Online Appendix ™When There is No Place to Hide ... · The BKT model is an 8-factor model that consists of the FH-seven factor model augmented by the correlation risk factor.1 Table

Online Appendix’When There is No Place to Hide: Correlation Risk and

the Cross-Section of Hedge Fund Returns’

A. Benchmark factor summary statistics

The BKT model is an 8-factor model that consists of the FH-seven factor model augmented

by the correlation risk factor.1 Table A1 shows diagnostic statistics for the different factors

that we use.

[Insert Table A1 here]

B. Date base and fund return summary statistics

There are two main reasons why we use the BarclayHedge data base for our analysis. First,

the Barclayhedge data base contains information about funds’aggregate net long and short

exposures based on market value, which is necessary to test the relationship between correla-

tion risk and net exposure. The TASS/Lipper database, another high quality and frequently

used hedge fund database, does not contain this information.

Second, the BarclayHedge data base is the highest quality commercial hedge fund data

base. A recent comprehensive study of the main commercial hedge fund data bases by Joen-

vaara, Kosowski and Tolonen (2012, abbreviated JKT (2012)) finds that the BarclayHedge

data base is the most high quality data base in many respects. The authors compare 5 data

bases (the BarclayHedge, TASS, HFR, Eurekahedge and Morningstar data bases) and find

that Barclayhedge has the largest number of funds (10520), compared to 8788 funds in the

TASS data base. Moreover, BarclayHedge has one of the highest percentages of dead/defunct

funds (66 percent), thus making it least likely to suffer from survivorship bias. Out of these

data bases, only Barclayhedge has information on net exposure. The BarclayHedge data base

accounts for the largest contribution to the aggregate database that JKT(2012) create. The

1The Fung and Hsieh (2001) model has been extended to consider other potential attributes. Fung andHsieh (1997, 2000, 2001), Mitchell and Pulvino (2001) and Agarwal and Naik (2004) discuss the non-linearityof hedge fund strategies and show that a passive rolling strategy based on options helps to explain hedgefund returns. Other papers that investigate hedge fund performance relative to the Fung and Hsieh (2001)model include Bondarenko (2004), Kosowski, Naik, and Teo (2007) and Fung, Hsieh, Ramadorai, and Naik(2008). Results available from the authors upon request show that our findings are robust to the eightfactor specification of the Fung-Hsieh model, which includes the return of a stock index lookback straddle(PTFSSTK).

authors also note that BarclayHedge is superior in the terms of Assets under Management

(AuM) coverage, since it has the longest AuM time-series (58 percent), suggesting different

behavior when aggregate returns are calculated on a value-weighted basis. The amount of

missing AuM observations varies significantly across data vendors, being lowest for Barclay-

Hedge (12 percent) and HFR (20%) and significantly higher for EurekaHedge (36%), TASS

(35%), and Morningstar (34%). JKT (2012) do find, however, that economic inferences based

on the Barclayhedge and TASS data bases are similar in a number of dimensions. For instance,

BarclayHedge, HFR and TASS show economically significant performance persistence for the

equal-weighted portfolios at semi-annual horizons.

We use US Dollar denominated hedge fund share classes and require funds to have at least

24 monthly observations.

B.1. Correlation Swap Time-Series Data

A correlation swap is a contract that pays the difference between a standard estimate of the

realized correlation and the fixed correlation swap rate. Since these contracts cost zero to

enter, the correlation swap rate is the arbitrage free price, i.e., the risk-adjusted expected

value, of the realized correlation. Our data consists of daily implied and realized correlation

quotes of one month (three month) maturity correlation swaps for the S&P500 from April

2000 until December 2008 (from January 2009 until June 2012). A positive (long) position in

a correlation swap is a claim to a payoff proportional to the difference between the realized

correlation during the tenor of the contract and the correlation swap rate fixed at the beginning

of the month.2

Since correlation swap quotes are only available after March 2000, we create a synthetic

correlation swap time series for the time period from January 1996 to March 2000, using

the model-free approaches discussed in Carr and Madan (1998), Britten-Jones and Neuberger

(2000) and DMV (2006). For the period from April 2000 to December 2008, we find that

the correlation between the synthetic correlation proxy and the correlation quotes time series

is 92 percent, which supports the use of the synthetic time series in the 1996-2000 period.

In order to synthesize correlation swap prices before April 2000, we use options data from

2The reason for the use of three month correlation swaps from January 2009 onwards is due to dataavailability. Our data sources provided us with 3 month correlation swaps data for the second part of thesample (2009-2012). The correlation between the three month and one month correlation swaps is close to 80percent during the 2000-2008 period. Given this high correlation between the time series and the fact thatour results remain qualitatively unchanged when we compare the sample ending in 2008 and 2012, this choicedoes not qualitatively affect our conclusions.

1

Optionmetrics, for S&P500 index options and all individual stock options in the S&P500 list,

as well as index and individual stock data. Since this database covers option prices backwards

only until January 1996, we focus in our study on hedge fund returns in the sample period

from January 1996 to June 2012.

From the OptionMetrics database, we select all put and call options on the index and

on the index components. We work with best bid and ask closing quotes, rather than the

interpolated volatility surfaces provided by OptionMetrics, and use the midquotes for these

option data (average of bid and ask). We retain options that have time-to-maturities up

to one year and have at least three strike prices at each of the two nearest maturities. We

discard options with zero open interest, with zero bid prices, with negative bid-ask spread,

and with missing implied volatility or delta. Finally, we use the T-bill rate with 1-month

constant maturity to approximate the 30-days risk-free rate. The T-bill rate is obtained from

the Federal Reserve database.

To provide further background on the empirical features of the correlation risk premium,

Figure A1 shows that the six-month moving average of our correlation risk proxy is highly

time varying. During the early part of the period, the returns for selling correlation were quite

large. Similar to other markets, such as credit markets, risk capital has flowed into strategies

attempting to exploit the negative correlation risk premium, thus reducing the spread between

implied and realized correlation over time. Moreover, while during the periods 2002-2005 and

2009-2012 selling correlation was highly profitable, the opposite was true in the period 2007-

2008.

[Insert Figure A1 here]

Figure A2 plots a moving average of the implied and realized correlation over our sample.

[Insert Figure A2 here].

C. Synthesizing Correlation Risk and Variance Risk Proxies

Implied Correlation and Correlation Risk Proxy. Correlation swap rates can be approximated

using a cross-section of market index and individual stock variance swaps, which in turn can

be synthesized from the cross-section of market index and individual stock options using well-

known techniques. As an approximation to the correlation swap rate, we make use of the

2

concept of implied correlation (see, for instance, DMV, 2006), defined by:

ICt,T :=EQt [RV I

t,T ]−∑n

i=1w2iE

Qt [RV i

t,T ]∑i 6=j wiwj

√EQt [RV i

t,T ]EQt [RV it,T ]

=SV I

t,T −∑n

i=1w2i SV

it,T∑

i 6=j wiwj

√SV i

t,TSVjt,T

, (1)

where RV It,T (SV

It,T ) andRV

it,T (SV

it,T ) are the S&P500 index and single stock realized variances

(variance swap rates) over time span [t, T ], and wi is the market capitalization weight of stock

i. Our synthetic correlation risk proxy for the time period from January 1996 to March 2000

is given by:

CRt,T = L · (RCt,T − ICt,T ) , (2)

where L is the given notional value. Note that ICt,T can be computed using only information

about index and single stock variance swap rates. The intuition is as follows. The numerator

is the risk-neutral expectation of a payoff given by:

RV It,T −

n∑i=1

w2iRVit,T =

∑i 6=j

wiwj

∫ T

t

visvjsρijs ds (3)

where vis is the individual instantaneous volatility of stock i and ρijs is the instantaneous pair-

wise correlation between stock i and j, assuming a pure-diffusion return process. Therefore,

the implied correlation can be interpreted as the risk-neutral expected average correlation,

i.e., ICt,T = EQt [∫ Ttρsds] for some appropriate average correlation process ρt, say, such that:∑

i 6=j

wiwjICt,T

√SV i

t,TSVjt,T =

∑i 6=j

wiwjICt,T

√EQt [RV i

t,T ]EQt [RV it,T ] (4)

= EQt

[∑i 6=j

wiwj

∫ T

t

visvjsρijs ds

].

A concrete verification of the quality of proxy (2) as a correlation risk proxy can be gauged

by comparing the statistical behaviour of definitions (1) and (2) for the sample period after

April 2000, where quoted correlation swaps are available. For that period, we find a remarkable

coincidence of these two time series, with a correlation between proxies of 0.92, which supports

the use of (2) as a market proxy for correlation risk before April 2000. For comparison, the

correlation between the correlation risk proxy and a proxy for index variance risk is only about

0.25 in the same time period.

Variance Swap Rates and Proxies of Variance Risk. In order to compute the implied

correlation (1), it is necessary to compute the index and single stock variance swap rates

3

SV It,T and SV i

t,T , i = 1, . . . , N . Variance swap rates are also necessary to compute direct

proxies of variance risk. Similar to correlation swaps, a variance swap is a contract that pays

at the contract’s maturity a payoff given by the difference between realized variance RVt,Tand variance swap rate SVt,T , multiplied by the notional amount invested:

(RVt,T − SVt,T )L . (5)

By construction, since the initial price of a variance swap is zero, the variance swap rate is

the arbitrage-free price of the future realized variance:

SVt,T = EQt [RVt,T ] . (6)

In particular, the variance risk premium of an asset with realized variance RVt,T is given by:

V RPt,T = EPt [RVt,T ]− EQt [RVt,T ] = EPt [RVt,T ]− SVt,T . (7)

Empirically, the average variance swap payofffor the index variance is negative, which indicates

the existence of a negative risk premium for market variance risk. However, the market

variance risk premium is not a pure indicator of ex-ante excess returns deriving from exposure

to pure variance risk, because the index variance is a weighted sum of single stock variances

and covariances. Therefore, in order to proxy for aggregate variance risk, we use the market

weighted sum of the payoffs of individual stock variance swaps, defined by:

V Rt =n∑i=1

wi(RVit,T − SV i

t,T )Li . (8)

Synthetic Variance Swap Rates. In order to compute index and single stock variance swap

rates, we use the standard industry approach and synthesize them from plain (listed) vanilla

option prices. This approach also avoids to a good extent the liquidity problems related to

the variance swap quotes of individual stocks. In an arbitrage-free market and under the

assumption of a continuous swap rate process, the following relation holds (see, e.g., Carr and

Madan, 1998, Britten-Jones and Neuberger, 2000 and Carr and Wu, 2009):

SVt,T = EQt [RVt,T ] =2

(T − t)B(t, T )

∫ ∞

0

Θt(K,T )

K2dK, (9)

where B(t, T ) is the price of a zero coupon bond with maturity T and Θt(K,T ) denotes the

price of call and put option with strike K and maturity T on an underlying asset with realized

4

variance RVt,T .3 We use this relation to compute index and single stock variance swap rates.

The return of the correlation risk factor can be interpreted as the return on a correlation swap

with a $1 notional amount, abstracting from margin payments.

D. Benchmark factor summary statistics

As mentioned, see Section II.A of the paper, the BKT model is an 8-factor model that consists

of the FH-seven factor model augmented by the correlation risk factor.

Similarities and Differences Between Volatility and Correlation Risk. What are empirical

differences of correlation and index variance risk premia? Table A1 reports summary statistics

of our monthly risk factors for index variance risk and for correlation risk, which correspond

to the returns of long positions in index variance and correlation swaps, respectively. The

average excess return on the S&P500 index in our sample is 0.42 percent per month. The

average index variance risk and correlation risk proxies are -17.77 (in percent squared permonth) and -10.70 percent per month, respectively.

As a preliminary step, we report the unconditional correlation between the correlation risk

factor and value-weighted hedge fund index returns.


E. Ranking Funds by Full-sample versus rolling betas

In Table 3 and 4 of the paper we are careful to rank funds by rolling betas following the

methodology described in Pastor and Stambaugh (2003). As a robustness check in Table

A3 below we also report results for the case when funds are ranked based on full-sample

betas. Panel A of Table A3 reports the betas and t-statistics of betas. Panel B of Table A3

reports the alphas and the return contribution of the different beta exposures. The overall

conclusion from the two approaches is qualitatively the same. Funds in the bottom decile have

a significantly higher lower alpha than funds in the top decile once correlation risk is taken

into account.


3For a variance swap such that T − t = 30 days, we compute the realized (annualized) variance as:

RVt,t+30 =365

30

30∑i=1

R2t+i,

where Rt+i is the daily return of the underlying asset at the end of day i = 1, . . . , 30.

5

F. The Cross-Sectoin of Hedge Fund Correlation Risk Exposures:

Two Hedge Fund Strategies Under the Magnifying Glass

Option Trader. In recent years, equity and credit derivative hedge funds have sprung up, which

explicitly trade alternative asset classes, such as variance and correlation. Some of these funds

directly use options, variance swaps or correlation swaps.4 Other funds use structured credit

products and take long-short positions in different tranches of asset-backed securities, such

as CDOs and CLOs, thus taking explicit bets on changes in the default correlations of the

underlying reference entities.5 Panel A and B of Table A4 presents our findings for Option

Trader strategies. It is interesting to note that in this category all deciles have a negative

correlation risk beta. The results in this table are based on rolling regressions and therefore

it is not guaranteed that the correlation risk betas of the funds in the bottom decile would be

lower than those in the top decile. Nevertheless, we find that this is the case, which suggests

that the risk properties of funds are relatively stable over time. We find that this group

of funds differs from Long/Short Equity and Low Net Exposure funds, to the extent that

the average return of funds with the largest positive correlation risk exposure in the Option

Trader group is smaller than the average return of funds with the most negative correlation

risk exposure in the LNE and LSE classes. The portfolio of Option Trader funds in the

bottom decile has a return of 6.63 percent per year, which is lower than the average return

of 11.47 percent per year of the portfolio in the highest correlation risk beta decile. However,

correlation risk exposure explains about 7 percent of the difference of average returns between

the highest and lowest decile groups. BKT model alphas are −4.68 and 5.89 percent per

year for the highest and lowest correlation risk beta deciles, respectively, which shows that

Options Trader funds performance is dependent on the latent correlation risk exposure, which

generates economically significant differences in excess returns as a result. Correcting for

exposure to correlation risk, the risk-adjusted performance of Option Trader strategies can

change dramatically: The alpha of the lowest (highest) correlation risk beta quintile according

to FH model is about 0.89 (7.96) percent per year, but the alpha according to BKT model

is about minus 4.68 (plus 5.89) percent per year! These features might derive from the fact

that Option Trader Funds explicitly try to model their risk exposures to correlation risk:

While Long/Short Equity funds might inadvertently expose themselves to correlation risk

shocks, Options Trader funds are likely to be more aware of the importance of measuring and

4See, e.g., Granger and Allen (2005) JPMorgan report ’Correlation Vehicles’.5’We have hedge fund clients who are very active traders of volatility, correlation and dispersion. Trading

correlation and dispersion as an asset class can have a diversification effect,...’ (Denis Frances, Global Headof Equity Derivatives Flow Sales at BNP Paribas, FTfm, 28/1/2008).

6

managing this particular source of risk; see, e.g., Granger and Allen (2005). They might even

want to bet on it.


Funds of Funds. Funds of Funds are an interesting subcategory that consists of portfolios of

individual hedge funds. They differ from individual hedge funds in several respects including

an additional fee layer on top of the fees related to the underlying individual funds. As Table

2 in the paper shows they generate the lowest alpha among all investment styles. Funds of

funds are typically treated separately in hedge fund studies since they affect performance

persistence results as they consistently generate among the lowest average returns compared

to individual hedge fund styles. Since they consist of a portfolio of individual hedge fund

styles, their negative correlation risk exposure documented in Table 2 can be interpreted as

contain the risk that in crisis times these strategies become correlated. This is indeed what

was observed in 2008 when many funds of funds suffered large losses. Panels C and D of Table

A4 shows that sorting funds of funds on rolling betas leads to portfolios that have relatively

low Fung and Hsieh alphas and even lower BKT alphas with several deciles of the post-ranking

returns showing statistically significant exposure to correlation risk.

Managed Futures Funds. The Managed Futures fund category consists of quite a diverse

set of funds that predominantly use liquid futures and derivatives markets to implement

their strategies. This category includes discretionary and systematic Managed Futures funds,

including trend-following funds. We make use of our performance attribution approach based

on the 8-factor BKT model (see Equation (1) in the main paper) to split the impact of index

variance risk on hedge fund returns into its two main components: Correlation risk and average

variance risk of the index constituents. Panel C of Table 2 in paper shows that correlation

risk exposure, rather than variance risk exposure, is the main driver of the risk-return profile

of Managed futures funds. In Panel E and F of Table A4 we examine these funds further and

find that Managed futures funds in the decile with the most negative correlation risk exposure

have the highest return (11.17 percent per year) and the highest FH model alpha (8 percent

per year). In contrast, the portfolio of funds in decile 10 produces an average return of 8.88

percent per year. However, 5.4 percent per year of the apparently superior performance of

the portfolio in decile 1 is explained by a significant negative correlation risk exposure. While

managed futures funds may invest in hundreds of derivatives, based on historical covariance

matrices, the managed futures category is exposed to unexpected changes in correlation of

risky assets.

7

G. Robustness Checks

In this section, we document the extent to which our results are robust to: (i) inclusion of

leverage; (ii) inclusion of liquidity risk factors; (iii) the use of TASS data; (iv) controlling

for variance risk premia in Fama-Macbeth regressions; (v) using equal-weighted, instead of

value-weighted, indices.

G.1. Leverage

In this section we document that our results are robust to the inclusion of a leverage variable.

In standard hedge fund data, “leverage” is not explicitly defined in a standardized way, for

instance, whether it should be computed in dollar notionals or delta equivalents. Hedge funds

simply receive from the data provider a field label "leverage" to fill in. Thus, those numbers

are likely affected by self-reporting problems. We compute two measures of leverage using

the data download in June 2012: (a) self-reported leverage; (b) gross exposure, i.e. longs +

shorts. We find that the correlation between net exposure and gross exposure is 0.27; the

correlation between net exposure and (self-reported) leverage is essentially zero; and the one

between leverage and gross exposure is about 0.42.

Moreover, while in the data some no-arb funds carry large leverage and low net exposure,

we also see funds that use leverage in portfolios with positive net exposure. Long-short equity

funds for example have on average a leverage of 1.53, but a relatively low net exposure of

28.9. In contrast, Fixed-Income relative value funds have an average leverage of 2.1, but a net

exposure of 72.0.

The analysis suggests that leverage and net exposure are distinct concepts in the data.

This is true both when we use self-reported measures of leverage and when we manually

compute the gross exposure.

We also sort hedge funds into leverage and net exposure deciles. We find that while

correlation risk betas are increasing in net exposure (see Figure 1 in the main paper and

Table A5), they tend not to any clearly increasing or decreasing relationship with leverage

(see Table A6).


Moreover, we find that different leverage deciles have similar correlation risk beta (−0.011

for the 9th decile vs, −0.012 for the 1st decile). Thus, differences in leverage are largely

unrelated to economically relevant differences in correlation risk beta, once all other factors

8

are controlled for. Overall, this evidence implies that in the data leverage is a different concept

than correlation risk exposure.


We also apply a double sort. We sort funds into four quartiles according to their leverage

and into four quartiles according to their correlation risk beta. In Table A7 we find that

even for the low leverage quartile, the dispersion in correlation betas is very substantial and

explains an important fraction of the cross-section in expected returns. For the high leverage

quartile, the spread is still very significant, but only marginally higher than for the low quartile

leverage bin. This is final support that, in the data, leverage and correlation risk exposure

are different concepts.


G.2. Robustness to Liquidity Risk Factor

Recent work by Aragon (2007) documents that hedge funds alphas are linked to hedge fund

lock-up periods, which suggests a potential relation between hedge funds alpha and asset liq-

uidity. Sadka (2010) shows that a (non-tradable) equity market liquidity factor explains cross-

sectional differences in hedge fund returns. Although liquidity and correlation are sometimes

interpreted as related economic phenomena, we find that they capture different characteristics

of hedge fund returns. We consider liquidity proxies that have tradable factor interpretations,

as the other factors in the BKT model. Then, we augment the BKT model with two liquidity

proxies: (a) the Fontaine and Garcia (2012) liquidity factor, for the fixed income market, and

(b) the Pastor and Stambaugh (2003) liquidity factor, for the equity market.6 The advantage

of this approach, with respect to a projection on non-tradable factors, is that the intercept

of a performance attribution regression can be interpreted as risk-adjusted performance or

"alpha". Table A8 shows that a significant component of correlation risk is not related to

liquidity risk. Even after controlling for these two factors, correlation risk is not subsumed by

liquidity risk and it remains a significant explanatory factor in hedge fund returns.


We find that value-weighted indices of all funds and Low Net Exposure funds, for example,

continue to have a statistically and economically significant negative beta with respect to

correlation risk, even after augmenting the BKT model by the two liquidity proxies.

6We thank Jean-Sebastien Fontaine and Rene Garcia for kindly providing us with their data.

9

G.3. Robustness to use of TASS Data base

The hypothesis that funds with low net exposure have high correlation risk beta cannot be

directly tested within the TASS database since it does not contain information about funds’

net exposure. We can test indirectly whether our results are robust when using TASS data

by focusing on certain investment objectives. We focus on Long/Short Equity funds, which

we expect to have statistically and economically significant exposure to the correlation risk

factor. We estimate the model, and run regressions using our risk factors to compare the

slope coeffi cients. Table A8 shows that Long/Short Equity funds have a correlation risk beta

t-statistics of -2.55 which is significant at the 1 percent level. In the baseline BarclayHedge

data results, the Long/Short Equity funds have a correlation risk beta t-statistic of -2.06 which

is very close to the finding in the TASS data. The TASS data also confirms the findings based

on the BarclayHedge data that the average fund has a negative and statistically significant

correlation risk beta (the t-statistic of the correlation risk beta of All funds in the TASS

data is −1.67). Although we cannot test for it directly, it is reasonable to assume that

within these Long/Short Equity funds those TASS funds with low net exposure are likely

to have even higher correlation risk beta than the average Long-Short Equity fund. Funds

of Funds are another hedge fund style that we found to have high correlation risk, since

these funds pursue different strategies at the same time, which may generate diversification

in normal times, but in bad times when correlations increase may lead to losses. We find

that Funds of Funds have statistically significant negative loadings on the correlation risk

factor in the BarclayHedge data base (Table II, Panel B, t-statistic of −1.81). These results

are confirmed by the results using the TASS data base which also contains a group of funds

that are Multi-Strategy funds (Table A9). The t-statistic (−2.18) in the TASS data is also

statistically significant and negative.


When using the TASS data base to examine the cross-sectional pricing tests in Table 5

of the paper we also find that our results are robust. Similar to the specification using the

BarclayHedge data we find that correlation risk is also priced in the cross-section of hedge

fund when using the TASS data.

G.4. Variance and Correlation Risk Premia

Table 2 Panel C of the paper shows that correlation risk remains statistically significant when

a variance risk residual is added to the BKT model in a time series specification. Table

10

A10 tests whether the same holds true also in Fama-Macbeth regressions. We find that the

correlation risk premium is indeed statistically significant, while the variance risk proxy is not,

thus lending further support to the BKT model.


G.5. Equal-Weighted Versus Value-Weighted Indices

Our findings that value-weighted indices of Low Net Exposure and Long Short Equity funds

have statistically significant correlation risk exposures are corroborated by the evidence for

equal-weighted indices presented in Table A11, which is based on the BarclayHedge data.


An equal-weighted average of all individual hedge funds has a correlation risk beta of -

0.01, with a t-statistic of -1.84 (p−value=0.07). Using equal-weighted indices of All Low NetExposure funds, leads to a statistically significant negative correlation risk beta (tβCR = −1.61,

p-value=0.09). An equally-weighted index of Long-Short Equity funds also has a statistically

significant exposure to correlation risk (tβCR = −3.1, p-value=0.01). Similar results hold for

equally-weighted indices of Merger Arbitrage and Option Trader funds. The same is not true

for Managed Futures funds, suggesting that some of the previous results might partly be

driven by Managed Futures funds that are larger, in terms of assets under management, than

the average fund.

G.6. Robustness to Use of Dispersion Trade Returns

Index-Level Results As described above we use data on correlation swaps as a cor-

relation risk proxy. The source of the correlation swap data also provided us with data on

implied correlations from dispersion trades which are an alternative approach to trading cor-

relation in equity markets. Instead of using the implied correlation from correlation swaps,

we use the implied correlation from dispersion trades to construct the time series of returns

for a correlation swap. In this subsection we show the robustness of our results to the use of

dispersion trade data. Table A12 reports results from regressing index level fund returns on

the dispersion trade return. The results are consistent with our earlier findings from Table 2 in

the paper. As Panel B of Table A12 shows, All funds have a statistically significant exposure

to the correlation risk factor (t-statitstic of −1.89). All Low Net Exposure funds and Long

11

Short Equity funds have an even higher exposure to to correlation risk exposure (t-statitstic

of −2.89 and −2.81, respectively). The table also confirms earlier results that Option Trader

funds, Funds of Funds and Managed Futures funds have statistically significant correlation

risk exposure in the BarclayHedge data base.


Our results are also robust to the use of the dispersion trade data for benchmarking index

level returns based on the TASS data. Table A13 reproduces the analysis from Table A9

using TASS data and a correlation risk factor based on dispersion trade data. It shows that

All Funds and Long Short Equity funds are statistically significantly exposed to correlation

risk. The t-statistics of −1.99 and −3.20 are even higher than in Table A9. In this sense our

baseline results in the paper that use the correlation swap implied correlations are conservative

as we obtain even stronger results using the dispersion trade implied correlation in tables A12

and A13.


Cross-sectional results In tables A14 and A15 we find that our conclusions also remain

qualitatively unchanged when using the dispersion trade implied correlation for the cross-

sectional pricing tests. Table A14 reproduces the analysis in Table 4 using dispersion trade

data and we find that the correlation risk premium is statistically significant and negative

using the Barclayhedge data.


Table A15 confirms the robustness of our results for the TASS data. It shows that the

correlation risk premium is also negative and statistically significant when using the TASS

data and data on implied correlations from the dispersion trades.


H. References

Agarwal, V. and N.Y. Naik, 2004, Risk and portfolio decisions involving hedge funds, Review

of Financial Studies, 17, 63—98.

12

Aragon, G. O., 2007, Share restrictions and asset pricing: evidence from the hedge fund

industry, Journal of Financial Economics 83, 33-58.

Bondarenko,O., 2004, Market price of variance risk and performance of hedge funds, University

of Illinois Working paper.

Britten-Jones, M., and A. Neuberger., 2000, Option prices, implied price processes, and sto-

chastic volatility, Journal of Finance 55, 839-866.

Carr, P. and D. Madan, 1998, Towards a theory of volatility trading, in Jarrow, R. (ed.),

Volatility: New Estimation Techniques for Pricing Derivatives, RISK Publications, London.

Carr, P. and L. Wu, 2009, Variance risk premiums, Review of Financial Studies 22 (3), 1311-

1341.

Driessen, J., Maenhout, P. and Vilkov, G. 2006, Option-implied correlations and the price of

correlation risk, Working Paper.

Fontaine, J.-S., and R. Garcia, 2012, Bond liquidity premia, Review of Financial Studies 25(4),

1207-1254.

Fung, W., and D.A. Hsieh, 1997, Empirical characteristics of dynamic trading sStrategies:

The case of hedge funds, Review of Financial Studies 10, 275-302.

Fung, W., and D.A. Hsieh, 2000, Performance characteristics of hedge funds and CTA Funds:

Natural versus spurious biases, Journal of Financial and Quantitative Analysis 35, 291-307.

Fung, W., and D.A. Hsieh, 2001, The risk in hedge fund strategies: Theory and evidence from

trend followers, Review of Financial Studies 14, 313-341.

Fung, W., D. A. Hsieh, N.N. Naik and T. Ramadorai, 2008, Hedge funds: performance, risk

and capital formation, Journal of Finance 63 (4), 1777-1803.

Granger, N and Allen, P., 2005, Correlation Trading, JPMorgan Report, European Equity

Derivatives Strategy.

Joenvaara J., Kosowski R., Tolonen P., 2012, New ’Stylized Facts’About Hedge Funds and

Database Selection Bias, SSRN Working Paper available at http://papers.ssrn.com/sol3/ pa-

pers.cfm?abstract_id=1989410.

Kosowski, R., Naik, N. and M. Teo, 2007, Do hedge funds deliver alpha? A bootstrap and

Bayesian approach, Journal of Financial Economics 84, 229-264.

Mitchell, M. and T. Pulvino, 2001, Characteristics of risk in risk arbitrage, Journal of Finance

56, 2135-75.

13

Pastor, Lubos, and R. F. Stambaugh, 2003, Liquidity risk and expected stock returns, Journal

of Political Economy 111, 642—685.

Sadka, R., 2010, Liquidity risk and the cross-section of hedge-fund returns, Journal of Finan-

cial Economics, Vol. 98, Issue1, 54-71.

14

Table A1: Summary Statistics for Benchmark Factors

Panel A: Summary Statistics

Mean Std Skew. Kurt. Min. Med. Max. Alpha Beta SR TM Msq

VRP500 -17.76 38.02 6.35 69.95 -109.98 -18.50 391.38 -16.06 -3.97 -0.47 4.04 -1.95

CR -10.70 15.63 -0.51 3.38 -63.39 -8.79 29.40 -10.12 -1.36 -0.68 7.46 -2.97

S&PmRf 0.43 4.68 -0.58 3.66 -16.88 0.92 10.93 0.00 1.00 0.09 0.00 0.66

SCMLC 0.10 3.55 0.26 7.43 -16.38 0.04 18.41 0.08 0.06 0.03 1.33 0.37

BD10RET 0.30 2.25 0.05 4.34 -7.57 0.23 9.42 0.36 -0.12 0.14 -3.01 0.87

BAAMTSY 0.19 2.14 -1.26 15.28 -14.37 0.18 8.11 0.11 0.20 0.09 0.52 0.66

PTFSBD -1.54 15.11 1.42 5.87 -25.95 -3.79 68.86 -1.20 -0.80 -0.10 1.50 -0.24

PTFSFX 0.00 18.65 1.09 4.26 -30.00 -4.00 69.22 0.39 -0.92 0.00 -0.43 0.24

PTFSCOM 0.13 13.95 1.12 5.05 -23.04 -2.54 64.75 0.35 -0.52 0.01 -0.68 0.28

Panel B: Autocorrelation Function

Lag 1 2 3 4 5 6 7 8 9 10 11 12

ACF CR 0.66 0.61 0.56 0.55 0.56 0.48 0.43 0.45 0.44 0.45 0.43 0.41

ACF VR 0.26 -0.07 0.04 0.00 0.00 -0.08 -0.06 0.00 0.09 0.06 0.06 0.03

This table reports the summary statistics for different benchmark factors. The sample period is from January 1996

to June 2012. Panel A reports the statistical properties for non-overlapping monthly returns of the variance risk

and correlation risk factors as well as the Fung and Hsieh model risk factors. Columns 2 to 8 report the mean,

standard deviation, skewness, kurtosis, minimum, median and maximum of monthly returns. Columns 9 to 13

report alpha and beta coefficients (with respect to the S&P500), the annualized Sharpe Ratio (SR), Treynor’s

measure (TM), and the M-squared measure. Alpha and Sharpe Ratio in this table are expressed in percent per

month. The variance risk factor is constructed from realized and implied volatility estimates. VR and CR

correspond to long variance and long correlation swap strategies. VR is reported in percentages squared per

month. From January 1996 until March 2000 CR is based on synthetic correlation swaps, followed by market

quotes from April 2000 until June 2012. Panel B reports the autocorrelation function (ACF) for the monthly

variance risk and correlation risk premium.

Table A2: Correlation Matrix of Risk Factors and Hedge Funds Indices

CR

AL

L (

exce

pt

Fo

F)

Lo

ng

/Sh

ort

Eq

uit

y (

LS

E)

Lo

w N

et E

xp

osu

re (

LN

E)

Eq

uit

y L

on

g (

EL

)

Eq

uit

y M

ark

et N

eutr

al (

EM

N)

Op

tio

ns

Tra

der

(O

PT

)

Ev

ent

Dri

ven

(E

D)

Dis

tres

sed

Sec

uri

ties

(D

S)

Mer

ger

Arb

itra

ge

(MA

)

Fix

ed I

nco

me

Rel

ativ

e V

alue

(FI)

Conver

tible

Arb

itra

ge

(CA

)

Mac

ro (

MA

C)

Em

erg

ing

Mar

ket

s (E

MG

)

Funds

of

Funds

(FO

F)

Mult

i-st

rate

gy (

MU

L)

Man

aged

Futu

res

(MF

)

CR 1.00 -0.33 -0.36 -0.33 -0.36 -0.24 -0.46 -0.32 -0.26 -0.32 -0.16 -0.33 -0.25 -0.22 0.02 -0.27 -0.09

All -0.33 1.00 0.84 0.75 0.76 0.60 0.35 0.70 0.66 0.66 0.46 0.73 0.74 0.71 0.03 0.67 0.61

LSE -0.36 0.84 1.00 0.88 0.86 0.56 0.34 0.72 0.66 0.71 0.40 0.81 0.77 0.74 -0.01 0.64 0.19

LLNE -0.33 0.75 0.88 1.00 0.73 0.56 0.34 0.61 0.56 0.63 0.39 0.71 0.68 0.62 -0.01 0.52 0.24

EL -0.36 0.76 0.86 0.73 1.00 0.54 0.28 0.78 0.68 0.74 0.39 0.78 0.61 0.79 -0.04 0.61 0.05

EMN -0.24 0.60 0.56 0.56 0.54 1.00 0.19 0.52 0.41 0.51 0.24 0.48 0.41 0.43 0.00 0.43 0.27

OPT -0.46 0.35 0.34 0.34 0.28 0.19 1.00 0.31 0.24 0.32 0.22 0.28 0.35 0.26 -0.01 0.23 0.15

ED -0.32 0.70 0.72 0.61 0.78 0.52 0.31 1.00 0.84 0.79 0.49 0.73 0.59 0.79 0.02 0.79 0.04

DS -0.26 0.66 0.66 0.56 0.68 0.41 0.24 0.84 1.00 0.62 0.49 0.69 0.52 0.70 0.04 0.71 0.08

MA -0.32 0.66 0.71 0.63 0.74 0.51 0.32 0.79 0.62 1.00 0.49 0.70 0.56 0.68 0.00 0.73 0.05

FI -0.16 0.46 0.40 0.39 0.39 0.24 0.22 0.49 0.49 0.49 1.00 0.58 0.40 0.51 0.01 0.54 0.12

CA -0.33 0.73 0.81 0.71 0.78 0.48 0.28 0.73 0.69 0.70 0.58 1.00 0.60 0.78 -0.03 0.75 0.07

MAC -0.25 0.74 0.77 0.68 0.61 0.41 0.35 0.59 0.52 0.56 0.40 0.60 1.00 0.60 0.04 0.54 0.29

EMG -0.22 0.71 0.74 0.62 0.79 0.43 0.26 0.79 0.70 0.68 0.51 0.78 0.60 1.00 0.00 0.67 0.04

FOF 0.02 0.03 -0.01 -0.01 -0.04 0.00 -0.01 0.02 0.04 0.00 0.01 -0.03 0.04 0.00 1.00 0.05 0.04

MUL -0.27 0.67 0.64 0.52 0.61 0.43 0.23 0.79 0.71 0.73 0.54 0.75 0.54 0.67 0.05 1.00 0.12

MF -0.09 0.61 0.19 0.24 0.05 0.27 0.15 0.04 0.08 0.05 0.12 0.07 0.29 0.04 0.04 0.12 1.00

This table reports the correlation matrix of the correlation risk factor and the hedge fund index returns. The sample period is from

January 1996 to June 2012.

Table A3: Properties of Portfolios Sorted on Correlation Risk (Full-Sample Betas)

Panel A. All Funds: Properties of Portfolios Sorted on Correlation Risk

low 2 3 4 5 6 7 8 9 high H-L

beta_CR -0.06 -0.04 -0.03 -0.02 -0.01 0.00 0.00 0.01 0.02 0.05 0.11

t_beta_CR -8.21 -6.07 -4.51 -2.73 -1.60 -0.70 0.81 1.80 3.76 7.19 12.34

beta_S&P500 0.15 0.20 0.22 0.30 0.24 0.31 0.30 0.33 0.36 0.32 0.17

beta_SCMLC 0.19 0.16 0.15 0.17 0.12 0.15 0.15 0.14 0.15 0.07 -0.12

beta_BD10RET 0.08 0.11 0.11 0.11 0.15 0.09 0.10 0.08 0.07 -0.01 -0.09

beta_BAAMTSY 0.04 0.19 0.23 0.25 0.34 0.30 0.28 0.30 0.29 0.22 0.18

beta_PTFSBD 0.01 0.01 0.00 0.00 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 -0.02

beta_PTFSFX 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.02 0.01 -0.01

beta_PTFSCOM 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.00 0.00 -0.02

t_beta_S&P500 5.50 7.51 8.80 11.80 9.17 12.87 13.67 14.73 16.01 13.52 5.18

t_beta_SCMLC 6.05 5.62 5.29 5.96 4.21 5.74 6.13 5.77 6.06 2.52 -3.36

t_beta_BD10RET 1.44 2.27 2.37 2.33 3.10 1.90 2.29 1.91 1.58 -0.28 -1.45

t_beta_BAAMTSY 0.63 3.47 4.27 4.51 6.21 5.97 5.98 6.31 6.11 4.35 2.67

t_beta_PTFSBD 0.81 1.27 -0.04 -0.16 -1.24 -0.96 -1.38 -1.43 -1.57 -1.31 -1.65

t_beta_PTFSFX 2.85 3.18 3.60 3.62 2.88 3.22 3.13 2.16 3.31 1.90 -1.05

t_beta_PTFSCOM 2.51 2.45 2.09 1.99 1.50 0.70 1.19 0.86 0.30 0.03 -2.14

This table reproduces the analysis of Tables 3 and 4 in the main paper for all funds with full-sample betas. Panel A

reports betas and their t-statistics for decile portfolios containing individual hedge funds. All funds are sorted into equal-

weight decile portfolios based on their BKT correlation risk beta t-statistic calculated for the full sample. Column 2

reports results for decile 1, which contains individual hedge funds with the most extreme negative correlation risk beta.

Given the construction of the CR time-series, funds in this decile can be interpreted as selling insurance against

unexpected increases in correlation. Column 11 reports results for decile 10, which contains funds with the highest

correlation risk beta. These funds can be interpreted as buying insurance against unexpected increases in correlation. The

last column reports the difference between the high and the low portfolio. Rows 1 and 2 in Panel A report the BKT model

correlation risk beta and its t-statistic. Rows 3 to 16 report additional properties of the decile portfolios such as the betas

and t-statistics of beta of the other factors in the BKT model. Rows 1 and 2 (3 and 4) in Panel B report the Fung-Hsieh

(BKT) model alphas. Rows 7 to 12 in Panel B report the economic contribution of each factor to the total return of the

portfolio. This is measured as the risk exposure multiplied by the factor's average return. Alpha and hedge funds returns

are annualized and expressed in a percentage format. The Fung and Hsieh (2004) factors are S&P 500 return minus the

risk-free rate (S&P500), Wilshire small cap minus large cap return (SCMLC), change in the constant maturity yield of the

U.S. ten-year Treasury bond adjusted for the duration of the ten-year bond (BD10RET), change in the spread of Moody's

BAA bond over ten-year Treasury bond appropriately adjusted for duration (BAAMTSY), bond PTFS (PTFSBD),

currency PTFS (PTFSFX), and commodities PTFS (PTFSCOM), where PTFS is primitive trend-following strategy.

Decile Portfolio

Postranking Correlation Risk Betas

Additional Properties

Panel B. All funds: Alphas of Equally-Weighted Portflios Sorted on Correlation Betas

FHAlpha (% p.a.) 8.09 6.81 5.91 6.05 4.47 4.68 4.26 4.27 3.82 6.14

t_alpha 5.27 5.05 4.67 4.88 3.66 4.14 4.08 4.00 3.47 4.85

BKT Alpha (% p.a.) 0.40 1.49 2.05 3.69 3.10 4.12 4.86 5.62 6.67 11.87

t_alpha 0.24 0.98 1.39 2.47 2.08 2.97 3.80 4.32 5.10 8.61

Economic Contribution of Each Factor

contrib_CR 7.99 5.53 4.01 2.45 1.43 0.58 -0.62 -1.41 -2.96 -5.95

contrib_S&P500 0.79 1.01 1.15 1.56 1.21 1.58 1.55 1.70 1.85 1.65

contrib_SCMLC 0.23 0.20 0.18 0.21 0.15 0.19 0.19 0.18 0.19 0.08

contrib_BD10RET 0.28 0.41 0.42 0.42 0.55 0.32 0.35 0.30 0.25 -0.05

contrib_BAAMTSY 0.09 0.45 0.53 0.57 0.78 0.70 0.65 0.70 0.68 0.51

contrib_PTFSBD -0.12 -0.17 0.01 0.02 0.17 0.12 0.16 0.17 0.19 0.16

contrib_PTFSFX 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

contrib_PTFSCOM 0.03 0.03 0.03 0.02 0.02 0.01 0.01 0.01 0.00 0.00

Alpha Before and After Controlling for Correlation Risk

Table A4: Portflios Sorted on Correlation Risk - Different Investment Objectives

Panel A. Option Trader: Properties of Portfolios Sorted on Correlation Risk

low 2 3 4 5 6 7 8 9 high H-L

beta_CR -0.08 -0.16 -0.11 -0.08 -0.10 -0.08 -0.09 -0.08 -0.04 -0.03 0.06

t_beta_CR -2.64 -5.07 -5.51 -3.16 -3.26 -2.83 -2.87 -2.51 -1.56 -1.19 1.38

beta_S&P500 0.06 -0.01 0.04 -0.07 -0.14 0.02 -0.09 -0.04 0.05 0.23 0.16

beta_SCMLC -0.05 -0.02 0.01 0.15 0.23 0.20 0.37 0.43 0.13 0.21 0.23

beta_BD10RET 0.34 0.24 0.10 0.40 0.18 0.25 -0.05 -0.13 -0.01 -0.15 -0.48

beta_BAAMTSY 0.80 0.47 0.18 0.47 0.31 0.40 0.26 0.56 0.46 0.06 -0.71

beta_PTFSBD 0.02 0.03 0.01 -0.02 -0.06 -0.05 -0.03 -0.02 -0.01 0.00 -0.03

beta_PTFSFX -0.03 -0.01 0.00 0.01 0.00 0.01 0.00 0.02 0.01 -0.01 0.02

beta_PTFSCOM -0.03 -0.03 0.02 -0.01 0.01 0.02 0.04 -0.02 -0.04 -0.01 0.02

t_beta_S&P500 0.75 -0.08 0.73 -0.95 -1.69 0.22 -1.16 -0.48 0.67 3.35 1.47

t_beta_SCMLC -0.53 -0.25 0.19 1.96 2.65 2.23 4.14 4.47 1.74 2.75 1.92

t_beta_BD10RET 2.23 1.64 1.00 3.18 1.23 1.76 -0.35 -0.80 -0.10 -1.25 -2.48

t_beta_BAAMTSY 4.75 2.81 1.63 3.36 1.93 2.51 1.58 3.21 3.31 0.46 -3.31

t_beta_PTFSBD 0.65 1.33 0.34 -1.21 -2.48 -2.10 -1.16 -0.69 -0.61 -0.16 -0.94

t_beta_PTFSFX -1.34 -0.72 -0.11 0.40 0.03 0.41 0.06 0.93 0.58 -0.33 0.97

t_beta_PTFSCOM -1.32 -1.34 1.37 -0.28 0.48 1.04 1.81 -0.81 -1.85 -0.48 0.58

Panel B. Option Trader: Alphas of Equally-Weighted Portflios Sorted on Correlation Betas

FHAlpha (% p.a.) 0.89 5.42 9.88 0.31 4.23 1.41 6.92 8.13 7.70 7.96

t_alpha 0.22 1.30 3.53 0.09 1.10 0.37 1.79 1.96 2.37 2.46

BKT Alpha (% p.a.) -4.68 -5.14 2.28 -5.28 -2.29 -4.25 1.08 2.65 4.99 5.89

t_alpha -1.03 -1.17 0.78 -1.41 -0.54 -1.00 0.25 0.57 1.36 1.60


contrib_CR 5.82 10.98 7.89 5.80 6.77 5.88 6.07 5.70 2.82 2.15

contrib_S&P500 0.08 -0.01 0.06 -0.11 -0.22 0.03 -0.15 -0.07 0.07 0.37

contrib_SCMLC -0.27 -0.10 0.05 0.68 1.04 0.88 1.66 1.93 0.60 0.94

contrib_BD10RET 1.32 0.93 0.38 1.53 0.67 0.96 -0.19 -0.48 -0.04 -0.59

contrib_BAAMTSY 2.26 1.30 0.50 1.31 0.86 1.11 0.71 1.55 1.27 0.18

contrib_PTFSBD -0.36 -0.75 -0.13 0.58 1.35 1.14 0.64 0.41 0.29 0.08

contrib_PTFSFX -0.09 -0.03 0.00 0.01 0.00 0.02 0.00 0.04 0.02 -0.01

contrib_PTFSCOM 0.18 0.23 -0.16 0.04 -0.08 -0.17 -0.31 0.15 0.27 0.07

This table reproduces the analysis of Tables 3 and 4 in the main paper for different investment objectives using rolling betas. Panel A

reports betas and their t-statistics for decile portfolios containing option trader hedge funds. Each year from January 1999 until 2011

funds are sorted into equal-weight decile portfolios based on their BKT correlation risk beta t-statistic calculated using the previous 36

monthly returns. Column 2 reports results for decile 1, which contains individual hedge funds with the most extreme negative

correlation risk beta. Given the construction of the CR time-series, funds in this decile can be interpreted as selling insurance against

unexpected increases in correlation. Column 11 reports results for decile 10, which contains funds with the highest correlation risk

beta. These funds can be interpreted as buying insurance against unexpected increases in correlation. The last column reports the

difference between the high and the low portfolio. Rows 1 and 2 in Panel A report the BKT model correlation risk beta and its t-

statistic. Rows 3 to 16 reports additional properties of the decile portfolios such as the betas and t-statistics of beta of the other factors

in the BKT model. Rows 1 and 2 (3 and 4) in Panel B report the Fung-Hsieh (BKT) model alphas for option trader funds. Rows 5 to

12 in Panel B report the economic contribution of each factor to the total return of the portfolio. This is measured as the risk exposure

multiplied by the factor's average return. Alpha and hedge funds returns are annualized and expressed in a percentage format. Panels C

and D (E and F) report results for Funds of Funds (Managed Futures Funds).

Decile Portfolio




Panel C. Funds of Funds: Properties of Portfolios Sorted on Correlation Risk

low 2 3 4 5 6 7 8 9 high H-L

beta_CR -0.01 -0.01 -0.01 -0.01 -0.01 -0.02 -0.02 -0.02 -0.01 -0.02 0.00

t_beta_CR -1.45 -0.83 -0.93 -1.54 -2.10 -2.28 -2.07 -2.11 -1.76 -1.92 0.07

beta_S&P500 0.20 0.23 0.21 0.20 0.22 0.20 0.20 0.20 0.22 0.21 0.01

beta_SCMLC 0.07 0.09 0.08 0.12 0.17 0.17 0.17 0.18 0.16 0.14 0.08

beta_BD10RET 0.05 0.03 0.07 0.06 0.10 0.10 0.08 0.12 0.12 0.15 0.11

beta_BAAMTSY 0.28 0.28 0.33 0.30 0.28 0.32 0.32 0.32 0.29 0.23 -0.03

beta_PTFSBD -0.03 -0.02 -0.02 -0.02 -0.02 -0.01 -0.01 -0.01 -0.01 -0.01 0.02

beta_PTFSFX 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.00

beta_PTFSCOM 0.02 0.02 0.01 0.01 0.01 0.01 0.00 0.00 0.00 0.00 -0.02

t_beta_S&P500 5.64 7.07 6.87 7.69 8.45 7.64 7.03 6.91 7.57 6.54 0.22

t_beta_SCMLC 1.68 2.37 2.51 3.99 5.69 5.83 5.27 5.41 4.88 3.96 1.71

t_beta_BD10RET 0.79 0.54 1.25 1.21 2.00 2.07 1.54 2.21 2.25 2.50 1.39

t_beta_BAAMTSY 3.62 4.09 5.21 5.37 5.04 5.76 5.32 5.15 4.63 3.42 -0.32

t_beta_PTFSBD -2.81 -1.78 -1.97 -2.55 -2.15 -1.97 -1.56 -1.13 -1.06 -1.02 1.66

t_beta_PTFSFX 1.54 0.90 1.26 1.13 1.09 1.09 1.45 1.47 1.28 2.03 0.23

t_beta_PTFSCOM 1.55 1.69 1.52 1.36 0.83 0.84 0.05 0.05 0.26 -0.13 -1.47

Panel D. Funds of Funds: Alphas of Equally-Weighted Portflios Sorted on Correlation Betas

FHAlpha (% p.a.) 2.57 2.15 1.30 1.72 1.52 0.56 0.85 0.17 0.06 0.95

t_alpha 1.52 1.40 0.92 1.38 1.22 0.45 0.62 0.13 0.04 0.63

BKT Alpha (% p.a.) 0.84 1.24 0.37 0.36 -0.32 -1.43 -1.13 -1.88 -1.64 -1.10

t_alpha 0.40 0.66 0.21 0.24 -0.21 -0.95 -0.68 -1.12 -0.98 -0.60


contrib_CR 1.80 0.95 0.97 1.41 1.92 2.07 2.06 2.14 1.77 2.13

contrib_S&P500 1.03 1.18 1.05 1.04 1.14 1.02 1.03 1.03 1.12 1.07

contrib_SCMLC 0.08 0.11 0.10 0.14 0.20 0.21 0.21 0.22 0.19 0.17

contrib_BD10RET 0.19 0.12 0.26 0.22 0.36 0.37 0.30 0.44 0.45 0.55

contrib_BAAMTSY 0.63 0.65 0.76 0.69 0.65 0.74 0.75 0.73 0.66 0.53

contrib_PTFSBD 0.53 0.30 0.31 0.35 0.29 0.27 0.23 0.17 0.16 0.17

contrib_PTFSFX 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

contrib_PTFSCOM 0.03 0.03 0.02 0.02 0.01 0.01 0.00 0.00 0.00 0.00

Decile Portfolio




Panel E. Managed Futures Funds: Properties of Portfolios Sorted on Correlation Risk

low 2 3 4 5 6 7 8 9 high H-L

beta_CR -0.04 -0.03 -0.03 -0.02 -0.02 -0.02 -0.02 -0.01 0.00 0.00 0.05

t_beta_CR -2.92 -2.18 -2.39 -1.42 -1.41 -1.36 -1.71 -1.25 -0.08 0.05 2.85

beta_S&P500 -0.05 -0.02 0.02 0.04 0.06 0.04 0.01 0.09 0.09 0.13 0.18

beta_SCMLC 0.05 0.00 -0.01 0.05 0.05 0.09 0.02 0.07 0.08 0.03 -0.01

beta_BD10RET 0.16 0.22 0.19 0.30 0.29 0.23 0.14 0.19 0.16 0.16 0.01

beta_BAAMTSY 0.10 0.14 0.07 0.14 0.00 -0.01 0.06 0.07 0.10 0.08 0.00

beta_PTFSBD 0.03 0.02 0.02 0.02 0.02 0.01 0.01 0.02 0.01 0.01 -0.02

beta_PTFSFX 0.04 0.05 0.05 0.05 0.05 0.05 0.04 0.05 0.03 0.03 0.00

beta_PTFSCOM 0.06 0.04 0.05 0.04 0.04 0.03 0.03 0.03 0.04 0.03 -0.03

t_beta_S&P500 -0.94 -0.43 0.43 0.90 1.38 0.98 0.28 2.34 2.60 3.25 2.99

t_beta_SCMLC 0.80 0.00 -0.18 1.08 1.03 1.96 0.56 1.68 2.09 0.78 -0.17

t_beta_BD10RET 1.57 2.35 2.22 3.60 3.48 2.87 2.02 2.58 2.52 2.11 0.05

t_beta_BAAMTSY 0.90 1.37 0.68 1.46 0.02 -0.06 0.77 0.77 1.37 1.00 -0.02

t_beta_PTFSBD 2.14 1.77 1.79 1.30 1.36 1.00 1.21 1.92 1.28 1.20 -1.15

t_beta_PTFSFX 3.04 4.55 4.73 5.11 4.52 4.86 5.14 5.34 4.29 3.65 -0.34

t_beta_PTFSCOM 3.76 2.89 3.62 2.92 3.06 2.74 2.39 2.70 3.77 2.36 -1.81

Panel F. Managed Futures Funds: Alphas of Equally-Weighted Portflios Sorted on Correlation Betas

FHAlpha (% p.a.) 8.00 5.85 6.00 4.10 4.28 4.64 4.27 2.35 1.48 4.78

t_alpha 3.12 2.47 2.82 1.95 2.02 2.36 2.41 1.25 0.93 2.61

BKT Alpha (% p.a.) 2.81 2.22 2.44 1.98 2.17 2.74 2.13 0.69 1.39 4.85

t_alpha 0.91 0.77 0.95 0.77 0.84 1.14 0.99 0.30 0.71 2.15


contrib_CR 5.40 3.77 3.70 2.20 2.19 1.97 2.22 1.73 0.09 -0.07

contrib_S&P500 -0.26 -0.11 0.10 0.20 0.32 0.21 0.05 0.48 0.45 0.65

contrib_SCMLC 0.06 0.00 -0.01 0.07 0.06 0.11 0.03 0.09 0.10 0.04

contrib_BD10RET 0.58 0.81 0.68 1.11 1.08 0.82 0.52 0.71 0.59 0.57

contrib_BAAMTSY 0.23 0.33 0.15 0.32 0.00 -0.01 0.14 0.15 0.23 0.19

contrib_PTFSBD -0.60 -0.46 -0.42 -0.30 -0.32 -0.22 -0.24 -0.40 -0.23 -0.24

contrib_PTFSFX 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

contrib_PTFSCOM 0.09 0.07 0.08 0.06 0.06 0.05 0.04 0.05 0.06 0.04



Decile Portfolio


Table A5: Correlation Risk for Funds Sorted By Net Exposure

low 2 3 4 5 6 7 8 9 high H-L

beta_CR -0.003 -0.013 -0.016 -0.010 -0.007 -0.015 0.003 0.003 0.015 0.000 0.00

Return (% p.a.) 10.08 11.31 12.45 12.90 12.33 14.51 13.45 13.17 11.56 9.46 -0.62

FH7 Alpha (% p.a.) 5.71 6.03 7.34 7.35 6.31 7.90 5.74 5.48 5.04 1.84 -3.87

t_alpha 4.49 4.84 5.63 5.42 4.91 4.90 3.92 2.60 3.05 1.06 -3.43

BKT Alpha (% p.a.) 5.39 4.42 5.37 6.13 5.47 6.04 6.15 5.83 6.86 1.89 -3.50

beta_CR -0.003 -0.013 -0.016 -0.010 -0.007 -0.015 0.003 0.003 0.015 0.000 0.00

beta_S&P500 0.111 0.252 0.266 0.376 0.407 0.514 0.588 0.582 0.450 0.559 0.45

beta_SCMLC 0.095 0.213 0.258 0.248 0.239 0.324 0.328 0.234 0.143 0.244 0.15

beta_BD10RET 0.049 0.071 0.008 -0.029 -0.013 -0.027 0.035 -0.015 0.007 0.091 0.04

beta_BAAMTSY 0.194 0.169 0.135 0.164 0.268 0.267 0.439 0.551 0.497 0.463 0.27

beta_PTFSBD -0.011 -0.009 -0.009 -0.009 -0.010 -0.007 -0.018 -0.021 -0.005 -0.012 0.00

beta_PTFSFX 0.015 0.005 0.010 0.014 0.013 0.010 0.012 0.018 0.006 0.015 0.00

beta_PTFSCOM -0.004 0.007 -0.003 -0.006 -0.003 0.002 -0.003 -0.011 -0.001 -0.010 -0.01

t_alpha 3.45 2.91 3.39 3.70 3.47 3.07 3.42 2.25 3.40 0.89 -2.10

t_beta_CR -0.36 -1.84 -2.15 -1.27 -0.93 -1.64 0.40 0.23 1.56 0.04 0.42

t_beta_S&P 4.10 9.61 9.73 13.13 14.97 15.11 18.91 12.98 12.90 15.18 15.68

contrib_alpha 5.39 4.42 5.37 6.13 5.47 6.04 6.15 5.83 6.86 1.89 -3.50

contrib_CR 0.33 1.67 2.04 1.27 0.88 1.94 -0.43 -0.36 -1.90 -0.06 -0.39

contrib_S&P500 0.57 1.29 1.36 1.93 2.09 2.63 3.01 2.98 2.31 2.86 2.30

In this table, we report regression coefficients for individual hedge funds that are sorted by their Net Exposure. Column 3

reports results for decile 1, which contains individual hedge funds with the lowest net exposure. Column 12 reports results for

decile 10, which contains funds with the highest net exposure. Rows 1 and 6 report the BKT model correlation risk beta.

Row 2 reports the average absolute return per year. Rows 3 to 4 report FH model results. Rows 5 to 16 report BKT model

results. Rows 14 to 16 report t-statistics for several BKT model betas. Rows 17 to 19 report the contribution of alpha and

several BKT model betas to the total absolute return. Alpha and hedge funds returns are annualized and expressed in a

percentage format. The sample period is from January 1996 to June 2012.

FH7 Model

Coefficients

BKT Model

Coefficients

Table A6: Correlation Risk for Funds Sorted By Leverage

low 2 3 4 5 6 7 8 9 high H-L

beta_CR -0.012 -0.012 -0.004 -0.002 -0.014 -0.027 -0.024 -0.010 -0.011 -0.008 0.00

Return (% p.a.) 9.95 11.01 10.94 13.11 8.33 10.18 14.10 14.16 11.76 10.67 0.72

FH7 Alpha (% p.a.) 4.83 4.80 4.71 7.15 2.47 6.80 10.01 8.75 6.14 5.70 0.87

t_alpha 5.24 3.60 3.84 5.36 1.22 4.86 5.68 7.61 5.38 5.87 0.63

BKT Alpha (% p.a.) 3.37 3.36 4.21 6.84 0.71 3.41 7.01 7.47 4.76 4.77 1.40

beta_CR -0.012 -0.012 -0.004 -0.002 -0.014 -0.027 -0.024 -0.010 -0.011 -0.008 0.00

beta_S&P500 0.313 0.371 0.401 0.384 0.201 0.023 0.073 0.307 0.299 0.187 -0.13

beta_SCMLC 0.206 0.180 0.189 0.235 0.099 0.019 0.076 0.212 0.187 0.074 -0.13

beta_BD10RET -0.012 0.028 0.047 0.030 0.230 0.161 0.193 0.054 0.049 0.076 0.09

beta_BAAMTSY 0.137 0.342 0.319 0.252 0.409 0.059 0.093 0.189 0.227 0.217 0.08

beta_PTFSBD -0.004 -0.015 -0.009 -0.008 0.002 0.028 0.017 -0.002 -0.013 -0.013 -0.01

beta_PTFSFX 0.009 0.012 0.009 0.007 0.041 0.037 0.034 0.011 0.010 0.007 0.00

beta_PTFSCOM 0.001 -0.001 -0.002 0.000 0.025 0.032 0.034 0.011 -0.002 0.005 0.00

t_alpha 3.01 2.06 2.80 4.18 0.29 2.05 3.28 5.33 3.42 4.01 1.62

t_beta_CR -2.27 -1.54 -0.57 -0.32 -1.23 -3.52 -2.43 -1.57 -1.71 -1.36 1.07

t_beta_S&P 16.19 13.20 15.41 13.58 4.72 0.79 1.98 12.67 12.45 9.12 -8.49

contrib_alpha 3.37 3.36 4.21 6.84 0.71 3.41 7.01 7.47 4.76 4.77 1.40

contrib_CR 1.52 1.50 0.51 0.32 1.83 3.52 3.12 1.33 1.43 0.97 -0.55

contrib_S&P500 1.60 1.90 2.06 1.97 1.03 0.12 0.37 1.57 1.53 0.96 -0.64

-0.012 -0.012 -0.004 -0.002 -0.014 -0.027 -0.024 -0.01 -0.011 -0.008 0.004

9.948 11.01 10.94 13.11 8.327 10.18 14.1 14.16 11.76 10.67 0.721

4.834 4.804 4.708 7.147 2.47 6.805 10.01 8.748 6.141 5.704 0.869

5.241 3.604 3.837 5.359 1.224 4.864 5.675 7.614 5.378 5.872 0.631

3.369 3.358 4.213 6.844 0.708 3.414 7.012 7.472 4.761 4.769 1.401

-0.012 -0.012 -0.004 -0.002 -0.014 -0.027 -0.024 -0.01 -0.011 -0.008 0.004

0.313 0.371 0.401 0.384 0.201 0.023 0.073 0.307 0.299 0.187 -0.126

0.206 0.18 0.189 0.235 0.099 0.019 0.076 0.212 0.187 0.074 -0.132

-0.012 0.028 0.047 0.03 0.23 0.161 0.193 0.054 0.049 0.076 0.088

0.137 0.342 0.319 0.252 0.409 0.059 0.093 0.189 0.227 0.217 0.08

-0.004 -0.015 -0.009 -0.008 0.002 0.028 0.017 -0.002 -0.013 -0.013 -0.009

0.009 0.012 0.009 0.007 0.041 0.037 0.034 0.011 0.01 0.007 -0.002

0.001 -0.001 -0.002 -4E-04 0.025 0.032 0.034 0.011 -0.002 0.005 0.004

3.011 2.062 2.796 4.176 0.287 2.049 3.283 5.327 3.419 4.014 1.616

-2.266 -1.536 -0.568 -0.32 -1.233 -3.52 -2.431 -1.572 -1.714 -1.36 1.069

16.19 13.2 15.41 13.58 4.716 0.794 1.98 12.67 12.45 9.121 -8.488

3.369 3.358 4.213 6.844 0.708 3.414 7.012 7.472 4.761 4.769 1.401

1.523 1.503 0.514 0.316 1.83 3.523 3.12 1.325 1.434 0.971 -0.552

1.604 1.903 2.056 1.971 1.032 0.117 0.375 1.574 1.535 0.96 -0.644

0.315 0.787 0.734 0.581 0.94 0.136 0.213 0.435 0.523 0.5 0.184

In this table, we report regression coefficients for individual hedge funds that are sorted by their leverage. Column 3 reports

results for decile 1, which contains individual hedge funds with the lowest leverage. Column 12 reports results for decile 10,

which contains funds with the highest leverage. Rows 1 and 6 report the BKT model correlation risk beta. Row 2 reports the

average absolute return per year. Rows 3 to 4 report FH model results. Rows 5 to 16 report BKT model results. Rows 14 to 16

report t-statistics for several BKT model betas. Rows 17 to 19 report the contribution of alpha and several BKT model betas to

the total absolute return. Alpha and hedge funds returns are annualized and expressed in a percentage format. The sample period

is from January 1996 to June 2012.

FH7 Model

Coefficients

BKT Model

Coefficients

Table A7: Funds Sorted By Leverage and Correlation Risk Beta

Panel A: Low Leverage low 2 3 4 5 6 7 8 9 high H-L

beta_CR -0.054 -0.028 -0.023 -0.018 -0.012 -0.004 -0.003 0.007 0.019 0.031 0.08

Return (% p.a.) 12.22 10.05 10.92 11.45 9.24 10.49 10.92 9.31 8.23 7.99 -4.23

FH7 Alpha (% p.a.) 6.75 5.05 4.85 4.76 3.99 3.46 4.43 3.20 1.34 2.40 -4.35

t_alpha 4.26 3.85 3.33 3.17 3.97 2.13 3.37 2.38 0.80 1.55 -2.71

BKT Alpha (% p.a.) 0.06 1.56 1.95 2.55 2.47 2.99 4.02 4.01 3.64 6.17 6.11

beta_CR -0.054 -0.028 -0.023 -0.018 -0.012 -0.004 -0.003 0.007 0.019 0.031 0.08

beta_S&P500 0.309 0.312 0.340 0.363 0.268 0.440 0.427 0.430 0.389 0.389 0.08

beta_SCMLC 0.280 0.218 0.234 0.258 0.123 0.194 0.162 0.180 0.161 0.148 -0.13

beta_BD10RET -0.007 -0.056 0.059 0.059 0.030 0.032 0.056 0.067 0.050 0.045 0.05

beta_BAAMTSY 0.134 0.202 0.324 0.435 0.192 0.420 0.391 0.216 0.587 0.141 0.01

beta_PTFSBD -0.008 0.006 -0.006 -0.020 -0.014 -0.032 -0.006 -0.006 -0.023 -0.012 0.00

beta_PTFSFX 0.008 0.012 0.005 0.015 0.009 0.014 0.007 0.007 0.012 0.014 0.01

beta_PTFSCOM -0.001 -0.001 -0.002 -0.005 -0.004 0.002 0.005 0.008 -0.007 -0.002 0.00

t_alpha 0.03 1.00 1.12 1.40 2.02 1.50 2.49 2.43 1.79 3.35 2.76

t_beta_CR -6.59 -3.89 -2.85 -2.09 -2.15 -0.41 -0.44 0.85 1.95 3.54 8.04

t_beta_S&P 10.18 11.65 11.23 11.53 12.69 12.77 15.29 15.09 11.07 12.24 1.92

contrib_alpha 0.06 1.56 1.95 2.55 2.47 2.99 4.02 4.01 3.64 6.17 6.11

contrib_CR 6.95 3.63 3.01 2.29 1.58 0.49 0.42 -0.85 -2.39 -3.92 -10.87

contrib_S&P500 1.58 1.60 1.74 1.86 1.37 2.26 2.19 2.21 2.00 2.00 0.41

Panel B: 2nd Quartile low 2 3 4 5 6 7 8 9 high H-L

beta_CR -0.049 -0.043 -0.029 -0.022 -0.037 -0.028 0.009 0.013 0.043 0.031 0.08

Return (% p.a.) 11.48 12.62 19.40 14.48 14.74 9.68 14.92 11.96 7.84 10.82 -0.67

FH7 Alpha (% p.a.) 6.35 7.61 14.17 10.55 8.33 5.74 8.84 6.45 0.74 5.51 -0.84

t_alpha 2.57 3.38 5.08 3.51 3.28 1.34 4.41 3.04 0.22 3.44 0.87

BKT Alpha (% p.a.) 0.24 5.52 10.63 7.87 5.39 4.36 9.98 7.04 6.08 9.38 9.14

beta_CR -0.049 -0.043 -0.029 -0.022 -0.037 -0.028 0.009 0.013 0.043 0.031 0.08

beta_S&P500 0.123 0.267 0.302 0.455 0.402 0.833 0.491 0.474 0.697 0.351 0.23

beta_SCMLC 0.268 0.022 0.222 0.314 0.140 0.144 0.231 0.057 0.258 0.096 -0.17

beta_BD10RET 0.064 0.046 0.030 -0.190 0.314 -0.294 -0.041 0.118 -0.084 0.067 0.00

beta_BAAMTSY 0.151 0.232 0.078 -0.043 0.413 0.124 0.210 0.338 0.143 0.220 0.07

beta_PTFSBD -0.027 -0.005 -0.008 0.051 -0.018 0.034 -0.008 -0.044 -0.032 0.003 0.03

beta_PTFSFX 0.007 0.034 0.014 -0.003 0.010 0.019 0.011 0.023 0.015 0.004 0.00

beta_PTFSCOM 0.002 -0.013 -0.016 0.006 0.010 0.012 -0.002 0.017 -0.007 -0.005 -0.01

t_alpha 0.08 2.32 3.13 2.14 1.86 0.93 4.06 3.07 1.47 4.92 2.47

t_beta_CR -3.60 -2.33 -1.80 -1.26 -2.05 -0.77 0.80 0.69 2.24 3.51 4.63

t_beta_S&P 2.42 5.18 5.15 7.15 7.58 8.33 11.56 9.86 9.86 10.64 3.60

contrib_alpha 0.24 5.52 10.63 7.87 5.39 4.36 9.98 7.04 6.08 9.38 9.14

contrib_CR 6.34 2.58 3.68 2.78 2.94 1.64 -1.18 -0.69 -5.51 -4.02 -10.36

contrib_S&P500 0.63 1.50 1.55 2.33 0.87 3.35 2.52 0.65 3.46 1.80 1.17

In this table, we report regression coefficients for individual hedge funds that are sorted first by fund leverage (into quartiles) and

then by the t-statistic of the correlation risk beta. Column 3 reports results for decile 1, which contains individual hedge funds

with the lowest leverage. Column 12 reports results for decile 10, which contains funds with the highest leverage. Rows 1 and 6

report the BKT model correlation risk beta. Row 2 reports the average absolute return per year. Rows 3 to 4 report FH model

results. Rows 5 to 16 report BKT model results. Rows 14 to 16 report t-statistics for several BKT model betas. Rows 17 to 19

report the contribution of alpha and several BKT model betas to the total absolute return. Alpha and hedge funds returns are

annualized and expressed in a percentage format. The sample period is from January 1996 to June 2012. Panels A, B, C and D

report results for the first (lowest), second, third and fourth (highest) leverage quartile, respectively.

FH7 Model

Coefficients

BKT Model

Coefficients

FH7 Model

Coefficients

BKT Model

Coefficients

Panel C: 3rd Quartile low 2 3 4 5 6 7 8 9 high H-L

beta_CR -0.059 -0.033 -0.007 -0.024 -0.016 -0.009 -0.011 0.001 0.033 0.055 0.11

Return (% p.a.) 12.36 12.59 9.73 11.46 9.96 8.44 11.06 11.20 13.43 2.58 -9.78

FH7 Alpha (% p.a.) 7.51 7.50 3.91 4.64 4.86 3.86 5.16 5.59 8.35 -2.80 -10.31

t_alpha 4.75 4.51 2.64 1.47 2.31 2.22 1.82 2.82 2.41 -1.24 -5.99

BKT Alpha (% p.a.) 0.25 3.37 2.98 1.69 2.98 3.46 3.77 5.69 12.38 4.02 3.77

beta_CR -0.059 -0.033 -0.007 -0.024 -0.016 -0.009 -0.011 0.001 0.033 0.055 0.11

beta_S&P500 0.202 0.166 0.268 0.593 0.213 0.276 0.405 0.335 0.343 0.251 0.05

beta_SCMLC 0.199 0.120 0.135 0.542 0.037 0.099 0.297 0.086 0.253 0.111 -0.09

beta_BD10RET -0.041 0.087 0.044 -0.058 0.002 0.126 -0.017 0.146 0.040 0.093 0.13

beta_BAAMTSY 0.176 0.225 0.287 0.106 0.197 0.176 0.204 0.503 0.092 0.464 0.29

beta_PTFSBD -0.010 -0.013 -0.031 -0.007 -0.027 -0.023 -0.022 -0.020 0.001 0.001 0.01

beta_PTFSFX 0.006 0.001 0.013 0.023 0.021 0.017 0.020 0.015 0.010 0.008 0.00

beta_PTFSCOM -0.001 0.001 0.001 -0.004 -0.021 0.004 -0.018 0.000 -0.012 -0.011 -0.01

t_alpha 0.15 1.70 1.65 0.44 1.17 1.84 1.09 2.47 2.92 1.52 1.16

t_beta_CR -7.32 -3.62 -0.88 -1.32 -1.31 -0.56 -0.71 0.09 1.64 4.46 7.77

t_beta_S&P 6.81 4.87 8.54 8.88 4.87 7.44 6.85 7.95 4.68 5.49 0.77

contrib_alpha 0.25 3.37 2.98 1.69 2.98 3.46 3.77 5.69 12.38 4.02 3.77

contrib_CR 7.54 4.30 0.96 3.06 1.95 0.45 1.43 -0.10 -4.18 -7.10 -14.64

contrib_S&P500 1.03 0.85 1.37 3.04 1.10 0.11 1.95 0.69 1.76 1.29 0.25

Panel D: High Leverage low 2 3 4 5 6 7 8 9 high H-L

beta_CR -0.061 -0.033 -0.019 -0.023 -0.008 -0.021 -0.006 0.001 0.020 0.033 0.09

Return (% p.a.) 13.78 11.07 9.23 9.81 9.72 10.86 10.07 9.43 8.28 11.54 -2.25

FH7 Alpha (% p.a.) 8.68 5.87 3.58 3.60 3.43 5.37 4.28 2.97 1.25 5.48 -3.19

t_alpha 4.86 3.77 3.20 2.40 1.93 3.42 2.80 2.21 0.71 3.15 -1.71

BKT Alpha (% p.a.) 1.17 1.75 1.25 0.79 2.39 2.82 3.54 3.07 3.72 9.58 8.40

beta_CR -0.061 -0.033 -0.019 -0.023 -0.008 -0.021 -0.006 0.001 0.020 0.033 0.09

beta_S&P500 0.276 0.239 0.321 0.313 0.217 0.170 0.334 0.366 0.488 0.507 0.23

beta_SCMLC 0.342 0.196 0.189 0.215 0.117 0.073 0.163 0.167 0.251 0.115 -0.23

beta_BD10RET 0.040 0.048 0.043 0.107 0.184 0.157 -0.015 0.174 0.003 -0.033 -0.07

beta_BAAMTSY 0.002 0.230 0.157 0.250 0.394 0.335 0.349 0.224 0.394 0.306 0.30

beta_PTFSBD 0.001 -0.001 -0.016 -0.023 -0.030 -0.013 -0.014 -0.020 -0.027 -0.003 0.00

beta_PTFSFX 0.001 0.002 0.008 0.012 0.008 0.003 0.009 0.009 0.011 0.007 0.01

beta_PTFSCOM -0.002 -0.001 0.007 0.002 0.007 -0.003 -0.001 0.011 0.029 -0.010 -0.01

t_alpha 0.59 0.95 0.93 0.44 1.10 1.48 1.88 1.86 1.73 4.62 3.57

t_beta_CR -6.56 -3.87 -3.00 -2.68 -0.82 -2.32 -0.68 0.10 1.98 3.41 8.38

t_beta_S&P 8.07 7.50 13.84 10.01 5.77 5.19 10.28 12.84 13.12 14.16 5.33

contrib_alpha 1.17 1.75 1.25 0.79 2.39 2.82 3.54 3.07 3.72 9.58 8.40

contrib_CR 7.80 4.28 2.43 2.91 1.08 2.65 0.77 -0.10 -2.57 -4.25 -12.05

contrib_S&P500 1.41 1.22 1.65 1.61 1.11 0.87 1.71 1.88 2.50 2.60 1.19

BKT Model

Coefficients

FH7 Model

Coefficients

BKT Model

Coefficients

FH7 Model

Coefficients

Table A8 Robustness to Liquidity Factor

Panel A: BKT

All ALNE LSE LLSE EL EMN OPT ED DS MA FI CA MAC EMG FOF MUL MF

HF ret (% p.a.) 6.88 6.49 7.09 5.99 6.83 3.43 10.51 7.64 6.60 4.71 5.31 5.39 7.67 9.30 4.56 7.54 7.45

IR (p.a.) 0.16 0.09 0.13 0.06 0.10 0.11 0.01 0.14 0.23 0.24 0.16 0.03 0.13 0.12 0.01 0.38 0.07

Alpha (% p.a.) 3.23 2.06 2.84 1.49 2.27 1.79 0.38 3.67 4.36 2.81 2.94 0.70 3.80 5.98 0.13 5.77 2.87

Beta CR -0.01 -0.02 -0.01 -0.02 0.00 0.00 -0.07 -0.01 0.00 0.00 0.00 -0.01 -0.01 0.02 -0.01 -0.01 -0.03

Beta SNP 0.19 0.22 0.28 0.21 0.58 0.11 0.02 0.21 0.10 0.11 0.02 0.23 0.20 0.50 0.21 0.05 0.01

Beta SCM 0.11 0.20 0.23 0.19 0.24 -0.03 0.06 0.09 0.08 0.06 0.03 0.14 0.21 0.16 0.12 0.03 0.05

Beta BD10RET 0.16 0.12 0.08 0.13 0.08 0.09 0.09 -0.04 -0.04 0.05 0.18 0.18 0.19 0.08 0.13 0.00 0.35

Beta BAAmTSY 0.19 0.14 0.09 0.14 0.22 0.08 0.10 0.32 0.28 0.14 0.36 0.48 0.03 0.68 0.30 0.22 0.09

Beta PTFSBD 0.00 -0.01 -0.01 -0.01 -0.01 -0.01 -0.02 -0.04 -0.03 -0.01 -0.02 -0.01 -0.01 -0.04 -0.02 -0.01 0.02

Beta PTFSFX 0.02 0.00 0.01 0.00 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.05

Beta PTFSCOM 0.02 0.01 0.01 0.01 0.00 0.01 0.02 0.00 0.00 0.00 0.00 0.00 0.02 0.00 0.01 0.00 0.03

t-stat Alpha 2.29 1.31 1.88 0.84 1.39 1.59 0.15 2.01 3.27 3.40 2.25 0.43 1.86 1.74 0.08 5.34 1.03

t-stat CR -1.75 -2.18 -2.06 -2.11 -0.27 -0.49 -6.09 -1.35 -0.61 -1.05 -0.46 -1.45 -1.32 0.98 -1.81 -1.22 -1.98

t-stat SNP 7.79 8.22 10.70 6.74 20.69 5.61 0.39 6.76 4.26 7.91 0.76 8.05 5.56 8.41 7.50 2.65 0.13

t-stat SCM 3.94 6.62 7.78 5.60 7.64 -1.57 1.26 2.68 3.01 3.69 1.22 4.37 5.32 2.47 3.83 1.60 0.86

t-stat BD10RET 3.41 2.37 1.70 2.21 1.51 2.41 1.11 -0.72 -0.85 1.87 4.32 3.35 2.89 0.68 2.53 0.10 3.85

t-stat BAAmTSY 3.59 2.35 1.67 2.07 3.57 1.81 1.06 4.73 5.78 4.62 7.42 8.02 0.42 5.34 5.09 5.54 0.84

t-stat PTFSBD -0.36 -1.35 -1.06 -0.92 -1.39 -2.60 -2.07 -4.36 -5.20 -3.01 -3.41 -1.13 -1.05 -2.37 -2.27 -1.71 1.36

t-stat PTFSFX 3.22 0.68 1.56 0.49 0.93 2.11 1.10 1.81 1.14 1.82 -0.79 -0.03 1.03 0.52 1.56 0.20 4.42

t-stat PTFSCOM 2.23 1.02 0.93 1.00 0.41 1.33 1.67 -0.27 0.41 -0.68 0.21 -0.56 1.74 -0.16 1.26 -0.26 2.35

adj R^2 45.31 50.97 59.45 41.76 81.04 24.35 21.53 52.71 49.21 51.92 34.33 61.46 29.62 52.67 50.58 32.24 26.28

Panel B: BKT + Fontaine and Garcia (2012) Liquidity Factor


HF ret (% p.a.) 7.11 6.81 7.45 6.34 7.32 3.57 10.59 7.99 6.87 4.88 5.39 5.62 7.85 9.80 4.85 7.67 7.62

IR (p.a.) 0.17 0.10 0.15 0.07 0.11 0.12 0.01 0.14 0.23 0.25 0.16 0.04 0.14 0.12 0.01 0.38 0.08

Alpha (% p.a.) 3.36 2.26 3.15 1.75 2.58 1.84 0.43 3.65 4.22 2.96 2.90 0.83 4.05 5.92 0.17 5.83 2.94

Beta CR -0.01 -0.02 -0.02 -0.02 0.00 0.00 -0.07 -0.01 -0.01 0.00 0.00 -0.01 -0.01 0.01 -0.01 -0.01 -0.03

Beta SNP 0.19 0.22 0.27 0.20 0.58 0.11 0.02 0.22 0.10 0.11 0.02 0.23 0.20 0.51 0.21 0.05 0.01

Beta SCM 0.11 0.20 0.23 0.19 0.24 -0.03 0.06 0.09 0.07 0.06 0.03 0.14 0.21 0.16 0.12 0.03 0.04

Beta BD10RET 0.16 0.12 0.09 0.13 0.09 0.09 0.09 -0.05 -0.04 0.05 0.18 0.18 0.20 0.07 0.13 0.00 0.35

Beta BAAmTSY 0.18 0.13 0.10 0.14 0.22 0.07 0.09 0.30 0.26 0.15 0.35 0.49 0.04 0.65 0.28 0.22 0.07

Beta PTFSBD 0.00 -0.01 0.00 0.00 -0.01 -0.01 -0.02 -0.04 -0.03 -0.01 -0.02 -0.01 -0.01 -0.04 -0.01 -0.01 0.03

Beta PTFSFX 0.02 0.00 0.01 0.00 0.01 0.01 0.01 0.01 0.00 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.05

Beta PTFSCOM 0.02 0.01 0.01 0.01 0.00 0.01 0.02 0.00 0.00 0.00 0.00 -0.01 0.02 0.00 0.01 0.00 0.04

Beta Liq 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

t-stat Alpha 2.39 1.43 2.10 0.98 1.59 1.62 0.17 1.98 3.20 3.56 2.20 0.50 1.96 1.70 0.11 5.33 1.06

t-stat CR -1.89 -2.29 -2.14 -2.23 -0.36 -0.61 -6.03 -1.45 -0.84 -1.03 -0.51 -1.49 -1.26 0.87 -1.97 -1.20 -2.18

t-stat SNP 7.78 8.16 10.59 6.64 20.62 5.57 0.37 6.82 4.59 7.70 0.81 7.87 5.48 8.41 7.57 2.65 0.16

t-stat SCM 3.95 6.64 7.92 5.65 7.76 -1.58 1.25 2.62 2.92 3.76 1.18 4.36 5.33 2.41 3.79 1.60 0.82

t-stat BD10RET 3.40 2.40 1.81 2.28 1.64 2.37 1.10 -0.77 -1.02 2.00 4.23 3.39 2.91 0.62 2.46 0.11 3.82

t-stat BAAmTSY 3.46 2.29 1.83 2.12 3.70 1.71 1.03 4.39 5.24 4.78 7.11 7.92 0.48 5.02 4.80 5.36 0.66

t-stat PTFSBD 0.07 -0.93 -0.57 -0.43 -0.89 -2.17 -1.92 -4.14 -5.01 -2.76 -3.27 -0.86 -1.04 -2.17 -1.87 -1.68 1.83

t-stat PTFSFX 3.24 0.73 1.73 0.64 1.11 2.19 1.10 1.65 0.89 1.89 -0.84 0.07 0.93 0.43 1.52 0.08 4.48

t-stat PTFSCOM 2.34 1.09 0.96 1.02 0.40 1.38 1.65 -0.14 0.64 -0.72 0.25 -0.59 1.81 -0.05 1.40 -0.17 2.44

t-stat Liq -0.84 -0.48 0.52 -0.12 0.38 -0.84 -0.14 -1.31 -3.00 1.23 -0.70 0.13 0.65 -1.17 -1.56 0.01 -1.55

adj R^2 45.85 50.75 59.58 41.51 81.11 23.79 20.99 52.34 50.87 51.50 33.86 61.02 29.59 52.26 50.84 31.73 28.43

This table reports several performance measures of hedge fund index returns for different investment objectives. Panel A reports results

based on the baseline eight-factor BKT model and sample period of January 1996 - June 2012. The columns show the annualized hedge

fund index return, the annualized information ratio and alpha, the BKT beta and the t-statistics of the alpha and BKT betas. Panel B reports

the alphas of an augemented BKT model that also includes the Fontaine and Garcia (2012) liquidity risk factor (available for the period

January 1996 - March 2012). Panel C reports the alphas of a BKT model that also includes the Pastor and Stambaugh (2003) tradable

liquidity risk factor (available for the period January 1996 - December 2011).

Panel C: BKT + Pastor and Stambaugh (2003) Liquidity Factor


HF ret (% p.a.) 7.01 6.70 7.24 6.20 6.80 3.51 10.71 7.65 6.59 4.82 5.26 5.33 7.87 9.40 4.67 7.65 7.71

IR (p.a.) 0.14 0.08 0.13 0.07 0.08 0.10 0.00 0.12 0.22 0.24 0.14 0.01 0.12 0.11 -0.01 0.36 0.06

Alpha (% p.a.) 2.85 1.89 2.68 1.75 1.78 1.54 0.16 3.21 4.14 2.90 2.71 0.14 3.55 5.40 -0.34 5.61 2.54

Beta CR -0.01 -0.02 -0.02 -0.02 0.00 0.00 -0.07 -0.01 0.00 0.00 0.00 -0.01 -0.01 0.01 -0.01 -0.01 -0.03

Beta SNP 0.19 0.22 0.27 0.20 0.58 0.11 0.02 0.21 0.10 0.11 0.02 0.22 0.20 0.50 0.20 0.05 0.00

Beta SCM 0.11 0.20 0.23 0.19 0.24 -0.03 0.06 0.09 0.08 0.06 0.03 0.14 0.21 0.16 0.12 0.03 0.05

Beta BD10RET 0.17 0.13 0.09 0.13 0.10 0.09 0.09 -0.04 -0.03 0.05 0.19 0.19 0.20 0.08 0.14 0.01 0.36

Beta BAAmTSY 0.17 0.13 0.08 0.14 0.20 0.07 0.08 0.30 0.28 0.14 0.35 0.47 0.01 0.65 0.28 0.21 0.08

Beta PTFSBD 0.00 -0.01 0.00 0.00 -0.01 -0.01 -0.02 -0.04 -0.03 -0.01 -0.02 -0.01 -0.01 -0.04 -0.02 -0.01 0.02

Beta PTFSFX 0.02 0.01 0.01 0.00 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.05

Beta PTFSCOM 0.02 0.01 0.01 0.01 0.00 0.01 0.02 0.00 0.00 0.00 0.00 0.00 0.02 0.00 0.01 0.00 0.04

Beta Liq 0.04 0.03 0.03 0.00 0.05 0.03 0.03 0.04 0.02 0.00 0.02 0.05 0.04 0.06 0.05 0.02 0.04

t-stat Alpha 1.98 1.17 1.74 0.96 1.08 1.32 0.06 1.69 2.98 3.37 1.99 0.08 1.67 1.50 -0.21 4.99 0.89

t-stat CR -1.99 -2.37 -2.28 -2.22 -0.54 -0.68 -6.11 -1.45 -0.63 -1.15 -0.44 -1.62 -1.39 0.82 -1.99 -1.32 -2.11

t-stat SNP 7.66 8.08 10.57 6.59 20.70 5.45 0.37 6.62 4.18 7.74 0.73 7.83 5.51 8.24 7.36 2.65 -0.03

t-stat SCM 4.00 6.66 7.90 5.64 7.80 -1.55 1.21 2.64 3.00 3.67 1.27 4.38 5.29 2.43 3.86 1.57 0.88

t-stat BD10RET 3.57 2.53 1.88 2.23 1.81 2.52 1.14 -0.58 -0.72 1.90 4.36 3.56 2.97 0.72 2.72 0.21 3.88

t-stat BAAmTSY 3.31 2.12 1.51 2.08 3.36 1.62 0.89 4.39 5.49 4.45 7.09 7.64 0.17 4.99 4.75 5.14 0.78

t-stat PTFSBD -0.01 -0.99 -0.55 -0.40 -0.87 -2.26 -1.98 -4.19 -5.01 -2.68 -3.30 -0.88 -1.05 -2.23 -2.00 -1.75 1.73

t-stat PTFSFX 3.40 0.81 1.73 0.58 1.21 2.34 1.17 1.81 1.07 1.78 -0.77 0.18 0.93 0.56 1.73 0.18 4.56

t-stat PTFSCOM 2.42 1.08 1.03 1.00 0.56 1.41 1.57 -0.07 0.67 -0.73 0.30 -0.47 1.79 -0.05 1.44 -0.18 2.46

t-stat Liq 1.73 1.24 1.15 -0.03 1.82 1.41 0.77 1.27 0.83 0.14 0.75 1.70 1.05 0.98 1.83 1.10 0.85

adj R^2 46.46 51.02 59.73 41.38 81.38 24.14 21.50 51.95 48.23 51.03 33.85 61.36 29.87 51.94 50.84 32.19 27.90

Table A9: Return Decomposition of Hedge Fund Index Returns - TASS data

Panel A: FH -7 Model Alpha and Betas

All LSE EMKN ED FI CA MAC EMG FOF MULTI

HF ret (% p.a.) 7.93 9.12 5.92 7.60 4.45 5.19 9.29 9.27 4.54 6.73

Alpha (% p.a.) 5.28 5.81 4.72 5.80 2.55 3.17 6.57 5.37 2.14 3.42

Beta S&P 0.24 0.42 0.11 0.14 0.05 0.07 0.11 0.44 0.19 0.30

Beta SCM 0.14 0.33 0.00 0.08 0.01 0.01 -0.07 0.22 0.10 0.21

Beta BD10RET 0.14 0.08 0.06 -0.02 0.12 0.04 0.37 -0.01 0.11 0.16

Beta BAAmTSY 0.22 0.12 0.12 0.26 0.35 0.51 0.24 0.34 0.27 0.19

Beta PTFSBD -0.01 -0.01 -0.01 -0.03 -0.02 -0.02 -0.01 -0.03 -0.01 -0.02

Beta PTFSFX 0.01 0.01 0.01 0.01 -0.01 -0.01 0.01 0.01 0.01 0.00

Beta PTFSCOM 0.02 0.01 0.01 0.00 0.01 0.00 0.02 0.00 0.01 0.01

t-stat Alpha 3.92 3.57 5.50 6.64 2.27 2.79 2.50 2.01 1.75 1.65

t-stat S&P 8.85 13.01 6.57 8.08 2.27 3.04 2.19 8.44 7.76 7.37

t-stat SCM 4.28 8.69 -0.02 4.01 0.51 0.33 -1.15 3.44 3.60 4.25

t-stat BD10RET 2.53 1.23 1.74 -0.70 2.57 0.87 3.56 -0.07 2.20 1.97

t-stat BAAmTSY 3.55 1.62 3.13 6.66 6.92 9.89 1.98 2.86 4.88 2.02

t-stat PTFSBD -1.67 -1.00 -1.31 -4.80 -3.10 -2.77 -0.94 -2.01 -2.04 -1.93

t-stat PTFSFX 1.35 1.32 1.34 1.16 -1.10 -0.89 1.12 0.85 1.49 0.09

t-stat PTFSCOM 2.10 1.11 1.13 0.10 0.91 -0.11 1.40 0.23 1.69 1.01

adj R^2 46.04 62.88 28.66 61.41 34.67 51.92 8.67 45.31 45.55 37.26

Panel B: BKT


HF ret (% p.a.) 7.93 9.12 5.92 7.60 4.45 5.19 9.29 9.27 4.54 6.73

Alpha (% p.a.) 3.37 2.90 3.79 5.29 3.43 2.25 4.73 6.87 0.27 1.15

Beta CR -0.02 -0.02 -0.01 0.00 0.01 -0.01 -0.01 0.01 -0.02 -0.02

Beta S&P 0.22 0.39 0.10 0.13 0.06 0.06 0.09 0.46 0.17 0.28

Beta SCM 0.14 0.34 0.00 0.08 0.01 0.01 -0.07 0.21 0.11 0.21

Beta BD10RET 0.14 0.09 0.06 -0.02 0.11 0.04 0.38 -0.01 0.11 0.17

Beta BAAmTSY 0.21 0.11 0.12 0.26 0.35 0.50 0.23 0.35 0.26 0.18

Beta PTFSBD -0.01 -0.01 -0.01 -0.03 -0.02 -0.02 -0.02 -0.03 -0.02 -0.02

Beta PTFSFX 0.01 0.01 0.01 0.01 -0.01 0.00 0.02 0.01 0.01 0.00

Beta PTFSCOM 0.02 0.01 0.01 0.00 0.01 0.00 0.02 0.01 0.01 0.01

t-stat Alpha 2.05 1.47 3.61 4.93 2.49 1.61 1.47 2.10 0.18 0.45

t-stat CR -2.02 -2.55 -1.54 -0.83 1.10 -1.15 -0.99 0.80 -2.18 -1.55

t-stat S&P 7.61 11.40 5.61 7.24 2.51 2.43 1.69 8.16 6.54 6.35

t-stat SCM 4.42 8.94 0.06 4.04 0.45 0.40 -1.09 3.39 3.75 4.34

t-stat BD10RET 2.69 1.43 1.85 -0.64 2.49 0.95 3.62 -0.13 2.37 2.08

t-stat BAAmTSY 3.50 1.53 3.08 6.62 6.96 9.84 1.94 2.88 4.84 1.96

t-stat PTFSBD -1.77 -1.13 -1.39 -4.83 -3.05 -2.83 -0.98 -1.97 -2.16 -2.01

t-stat PTFSFX 1.44 1.43 1.41 1.19 -1.14 -0.85 1.16 0.82 1.59 0.15

t-stat PTFSCOM 1.86 0.81 0.94 0.00 1.03 -0.25 1.27 0.32 1.43 0.82

adj R^2 46.90 63.93 29.17 61.35 34.75 52.00 8.66 45.21 46.60 37.72

This table reports alpha and beta coefficiencts of hedge fund index returns for different investment objectives for the

TASS hedge fund data base. The investment objectives are all funds (ALL), Long/Short Equity (LSE), Equity Market

Neutral (EMKN), Event Driven (ED), Fixed Income (FI), Convertible Arbitrage (CA), Macro (MAC), Emerging Markets

(EMG), Funds of Funds (FoF) and Multi-Strategy (MUL). Panel A reports results based on the seven-factor Fung-Hsieh

model. The columns show the annualized hedge fund index return, the annualized alpha, the FH betas and the t-statistics

of the alpha and FH betas. Panel B reports the alphas for the BKT 8-factor model. Panel C is based on a 9-factor model

that includes the BKT model factors and a value-weighted index of individual options variance risk factor (VW Indiv.

VR). The sample period is January 1996 to June 2012.

Panel C: BKT + VW Indiv. VR


HF ret (% p.a.) 8.27 9.64 6.09 7.88 4.49 5.27 9.61 9.72 4.86 7.08

Alpha (% p.a.) 4.00 2.99 4.59 6.52 5.16 4.89 4.87 7.98 2.59 1.92

Beta CR -0.02 -0.03 -0.01 0.00 0.01 0.00 -0.02 0.01 -0.01 -0.02

Beta VW IVR -0.08 0.06 -0.14 -0.23 -0.38 -0.57 0.03 -0.19 -0.45 -0.12

Beta S&P 0.21 0.39 0.10 0.13 0.05 0.05 0.10 0.46 0.16 0.27

Beta SCM 0.14 0.34 0.00 0.08 0.00 -0.01 -0.07 0.21 0.09 0.21

Beta BD10RET 0.14 0.09 0.06 -0.04 0.09 0.01 0.38 -0.03 0.09 0.16

Beta BAAmTSY 0.19 0.12 0.09 0.21 0.28 0.38 0.23 0.30 0.17 0.16

Beta PTFSBD -0.01 -0.01 0.00 -0.02 -0.02 -0.02 -0.01 -0.03 -0.01 -0.02

Beta PTFSFX 0.01 0.01 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00

Beta PTFSCOM 0.02 0.01 0.00 0.00 0.01 0.00 0.02 0.01 0.01 0.01

t-stat Alpha 2.16 1.36 3.92 5.45 3.39 3.22 1.33 2.15 1.58 0.67

t-stat CR -1.97 -2.70 -1.38 -0.53 1.57 -0.38 -1.01 0.83 -1.73 -1.51

t-stat VW IVR -0.47 0.28 -1.29 -2.05 -2.61 -3.92 0.09 -0.55 -2.87 -0.45

t-stat S&P 7.41 11.26 5.23 6.86 1.96 1.92 1.68 7.91 6.07 6.11

t-stat SCM 4.25 8.87 -0.16 3.61 -0.05 -0.36 -1.03 3.19 3.22 4.13

t-stat BD10RET 2.47 1.43 1.63 -1.10 2.07 0.21 3.51 -0.29 1.81 1.91

t-stat BAAmTSY 2.68 1.43 2.08 4.61 4.86 6.62 1.66 2.11 2.75 1.41

t-stat PTFSBD -1.54 -0.77 -0.83 -4.44 -2.59 -2.80 -0.87 -1.86 -1.67 -1.78

t-stat PTFSFX 1.39 1.44 1.66 1.28 -0.77 -0.83 1.07 0.77 1.76 0.18

t-stat PTFSCOM 1.89 0.83 0.88 0.02 0.87 -0.29 1.30 0.34 1.43 0.74

adj R^2 46.85 64.04 29.17 61.60 35.97 55.56 8.17 44.71 48.50 36.98

Table A10: The Cross-section of Hedge Fund Excess Returns and Correlation Risk Exposure

GLS WLS GLS WLS

Intercept 0.33 0.51 0.33 0.51

tstat (8.39) (3.98) (7.77) (3.73)

Correl Risk -2.39 -4.65 -2.39 -4.65

tstat -(1.93) -(2.69) -(1.9) -(2.59)

Variance Rik (.26) (.1) (.26) (.1)

tstat (4.1) (1.31) (4.07) (1.28)

Mkt Risk 0.02 0.14 0.02 0.14

tstat (.07) (.29) (.07) (.28)

GLS WLS GLS WLS

Intercept 0.33 0.47 0.33 0.47

tstat (8.25) (3.88) (7.19) (3.52)

Correl Risk -2.50 -4.64 -2.50 -4.64

tstat -(2.02) -(2.72) -(1.96) -(2.56)

Variance Rik (.26) (.13) (.26) (.13)

tstat (4.08) (1.68) (4.01) (1.62)

Mkt Risk 0.04 0.08 0.04 0.08

tstat (.11) (.17) (.11) (.16)

SCMBC -0.40 -0.15 -0.40 -0.15

tstat -(1.45) -(.41) -(1.41) -(.39)

BD10RET 0.50 0.26 0.50 0.26

tstat (2.73) (.99) (2.64) (.93)

BAAmTSY -0.24 -0.01 -0.24 -0.01

tstat -(1.42) -(.04) -(1.38) -(.04)

PTFSBD -(1.01) -(.04) -(1.01) -(.04)

tstat -(.81) -(.02) -(.78) -(.02)

PTFSFX 3.31 0.35 3.31 0.35

tstat (2.13) (.15) (2.04) (.14)

PTFSCOM 0.28 -0.01 0.28 -0.01

tstat (.24) -(.01) (.23) -(.01)

This table reports estimates for the risk premia on the market index and the Fung and Hsieh (2004) factors, the correlation

risk factor (CR) as well as the value-weighted index of individual options variance risk factor (VW Indiv. VR, see Panel C

of Table 2 in the paper). Portfolios are formed based on rolling beta estimates. In Panel A, we report results for the market

and the correlation risk factor augmented by VW Indiv. VR (Model I). In Panel B, we report results for the BKT model

augmented by VW Indiv. VR. The estimation methods are GLS and WLS versions of the (Fama-MacBeth) two-pass

regression methodology. t-statistics are in brackets. t-statistics in columns four to six are calculated using standard errors

based Shanken (1992) errors-in-variables (EIV) adjustment. The cross-sectional regressions are based on 125 portfolios

(based on triple sorts using the market, size and correlation betas). Each year from January 1999 until 2011 funds are sorted

into these portfolios based on their betas calculated using the previous 36 monthly returns. The sample period is January

1996 to June 2012.

With Shanken's Correction


Panel A: Model 1 (Correlation Risk + Market Risk + VW Indiv. VR)

Panel B: Model 2 ( BKT + VW Indiv. VR)

Table A11: Return Decomposition of Equally-Weighted Hedge Fund Index Returns


All ALNE LSE LLNE EL EMN OPT ED DS MA FI CA MAC EMG FOF MUL MF

HF ret (% p.a.) 8.00 8.06 9.20 8.61 9.39 4.43 12.98 8.78 7.46 5.14 5.70 5.00 7.82 10.44 4.04 7.63 7.42

IR (p.a.) 0.37 0.38 0.36 0.34 0.27 0.30 0.29 0.44 0.28 0.36 0.29 0.12 0.28 0.15 0.07 0.47 0.30

Alpha (% p.a.) 5.42 5.97 6.67 6.66 4.86 3.40 10.00 6.16 4.95 3.67 3.70 1.94 5.18 5.81 1.33 5.91 6.41

Beta SNP 0.28 0.21 0.35 0.20 0.65 0.10 0.25 0.26 0.16 0.13 0.08 0.17 0.29 0.53 0.22 0.11 0.07

Beta SCM 0.15 0.17 0.26 0.19 0.36 0.01 0.05 0.15 0.10 0.05 -0.01 0.07 0.15 0.18 0.13 0.05 0.04

Beta BD10RET 0.09 0.05 0.04 0.05 0.01 0.06 0.22 -0.01 -0.03 0.07 0.14 0.14 0.15 -0.01 0.10 0.06 0.19

Beta BAAmTSY 0.25 0.19 0.10 0.16 0.28 0.06 0.37 0.30 0.42 0.14 0.34 0.59 0.10 0.52 0.31 0.32 0.09

Beta PTFSBD 0.00 -0.01 0.00 -0.01 -0.01 -0.01 0.00 -0.02 -0.04 -0.01 -0.02 -0.01 -0.01 -0.03 -0.02 -0.01 0.02

Beta PTFSFX 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.02 0.02 0.01 0.00 0.04

Beta PTFSCOM 0.01 0.00 0.01 0.01 0.00 0.00 0.01 0.00 0.00 0.00 0.00 -0.01 0.02 -0.01 0.01 0.00 0.04

t-stat Alpha 5.26 5.32 5.04 4.75 3.83 4.23 4.01 6.17 3.93 5.01 4.08 1.64 3.96 2.17 1.05 6.59 4.16

t-stat SNP 13.78 9.41 13.22 7.07 25.67 6.02 5.15 13.27 6.57 8.96 4.49 7.46 11.15 10.01 8.96 6.34 2.19

t-stat SCM 5.99 6.26 8.26 5.71 11.92 0.61 0.92 6.46 3.39 2.88 -0.56 2.45 4.87 2.83 4.32 2.34 1.00

t-stat BD10RET 2.16 1.23 0.68 0.84 0.16 1.83 2.21 -0.24 -0.66 2.43 3.76 2.87 2.87 -0.12 2.06 1.58 3.02

t-stat BAAmTSY 5.34 3.68 1.61 2.58 4.92 1.58 3.32 6.61 7.41 4.23 8.29 10.98 1.76 4.28 5.45 7.88 1.37

t-stat PTFSBD -0.39 -1.54 -0.50 -1.00 -0.70 -2.00 0.23 -4.01 -5.04 -2.16 -3.13 -1.85 -1.14 -1.91 -2.06 -1.43 1.94

t-stat PTFSFX 3.30 1.67 1.45 1.59 1.36 2.28 0.78 2.21 0.95 1.91 -0.51 -0.01 3.30 1.44 1.79 0.92 5.30

t-stat PTFSCOM 1.92 0.40 0.66 0.84 0.30 0.45 0.44 -0.10 0.02 -0.90 0.81 -1.01 2.41 -0.55 1.07 0.24 3.96

adj R^2 66.13 53.23 62.87 39.94 86.50 22.24 21.88 72.63 59.49 48.29 45.62 64.53 50.56 54.49 52.85 50.33 32.41

Panel B: BKT


HF ret (% p.a.) 8.00 8.06 9.20 8.61 9.39 4.43 12.98 8.78 7.46 5.14 5.70 5.00 7.82 10.44 4.04 7.63 7.42

IR (p.a.) 0.23 0.24 0.17 0.19 0.16 0.19 0.08 0.30 0.18 0.21 0.18 0.04 0.19 0.14 -0.01 0.32 0.19

Alpha (% p.a.) 4.09 4.69 3.83 4.56 3.58 2.62 3.12 5.11 3.95 2.68 2.74 0.88 4.28 6.49 -0.26 4.95 4.99

Beta CR -0.01 -0.01 -0.02 -0.02 -0.01 -0.01 -0.06 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 0.01 -0.01 -0.01 -0.01

Beta SNP 0.27 0.19 0.32 0.17 0.63 0.09 0.18 0.25 0.15 0.12 0.07 0.16 0.28 0.54 0.21 0.10 0.05

Beta SCM 0.15 0.17 0.26 0.19 0.36 0.01 0.07 0.15 0.10 0.05 -0.01 0.07 0.15 0.18 0.13 0.05 0.04

Beta BD10RET 0.09 0.06 0.05 0.06 0.01 0.06 0.25 -0.01 -0.03 0.07 0.14 0.14 0.15 -0.02 0.11 0.06 0.19

Beta BAAmTSY 0.24 0.18 0.09 0.16 0.28 0.06 0.36 0.29 0.42 0.14 0.34 0.58 0.10 0.52 0.31 0.32 0.09

Beta PTFSBD 0.00 -0.01 -0.01 -0.01 -0.01 -0.01 0.00 -0.02 -0.04 -0.01 -0.02 -0.01 -0.01 -0.03 -0.02 -0.01 0.02

Beta PTFSFX 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.02 0.02 0.01 0.00 0.04

Beta PTFSCOM 0.01 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 -0.01 0.00 -0.01 0.02 -0.01 0.01 0.00 0.04

t-stat Alpha 3.26 3.43 2.41 2.67 2.30 2.66 1.06 4.19 2.56 3.00 2.47 0.61 2.67 1.97 -0.17 4.52 2.65

t-stat CR -1.84 -1.61 -3.10 -2.13 -1.43 -1.38 -4.05 -1.50 -1.12 -1.93 -1.50 -1.27 -0.97 0.36 -1.78 -1.51 -1.31

t-stat SNP 12.29 8.25 11.51 5.90 23.52 5.13 3.55 11.89 5.73 7.74 3.66 6.52 10.05 9.45 7.77 5.39 1.58

t-stat SCM 6.12 6.36 8.60 5.87 12.01 0.69 1.18 6.55 3.45 3.01 -0.48 2.52 4.92 2.80 4.43 2.42 1.07

t-stat BD10RET 2.29 1.34 0.91 0.99 0.26 1.93 2.58 -0.14 -0.58 2.57 3.87 2.95 2.93 -0.15 2.19 1.69 3.11

t-stat BAAmTSY 5.29 3.62 1.52 2.51 4.87 1.52 3.28 6.57 7.37 4.18 8.25 10.94 1.72 4.28 5.40 7.84 1.31

t-stat PTFSBD -0.48 -1.61 -0.65 -1.11 -0.76 -2.07 0.05 -4.09 -5.09 -2.26 -3.20 -1.91 -1.18 -1.89 -2.15 -1.50 1.88

t-stat PTFSFX 3.39 1.74 1.60 1.69 1.41 2.34 0.97 2.27 1.00 2.00 -0.45 0.04 3.33 1.42 1.87 0.98 5.36

t-stat PTFSCOM 1.69 0.20 0.29 0.59 0.13 0.29 -0.03 -0.28 -0.11 -1.13 0.63 -1.15 2.28 -0.50 0.85 0.06 3.779

adj R^2 66.55 53.62 64.47 41.04 86.58 22.61 27.72 72.81 59.55 49.01 45.97 64.64 50.55 54.28 53.38 50.66 32.66

This table reports alpha and beta coefficiencts of equally-weighted hedge fund index returns for different investment objectives (see Table 1 in the

paper for abbreviations). Panel A reports results based on the seven-factor Fung-Hsieh model. The columns show the annualized hedge fund index

return, the annualized alpha, the betas and the t-statistics of the alpha and betas. Panel B reports the alphas for the BKT 8-factor model. The sample

period is January 1996 to June 2012.

Table A12: Return Decomposition of Hedge Fund Index Returns - Dispersion Trade Data



HF ret (% p.a.) 6.88 6.49 7.09 5.99 6.83 3.43 10.51 7.64 6.60 4.71 5.31 5.39 7.67 9.30 4.56 7.54 7.45

IR (p.a.) 0.29 0.22 0.27 0.18 0.13 0.16 0.29 0.24 0.32 0.35 0.22 0.11 0.23 0.10 0.10 0.53 0.19

Alpha (% p.a.) 4.65 4.05 4.64 3.66 2.53 2.12 8.98 5.09 4.83 3.31 3.28 2.07 5.35 4.03 1.79 6.53 6.05

Beta S&P 0.20 0.25 0.30 0.23 0.59 0.11 0.11 0.23 0.10 0.12 0.02 0.24 0.21 0.48 0.22 0.06 0.04

Beta SCM 0.10 0.20 0.22 0.19 0.24 -0.03 0.04 0.09 0.08 0.06 0.03 0.14 0.21 0.17 0.11 0.03 0.04

Beta BD10RET 0.15 0.11 0.08 0.12 0.08 0.09 0.06 -0.05 -0.04 0.05 0.18 0.17 0.19 0.08 0.12 0.00 0.34

Beta BAAmTSY 0.19 0.14 0.10 0.14 0.22 0.08 0.12 0.32 0.29 0.14 0.36 0.49 0.04 0.67 0.30 0.22 0.09

Beta PTFSBD 0.00 -0.01 -0.01 -0.01 -0.01 -0.01 -0.02 -0.04 -0.03 -0.01 -0.02 -0.01 -0.01 -0.04 -0.02 -0.01 0.02

Beta PTFSFX 0.02 0.00 0.01 0.00 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.05

Beta PTFSCOM 0.02 0.01 0.01 0.01 0.00 0.01 0.03 0.00 0.00 0.00 0.00 0.00 0.02 0.00 0.01 0.00 0.04

t-stat Alpha 4.03 3.12 3.73 2.50 1.90 2.30 4.13 3.41 4.45 4.91 3.10 1.55 3.21 1.43 1.38 7.40 2.65

t-stat S&P 8.97 9.55 12.15 7.96 22.33 6.22 2.53 7.74 4.81 8.88 0.99 9.15 6.45 8.64 8.67 3.30 0.89

t-stat SCM 3.83 6.45 7.62 5.44 7.65 -1.60 0.85 2.61 2.98 3.63 1.20 4.29 5.24 2.53 3.71 1.53 0.75

t-stat BD10RET 3.27 2.20 1.54 2.05 1.50 2.39 0.64 -0.81 -0.90 1.80 4.30 3.25 2.80 0.75 2.39 0.01 3.69

t-stat BAAmTSY 3.64 2.42 1.74 2.14 3.60 1.84 1.20 4.78 5.82 4.67 7.46 8.07 0.48 5.30 5.14 5.59 0.92

t-stat PTFSBD -0.28 -1.25 -0.96 -0.82 -1.39 -2.59 -1.65 -4.29 -5.19 -2.96 -3.40 -1.07 -0.99 -2.41 -2.18 -1.65 1.44

t-stat PTFSFX 3.14 0.59 1.46 0.40 0.92 2.10 0.79 1.75 1.12 1.78 -0.81 -0.08 0.98 0.56 1.48 0.15 4.31

t-stat PTFSCOM 2.45 1.28 1.18 1.25 0.45 1.41 2.22 -0.11 0.49 -0.55 0.27 -0.38 1.91 -0.28 1.48 -0.12 2.59

adj R^2 44.71 50.00 58.75 40.70 81.13 24.65 6.62 52.51 49.38 51.89 34.60 61.23 29.35 52.68 49.99 32.06 25.14

Panel B: BKT 8-Factor Model


HF ret (% p.a.) 6.88 6.49 7.09 5.99 6.83 3.43 10.51 7.64 6.60 4.71 5.31 5.39 7.67 9.30 4.56 7.54 7.45

IR (p.a.) 0.23 0.14 0.19 0.10 0.11 0.13 0.16 0.21 0.32 0.29 0.22 0.08 0.17 0.11 0.05 0.48 0.14

Alpha (% p.a.) 3.89 2.75 3.42 2.25 2.19 1.80 4.62 4.61 5.12 2.85 3.47 1.58 4.28 4.47 0.94 6.31 4.58

Beta CR -0.01 -0.02 -0.02 -0.02 0.00 0.00 -0.06 -0.01 0.00 -0.01 0.00 -0.01 -0.01 0.01 -0.01 0.00 -0.02

Beta S&P 0.19 0.22 0.28 0.21 0.58 0.11 0.03 0.22 0.11 0.11 0.02 0.23 0.19 0.49 0.21 0.05 0.02

Beta SCM 0.11 0.20 0.23 0.19 0.24 -0.03 0.06 0.09 0.08 0.06 0.03 0.14 0.21 0.17 0.12 0.03 0.04

Beta BD10RET 0.16 0.13 0.09 0.13 0.08 0.09 0.10 -0.04 -0.04 0.05 0.18 0.18 0.20 0.08 0.13 0.00 0.35

Beta BAAmTSY 0.19 0.14 0.10 0.14 0.22 0.08 0.12 0.32 0.28 0.14 0.36 0.49 0.04 0.67 0.30 0.22 0.10

Beta PTFSBD 0.00 -0.01 -0.01 -0.01 -0.01 -0.01 -0.02 -0.04 -0.03 -0.01 -0.02 -0.01 -0.01 -0.04 -0.02 -0.01 0.02

Beta PTFSFX 0.02 0.00 0.01 0.00 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.05

Beta PTFSCOM 0.02 0.01 0.01 0.01 0.00 0.01 0.02 0.00 0.00 0.00 0.00 0.00 0.02 0.00 0.01 0.00 0.03

t-stat Alpha 3.20 2.03 2.65 1.47 1.55 1.85 2.19 2.91 4.44 4.02 3.08 1.11 2.44 1.50 0.68 6.73 1.90

t-stat CR -1.89 -2.89 -2.81 -2.77 -0.71 -0.97 -6.21 -0.91 0.74 -1.94 0.50 -1.03 -1.82 0.44 -1.87 -0.71 -1.84

t-stat S&P 8.10 8.48 11.02 6.95 21.13 5.67 0.85 7.14 4.81 8.00 1.09 8.46 5.68 8.38 7.81 2.95 0.32

t-stat SCM 3.93 6.69 7.87 5.65 7.66 -1.56 1.19 2.64 2.95 3.74 1.18 4.33 5.34 2.50 3.81 1.56 0.83

t-stat BD10RET 3.44 2.47 1.80 2.30 1.55 2.46 1.20 -0.73 -0.95 1.97 4.24 3.32 2.96 0.71 2.55 0.07 3.86

t-stat BAAmTSY 3.69 2.50 1.80 2.21 3.60 1.85 1.39 4.79 5.81 4.73 7.44 8.08 0.50 5.28 5.20 5.59 0.95

t-stat PTFSBD -0.36 -1.40 -1.11 -0.97 -1.42 -2.63 -2.09 -4.33 -5.14 -3.07 -3.37 -1.11 -1.08 -2.38 -2.28 -1.68 1.36

t-stat PTFSFX 3.15 0.58 1.47 0.39 0.92 2.09 0.82 1.74 1.13 1.78 -0.81 -0.09 0.97 0.56 1.47 0.15 4.32

t-stat PTFSCOM 2.18 0.90 0.81 0.89 0.35 1.26 1.56 -0.24 0.58 -0.82 0.33 -0.52 1.66 -0.22 1.22 -0.21 2.33

adj R^2 45.45 51.86 60.19 42.71 81.09 24.63 22.01 52.46 49.26 52.59 34.34 61.25 30.20 52.48 50.64 31.88 26.07

This table reproduces the analysis in Table 2 of the paper using disperision trade instead of correlation swap data for the correlation risk factor.

This table reports alpha and beta coefficiencts of hedge fund index returns for different investment objectives using the BarclayHedge database.

All Low Net Exposure (ALNE) funds are all hedge funds that are reported to have a net long/short exposure below 30 percent. LSE Low Net

Exposure (LLNE) funds are Long/Short Equity (LSE) funds that are reported to have a net long/short exposure below 30 percent. The other

investment objectives are Equity Long (EL), Equity Market Neutral (EMN), Option Trader (OPT), Event Driven (ED), Distressed Securities

(DS), Merger Arbitrage (MA), Fixed Income (FI), Convertible Arbitrage (CA), Macro (MAC), Emerging Markets (EMG), Funds of Funds

(FoF), Multi-Strategy (MUL) and Managed Futures (MF). Panel A reports results based on the seven-factor Fung-Hsieh model. The columns

show the annualized hedge fund index return, the annualized alpha, the FH betas and the t-statistics of the alpha and FH betas. Panel B reports

the alphas for the BKT 8-factor model (based on implied correlations from dispersion trades). Panel C is based on a 9-factor model that

includes the BKT model factors and a value-weighted index of individual options variance risk factor (VW Indiv. VR). For Panels A and B

(Panel C) the sample period is January 1996 to June 2012 (February 2012).



HF ret (% p.a.) 7.18 6.86 7.48 6.37 7.30 3.60 10.66 7.98 6.83 4.89 5.36 5.63 7.92 9.94 4.87 7.70 7.76

IR (p.a.) 0.25 0.17 0.18 0.11 0.13 0.17 0.18 0.25 0.37 0.32 0.25 0.16 0.13 0.18 0.15 0.44 0.14

Alpha (% p.a.) 4.86 3.62 3.71 2.71 2.84 2.69 6.01 6.39 6.80 3.67 4.52 3.69 3.67 8.36 3.30 6.70 5.37

Beta CR -0.01 -0.02 -0.01 -0.02 0.00 0.00 -0.06 0.00 0.01 0.00 0.00 0.00 -0.01 0.01 -0.01 0.00 -0.02

Beta VW IVR -0.14 -0.11 0.04 -0.01 -0.02 -0.15 -0.39 -0.37 -0.37 -0.16 -0.26 -0.45 0.19 -0.74 -0.49 -0.06 -0.07

Beta S&P 0.19 0.22 0.28 0.21 0.58 0.10 0.02 0.21 0.10 0.11 0.02 0.22 0.20 0.47 0.20 0.05 0.01

Beta SCM 0.10 0.20 0.23 0.19 0.24 -0.04 0.04 0.08 0.06 0.05 0.02 0.12 0.22 0.14 0.10 0.03 0.04

Beta BD10RET 0.15 0.12 0.09 0.13 0.08 0.08 0.07 -0.07 -0.06 0.04 0.17 0.15 0.21 0.03 0.10 0.00 0.35

Beta BAAmTSY 0.16 0.12 0.11 0.15 0.22 0.05 0.04 0.24 0.21 0.11 0.30 0.40 0.07 0.51 0.20 0.21 0.09

Beta PTFSBD 0.00 -0.01 0.00 0.00 -0.01 -0.01 -0.02 -0.04 -0.03 -0.01 -0.02 -0.01 -0.01 -0.04 -0.01 -0.01 0.02

Beta PTFSFX 0.02 0.00 0.01 0.00 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.05

Beta PTFSCOM 0.02 0.01 0.01 0.01 0.00 0.01 0.02 0.00 0.01 0.00 0.00 0.00 0.02 0.00 0.01 0.00 0.04

t-stat Alpha 3.48 2.33 2.50 1.54 1.76 2.40 2.47 3.51 5.19 4.50 3.49 2.29 1.81 2.44 2.13 6.17 1.94

t-stat CR -1.37 -2.41 -2.47 -2.43 -0.34 -0.47 -5.77 -0.41 1.32 -1.36 0.80 -0.38 -1.83 1.04 -1.08 -0.47 -1.54

t-stat VW IVR -0.92 -0.68 0.24 -0.03 -0.09 -1.28 -1.50 -1.90 -2.58 -1.77 -1.85 -2.56 0.87 -2.01 -2.92 -0.53 -0.22

t-stat S&P 7.84 8.21 10.89 6.80 20.86 5.36 0.54 6.74 4.40 7.56 0.73 7.92 5.75 8.01 7.33 2.87 0.27

t-stat SCM 3.70 6.43 7.79 5.54 7.56 -1.77 0.88 2.24 2.46 3.33 0.82 3.80 5.37 2.07 3.27 1.41 0.79

t-stat BD10RET 3.14 2.27 1.81 2.27 1.53 2.10 0.87 -1.11 -1.43 1.60 3.82 2.80 3.01 0.22 1.94 -0.08 3.71

t-stat BAAmTSY 2.68 1.80 1.72 1.93 3.09 0.95 0.42 3.05 3.62 3.11 5.39 5.64 0.83 3.41 3.00 4.37 0.76

t-stat PTFSBD 0.04 -1.00 -0.64 -0.52 -0.86 -2.16 -2.02 -4.07 -4.88 -2.67 -3.16 -0.69 -1.12 -2.10 -1.82 -1.63 1.70

t-stat PTFSFX 3.22 0.67 1.58 0.54 1.07 2.27 0.90 1.74 1.13 1.87 -0.72 0.13 0.79 0.61 1.67 0.05 4.42

t-stat PTFSCOM 2.27 0.96 0.87 0.93 0.38 1.29 1.51 -0.15 0.74 -0.82 0.37 -0.55 1.74 -0.18 1.34 -0.13 2.38

adj R^2 45.62 51.26 59.86 41.89 81.11 24.27 22.40 52.53 50.33 52.41 35.01 62.05 30.11 53.00 52.21 31.48 26.68

Table A13: Return Decomposition of Hedge Fund Index Returns -Dispersion Trade and TASS Data



HF ret (% p.a.) 7.93 9.12 5.92 7.60 4.45 5.19 9.29 9.27 4.54 6.73

Alpha (% p.a.) 5.28 5.81 4.72 5.80 2.55 3.17 6.57 5.37 2.14 3.42

Beta S&P 0.24 0.42 0.11 0.14 0.05 0.07 0.11 0.44 0.19 0.30

Beta SCM 0.14 0.33 0.00 0.08 0.01 0.01 -0.07 0.22 0.10 0.21

Beta BD10RET 0.14 0.08 0.06 -0.02 0.12 0.04 0.37 -0.01 0.11 0.16

Beta BAAmTSY 0.22 0.12 0.12 0.26 0.35 0.51 0.24 0.34 0.27 0.19

Beta PTFSBD -0.01 -0.01 -0.01 -0.03 -0.02 -0.02 -0.01 -0.03 -0.01 -0.02

Beta PTFSFX 0.01 0.01 0.01 0.01 -0.01 -0.01 0.01 0.01 0.01 0.00

Beta PTFSCOM 0.02 0.01 0.01 0.00 0.01 0.00 0.02 0.00 0.01 0.01

t-stat Alpha 3.92 3.57 5.50 6.64 2.27 2.79 2.50 2.01 1.75 1.65

t-stat S&P 8.85 13.01 6.57 8.08 2.27 3.04 2.19 8.44 7.76 7.37

t-stat SCM 4.28 8.69 -0.02 4.01 0.51 0.33 -1.15 3.44 3.60 4.25

t-stat BD10RET 2.53 1.23 1.74 -0.70 2.57 0.87 3.56 -0.07 2.20 1.97

t-stat BAAmTSY 3.55 1.62 3.13 6.66 6.92 9.89 1.98 2.86 4.88 2.02

t-stat PTFSBD -1.67 -1.00 -1.31 -4.80 -3.10 -2.77 -0.94 -2.01 -2.04 -1.93

t-stat PTFSFX 1.35 1.32 1.34 1.16 -1.10 -0.89 1.12 0.85 1.49 0.09

t-stat PTFSCOM 2.10 1.11 1.13 0.10 0.91 -0.11 1.40 0.23 1.69 1.01

adj R^2 46.04 62.88 28.66 61.41 34.67 51.92 8.67 45.31 45.55 37.26

Panel B: BKT


HF ret (% p.a.) 7.93 9.12 5.92 7.60 4.45 5.19 9.29 9.27 4.54 6.73

Alpha (% p.a.) 4.34 4.01 4.22 5.77 2.99 3.24 6.00 5.48 1.16 2.51

Beta CR -0.01 -0.02 -0.01 0.00 0.01 0.00 -0.01 0.00 -0.01 -0.01

Beta S&P 0.22 0.39 0.10 0.14 0.06 0.07 0.10 0.45 0.17 0.29

Beta SCM 0.14 0.34 0.00 0.08 0.01 0.01 -0.07 0.22 0.11 0.21

Beta BD10RET 0.15 0.10 0.06 -0.02 0.11 0.04 0.38 -0.01 0.12 0.17

Beta BAAmTSY 0.22 0.12 0.12 0.26 0.35 0.51 0.24 0.34 0.27 0.19

Beta PTFSBD -0.01 -0.01 -0.01 -0.03 -0.02 -0.02 -0.02 -0.03 -0.02 -0.02

Beta PTFSFX 0.01 0.01 0.01 0.01 -0.01 -0.01 0.01 0.01 0.01 0.00

Beta PTFSCOM 0.02 0.01 0.00 0.00 0.01 0.00 0.02 0.00 0.01 0.01

t-stat Alpha 3.06 2.38 4.66 6.21 2.51 2.68 2.15 1.93 0.90 1.14

t-stat CR -1.99 -3.20 -1.66 -0.09 1.12 0.16 -0.61 0.12 -2.29 -1.25

t-stat S&P 7.96 11.82 5.84 7.69 2.49 2.95 1.92 8.09 6.85 6.71

t-stat SCM 4.40 9.02 0.05 4.00 0.47 0.32 -1.12 3.43 3.74 4.30

t-stat BD10RET 2.71 1.52 1.88 -0.69 2.47 0.85 3.60 -0.08 2.41 2.06

t-stat BAAmTSY 3.60 1.69 3.17 6.64 6.91 9.86 1.99 2.85 4.96 2.04

t-stat PTFSBD -1.77 -1.17 -1.40 -4.79 -3.05 -2.76 -0.96 -1.99 -2.17 -1.99

t-stat PTFSFX 1.35 1.32 1.34 1.15 -1.09 -0.89 1.11 0.85 1.49 0.08

t-stat PTFSCOM 1.83 0.69 0.90 0.09 1.05 -0.09 1.30 0.24 1.38 0.84

adj R^2 46.87 64.60 29.32 61.21 34.76 51.67 8.37 45.03 46.73 37.44

This table reports alpha and beta coefficiencts of hedge fund index returns for different investment objectives for the TASS hedge fund data

base. The investment objectives are all funds (ALL), Long/Short Equity (LSE), Equity Market Neutral (EMKN), Event Driven (ED), Fixed

Income (FI), Convertible Arbitrage (CA), Macro (MAC), Emerging Markets (EMG), Funds of Funds (FoF) and Multi-Strategy (MUL).

Panel A reports results based on the seven-factor Fung-Hsieh model. The columns show the annualized hedge fund index return, the

annualized alpha, the FH betas and the t-statistics of the alpha and FH betas. Panel B reports the alphas for the BKT 8-factor model (based

on implied correlations from dispersion trades). Panel C is based on a 9-factor model that includes the BKT model factors and a value-

weighted index of individual options variance risk factor (VW Indiv. VR). The sample period is January 1996 to June 2012.



HF ret (% p.a.) 8.27 9.64 6.09 7.88 4.49 5.27 9.61 9.72 4.86 7.08

Alpha (% p.a.) 5.08 4.26 5.05 7.16 4.64 5.71 6.44 6.64 3.40 3.49

Beta CR -0.01 -0.02 0.00 0.00 0.01 0.00 -0.01 0.00 -0.01 -0.01

Beta VW IVR -0.09 0.07 -0.15 -0.26 -0.38 -0.60 -0.01 -0.16 -0.46 -0.15

Beta S&P 0.22 0.39 0.10 0.13 0.04 0.05 0.11 0.45 0.16 0.28

Beta SCM 0.14 0.34 0.00 0.07 0.00 -0.01 -0.07 0.21 0.09 0.20

Beta BD10RET 0.14 0.10 0.06 -0.04 0.09 0.00 0.38 -0.03 0.09 0.16

Beta BAAmTSY 0.19 0.14 0.10 0.21 0.28 0.38 0.23 0.30 0.18 0.16

Beta PTFSBD -0.01 -0.01 0.00 -0.02 -0.02 -0.02 -0.01 -0.03 -0.01 -0.02

Beta PTFSFX 0.01 0.01 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00

Beta PTFSCOM 0.02 0.01 0.00 0.00 0.01 0.00 0.02 0.01 0.01 0.01

t-stat Alpha 3.10 2.19 4.88 6.77 3.45 4.27 1.99 2.02 2.34 1.37

t-stat CR -1.60 -2.87 -1.16 0.63 1.64 0.91 -0.46 0.35 -1.47 -0.96

t-stat VW IVR -0.53 0.33 -1.32 -2.28 -2.63 -4.17 -0.02 -0.46 -2.90 -0.55

t-stat S&P 7.77 11.67 5.48 7.34 1.91 2.32 1.92 7.88 6.37 6.46

t-stat SCM 4.19 8.88 -0.19 3.52 -0.03 -0.46 -1.08 3.23 3.18 4.06

t-stat BD10RET 2.45 1.50 1.62 -1.23 2.02 0.06 3.45 -0.25 1.81 1.86

t-stat BAAmTSY 2.72 1.60 2.12 4.48 4.74 6.47 1.64 2.11 2.79 1.42

t-stat PTFSBD -1.56 -0.87 -0.85 -4.36 -2.53 -2.71 -0.86 -1.86 -1.70 -1.78

t-stat PTFSFX 1.30 1.32 1.60 1.28 -0.70 -0.83 1.03 0.80 1.69 0.12

t-stat PTFSCOM 1.91 0.78 0.88 0.16 0.90 -0.12 1.36 0.29 1.44 0.79

adj R^2 46.47 64.21 28.96 61.62 36.04 55.73 7.76 44.54 48.27 36.52

Table A14: The Cross-section of Hedge Fund Excess Returns and Correlation Risk Exposures - Dispersion Trade Data

GLS WLS GLS WLS

Intercept 0.32 0.42 0.32 0.42

tstat (5.29) (2.92) (4.71) (2.78)

Correl Risk -9.06 -5.78 -9.06 -5.78

tstat -(6.03) -(2.6) -(5.84) -(2.51)

Mkt Risk 0.15 0.19 0.15 0.19

tstat (.41) (.4) (.4) (.39)

GLS WLS GLS WLS

Intercept 0.32 0.33 0.32 0.33

tstat (5.09) (2.45) (4.38) (2.2)

Correl Risk -9.11 -5.37 -9.11 -5.37

tstat -(6.05) -(2.42) -(5.79) -(2.25)

Mkt Risk 0.16 0.25 0.16 0.25

tstat (.44) (.53) (.43) (.5)

SCMBC -0.44 0.26 -0.44 0.26

tstat -(1.59) (.68) -(1.54) (.63)

BD10RET 0.10 -0.19 0.10 -0.19

tstat (.54) -(.73) (.51) -(.68)

BAAmTSY -0.26 -0.20 -0.26 -0.20

tstat -(1.55) -(.89) -(1.5) -(.84)

PTFSBD 3.87 1.40 3.87 1.40

tstat (3.04) (.7) (2.89) (.64)

PTFSFX 3.36 6.43 3.36 6.43

tstat (2.01) (2.58) (1.89) (2.38)

PTFSCOM 1.80 1.11 1.80 1.11

tstat (1.49) (.61) (1.41) (.56)

This table reproduces the analysis in Table 5 of the paper using dispersion trade instead of correlation swap data for the correlation risk

factor. Portfolios are formed based on rolling beta estimates. This table reports estimates for the risk premia on the market index, the Fung

and Hsieh (2004) factors and the correlation risk factor (CR). In Panel A, we report results for the market and the correlation risk factor

(Model I). In Panel B, we report results for the BKT eight-factor model. The estimation methods are GLS and WLS versions of the (Fama-

MacBeth) two-pass regression methodology. t-statistics are in brackets. t-statistics in columns four to six are calculated using standard

errors based on Shanken (1992) errors-in-variables (EIV) adjustment. The cross-sectional regressions are based on 125 portfolios (based

on triple sorts using the market, size and correlation betas). Each year from January 1999 until 2011 funds from the BarclayHedge

database are sorted into these portfolios based on their betas calculated using the previous 36 monthly returns. The sample period is


Panel A: Model 1 (Correlation Risk and Market Risk)


Panel B: Model 2 (Correlation risk factor and FH(2004) Model)


Table A15: The Cross-section of Hedge Fund Excess Returns and Correlation Risk Exposures - Dispersion Trade / TASS Data

GLS WLS GLS WLS

Intercept 0.30 0.45 0.30 0.45

tstat (6.64) (3.34) (6.03) (3.07)

Correl Risk -8.14 -7.31 -8.14 -7.31

tstat -(5.55) -(3.47) -(5.43) -(3.29)

Mkt Risk 0.12 -0.06 0.12 -0.06

tstat (.34) -(.13) (.34) -(.12)

GLS WLS GLS WLS

Intercept 0.29 0.50 0.29 0.50

tstat (6.27) (4.07) (5.41) (3.68)

Correl Risk -8.50 -7.41 -8.50 -7.41

tstat -(5.77) -(3.56) -(5.56) -(3.33)

Mkt Risk 0.16 -0.03 0.16 -0.03

tstat (.47) -(.07) (.46) -(.07)

SCMBC 0.24 -0.13 0.24 -0.13

tstat (.85) -(.34) (.83) -(.32)

BD10RET 0.44 0.19 0.44 0.19

tstat (2.39) (.74) (2.29) (.69)

BAAmTSY -0.29 -0.30 -0.29 -0.30

tstat -(1.74) -(1.5) -(1.69) -(1.43)

PTFSBD -0.74 0.52 -0.74 0.52

tstat -(.6) (.29) -(.58) (.27)

PTFSFX 2.41 1.62 2.41 1.62

tstat (1.53) (.75) (1.46) (.7)

PTFSCOM 1.15 -0.07 1.15 -0.07

tstat (.96) -(.04) (.91) -(.04)

This table reproduces the analysis in Table 6 of the paper using dispersion trade instead of correlation swap data for the correlation risk

factor. Portfolios are formed based on rolling beta estimates. This table reports estimates for the risk premia on the market index, the Fung

and Hsieh (2004) factors and the correlation risk factor (CR). In Panel A, we report results for the market and the correlation risk factor

(Model I). In Panel B, we report results for the BKT eight-factor model. The estimation methods are GLS and WLS versions of the (Fama-

MacBeth) two-pass regression methodology. t-statistics are in brackets. t-statistics in columns four to six are calculated using standard

errors based on Shanken (1992) errors-in-variables (EIV) adjustment. The cross-sectional regressions are based on 125 portfolios (based

on triple sorts using the market, size and correlation betas). Each year from January 1999 until 2011 funds from the TASS database are

sorted into these portfolios based on their betas calculated using the previous 36 monthly returns. The sample period is January 1996 to

June 2012.

Panel A: Model 1 (Correlation Risk and Market Risk)


Panel B: Model 2 (Correlation risk factor and FH(2004) Model)


Figure A1: Moving Average Plot of Correlation Risk Premium and S&P500 Return

This figure plots the 12-month moving average of the return of the correlation swap (based on correlation swap market

quotes and abbreviated CR_MA) and the S&P500 return (S&P_RF_MA) over time. The sample period is from


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This figure shows the six-month moving average of the implied (IC_MA) and the realized (RC_MA)

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Figure A2: Implied and Realized Correlation from Correlation Swap Quotes

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Online Appendix ™When There is No Place to Hide ... · The BKT model is an 8-factor model that consists of the FH-seven factor model augmented by the correlation risk factor.1 Table

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