7 EMPIRICAL RESULTS
7.1 Determinants of Derivatives Use
Table 9 presents the logistic regression statistics for the determinants of the use of different derivatives by hedge funds. The results are controlled for different hedge fund strategies. However, when the number of funds in the strategy category is less than 10, the strategy is not included because the variable may capture infor-mation which only concerns just an individual hedge fund.
The regression statistics in Table 9 provide evidence that, as the use of leverage
and asset specialization for the underlying asset class of an option increases, so
does the probability of a hedge fund to use the option. Excluding warrants issued
with fixed-income securities, the use of leverage coincides statistically
signifi-cantly with the use of all derivatives by hedge funds at the 1% level. This result
may also support the view that these options for speculative trading are inferior to other derivatives in hedge funds. Asset specialization coincides statistically sig-nificantly with the use of all derivatives examined except other derivatives for currency than options, at least at the 5% level. To sum up the results in Table 9, the use of leverage and asset specializations are important factors of the use of options by hedge funds, but also other derivatives.
The results for other variables than leverage and asset specialization partly differ from the results of Chen (2009) suggesting that the use of derivatives by hedge funds is associated with higher incentive fees, less restrictive redemption policy, managerial ownership and effective auditing. In particular, higher incentive fee is only found to coincidence statistically significantly with the use of derivatives in the case of equity options. By contrast, higher incentive fee has a negative and statistically significant coincidence with derivatives use in the cases of warrants issued with fixed-income securities and other derivatives than options for com-modities. If performance based compensation attracts skilled managers, those managers who use options for equity should be outperformers while those man-agers who use options for commodity should be underperformers. This evidence is thus consistent with the expectation that equity options are used for informed trading, and thus also consistent with the evidence of Aragon et al. (2007).
The evidence for the coincidence of personal capital and the use of derivatives is found to be fairly consistent with the results of Chen (2008) as the incidence is statistically significant in 4 out of 10 regressions. The use of auditing services, instead, is not found to have any positive coincidence with the use of derivatives in contrast to Chen (2009). Also, the evidence for the coincidence of less restric-tive redemption policy and the use of derivarestric-tives is mixed in this study. Longer restriction periods are, in fact, associated with the use of warrants, which is a rea-sonable finding as warrants may be highly illiquid and managers need longer re-demption periods when investing in these assets. Consistent with Pinnuck (2004), the test statistics of this study also yield evidence that all options and warrants examined are more popular among bigger hedge funds.
The AE_OTHER variable indicates whether a fund using equity index futures as
the derivative is the only equity derivative reported by TASS which has a linear
payoff. The results are consistent with the assumption related to the first
hypothe-sis that the derivative is a substitute for illiquidity risk premium. This conhypothe-sistency
is the statistically highly significant and negative incidence between the use of the
derivative and longer restriction and lockup periods which are related to higher
illiquidity risk premium (see Aragon 2007).
Table 9. Logistic Regression Statistics of Derivatives Use on Leverage and Asset Specialization
This table presents parameter the estimates of cross-sectional analysis for the use of the deriva-tives of hedge funds. The model for the cross-sectional analysis is the following (Model 1):
log Pr ( DERIVATIVE
ji= 1 )
where DERIVATIVE
jidefines the use of derivative j by a fund i; SPECIALIZATION
idefines a dummy variable for the specialization for the same asset as the asset class of
DERIVATIVE
i, and CONTROL
idefines an additional control variable j of fund i. These control variables include dummy variables for invested asset classes, other asset focuses than same of DERIVATIVE
i. The standard errors are QML (Huber/White) heteroskedasticity robust z-statistics are given in italics. The sample includes 3,382 observations. See Table 1 for definitions of the variables.
AE_OPTION AF_OPTION AC_OPTION ACUR_OPTION Variable Coef. z Coef. z Coef. z Coef. z
* refers to a statistical significance at the 10% level; ** refers to a statistical significance at the 5% level; *** refers to a statistical significance at the 1% level
Table 9. Continued
AE_OTHER AF_OTHER AC_OTHER ACUR_OTHER
Variable Coef. z Coef. z Coef. z Coef. z C -8.073*** -4.52 - -2.83 -6.814** -2.10 -5.477** -2.29 PRIMARY 0.483*** 4.03 0.415*** 4.91 1.330*** 3.57 0.285 1.15 LEVERAGED 0.821*** 7.05 0.671*** 7.55 1.776*** 5.50 0.842*** 4.91 S_CA -0.434 -1.48 -0.442** -2.40 -0.558 -1.29 S_ED -0.739*** -3.00 - -4.78 -0.146 -0.41 S_ELS 0.184 0.94 -0.408** -2.51 -0.424 -1.21 -0.216 -0.64 S_EM -0.279 -1.15 -0.287* -1.66 -0.079 -0.15 -0.194 -0.53 S_EMN -0.009 -0.03 -0.329 -1.55 -0.099 -0.16 -1.084** -2.42 S_FI 0.218 0.43 0.484** 2.53 -0.631 -1.53 S_GM 1.083*** 3.43 0.225 1.16 1.167*** 2.77 0.845** 1.97 S_MF 1.861*** 5.99 0.880*** 4.49 2.529*** 5.95 1.014** 2.30 LNSIZE 0.053** 1.62 0.082*** 3.34 0.037 0.52 0.089* 1.89 LNAGE 0.138 0.56 -0.114 -0.68 0.063 0.14 -0.068 -0.21 HMARK 0.235* 1.75 0.160 1.56 0.110 0.33 0.170 0.93 IFEE 0.001 0.07 -0.008 -1.17 -0.023 -1.15 -0.032** -2.57 MFEE 0.247** 2.52 0.143*** 2.83 0.000 0.00 0.046 0.38 MIN(Million$) 0.201*** 4.67 0.216*** 4.76 0.147*** 3.00 0.271*** 5.91 RESTRICTION -0.006*** -3.12 -0.002 -1.34 -0.003 -0.68 0.000 0.12 LOCKUP -0.030*** -3.35 -0.008 -1.27 -0.035 -1.54 - -4.51 AUDIT -0.236* -1.95 0.088 1.00 -0.175 -0.58 0.065 0.35 PERCAPITAL 0.227** 2.26 0.184** 2.51 0.176 0.76 0.407** 2.65 OPENTOPUBLIC 0.163 1.29 0.106 1.15 0.310 1.06 0.261 1.34 OPENENDED 0.381*** 3.32 -0.011 -0.13 0.074 0.28 0.346 1.95
Time-Dummies Yes Yes Yes Yes
Asset Dummies Yes Yes Yes Yes Log likelihood -1417.850 -877.697 -344.853 -718.906
McFadden R 0.313 0.553 0.756 0.654
LR statistic (38 df) 1291.770 2171.461 2137.032 2723.135 Probability (LR stat) 0.000 0.000 0.000 0.000 Obs with Dep=0 2370 2478 2884 2350 Obs with Dep=1 1012 904 498 1032
* refers to a statistical significance at the 10% level; ** refers to a statistical significance at the 5% level; *** refers to a statistical significance at the 1% level.
Table 9. Continued
Log likelihood -1406.788 -628.524McFadden R 0.241 0.329
LR statistic (38 df) 891.461 616.016 Probability (LR stat) 0.000 0.000 Obs with Dep=0 2580.000 3114.000 Obs with Dep=1 802.000 268
* refers to a statistical significance at the 10% level; ** refers to a statistical significance at the 5% level; *** refers to a statistical significance at the 1% level