 0.389 0.371 0.388 0.429 0.513 0.124 0.220 0.117 (1.92) (2.56) (3.09) (3.72) (4.22) (0.85) (1.80) (0.93) 5 - High SED 1.035 0.799 0.660 0.680 0.752 –0.283 –0.242 –0.226 (2.90) (3.08) (3.09) (3.68) (3.61) (–1.10) (–0.96) (–0.95) Average 0.296 0.368 0.330 0.348 0.407 0.111 0.166 0.114 (1.27) (2.29) (2.43) (2.78) (2.91) (0.73) (1.26) (0.89) B. Sequential sorting, first on SED and then on SEV 1 Low SEV 2 3 4 5 High SEV 5-1 F-H Alpha NPPR Alpha 1 - Low SED –0.260 0.137 0.125 0.003 0.017 0.277 0.312 0.208 (–0.83) (0.65) (0.69) (0.01) (0.06) (0.97) (1.13) (0.73) 2 0.116 0.287 0.213 0.308 0.334 0.218 0.262 0.232 (0.57) (2.09) (1.74) (2.65) (2.65) (1.36) (1.70) (1.55) 3 0.201 0.245 0.264 0.320 0.419 0.218 0.276 0.240 (1.04) (1.94) (2.45) (3.34) (3.92) (1.65) (2.48) (2.34) 4 0.389 0.371 0.388 0.429 0.513 0.124 0.220 0.117 (1.92) (2.56) (3.09) (3.72) (4.22) (0.85) (1.80) (0.93) 5 - High SED 1.035 0.799 0.660 0.680 0.752 –0.283 –0.242 –0.226 (2.90) (3.08) (3.09) (3.68) (3.61) (–1.10) (–0.96) (–0.95) Average 0.296 0.368 0.330 0.348 0.407 0.111 0.166 0.114 (1.27) (2.29) (2.43) (2.78) (2.91) (0.73) (1.26) (0.89) This table reports the performance of hedge fund portfolios, first sorting funds on the manager’s skill at exploiting volatility concerns (SEV) and then on their skill at exploiting disaster concerns (SED) in panel A, and first sorting on SED and then sorting on SEV in panel B. We hold portfolios for one month and calculate equally weighted portfolio returns. The SEV is estimated using a 24-month rolling-window regression of funds’ monthly excess returns on VIX in the presence of market excess returns, similar to the estimation of SED using RIX. We report mean excess returns in percentages and Newey and West (1987) t-statistics in parentheses. The last three columns of each panel report the excess returns, the Fung-Hsieh alphas, and the NPPR alphas of the high-minus-low SED portfolios. Table 11 Hedge fund portfolios sorted on SED and SEV A. Sequential sorting, first on SEV and then on SED 1 Low SED 2 3 4 5 High SED 5-1 F-H alpha NPPR alpha 1 - Low SEV 0.111 0.330 0.505 0.941 1.183 1.073 1.158 0.892 (0.36) (1.47) (2.32) (3.58) (3.36) (4.30) (4.41) (3.52) 2 0.067 0.277 0.259 0.479 0.639 0.572 0.729 0.528 (0.29) (2.06) (1.77) (3.59) (3.19) (3.40) (4.56) (3.17) 3 0.103 0.194 0.297 0.359 0.629 0.526 0.586 0.509 (0.58) (1.54) (2.79) (3.69) (4.35) (3.71) (4.21) (3.67) 4 0.137 0.279 0.242 0.260 0.566 0.429 0.556 0.364 (0.72) (2.23) (2.19) (2.45) (4.82) (3.19) (4.67) (3.10) 5 - High SEV –0.092 0.032 0.107 0.286 0.524 0.616 0.818 0.648 (–0.30) (0.17) (0.61) (2.02) (3.29) (2.47) (3.65) (2.73) Average 0.065 0.223 0.282 0.465 0.708 0.643 0.770 0.588 (0.30) (1.56) (2.06) (3.50) (4.14) (4.44) (5.65) (4.29) A. Sequential sorting, first on SEV and then on SED 1 Low SED 2 3 4 5 High SED 5-1 F-H alpha NPPR alpha 1 - Low SEV 0.111 0.330 0.505 0.941 1.183 1.073 1.158 0.892 (0.36) (1.47) (2.32) (3.58) (3.36) (4.30) (4.41) (3.52) 2 0.067 0.277 0.259 0.479 0.639 0.572 0.729 0.528 (0.29) (2.06) (1.77) (3.59) (3.19) (3.40) (4.56) (3.17) 3 0.103 0.194 0.297 0.359 0.629 0.526 0.586 0.509 (0.58) (1.54) (2.79) (3.69) (4.35) (3.71) (4.21) (3.67) 4 0.137 0.279 0.242 0.260 0.566 0.429 0.556 0.364 (0.72) (2.23) (2.19) (2.45) (4.82) (3.19) (4.67) (3.10) 5 - High SEV –0.092 0.032 0.107 0.286 0.524 0.616 0.818 0.648 (–0.30) (0.17) (0.61) (2.02) (3.29) (2.47) (3.65) (2.73) Average 0.065 0.223 0.282 0.465 0.708 0.643 0.770 0.588 (0.30) (1.56) (2.06) (3.50) (4.14) (4.44) (5.65) (4.29) B. Sequential sorting, first on SED and then on SEV 1 Low SEV 2 3 4 5 High SEV 5-1 F-H Alpha NPPR Alpha 1 - Low SED –0.260 0.137 0.125 0.003 0.017 0.277 0.312 0.208 (–0.83) (0.65) (0.69) (0.01) (0.06) (0.97) (1.13) (0.73) 2 0.116 0.287 0.213 0.308 0.334 0.218 0.262 0.232 (0.57) (2.09) (1.74) (2.65) (2.65) (1.36) (1.70) (1.55) 3 0.201 0.245 0.264 0.320 0.419 0.218 0.276 0.240 (1.04) (1.94) (2.45) (3.34) (3.92) (1.65) (2.48) (2.34) 4 0.389 0.371 0.388 0.429 0.513 0.124 0.220 0.117 (1.92) (2.56) (3.09) (3.72) (4.22) (0.85) (1.80) (0.93) 5 - High SED 1.035 0.799 0.660 0.680 0.752 –0.283 –0.242 –0.226 (2.90) (3.08) (3.09) (3.68) (3.61) (–1.10) (–0.96) (–0.95) Average 0.296 0.368 0.330 0.348 0.407 0.111 0.166 0.114 (1.27) (2.29) (2.43) (2.78) (2.91) (0.73) (1.26) (0.89) B. Sequential sorting, first on SED and then on SEV 1 Low SEV 2 3 4 5 High SEV 5-1 F-H Alpha NPPR Alpha 1 - Low SED –0.260 0.137 0.125 0.003 0.017 0.277 0.312 0.208 (–0.83) (0.65) (0.69) (0.01) (0.06) (0.97) (1.13) (0.73) 2 0.116 0.287 0.213 0.308 0.334 0.218 0.262 0.232 (0.57) (2.09) (1.74) (2.65) (2.65) (1.36) (1.70) (1.55) 3 0.201 0.245 0.264 0.320 0.419 0.218 0.276 0.240 (1.04) (1.94) (2.45) (3.34) (3.92) (1.65) (2.48) (2.34) 4 0.389 0.371 0.388 0.429 0.513 0.124 0.220 0.117 (1.92) (2.56) (3.09) (3.72) (4.22) (0.85) (1.80) (0.93) 5 - High SED 1.035 0.799 0.660 0.680 0.752 –0.283 –0.242 –0.226 (2.90) (3.08) (3.09) (3.68) (3.61) (–1.10) (–0.96) (–0.95) Average 0.296 0.368 0.330 0.348 0.407 0.111 0.166 0.114 (1.27) (2.29) (2.43) (2.78) (2.91) (0.73) (1.26) (0.89) This table reports the performance of hedge fund portfolios, first sorting funds on the manager’s skill at exploiting volatility concerns (SEV) and then on their skill at exploiting disaster concerns (SED) in panel A, and first sorting on SED and then sorting on SEV in panel B. We hold portfolios for one month and calculate equally weighted portfolio returns. The SEV is estimated using a 24-month rolling-window regression of funds’ monthly excess returns on VIX in the presence of market excess returns, similar to the estimation of SED using RIX. We report mean excess returns in percentages and Newey and West (1987) t-statistics in parentheses. The last three columns of each panel report the excess returns, the Fung-Hsieh alphas, and the NPPR alphas of the high-minus-low SED portfolios. We also employ the $$\left. VaR\right.$$-based measures used by Joenväärä and Kauppila (2015) to proxy for intermediate tails. This is because the estimation, based on a 24-month rolling window of realized returns, makes these measures likely to capture the moderate market shocks in the two-year window. In contrast, our option-based measures capture disaster concerns ex ante, without being constrained by the short sample of historical realized returns. Tables IA-8 and IA-9 of the Internet Appendix report a series of independent sorting and sequential sorting portfolio results similar to those shown in Table 11, confirming that the SED effect on fund performance is significant controlling for these $$\left. VaR\right.$$-based measures. Collectively, these investigations provide evidence against the interpretation that high-SED funds are delivering superior performance by taking positions on intermediate tail shocks. 4.4 Other skills In this section, we show that SED explains cross-sectional fund performance in a distinctively different way than four other skill variables proposed in the literature: (1) The R-squared measure of regressing fund returns on the Fung-Hsieh factors, which captures the skill of funds at managing their exposure to systematic risk (Titman and Tiu 2011); (2) The strategy distinctiveness index (SDI) based on the correlation of individual fund returns with the average returns of peer funds in the same style category, which captures skill at pursuing unique investment strategies (Sun, Wang, and Zheng 2012); (3) The fund’s returns during market downturns or downside returns, which captures skill at managing downside risk (Sun, Wang, and Zheng 2013); and (4) The liquidity, market, and volatility timing measures of Cao et al. (2013). Table 12 presents Fama and MacBeth (1973) regressions of funds’ monthly excess returns in month $$t+1$$ on SED as well as these other skill measures in month t. To mitigate the potential error-in-variable (EIV) problem due to estimation errors in SED measures, we use each fund’s SED decile ranking as the regressor.23 We control for various fund characteristics, such as assets under management, age, lagged returns, management fees, incentive fees, high water mark, personal capital invested, leverage, lockup, and redemption notice period, and the betas with respect to a set of hedge fund risk factors (see Section 3.3 and 4.2 for details of these variables). We observe significant positive coefficients on SED decile rankings when we include the market beta and fund characteristics in Columns 1 and 2. Importantly, the coefficients are remarkably stable and significant when we further include the R-Squared, SDI, and downside return in Column 3 and the liquidity, market, and volatility timing measures in Column 4. In addition, Table IA-10 of the Internet Appendix reports double-sorted portfolios on SED and other skill measures, which also mitigate the EIV problem and further confirm the distinctiveness of SED from other skill variables. Table 12 Distinctiveness of SED from other skills (1) (2) (3) (4) SED 0.0005 0.0004 0.0004 0.0005 (2.41) (2.47) (2.50) (3.03) Market beta 0.0024 0.0036 0.0056 0.0021 (0.63) (1.14) (1.77) (0.49) R-squared $$-$$0.0022 ($$-$$0.80) SDI $$-$$0.0023 ($$-$$0.97) Downside return 0.0958 (2.63) Liquidity timing 0.0000 ($$-$$0.16) Market timing 0.0002 (1.25) Volatility timing $$-$$0.0384 ($$-$$1.94) AUM $$-$$0.0003 $$-$$0.0005 $$-$$0.0002 ($$-$$1.75) ($$-$$2.05) ($$-$$0.97) AGE $$-$$0.0002 $$-$$0.0002 $$-$$0.0004 ($$-$$0.82) ($$-$$0.74) ($$-$$1.34) Lagged return 0.1144 0.1064 0.1116 (7.36) (7.08) (5.14) Management fee 0.0849 0.1241 0.0890 (1.97) (2.70) (2.35) Incentive fee 0.0057 0.0087 0.0031 (2.72) (2.31) (1.34) High water mark 0.0012 0.0009 0.0013 (3.50) (2.32) (3.27) Personal capital invested 0.0003 0.0002 0.0003 (1.17) (0.56) (1.09) Leverage used 0.0006 0.0006 0.0004 (2.03) (1.30) (1.34) Lockup required 0.0012 0.0007 0.0003 (3.59) (1.68) (1.19) Redemption notice period 0.0000 0.0000 0.0000 (1.51) (1.04) (2.03) Intercept 0.0001 $$-$$0.0015 $$-$$0.0001 $$-$$0.0021 (0.06) ($$-$$0.84) ($$-$$0.02) ($$-$$1.21) Avg. # of funds per month 1485 1480 995 1212 Avg. adjusted R-squared 0.157 0.210 0.233 0.240 Number of months 157 157 157 151 (1) (2) (3) (4) SED 0.0005 0.0004 0.0004 0.0005 (2.41) (2.47) (2.50) (3.03) Market beta 0.0024 0.0036 0.0056 0.0021 (0.63) (1.14) (1.77) (0.49) R-squared $$-$$0.0022 ($$-$$0.80) SDI $$-$$0.0023 ($$-$$0.97) Downside return 0.0958 (2.63) Liquidity timing 0.0000 ($$-$$0.16) Market timing 0.0002 (1.25) Volatility timing $$-$$0.0384 ($$-$$1.94) AUM $$-$$0.0003 $$-$$0.0005 $$-$$0.0002 ($$-$$1.75) ($$-$$2.05) ($$-$$0.97) AGE $$-$$0.0002 $$-$$0.0002 $$-$$0.0004 ($$-$$0.82) ($$-$$0.74) ($$-$$1.34) Lagged return 0.1144 0.1064 0.1116 (7.36) (7.08) (5.14) Management fee 0.0849 0.1241 0.0890 (1.97) (2.70) (2.35) Incentive fee 0.0057 0.0087 0.0031 (2.72) (2.31) (1.34) High water mark 0.0012 0.0009 0.0013 (3.50) (2.32) (3.27) Personal capital invested 0.0003 0.0002 0.0003 (1.17) (0.56) (1.09) Leverage used 0.0006 0.0006 0.0004 (2.03) (1.30) (1.34) Lockup required 0.0012 0.0007 0.0003 (3.59) (1.68) (1.19) Redemption notice period 0.0000 0.0000 0.0000 (1.51) (1.04) (2.03) Intercept 0.0001 $$-$$0.0015 $$-$$0.0001 $$-$$0.0021 (0.06) ($$-$$0.84) ($$-$$0.02) ($$-$$1.21) Avg. # of funds per month 1485 1480 995 1212 Avg. adjusted R-squared 0.157 0.210 0.233 0.240 Number of months 157 157 157 151 This table reports Fama and MacBeth (1973) regressions of hedge fundsâŁTM excess returns in month t + 1 on their SED decile rankings in month t, controlling for other skill measures, as well as the same set of fund characteristics used in Table 2. We consider four sets of other skill variables: (1) The R-squared measure of regressing fund returns on the Fung-Hsieh factors, which capture the skill of fundsâŁTM managers in managing their exposure to systematic risk (Titman and Tiu 2011); (2) the strategy distinctiveness index (SDI), based on the correlation of individual fund returns with the average returns of peer funds in the same style category, which captures managersâŁTM skill at pursuing unique investment strategies (Sun, Wang, and Zheng 2012); (3) fund returns during market downturns or downside returns, which capture managersâŁTM skill at managing downside risk (Sun, Wang, and Zheng 2013); and (4) liquidity, market, and volatility timing measures (Cao et al. 2013). We report the time-series average of the Fama-MacBeth regression coefficients, with Newey and West (1987) t-statistics in parentheses. We include the market beta and fund characteristics in Columns 1 and 2 and further include the R-squared, SDI, and downside returns in Column 3, and the liquidity, market, and volatility timing measures in Column 4. Table 12 Distinctiveness of SED from other skills (1) (2) (3) (4) SED 0.0005 0.0004 0.0004 0.0005 (2.41) (2.47) (2.50) (3.03) Market beta 0.0024 0.0036 0.0056 0.0021 (0.63) (1.14) (1.77) (0.49) R-squared $$-$$0.0022 ($$-$$0.80) SDI $$-$$0.0023 ($$-$$0.97) Downside return 0.0958 (2.63) Liquidity timing 0.0000 ($$-$$0.16) Market timing 0.0002 (1.25) Volatility timing $$-$$0.0384 ($$-$$1.94) AUM $$-$$0.0003 $$-$$0.0005 $$-$$0.0002 ($$-$$1.75) ($$-$$2.05) ($$-$$0.97) AGE $$-$$0.0002 $$-$$0.0002 $$-$$0.0004 ($$-$$0.82) ($$-$$0.74) ($$-$$1.34) Lagged return 0.1144 0.1064 0.1116 (7.36) (7.08) (5.14) Management fee 0.0849 0.1241 0.0890 (1.97) (2.70) (2.35) Incentive fee 0.0057 0.0087 0.0031 (2.72) (2.31) (1.34) High water mark 0.0012 0.0009 0.0013 (3.50) (2.32) (3.27) Personal capital invested 0.0003 0.0002 0.0003 (1.17) (0.56) (1.09) Leverage used 0.0006 0.0006 0.0004 (2.03) (1.30) (1.34) Lockup required 0.0012 0.0007 0.0003 (3.59) (1.68) (1.19) Redemption notice period 0.0000 0.0000 0.0000 (1.51) (1.04) (2.03) Intercept 0.0001 $$-$$0.0015 $$-$$0.0001 $$-$$0.0021 (0.06) ($$-$$0.84) ($$-$$0.02) ($$-$$1.21) Avg. # of funds per month 1485 1480 995 1212 Avg. adjusted R-squared 0.157 0.210 0.233 0.240 Number of months 157 157 157 151 (1) (2) (3) (4) SED 0.0005 0.0004 0.0004 0.0005 (2.41) (2.47) (2.50) (3.03) Market beta 0.0024 0.0036 0.0056 0.0021 (0.63) (1.14) (1.77) (0.49) R-squared $$-$$0.0022 ($$-$$0.80) SDI $$-$$0.0023 ($$-$$0.97) Downside return 0.0958 (2.63) Liquidity timing 0.0000 ($$-$$0.16) Market timing 0.0002 (1.25) Volatility timing $$-$$0.0384 ($$-$$1.94) AUM $$-$$0.0003 $$-$$0.0005 $$-$$0.0002 ($$-$$1.75) ($$-$$2.05) ($$-$$0.97) AGE $$-$$0.0002 $$-$$0.0002 $$-$$0.0004 ($$-$$0.82) ($$-$$0.74) ($$-$$1.34) Lagged return 0.1144 0.1064 0.1116 (7.36) (7.08) (5.14) Management fee 0.0849 0.1241 0.0890 (1.97) (2.70) (2.35) Incentive fee 0.0057 0.0087 0.0031 (2.72) (2.31) (1.34) High water mark 0.0012 0.0009 0.0013 (3.50) (2.32) (3.27) Personal capital invested 0.0003 0.0002 0.0003 (1.17) (0.56) (1.09) Leverage used 0.0006 0.0006 0.0004 (2.03) (1.30) (1.34) Lockup required 0.0012 0.0007 0.0003 (3.59) (1.68) (1.19) Redemption notice period 0.0000 0.0000 0.0000 (1.51) (1.04) (2.03) Intercept 0.0001 $$-$$0.0015 $$-$$0.0001 $$-$$0.0021 (0.06) ($$-$$0.84) ($$-$$0.02) ($$-$$1.21) Avg. # of funds per month 1485 1480 995 1212 Avg. adjusted R-squared 0.157 0.210 0.233 0.240 Number of months 157 157 157 151 This table reports Fama and MacBeth (1973) regressions of hedge fundsâŁTM excess returns in month t + 1 on their SED decile rankings in month t, controlling for other skill measures, as well as the same set of fund characteristics used in Table 2. We consider four sets of other skill variables: (1) The R-squared measure of regressing fund returns on the Fung-Hsieh factors, which capture the skill of fundsâŁTM managers in managing their exposure to systematic risk (Titman and Tiu 2011); (2) the strategy distinctiveness index (SDI), based on the correlation of individual fund returns with the average returns of peer funds in the same style category, which captures managersâŁTM skill at pursuing unique investment strategies (Sun, Wang, and Zheng 2012); (3) fund returns during market downturns or downside returns, which capture managersâŁTM skill at managing downside risk (Sun, Wang, and Zheng 2013); and (4) liquidity, market, and volatility timing measures (Cao et al. 2013). We report the time-series average of the Fama-MacBeth regression coefficients, with Newey and West (1987) t-statistics in parentheses. We include the market beta and fund characteristics in Columns 1 and 2 and further include the R-squared, SDI, and downside returns in Column 3, and the liquidity, market, and volatility timing measures in Column 4. 5. Additional Analyses and Robustness Checks In this section, we present results from additional analyses and robustness checks. First, we extend our baseline analysis of monthly SED deciles by holding them for horizons ranging from 3 months to 18 months. To deal with returns from overlapped holding months, we follow the independently managed portfolio approach introduced by Jegadeesh and Titman (1993) and calculate average monthly returns. As shown in Table IA-11, we observe significant performance persistence up to 12 months, with high-skill funds on average outperforming low-skill funds by 0.84%, 0.74%, and 0.44% per month for a holding horizon of three, six, and twelve months, respectively, with Newey-West t-statistics ranging from 1.9 to 2.6. Second, we examine the returns of SED-sorted portfolios in different hedge fund investment styles and different size groups. In panel A of Table IA-12, for most of the twelve TASS investment styles, we observe a strong and positive relation between SED and portfolio returns. In nine investment styles, high-SED funds outperform low-SED funds; for two investment styles (managed futures and global macro) we find positive but statistically insignificant return differences between high and low SED quintiles. In panel B of Table IA-12, we observe a strong relation between SED and fund performance across different fund size groups at the time of portfolio formation (measured by net asset value, NAV). The high-minus-low SED portfolios earn 0.96% and 0.75% per month, respectively, for funds within the lowest and highest NAV groups, both at least three standard errors from zero.24 Third, rather than equal-weighted returns in the baseline analysis, specification (1) of Table IA-13 shows that value-weighted (by funds’ monthly assets under management) excess returns and the Fung-Hsieh alpha of the high-minus-low SED portfolio are above 1% per month with significant t-statistics. The results remain the same if we use alphas from the NPPR 10-factor model. Specifications (2) and (3) of Table IA-13 show that the return spreads of the high-minus-low SED portfolios are 1.6% and 0.91% per month during December and non-December months, respectively, and both are statistically significant. That is, our SED-based results are robust to the December effect documented by Agarwal, Daniel, and Naik (2011). Fourth, we alternatively measure rare disaster concerns using 90-day options (rather than the 30-day options used in the baseline analysis) and 30-day OTM puts on the S&P 500 index (rather than on the sector indices, like in baseline analysis), and calculate the fund’s SED accordingly.25 Specifications (4) and (5) of Table IA-13 show that the SED effect on hedge fund performance is robust to these alternative measures of disaster concerns. In an unreported analysis, we also construct a $$\mathbb{RIX}$$ measure by averaging disaster concern measures based on S&P 500 index options and sector index options, and find similar results. Fifth, specification (6) of Table IA-13 reports the performance of SED-based hedge fund portfolios using the manipulation-proof performance measure (MPPM) developed by Goetzmann et al. (2007), the Sharpe ratio, and the information ratio benchmarked on the Fung-Hsieh model. We take into account potential hedge fund return smoothing when estimating the Sharpe ratio and information ratio (Getmansky, Lo, and Makarov 2004; Bollen and Pool 2008). We find that high-SED funds outperform low-SED funds significantly based on these alternative performance metrics. Finally, Tables IA-14 and IA-15 show that the SED effect using the sample of hedge funds covered by the HFR and CISDM databases remains similar to the baseline result, which uses the Lipper TASS database. Furthermore, the conditional test results of fund performance in normal versus stressful times are also similar. 6. Conclusions We provide novel evidence that hedge fund managers who possess better skills at exploiting rare disaster concerns (SED) deliver superior future fund performance while being less exposed to disaster risk. The key to our finding is the differentiation between ex ante market disaster concerns and ex post disaster shocks. The former often contains a premium beyond compensations for disaster risk exposure. Consequently, fund managers can deliver superior future fund performance if they are good at identifying the existence and magnitude of this overpaid premium. We argue that the covariance between hedge fund returns and ex ante disaster concerns can identify skillful fund managers, based on the idea that when the market’s disaster concern is high, funds with managers more skilled at identifying the value of the fear premium should earn higher contemporaneous returns than others. Consistent with our hypothesis, we find that the SED estimates using a rare disaster concern index calculated from out-of-the-money put options show substantial heterogeneity and significant persistence. Importantly, funds in the highest SED decile outperform funds in the lowest decile by 0.96% per month on average, and even more during stressful market times. High-SED funds are also less exposed to disaster risk, and their managers possess skills of managing leverage and timing extreme market conditions. Overall, our results present strong evidence that a group of skilled hedge fund managers deliver superior future fund performance by actively exploiting disaster concerns, which differs from the popular view that hedge funds earn higher average returns by simply taking disaster risk exposure (Mitchell and Pulvino 2001; Agarwal and Naik 2004). Who buys the insurance against rare disaster events? Are the buyers of the insurance the same investors who also invest in the hedge funds selling such insurance? Answers to these questions may reveal agency issues within the organization of institutional investors, and agency issues between hedge funds and investors. We leave them for future research. We are grateful to the editor, Laura Starks, and two anonymous referees for many helpful suggestions. We thank Warren Bailey, Sanjeev Bhojraj, Craig Burnside, Martijn Cremers, Zhi Da, Christian Dorion, Itamar Drechsler, Ravi Jagannathan, Bob Jarrow, Alexandre Jeanneret, Andrew Karolyi, Soohun Kim, Veronika Pool, Tim Loughran, Bill McDonald, Roni Michaely, Pam Moulton, Narayan Naik, David Ng, Maureen O’Hara, Sugata Ray, Gideon Saar, Paul Schultz, David Schumacher, Berk Sensory, Mila Getmansky Sherman, Shu Yan, Jianfeng Yu, Lu Zheng, and Hao Zhou and seminar and conference participants at the City University of Hong Kong, Cornell, HEC Montreal, University of Notre Dame, Texas A&M University, University of Hawaii, the 2013 CICF, the 2013 EFA, the 2013 FMA, the 2014 MFA, the 2015 AFA, the 3rd Luxembourg Asset Management Summit, and the 6th Paris Hedge Fund Research Conference for helpful comments. Special thanks to Zheng Sun for help with the clustering analysis, to Kuntara Pukthuanthong for data on benchmark factors, and to Sang Seo and Jessica Wachter for data on model-implied option prices. Financial support from the Q-group is gratefully acknowledged. Some data used in this study are available from authors’ websites. The views expressed here are those of the authors and not necessarily those of any affiliated institution. Supplementary data can be found on The Review of Financial Studies Web site. Appendix. Technical Details Our rare disaster concern index quantifies ex ante market expectations about rare disaster events in the future. In particular, the value of $$\mathbb{RIX}$$ depends on the price difference between two option-based replication portfolios of variance swap contracts. The first portfolio accounts for mild market volatility shocks, and the second for the extreme volatility shocks induced by market jumps associated with rare event risks. By construction, the $$\mathbb{RIX}$$ is essentially the price for an insurance contract against extreme downside movements of the market in the future. Consider an underlying asset whose time-$$t$$ price is $$S_{t}$$. We assume for simplicity that the asset does not pay dividends. An investor holding this security is concerned about its price fluctuations over a time period $$[t,T]$$ One way to protect him or herself against price changes is to buy a contract that delivers payments equal to the extent of price variations over $$[t,T]$$, minus a prearranged price. Such a contract is called a “variance” swap contract, as the price variations are essentially related to the stochastic variance of the price process. The standard variance swap contract in practice pays \begin{equation} \left( \ln \frac{S_{t+\Delta }}{S_{t}}\right) ^{2}+\left( \ln \frac{S_{t+2\Delta }}{S_{t+\Delta }}\right) ^{2}+\cdots +\left( \ln \frac{S_{T}}{S_{T-\Delta }}\right) ^{2}-\mathbb{VP} \label{VarianceSwapDef1} \end{equation} (A1) at time $$T$$, where $$\mathbb{VP}$$ is the prearranged price of the contract. That is, the variance swap contract uses the sum of squared log returns to measure price variations. For the convenience of pricing, a continuous-time setup is usually employed with $$\left. \Delta \rightarrow 0\right.$$. Then the fair price $$\mathbb{VP}$$ is \begin{equation*} \mathbb{VP}=\mathbb{E}_{t}^{\mathbb{Q}}\left\{ \lim_{\Delta \rightarrow 0} \left[ \left( \ln \frac{S_{t+\Delta }}{S_{t}}\right) ^{2}+\left( \ln \frac{ S_{t+2\Delta }}{S_{t+\Delta }}\right) ^{2}+\cdots +\left( \ln \frac{S_{T}}{ S_{T-\Delta }}\right) ^{2}\right] \right\} , \end{equation*} where $$\mathbb{Q}$$ is the risk-neutral measure. The limit inside the expectation is the quadratic variation of the log price process, denoted as $$\left. [\ln S,\ln S]_{t}^{T}\right.$$, which is the continuous-time sum of squared log returns. In principle, replication portfolios consisting of out-of-the-money (OTM) options written on $$\left. S_{t}\right.$$ can be used to replicate the time-varying payoff associated with the variance swap contract and hence to determine the price $$\left. \mathbb{VP}\right.$$. We now introduce two replication portfolios and their implied prices for the variance swap contract. The first replication portfolio, which underlies the construction of VIX by the Chicago Board Options Exchange (CBOE), focuses on the limit of the discrete sum of squared log returns, determining $$\left. \mathbb{VP}\right.$$ as \begin{equation} \mathbb{IV}\equiv \frac{2e^{r\tau }}{\tau }\left\{ \int_{K>S_{t}}\frac{1}{K^{2}}C(S_{t};K,T)dK+\int_{K<S_{t}}\frac{1}{K^{2}}P(S_{t};K,T)dK\right\} , \label{IV} \end{equation} (A2) where $$\left. r\right.$$ is the constant risk-free rate, $$\left. \tau \equiv T-t\right.$$ is the time-to-maturity, and $$\left. C(S_{t};K,T)\right.$$ and $$\left. P(S_{t};K,T)\right.$$ are the prices of call and put options with strike $$\left. K\right.$$ and maturity date $$\left. T\right.$$, respectively. As seen in Equation (A2), this replication portfolio holds positions in OTM calls and puts with a weight inversely proportional to their squared strikes. $$\mathbb{IV}$$ has been employed in the literature to construct measures of variance risk premiums (Bollerslev, Tauchen, and Zhou 2009; Carr and Wu 2009; Drechsler and Yaron 2011). The intuition behind the construction of the second replication portfolio is that $$\left. \mathbb{VP}\right.$$ is equal to the variance of the holding period log return, that is, $$\left. \mathbb{VP}=Var_{t}^{\mathbb{Q}}\left( \ln S_{T}/S_{t}\right) \right.$$, as shown in Du and Kapadia (2012).26 This replication portfolio relies on $$\left. Var_{t}^{\mathbb{Q}}\left( \ln S_{T}/S_{t}\right) \right.$$, which avoids the discrete sum approximation, and determines $$\left. \mathbb{VP}\right.$$ as \begin{align} \mathbb{V} &\equiv \frac{2e^{r\tau }}{\tau }\left\{ \int_{K>S_{t}}\frac{1-\ln\left( K/S_{t}\right) }{K^{2}}C(S_{t};K,T)dK \right. \notag \\ &\quad \left.+\int_{K<S_{t}}\frac{1-\ln\left( K/S_{t}\right) }{K^{2}}P(S_{t};K,T)dK\right\}. \label{V} \end{align} (A3) The second replication portfolio described in Equation (A3) differs from the first replication portfolio in Equation (A2) by assigning greater (lesser) weights to more deeply OTM put (call) options. As the strike price $$\left. K\right.$$ declines (increases), that is, put (call) options become more out of the money, $$\left. 1-\ln \left( K/S_{t}\right) \right.$$ becomes larger (smaller). As more deeply OTM options protect investors against greater price changes, it is intuitive that the difference between $$\mathbb{IV}$$ and $$\mathbb{V}$$ captures investors’ expectations about the distribution of large price variations. To quantify the difference more explicitly and obtain a measure of rare events, we assume the price process follows the Merton (1976) jump-diffusion model: \begin{equation} \frac{dS_{t}}{S_{t}}=\left( r-\lambda \mu _{J}\right) dt+\sigma dW_{t}+dJ_{t}, \label{JumpModel1} \end{equation} (A4) where $$\left. r\right.$$ is the constant risk-free rate, $$\left. \sigma \right.$$ is the volatility, $$\left. W_{t}\right.$$ is a standard Brownian motion, $$\left. J_{t}\right.$$ is a compound Poisson process with jump intensity $$\left. \lambda \right.$$, and the compensator for the Poisson random measure $$\left. \omega \left[ dx,dt\right] \right.$$ is equal to $$\left. \lambda \frac{1}{\sqrt{2\pi }\sigma _{J}}\exp \left( -\left( x-\mu_{J}\right) ^{2}/2\right) \right.$$. The jump process $$\left. J_{t}\right.$$ drives large price variations with an average size of $$\left. \mu_{J}\right.$$. Rare event risks, however, are not likely to be captured by price jumps of average sizes within a range of the standard deviation $$\left. \sigma _{J}\right.$$. Instead, we focus on the high-order moments of the Poisson random measure $$\left. \omega \left[ dx,dt\right] \right.$$, for example, skewness and kurtosis, which are associated with unlikely but extreme price jumps. We now quantify the difference between $$\left. \mathbb{IV}\right.$$ and $$\left. \mathbb{V}\right.$$ under the Merton (1976) framework. First, as shown by Carr and Madan (1998), Demeterfi et al. (1999), and Britten-Jones and Neuberger (2000), when the price process $$\left. S_{t}\right.$$ does not have jumps, that is, $$\left. dJ_{t}=0\right.$$, \begin{equation*} \mathbb{IV}=\mathbb{E}_{t}^{\mathbb{Q}}\left( \int_{t}^{T}\sigma ^{2}dt\right) =\mathbb{VP}. \end{equation*} That is, $$\left. \mathbb{IV}\right.$$ captures the price variation induced by the Brownian motion. However, for a price process with a jump term of $$\left. dJ_{t}\neq 0\right.$$, it is no longer the case that $$\left. \mathbb{IV=VP}\right.$$ because $$\left. \mathbb{VP}\right.$$ now contains price variations induced by jumps. Rather, as shown by Du and Kapadia (2012), $$\mathbb{V}=$$$$\mathbb{VP}$$ whether $$\left. dJ_{t}\right.$$ is zero or not. More importantly, the difference between $$\mathbb{IV}$$ and $$\mathbb{V}$$ under the Merton (1976)model is (see Du and Kapadia 2012 for a proof): \begin{equation} \mathbb{V}-\mathbb{IV}=2\mathbb{E}_{t}^{\mathbb{Q}}\int_{t}^{T}\int_{R_{0}}\left( 1+x+x^{2}/2-e^{x}\right) \omega \left[ dx,dt\right] . \label{VminusIV} \end{equation} (A5) That is, $$\left. \mathbb{V}-\mathbb{IV}\right.$$ captures all the high-order ($$\left. \geq 3\right.$$) moments of the Poisson random measure $$\left. \omega \left[ dx,dt\right] \right.$$, associated with unlikely but extreme price jumps. In fact, Equation (A5) holds for the entire class of Lévy processes, and approximately for stochastic volatility models with negligible errors, as shown by Du and Kapadia (2012). We further focus on downside rare event risks associated with unlikely but extreme negative price jumps. In particular, we consider the downside versions of both $$\mathbb{IV}$$ and $$\mathbb{V}$$: \begin{align} \mathbb{IV}^{-} &\equiv \frac{2e^{r\tau }}{\tau }\int_{K<S_{t}}\frac{1}{K^{2}}P(S_{t};K,T)dK, \notag \\ \mathbb{V}^{-} &\equiv \frac{2e^{r\tau }}{\tau }\int_{K<S_{t}}\frac{1-\ln\left( K/S_{t}\right) }{K^{2}}P(S_{t};K,T)dK, \label{DownIVandV} \end{align} (A6) where only OTM put options that protect investors against negative price jumps are used. We then define our rare disaster concern index as \begin{equation} \mathbb{RIX}\equiv \mathbb{V}^{-}-\mathbb{IV}^{-}=2\mathbb{E}_{t}^{\mathbb{Q}}\int_{t}^{T}\int_{R_{0}}\left( 1+x+x^{2}/2-e^{x}\right) \omega ^{-}\left[dx,dt\right] , \label{RIX} \end{equation} (A7) where the second equality can be shown to be similar to Equation (A5), with $$\left. \omega ^{-}\left[ dx,dt\right] \right.$$ the Poisson random measure associated with negative price jumps. Footnotes 1 “Supplying disaster insurance” here does not literally mean hedge funds write a disaster insurance contract to investors. As argued by Stulz (2007), hedge funds, as a group of sophisticated and skillful investors who frequently use short sales, leverage, and derivatives, are capable of supplying earthquake-type rare disaster insurance through dynamic trading strategies, market timing, and asset allocations. 2 In the same vein, Sialm, Sun, and Zheng (2012) use fund-of-funds return loadings on some local/nonlocal factors to measure a fund’s local bias, different from the conventional risk–$$\beta$$ interpretation. 3 We also run time-series regressions of the monthly excess returns of various Hedge Fund Research Inc. (HFRI) hedge fund indices on the market excess return and rare disaster concern index ($$\mathbb{RIX}$$). We find significantly negative $$\mathbb{RIX}$$ loadings, confirming that payoffs of many hedge fund strategies resemble those of writing put options (Lo 2001; Goetzmann et al. 2002; Agarwal and Naik 2004). 4 Other recent studies include Aragon (2007), Fung et al. (2008), Liang and Park (2008), Agarwal, Daniel, and Naik (2009), Aggarwal and Jorion (2010), and Li, Zhang, and Zhao (2011). 5 Theoretically, such overpricing or concerns can arise from the crash aversion described by Bates (2008), the aversion to uncertainty on disaster risk described by Liu, Pan, and Wang (2005), and the probability weighting of tail events described by Barberis and Huang (2008) and Barberis (2013), among other channels. The prices of disaster insurance contracts in such models contain a premium in equilibrium higher than that in standard rational disaster risk models with tail risk probability fitted to the historical observations. Skilled managers are not constrained by these mechanisms in their investment decisions, probably because they have advantages arising from superior research, information, and experiences. In consequence, they can extract such premiums and earn profits by providing disaster insurance. 6 The variance here refers to stochastic changes of the asset price, and hence is different from (and more general than) the second-order central moment of the asset return distribution. 7 Using the mid-quote price makes it possible that two put options with the same maturity but different strikes end up having the same option price. In this case, we discard the one that is further away from at-the-money (ATM). 8 Table IA-1 of the Internet Appendix reports the average daily open interest of sector-level index put options with maturities between 14 and 60 days. We categorize the puts into groups according to their moneyness. Although the number of option contracts varies across different sector indices, we observe a substantial amount of daily open interest for OTM put options (e.g., moneyness $$K/S\leq 0.90$$). 9 The database covers both “live” funds that continue reporting monthly returns to the database and “graveyard” funds that are delisted from the database (because of, e.g., liquidation, no longer reporting, mergers, or being closed to new investment), based on the snapshot as of July 2010, that is, the end of our sample period. 10 During the sample period from January 1994 to June 2010, the monthly mean returns of PTFSBD, PTFSSTK, and PTFSCOM (all trend-following factors) are $$-$$1.7%, $$-$$5.1%, and $$-$$0.4%, respectively, and the median returns are $$-$$5.2%, $$-$$6.6%, and $$-$$3.0%, respectively. 11 We discuss extreme market timing in Section 4.4. 12 We also observe that the monthly alpha difference ($$\left. 47\right.$$ basis points) between the 8-factor model and the 10-factor model mainly comes from low-SED funds: $$\left. -0.63\%\right.$$ (t-statistic = $$\left. -2.8\right.$$) under the 8-factor model versus $$\left. -0.09\%\right.$$ (t-statistic = $$\left. -0.3\right.$$). In other words, the 10-factor model has the most significant impact on adjusting the returns of low-SED funds, but not high-SED funds. 13 In an unreported analysis, we also estimate alphas using the set of global asset pricing factors recently developed in the literature, including value, momentum, betting-against-beta, and futures-based trend-following (Asness, Moskowitz, and Pedersen 2013; Frazzini and Pedersen 2014; Moskowitz, Ooi, and Pedersen 2012; Baltas and Kosowski 2012). Our results are unchanged. The alphas of high-minus-low SED portfolios remain highly significant, and they range from 0.83% to 1.20% per month, depending on the model specification. 14 Alternatively, we follow Jagannathan, Malakhov, and Novikov (2010) to mitigate the backfilling bias by excluding the first 25 months from the history of each fund. The return spread of the high-minus-low SED portfolio is 0.89% per month with a t-statistic of 2.6, whereas the Fung-Hsieh 8-factor alpha and the NPPR 10-factor alpha are 1.15% and 0.81%, respectively; both are at least three standard errors from zero. 15 Relatedly, back-of-the-envelope calculations based on the capital asset pricing model (CAPM) beta of high-SED funds imply that we need a persistent market loss of 23%–52% per year to wipe out the funds (defined as when the fund return decreases to zero) of the three highest SED fund portfolios. The patterns are consistent with the evidence on fund liquidation rates presented in Table 3: high-SED funds usually have a lower liquidation rate (approximately 2.13% in the decile 10 portfolio of funds), while low-SED funds have a higher liquidation rate (about 3.56% in the decile 1 portfolio of funds). 16 It is also important to recognize that hedge funds are actively managed assets, and the relationship between rare disaster concerns and returns is different for them than it is for passively managed assets. For example, in the context of passively managed assets, including MSCI international equity indices, foreign currencies, global government bonds, and commodity futures, Gao, Lu, and Song (2017) find high RIX-beta assets are favorable securities because they deliver contemporaneously higher returns when the market is fearful about rare disasters. High RIX-beta assets receive higher demand today and their prices are being pushed up, and they subsequently earn lower returns in the future. In other words, high-RIX beta assets provide protection against market disaster concerns and the high demand from investors for such assets leads to lower expected returns. 17 The $$\mathbb{RIX}^{C}$$ can be regarded as the “unexpected” or “shock” version of $$\mathbb{RIX}$$, where $$\mathbb{RIX}^{M}$$ proxies for the rationally expected disaster shock that investors learn from the historical data. Besides taking the difference between $$\mathbb{RIX}$$ and $$\mathbb{RIX}^{M}$$, we also regress the $$\mathbb{RIX}$$ on $$\mathbb{RIX}^{M}$$ and use the residual as the unexpected $$\mathbb{RIX}$$. Conclusions are similar. 18 The positive returns of certain high-SED funds in Column 3 are due to the fact that NBER recessions include the period of March–May 2009, when monthly market returns were up by about 5%–10% in response to the Federal Reserve’s confirmation of its large-scale asset purchases. Removing these three months from the stressful times category makes the returns of high-SED fund deciles insignificantly different from zero. We thank Narayan Naik for suggesting an alternative definition of stressful times. 19 According to Markit’s (2009) credit derivatives glossary, the definition of short credit is, “This [short credit] is the credit risk position of the Protection Buyer, who sold the credit risk of a bond to the Protection Seller” (p. 35). 20 We also use a CDS factor, measured by the average of five corporate and sovereign CDS indices across different regions from Markit, to identify short credit funds. Results, reported in Table IA-5 of the Internet Appendix, are similar. For example, the high-minus-low SED portfolio earns above 1% per month (t-statistic = 3.1) after we exclude the short credit funds. 21 Results are similar when we use the covariance between the fund’s monthly excess return at $$t-1$$ and the next-period $$\mathbb{RIX}$$ at $$t$$ and the average fund return over $$t-1$$ to $$t-3$$, $$t-1$$ to $$t-6$$, $$t-1$$ to $$t-9$$, and $$t-1$$ to $$t-12$$. 22 In our baseline analysis, factor loadings on Fung-Hsieh’s option-based lookback straddle factors are also revealing. First, as shown in the Internet Appendix (Table IA-3), high-SED funds have small and statistically insignificant exposure to these three option straddle factors. Second, the return difference between high-SED and low-SED funds have small and statistically insignificant exposure to these three option straddle factors. 23 It is well documented that the EIV problem in the context of univariate regression usually introduces a downward bias in coefficient estimates, and hence works against us on finding any significant effect for SED. When we regress funds’ monthly excess returns only on their SED measures, we find the coefficient is 0.0022, with a Newey-West t-statistic of 2.2, suggesting that the SED effect is unlikely to be driven by the EIV problem. 24 Results are similar if we measure fund size by assets under management. 25 Throughout the paper we have constructed $$\mathbb{RIX}$$ using out-of-the-money puts on sector indices. 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