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Independent directors and favoritism: when multiple board affiliations prevail in mutual fund families.

B. IDMAs and Family-Level Allocations of Underpriced Initial Public Offerings

1. Summary Statistics for Allocations of Initial Public Offerings

To address whether fund performance or IPO allocations are different across the Number of Directorships (or the Overlapping Rate) groups, the following procedure is used. The four-factor alpha of a fund in year t is ranked within the fund family by quartile. In addition, funds are annually sorted into Number of Directorships (or Overlapping Rate) quintiles. The average rankings based on the four-factor alpha within each family are calculated within each of the five Number of Directorships (or Overlapping Rate) portfolios and then the time series average of these rankings is taken over the entire sample period. Table V reports the average rankings based on: (1) raw return, (2) the four-factor alpha, (3) the average number of IPOs deals per fund, (4) the average first day IPO underpricing return, and (5) the average dollar amount of underpricing, which is defined as the first day IPO price increase times the number of shares held by a fund.

In Table V (Panel B), funds with a higher Overlapping Rate have, on average, neither a higher nor a lower return performance. Instead, funds with a higher Overlapping Rate have, on average, higher rankings within the fund family in terms of numbers of IPOs allocated, the first day return of the allocated IPOs, and the average dollar amount of any underpricing. These results are consistent with the view that IDMAs are positively associated with IPO allocations. These patterns become unclear when I look at the corresponding cells in Panel A when Number of Directorships is the ranking criterion.

2. Base Model Specifications

In this section, I use a multivariate ordered logistic regression model to examine the preferential allocation of IPO underpricing returns. I continue the two samples of actual pairs in the cases of both past performance and total fees described in Section II.B.3. In particular, the family ranking of the high family value fund in a pair (in terms of IPO underpricing return in a given year) is compared to the ranking of its corresponding low family value fund. The categories of dependent variables in multivariate ordered logistic regressions are based on the ranking difference, where [IPORet.sup.H>L] equal to three is assigned when the ranking of the high family value fund is higher than that of the low family value fund by three quartiles (e.g., high performing fund's family ranking = 4 (highest) and low performing fund's family ranking = 1 (lowest)); [IPORet.sup.H>L] equal to two is assigned when the ranking of a high family value fund is ranked higher than its counterpart by two quartiles, and [IPORet.sup.H>L] takes a value of one if the high family value fund is ranked higher than its counterpart by one quartile and zero otherwise. Family dummies and year dummies are included in the models to control for family and time fixed effects. W is a matrix of control variables defined in Equation (4). Standard errors are also adjusted upward by using a cluster-robust standard error. (7) The following ordered logistic regression model is estimated:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5)

To account for the IPO shares held, the dollar amount of any underpricing is also used by calculating the first day underpricing times the number of shares held in the fund. I also calculate a fund family's rank in terms of the dollar amount of its underpricing in year t. A dummy variable is set equal to one if the high family value fund's family ranking in terms of dollar amount of IPO underpricing is higher than that of the low family value fund in a pair in year t. The following probit regression is performed:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (6)

Results for the past performance case. Table VI (Panels A and B) presents the results for the past performance case. Panel A reports the results based on IPO underpricing returns, while Panel B provides the results based on the dollar amount of any underpricing. With respect to the IDMAs of low performing funds, the coefficients of Overlapping Ratio for low performing funds (i.e., Overlapping Ratio (Low) in Column 3, Relative Number of Directorships in Column 5, or Relative Overlapping Ratio in Column 6) are all significantly negative. I can further obtain predicted probabilities and marginal effects on the variables after the models are estimated. (8) The average marginal effect of Overlapping Ratio (Low) is 11.34% for outcome-level [IPORet.sup.H>L] = 0, indicating that one instant change in Overlapping Ratio (Low) will increase the likelihood of no preferential underpriced IPO allocations by 11.34%. The results suggest that IDMAs for low performing funds will decrease the controversial practice of intrafamily fund favoritism as it relates to the unequal allocation of underpriced IPOs.

With respect to the separate effect of IDMAs for high performing funds, the coefficients of Number of Directorships (High) and Overlapping Ratio (High) are statistically insignificant under Specification Columns (2) and (4), indicating that IDMAs for high performing funds will neither increase nor decrease fund favoritism in terms of IPO allocation. Furthermore, I find limited evidence that the common agency issue counteracts the effect of IDMAs on underpriced IPO allocations, with only one of the six specifications showing a significant positive coefficient in Column (5) of Panel A.

My findings are robust when I utilize the dollar amount of underpricing as my dependent variable. The results are reported in Table VI (Panel B). The coefficients of Number of Directorships (Low) in Column (1), Overlapping Ratio (Low) in Column (3), Relative Number of Directorships in Column (5), and Relative Overlapping Ratio in Column (6) are all significantly negative. In addition, the average marginal effect of Overlapping Ratio (Low) is -9.9% for IPODollar [amount.sup.H>L.sub.i,t], indicating that IDMAs for low family value funds can decrease the likelihood of preferential IPO allocations in terms of the dollar amount of underpricing by 9.9%. However, the coefficients of Number of Directorships (High) in Column (2) and Overlapping Ratio (High) in Column (4) are statistically insignificant. Furthermore, I find limited evidence of a common agency problem in which two of the six specifications demonstrate that the negative relationship between IDMAs and the unequal allocation of IPOs in terms of the dollar amount of underpricing will be adversely affected by an increase in the proportion of overlapping independent directors between the pair of high and low performing funds. For the other independent variables presented in Panels A and B of Table VI, I find some evidence that an independent chair can decrease the unequal allocation of underpriced IPOs among high and low performing funds, with four of the 12 specifications showing a significant negative coefficient.

Overall, the results are not consistent with the Favoritism Hypothesis, but they are generally consistent with the Information Hypothesis, which posits that the higher the average independent director's overlap rate between a low performing fund and the rest of the fund's family, the less likely the low performing fund will be sacrificed in terms of unequal allocations of underpriced IPOs. However, there is an asymmetric effect in that IDMAs for low performing funds decrease the likelihood of cross-fund subsidization, while IDMAs for high performing funds neither increase nor decrease the likelihood of cross-fund subsidization. Furthermore, there is only limited evidence that the negative relationship between IDMA measures and the unequal allocation of underpriced IPOs will be adversely affected by an increase in the overlap rate of independent directors who sit on of the boards of paired high and low performing funds. I also find little evidence that there is a common agency problem dominating the information advantage of IDMAs, as I do not observe a positive net value when the combination value of IDMAs and an interaction term (i.e., [[beta].sub.1] plus [[beta].sub.2]) is considered across all of the specifications.

Results for the fee case. Panels C and D present the results for the total fee case. Panel C reports the results based on the IPOs' underpricing returns, while Panel D reports the results based on the dollar amount of underpricing.

For IDMAs in low fee funds, under the eight specifications reported in Columns (1), (3), (5), and (6) in Panels C and D, six specifications report significantly negative coefficients for the IDMA measures whether I consider: (1) the measure of the Relative Number of Directorships or the measure of the Relative Overlapping Ratio as the explanatory variable of interest or (2) IPO underpricing returns or the dollar amount of underpricing as the dependent variable. When I consider the magnitude of these effects, the average marginal effect of Overlapping Ratio (Low) is 20.82% for outcome-level [IPORet.sup.H>L] = 0 indicating that one instant change in Overlapping Ratio (Low) will increase the likelihood of no preferential underpriced IPO allocations by 20.82% in the total fee case. In addition, the average marginal effect of Overlapping Ratio (Low) is 18.33% for IPODollar [amount.sup.H>L.sub.i,t] = 1, indicating that in the total fee case, IDMAs for low family value funds can decrease the likelihood of preferential IPO allocations in terms of the dollar amount of underpricing by 18.33%.

The coefficients of the Number of Directorships (High) and the Overlapping Ratio (High) are statistically insignificant under all of the four specifications (shown in Columns 2 and 4 in Panels C and D). Furthermore, I find no evidence that the common agency issue will counteract the effect of IDMAs on the unequal allocation of underpriced IPOs based on the fee case.

For the other variables, the presence of an independent chair in the low fee funds decreases the likelihood of receiving a lower allocation of underpriced IPOs with eight of the 12 specifications presenting a significantly negative relationship between an independent chair dummy in the low fee fund and an unequal allocation of underpriced IPOs. These results are consistent with the IPO results for past performance case and indicate (to some extent) the effectiveness of independent chairs in monitoring the complex-level allocation of investment opportunities. Although I do not show all of the results for the control variables, I find that the smaller the expense ratio differential across low and high fee funds, the lower the likelihood of receiving a smaller allocation of underpriced IPOs. The results are statistically significant across the models of IPO underpricing returns and the dollar amount of underpricing. Moreover, they are consistent with Gaspar et al.'s (2006) finding that fund expenses are associated with family preferential strategies. Furthermore, the coefficient of Diff_Turnover Ratio is significantly negative in four of the 12 specifications, suggesting that a fund with a relatively higher turnover ratio is less likely to suffer from an IPO allocation bias. For family characteristics, the number of funds within the family has a positive impact on the probability of an unequal allocate ion of underpriced IPOs. The results are generally consistent with Guedj and Papastaikoudi's (2008) finding that the number of funds within a family can be interpreted as the measure of latitude that a family has in allocating resources unevenly between funds. Additionally, the coefficients of the star family affiliation dummy evaluated in the prior year are significantly negative among various specifications, suggesting that family with star funds can reduce an investor's information costs as suggested by Huang, Wei, and Yan (2007). Thus, the likelihood of an IPO allocation bias in the next period decreases.

Overall, I consider potential resource shifting in favor of high fee funds at the expense of low fee funds. Although the findings still do not support the agency cost view of IDMAs, they are consistent with the idea that IDMAs can equip independent directors with the knowledge to monitor complex-level investment opportunities, such as underpriced IPOs. However, I find an asymmetry between IDMAs for high fee funds and IDMAs for low fee funds. In addition, using fee as a dimension to identify intrafamily subsidization, I still find no evidence that the common agency issue will counteract the monitoring effect of IDMAs on the unequal allocation of underpriced IPOs. (9)

3. 2SLS

I also perform a 2SLS regression analysis. To address endogeneity issues in my 2SLS analysis, I use not only the same set of instruments used in the previous sections, but also a probit model with endogenous covariates. The dependent variable is a dummy variable that is equal to one if the ranking of high family value funds is higher than that of the low family value funds and zero otherwise. Before I report the 2SLS results, I do a robustness check by including the residuals from the first stage of 2SLS as a regressor in the second stage of 2SLS and perform a Wald test of exogeneity. The Chi-square value is 5.49 with a p-value of 0.019. Since the coefficient of the residual is significantly different from zero, the null of exogeneity is rejected. Thus, 1 continue to treat Overlapping Rate as endogenous in the model specifications when the unequal allocation of underpriced IPOs is investigated. I report the 2SLS results for both the past performance case and the total fee case in Panels A and B of Table VII.

I find that in Panel A of Table VII, the coefficients of IDMA measures are significantly negative across all model specifications including Overlapping Ratio (Low), Overlapping Ratio (High), and Relative Overlapping Ratio. In Panel B of Table VII, the coefficients of Overlapping Ratio (Low) are significantly negative. In summary, the model specifications in Tables VI and VII provide evidence that IDMAs provide expertise to monitor the unequal allocations of underpriced IPOs across high and low family value funds within a fund family, especially for IDMAs in low family value funds.

V. Specific Channels Through Which IDMAs Benefit Funds

A. Fee Set

Independent directors are required to approve the fund's advisory fees on an annual basis. Fund shareholders stand to benefit substantially when the process of negotiation between a fund's independent directors and investment advisers leads to lower fees. There is evidence that serving on multiple boards may lead to lower fees (Tufano and Sevick, 1997). This study revisits whether serving on multiple boards may lead to lower fund fees using the following model specification:

[Fee.sub.i,t] = [alpha] + [[beta].sub.1] Number of [Directorships.sub.i,t] for Overlapping [Rate.sub.i,t]) + W + [[epsilon].sub.i,t]. (7)

The dependent variable is a fund's total fees, which are calculated as total loads divided by seven plus the annual expense. Table VIII reports the results of the OLS regression and 2SLS analyses. Consistent with the study of Tufano and Sevick (1997), board structure appears to be relevant to fee setting. I find that the IDMA measure, which is based on the number of directorships held by independent directors (i.e., Number of Directorships) or the average independent director overlap rate between a fund and the rest of the fund's family (i.e., Overlapping Rate), is significantly negatively associated with the fees under both OLS specifications and 2SLS specifications. Specifically, when the average independent director overlap rate (i.e., Overlapping Rate) of a fund increases by 25%, it results in a five-six basis points decrease in the fund fee. The results are consistent with Tufano and Sevick's (1997) finding that the percentage of the sponsor's assets overseen by independent directors is negatively associated with fees, suggesting that serving on multiple boards may allow independent directors either to develop greater expertise or to exert greater bargaining leverage in fee negotiations. In addition, I find some evidence that funds with larger boards tend to charge significantly higher fees. If lower fees can be a sign of more effective board oversight, this result is consistent with Yermack (1996) and Tufano and Sevick's (1997) finding that smaller boards are more effective. In addition, in one of the three specifications, I find evidence that the presence of an independent chair is associated with lower fees.

For control variables, consistent with the study of Tufano and Sevick (1997), I find little evidence that fees are related to fund performance during the prior year under any specification. I also find a positive relationship between the fund turnover ratio and fees in all of the specifications. This result is consistent with the findings of Gil-Bazo and Ruiz-Verdu (2009) that turnover is associated with increases in total investor ownership costs. I see some evidence of economies of scale at the fund level and at the sponsor level in the 2SLS specification with fees inversely related to fund size and family size, respectively. The findings are consistent with Tufano and Sevick (1997) and Gil-Bazo and Ruiz-Verdu's (2009) findings that economies of scale can reduce operating costs for larger funds and that there are management company characteristics other than the company's total size that are related to fees.

B. Return Gap and Fund Opaqueness

Mutual fund investors do not observe all fund manager actions. Unobserved actions can have a hidden benefit, such as interim trades by skill managers and hidden costs to investors (Kacperczyk et al., 2008). Examples of hidden costs include insider preferences, window dressing, and excessive risk-taking in violation of stated investment objectives (Brown, Harlow, and Starks, 1996; Chevalier and Ellison, 1997; Carhart et al., 2002; Gaspar et al., 2006; Meier and Schaumburg, 2004; Nanda et al., 2004; Davis and Kim, 2007). Independent directors have responsibilities related to corporate governance as representatives of the shareholders' interests and are called on to judge practices that are difficult to monitor or resolve. Multiple board affiliations can familiarize independent directors with various member funds' operations and trading strategies, incentive schemes and tournaments in mutual fund families, and allocation issues related to complex-level investment opportunities. Therefore, IDMAs may be capable of monitoring a fund manager's unobserved actions.

Kacperczyk et al. (2008) propose a return gap to proxy for fund managers' unobserved actions. The return gap is a direct measure of the value created (or destroyed) by a fund manager's undisclosed actions relative to the previously disclosed holdings and is positively (negatively) related to the hidden benefit (cost) of manager's unobserved actions. I examine whether IDMAs, proxied by the Number of Directorships or the Overlapping Rate, can increase hidden benefits and/or decrease hidden costs induced from a fund manager's unobserved actions. The dependent variable is the return gap, denoted as RG, which is the difference between the actual fund performance and the performance of a hypothetical portfolio that invests in the previously disclosed fund holdings. OLS regressions are performed when the family and time dummy variables are controlled in the specifications and the standard errors are adjusted upward for clustering at the fund family level.

[RG.sub.i,t] = [alpha] + [[beta].sub.1] Number of Directorships [(or Overlapping Rate).sub.i,t] + W + [[epsilon].sub.i,t]. (8)

All of the independent variables were previously defined in Section V. Table IX reports the results. In Columns (1) and (2) of Table IX, the coefficients of the Number of Directorships and Overlapping Rate are significantly positively related to the return gap, suggesting that IDMAs can be associated with the return gap created by a fund manager's undisclosed actions relative to the previously disclosed holdings. I find that IDMAs appear to have an economically meaningful effect on return gap. For example, a 25% increase in the Overlapping Rate brings an annual 2.01% increase in the return gap. The results reinforce the evidence in favor of the Information Hypothesis.

Next, Kacperczyk et al. (2008) find that a fund's opaqueness might proxy for agency problems in which the opaqueness of a fund's investment strategy is measured by the correlation coefficient between monthly holdings and investor returns. They find that Return Gap is negatively related to the opaqueness of a fund's investment strategy. To examine whether IDMAs can enhance information exchange by increasing hidden benefits or decreasing hidden costs for funds with less transparency, I rank the correlation coefficient between a fund's monthly holdings and its investor returns in the previous year. A dummy variable, Opaque, takes a value of one if the fund's correlation coefficient is among the bottom one-third of equity funds in the corresponding year, and zero otherwise. Opaque rank is interacted with the Number of Directorships and the Overlapping Rate and the interaction term is included in the specifications. One might have concerns that both IDMAs and fund managers who manage more than one fund within a management company may be channels associated with a fund's hidden benefits/costs. Thus, I control the average manager overlap rate between the fund and the rest of its family as a robust check. The results are reported in Column (5). The OLS regression analysis is performed when the family and time dummy variables are controlled in the following specifications:

[RG.sub.i,t] = [alpha] + [[beta].sub.1] Overlapping [Rate.sub.i,t] + [[beta].sub.2][Opaque.sub.i,t-1] + [[beta].sub.3][Opaque.sub.i,t-1] x Overlapping [Rate.sub.i,t] + W + [[epsilon].sub.i,t] (9)

The results are reported in Columns (3) and (4) of Table IX and the t-statistics reported in the regressions are based on robust standard errors clustered by fund family. I find that the coefficients of Opaque are all significantly negative, a result that is consistent with the finding of Kacperczyk et al. (2008) and suggests that a fund's opaqueness may proxy for the agency problems inherent in the unobserved action of mutual funds. However, the coefficient of the interaction term between Opaque and the Number of Directorships and the interaction term between Opaque and the Overlapping Rate are significantly positive in Columns (3) to (5). Therefore, when fund transparency is considered in the specifications, the model results suggest that for less transparent funds, a 25% increase in the Overlapping Rate of independent directors will increase fund return by 3.90% to 5.09% indicating an economically meaningful effect of IDMAs on fund performance.

I note that the coefficients of the Number of Directorships and the Overlapping Rate become statistically insignificant once Opaque and the interaction terms of Opaque and the IDMA measures are included in the regressions. The results indicate that the positive relationship between IDMA measures and the return gap presented in Columns (1) and (2) can primarily be attributed to those funds whose investment strategy is opaque. These findings suggest that effective IDMAs can increase hidden benefits and/or decrease hidden costs, especially for funds with less transparency.

With respect to the other characteristics in Table IX, an independent chair can play an effective monitoring role in increasing the hidden benefits or decreasing the hidden costs of a fund. In addition, Chen et al. (2004) find that mutual fund performance increases with fund family size. Consistent with these authors' findings and the findings of Kacperczyk et al. (2008), this study finds that larger fund families (proxied by lag_log(Mtna_family)) tend to exhibit higher return gaps. Interestingly, the number of funds offered by a fund family is negatively correlated with the return gap in four of five specifications. The results are consistent with Guedj and Papastaikoudi's (2008) findings that the number of funds offered by a fund family may be associated with the family's latitude to allocate resources unevenly between funds. Therefore, the number of funds offered by a fund family may be associated with the hidden costs of affiliated funds resulting in a negative relationship with the return gap. (10)

C. Cross-Fund Learning Within Fund Families

To address the issue of whether IDMAs can increase cross-fund learning within a fund family, thus enhancing information transfers, I examine whether IDMAs will result in a higher level of correlated idiosyncratic shocks with the other funds in a family. The idiosyncratic returns of each fund are measured using prior year monthly returns and a four-factor model. The correlation of idiosyncratic returns, denoted as Correlation of Idiosyncratic Returns, is calculated as the average of the pairwise correlations between a fund's idiosyncratic returns and every other fund's idiosyncratic returns in its family. In addition, Brown and Wu (2016) find that a fund's performance can be attributed to a fund-specific component and a common component shared by all of the funds in the family. They measure the common component using the average manager overlap rate between the fund and the rest of its family. Then I include the average manager overlap rate between the fund and the rest of its family in my specifications, in which for each pair of funds, the manager overlap rate is defined as the number of managers common to the two funds divided by the average number of managers of the two funds. I perform the following regression analysis when time and family dummy variables are controlled and the standard error is adjusted for clustering at the family level:

Correlation of Idiosyncratic [Returns.sub.i,t] = [alpha] + [[beta].sub.1] [Overlapping Rate(Independent Directors).sub.i,t] + [[beta].sub.2] [Overlapping Rate (Managers).sub.i,t] + W + [[epsilon].sub.i,t]. (10)

The control variables used are defined above. Table X reports the results. I find a positive relationship between the Overlapping Rate and the Correlation of Idiosyncratic Returns in Column (3) when the average manager overlap rate is not included in the specification. As Column (4) indicates, the coefficient of Overlapping Rate remains positive and significantly different from zero when I include the average manager overlap rate in the specification. The positive relationship between the average manager overlap and the idiosyncratic returns of each fund is consistent with Brown and Wu's (2016) finding that the manager overlap rate can be used to measure the common component shared by all of a family's funds. I also provide evidence that IDMAs can be another source of cross-fund learning. The model results demonstrate that Correlation of Idiosyncratic Returns increased by 1.62% to 5.15% when there is a 25% increase in the Overlapping Rate of independent directors. Alternatively, Correlation of Idiosyncratic Returns increased by 3.43%-3.74% when there is a 25% increase in the Overlapping Rate of fund managers. However, the coefficients of the Number of Directorships are not significant in Columns (1) and (2) when the number of funds offered by the family is not taken into account.

I also perform an F-value of Wu-Hausman and the F test is 59.116 with a p-value of 0.000 based on Column (3). The Chi-squared value of the Durbin-Wu-Hausman Chi-squared test is 58.793 with a p-value of 0.000. Because both test statistics are highly significant, the null of exogeneity is rejected. The Overlapping Rate is treated as endogenous when the dependent variable is the Correlation of Idiosyncratic Returns. Then I perform a 2SLS analysis in which the setup of the model in Column (6) (Column 7) is identical to that of the model in Column (3) (Column 4) except that the Overlapping Rate is instrumented by the four instruments as defined earlier and 2SLS estimates are reported. My results are robust. I find that the coefficient of the Overlapping Rate is also positive and statistically significant in Columns (6) and (7) when the average manager overlap is included in the specification Column (7). The results indicate that IDMAs are positively associated with cross-fund learning within fund families, a finding that reinforces my Information Hypothesis of IDMAs.

VI. Conclusion and Policy Implications

Oversight of multiple funds has been a controversial issue in the mutual fund industry. The advantage of the practice is that mutual funds within a fund family share the same investment adviser and other key service providers. Efficiencies can be achieved when independent directors oversee multiple boards. Beyond efficiency, the oversight of significant assets can enhance an independent director's knowledge and expertise and increase their ability to influence fund family and key service providers. As a result, multiple board affiliations can enhance an independent director's effectiveness in serving the interests of shareholders.

The disadvantages of overseeing multiple funds involve concerns that independent directors may not devote sufficient time and attention to matters specific to each fund. More important than busyness concerns are favoritism concerns. Specifically, independent directors may trade off the interests of one fund relative to another in a manner consistent with the fund family's interests.

My study investigates the roles of independent directors in dealing with potential intrafamily fund favoritism. Based on 63,055 independent director records from 55 fund sponsors over seven years collected from Statements of Additional Information filed with the SEC, I find some evidence to support the effectiveness of independent directors with multiple board affiliations. I determine that strategic cross-fund subsidization to enhance the performance of high family value funds at the expense of low family value fund decreases when independent directors in low family value funds oversee multiple boards. However, a fund can be adversely affected by other fiduciary duties imposed on the independent directors by other funds via common independent directors. I do not find that a common agency problem dominates the information advantage in a manner that would result in favoritism consistent with the fund family's interests.

This study also provides evidence that IDMAs can play a positive role in decreasing total fees, enhancing information exchange (especially for less transparent funds) and increasing cross-fund learning within fund families. I also investigate the characteristics of independent directors with multiple board affiliations. I find that independent directors who are retired executives of other firms or who have longer tenure are positively associated with multiple board directorships, a result consistent with effective board expertise.

Under governance rules adopted by the US Securities and Exchange Commission, since 2006, virtually all investment company boards are required to conduct annual self-assessments. Instead of imposing an arbitrary limit on the number of funds a director may oversee, the Securities and Exchange Commission has required that boards evaluate their performance in this regard as part of the annual self-assessment. I provide evidence in support of this policy in my finding that independent directors with multiple board affiliations can facilitate the transfer of information across funds in a fund family.

Appendix

Definitions of Variables
Fund-Level Variable  Definition

Board Characteristics

Number of            Natural logarithm of the average number of funds
Directorships        overseen by independent directors in a fund in
                     year t.

Overlapping Rate     For each pair of funds within a fund family in
                     year t, Overlapping Rate is defined as the ratio
                     of the number of independent directors overseeing
                     both funds to the average number of independent
                     directors of the two funds. Fund-level Overlapping
                     Rate is then defined as the average independent
                     director overlap rate between a fund and the rest
                     of the fund's family.

Independent Ratio    Percentage of independent directors on the board.

Board Size           Number of directors on the board.

Independent Chair    Independent chair dummy.

Independent Director Characteristics

Independent-         Independent directors are categorized into one of
Director             four occupations:
Employment           (1) executives from other firms, (2) retired
Characteristics      executives from other firms, (3) academics, and
(Executive,          (4) other. Executive is defined as the number of
Retired Executive,   executives from other firms divided by the board
Academics, Others)   size. Retired Executive is defined as the number
                     of retired executives from other firms divided by
                     the board size. Academics is defined as the number
                     of academic professors divided by the board size.

Avg. Ind.            The average age of independent directors in a
Director Age         fund.

Ind. Director's      The number of independent directors who are over
Age Over 60          59 years old divided by board size.

Average Tenure       The sum of the number of years that the
                     independent directors have served on the board
                     divided by the number of independent directors.

Performance Shifting and IPO Allocations

Performance          Past Performer Case: A fund is classified as "high
Shifting             performing" ("low performing") if the fund's four-
                     factor alpha in year t ranked above the 75th
                     (below the 25th) percentile within the same
                     investment style based on the CRSP data set. The
                     high performing fund i is paired to the low
                     performing fund j under the same fund family in
                     year t (referred to as an "actual pair") and the
                     difference in performance between the high and low
                     performing funds is calculated. A "matched pair"
                     is also constructed when the above mentioned high
                     performing and low performing funds in an "actual
                     pair" are replaced by very similar funds in the
                     same investment style and belonging to the same
                     decile in terms of total net assets and four-
                     factor alpha, but not in the same fund family. A
                     fund is randomly selected from the pool of funds
                     meeting these selection criteria. The extra return
                     difference due to family affiliation (i.e.,
                     performance shifting) can be calculated by
                     subtracting the performance difference of a
                     matched pair from the performance difference of an
                     actual pair.

                     Total Fee Case: Total fee is calculated as total
                     loads divided by seven plus the annual expense.
                     The procedure to construct the actual pair and
                     matched pair is similar to that described in the
                     past performer case, except that a fund is
                     classified as "high fee" ("low fee") if the fund's
                     total fee in year t is ranked above the 75th
                     (below the 25th) percentile within the same fund
                     family. A matched pair is constructed when the
                     high and low fee funds in an actual pair are
                     replaced by very similar funds in the same
                     investment style and belonging to the same decile
                     in terms of total fees and total net assets in the
                     corresponding year, but not in the same fund
                     family.

[IPORet.sup.H>L]     For each fund, the average first day IPO
                     underpricing return in year t is calculated, where
                     the underpricing return is defined as the
                     percentage increase from the offer price to the
                     first day closing price. Funds are partitioned
                     into quartiles within the family based on their
                     average IPO underpricing returns in year t. Then,
                     in an actual pair, [IPORet.sup.H>L] takes a value
                     of three when the ranking of the high performing
                     fund (high fee fund) is higher than that of the
                     family-matched low performing fund (low fee fund)
                     by three. [IPORet.sup.H>L] takes a value of two
                     when the ranking of the high performing fund (high
                     fee fund) is higher than that of its counterpart
                     by two. [IPORet.sup.H>L] takes a value of one when
                     the ranking of the high performing fund (high fee
                     fund) is higher than that of its counterpart by
                     one, and zero otherwise.

[IPO Dollar          For each fund in year t, the dollar amount of
amount.sup.H>L]      underpricing is obtained by calculating the first
                     day underpricing times the number of shares held
                     in the fund. Funds are partitioned into quartiles
                     within the family based on their IPO underpricing
                     amount in year t. In an actual pair, [IPO Dollar
                     amount.sup.H>L] takes a value of one when the
                     ranking of the high performing fund (high fee
                     fund) is higher than that of the family-matched
                     low performing fund (low fee fund), and zero
                     otherwise.

Relative Number      Natural logarithm of the ratio of the average
of Directorships     number of funds overseen by independent directors
                     who sit on low performing funds (low fee fund) to
                     the average number of funds overseen by
                     independent directors who sit on high performing
                     funds (high fee fund).

Relative             Ratio of the overlapping rate of the low
Overlapping Rate     performing fund (low fee fund) to the overlapping
                     rate of the high performing fund (high fee fund).

Diff_BoardSize       The difference between the board size of the low
                     performing fund (low fee fund) and the board size
                     of the high performing fund (high fee fund).

Diff_IndRatio        The difference in the percentage of independent
                     directors on the low performing fund's (low fee
                     fund) board and on the high performing fund's
                     (high fee fund) board.

Chair Dummy          Takes a value of one if the chairman in the low
                     performing fund (low fee fund) is independent
                     regardless as to whether the chairman in the high
                     performing fund (high fee fund) is independent,
                     and zero otherwise.

Return Gap, Fund Opaqueness, and Cross-Fund Learning

Return Gap           Following the methodology of Kacperczyk et al.
                     (2008), the Return Gap is the difference between
                     the actual fund performance and the performance of
                     a hypothetical portfolio that invests in the
                     previously disclosed fund holdings.

Opaque               The correlation coefficient between actual fund
                     performance and the performance of a hypothetical
                     portfolio that invests in the previously disclosed
                     fund holdings is calculated. The correlation
                     coefficient in the previous year is ranked among
                     equity funds in the corresponding year. A dummy
                     variable, Opaque, takes a value of one if the
                     fund's correlation coefficient is among the bottom
                     one-third among equity funds in the corresponding
                     year, and zero otherwise.

Correlation of       For each fund in year t, the idiosyncratic returns
Idiosyncratic        are estimated by using a rolling 12-month window
Returns              and a four-factor model. The correlation of
                     idiosyncratic returns is calculated as the average
                     of the pairwise correlations between a fund's
                     idiosyncratic returns and each other fund's
                     idiosyncratic returns in its family in year t.

Instrumental Variables

Change in Gaps       The change in the absolute value of the minimum
                     (0, percentage of independent director-75%) for
                     each fund in the period after 2003.

ln(# of firms)       Natural logarithm of one plus the number of
                     financial firms (i.e., firms with SIC codes
                     ranging from 6000 to 6999) with headquarters in
                     the same state as the fund's management company in
                     period t.

Industry Dummy =     For the first available fund in a fund's Lipper
1 if year            objective style. Industry Dummy = 1 if year
inception < 1980     inception < 1980 means that the first available
                     fund's year of inception is prior to 1980.

ln(Demand)           Natural logarithm of one plus the ratio of the
                     number of independent directors to the number of
                     board seats available in the fund's Lipper
                     objective style in the sample.

Industry Dummy =     The first available fund's year of inception in
1 if [year.sup.old   the low performing fund's (low fee fund's) Lipper
.sub.inception] <    objective style is earlier than that in the high
[year.sup.new        performing fund's (high fee fund's) Lipper
.sub.inception]      objective style.

Diff_Demand          (Ratio of the number of independent directors to
                     the number of board seats available in the low
                     performing fund's (low fee fund's) Lipper
                     objective) -(Ratio of the number of independent
                     directors to the number of board seats available
                     in the high performing fund's (high fee fund's)
                     Lipper objective)

Control Variables

Fund Expense         The expense ratio of a fund in year t.

Fund Age             Fund's age in year t.

Fund Size            The total net assets of a fund in year t.

Fund's Carhart's     Carhart's (1997) four-factor alpha of a fund in
(1997) four-         year t.
factor alpha

Fund Turnover        Fund Turnover Ratio in year t. CRSP defines it as
                     the minimum of aggregated sales or aggregated
                     purchases of securities divided by the average
                     12-month total net assets of the fund.

Std-family           Cross-fund standard deviation of the four-factor
                     alpha of all member funds within a family in year
                     t.

Alpha-family         Family-level performance, calculated as the
                     TNA-weighted average of the fund-level Carhart's
                     (1997) four-factor alpha in year t.

Mtna-ffamily         Fund family total net assets under management in
                     year t.

N-family             Total number of member funds within the fund
                     family in year t.

PC_dummy             A dummy variable that is equal to one if there is
                     another fund managed by the same fund family with
                     performance in the top 5% of its category in year
                     t, that is, a "star" fund, and zero otherwise.


I thank an anonymous referee and Raghavendra Rau (Editor). Their insightful comments contributed enormously to this paper. I am grateful for the valuable comments and suggestions from Hsuan-Chi Chen, Yanzhi (Andrew) Wang, seminar participants at the National Cheng-chi University in Taiwan, and especially from Konan Chan and Hong-Yi Chen. I am also grateful for the research assistance of Pei Lan Su, Ya Ting Wu, Kate Valencia, Weng-Feng Wang, and Yi Hsun Lee. I gratefully acknowledge the financial support from the Ministry of Science and Technology in Taiwan (100-2410-H-003019- MY3; 103-2410-H-003-031104-2410-H-003-004-) and from the library of the National Taiwan Normal University in Taiwan.

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Christine (Whuei-wen) Lai *

* Christine (Whuei-wen) Lai is at Graduate Institute of Management in the College of Management at National Taiwan Normal University in Taiwan.

(1) These perspectives include fee setting (Tufano and Sevick, 1997; Del Guercio, Dann, and Partch, 2003; Kuhnen, 2005; Evans and Fahlenbrach, 2012), fund performance (Meschke, 2007; Adams, Mansi, and Nishikawa, 2010), organizational structure (Ferris and Yan, 2009), fund mergers (Khorana, Tufano, and Wedge, 2007), fund scandals (Ferris and Yan, 2007), fund protection against market timing (Zitzewitz, 2003), and manager turnover (Dangl, Wu, and Zechner, 2008; Ding and Wermers, 2009; Fu and Wedge, 2011). Ferris, Jagannathan, and Pritchard (2003) and Fich and Shivdasani (2006) examine the issue of multiple board appointments in corporate firms.

(2) Brown and Wu (2016) model a fund's performance as a combination of a fund-specific component and a common component shared by all of a family's funds. They measure the common component using the average manager overlap rate between the fund and the rest of its family.

(3) Tate and Jackson (2000) note that other responsibilities include electing officers, serving on committees, monitoring a fund's investment performance, monitoring personal trading policies, monitoring the use of derivatives, monitoring soft dollar practices, declaring dividends, monitoring disclosure and general investor communications, and monitoring regulatory compliance and overall business operations.

(4) Following the seminal contribution of Bernheim and Whinston, common agency literature has addressed a variety of problems in the fields of auctions (Bernheim and Whinston, 1986b), public goods provision through voluntary contributions (Laussel and Le Breton, 1998), and government policy making (Dixit, Grossman, and Helpman, 1997). Other studies extend the applicability of the common agency framework (David, 1998; Fraysse, 1993; Kahn and Mookherjee, 1998; Martimort, 1996a, 1996b) to the relationship between two companies with (1) a common input supplier, (2) a common retailer or wholesale agent, (3) a common research agency, and (4) a common consultant (Mezzetti, 1997).

(5) I begin with the top 60 sponsors ranked by total net assets at the end of 2008. On average, these families manage 90% of the total assets in the universe of CRSP equity funds over the sample period. However, I delete five of the 60 fund families due to issues related to data availability on EDGAR.

(6) I run separate regressions both with and without interaction terms. The results in both sets of specifications are similar in terms of sign and significance, except that the IDMA measure is the Relative Number of Directorships. The coefficient of the Relative Number of Directorships is -1.519 with statistical significance when the interaction term is not included in the model. However, the coefficient of the Relative Number of Directorships becomes insignificant when the interaction term is included in the model, as shown in Column (5) of Table IV, Panel A. For brevity, I only report the regressions with interaction terms.

(7) In the analysis of ordered logistic regression models, I consider alternative methodologies suggested by Cameron and Miller (2015) in the article of "A Practitioner's Guide to Cluster-Robust Inference." I use the most conservative method to compute standard errors.

(8) The marginal effect based on predicted probabilities for a given fund in a probit model is defined as [partial derivative]P[IPO Dollar [amount.sup.H>L.sub.i,t] = l|[x.sub.kit,]; [[beta].sub.0], ... , [[beta].sub.k]]/[partial derivative][x.sub.kit] for a given fund i. For the marginal effect of IDMA measures, I report the average marginal effect as the average of all of the marginal effects across funds. Similarly, I obtain predicted probabilities after the ordered logistic model is specified, and I see how the probabilities of membership in each category of [IPORet.sup.H>L] change for one instant change in the IDMA measure, leaving the other variable value as is.

(9) One may have concerns that both IDMAs and fund managers who manage more than one fund within a management company may be channels associated with a fund's information transfer. Thus, I control the average manager overlap rate between the fund and the rest of its family in model specifications as a robustness check. In order to calculate average manager overlap rate, I collect fund manager information from the CRSP Survivor-Bias-Free US Mutual Fund database. I address the issues of anonymous management and inconsistency in fund manager names when I collect fund manager information. Then I calculate the average manager overlap rate between the fund and the rest of its family, in which for each pair of funds, the manager overlap rate is defined as the number of managers common to the two funds divided by the average number of managers of the two funds. I find that, in the IDMAs and Cross Fund Subsidization analysis, my current results are robust when I include the average manager overlap rate in the model specifications. Since there is anonymous management (e.g., team management) in the mutual fund industry, I lose observations when I include the average manager overlap rate in the models. For brevity, I do not report the results, but they are available upon request.

(10) When the return gap is the dependent variable, I also perform an exogeneity test in which the null hypothesis of the Durbin and Wu-Hausman tests is that the Overlapping Rate can be treated as exogenous. The test statistics of both the Wu-Hausman F test (F-statistic= 1.425; p-value = 0.233) and the Durbin-Wu-Hausman Chi-squared tests (Chisquared= 1.441; p-value = 0.230) are not statistically significantly different from zero, so the null of exogeneity is not rejected. Then I only report the OLS results in Table IX.
Table I. Summary Statistics: Fund and Family Characteristics

This table reports summary statistics for the equity funds in the
sample. The sample covers the period from 2002 to 2008 including
3,925 fund-year observations. Board Characteristics include board
size (Board Size), the percentage of independent directors
(Independent Directors), and an independent chair dummy
(Independent Chair). # of Directorships is measured by using the
average number of directorships held by independent directors at
the fund level. Overlapping Rate for a fund in year t is
calculated by averaging the pairwise independent director overlap
rate between the fund itself and other funds in the family, while
the independent director overlap rate is calculated as the ratio
of the number of independent directors overseeing both funds to
the average number of independent directors of the two funds.
Fund Characteristics include Carhart's (1997) four-factor alpha
(4-Factor Alpha), fund expense (Expense Ratio), year-end fund age
(Age), year-end fund asset size (Fund Size), and the turnover
ratio of a fund. Return Gap is defined as the differential
between the actual fund performance and the performance of a
hypothetical portfolio that invests in the previously disclosed
fund holdings. Correlation of Idiosyncratic Returns is calculated
as the average of the pairwise correlations between a fund's
idiosyncratic returns (based on the four-factor model) and each
other fund's idiosyncratic returns in its family in year t. # IPO
per Fund is measured by the number of IPOs held by a fund over
year t. IPO Underpricing Return (%) reports the average first day
IPO underpricing return in which the IPOs are held by a fund over
year t. Fund Family Characteristics include the total net assets
under management of a fund family (TNA Family ($millions)) in
year t, the total number of member funds managed by the family
(# of Funds), family-level performance (Alpha Family), which is
calculated as the TNA-weighted average of the fund-level Carhart
(1997) four-factor alpha, and the cross-fund standard deviation
of the four-factor alpha of all member funds within family (Std
Family). These family measures are constructed in accordance with
the definitions of Sirri and Tufano (1998). PC_dummy is a dummy
variable that is equal to one if there is another fund managed by
the same fund family with performance in the top 5% of its
category, and zero otherwise.

                                    Mean         Median      Std. Dev.

Governance characteristics
  Board Size                          10.44        10.00          3.79
  Independent Directors (%)           77.99        80.00         12.22
  Independent Chair (dummy)            0.46         0.00          0.50
  Number of Directorships (per        46.99        42.27         29.40
    fund)
  Overlapping Rate (%)                90.29        95.19         14.14
Fund characteristics
  4-Factor Alpha (monthly)(%)          0.07        -0.04          2.70
  Expense Ratio (%)                    1.20         1.21          0.52
  Age (years)                          8.68         7.28          8.31
  Fund Size ($millions)            1,349.00       338.00      4,076.00
  Turnover Ratio (%)                  76.75        59.00         76.42
  Return Gap (%)                       0.09         0.01          1.21
  Correlation of Idiosyncratic        15.06        14.32         22.84
    Returns (4-factors) (%)
IPO characteristics
  # IPO per Fund                       3.01         2.00          3.66
  IPO Underpricing Return (%)         18.36        14.41         18.58
Family characteristics
  TNA Family ($millions)         181,401.00    89,882.00    268,764.00
  # of Funds                         417.00       403.00        246.00
  Alpha Family (monthly) (%)           0.07         0.04          0.21
  Std Family (%)                       1.08         0.78          0.99
  PC_dummy                             0.94         1.00          0.24

                                    5th          95th
                                 Percentile   Percentile

Governance characteristics
  Board Size                          6.00         17.00
  Independent Directors (%)          55.56         92.31
  Independent Chair (dummy)           0.00          1.00
  Number of Directorships (per        7.50         91.90
    fund)
  Overlapping Rate (%)               61.15         99.44
Fund characteristics
  4-Factor Alpha (monthly)(%)        -1.35          1.50
  Expense Ratio (%)                   0.22          2.00
  Age (years)                         1.00         22.84
  Fund Size ($millions)               5.00      5,399.00
  Turnover Ratio (%)                  5.00        203.00
  Return Gap (%)                     -0.85          1.17
  Correlation of Idiosyncratic      -20.00         51.82
    Returns (4-factors) (%)
IPO characteristics
  # IPO per Fund                      1.00         11.00
  IPO Underpricing Return (%)        -4.33         57.50
Family characteristics
  TNA Family ($millions)          5,047.00    528,633.00
  # of Funds                         58.00        923.00
  Alpha Family (monthly) (%)         -0.18          0.40
  Std Family (%)                      0.32          2.85
  PC_dummy                            0.00          1.00

Table II. Determinants of Independent Directors with Multiple
Board Affiliations

This study's analysis is limited to the set of funds that belong
to the top 55 sponsors of US mutual funds, ranked by the dollar
value of net assets under management at the end of 2008. These
fund families manage more than 80% of the total assets in the
universe of CRSP equity funds over the sample period from 2002 to
2008. I collect board members' names from fund prospectuses (Form
485) filed with the SEC for all available funds (including equity
and bond funds) in the EDGAR Pro database from 2002 to 2008. This
procedure allows me to have 7,639 preliminary fund-year
observations including 63,055 records of independent directors.
Based on the 63,055 records of independent directors, I calculate
the number of board affiliations for each independent director
and have 3,303 nonrepeated independent director-year
observations. Panel A reports the summary statistics based on
3,303 nonrepeated director-year observations. Retired (%)
indicates the percentage of independent directors who are retired
in the sample. In Panel B, I use the Fama-MacBeth (1973) method
to examine the determinants of IDMAs at the director level. The
dependent variable is the natural logarithm of the number of
funds overseen by an independent director in year t. Independent
directors are categorized into one of four occupations:
executives from other firms (Executive), retired executives from
other firms (Retired Executive), academics (Academics), and
other. I also control for family and year dummies. Standard
errors are adjusted to correct for heteroskedasticity and
autocorrelation using the Newey-West (1987) estimator with lag
one. Panel B reports the Fama-MacBeth (1973) regression results
based on 3,303 director-year observations. In the interest of
brevity, the coefficients of year and family dummies are not
reported. When I investigate fund-level characteristics, I
restrict my sample to equity funds including 3,925 fund-year
observations of equity funds. Panel C presents the determinants
of Number of Directorships and Overlapping Rate on fund level by
using the 3,925 fund-year observations of equity funds. Retired
Executive (Executive, Academics, or Independent Director's Age
Over 60) is then defined as the number of retired executives from
other firms (executives, professors, or independent directors
over 60 years of age) divided by board size. Year dummies and
family dummies are included in the models. The standard errors
are adjusted upward for clustering at the fund family level.
Definitions of all of the variables are provided in the Appendix.

Panel A. Director-Level Summary
(N = 3,303 Director-Year Observations)
                                                       Summary
Attributes
                                                        10.57
Retired (%)                                              7.72
Executive (%)                                            0.67
Retired Executive (%)                                    6.87
Academics (%)                                           48.86
Ind. Director's Age over 60 (%)                         32.70
Tenure > 5 years (%)                                    62.45
Average (years old)

Panel B. Fama-MacBeth Regression: Determinants of IDMAs on
Director-Level Dependent Variable: ln(Number of Directorships
of Independent Director) N = 3,303 Director-Year Observations

                                                    Ind.
                                                 Director's
              Retired                              Age
             Executive  Executive    Academics   Over 60     Tenure

Coefficient   0.492 **    0.096      0.347 ***    -0.046      -0.003
r-value      (2.312)     (1.287)    (6.158)      (-0.531)    (-1.272)

Panel C. OLS Regressions: Determinants of IDMAs on Fund Level
(N = 3,925 Fund Year Observations)

                                        Number of
                                      Directorships   Overlapping
                                           (1)         Rate (2)

Change in Gaps                          -0.015 **      -0.007 ***
                                       (-1.983)       (-3.277)
Retired [Executive.sub.t]                1.719 *        0.397 *
                                        (1.911)        (1.780)
[Executive.sub.t]                       -0.671         -0.069
                                       (-0.664)       (-0.353)
[Academics.sub.t]                        1.159 *       -0.125
                                        (1.751)       (-1.140)
Avg. Ind. Director [Age.sub.t]          -0.018         -0.017 ***
                                       (-0.873)       (-2.696)
Ind. Director's Age Over [60.sub.t]      0.107         -0.008
                                        (0.346)       (-0.185)
Avg. [Tenure.sub.t]                      0.006          0.002 *
                                        (0.557)        (1.723)
Board [Size.sub.t-1]                    -0.030         -0.005
                                       (-1.351)       (-1.185)
Independent [Ratio.sub.t-1]             -0.095          0.387 **
                                       (-0.163)        (2.338)
Independent [Chair.sub.t-1] (dummy)     -0.150         -0.008
                                       (-0.731)       (-0.332)
Expense [Ratio.sub.t-1]                 -0.036         -0.015
                                       (-0.625)       (-1.536)
[Age.sub.t-1]                            0.001         -0.001
                                        (0.070)       (-1.475)
Total Net [Asset.sub.t-1]                0.001          0.001
                                        (0.149)        (0.754)
4-Factor [Alpha.sub.t-1]                -0.004          0.001
                                       (-0.645)        (1.085)
Turnover [Ratio.sub.t-1]                 0.043 *        0.001
                                        (1.683)        (0.398)
[Std_family.sub.t-1]                     0.043          0.001
                                        (1.483)        (0.005)
[Alpha_family.sub.t-1]                   0.072          0.023
                                        (0.740)        (1.432)
[Mtna_family(1M).sub.t-1]               -0.135          0.008
                                       (-1.492)        (0.412)
N_family [(X100).sub.t-1]                0.627 ***      0.023
                                        (5.082)       (-1.168)
[PC_dummy.sub.t-1]                       0.166          0.018
                                        (1.514)        (0.700)
Intercept                                0.633          1.834 ***
                                        (0.386)        (4.686)
Year/family dummies                     Yes/yes        Yes/yes
Clustered standard error               Yes/family     Yes/family
N                                        3,925          3,925
Adjusted [R.sup.2]                       0.654          0.488

*** Significant at the 0.01 level.

** Significant at the 0.05 level.

* Significant at the 0.10 level.

Table III. Effects of Multiple Directorships on Performance
Shifting: Summary Statistics

Panel A reports a comparison between the high and the low family
value funds in terms of the IDMAs measures. Panel B and C provide
the statistics for performance shifting. Panel B presents
performance shifting across high and low performing funds. Panel
C reports performance shifting across high and low fee funds.
Performance shifting across groups is reported based on (1) the
rankings of the average number of directorships held by
independent directors of low performing (or low fee) funds (i.e.,
Number of Directorships) or (2) the overlapping rate of low
performing (or low fee) funds (i.e., Overlapping Rate).
Performance shifting is defined as follows. In Panel B, a fund is
classified as "high performing" ("low performing") if the fund's
four-factor alpha in year t is ranked above the 75th (below the
25th) percentile within the same investment style based on the
CRSP data set. "High performing fund" i is paired with "low
performing fund" j in the same fund family in year t (referred to
as the "actual pair"), and the difference in performance between
the high and low performing funds is calculated. A "matched pair"
is also constructed when the above mentioned high and low
performing funds in an actual pair are replaced by very similar
funds in the same investment style and belonging to the same
decile in terms of total net assets and the four-factor alpha,
but not in the same fund family. A fund is randomly selected from
the pool of funds meeting these selection criteria. The extra
return difference attributable to family affiliation (i.e.,
performance shifting) can be calculated by subtracting the
performance difference of the matched pair from the performance
difference of the actual pair. In Panel C, the procedure for
constructing an actual pair and a matched pair is similar to that
described in Panel B, except that a fund is classified as "high
fee" ("low fee") if the fund's total fee (including expense ratio
and loads/7) in year t is ranked above the 75th (below the 25th)
percentile within the same fund family.

Panel A. IDMAs Across High and Low Family Value Funds

                                        Performance

                            Low       High     Difference     t

Number of Directorships    55.75      56.28    -0.53 ***    -3.28
Overlapping                90.54      91.30    -0.76 ***    -3.12
  Rate (%)

                                         Total Fee

                            Low       High     Difference     t

Number of Directorships    54.59      53.66     0.93 ***     7.72
Overlapping                94.79      94.29     0.50 **      2.01
  Rate (%)

Panel B. Performance Shifting Across High and Low
Performing Equity Funds

                                       Std.      5th          95th
                     Mean     Median   Dev.   Percentile   Percentile

Performance          0.20      0.04    8.16     -2.08         2.56
  Shifting
  (monthly) (%)

Rank                              Performance Shifting

Number of                              Std.      5th          95th
Directorships        Mean     Median   Dev.   Percentile   Percentile

1 (Lowest)           0.36      0.05    6.87     -1.14         5.71
2                   -0.09      0.04    2.32     -1.33         1.36
3 (Highest)         -0.36      0.03    2.41     -2.89         1.77
3-1 difference      -0.72
t-value            (-0.84)

Overlapping Rate

1 (Lowest)           0.67      0.03    9.98     -2.61         2.07
2                    0.10      0.05    6.13     -2.10         3.41
3 (Highest)          0.01      0.04    1.68     -1.89         1.27
3-1 difference      -0.66 *
t-value            (-1.65)

Panel C. Performance Shifting Across High and Low Fee Equity Funds

                                         Std.      5th          95th
                     Mean       Median   Dev.   Percentile   Percentile

Performance          0.01       -0.05    3.40     -3.26         2.59
  Shifting
  (monthly) (%)

Rank                               Performance Shifting

Number of                                Std.      5th          95th
Directorships         Mean      Median   Dev.   Percentile   Percentile

1 (Lowest)           0.10       -0.01    4.66     -3.34         2.74
2                   -0.12       -0.01    2.84     -2.91         2.65
3 (Highest)         -0.22       -0.13    2.40     -3.31         2.29
3-1 difference      -0.32 **
t-value            (-2.26)

Overlapping Rate

1 (Lowest)           0.29       -0.04    4.71     -3.50         2.89
2                   -0.10       -0.06    1.82     -3.32         2.48
3 (Highest)         -0.21       -0.04    2.87     -2.60         2.23
3-1 difference      -0.50 ***
t-value            (-3.37)

*** Significant at the 0.01 level.

** Significant at the 0.05 level.

* Significant at the 0.10 level.

Table IV. The Effects of Multiple Directorships on Performance
Shifting: Regression Results

A high family value fund is defined as a high past performer or a
high total fee fund, while a low family value fund is defined in
terms of a lower past performer or a lower total fee fund. Panels A
and B present the results of IDMAs for past performance/total fee
cases based on OLS regressions. Panels C provides the results of
IDMAs for past performance/total fee cases using 2SLS regressions
to correct for endogeneity. The dependent variable is performance
shifting to enhance the performance of the high family value fund
at the expense of the low family value fund (in terms of
percentage), which is defined as the extra return difference
attributable to family affiliation and can be calculated by
subtracting the performance difference of the matched pair from the
performance difference of the actual pair. The actual pair and
matched pair are explained in Table III. For the independent
variables, Number of Directorships is defined as the natural
logarithm of the average number of funds overseen by a fund's
independent directors. Number of Directorships (High) indicates the
number of directorships for the high family value fund. Overlapping
Rate is the average independent director overlap rate between a
fund and the rest of the fund's family. I also use Relative Number
of Directorships, which is the natural logarithm of the ratio of
the average number of funds overseen by independent directors who
sit on low family value funds to the average number of funds
overseen by independent directors who sit on high family value
funds, and Relative Overlapping Rate, the ratio of the overlapping
rate of low family value funds to the overlapping rate of high
family value funds. I also calculate the overlap rate of
independent directors who sit on a pair of high and low family
value funds, referred to as Common Ind., to assess the impact of
the **common agency ** issue. I interact Common Ind. with each of the
IDMA measures, denoted as the Common Ind. x IDMA Measure. That is,
in Panels A and B, the interaction term is Common Ind. x Number of
Directorships (Low) (Column 1), Common Ind. x Number of
Directorships (High) (Column 2), Common Ind. x Overlapping Rate
(Low) (Column 3), Common Ind. x Overlapping Rate (High) (Column 4),
Common Ind. x Relative Number of Directorships (Column 5), or
Common Ind. x Relative Overlapping Rate (Column 6). Diff_BaordSize
is the difference between the board size of the low family value
fund and the board size of the high family value fund.
Diff_IndRatio is the difference in the percentage of independent
directors on the board of the low family value fund and the
percentage on the board of the high family value fund. Chair Dummy
takes a value of one if the chairman in the low family value fund
is independent regardless as to whether the chairman in the high
family value fund is independent or not, and zero otherwise. I
control fund characteristics, including differences in expense
ratios, fund ages, fund sizes, fund turnover ratios, and fund
four-factor alphas in the prior year, between low and high family
value funds. Family characteristics in the prior year are
controlled. The instruments used in 2SLS models are based on Change
in Gaps, defined as the change in the absolute value of the minimum
(0, percentage of independent director-75%) for each fund in the
period after 2003. ln(# of firms) is defined as the natural
logarithm of one plus the number of firms located in the same state
as that of the fund's management company. For the first available
fund in a fund's Lipper objective style, Industry Dummy = 1 if year
inception < 1980 indicates that the first available fund's year of
inception is prior to 1980. In (Demand) indicates the natural
logarithm of one plus the ratio of the number of independent
directors to the number of board seats available in the fund's
Lipper objective style in the sample. In Columns (3), (4), (5),
(8), (9), and (10) of Panel C based on 2SLS, I instrument the
interaction terms in each column with interactions between my four
main instrumental variables (i.e., Change in Gaps, ln(# of firms),
Industry Dummy = 1 if year inception < 1980, and In (Demand)) and
the Common Ind. For example, when I instrument for the interaction
of Overlapping Rate (Low) with Common Ind. in Column (3), the
instruments are the products of Common Ind. and Change in Gap for
low family value funds, ln(# of firms), Industry Dummy = I if year
inception < 1980 for low family value funds, and ln(Demand) for low
family value funds. I control for year dummies and family dummies
in the OLS models and both stages of 2SLS models, and the
t-statistics reported in parentheses are calculated based on the
cluster-robust standard error at the fund family level. Definitions
of all of the variables and instruments are provided in the
Appendix.

Panel A. Base Models-Past Performance Case

                                    (1)           (2)           (3)

Number of Directorship (Low)     -0.901 **
Number of Directorship (High)   (-2.303)       -0.716 **
                                              (-2.095)
Overlapping Rate (Low)                                       -2.553 **
                                                            (-2.119)
Overlapping Rate (High)

Relative Number of
  Directorships
Relative Overlapping Rate

Common Ind. x IDMA Measure        0.301         0.131         0.367
                                 (1.081)       (0.555)       (0.418)
Dif_BoardSize                     0.423 **      0.319 *       0.407 **
                                 (2.285)       (1.903)       (2.136)
Diff_IndRatio (%)                -0.041        -0.063        -0.064
                                (-1.140)      (-1.482)      (-1.376)
Chair (dummy)                    -0.180         0.021        -0.054
                                (-0.424)       (0.051)      (-0.140)
Diff_Expense [Ratio.sub.t-1]     -0.127        -0.086        -0.124
  (%)                           (-0.212)      (-0.146)      (-0.206)
[Diff_Age.sub.t-1]               -0.029        -0.031        -0.031
                                (-1.303)      (-1.357)      (-1.353)
[Diff_Mtna.sub.t-1] ($B.)       -36.278       -27.460       -27.829
                                (-0.818)      (-0.690)      (-0.673)
[Diff_Alpha.sub.t-1] (%)         -0.714 ***    -0.716 ***    -0.715 ***
                                (-3.845)      (-3.847)      (-3.836)
Diff_Turnover [Ratio.sub.t-1]    -0.137        -0.157        -0.122
                                (-0.620)      (-0.707)      (-0.570)
[Std_famify.sub.t-1] (%)          0.001        -0.039         0.003
                                 (0.006)      (-0.331)       (0.024)
[Alpha_family.sub.t-1] (%)        0.453         0.370         0.381
                                 (0.509)       (0.410)       (0.429)
Mtna_family [($M).sub.t-1]       -0.001        -0.001        -0.001
                                (-0.860)      (-0.823)      (-0.256)
N_family [(X100).sub.t-1]         0.001        -0.001        -0.001
                                 (0.015)      (-0.137)      (-0.537)
[PC_dummy.sub.t-1]                0.919         0.880         0.881
                                 (1.151)       (1.034)       (1.029)
Year/family dummies               Yes/yes       Yes/yes       Yes/yes
Clustered standard error        Yes/family    Yes/family    Yes/family
N                                   3,056        3,056         3,056
Adj. [R.sup.2]                    0.213       0.213           0.213

                                    (4)           (5)           (6)

Number of Directorship (Low)
Number of Directorship (High)
Overlapping Rate (Low)
Overlapping Rate (High)          -2.791 **
                                (-2.043)
Relative Number of                             -1.081
  Directorships                               (-1.014)
Relative Overlapping Rate                                    -2.559 **
                                                            (-2.339)
Common Ind. x IDMA Measure        0.314        -0.730         0.486
                                 (0.365)      (-0.665)       (0.541)
Dif_BoardSize                     0.326 *       0.427 *       0.376
                                 (1.887)       (1.821)       (1.633)
Diff_IndRatio (%)                -0.058        -0.053        -0.060
                                (-1.322)      (-1.232)      (-1.259)
Chair (dummy)                    -0.055        -0.945         0.017
                                (-0.137)      (-1.415)       (0.050)
Diff_Expense [Ratio.sub.t-1]     -0.105        -0.153        -0.151
  (%)                           (-0.175)      (-0.252)      (-0.247)
[Diff_Age.sub.t-1]               -0.031        -0.027        -0.032
                                (-1.360)      (-1.231)      (-1.345)
[Diff_Mtna.sub.t-1] ($B.)       -23.399       -39.251       -36.480
                                (-0.609)      (-0.816)      (-0.787)
[Diff_Alpha.sub.t-1] (%)         -0.715 ***    -0.717 ***    -0.720 ***
                                (-3.837)      (-3.896)      (-3.900)
Diff_Turnover [Ratio.sub.t-1]    -0.129        -0.143        -0.137
                                (-0.602)      (-0.614)      (-0.589)
[Std_family.sub.t-1] (%)          0.002         0.082        -0.025
                                 (0.019)       (0.664)      (-0.205)
[Alpha_family.sub.t-1] (%)        0.353         0.539         0.400
                                 (0.390)       (0.553)       (0.445)

Mtna_family [($M).sub.t-1]       -0.001        -0.001        -0.001
                                (-0.089)      (-0.954)      (-0.479)
N_family [(X100).sub.t-1]        -0.001        -0.003        -0.001
                                (-0.547)      (-1.589)      (-0.191)
[PC_dummy.sub.t-1]                1.064         0.235         0.869
                                 (1.199)       (0.264)       (0.947)
Year/family dummies               Yes/yes       Yes/yes       Yes/yes
Clustered standard error        Yes/family    Yes/family    Yes/family
N                                  3,056         3,056         3,056
Adj. [R.sup.2]                    0.213         0.213         0.208

Panel B. Base Models-Total Fee Case

                                    (1)           (2)           (3)

Number of Directorship (Low)     -0.257
                                (-0.597)
Number of Directorship (High)                  -0.412
                                              (-0.905)
Overlapping Rate (Low)                                        0.072
                                                             (0.040)
Overlapping Rate (High)
Relative Number of
  Directorships
Relative Overlapping Rate
Common Ind. x IDMA Measure       -0.431 *      -0.345        -2.020 *
                                (-1.897)      (-1.440)      (-1.850)
Diff_BoardSize                   -0.119        -0.133        -0.108
                                (-1.100)      (-1.329)      (-1.056)
Diff_IndRatio (%)                -0.022        -0.015        -0.022
                                (-0.577)      (-0.404)      (-0.597)
Chair (dummy)                    -0.666        -0.658        -0.702
                                (-0.982)      (-0.946)      (-0.889)
Diff_Expense [Ratio.sub.t-1]     -0.090        -0.142        -0.025
  (%)                           (-0.362)      (-0.552)      (-0.106)
[Diff-Age.sub.t-1]               -0.002        -0.002        -0.001
                                (-0.225)      (-0.259)      (-0.101)
[Diff_Mtna.sub.t-1] ($B.)         2.708         4.896         3.577
                                 (0.123)       (0.215)       (0.164)
[Diff_Alpha.sub.t-1] (%)         -0.503 ***    -0.501 ***    -0.504 ***
                                (-6.081)      (-5.916)      (-5.881)
Diff_Turnover [Ratio.sub.t-1]    -0.001 **     -0.001 *      -0.001 **
                                (-2.056)      (-1.765)      (-2.000)
[Std.family.sub.t-1] (%)          0.200         0.211         0.183
                                 (1.072)       (1.126)       (1.026)
[Alpha-family.sub.t-1] (%)       -0.250        -0.262        -0.211
                                (-0.250)      (-0.261)      (-0.204)
Mtna_family [($M).sub.t-1]       -0.001        -0.001        -0.001
                                (-1.563)      (-1.541)      (-1.223)
N_family [(x 100).sub.t-1]       -0.001        -0.001        -0.002 *
                                (-1.332)      (-1.152)      (-1.749)
[PC_dummy.sub.t-1]               -0.393        -0.244        -0.663
                                (-0.593)      (-0.346)      (-0.879)
Year/family dummies               Yes/yes       Yes/yes       Yes/yes
Clustered standard error        Yes/family    Yes/family    Yes/family
N                                  4,017         4,017         4,017
Adj. [R.sup.2]                     0.165         0.164         0.164

                                    (4)           (5)           (6)

Number of Directorship (Low)
Number of Directorship (High)
Overlapping Rate (Low)
Overlapping Rate (High)           1.334
                                 (1.027)
Relative Number of                             -0.603
  Directorships                               (-0.484)
Relative Overlapping Rate                                    -0.692
                                                            (-0.818)
Common Ind. x IDMA Measure       -1.858 *      -2.352 **     -1.682 **
                                (-1.674)      (-2.101)      (-2.302)
Diff_BoardSize                    0.013        -0.006         0.049
                                 (0.215)      (-0.051)       (0.492)
Diff_IndRatio (%)                 0.019         0.003         0.009
                                 (1.027)       (0.108)       (0.374)
Chair (dummy)                     0.357        -0.650        -0.615
                                 (0.759)      (-0.805)      (-0.787)
Diff_Expense [Ratio.sub.t-1]      0.240         0.035        -0.023
  (%)                            (1.065)       (0.154)      (-0.009)
[Diff-Age.sub.t-1]               -0.002         0.004         0.004
                                (-0.188)       (0.626)       (0.666)
[Diff_Mtna.sub.t-1] ($B.)        11.146        -9.659       -11.152
                                 (0.484)      (-0.489)      (-0.567)
[Diff_Alpha.sub.t-1] (%)         -0.404 ***    -0.442 ***    -0.442 ***
                                (-3.752)      (-6.348)      (-6.384)
Diff_Turnover [Ratio.sub.t-1]    -0.001        -0.001 *      -0.001 *
                                (-1.457)      (-1.769)      (-1.787)
[Std.family.sub.t-1] (%)          0.227 ***     0.211         0.216
                                 (2.769)       (1.282)       (1.315)
[Alpha-family.sub.t-1] (%)       -0.109        -0.039        -0.045
                                (-0.145)      (-0.039)      (-0.046)
Mtna_family [($M).sub.t-1]       -0.001        -0.001        -0.001
                                (-1.000)      (-1.317)      (-1.353)
N_family [(x 100).sub.t-1]       -0.001        -0.001        -0.001
                                (-1.463)      (-1.520)      (-1.503)
[PC_dummy.sub.t-1]               -0.218        -0.517        -0.383
                                (-0.438)      (-0.793)      (-0.602)
Year/family dummies               Yes/yes       Yes/yes       Yes/yes
Clustered standard error        Yes/family    Yes/family    Yes/family
N                                  4,017         4,017         4,017
Adj. [R.sup.2]                     0.202         0.126         0.126

Panel C. 2SLS Performance Case and Total Fee Case Dependent
Variable: Overlapping Rate (1st Stage); Performance Shifting
(2nd Stage)

                                            Performance Case

                                1st Stage      2nd Stage     2nd Stage
                               Overlapping        (No          (With
                                   Rate       Interaction   Interaction
                                  (Low)          Term)         Term)
                                   (1)            (2)           (3)

Overlapping Rate (Low)                         -3.394 **     -3.836 **
                                              (-2.447)      (-2.214)
Overlapping Rate (High)
Relative Overlapping Rate
Common [Ind..sup.L and H] x                                   0.781
  IDMA Measure                                               (1.400)
Diff_BoardSize                   0.0212 ***     0.418 ***     0.429 ***
                                (4.678)        (3.332)       (3.434)
Diff_IndRatio (%)               -0.005 ***     -0.063 **     -0.069 **
                               (-5.011)       (-2.233)      (-2.315)
Chair (dummy)                    0.045 ***     -0.039         0.021
                                (4.112)       (-0.127)       (0.072)
Change in Gaps                  -0.003 ***
                               (-2.650)
ln(# of firms)                  -0.028 ***
                               (-5.332)
Industry Dummy = 1 if            0.124 *
  year inception < 1980         (1.807)
ln(Demand)                       1.260 ***
                                (8.040)
Retired Executive               -0.451 **
                               (-2.407)
Executive                        0.239 ***
                                (3.093)
Academics                        0.362 ***
                                (5.966)
Avg. Ind Director Age            0.003 *
                                (1.866)
Ind. Director's Age Over 60      0.097 **
                                (3.267)
Avg. Tenure                      0.001 *
                                (1.684)
Control Variables                  Yes            Yes           Yes
Year/Family Dummies              Yes/yes        Yes/yes       Yes/yes
Clustered standard error                      Yes/family    Yes/family
N                                 3,056          3,056         3,056
Adj. [R.sup.2]                    0.773          0.213         0.213
F-statistic (excluded                            0.000         0.000
  instruments) p-value
Hansen J statistic (p-value)                     0.190         0.264

                                    Performance Case

                                2nd Stage     2nd Stage
                                  (With         (With
                               Interaction   Interaction
                                  Term)         Term)
                                   (4)           (5)

Overlapping Rate (Low)
Overlapping Rate (High)         -3.942 **
                               (-2.454)
Relative Overlapping Rate                     -2.871 **
                                             (-1.972)
Common [Ind..sup.L and H] x      0.618        -0.163
  IDMA Measure                  (1.159)      (-0.165)
Diff_BoardSize                   0.315 **      0.396 ***
                                (2.470)       (2.667)
Diff_IndRatio (%)               -0.059 **     -0.058 **
                               (-2.126)      (-2.184)
Chair (dummy)                   -0.011        -0.035
                               (-0.036)      (-0.090)
Change in Gaps
ln(# of firms)
Industry Dummy = 1 if
  year inception < 1980
ln(Demand)
Retired Executive
Executive
Academics
Avg. Ind Director Age
Ind. Director's Age Over 60
Avg. Tenure
Control Variables                  Yes           Yes
Year/Family Dummies              Yes/yes       Yes/yes
Clustered standard error       Yes/family    Yes/family
N                                 3,056         3,056
Adj. [R.sup.2]                    0.213         0.212
F-statistic (excluded             0.000         0.000
  instruments) p-value
Hansen J statistic (p-value)      0.226         0.060

                                             Total Fee Case

                                1st Stage      2nd Stage     2nd Stage
                               Overlapping        (No          (With
                                   Rate       Interaction   Interaction
                                  (Low)          Term)         Term)
                                   (6)            (7)           (8)

Overlapping Rate (Low)                         -2.001 **     -2.516
                                              (-2.157)      (-1.565)
Overlapping Rate (High)
Relative Overlapping Rate
Common [Ind..sup.L and H] x                                   0.348
  IDMA Measure                                               (0.379)
Diff_BoardSize                    0.004        -0.048        -0.002
                                 (0.863)      (-0.534)      (-0.014)
Diff_IndRatio (%)                -0.007 ***    -0.019 *      -0.003
                               (-11.058)      (-1.833)      (-0.134)
Chair (dummy)                     0.048 ***    -0.478        -0.402
                                 (5.556)      (-0.959)      (-0.827)
Change in Gaps                   -0.003 **
                                (-6.039)
ln(# of firms)                   -0.007 *
                                (-1.843)
Industry Dummy = 1 if             0.267 ***
  year inception < 1980          (4.385)
ln(Demand)                        1.668 ***
                                (10.634)
Retired Executive                 0.197
                                 (1.319)
Executive                         0.492 ***
                                 (6.941)
Academics                         0.116 ***
                                 (3.257)
Avg. Ind Director Age            -0.006 ***
                                (-4.005)
Ind. Director's Age Over 60       0.264 ***
                                (11.610)
Avg. Tenure                       0.002 ***
                                 (4.386)
Control Variables                  Yes            Yes           Yes
Year/Family Dummies              Yes/yes        Yes/yes       Yes/yes
Clustered standard error                      Yes/family    Yes/family
N                                 4,017          4,017         4,017
Adj. [R.sup.2]                    0.737          0.125         0.117
F-statistic (excluded                            0.000         0.000
  instruments) p-value
Hansen J statistic (p-value)                     0.093         0.001

                                     Total Fee Case

                                2nd Stage     2nd Stage
                                  (With         (With
                               Interaction   Interaction
                                  Term)         Term)
                                   (9)          (10)

Overlapping Rate (Low)
Overlapping Rate (High)         -2.601 *
                               (-1.743)
Relative Overlapping Rate                     -0.552
                                             (-0.813)
Common [Ind..sup.L and H] x      0.588        -2.107 **
  IDMA Measure                  (0.609)      (-2.318)
Diff_BoardSize                  -0.099         0.072
                               (-0.787)       (0.504)
Diff_IndRatio (%)                0.011        -0.011
                                (0.555)      (-0.448)
Chair (dummy)                   -0.417        -0.587
                               (-0.850)      (-0.774)
Change in Gaps
ln(# of firms)
Industry Dummy = 1 if
  year inception < 1980
ln(Demand)
Retired Executive
Executive
Academics
Avg. Ind Director Age
Ind. Director's Age Over 60
Avg. Tenure
Control Variables                  Yes           Yes
Year/Family Dummies              Yes/yes       Yes/yes
Clustered standard error       Yes/family    Yes/family
N                                 4,017         4,017
Adj. [R.sup.2]                    0.117         0.123
F-statistic (excluded             0.000         0.000
  instruments) p-value
Hansen J statistic (p-value)      0.156         0.002

*** Significant at the 0.01 level.

** Significant at the 0.05 level.

* Significant at the 0.10 level.

Table V. Fund Performance and IPO Allocations Across Groups

This table is based on 3,925 fund-year observations of equity
funds. Number of Directorships at the fund level is defined as the
average number of funds overseen by independent directors in a fund
in year t. Overlapping Rate is defined as the average independent
director overlap rate between a fund and the rest of the fund's
family, and the independent director overlap rate is defined as the
ratio of the number of independent directors overseeing the fund
and other funds in the family to the average number of independent
directors of the two funds. The value in each cell can be explained
as follows. The four-factor alpha of a fund in year t is ranked
within the fund family by quartile. Each year, funds are sorted
into Number of Directorships or Overlapping Rate) by quintiles. The
average rankings based on the four-factor alpha within the family
is calculated within each of the five fund portfolios (sorted by
Number of Directorships or Overlapping Rate). Then I calculate the
time-series average of these rankings over the entire sample
period. The table reports the statistics of the average rankings
based on (1) raw return, (2) the four-factor alpha, (3) the average
number of IPO deals per fund, (4) the average first day IPO
returns, and (5) the average dollar amount of underpricing, which
is defined as the first day IPO price increase times the number of
shares held by a fund. Panel A reports the results of Number of
Directorships, while Panel B reports the results of Overlapping
Rate.

Panel A. Equity Mutual Funds, Sorted by Number of Directorships

               Ranking Within
               Family (Lowest =          Ranking Within Family
Rank           1, Highest = 5)         (Lowest = 1, Highest = 5)

                        Four-                                 Dollar
Number of       Raw     Factor      IPO          IPO        Amount of
Directorships  Return   Alpha       Size       Returns     Underpricing

                (1)      (2)        (3)          (4)           (5)

1 (Lowest)      2.54     2.51       2.49         2.50          2.49
2               2.57     2.50       2.41         2.47          2.46
3               2.57     2.53       2.41         2.39          2.43
4               2.55     2.49       2.53         2.47          2.51
5 (Highest)     2.50     2.51       2.43         2.44          2.46
Total           2.55     2.51       2.46         2.45          2.46
5-1             0.01     0.00      -0.06        -0.06         -0.03
  difference
t-value        (0.65)   (0.31)    (-1.39)      (-1.11)       (-0.96)

Panel B. Equity Mutual Funds, Sorted by Overlapping Rate

               Ranking Within
               Family (Lowest =          Ranking Within Family
Rank           1 Highest = 5)          (Lowest = 1, Highest = 5)

                        Four-                                 Dollar
Overlapping     Raw     Factor      IPO          IPO        Amount of
Rate           Return   Alpha       Size       Returns     Underpricing

                (1)      (2)        (3)          (4)           (5)

1 (Lowest)      2.56     2.47      2.29         2.30         2.30
2               2.53     2.52      2.40         2.40         2.44
3               2.57     2.50      2.46         2.42         2.45
4               2.54     2.53      2.54         2.53         2.54
5 (Highest)     2.58     2.53      2.58         2.55         2.55
Total           2.55     2.51      2.45         2.44         2.46
5-1             0.02     0.06      0.29 ***     0.25 ***     0.25 ***
  difference
t-value        (0.32)   (1.06)    (6.89)       (6.30)       (6.14)

*** Significant at the 0.01 level.

Table VI. Multiple Directorships on the Allocation
of Underpricing IPOs

Panels A and B present the results for the past performance case.
Panel A estimates the effect of IDMA measures on Underpriced
Return (i.e., [IPORe.sup.H>L]) using ordered logistic models,
while Panel B estimates the effect of IDMA measures on Dollar
Amount of Underpricing (i.e., IPODollar [amount.sup.H>L]) using
probit models. Similarly, Panels C and D provide the results for
the total fee case based on the ordered logistic and probit
models, respectively. The dependent variable, IPORetH>L, is
defined as follows. In the performance case, a fund is classified
as "high performing" ("low performing") if the fund's four-factor
alpha in year t ranked above the 75th (below the 25th) percentile
within the same investment style based on the CRSP data set. The
high performing fund i is paired to low performing fund j under
the same fund family in year t (referred to as the actual pair).
In the total fee case, a fund is classified as "high fee" ("low
fee") if the fund's total fee (expense ratio plus loads/7) in
year t is ranked above the 75th (below the 25th) percentile
within the equity funds in the same fund family. High fee fund i
is paired to low fee fund j under the same fund family in year t
(referred to as the actual pair). I then calculate the yearly
average first day IPO underpricing returns of each fund and
measure the family quartile ranking of the fund in terms of its
average IPO underpricing return in year t. The IPO family ranking
of a high performing fund (or high fee fund) is compared to the
ranking of the low performing fund (or low fee fund) in an actual
pair. The categories of dependent variables in the multivariate
ordered logistic models are based on the ranking difference,
where an [IPORet.sub.t.sup.H>L] equal to three is assigned when
the ranking of the high family value fund (i.e., high past
performer or high fee fund) is higher than that of the low family
value fund (i.e., low past performer or low fee fund) by three
quartiles. [IPORet.sub.t.sup.H>L] equal to two is assigned when
the high family value fund is ranked higher than its counterpart
by two quartiles, and [IPORet.sub.t.sup.H>L] takes a value of one
if the high family value fund is ranked higher than its
counterpart by one quartile, and zero otherwise. The dependent
variable in Panels B and D is defined similarly to
[IPORet.sub.t.sup.H>L] in this manner, except that I use the
dollar amount of underpricing by calculating the first day
underpricing times the number of shares held, and I use the dummy
IPODollar [amount.sup.H>L] to represent that the high family
value fund has a higher dollar amount of underpricing than that
of the low family value fund and zero otherwise. Year dummies and
family dummies are included in all of the models. The
z-statistics reported in parentheses are calculated based on the
cluster-robust standard error at the fund family level.
Definitions of all of the variables are provided in the Appendix.

Panel A. Ordered Logistic Models (Dependent:
Underpriced Return, [IPORet.sup.H>L])--Performance Case

                                   (1)           (2)           (3)

Number of Directorships        -0.234
  (Low)                        (-1.418)
Number of Directorships                      0.037
  (High)                                     (0.175)
Overlapping Rate (Low)                                     -1.020 *
                                                           (-1.727)
Overlapping Rate (High)

Relative Number of
  Directorships
Relative Overlapping Rate

Common Ind. x IDMA Measure       0.112         0.072         0.232
                                (1.483)       (0.694)       (0.740)
Diff_BoardSize                  -0.063        -0.085        -0.038
                               (-0.967)      (-1.207)      (-0.621)
Diff_IndRatio (%)                0.015         0.010         0.012
                                (1.162)       (0.759)       (0.971)
Chair (dummy)                   -0.091        -0.493 **     -0.163
                               (-0.398)      (-2.131)      (-0.569)
Intercept1                       1.659         2.258         1.949
Intercept2                       1.902         2.515         2.196
Intercept3                       5.661         6.222         5.964
Control variables                  Yes           Yes           Yes
Year/family dummies              Yes/yes       Yes/yes       Yes/yes
Clustered standard error       Yes/family    Yes/family    Yes/family
N (fund pairs)                   2,989         2,989         2,989
Pseudo [R.sup.2]/                0.079         0.082         0.089
  Adj. [R.sup.2]
Wald Chi-Squared               348.30        354.39        359.71

                                   (4)           (5)           (6)

Number of Directorships
  (Low)
Number of Directorships
  (High)
Overlapping Rate (Low)

Overlapping Rate (High)        -0.425
                               (-0.705)
Relative Number of                           -2.464 ***
  Directorships                              (-3.349)
Relative Overlapping Rate                                   -1.282 **
                                                           (-2.050)
Common Ind. x IDMA Measure       0.001         0.889 **      0.422
                                (0.004)       (2.084)       (1.520)
Diff_BoardSize                  -0.073         0.034         0.011
                               (-1.212)       (0.491)       (0.167)
Diff_IndRatio (%)                0.015         0.022         0.016
                                (1.350)       (1.430)       (1.116)
Chair (dummy)                   -0.228        -0.479 *      -0.100
                               (-0.821)      (-1.855)      (-0.346)
Intercept1                       2.272         0.881         1.187
Intercept2                       2.518         1.128         1.433
Intercept3                       6.286         4.898         5.199
Control variables                  Yes           Yes           Yes
Year/family dummies              Yes/yes       Yes/yes       Yes/yes
Clustered standard error       Yes/family    Yes/family    Yes/family
N (fund pairs)                   2,989         2,989         2,989
Pseudo [R.sup.2]/                0.088         0.091         0.088
  Adj. [R.sup.2]
Wald Chi-Squared               356.64        333.86        322.73

Panel B. Probit Models (Dependent: Dollar Amount of
Underpricing, [IPODollar amount.sup.H>L])-Performance Case

                                   (1)           (2)           (3)

Number of Directorships         -0.213 ***
  (Low)                        (-2.381)
Number of Directorships                       -0.112
  (High)                                     (-1.036)
Overlapping Rate (Low)                                      -0.497 *
                                                           (-1.651)
Overlapping Rate (High)

Relative Number of
  Directorships
Relative Overlapping Rate

Common Ind. x IDMA Measure       0.078 **      0.070         0.102
                                (1.989)       (1.287)       (0.679)
Diff_BoardSize                  -0.026        -0.039        -0.018
                               (-0.766)      (-1.101)      (-0.530)
Diff_IndRatio (%)                0.001        -0.001        -0.001
                                (0.077)      (-0.072)      (-0.062)
Chair (dummy)                   -0.088        -0.322 ***    -0.098
                               (-0.784)      (-2.741)      (-0.700)
Intercept1                      -0.705 ***    -0.898 ***    -1.090 ***
                               (-2.394)      (-2.744)      (-3.346)
Control variables                  Yes           Yes           Yes
Year/family dummies              Yes/yes       Yes/yes       Yes/yes
Clustered standard error       Yes/family    Yes/family    Yes/family
N (fund pairs)                   2,989         2,989         2,989
Pseudo [R.sup.2]/                0.092         0.102         0.104
  Adj. [R.sup.2]
Wald Chi-Squared               333.69        363.14        361.29

                                   (4)           (5)           (6)

Number of Directorships
  (Low)
Number of Directorships
  (High)
Overlapping Rate (Low)

Overlapping Rate (High)         -0.137
                               (-0.447)
Relative Number of                            -1.481 ***
  Directorships                              (-4.092)
Relative Overlapping Rate                                   -0.683 **
                                                           (-2.290)
Common Ind. x IDMA Measure      -0.014         0.453 **      0.178
                               (-0.092)       (2.257)       (1.332)
Diff_BoardSize                  -0.034         0.025         0.010
                               (-1.048)       (0.697)       (0.279)
Diff_IndRatio (%)                0.002         0.001         0.001
                                (0.345)       (0.011)       (0.005)
Chair (dummy)                   -0.135        -0.292 **     -0.089
                               (-0.976)      (-2.146)      (-0.635)
Intercept1                      -1.310 ***    -0.410        -0.672 **
                               (-3.983)      (-1.367)      (-1.919)
Control variables                  Yes           Yes           Yes
Year/family dummies              Yes/yes       Yes/yes       Yes/yes
Clustered standard error       Yes/family    Yes/family    Yes/family
N (fund pairs)                   2,989         2,989         2,989
Pseudo [R.sup.2]/                0.103         0.100         0.105
  Adj. [R.sup.2]
Wald Chi-Squared               356.24        339.13        338.55

Panel C. Ordered Logistic Models (Dependent:
Underpriced Return, [IPORet.sup.H>L])--Total Fee Case

                                   (1)           (2)           (3)

Number of Directorships          0.225
  (Low)                         (1.251)
Number of Directorships                        0.205
  (High)                                      (1.316)
Overlapping Rate (Low)                                      -1.593 **
                                                           (-2.129)
Overlapping Rate (High)

Relative Number of
  Directorships
Relative Overlapping Rate

Common Ind. x IDMA Measure      -0.081        -0.033         0.297
                               (-0.806)      (-0.392)       (0.923)
Diff BoardSize                  -0.062        -0.058        -0.025
                               (-1.174)      (-1.053)      (-0.452)
Diff_IndRatio (%)                0.005        -0.001         0.011
                                (0.644)      (-0.076)       (1.174)
Chair (dummy)                   -0.189        -0.201        -0.943 ***
                               (-1.181)      (-1.271)      (-4.511)
Interceptl                       2.214         2.277         0.772
Intercept2                       2.332         2.395         0.888
Intercept3                       7.242         7.305         5.718
Control variables                  Yes           Yes           Yes
Year/family dummies              Yes/yes       Yes/yes       Yes/yes
Clustered standard error       Yes/family    Yes/family    Yes/family
N (fund pairs)                   3,961         3,961         3,961
Pseudo [R.sup.2]/                0.096         0.096         0.108
  Adj. [R.sup.2]
Wald Chi-Squared               433.95        430.00        460.80

                                   (4)           (5)           (6)

Number of Directorships
  (Low)
Number of Directorships
  (High)
Overlapping Rate (Low)

Overlapping Rate (High)          0.621
                                (1.270)
Relative Number of                            -1.296 ***
  Directorships                              (-2.983)
Relative Overlapping Rate                                   -2.095 **
                                                           (-2.205)
Common Ind. x IDMA Measure      -0.172        -0.151        -0.080
                               (-0.548)      (-0.436)      (-0.245)
Diff BoardSize                  -0.050        -0.001         0.033
                               (-0.847)      (-0.023)       (0.555)
Diff_IndRatio (%)                0.060 ***    -0.010        -0.011
                                (3.310)      (-1.256)      (-1.341)
Chair (dummy)                   -0.943 ***    -1.013 ***    -0.936 ***
                               (-4.562)      (-4.845)      (-4.417)
Interceptl                       2.489         0.981        -0.154
Intercept2                       2.614         1.101        -0.033
Intercept3                       7.557         6.046         4.912
Control variables                  Yes           Yes           Yes
Year/family dummies              Yes/yes       Yes/yes       Yes/yes
Clustered standard error       Yes/family    Yes/family    Yes/family
N (fund pairs)                   3,961         3,961         3,961
Pseudo [R.sup.2]/                0.122         0.118         0.118
  Adj. [R.sup.2]
Wald Chi-Squared               539.76        533.58        500.44

Panel D. Probit Models (Dependent: Dollar Amount of
Underpricing, [IPODollar amount.sup.H>L])--Total Fee Case

                                   (1)           (2)           (3)

Number of Directorships          0.073
  (Low)                         (0.786)
Number of Directorships                        0.097
  (High)                                      (1.085)
Overlapping Rate (Low)                                      -0.807 **
                                                           (-2.071)
Overlapping Rate (High)

Relative Number of
  Directorships
Relative Overlapping Rate

Common Ind. x IDMA Measure      -0.029        -0.020         0.192
                               (-0.557)      (-0.427)       (1.109)
Diff_BoardSize                  -0.028        -0.026        -0.011
                               (-0.952)      (-0.851)      (-0.353)
Diff_IndRatio (%)               -0.001        -0.004         0.003
                               (-0.267)      (-0.726)       (0.522)
Chair (dummy)                   -0.016        -0.013        -0.457 ***
                               (-0.179)      (-0.150)      (-3.992)
Intercept1                      -1.238 ***    -1.329 ***    -0.655 *
                               (-4.775)      (-5.111)      (-1.805)
Control variables                  Yes           Yes           Yes
Year/family dummies              Yes/yes       Yes/yes       Yes/yes
Clustered standard error       Yes/family    Yes/family    Yes/family
N (fund pairs)                   3,961         3,961         3,961
Pseudo [R.sup.2]/                0.117         0.117         0.132
  Adj. [R.sup.2]
Wald Chi-Squared               478.47        470.94        496.62

                                   (4)           (5)           (6)

Number of Directorships
  (Low)
Number of Directorships
  (High)
Overlapping Rate (Low)

Overlapping Rate (High)          0.455
                                (1.577)
Relative Number of                            -0.841 ***
  Directorships                              (-3.840)
Relative Overlapping Rate                                   -1.166 **
                                                           (-2.469)
Common Ind. x IDMA Measure      -0.054        -0.026        -0.041
                               (-0.325)      (-0.143)      (-0.244)
Diff_BoardSize                  -0.025         0.006         0.027
                               (-0.826)       (0.198)       (0.817)
Diff_IndRatio (%)                0.025 ***    -0.009 **     -0.009 *
                                (2.923)      (-1.976)      (-1.883)
Chair (dummy)                   -0.466 ***    -0.511 ***    -0.437 ***
                               (-4.086)      (-4.389)      (-3.792)
Intercept1                      -1.643 ***    -0.634 **     -0.037
                               (-5.999)      (-2.458)      (-0.083)
Control variables                  Yes           Yes           Yes
Year/family dummies              Yes/yes       Yes/yes       Yes/yes
Clustered standard error       Yes/family    Yes/family    Yes/family
N (fund pairs)                   3,961         3,961         3,961
Pseudo [R.sup.2]/                0.147         0.143         0.143
  Adj. [R.sup.2]
Wald Chi-Squared               575.31        554.84        534.46

*** Significant at the 0.01 level.

** Significant at the 0.05 level.

* Significant at the 0.10 level.

Table VII. The Effect of Multiple Directorships on the Allocation
of Underpricing IPOs-2SLS Regression Analysis

Panels A and B use a probit model with endogenous covariate
models to address endogeneity issues. Panel A presents the
results for the performance case, while Panel B presents the
results for the total fee case. The dependent variable is a dummy
equal to one when the high family value fund is ranked higher
than the low family value fund in terms of average IPO
underpricing returns, and zero otherwise. I also use the other
dependent variable for a robustness check. In other words, the
dependent variable is a dummy equal to one when the high family
value fund is ranked higher than the low family value fund in
terms of the dollar amount of underpricing, and zero otherwise.
The instruments used in the 2SLS models are based on Change in
Gaps, defined as the change in the absolute value of the minimum
(0, percentage of independent director-75%) for each fund in the
period after 2003. ln(# of firms) is defined as the natural
logarithm of one plus the number of firms located in the same
state as that of the fund's management company. For the first
available fund in a fund's Upper objective style, Industry Dummy
= 1 if year inceptions 1980 indicates that the first available
fund's year of inception is prior to 1980. ln(Demand) indicates
the natural logarithm of one plus the ratio of the number of
independent directors to the number of board seats available in
the fund's Lipper objective style in the sample. I also calculate
the overlap rate of independent directors who sit on a pair of
high and low family value funds, referred to as Common Ind., to
assess the impact of the "common agency" issue. When interaction
terms are included in the models, I instrument the interaction
term in each column with interactions between my four main
instrumental variables (i.e., Change in Gaps, ln(# of firms),
Industry Dummy = 1 if year inception < 1980, and ln(Demand)) and
the Common Ind.). I control for year and family dummies in both
stages of the 2SLS models, and the z-statistics reported in
parentheses are calculated based on the cluster-robust standard
error at the fund family level. Definitions of all of the
variables and the instruments are provided in the Appendix.

Panel A. 2SLS--Performance Case

                           1st Stage : Dependent Variable-Overlapping
                              Rate; OLS Model; 2nd Stage: Dependent
                             Variable-Preferential IPO allocations;
                                            Probit Model

                                      Without Interaction Term

                            1st Stage                     2nd Stage
                             Overlap       2nd Stage        Dollar
                               Rate       Underpriced     Amount of
                              (Low)          Return       Underprice

                               (1)            (2)            (3)

Overlapping Rate (Low)                     -1.982 ***     -2.069 ***
                                          (-2.779)       (-2.831)
Overlapping Rate (High)

Relative Overlapping
  Rate
[Common Ind..sup.L
  and H] x IDMA Measure
Diff_BoardSize               0.026 ***      0.016          0.026
                            (7.741)        (0.445)        (0.704)
Diff_IndRatio (%)           -0.003 ***      0.005         -0.003
                           (-5.768)        (0.727)       (-0.431)
Chair (dummy)                0.043 ***      0.130          0.134
                            (5.099)        (1.140)        (1.163)
Change in Gaps              -0.003 ***
                           (-2.799)
ln(# of firms)              -0.018 ***
                           (-3.359)
Industry Dummy = 1          -0.041 ***
  if year inception        (-4.038)
  < 1980
ln(Demand)                   0.095
                            (1.312)
Retired Executive            0.138
                            (0.886)
Executive                    0.136 ***
                            (2.633)
Academics                    0.068
                            (1.625)
Avg. Ind. Director          -0.015 ***
  Age                      (-7.551)
Ind. Director's              0.140 ***
  Age Over 60               (5.866)
Avg. Tenure                  0.005 ***
                            (6.264)
Intercept                    1.827 ** *     0.300          0.358
                            (14.606)       (0.361)        (0.419)
Control variables              Yes            Yes            Yes
Year/family dummies          Yes/yes        Yes/yes        Yes/yes
Clustered standard error                   Yes/family     Yes/family
N                             2,989          2,989          2,989
Wald Chi-Squared              0.810       381.61 ***     363.03 ** *
                              (Adj.
                            [R.sup.2])
Wald test of exogeneity                      0.019          0.017
  (p-value)

                           1st Stage : Dependent Variable-Overlapping
                              Rate; OLS Model; 2nd Stage: Dependent
                             Variable-Preferential IPO allocations;
                                          Probit Model

                                     With Interaction Term

                                           2nd Stage
                            2nd Stage        Dollar       2nd Stage
                           Underpriced     Amount of     Underpriced
                              Return       Underprice       Return

                               (4)            (5)            (6)

Overlapping Rate (Low)      -2.047 ***     -1.990 ***
                           (-2.954)       (-2.832)
Overlapping Rate (High)                                   -2.474 **
                                                         (-2.639)
Relative Overlapping
  Rate
[Common Ind..sup.L           0.529 ***      0.504 **       0.707 ***
  and H] x IDMA Measure     (2.704)        (2.566)        (3.189)
Diff_BoardSize               0.025          0.032         -0.045
                            (0.676)        (0.851)       (-1.285)
Diff_IndRatio (%)           -0.002         -0.008          0.017 **
                           (-0.283)       (-1.200)        (2.259)
Chair (dummy)                0.206 *        0.210 *        0.285 ***
                            (1.806)        (1.826)        (2.679)
Change in Gaps

ln(# of firms)

Industry Dummy = 1
  if year inception
  < 1980
ln(Demand)

Retired Executive

Executive

Academics

Avg. Ind. Director
  Age
Ind. Director's
  Age Over 60
Avg. Tenure

Intercept                   -0.188         -0.258          0.023
                           (-0.289)       (-0.389)        (0.027)
Control variables              Yes            Yes            Yes
Year/family dummies          Yes/yes        Yes/yes        Yes/yes
Clustered standard error    Yes/family     Yes/family     Yes/family
N                             2,989          2,989          2,989
Wald Chi-Squared           365.63 ***     346.82 ** *    389.53 ***

Wald test of exogeneity       0.032          0.069          0.000
  (p-value)

                           1st Stage : Dependent Variable-Overlapping
                              Rate; OLS Model; 2nd Stage: Dependent
                             Variable-Preferential IPO allocations;
                                          Probit Model

                                      With Interaction Term

                            2nd Stage                     2nd Stage
                              Dollar       2nd Stage        Dollar
                            Amount of     Underpriced     Amount of
                            Underprice       Return       Underprice

                               (7)            (8)             (9)

Overlapping Rate (Low)

Overlapping Rate (High)     -2.352 **
                           (-2.648)
Relative Overlapping                       -5.406 ***     -5.254 ***
  Rate                                    (-3.988)       (-3.919)
[Common Ind..sup.L           0.678 ***     -0.237         -0.226
  and H] x IDMA Measure     (3.177)       (-1.006)       (-0.975)
Diff_BoardSize              -0.033          0.337 ***      0.332 ***
                           (-0.947)        (3.276)        (3.251)
Diff_IndRatio (%)            0.010         -0.027 **      -0.035 **
                            (1.414)       (-2.020)       (-2.659)
Chair (dummy)                0.303 ** *    -0.199         -0.226
                            (2.853)       (-1.172)       (-1.356)
Change in Gaps

ln(# of firms)

Industry Dummy = 1
  if year inception
  < 1980
ln(Demand)

Retired Executive

Executive

Academics

Avg. Ind. Director
  Age
Ind. Director's
  Age Over 60
Avg. Tenure

Intercept                   -0.126          4.214 ***      4.138 ***
                           (-0.153)        (2.830)        (2.802)
Control variables              Yes            Yes            Yes
Year/family dummies          Yes/yes        Yes/yes        Yes/yes
Clustered standard error    Yes/family     Yes/family     Yes/family
N                             2,989          2,989          2,989
Wald Chi-Squared           372.89 ***     258.34 ***     243.79 ***

Wald test of exogeneity       0.000          0.000          0.000
  (p-value)

Panel B. 2SLS--Total Fee Case

                           1st Stage : Dependent Variable-Overlapping
                              Rate; OLS Model; 2nd Stage: Dependent
                              Variable-Preferential IPO allocations;
                           Probit Model

                           Without Interaction Term

                            1st Stage                     2nd Stage
                             Relative      2nd Stage        Dollar
                             Overlap      Underpriced     Amount of
                               Rate          Return       Underprice

                               (1)            (2)            (3)

Overlapping Rate (Low)                     -1.174 *       -1.344 **
                                          (-1.796)       (-2.096)
Overlapping Rate (High)

Relative Overlapping
  Rate
[Common Ind..sup.L
  and H] x IDMA Measure
Diff_BoardSize               0.021 ***     --0.013        -0.007
                            (6.086)       (-0.391)       (-0.213)
Diff_IndRatio (%)           -0.001          0.002          0.001
                           (-0.688)        (0.410)        (0.145)
Chair (dummy)                0.041 ***     -0.446 ***     -0.406 ***
                            (5.148)       (-3.752)       (-3.441)
Change in Gaps              -0.003 ***
                           (-8.572)
ln(# of firms)              -0.038 ***
                           (-5.350)
Industry Dummy = 1           0.064 *
  if year inception <       (1.768)
  1980
ln(Demand)                   0.352 ***
                            (3.786)
Retired Executive            0.611 ***
                            (6.268)
Executive                    0.040
                            (0.905)
Academics                    0.066 **
                            (2.414)
Avg. Ind. Director Age      -0.019 ***
                           (-11.172)
Ind. Director's Age over     0.030 **
  60                        (2.134)
Avg. Tenure                  0.004 ***
                            (6.691)
Intercept                    1.966 ***     -0.030          0.059
                            (15.293)      (-0.044)        (0.088)
Control variables              Yes            Yes            Yes
Year/family dummies          Yes/yes        Yes/yes        Yes/yes
Clustered standard error                   Yes/family     Yes/family
N                             3,961          3,961          3,961
Wald Chi-Squared              0.492       485.43 ***     498.53 ***
                              (Adj.
                            [R.sup.2])
Wald test of exogeneity                      0.040          0.007
  (p-value)

                           1st Stage : Dependent Variable-Overlapping
                              Rate; OLS Model; 2nd Stage: Dependent
                              Variable-Preferential IPO allocations;
                                          Probit Model

                                     With Interaction Term

                                           2nd Stage
                            2nd Stage        Dollar       2nd Stage
                           Underpriced     Amount of     Underpriced
                              Return       Underprice       Return

                               (4)            (5)            (6)

Overlapping Rate (Low)      -2.338 **      -2.632 **
                           (-2.160)       (-2.498)
Overlapping Rate (High)                                   -0.559
                                                         (-0.787)
Relative Overlapping
  Rate
[Common Ind..sup.L           0.518          0.602 *        0.101
  and H] x IDMA Measure     (1.625)        (1.960)        (0.378)
Diff_BoardSize              -0.003          0.003         -0.036
                           (-0.085)        (0.100)       (-1.047)
Diff_IndRatio (%)            0.009          0.009          0.036 ***
                            (1.381)        (1.376)        (3.687)
Chair (dummy)               -0.492 ***     -0.462 ***     -0.519 ***
                           (-4.021)       (-3.824)       (-4.245)
Change in Gaps

ln(# of firms)

Industry Dummy = 1
  if year inception <
  1980
ln(Demand)

Retired Executive

Executive

Academics

Avg. Ind. Director Age

Ind. Director's Age over
  60
Avg. Tenure

Intercept                    0.629          0.765         -0.697
                            (0.734)        (0.909)       (-1.304)
Control variables              Yes            Yes            Yes
Year/family dummies          Yes/yes        Yes/yes        Yes/yes
Clustered standard error    Yes/family     Yes/family     Yes/family
N                             3,961          3,961          3,961
Wald Chi-Squared           495.67 ***     516.81 ***     564.20 ***

Wald test of exogeneity       0.162          0.289          0.643
  (p-value)

                           1st Stage : Dependent Variable-Overlapping
                              Rate; OLS Model; 2nd Stage: Dependent
                              Variable-Preferential IPO allocations;
                                            Probit Model

                                       With Interaction Term

                            2nd Stage                     2nd Stage
                              Dollar       2nd Stage        Dollar
                            Amount of     Underpriced     Amount of
                            Underprice       Return       Underprice

                               (7)            (8)            (9)

Overlapping Rate (Low)

Overlapping Rate (High)     -0.921
                           (-1.294)
Relative Overlapping                        0.952          0.793
  Rate                                     (0.753)        (0.617)
[Common Ind..sup.L           0.228          0.288          0.223
  and H] x IDMA Measure     (0.866)        (1.236)        (0.962)
Diff_BoardSize              -0.039         -0.057         -0.048
                           (-1.181)       (-1.047)       (-0.868)
Diff_IndRatio (%)            0.029 ***      0.010          0.007
                            (3.410)        (0.955)        (0.640)
Chair (dummy)               -0.494 ***     -0.539 ***     -0.484 ***
                           (-4.087)       (-4.471)       (-4.047)
Change in Gaps

ln(# of firms)

Industry Dummy = 1
  if year inception <
  1980
ln(Demand)

Retired Executive

Executive

Academics

Avg. Ind. Director Age

Ind. Director's Age over
  60
Avg. Tenure

Intercept                   -0.541         -2.403 *       -2.261
                           (-1.009)       (-1.752)       (-1.612)
Control variables              Yes            Yes            Yes
Year/family dummies          Yes/yes        Yes/yes        Yes/yes
Clustered standard error    Yes/family     Yes/family     Yes/family
N                             3,961          3,961          3,961
Wald Chi-Squared           570.79 ***     542.09 ***     546.65 ***

Wald test of exogeneity       0.378          0.035          0.078
  (p-value)

*** Significant at the 0.01 level.

** Significant at the 0.05 level.

* Significant at the 0.10 level.

Table VIII. The Impact of Independent Directors with Multiple
Affiliations on Fund Fees

This table presents evidence of the ability of independent
directors with multiple board affiliations to decrease total fund
fees. The dependent variable is the total fee (as a percentage),
which is calculated as the total loads divided by seven plus the
annual expense. The proxies for IDMAs are Number of Directorships
and Overlapping Rate, where the former is defined as the average
number of funds overseen by independent directors in a fund and
the latter is defined as the average independent director overlap
rate between a fund and the rest of the fund's family.
Definitions of the variables are provided in the Appendix. All of
the specifications include year and family dummies. The
t-statistics are clustered by fund family in all columns.

                                               OLS

                            Estimate    t-value    Estimate    t-value

                              (1)         (2)        (3)         (4)

In (Number of              -0.087 *     -1.877
  Directorships)
Overlapping Rate                                  -0.203 **    -2.247
Board [Size.sub.t-1]        0.0ll        1.121     0.024 **     2.002
Independent                -0.214       -1.463     0.076        0.309
  [Ratio.sub.t-1]
Independent                 0.039        0.427    -0.001       -0.010
  [Chair.sub.t-1]
Change in Gaps
ln(# of firms)
Industry Dummy = 1 if
  year inception < 1980
ln{Demand)
Retired Executive
Executive
Academics
Avg. Ind. Director Age
Ind. Director's
  Age over 60
Avg. Tenure
Intercept                   1.204 *      1.957     0.824        0.932
Control variables             Yes                    Yes
Year/family dummies         Yes/yes                Yes/yes
Clustered standard error   Yes/family             Yes/family
F-statistic (p-value)
Hansen J statistic
  (p-value)
N                            3,323                  3,323
Adj. [R.sup.2]               0.520                  0.499

                                               2SLS

                                1st Stage              2nd Stage
                             Overlapping Rate        Total Fee (%)

                            Estimate    t-value    Estimate    t-value

                              (5)         (6)        (7)         (8)

In (Number of
  Directorships)
Overlapping Rate                                   -0.234 ***   -3.399
Board [Size.sub.t-1]       -0.007 ***    -2.996     0.015 ***    3.811
Independent                -0.557 ***   -11.169     0.141        1.643
  [Ratio.sub.t-1]
Independent                0.016         1.572    -0.121 ***   -3.890
  [Chair.sub.t-1]
Change in Gaps              0.002         1.488
ln(# of firms)              0.005         0.409
Industry Dummy = 1 if      -0.022        -0.669
  year inception < 1980
ln{Demand)                  0.367 **      2.276
Retired Executive           0.815 ***     6.166
Executive                   0.272 **      2.511
Academics                  -0.477 ***    -3.394
Avg. Ind. Director Age     -0.027 ***    -9.428
Ind. Director's             0.459 ***     8.749
  Age over 60
Avg. Tenure                 0.004 ***     4.702
Intercept                   2.648 ***    14.666     0.410        1.503
Control variables             Yes                     Yes
Year/family dummies         Yes/yes                 Yes/yes
Clustered standard error   Yes/family              Yes/family
F-statistic (p-value)                                0.000
Hansen J statistic                                   0.000
  (p-value)
N                            3,323                   3,323
Adj. [R.sup.2]               0.570                   0.452

*** Significant at the 0.01 level.

** Significant at the 0.05 level.

* Significant at the 0.10 level.

Table IX. The Impact of Independent Directors with Multiple
Affiliations on the Return Gap

This table presents evidence of the ability of independent
directors with multiple board affiliations to oversee the
unobserved actions of fund managers. The dependent variable is
Return Gap (%), defined by Kacperczyk et al. (2008), and is
measured by the differential between the actual fund performance
and the performance of a hypothetical portfolio that invests in
the previously disclosed fund holdings. The proxies for IDMAs are
Number of Directorships and Overlapping Rate, where the former is
defined as the average number of funds overseen by independent
directors in a fund and the latter is defined as the average
independent director overlap rate between a fund and the rest of
the fund's family. I also measure a fund's opaqueness by
calculating the correlation coefficient between actual fund
performance and the performance of a hypothetical portfolio that
invests in the previously disclosed fund holdings. The
correlation coefficient in the previous year is ranked among
equity funds in CRSP for the corresponding year. A dummy
variable, Opaque, takes a value of one if the fund's correlation
coefficient is among the bottom one-third of equity funds for the
corresponding year, and zero otherwise. 1 examine whether Number
of Directorships (Overlapping Rate) can increase the return gap
for funds with more opaqueness in investment strategies by
examining the effect of the interaction term on Opaque and Number
of Directorships (Overlapping Rate). I also include the average
manager overlap rate between the fund and the rest of its family
in my specifications, Overlapping Rate-Manager, where for each
pair of funds, the manager overlap rate is defined as the number
of managers common to the two funds divided by the average number
of managers of the two funds. Definitions of the other variables
are provided in the Appendix. All of the specifications include
year and family dummies. The t-statistics reported in parentheses
are clustered by fund family in all columns.

                               OLS Dependent Variable: Return Gap (%)

                                Estimate     Estimate     Estimate
                               (t-value)    (t-value)     (t-value)

                                  (1)          (2)           (3)

ln(Number of Directorships)      0.160 *                   0.086
                                (1.974)                   (1.159)
Overlapping [Rate.sub.t]_                     0.670 ***
  Indep. Directors                           (3.543)
Opaque, (Dummy)                                           -0.711 *
                                                         (-1.958)
[Opaque.sub.t] x                                           0.187 *
  # of [Directorships.sub.t]                              (1.789)
[Opaque.sub.t] x
  Overlapping [Rate.sub.t]
Overlapping Rate_Manager

Board [Size.sub.t-1]             0.011        0.016        0.010
                                (0.747)      (1.081)      (0.661)
Independent [Ratio.sub.t-1]     -0.611       -0.468       -0.623
                               (-1.539)     (-1.523)     (-1.628)
Independent [Chair.sub.t-1]      0.198        0.204 *      0.197 *
  (dummy)                       (1.642)      (1.698)      (1.673)
Constant                         0.900       -0.202        1.318 *
                                (1.260)     (-0.222)      (1.782)
Control variables                 Yes          Yes           Yes
Year/family dummies             Yes/yes      Yes/yes       Yes/yes
Clustered standard error       Yes/family   Yes/family   Yes/family
N                                2,943        2,943         2,943
Adj. [R.sup.2]                   0.054        0.055         0.055

                                OLS Dependent Variable:
                                     Return Gap (%)

                                Estimate      Estimate
                                (t-value)     (t-value)

                                   (4)           (5)

ln(Number of Directorships)

Overlapping [Rate.sub.t]_        0.224         0.214
  Indep. Directors              (1.356)       (0.994)
Opaque, (Dummy)                 -1.307 ***    -1.620 ***
                               (-2.844)      (-2.911)
[Opaque.sub.t] x
  # of [Directorships.sub.t]
[Opaque.sub.t] x                 1.299 ***     1.696 ***
  Overlapping [Rate.sub.t]      (3.030)       (3.130)
Overlapping Rate_Manager                       0.849
                                              (1.190)
Board [Size.sub.t-1]             0.017         0.032
                                (1.203)       (1.485)
Independent [Ratio.sub.t-1]     -0.403        -0.097
                               (-1.445)      (-0.248)
Independent [Chair.sub.t-1]      0.206 *       0.278 **
  (dummy)                       (1.740)       (1.805)
Constant                         0.224        -0.272
                                (0.255)      (-0.189)
Control variables                  Yes           Yes
Year/family dummies              Yes/yes       Yes/yes
Clustered standard error       Yes/family    Yes/family
N                                 2,943         2,118
Adj. [R.sup.2]                    0.060         0.069

*** Significant at the 0.01 level.

** Significant at the 0.05 level.

* Significant at the 0.10 level.

Table X. The Impact of Independent Directors with Multiple
Affiliations on Cross-Fund Learning

This table presents evidence of the ability of independent
directors with multiple board affiliations to enhance cross-fund
learning within the fund family. The dependent variable is the
correlation of idiosyncratic returns, denoted as Correlation of
Idiosyncratic Returns, which is calculated as the average of the
pairwise correlations between a fund's idiosyncratic returns
(based on Carhart's, 1997 four-factor models) and the
idiosyncratic returns of every other fund in its family.
Definitions of the other variables are provided
in Table IIII and the Appendix.

                                             OLS

                       Estimate     Estimate     Estimate     Estimate
                       t-value      t-value      t-value      t-value

                         (1)          (2)          (3)          (4)

ln(# of                 0.005       -0.006
  Directorships)       (0.319)     (-0.380)
Overlapping Rate_                                 0.087 **     0.065 *
  Independent                                    (2.541)      (1.723)
  Directors
Overlapping Rate_                    0.150 **                  0.142 **
  Manager                           (2.061)                   (2.020)
Board [Size             0.003        0.003        0.004        0.004
  .sub.t-1]            (1.220)      (1.247)      (1.460)      (1.559)
Independent [Ratio      0.074        0.065        0.0893       0.077
  .sub.t-1]            (1.117)      (1.059)      (1.644)      (1.418)
Independent [Chair     -0.027       -0.011       -0.027       -0.010
  .sub.t-1] (dummy)   (-1.331)     (-0.494)     (-1.322)     (-0.421)
Change in Gaps

ln(# of firms)

Industry Dummy = 1
  if year inception
  < 1980
ln(Demand)

Retired Executive

Executive

Academics

Avg. Ind. Director
  Age
Ind. Director's Age
  Over 60
Avg. Tenure

Intercept              -0.054       -0.156       -0.185       -0.253
                      (-0.242)     (-0.697)     (-0.790)     (-1.031)
Control variables        Yes          Yes          Yes          Yes
Year/family dummies    Yes/yes      Yes/yes      Yes/yes      Yes/yes
Clustered standard    Yes/family   Yes/family   Yes/family   Yes/family
  error
N                       3,323        2,260        3,323        2,260
Adj. [R.sup.2]          0.127        0.162        0.132        0.167
F-statistic
  (excluded
  instruments)
  p-value
Hansen/statistic
  (p-value)

                                       2SLS

                       1st Stage    2nd Stage     2nd Stage

                          (5)          (6)           (7)

ln(# of
  Directorships)
Overlapping Rate_                     0.206 **     0.608 ***
  Independent                        (2.165)      (3.489)
  Directors
Overlapping Rate_                                  0.137**
  Manager                                         (2.117)
Board [Size            -0.005***      0.003        0.002
  .sub.t-1]           (-4.038)       (1.138)      (0.867)
Independent [Ratio      0.389 ***    -0.013        0.070
  .sub.t-1]            (8.552)      (-0.205)      (1.434)
Independent [Chair      0.002        -0.027 **     0.010
  .sub.t-1] (dummy)    (0.196)      (-2.109)      (0.424)
Change in Gaps         -0.007 ***
                      (-9.892)
ln(# of firms)         -0.046 ***
                      (-5.975)
Industry Dummy = 1     -0.009
  if year inception   (-0.418)
  < 1980
ln(Demand)              0.092
                       (1.133)
Retired Executive       0.450 ***
                       (5.611)
Executive              -0.066
                      (-1.384)
Academics              -0.095 **
                      (-1.997)
Avg. Ind. Director     -0.015 ***
  Age                 (-7.376)
Ind. Director's Age    -0.033
  Over 60             (-1.363)
Avg. Tenure             0.002 ***
                       (2.975)
Intercept               1.908 ***     0.125       -0.283
                       (11.554)      (0.824)     (-1.589)
Control variables         Yes          Yes           Yes
Year/family dummies     Yes/yes      Yes/yes       Yes/yes
Clustered standard                  Yes/family   Yes/family
  error
N                        3,323        3,323         2,260
Adj. [R.sup.2]           0.472        0.143         0.181
F-statistic                           0.000         0.000
  (excluded
  instruments)
  p-value
Hansen/statistic                      0.215         0.296
  (p-value)

*** Significant at the 0.01 level.

** Significant at the 0.05 level.

* Significant at the 0.10 level.
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Title Annotation:p. 555-582
Author:Lai, Christine "Whuei-wen"
Publication:Financial Management
Date:Sep 22, 2016
Words:20069
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