Table 4. + γ 2 BEAR i

Full text

(1)

Stock Volatility Following Hedge Funds’ Reported Holdings

This table reports the output from cross-sectional regressions of future excess volatility against aggregate hedge fund demand for holding options on a particular security. For each of the three months following each quarter end we estimate the following two models:

Model 1: U V OLi = α + γDIRi+ δN ON DIRi+ i

Model 2: U V OLi = α + γ1BU LLi+ γ2BEARi+ δ1P P U Ti+ δ2ST RADi+ i,

where DIRi is the proportion of advisors disclosing a directional option position on underlying security i, among all advisors that hold at least one stock or option position in security i during the quarter.

N ON DIRi, BU LLi, BEARi, P P U Ti, and ST RADi are defined similarly for nondirectional, directional call, directional put, protective put, and straddle option positions, respectively. U V OLi denotes the difference between V OLi, the annualized realized volatility (sum of squared daily stock returns) of security i’s stock return over the subsequent month, and IV OLi, the annualized monthly lagged Black-Scholes implied volatility for security i. The table lists the annual averages of monthly estimates. The final rows report the full sample average of the monthly estimates along with t-statistics. Standard errors of the average coefficients are adjusted for the estimated autocorrelation of the coefficients. Raw data are winsorized at 99.5% and 0.5%. Robust t statistics are reported in final row of each panel. +, *, and **

denote significance at the 10%, 5%, and 1% levels. Results are reported for hedge fund Sample A.

Model 1 Model 2

Year cons DIR N ON DIR cons BU LL BEAR P P U T ST RAD

1999 -3.93 4.40 33.14 -3.93 5.10 5.11 31.51 69.12

2000 -2.39 2.70 27.56 -2.42 -3.52 18.83 26.75 62.37

2001 -3.96 0.21 23.63 -3.96 -5.68 14.02 23.86 1.50

2002 -1.65 -8.38 6.76 -1.69 -15.03 -1.39 10.16 22.09

2003 -4.54 -1.44 2.33 -4.53 -0.62 -2.32 5.92 -0.87

2004 -5.17 5.66 5.98 -5.20 7.63 -0.63 -1.56 13.19

2005 -5.61 -0.48 3.33 -5.66 -2.60 -2.21 -9.94 16.29

2006 -4.42 0.43 2.52 -4.43 -2.03 3.24 -4.79 6.91

1999-06 -3.96 0.39 13.16 -3.98 -2.09 4.33 10.24 23.83

t-statistic -5.53** 0.21 3.86** -5.56** -0.97 1.51 2.55** 2.66**

(2)

Stock Volatility Following Hedge Funds’ Reported Holdings Using Alternative Volatility Specifications

This table reports the output from alternative cross-sectional volatility forecasting regressions. First, for each of the three months following each quarter end we estimate the following two models:

Model 1: U V OLi = α + γDIRi+ δN ON DIRi+ i

Model 2: U V OLi = α + γ1BU LLi+ γ2BEARi+ δ1P P U Ti+ δ2ST RADi+ i,

where DIRi is the proportion of advisors disclosing a directional option position on underlying security i, among all advisors that hold at least one stock or option position in security i during the quarter.

N ON DIRi, BU LLi, BEARi, P P U Ti, and ST RADi are defined similarly for nondirectional, directional call, directional put, protective put, and straddle option positions, respectively. U V OLidenotes a measure of annualized excess volatility for stock i. In Panels A and B the dependent variable in each regression is replaced with V OL, while lagged monthly V OL and lagged monthly Black-Scholes implied volatility (IV OL) are included together as independent variables. Panel A takes V OL as the realized volatility measure calculated as in Eq. (1). Panel B takes V OL as the squared log price change over the horizon:

V OLit+k =

ln(Si,t+k0 /Si,t+k)2

×D252

i,t+k, where Si,t+k0 is the closing price of stock i on the third Friday of month t+k, Si,t+kis the opening price of stock i on the first day of month t+k, and Di,t+kis the number of daily return observations in month t + k up to an including the third Friday of the month, k = 1, 2, 3. The coefficients on lagged VOL and IVOL are estimated but not reported in the table. Panel C takes U V OL as (V OL − IV OL)/IV OL, where V OL is calculated as in Eq. (1). Panel D takes U V OL as the difference between V OL and IV OL, where V OL is calculated using the following autocovariance-adjusted realized volatility measure: V OLit+k=

r PDi,t+k

d=1 r2itd+ 2PDi,t+k

d=1 ritdrit,d−1

D252

i,t+k. The table reports the full sample average of the monthly estimates. t-statistics are reported below sample averages. +, *, and **

denote significance at the 10%, 5%, and 1% levels. Standard errors of the average coefficients are adjusted for the estimated autocorrelation of the coefficients. Raw data are winsorized at 99.5% and 0.5%. Results are reported for hedge fund Sample A.

Model 1 Model 2

cons DIR N ON DIR cons BU LL BEAR P P U T ST RAD

Panel A: Including lagged VOL and IVOL as regressors

estimate 3.39 1.79 13.06 3.38 -0.63 6.24 13.62 18.44

t-statistic 5.16** 0.95 4.02** 5.14** -0.30 1.92+ 3.56** 2.24*

Panel B: VOL calculated as the squared log price change

estimate -14.84 -0.29 16.68 -14.85 1.66 -5.13 16.57 26.22 t-statistic -10.54** -0.08 1.69+ -10.54** 0.36 -0.77 1.59 0.84 Panel C: UVOL scaled by IVOL

estimate -8.21 1.59 19.87 -8.23 -2.39 7.10 15.69 32.72

t-statistic -6.32** 0.57 3.93** -6.35** -0.70 1.70+ 2.87** 2.27*

(3)

Stock Returns Following Hedge Funds’ Reported Holdings

This table reports the output from cross-sectional regressions of future abnormal stock returns against aggregate hedge fund demand for holding stocks and options on a particular security. For each of the three months following each quarter end we estimate the following two models:

Model 1: Ri− Rib= α + βCOMi+ γDIRi+ δN ON DIRi+ i

Model 2: Ri− Rib= α + βCOMi+ γ1BU LLi+ γ2BEARi+ δ1P P U Ti+ δ2ST RADi+ i For each quarter end and underlying security i, Ri− Rib is the realized common stock return for security i in excess of the return on a size, book-to-market, and momentum characteristics-based benchmark portfolio over the 1, 2, and 3 months following the quarter end. DIRi is the proportion of advisors disclosing a directional option position on underlying security i, among all advisors that hold at least one stock or option position in security i during the quarter. N ON DIRi, BU LLi, BEARi, P P U Ti, and ST RADi are defined similarly for nondirectional, directional call, directional put, protective put, and straddle option positions, respectively. In Panel A COMi is the proportion of advisors disclosing a stock position, among all advisors filing Form 13F during the quarter. The table lists the annual averages of monthly estimates.

The final rows report the full sample average of the monthly estimates along with t-statistics. Panels B and C show full sample averages when stock ownership is defined as in Griffin and Xu (2009). Panel B takes COMi as the weight of stock i in the aggregate stock portfolio held by the sample hedge fund advisors, and Panel C takes COMi as the quarterly change in the aggregate fraction of stock i’s outstanding shares held by our sample advisors. All COM variables in Panels B and C are standardized to have zero mean and unit variance over the sample period. Results are also presented when COM is measured each quarter separately for advisor subsamples depending on whether the advisor holds fewer than (COM -F EW ) or more than (COM -M AN Y ) the sample median number of separate stock positions in Form 13F filings.

t-statistics are reported below sample averages. +, *, and ** denote significance at the 10%, 5%, and 1%

levels. Raw data are winsorized at 99.5% and 0.5%. Results are reported for hedge fund Sample A.

Panel A: Regressions of stock returns on stock and option positions

Model 1 Model 2

year cons COM DIR N ON DIR cons COM BU LL BEAR P P U T ST RAD

1999 -0.15 5.01 -1.46 -8.22 -0.14 4.61 8.26 -11.65 0.57 -23.84

2000 -0.40 7.72 -3.86 -16.44 -0.43 8.40 -2.67 -11.77 -26.23 -8.23 2001 0.75 -2.86 -3.69 -10.25 0.77 -3.17 0.53 -13.81 -10.53 -0.15 2002 -0.79 6.40 -6.90 -12.12 -0.78 6.00 -6.30 -8.31 -8.55 -11.46

2003 0.45 0.08 -4.17 1.97 0.46 -0.15 -4.29 -4.40 -3.56 5.16

2004 -0.52 6.44 -2.97 -1.19 -0.54 6.90 -1.88 -5.34 1.66 -3.98

2005 0.07 2.49 -3.70 -0.15 0.10 1.74 -1.99 -10.28 -2.25 2.78

2006 -0.05 2.00 -2.52 -1.75 -0.07 2.43 -3.91 1.48 0.03 -2.71

1999-06 -0.08 3.41 -3.66 -6.02 -0.08 3.35 -1.53 -8.01 -6.11 -5.30 t-statistic -0.32 2.05* -2.91** -2.68** -0.31 1.95* -0.94 -4.12** -2.29* -0.72

(4)

(cont.)

Panel B: COM defined as fraction of hedge fund stock ownership

cons COM COM -F EW COM -M AN Y BU LL BEAR P P U T ST RAD Stock Holdings Only

estimate 0.06 0.07 t-statistic 0.33 1.20

estimate 0.06 0.05 0.05

t-statistic 0.29 1.57 1.02

Stock and Option Holdings

estimate 0.10 0.08 -1.27 -7.69 -4.99 -7.53

t-statistic 0.54 1.44 -0.76 -3.82** -1.65+ -0.96

estimate 0.09 0.06 0.07 -1.47 -7.70 -5.17 -7.67

t-statistic 0.49 1.69+ 1.26 -0.87 -3.79** -1.87+ -0.97

Panel C: COM defined as change of hedge fund stock ownership

cons COM COM -F EW COM -M AN Y BU LL BEAR P P U T ST RAD Stock Holdings Only

estimate 0.10 0.05 t-statistic 0.62 1.01

estimate 0.09 0.06 0.05

t-statistic 0.58 1.59 0.97

Stock and Option Holdings

estimate 0.14 0.05 -0.69 -7.01 -4.64 -4.68

t-statistic 0.90 1.02 -0.43 -3.59** -1.63 -0.59

estimate 0.12 0.06 0.05 -0.02 -6.72 -4.81 -2.28

t-statistic 0.84 1.67+ 0.96 -0.01 -3.48** -1.76+ -0.33

(5)

Performance of Stock Portfolios Tracking Directional Option and Common Stock Holdings

The table reports average monthly returns for equally weighted stock portfolios formed based upon hedge fund advisors’ holdings of 13(f) reportable securities. Panel A reports results for portfolios that are long stocks underlying reported call (bull) and put (bear) options holdings. Panel B reports results for portfolios that are long stocks underlying reported common stock holdings (com), and for differences between the bull and com (bull diff) and bear and com (bear diff) portfolio returns. Quarterly reported underlying notional values of options holdings (for bull and bear) and market values of common stock holdings (for com) are used to construct advisor-specific portfolios of the underlying common stock. Monthly raw returns and performance of these portfolios are generated over the following quarter assuming monthly rebalancing at the previous quarter’s portfolio weights. The table reports the time series of the average raw return and performance across advisors. The GT measure is calculated by subtracting the time t return of the portfolio held at month t − 4 from the time t return of the portfolio held at t − 1. The CS measure is the difference between the time t return of the portfolio held at t − 1 and the time t return of the time t − 1 matching control portfolio. The return on a control portfolio is the value-weighted return on a group of stocks of similar market value, book-to-market ratio, and lagged one-year returns. The table reports average returns for all months by year and by the full sample period (1999–2006). t-statistics are reported below sample averages. +, *, and ** denote significance at the 10%, 5%, and 1% levels. Raw data are winsorized at 99.5% and 0.5%. Results are reported for hedge fund Sample A.

Abnormal Returns

Raw Returns GT Performance CS Performance

Panel A: Performance of stock portfolios tracking options

year bull bear diff bull bear diff bull bear diff

1999 4.58 0.26 4.32 3.00 -0.63 3.63 2.07 -1.15 3.22

2000 -1.93 -4.84 2.91 0.17 -2.60 2.77 0.21 -2.09 2.30

2001 1.46 -1.15 2.61 0.99 -0.34 1.33 1.15 -1.16 2.31

2002 -3.86 -3.41 -0.45 -2.09 -1.30 -0.79 -0.99 -0.96 -0.02

2003 4.03 3.71 0.32 1.15 1.40 -0.25 0.86 0.29 0.57

2004 1.26 0.33 0.93 0.81 -0.33 1.13 0.62 -0.56 1.18

2005 0.94 0.47 0.46 -0.02 -0.70 0.68 -0.55 -0.78 0.23

2006 1.32 0.82 0.50 0.35 0.12 0.23 0.44 0.28 0.16

1999-06 0.98 -0.47 1.45 0.54 -0.55 1.09 0.48 -0.77 1.24

statistic 1.57 -0.74 4.11** 1.92+ -1.85+ 3.39** 2.00* -3.39** 4.48**

Panel B: Performance of stock portfolios with and without option holdings

year bull diff bear diff com bull diff bear diff com bull diff bear diff com

1999 1.52 -2.80 3.06 1.35 -2.28 1.65 1.51 -1.71 0.56

2000 0.05 -2.86 -1.98 -0.06 -2.83 0.24 0.03 -2.27 0.18

2001 1.36 -1.26 0.10 1.51 0.19 -0.52 1.37 -0.93 -0.22

2002 -1.38 -0.93 -2.48 -2.34 -1.55 0.25 -0.74 -0.71 -0.25

2003 0.31 -0.01 3.72 0.86 1.12 0.28 0.54 -0.03 0.32

2004 0.31 -0.61 0.95 0.71 -0.42 0.09 0.37 -0.81 0.25

2005 -0.87 -1.33 1.81 -0.17 -0.85 0.15 -0.73 -0.96 0.18

2006 0.45 -0.04 0.86 0.41 0.18 -0.06 0.34 0.18 0.10

1999-06 0.22 -1.23 0.76 0.28 -0.81 0.26 0.34 -0.91 0.14

t-statistic 0.91 -4.67** 1.40 1.05 -2.63** 2.06* 1.59 -4.31** 1.54

Figure

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References

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