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

B. IDMAs and Family-Level Allocations of Underpriced Initial Public Offerings1. 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.

References

Adams, J.C., S.A. Mansi, and T. Nishikawa, 2010, "Internal Governance Mechanisms and Operational Performance: Evidence from Index Mutual Funds," Review of Financial Studies 23, 1261-1286.

Anderson, R.C., S.A. Mansi, and D.M. Reeb, 2004, "Board Characteristics, Accounting Report Integrity, and the Cost of Debt," Journal of Accounting and Economics 37, 315-342.

Beasley, M., 1996, "An Empirical Analysis of the Relation between the Board of Director Composition and Financial Statement Fraud" Accounting Review 71, 443-465.

Bernheim, B.D. and M.D. Whinston, 1986a, "Common Agency," Econometrica 54, 923-942.

Bernheim, B.D. and M.D. Whinston, 1986b, "Menu Auctions, Resource Allocations, and Economic Influence," Quarterly Journal of Economics 101, 1-31.

Bhattacharya, U., J.H. Lee, and VK. Pool, 2013, "Conflicting Family Values in Mutual Fund Families," Journal of Finance 68, 73-200.

Brickley, J.A., J.L. Coles, and R.L. Terry, 1994, "Outside Directors and the Adoption of Poison Pills," Journal of Financial Economics 35, 371-390.

Brown, D.P. and Y. Wu, 2016, "Mutual Fund Flows and Cross-Fund Learning Within Families," Journal of Finance 71, 383--424.

Brown, K.C., W.V Harlow, and L.T. Starks, 1996, "Of Tournaments and Temptations: An Analysis of Managerial Incentives in the Mutual Fund Industry," Journal of Finance 51, 85-110.

Cameron, C. and D.L. Miller, 2015, "A Practitioner's Guide to Cluster-Robust Inference," Journal of Human Resources 50, 317-372.

Carhart, M.M., 1997, "On Persistence in Mutual Fund Performance," Journal of Finance 52, 57-82.

Carhart, M.M., R. Kaniel, D.K. Musto, and A.V. Reed, 2002, "Leaning for the Tape: Evidence of Gaming Behavior in Equity Mutual Funds," Journal of Finance 57, 661-693.

Chen, H. and C.W. Lai, 2010, "Reputation Stretching in Mutual Fund Starts," Journal of Banking & Finance 34, 193-207.

Chen, J., H. Hong, M. Huang, and J.D. Kubik, 2004, "Does Fund Size Erode Mutual Fund Performance? The Role of Liquidity and Organization," American Economic Review 94, 1276-1302.

Chevalier, J. and G. Ellison, 1997, "Risk Taking by Mutual Funds as a Response to Incentives," Journal of Political Economy 105, 1167-1200.

Cici, G., S. Gibson, and R. Moussawi, 2010, "Mutual Fund Performance When Parent Firms Simultaneously Manage Fledge Funds," Journal of Financial Intermediation 19, 169-187.

Dangl, T., Y. Wu, and J. Zechner, 2008, "Market Discipline and Internal Governance in the Mutual Fund Industry," Review of Financial Studies 21, 2307-2343.

David, P.A., 1998, "Common Agency Contracting and the Emergence of "Open Science" Institutions," American Economic Review 88, 15-21.

Davis, G.F. and E.H. Kim, 2007, "Business Ties and Proxy Voting by Mutual Funds," Journal of Financial Economics 85, 552-570.

Del Guercio, D., L.Y. Dann, and M.M. Partch, 2003, "Governance and Boards of Directors in Closed-End Investment Companies," Journal of Financial Economics 69, 111-152.

Ding, B. and R. Wermers, 2009, "Mutual Fund Performance and Governance Structure: The Role of Portfolio Managers and Boards of Directors," SUNY at Albany Working paper.

Dixit, A., G.M. Grossman, and E. Helpman, 1997, "Common Agency and Coordination: General Theory and Application to Government Policy Making," Journal of Political Economy 105, 752-769.

Evans, R.B., 2010, "Mutual Fund Incubation," Journal of Finance 65, 1581-1611.

Evans, R.B. and R. Fahlenbrach, 2012, "Institutional Investors and Mutual Fund Governance: Evidence from Retail-Institutional Fund Twins," Review of Financial Studies 25, 3530-3571.

Fama, E.F. and J.D. MacBeth, 1973, "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy 81, 607-636.

Ferris, S.P., M. Jagannathan, and A.C. Pritchard, 2003, "Too Busy to Mind the Business? Monitoring by Directors with Multiple Board Appointments," Journal of Finance 58, 1087-1111.

Ferris, S.P. and X. Yan, 2007, "Do Independent Directors and Chairmen Matter? The Role of Boards of Directors in Mutual Fund Governance," Journal of Corporate Finance 13, 392-420.

Ferris, S.P. and X. Yan, 2009, "Agency Costs, Governance, and Organizational Forms: Evidence from the Mutual Fund Industry," Journal of Banking & Finance 33, 619-626.

Fich, E.M. and A. Shivdasani, 2006, "Are Busy Boards Effective Monitors?" Journal of Finance 61, 689-724.

Fraysse, J., 1993, "Common Agency: Existence of an Equilibrium in the Case of Two Outcomes," Econometrica 61, 1225-1229.

Fu, R. and L. Wedge, 2011, "Board Independence and Mutual Fund Manager Turnover," Financial Review 46, 621-641.

Gaspar, J., M. Massa, and P. Matos, 2006, "Favoritism in Mutual Fund Families? Evidence on Strategic Cross-Fund Subsidization," Journal of Finance 61, 73-104.

Gil-Bazo, J., and P. Ruiz-Verdu, 2009, "The Relation Between Price and Performance in the Mutual Fund Industry," Journal of Finance 64, 2153-2183.

Guedj, I. and J. Papastaikoudi, 2008, "Can Mutual Fund Families Affect the Performance of Their Funds?" University of Texas at Austin Working paper.

Hermalin, B. and M. Weisbach, 1998, "Endogenously Chosen Boards of Directors and Their Monitoring of the CEO," American Economic Review 88, 96-118.

Hermalin, B. and M. Weisbach, 2003, "Boards of Directors as an Endogenously Determined Institution: A Survey of the Economic Literature," Economic Policy Review 9, 7-26.

Huang, J., K.D. Wei, and H. Yan, 2007, "Participation Costs and the Sensitivity of Fund Flows to Past Performance," Journal of Finance 62, 1273-1311.

Jain, PC. and J.S. Wu, 2000, "Truth in Mutual Fund Advertising: Evidence on Future Performance and Fund Flows," Journal of Finance 55, 937-958.

Jensen, M.C., 1993, "The Modern Industrial Revolution, Exit, and the Failure of Internal Control Systems," Journal of Finance 48, 831-880.

Kacperczyk, M., C. Sialm, and L. Zheng, 2008, "Unobserved Actions of Mutual Funds," Review of Financial Studies 21, 2379-2416.

Kahn, C.M. and D. Mookheijee, 1998, "Competition and Incentives with Nonexclusive Contracts," RAND Journal of Economics 29, 443-465.

Khorana, A. and H. Servaes, 2005, "Conflicts of Interest and Competition in the Mutual Fund Industry," London Business School Working paper.

Khorana, A. and H. Servaes, 2012, "What Drives Market Share in the Mutual Fund Industry?" Review of Finance 16, 81-113.

Khorana, A., P. Tufano, and L. Wedge, 2007, "Board Structure, Mergers, and Shareholder Wealth: A Study of the Mutual Fund Industry," Journal of Financial Economics 85, 571-598.

Knyazeva, A., D. Knyazeva, and R.W. Masulis, 2013, "The Supply of Corporate Directors and Board Independence," Review of Financial Studies 26, 1561-1602.

Kuhnen, C.M., 2005, "Dynamic Contracting in the Mutual Fund Industry," Stanford University Working paper.

Kuhnen, C.M., 2009, "Business Networks, Corporate Governance, and Contracting in the Mutual Fund Industry," Journal of Finance 64, 2185-2220.

Laussel, D. and M. Le Breton, 1998, "Efficient Private Production of Public Goods Under Common Agency," Games and Economic Behavior 25, 194-218.

Martimort, D., 1996a, "Exclusive Dealing, Common Agency, and Multiprincipals Incentive Theory," RAND Journal of Economics 27, 1-31.

Martimort, D., 1996b, "The Multiprincipal Nature of Government," European Economic Review 40, 673-685.

Martimort, D. and L. Stole, 2003, "Contractual Externalities and Common Agency Equilibria," Advances in Theoretical Economics 3, Article 4.

Massa, M., 2003, "How Do Family Strategies Affect Fund Performance? When Performance-Maximization Is Not the Only Game in Town," Journal of Financial Economics 67, 249-304.

Meier, I. and E. Schaumburg, 2004, "Do Funds Window Dress? Evidence for US Domestic Equity Mutual Funds," Northwestern University Working paper.

Meschke, J., 2007, "An Empirical Examination of Mutual Fund Boards," University of Minnesota Working paper.

Mezzetti, C., 1997, "Common Agency with Horizontally Differentiated Principals," RAND Journal of Economics 28, 323-345.

Monks, R. and N. Minow, 1995, Corporate Governance, New York, NY, Blackwell Publishing.

Nanda, VK., Z. J. Wang, and L. Zheng, 2004, "Family Values and the Star Phenomenon," Review of Financial Studies 17, 677-698.

Newey, W.K. and K.D. West, 1987, "A Simple, Positive Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica 55, 703-708.

Nohel, T., Z.J. Wang, and L. Zheng, 2010, "Side-By-Side Management of Hedge Funds and Mutual Funds," Review of Financial Studies 23, 2342-2373.

Nutt, W.J., 1971, "A Study of Mutual Fund Independent Directors," University of Pennsylvania Law Review 120, 179-270.

Phillips, B., K. Pukthuanthong, and PR. Rau, 2016, Size matters only if you have a competitor: Dis-Economies of Scale in the Mutual Fund Industry Revisited, Available at SSRN: http://ssm.com/abstract=2313218 or http://dx.doi.org/10.2139/ssm.2313218.

Raheja, C.G., 2005, "Determinants of Board Size and Composition: A Theory of Corporate Boards," Journal of Financial and Quantitative Analysis 40, 283-306.

Reuter, J., 2006, "Are IPO Allocations for Sale? Evidence from Mutual Funds," Journal of Finance 61, 2289-2324.

Sirri, E.R. and P. Tufano, 1998, "Costly Search and Mutual Fund Flows," Journal of Finance 53, 1589-1622.

Stole, L.A., 1991, Mechanism Design Under Common Agency, Cambridge, MA, Program in Law and Economics, Harvard Law School.

Tate, S. and H. Jackson, 2000, "The Role of Independent Directors in Mutual Fund Governance," Harvard Law School Working paper.

Tufano, P. and M. Sevick, 1997, "Board Structure and Fee-Setting in the US Mutual Fund Industry," Journal of Financial Economics 46, 321-355.

Yermack, D., 1996, "Higher Market Valuation of Companies with a Small Board of Directors," Journal of Financial Economics 40, 185-212.

Zitzewitz, E., 2003, "Who Cares about Shareholders? Arbitrage-Proofing Mutual Funds," Journal of Law, Economics, & Organization 19, 245-280.

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 |
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Author: | Lai, Christine "Whuei-wen" |

Publication: | Financial Management |

Date: | Sep 22, 2016 |

Words: | 20069 |

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