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Abstract The academic literature has found mixed evidence that fund size is negatively related to performance. One reason for the lack of consensus may be that the fund size and performance relation is endogenous. In this paper, we identify a set of instrumental variables that influence fund size but are unrelated to expected fund performance. Using this specification, we find little evidence that fund size directly affects fund performance. However, an indirect relation manifests as a result of preferential allocation of investment strategies to smaller funds within fund families. Keywords: Mutual fund performance; Size-performance relation; Instrumental variables; Diseconomies of scale

Size Doesn’t Matter: Diseconomies of Scale in the Mutual Fund Industry Revisited

Abstract The academic literature has found mixed evidence that fund size is negatively related to performance. One reason for the lack of consensus may be that the fund size and performance relation is endogenous. In this paper, we identify a set of instrumental variables that influence fund size but are unrelated to expected fund performance. Using this specification, we find little evidence that fund size directly affects fund performance. However, an indirect relation manifests as a result of preferential allocation of investment strategies to smaller funds within fund families.

1. Introduction Despite extensive research, the academic literature has been unable to conclusively establish whether fund size is negatively related to performance. This is an important issue. Research has consistently shown that, on average, fund managers appear unable to outperform passive fund benchmarks. Berk and Green (2004) argue that this is because funds managed by skilled managers attract greater portfolio flows than funds managed by unskilled managers. Hence, if fund performance is inversely related to fund size, in equilibrium, both skilled and unskilled managers will earn similar expected future returns. Therefore, Berk and Green (2004) argue that the lack of observed outperformance among fund managers is not inconsistent with the hypothesis that at least some mutual fund managers are skilled. The crucial assumption in Berk and Green’s model is the existence of diseconomies of scale in mutual fund performance. While this assumption has been tested extensively, the literature has been unable to come to a definitive conclusion on the source (or existence) of diseconomies of scale in fund management. The major issue is that the fund size and performance relation is likely to be endogenous, i.e. fund size is only indirectly related to performance via other fund characteristics. For example, it is likely that larger funds and larger fund families are able to attract better qualified or skilled managers. Similarly, managerial incentives and effort may vary with fund size. Specifically, in an ideal world, the econometrician would like to estimate ∝= 𝑏1 𝑆𝑖𝑧𝑒 + 𝜀 where α measures fund performance. In the presence of omitted variables ω that are also related to size: 𝜔 = 𝑐1 𝑆𝑖𝑧𝑒 + 𝜉 and ∝= 𝑏1 𝑆𝑖𝑧𝑒 + 𝑏2 𝜔 + 𝜀, the econometrician estimates α = 𝑏̃1 Size + ἕ but plim 𝑏̃1 = 𝑏1 + 𝑐1 𝑏2. Hence 𝑏̃1 can either be positive or negative depending on the relative magnitudes and signs of b1, b2, and c1. A number of papers in the prior literature hypothesize that b1 - c1b2 is negative. For example, Chen, Hong, Huang, and Kubik (CHHK, 2004) attribute the negative sign to a classic diseconomies of scale story where the diseconomies of scale are driven by trading costs or price impact that increase with firm size (c1 > 0, b2 < 0, b1< c1b2). Specifically, CHHK document a negative relationship between fund size and fund performance, in particular for illiquid funds, but a positive relation between fund family size and fund performance. They argue that increased inflow to funds with illiquid holdings increases trading costs and price pressure on the stocks held by the fund and thus impedes fund performance. However, economies of scale in marketing costs by larger fund families result in improved performance. Yan (2008) documents similar results -1-

using superior proxies for liquidity. Edelen, Evans, and Kadlec (2007) find that relative trade size subsumes fund size in regressions of fund returns, and argue that trading costs are the primary source of diseconomies of scale for funds. Similarly, Petajisto (2013) shows that larger funds are more likely to be closet indexers who earn inferior returns, implying that the indexation strategies employed by larger funds drives the poor returns earned by these funds. Specifically, Petajisto (2013) performs a bi-directional sort on fund size and the level of active management, which he terms Active Share. He finds that, in general, fund size hurts performance, but this effect arises across and not within Active Share partitions. However, an equal number of papers hypothesize that b1 - c1b2 is positive. Elton, Gruber, and Blake (2012) find an insignificant positive relation between size and performance in a sample of US mutual funds in univariate sorts and an insignificant negative relation in multivariate regressions. They speculate that the reduction in expense ratios for larger funds outweighs possible diseconomies of scale when the funds increase in size. Bhojraj, Cho, and Yehuda (BCY, 2012) argue that 𝑏̃1 is positive because of private information. They show that the positive relation between family size and performance is limited to the time-frame before 2000, prior to the SEC establishing fair disclosure regulations. They argue that large fund families received material, nonpublic information from investment banks giving them an unfair advantage over smaller fund families. When fair disclosure regulations were established, this advantage was eliminated. Ma, Tang, and Gomez (2012) argue that managerial compensation for larger and more complex funds is more likely to include explicit performance-based incentives. Using a regression discontinuity design (RDD) approach, Reuter and Zitzewitz (2013) attribute the positive sign of 𝑏̃1 to managerial skill. Finally, a few papers argue that b1 - c1b2 = 0. For example, Ferreira, Keswani, Miguel, and Ramos (2013) analyze the relation between size and performance across 27 countries and find no evidence of a negative size-performance relation outside the United States. Pastor, Stambaugh, and Taylor (2014) argue that the active management industry has become more skilled over time. This upward trend in skill coincides with industry growth. Increased competition in the industry reduces the fund’s ability to outperform passive benchmarks. In this paper, to control for potential endogeneity bias, we identify a set of instrumental variables (IVs) that influence fund size but are unrelated to expected fund performance. The advantage of our approach is that we are able to examine the size-performance relation at both the -2-

fund and family levels, which prior research argues are influenced by differing factors. More importantly, our approach allows a broader examination of the relation between size and performance, utilizing both linear and non-linear modeling techniques. Our results suggest that the relationship between size and performance is non-linear. As we discuss in greater detail below, we identify an indirect relation between size and performance that manifests due to preferential treatment of smaller funds by the fund family. Specifically, our analysis draws on Phillips, Pukthuanthong, and Rau (PPR, 2014) who examine investor response to changes in holding period returns (HPR) reported by mutual funds. The change in HPR is influenced by both the most recent return which enters the horizon of calculation and the end-return which drops from the calculation. Thus, the change in HPR jointly and equally reflects the new information in the most recent return, and in the example of a 1 year HPR, stale information reflected in the return that was realized 13 months prior. PPR show that, due either to inattention or naivety, investors react with equal strength to the new and stale information components of HPR changes when allocating flows. PPR’s results form the basis of the economic intuition for our instruments. Specifically, investors observe an improvement in the fund’s HPR, but fail to appreciate that the source of the improvement is a stale, negative end-return dropping from the horizon of the HPR calculation. While this signal provides no new information regarding expected fund performance or managerial ability, it disproportionately increases asset allocations to the fund from investors chasing stale performance. Hence, there is an exogenous increase in fund size that is unrelated to expected fund performance. Pollet and Wilson (2008) and Lou (2012) show that funds that realize inflows typically expand current positions as opposed to diversifying. Thus growth from inflows increases fund size and would be expected to aggravate diseconomies of scale, to the extent they should exist. In this sense, stale performance chasing is a nearly ideal instrumental variable as it directly influences the endogenous regressor (fund size) but has no perceivable relation with manager skill or expected future fund performance. This approach is very much in the spirit of Berk and Green (2004). However, in contrast to investors reacting to the new information in the most recent return (which may allow investors to infer information regarding expected manager ability), investors are instead reacting to stale performance signals that arise as a function of the reporting format of HPRs. Specifically, they use the fact that some investors focus on the HPR being advertised rather than complete return histories. -3-

Our analysis proceeds as follows. First, we contrast our sample to samples used in the prior literature. To estimate the described IVs, we use monthly frequency investor allocation (flow) data, which is available from the Center for Research in Security Prices (CRSP) mutual fund database starting in 1992 and concluding in 2010 (at the time of data collection). CHHK utilize annual frequency flow data from CRSP, and thus examine a broader timeframe (1962-1999). Replicating their models with our sample, we find results consistent with theirs. Hence, any differences in results from our IV models are unlikely to be attributable to sample differences. We next establish that our instrument variables meet both the relevance and exclusion criteria required for IV specifications. Specifically, tests in the first stage of a 2SLS regression show both economic and statistical relevance (i.e. significant coefficients on the set of instrument variables) while crosssectional sorts show that performance does not directly vary with any of the instruments. We also document that no other fund characteristics vary with our instruments as this could introduce endogeneity of its own. The IV model is then implemented using the standard approach. In the first stage, we regress fund size on the instrument variables and controls drawn from the prior literature. In the second stage, we regress risk-adjusted returns on the predicted value of fund size from the first stage plus the same set of standard controls. The intuition is that fund size predicted from the first stage model is unbiased by endogenous influences (such as manager ability, compensation, Active Share or other unobserved factors, as previously discussed), allowing a cleaner examination of the relation between fund size and performance. If a relation between fund size and performance exists, it should manifest equally whether fund size or its predicted value is used in the model. In contrast, if an endogenous relation between fund size and performance is leading to a spurious association, we expect the relation between predicted fund size and performance to be insignificant. We find results consistent with the latter. Using the instrument variable specification, when we regress fund size on fund performance, the coefficient on fund size in the second stage is insignificant in all model specifications. Hence, the previously documented relation between fund size and performance appears to be endogenous. Berk and Green (2004), CHHK, Yan (2008) and others stress that the source of the diseconomies of scale lie in price pressure related trading costs. Hence a negative relation between size and performance should be more pronounced for funds holding more illiquid assets. Using liquidity proxies from CHHK, Yan (2008), and the Amihud Illiquidity Ratio (Amihud, 2002) and -4-

replicating their analysis however, we again find little evidence of a negative relation between size and performance while conditioning on the liquidity of fund holdings. An alternate possibility that has not previously been examined in the size-performance literature is that the relation between fund size and performance is actually non-linear. Therefore, using a linear specification in our models obscures the true relationship. In the microstructure literature, trading costs have typically been modeled as a linear function of trade size (Keim and Madhavan, 1988). More recent studies such as Frazzini, Israel, and Moskowitz (2012) model trading costs as a non-linear function of trade size. Additionally, in cases of extremely large trades or highly illiquid assets, the relation between price impact and trade size may be non-linear.1 Finally, endogenous factors related to size may influence performance in a non-linear fashion, potentially contributing to the mixed results previously reported in this literature. Hence, we next test for a non-linear relation between fund size and performance. Specifically, we replicate our prior analysis, estimating the models separately by fund size quintile. This alternative approach reveals a negative and non-linear relation between size and performance isolated to funds in the largest size quintile (the relation remains insignificant for funds in the other 4 quintiles). We show that this non-linear relation arises from the preferential allocation of investment strategies to the smaller funds in the fund family. Specifically, within fund families, managers must decide how to allocate the best ideas across funds. Some ideas will be general in application, but most ideas will be specific to certain management objectives and will have scale limitations. To minimize the price-impact related trading costs of individual strategies, the overall strategy of a large fund may consist of multiple sub-strategies being implemented with subsets of assets under management. In fund families with multiple funds in the same management objective, new ideas may be preferentially streamed to the smaller, more nimble fund (fund favoritism). Alternatively, just as a function of the size differential across funds, better strategies may make up a relatively larger proportion of the overall strategy for smaller funds (strategy rationing). We find evidence for both. Overall, partitioning our models by funds with and without a within-family competitor in the same objective, we observe a significant negative relation between

1

This situation is unlikely as mutual funds are constrained by fund mandates to hold reasonably liquid assets and can stagger trades over time to minimize trading costs. However, in extreme situations, such as fire sales (Coval and Stafford, 2007), a non-linear relation between trade size and price impact can be observed.

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size and performance only for large funds with within-family competitors. For funds without such a competitor, we find no evidence of a relation between fund size and performance. For more specific evidence, we contrast the holdings of pairs of small and large funds with common investment objectives in the same family. On average, 73% of the assets held by the small fund are also held by the large fund. In contrast, only 34% of the assets held by the large fund are correspondingly held by the small fund. In other words, strategies implemented by the small fund are also implemented with a portion of the assets of the large fund, suggesting strategy rationing across funds. We find that the unique holdings of the large fund underperform relative to those held by the small fund by 7.85% per annum on average. We also re-examine the changing relation between family size and performance, previously documented by BCY. If large fund families had access to material, non-public information from investment banks prior to fair disclosure regulation, under the fund favoritism hypothesis, we would expect that the resultant investment strategies would likewise be preferentially streamed to the smaller funds in the fund family. We estimate the IV specification at the fund family-level and then test the relation between fund performance and fund family size estimated from the first stage regression. In the baseline specification, we find marginal evidence of a positive relation between family size and fund performance in the pre-regulatory environment for gross fund returns, but find little evidence of a relation between family size and performance based on net returns or in the post-regulatory environment. Partitioning the model by funds with and without within-family competitors, we find however that the positive relation between family size and performance reverses for funds in the largest quintile in the pre-regulatory environment. In other words, the benefits of access to private information for large fund families appeared to be streamed predominantly (perhaps exclusively) to the smaller funds in the family. For funds with no within-family competition, the relation between family size and performance is insignificant across all 5 family size partitions. In the postregulatory period, a negative relation between family size and performance is likewise isolated to funds in the largest size partition with within-family competitors. Our results complement those of Gaspar, Massa, and Matos (2006) who find that mutual fund families strategically transfer performance across member funds to favor those more likely to increase overall family profits. Gaspar, Massa, and Matos argue that better allocations of underpriced initial public offering deals to smaller funds partly explain why high value funds -6-

outperform. However, we note that the strategic allocation of IPOs to smaller funds does not drive our results because the allocation of shares in the IPO is largely determined by the underwriter. Our results also complement Pomorski (2009) and Cohen, Polk, and Silli (2010) who show that the best ideas of mutual fund managers outperform the market. If the best ideas are rationed, our results point to a different explanation for why diseconomies of scale exist. Overall, we conclude that fund size does not appear to affect fund performance directly through liquidity or trading costs. The effect documented in prior literature appears to be driven by an endogenous relation between size and performance. In particular, the relation between size and performance appears to be non-linear. There is a significant, negative relation between size and performance only in a sub-sample of large funds with a smaller within-family competitor in the same management objective, suggesting that fund families preferentially allocate their best investment strategies to smaller funds. The rest of the paper is organized as follows. Section 2 describes the data and summary statistics. Section 3 replicates the analysis in CHHK and BCY to show that our results are unlikely to be driven by our sample. Section 4 validates our instruments and Sections 5 and 6 analyze the relation between fund size and performance at the fund and family-level, respectively. Section 7 concludes.

2.

Data and Summary Statistics As previously discussed, our primary data source is the CRSP Mutual Fund Database, the

same data source utilized by CHHK and BCY. As in those papers, we restrict our sample to include only actively managed, domestic, equity mutual funds and apply the additional restriction that the fund must report monthly frequency returns and total net assets (TNA).2 Multiple classes of the same fund are aggregated using a TNA-weighted approach. Our sample commences in 1992 when the CRSP database commences reporting of monthly TNA necessary to calculate monthly net asset flow (which is needed to calculate several of our instrument variables) and concludes in 2010, the end of the CRSP database at the time of data collection. The CHHK sample spans the years 1962 to 1999 as they utilize annual frequency TNA in their analysis while BCY utilize a very similar sample period of 1992 to 2008. 2

To identify actively managed mutual funds, we use the list of actively managed funds from Cremers and Petajisto (2009) available from Antti Petajisto’s website http://www.petajisto.net/data.html.

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Table I provides descriptive statistics for the key variables used in the study. To make our analysis as comparable as possible to CHHK, whose analysis we seek to extend, the organization of our tables and models mirrors their approach as closely as possible. Panel A of Table I reports average and standard deviation values, partitioned by fund size. To calculate the values in Panel A, we compute the cross-sectional average of each variable in each month. We then report the time-series average and the standard deviation of the cross-sectional averages by size quintile. On average, our sample includes 4,240 funds, resulting in size quintiles of approximately 850 funds each. This sample size is similar to BCY whose sample includes, on average, 4,834 funds in the 2001-2008 period but is six times greater in size than CHHK whose sample, on average, includes 741 funds.3 Focusing on cross-sectional differences across the size quintiles, and consistent with Elton, Gruber, and Blake (2012), smaller funds tend to charge higher fees as a percentage of TNA, reflecting, perhaps, economies of scale (not diseconomies) that exist in the mutual fund industry. It is also possible that smaller funds focus on more specialized, boutique investment styles for which they charge a premium. Smaller funds also tend to be younger and belong to smaller families with fewer funds. Otherwise, the remaining fund characteristics are comparable across size partitions. Contrasting our sample with CHHK, on average, funds and fund families in our sample are larger and younger, reflecting inflation and the rapid expansion of the mutual fund industry over the last two decades. For example, funds in the second smallest size quintile have an average size of 60 million USD relative to 22 million USD in the CHHK sample. This difference does not extend to the smallest size quintile, which are comparable across the two samples, 5.1 relative to 4.7 million USD, respectively. Thus, if anything, we would expect diseconomies of scale to be more pronounced in our sample, but this expectation would be offset by coincidental growth and improved liquidity in capital markets over the same period. The magnitude of the disparity in fees charged by small relative to large funds is greater in our sample. The difference in expense ratios between Q5 and Q2 is, on average, 1.06%, relative to 0.89% per year in CHHK. The magnitude of total loads charged by funds is typically lower in our sample across all five size quintiles, reflecting a general reduction in liquidity frictions over time in the mutual fund industry. Finally,

3

The differences in our sample relative to the sample in BCY likely arise from differences in identification of actively managed domestic funds. We utilize the list from Cremers and Petajisto (2009) which appear more reliable than the objective codes from CRSP utilized by BCY. We also apply an additional restriction requiring monthly net asset flow when they only require annual net asset flow.

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trading is more frequent in funds in our sample, with portfolio turnover values typically twice as high across all size partitions than those reported by CHHK. The remaining variables, flow and returns, are similar between the samples. Funds increased in size by approximately 25% each year and after-fee returns averaged -0.08% to -0.09% in both samples with minimal disparity across size partitions. As would be expected, given the high level of overlap between our and the BCY sample, our summary statistics are consistent with the values they report for the 2001-2008 period. Panel B of Table I reports the correlation matrix of the time-series averages reported in Panel A. The correlations are typically small (absolute values less than 20%) with a few exceptions. Specifically, as reflected in the cross-sectional differences across size portions, smaller funds tend to charge higher fees (correlation coefficient (ρ) of -0.34). Larger funds tend to be older and belong to larger families (ρ = 0.40 and 0.43, respectively). These general relations are similarly reported by CHHK and are also reflected in Panel C which, for robustness, excludes funds in the smallest size quintile from the sample.

3.

Baseline Regression Analysis We first confirm that the results reported by CHHK for the 1962 to 1999 period hold in our

sample. CHHK utilize OLS regressions in a data panel and correct residual correlation across years using the Fama and Macbeth (1973) approach. They find that larger funds realize lower relative returns both before and after fees. To establish a baseline of comparison for our incremental analysis, we replicate their tests with the exception that we follow Petersen (2009) and control for time series and cross-sectional fund correlations in residuals, using time fixed effects and standard errors clustered by fund. As in CHHK, we analyze fund risk-adjusted returns before (gross) and after (net) fees and expenses. In the unreported preliminary stage, we risk-adjust returns using 4 separate models: 1) the market model, 2) the Capital Asset Pricing Model (CAPM), 3) the Fama and French (1993) 3factor model and 4) the 3-factor model augmented with the Carhart (1997) momentum factor (4factor model). The risk-adjusted returns are calculated as residuals from the regression of monthly return to fund i on the benchmark factors from each model. 4 The results are reported in Panel A of

4

For the purposes of the CAPM risk adjustment model, fund beta is estimated over the prior 30 months. The market proxy is the value-weighted return to all NYSE, AMEX and NASDAQ stocks as reported by CRSP and we use the one-month Treasury bill rate as the risk free rate proxy.

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Table II. Our results are generally consistent with CHHK. The relation between fund size and performance is negative and significant for both gross and net returns (average t-statistics 2.78 and 2.51 for gross and net returns, respectively, compared to values of 2.66 and 2.39 in CHHK). Also consistent with CHHK, we find strong evidence of return-chasing in our sample (positive and significant coefficient for fund return lagged one period). The relations between fund return and the remaining considered fund characteristics are insignificant. An exception in the consistency between our results and CHHK is the relation between fund performance and family size. CHHK find that funds in larger families realize relatively stronger performance, which they attribute to economies of scale in marketing costs. In contrast, we find the opposite relation, that funds belonging to larger families realize incrementally worse relative performance. This finding is consistent with BCY who similarly document a negative relation between family size and fund performance in the 2001 to 2008 timeframe, which they attribute to a change in the regulatory environment in the mutual fund industry. Effective October 2000, the Securities and Exchange Commission (SEC) established the Selective Disclosure and Insider Trading regulation (SDIT) meant to address the selective release of material, non-public information.5 BCY show that the superior performance of large families declined immediately after the establishment of the SDIT regulation. This result suggests that the superior performance of larger fund families was related to selective disclosures of material information not available to smaller families who lacked preferential relations with investment banks. Following BCY, in Panels B and C of Table II, we partition our sample to the periods preceding (1992-1999) and following (2001-2010) the establishment of the SDIT regulation. Consistent with results reported by BCY, we find a positive and significant relation between family size and performance in the pre-SDIT period and that this relation reverses in the post-SDIT period. While this result is consistent with a reversal of an informational advantage for large fund families, it is perplexing that large fund families underperform smaller families in the post-SDIT period as the SDIT regulation should have leveled the playing field, not placed larger fund families at a disadvantage. Thus, the source of the relation between family size and fund performance remains an open question.

5

See Securities and Exchange Commission Release Nos. 33-7881, 34-43154, IC-24599, File No. S7-31-09.

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4.

Instrument Variables (IV) The objective of this paper is to examine the causal relation between fund size and

performance in greater detail. As previously discussed, a concern when interpreting the results presented in Table II is the potential for fund size to be endogenously related to expected future returns. Should this be the case, in equilibrium, fund size will be uncorrelated with future returns, confounding the estimation of the relation between fund size and performance. In our case, we need to identify an instrument for the endogenous regressor that meets what are commonly referred to as the relevance and exclusion conditions. 6 The exclusion condition requires that the correlation between the endogenous regressor and the instrument be non-zero after netting out the effects of all the exogenous variables. Drawing on equation (1) below, where fund size for fund i is the endogenous regressor and a matrices of exogenous fund characteristics (X) and IVs (Y) are included as independent variables, the relevance condition requires that at least one of the Y variables be statistically different from zero. 𝑆𝑖𝑧𝑒𝑖,𝑡 =∝ +𝛾𝑿𝑖,𝑡−1 + 𝛿𝒀𝑖,𝑡−1 + 𝜀𝑖,𝑡

(1)

The exclusion condition requires that the only way the IVs (Y) influence fund performance is via its effect on the endogenous variable fund size, i.e. cov(Y,ε)=0.

4.1. Instrument Variable Description The Investment Company Act of 1940 requires mutual fund companies to make quarterly disclosures to the SEC, reporting fees, past performance and portfolio holdings. 7 The National Association of Securities Dealers (NASD) notice number 94-60 specifies that past performance must be reported in the form of an HPR over the horizons of 1, 5, and 10 years for funds in existence over those horizons. The horizon must be at least one year long and must end with the latest calendar quarter. These requirements are designed to standardize performance reporting across funds and ensure that fund managers are not selecting reporting horizons which optimize disclosed performance. Investment companies are free to report other horizons as long as their 6

The development of our instrument variable approach follows the process described and recommended in Roberts and Whited (2012) and much of our terminology draws on their discussion on implementing instrument variable models. 7 Prior to 2004, disclosures were semi-annual.

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prominence is not greater than the required horizons. In particular, as a matter of convention, mutual funds typically also report the 3-year HPR perhaps because mutual fund rating agencies such as Morningstar or Lipper also rank funds on the basis of their past 1, 3, 5, and 10 year HPRs. PPR observe that the change in reported HPRs for a mutual fund over any period has only two influences, the magnitude of the return in the current period and the magnitude of the oldest return which drops from the horizon of calculation. These two returns have a similar impact on the HPR, though only the former is new information. The following five quarter return time series from PPR illustrates our approach:

Period

-1

-2

-3

-4

-5

Return

-2%

3%

4%

5%

-4%

The annual HPR for periods -2 to -5 is 8% while the corresponding annual HPR for periods -1 to -4 is 10%. 𝐻𝑃𝑅𝑡−1 = [(1 + −0.02)(1 + 0.03)(1 + 0.04)(1 + 0.05)] − 1 = 0.102 𝐻𝑃𝑅𝑡−2 = [(1 + 0.03)(1 + 0.04)(1 + 0.05)(1 + −0.04)] − 1 = 0.079

Even though the fund experienced a negative return in the most recent period (t=-1), the HPR increased as the end-return which dropped from the sample was more negative than the most recent period. This example illustrates that the change in the HPR is a function of the most recent return (-2%) which enters the horizon and the end-return (-4%) which drops from the horizon. As all other intervening returns are common in the return sequences (t-2, t-3, and t-4 in this example), they have no influence on the change in the HPR. Thus, the change in HPR is influenced by the new information reflected in the most recent fund return, and stale information that was disclosed to investors 1 year prior. Modeling investor response to the change in HPR, it then follows that flowt becomes a function of the new and end-return, linearly approximated by equation (2). All intervening returns are common between adjacent HPRs and have no influence on ΔHPR. Thus, equation (2) allows the decomposition of the change in the HPR into its only influences, the current

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return and end-return components, allowing us to differentiate stale performance chasing from the well documented investor response to the most recent return.

𝐹𝑙𝑜𝑤𝑖,𝑡 = 𝛼𝑖 + 𝛽𝑖,1 𝑅𝑖,𝑡−1 + 𝛽𝑖,𝑛 𝑅𝑖,𝑡−𝑛 + 𝜖𝑖,𝑡

(2)

Equation (2) is estimated by fund and year, separately for n= 13, 37, and 61 (end-returns related to the 1, 3 and 5 year HPR), where flow for fund i in month t is calculated as the percentage change in TNA while controlling for return (R) effects:

𝐹𝑙𝑜𝑤𝑖,𝑡 =

𝑇𝑁𝐴𝑖,𝑡 −𝑇𝑁𝐴𝑖,𝑡−1×(1+𝑅𝑖,𝑡 ) 𝑇𝑁𝐴𝑖,𝑡−1

(3)

The economic interpretation is as follows. While controlling for the magnitude of the new return (𝑅𝑖,𝑡−1 ), the more negative the end-return which drops from the horizon of the HPR calculation, the greater the resultant increase in the HPR. Thus, if investors interpret this signal as new information, a negative and significant relation is expected for the 𝛽𝑖,𝑛 coefficients which coincide with required HPR reporting periods (as only HPRs for these periods are disclosed to investors). Consistent with this premise, PPR show that the βn coefficients in equation (2), which relate to the end of the 1, 3, and 5 year HPR horizons, are negatively related to future flows. The coefficients for all other periods are not statistically different from the mean. PPR show that the sensitivity of investors to these stale information signals (i.e. the magnitude of the βn coefficients) varies across time as a function of uncertainty and stress in financial markets. PPR also show that their results are also robust to controlling (in equation 2) separately for all intermediate returns. Hence, our instruments draw on the fact that some investors focus on advertised HPRs rather than complete return history. Following PPR, we therefore obtain three separate instrument variables, the annual time series of β13, β37 , and β61 for each fund in our sample.

4.2. Exclusion Condition Tests To validate the selected IVs, we first examine the exclusion condition requirement. It is not possible to directly test the exclusion condition as the error term ε is unobservable. A common approach is to utilize falsification tests, examining the relation between the proposed instrument -13-

variable(s) and the dependent variable of analysis. 8 In our setting, the exclusion condition requires that no direct relation exist between stale return chasing and expected future fund performance except indirectly via fund size. The falsification tests are presented in Table III. In Panel A, as the fund characteristics are sorted by the return chasing coefficients estimated in equation (2) lagged one period, we examine fund characteristics in year t, following return chasing in year t-1. As discussed, we are primarily interested in the relation between stale return chasing and fund performance, but we include the other variables in our analysis to analyze how these variables relate to stale return chasing and thus, potentially indirectly with fund performance. It should be noted that the larger the end-return which drops from the HPR sample, the greater the decrease in the HPR. Hence the more negative the return chasing coefficient, the greater the stale return chasing reaction by investors. Thus, we expect a negative average value of the stale return chasing coefficient. Further, we also expect a negative relation between fund size and the stale return chasing coefficients. Focusing first on fund return, we fail to find a significant relation between expected fund performance and stale return chasing across all three measures, for both gross and net returns. The t-statistic for the difference in means t-test comparing the fifth and first quintiles of stale return chasing is less than 0.10 for all six of the fund return sorts. The difference in the top and bottom quintile average values are similarly not statistically different from zero for all of the other fund characteristics considered, with the exception that stale return chasing is typically greater for larger fund families and for larger funds in relation to the β61 coefficient sorts. This result is consistent with greater advertising expenditures by larger fund families, which PPR show to be the primary driver of stale return chasing. We also find some evidence that funds which experience greater stale return chasing tend to charge higher total loads, but this relation is only significant in the β13 coefficient sorts and marginally significant in the β37 sorts. As previously discussed, ultimately, we seek to establish that no relation exists between the instrument variables and manager ability. There are two potential concerns with our instruments. First, in our setting, PPR show that managers attempt to take advantage of stale performance chasing effects through selective advertising. We note that our instruments are potentially related to future performance should a relation exist between manager skill in stock selection and selective advertising. However, we argue such a relation is unlikely. Stale return 8

See, for example, Bennedsen, Nielsen, Perez-Gonzalez, and Wolfenzon (2007).

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effects manifest as a function of the mechanics of the HPR calculation and are common to all funds. Further, it takes very little skill to advertise performance selectively and fund managers are not necessarily involved in advertising performance – which is more likely to be handled by a publicity department. In particular, we do not believe it likely that a fund manager skilled in stock picking is also more skilled in advertising than other fund managers. As discussed by PPR, endreturn effects on reported fund performance are easily anticipated and timed. 9 The SEC rules on reporting performance over specific horizons were enacted precisely because selective advertising was so widespread among funds. Second, if larger funds typically advertise more broadly and include HPR information in those advertisements, then the flow of large funds may be more sensitive to stale performance signals. Thus, in the first stage estimates for larger funds would have a greater proportion of size explained by stale performance chasing, biasing the model. Hence, to alleviate concerns that our results are driven by the relation between size, advertising, and performance, we explicitly control for advertising expenditure in our tests below.

4.3. Relevance Condition Tests To examine the relevance of our selected instruments, we report the first stage of the 2SLS specification in Panel A of Table IV, in which we relate fund size at the end of year t to the IVs and fund characteristic controls in year t-1 (see equation (1)). As required by the relevance condition criteria, while controlling for the relation between fund size and the exogenous fund characteristics, we find a significant relation between each of the IVs and fund size (average tstatistic 2.95, min 2.54). We address the potential relation between size and advertising in two ways. First, in Panel A of Table IV, we partition the sample into size quintiles and replicate the first stage of the IV regression across each quintile separately. In each partition, the stale return chasing coefficients are statistically significant at either the 5% or 1% level and the adjusted R 2 is similar across

For example, the Wall Street Journal notes “Many mutual funds and investment advisers promote themselves based on their average annual performance over the prior five years. As of the end of February, their returns suddenly looked a lot better—not because the managers have gotten smarter or cut fees, but because of luck. That’s because the fiveyear period now begins in March 2009—a month in which U.S. stocks returned 9% as the financial crisis began to wane. By contrast, stocks lost nearly 11% in February 2009; that bloodbath has just dropped out of the five-year return sequence. According to Morningstar, the five-year average annual returns of more than 40 mutual funds improved by at least seven percentage points when the pages of the calendar flipped from February to March. … If the past is any guide, financial advisers will tout the suddenly higher returns of their funds, and money will pile in.” (Zweig, Jason, Joe Light and Liam Pleven, 2104, Lessons from the Bull Market, Wall Street Journal, March 7, 2014, C1). 9

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regressions (ranging from 17.19 to 18.71 with the smallest quintile approximately in the middle of the range and the large partition at the top of the range). 10 These partitions illustrate that the relevance condition is fulfilled across the range of fund sizes and the explanatory power of the stale return chasing coefficients is similar across partitions. It is noteworthy that the size of the stale return chasing coefficient is typically largest for the largest fund size partition (although this relation does not hold for the β61 coefficient). As previously discussed, this relation likely arises due to incremental advertising by larger mutual funds. To control for this potential bias, we first separately regress the three stale performance chasing coefficients on 12b-1 fee as a proxy for marketing effort. 11 The residuals of these regressions (stale performance chasing not explained by marketing, termed residual βn) is utilized as an alternative IV in the models reported in Panel B of Table IV. In these regressions, the size of the βn coefficients becomes more homogeneous and is typically largest for the third size quintile. This alternative specification is free of potential bias associated with a linear ranking of the relation between fund size and stale performance chasing and controls for any potential bias arising due to differential advertising practices across funds of different sizes. We utilize this alternative IV specification for robustness later in the paper. Table IV also allows us to infer the economic significance of the IVs. Drawing on the coefficients reported in Panel A, a joint one standard deviation shift in each of the three IVs is related to an increase in log fund size of 2.40 which reflects a 45% increase in size of the average fund or 32% of the inter quintile range in fund size. 12 Thus the IVs are both statistically and economically significant. Finally, the correlations between the three IV coefficients (by fund) are very low (maximum value 0.12 in the unreported 3×3 Pearson correlation coefficient matrix), suggesting each variable represents a unique mutual fund flow determinant. The corresponding VIF values for the coefficients in the regression are all below 2 (where a value of 5 is typically recognized to indicate potential collinearity bias), implying that collinearity does not appear to be an influence in this regression.

10

The explanatory power of the stale return chasing coefficients is similarly consistent across models (max 7.54 and min 6.87) if the exogenous controls are excluded from the model. 11 We obtain the same result if advertising spending on HPR is utilized as an alternative marketing proxy. We report the 12b-1 specification as the advertising dataset provided by PPR is limited to the years of 2005-2010, whereas 12b1 fees are available for the entire dataset. 12 From Table I, the reported average fund size is log(5.34) and the inter quintile range is 7.58.

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Briefly examining the control variables, consistent with the univariate sorts in Table III, we find that larger funds typically charge lower fees and belong to larger families. Consistent with contemporaneous return chasing effects, funds with larger gross returns receive disproportionate flows and are relatively larger in the subsequent period. Larger funds tend to realize greater fund and family-level flows in the prior period. As a second relevance condition test, we utilize the weak instrument test developed by Stock and Yogo (2005) which is based on the Cragg and Donald F statistic for an under-identified model. The Cragg and Donald F statistic in our model is 26.72 which is above the Stock-Yogo bias significance critical level of 24.58 (α=0.05), providing further confidence in the relevance of the selected instrument variables.

5.

Fund Size and Performance – IV Analysis The 2SLS regression results of the IV analysis are reported in Panel C of Table IV. The

2SLS IV model is executed in the standard manner - the endogenous regressor (fund size) is estimated in the first stage and fund performance is regressed on the predicted fund size value in the second stage, including the exogenous fund characteristics as controls in both stages. For the actual estimation, the first and second stages are estimated simultaneously, minimizing the impact of the two stage process on the standard errors of the estimated regressors in the second stage. In the second stage regression, we find little evidence of fund size influencing subsequent fund performance. For gross returns, the average t-statistic on the predicted fund size coefficient across the four risk adjustment methods is 1.26 (max 1.75). Similarly, for net returns, the average tstatistic is 1.49 (max 1.71). This contrasts with our results from Table II in which we find average t-statistics of 2.78 and 2.51 for gross and net returns, respectively and the comparable model in CHHK (Table 3) who report average t-statistics of 2.66 and 2.39, respectively. In the final rows of Panel B, we directly contrast the coefficient on fund size in the OLS and IV model specifications. On average, the size of the coefficient decreases by 43% and in all but two of the models, the difference between the OLS and IV coefficient is unique from zero at the 10% level. These results suggest that the negative relation between fund size and performance previously noted in the literature is largely indirect, and likely attributable to an endogenous relation between fund size and other characteristics that influence fund performance. However, we note that a marginal significant relation continues to exist even in the presence of our IV controls.

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We seek to isolate the source of this residual effect further in the paper (see Section 6). The remainder of the results are consistent between Tables II and Panel B of Table IV. We find limited predictive power for the remaining fund characteristic variables with the exception of persistence in performance (positive and significant relation between risk adjusted performance and lagged gross performance) and a negative and significant relation between lagged family size and fund size. We explore potential explanations for the relation between family size and fund performance in greater detail further in the paper.

5.1. The Role of Asset Liquidity CHHK and Yan (2008) find that diseconomies of scale are most pronounced amongst funds that hold more illiquid assets in their portfolios. They argue that this is because of the greater transaction costs and price impacts associated with trading these assets. Thus, it is possible that the average marginal relation we document in Table IV simply obscures cross-sectional variation in the relation driven by asset liquidity. To test this hypothesis, we draw jointly from CHHK and Yan (2008) and use three separate proxies for fund liquidity: 1) funds that self-identify as belonging to the small market cap investment objective, 2) portfolio return loading on the Fama and French (1993) SMB factor and 3) TNA-weighed Amihud Illiquidity Ratio (AIR, Amihud, 2002). To code the investment objective liquidity proxy, we set an indicator variable equal to 1 for all funds that self-identify as belonging to the Lipper Objective codes of SCCE, SCGE, SCVE or SC.13 The portfolio return loading on the SMB factor is estimated by year using monthly returns. To estimate the Amihud Illiquidity Ratio, we obtain portfolio holdings data jointly from CRSP and the Thomson Institutional Ownership 12s databases. In the timeframe of our sample, portfolio holdings disclosures were made either semi-annually or quarterly at the discretion of the fund until 2004, at which time quarterly holdings disclosures became mandatory. Using this data we calculate the average weight of each asset held in the portfolio by year. Stock level AIRs are calculated as the annual (T) average of the ratio of daily (t) absolute stock return (R) standardized by the dollar value of trading volume ($VOL): 𝐴𝐼𝑅𝑇 = 𝑎𝑣𝑒[ |𝑅𝑡 |⁄$𝑉𝑜𝑙𝑡 ]

13

(4)

Lipper forms the objective classifications based on language in the fund prospectus. Funds classified as small cap typically invest in companies with market capitalization less than $1 billion at the time of purchase.

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Portfolio level AIRs are then calculated as: 𝐴𝐼𝑅𝑗,𝑇 = ∑𝑘 𝑤𝑘,𝑗,𝑇 𝐴𝐼𝑅𝑘,𝑇

(5)

where AIRj,T is the AIR for portfolio j, wk,j is the average weight of stock k in portfolio j and AIRk is the average daily AIR of asset k from equation (4), all in year T. Since AIR captures the average price impact of trading one share, a larger AIR reflects a greater level of illiquidity.14 The results of the IV specification testing the cross-sectional relation between fund size and performance, conditioning on liquidity, are reported in Table V, with results for each proxy reported in separate panels.15 To capture the cross-sectional effect of portfolio liquidity, in the second stage of the IV specification, we interact the liquidity proxy with the fund size estimate from the first stage. Focusing first on the small market cap indicator (SCI, Panel A) and the SMB factor loading (Panel B) liquidity proxies, we find that funds in the small cap style and with high loadings on the SMB factor realize lower relative performance. However this relation is not significant, nor is the general relation between fund size and performance. More importantly, the interaction term between fund size and the two fund liquidity proxies, although negative, is also not significant (average t-statistic 0.94 and 1.24 in the net return models for the SCI and SMB loading liquidity proxies, respectively). Turning to the tests which utilize the AIR as the liquidity proxy in Panel C, we find a positive and typically significant relation between portfolio illiquidity and fund performance. This result is consistent with Dong, Feng, and Sadka (2011) who find that funds with high liquidityrisk exposure typically outperform funds with low exposure, which they attribute to a correlation between liquidity risk exposure and manager ability. However, the interaction coefficient of the interaction of fund AIR and fund size predicted from the first stage is negative in all models, suggesting that larger funds which hold more illiquid stocks tend to underperform relative to their peers. This relation is significant at the 5% level in the market and beta risk adjustment models, but significance is reduced to the 10% level once we control for the size risk premium in the 3-

14

While the literature identifies a host of liquidity measures, to ensure consistency with CHHK, we utilize the objective classifications which is the primary liquidity proxy utilized in their paper. In addition, we also use the loading on the SMB factor which they also explore in their paper. Finally we follow Lynch and Yan (2012) and Dong, Feng, and Sadka (2011) who utilize the Amihud liquidity measure in their analysis of liquidity risk in the mutual fund industry. 15 The first stage of the 2SLS specification is as reported in Panel A of Table IV.

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and 4-factor risk adjustment models (average t-statistic 1.75 in the net return models). To summarize the liquidity cross-sectional analysis, we find little evidence to suggest that fund size influences performance. Conditioning on liquidity does not alter this conclusion. Large funds that hold less liquid assets realize similar cross-sectional performance to smaller stocks holding similarly illiquid assets.

5.2. Non-linearity in the fund size and performance relation Our results thus far suggest that, on average, the relation between fund size and performance is typically insignificant, even for illiquid funds. However, as noted in the introduction, this conclusion is dependent on a linear relation between fund size and performance. Although it is unlikely that trading costs have a non-linear effect on performance, endogenous factors related to size may have a non-linear effect on performance. To test for a non-linear relation, we replicate Panel B of Table IV, partitioning the sample into fund size quintiles, and report the results in Panel A of Table VI. In the interest of brevity, we report only net return results for the 4-factor model, since results for gross returns and the other factor models are similar. The first row of the table reports average log fund size (measured as total net assets under management) by quintile, which increases in a reasonably monotonic fashion from 1.64 million USD in the first quintile to 9.22 million USD in the fifth quintile. Focusing on the coefficient on fund size from the first stage, we find that the relation between fund size and performance exhibits step function properties. For the smallest two quintiles, the coefficient on fund size is -0.03 and insignificant (t-statistics approximately 1.0). The fund size coefficient doubles in magnitude (0.08 and -0.06) for the third and fourth quintiles, while remaining insignificant at the 5% level (average t-statistic 1.85) and doubles again in magnitude for the largest fund size quintile (-0.12, t-statistic 2.80). The second to last row of Panel A reports the difference between the Small and Large quintiles with associated test statistics. The difference in the fund size coefficient between the two quintiles is statistically significant at the 5% level. The selection of quintile partitions, although common in the literature, is admittedly arbitrary. Thus, as a robustness test, we replicate the model for the full sample augmented with fund size from the first stage squared as an alternative method. The coefficient on squared fund size is negative and significant ( -0.11, tstatistic 2.40), confirming a non-linear relation between fund size and performance. We explore potential explanations for this relation in the next section. -20-

6.

An alternative hypothesis Why is the fund-size performance relation limited to only the largest funds in our sample?

One possible explanation is suggested by recent analyst commentary from John Spence and Timothy Stauts. 16 The PIMCO Total Return exchange traded fund (ETF) was launched by PIMCO on March 1, 2012. PIMCO marketed this fund as the ETF version of the PIMCO Total Return Bond Fund. Contrasting the size, performance, and comovement of the ETF and mutual fund versions of the funds, the ETF version attracted 4.3 billion USD in assets relative to the 285.6 billion USD of capital invested in the mutual fund. One year total returns were 12.62% relative to 7.61% for the ETF and mutual fund, respectively. Surprisingly, the R2 from the regression of ETF return on the mutual fund return was only 0.49. 17 Discussing the low commonality in performance between apparent clones of the same fund, Morningstar analyst Timothy Stauts comments: “When BOND (the ETF version of the fund) was launched with about $100 million in assets, Bill Gross was able to start fresh with a brand new portfolio. The recent outperformance shows how a highly skilled manager can add tremendous value in a little portfolio. It pays to be small… Because the ETF’s portfolio is relatively lean and nimble, PIMCO’s best individual bond ideas can make up a relatively larger portion of BOND than PIMCO Total Return. Effectively, the ETF is performing like Bill Gross’ best ideas list.” The essence of this idea is that within fund families, managers must decide how to allocate the best ideas across funds. Some of these ideas will be general in application, but most ideas will be specific to certain management objectives and will have scale limitations. To minimize the price impact related trading costs of individual strategies, the overall strategy of a large fund may consist of multiple sub-strategies, each being implemented with a portion of assets under management. In fund families with multiple funds in the same management objective, new ideas may be preferentially streamed to the smaller, more nimble fund. Alternatively, just as a function of the

See “PIMCO Total Return ETF Trounces Benchmark, Mutual Fund in First Year”, ETFtrends.com, March 1, 2013, http://www.etftrends.com/2013/03/pimco-total-return-etf-trounces-benchmark-mutual-fund-in-first-year/. 17 These statistics are reported by Ron Rowland, “The Successful Failure of PIMCO Total Return ETF”, March 1, 2013, http://investwithanedge.com/the-successful-failure-of-pimco-total-return-etf. 16

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size differential across funds, as noted in the commentary, better strategies may make up a relatively larger proportion of the overall strategy for smaller funds.

6.1. Predictions While the concept of favoritism in mutual fund families has been previously examined, however to our knowledge, we are the first to assert fund size as a selection factor for favoritism within fund families. Prior studies have attributed favoritism behavior to fund performance or fees. For example, Gaspar, Massa, and Matos (2006) find that fund families strategically transfer performance across funds, preferentially allocating underpriced IPOs to funds which are younger, have higher prior performance, or higher fees (high value funds). Fund families also organize offsetting trades between low and high value funds, reducing price pressure effects of the trades of high value funds. Guidj and Papastaikoudi (2004) find that better performing funds receive a disproportionate allocation of family resources by being assigned additional managers. This thesis also relates to a growing “Best Ideas” literature which examines the relative performance of components of manager’s portfolios. For example, Cohen, Polk and Silli (2010) term the stocks with the highest weight in the portfolio as the manager’s best ideas, the positions for which the manager has shown the greatest conviction. High conviction investments tend to outperform the rest of the portfolio but this relation does not vary with fund size. The performance gap between the best ideas and the rest of the portfolio was statistically indistinguishable for large relative to small funds. Pomorski (2009) reports similar results when identifying the “best ideas” of fund managers based on common trades by managers with similar information sets. Contributing to this literature, we hypothesize that the apparent inverse relation between size and fund performance stems from fund families preferentially allocating the best investment strategies to smaller funds. In other words, if there are a limited number of “best ideas”, differential allocation of these ideas to different funds in the same families may lead to apparent diseconomies of scale. This hypothesis gives rise to a series of testable predictions.

P1: If fund families are preferentially allocating the best investment ideas to smaller funds, a negative relation between size and performance should only be observed for large funds with a smaller within-family competitor in the same management objective. -22-

Fund families will typically avoid having competing funds in the same management objective, the exception being families that have closed (or anticipate closing) their primary fund in a given objective to new investment. Fund companies also often leverage the success of popular funds or star managers by starting a new fund, typically marketed as having similar investment strategies to attract new investors. In either case, the effects of investment strategy allocation or concentration across funds in the same family should only manifest in extremely large funds, which would be consistent with our previously discussed results. Second, when examining the holdings of within-family competing funds in the same management objective, the holdings of the small fund should reflect the family’s best investment strategies. Thus, the holdings of the large fund can be decomposed into the best investment ideas (holdings which overlap with the small fund) and secondary investment ideas (holdings unique to the large fund). Drawing on this expectation:

P2: Examining the holdings of the large and small fund, focusing on the degree of overlap in holdings, we expect a high degree of overlap between the small and large fund (i.e. a large proportion of the holdings of the small fund are also held by the large fund). Reflecting the broader number of strategies implemented by the large fund, a small proportion of the holdings of the large fund will be held by the small fund. Performance differences arise as the best strategies comprise a smaller relative proportion of the large fund portfolio.

The null prediction for P2 is that the large and small fund competitors implement unique strategies, with each fund receiving an equal allocation of investment ideas when they arise. Under the null, performance differences arise due to higher price pressure effects for the large fund. To test P1, we partition the sample into funds with and without a within-family competitor fund in the same management objective. Management objective matches are made using the Lipper classification system, from which we exclude funds with generic classifications to ensure that the funds we examine are true competitors with overlapping risk exposures. 18 In our sample, 68% of

18

Specifically, we focus on classifications that specify the market capitalization and risk objectives of the fund including LCCE, LCGE, LCVE, MCCE, MCGE, MCVE, SCCE, SCGE, SCVE and sector focused funds and exclude

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funds have a within-family competitor in the same management objective. If the fund sizeperformance relation manifests as a result of preferential distribution of investment ideas across funds in the same family, we expect superior performance by smaller funds in families with multiple funds in the same objective. Conversely, fund size should have little bearing on performance for families with only one fund in a given objective.

6.2. Competitor fund sub-sample analysis The results of the competitor fund regressions are presented in Panel B of Table VI. The models mirror those in Panel A, replicated by sub-sample. In the interest of brevity, we report coefficient values only for the variable of interest, fund size from the 2 nd stage. Model (1) reports output for the sub-sample of funds with a within-family competitor in the same management objective. For this sub-sample, the relation between fund size and performance is significant only for the largest size partition (t-statistic 2.86) and the coefficient is of significantly greater magnitude than the other partitions (-0.21 relative to -0.08 in the adjacent partition). The difference in the fund size coefficients between the Large and Small quintiles is statistically significant at the 1% level (t-stat 3.39). Contrasting the magnitude and precision of estimation of the size coefficient between the full and competing fund sub-sample, the coefficient is larger in the sub-sample and of greater significance, suggesting refinement in our modeling of the relation between fund size and performance. Model (2) presents results for the sub-sample of funds with no within-family competitor in the same management objective. Supporting our hypotheses, there is no discernible relation between fund size and performance for any of the size partitions and the magnitude of the coefficient on fund size is statistically indistinguishable between the three largest size partitions. In other words, the effect of fund size on performance is isolated to funds with within-family competitors in the same family. A possible alternative explanation is argued by Petajisto (2013) who shows that the portion of the portfolio actively managed (Active Share) decreases with fund size. As previously discussed, Petajisto finds that active share has significant explanatory power for fund performance across Active Share partitions. However, within Active Share partitions performance across size

funds with generic classifications such as G and GI. Lipper classifications become available in our dataset starting in 1999, thus by necessity the regressions in Panel B of Table VI are restricted to 1999 – 2010.

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partitions is indistinguishable. Regardless, to ensure our size sorts are not endogenously capturing performance differences attributable to active share, we replicate model (1) augmented with Active Share measured as: 1

𝐴𝑐𝑡𝑖𝑣𝑒 𝑆ℎ𝑎𝑟𝑒 = ∑𝑁 𝑖=1|𝑤𝑓𝑢𝑛𝑑,𝑖 − 𝑤𝑖𝑛𝑑𝑒𝑥,𝑖 | 2

(6)

where wfund,i is the weight of stock i in the fund’s portfolio and windex,i is the weight of stock i in the benchmark of the fund. 19 As reported by Petajisto (2013), we find that the effects of Active Share are most pronounced for small stocks. Importantly, inclusion of Active Share in our models, if anything, improves the strength of our results (the precision of the estimate is higher). As previously discussed, larger advertising expenditures by larger funds may have the potential to bias our IV specification. Hence, prior to estimating the first stage in the IV specifications, we regress the stale return chasing coefficients on advertising expenditures in the prior period that include HPR data. The residual from this regression (stale return chasing not explained by advertising) is then used in the first stage in the place of the stale return chasing coefficients. The output from this robustness test is reported in Panel C of Table VI, which reflects that the results are largely unaffected. A limitation of this model is advertising data is available only for the period of 2005-2010. Thus, we undertake a second robustness test using the 12b-1 fee of the fund as an alternative marketing effort proxy and find similar (untabulated) results. These robustness tests provide confidence that the IV specification is not biased by preferential advertising by large funds. To test P2, we form matched fund pairs, matching funds in the large size quintile with their smaller within-family competitor in the same management objective. The small fund match is drawn from the smallest two size quintiles. Where multiple matches are available, we select the smallest fund. Holdings data is obtained from CRSP and is available from 2004 – 2012. We utilize the holdings filings closest to the end of the year and then calculate fund returns over the following year calculated from monthly fund returns. The matching process results in non-overlapping, annual frequency holdings and return observations for each fund pair. Results of the holdings

Active share data is obtained from Antti Petajisto’s website (as used in Cremers and Petajisto (2009)), but is only available from 1990 to 2006. Hence, the robustness test in model (3) of Panel B, Table VI is similarly restricted to this timeframe. 19

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comparison and return analysis are reported in Table VII. We first examine the proportional overlap in holdings between the small and large fund based on coinciding holdings declarations in each year. We focus on the proportion of individual assets in common between funds ignoring the proportional weight of each asset. The weight of individual assets may vary across funds as a function of differing diversification requirements, funds size and the covariance matrix of the asset mix. Given that the gross majority of funds in our sample implement long only strategies, differing weights of the same asset across competitor funds likely does not reflect differing strategies but the influence of these other factors. On average, 73% of the assets held by the small fund in the fund pair are also held by the large fund. However, while the strategy of the small fund to a large degree is mirrored in the large fund, this strategy comprises a relatively small proportion of the large fund’s overall allocations. On average, only 34% of the holdings of the large fund are mirrored in the small fund. In other words, the strategy of the small fund is shared across funds but comprises a relatively small proportion of the overall strategy of the large fund. We next examine the return implications of strategy allocation across within-family competitor funds. We focus on raw returns as funds in the same detailed management objective share common risk exposures. Thus risk-adjusting returns by the average return to the management objective, as is common in the mutual fund literature, would have no effect on our inferences. The average annual returns to the small and large funds in the matched pairs are 5.48% and 3.92%, respectively, reflecting statistically superior performance by small funds of 2.07% per annum. 20 Isolating the unique holdings of the large fund, the asset-weighted return of the strategies implemented by the large fund in excess of the small fund strategy is -2.37%, reflecting a 7.87% performance differential between the best strategy implement by the small fund and the secondary strategies implemented by the large fund or a 5.98% differential between the actual return and the return to the unique holdings of the large fund. In sum, our evidence suggests that fund families preferentially allocate investment strategies across funds. Holdings are not unique across small and large within-family competitors. The holdings of the small fund are mirrored in the holdings of the large fund. However, large funds implement additional strategies which, on average, underperform those of the small fund by a significant margin. Our findings are consistent with fund families preferentially allocating their

20

T-test statistics are calculated with standard errors clustered by fund pair.

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best investment strategies to smaller funds, resulting in these strategies comprising a relatively small proportion of the overall strategy of the larger funds in the family.

7.

Family Size and Fund Performance – IV Analysis We now return to the question of the changing influence of family size on fund

performance. As previously discussed, BCY attribute the superior fund performance of larger fund families to preferential information disclosure by investment banks which ended with the establishment of the Selective Disclosure and Insider Trading regulation by the SEC in 2000. A perplexing feature of their results is the apparent underperformance of larger fund families in the post-regulation environment. While relationships between large fund families and investment banks may explain superior pre-regulation performance, it is unclear why large fund families would underperform in the post-regulatory environment. To explore this relation in more detail, we implement the same IV specification at the family-level. PPR show that stale return chasing occurs at both the fund and fund objective-level. Hence we extend their approach to measure stale return chasing at the family-level. Specifically, we use an adapted version of equation (2): Flowj,t = αi + βj,1 Rj,t-1 + βnRj,t-n + εi,t

(7)

where Flowj,t is the net asset flow to family j in month t, calculated as:

𝐹𝑙𝑜𝑤𝑗,𝑡 =

𝑇𝑁𝐴𝑗,𝑡 −𝑇𝑁𝐴𝑗,𝑡−1×(1+𝑅𝑗,𝑡 ) 𝑇𝑁𝐴𝑗,𝑡−1

(8)

where TNA is aggregate TNA and R is the TNA-weighted average return to all funds in family j excluding the fund of interest. Table VIII reports the fund family IV regression results. We first replicate the first stage regression (Panel A) to ensure the relevance condition holds in the fund family context. As noted at the fund-level in Panel A of Table IV, we find a significant relation between family size and the four family-level instrument variables (average t-statistic 3.71, min 2.53).

-27-

To examine the effect of the regulatory change on the relation between family size and fund performance, we partition the second stage estimates to the pre and post-regulation periods. In the pre-regulatory period, the relation between family size and fund performance is positive but only weakly significant. In the gross fund return estimates, the relation is statistically significant using an alpha of 10% in one of the four model specifications (none are significant using an alpha of 5%). Significance is reduced in the net fund return specification, with none of the specifications significant at a 10% level. In the post-regulatory period, the relation between family size and fund performance is negative and consistently insignificant at the 10% level. The final rows of Panel B and C report the difference between the OLS and IV estimates. Across the 16 reported models the difference are statistically significant in 12 of the models at the 10% level. In summary, we find weak evidence of superior performance for funds in large families in the pre-regulatory period based on returns pre-fees and find no evidence of a relation between fund family size and performance in the post-regulatory period.

7.1.Competitor Fund Subsample analysis As in the fund-level analysis, it is possible that the relation between fund performance and family size is non-linear. Further, if large fund families have access to non-public information from investment banks, under the hypotheses discussed in Section 6, we expect the resulting investment strategies to be implemented within the smaller funds in the family. To test these predictions, we partition the sample by fund family size, replicating the model by size partition. As in the fundlevel analysis, in the interest of brevity, we focus on net fund returns adjusted using the 4-factor model. Our results are reported in Table IX. The results for gross returns and net returns adjusted using the other factor models are similar and lead to the same conclusions. Panel A reports IV regression estimates of fund performance related to family size partitioned by family size, estimated separately before and after establishment of fair disclosure requirements by the SEC. In contrast to the fund-level size partition tests, the effect of family size on fund performance is more homogeneous across partitions. Absolute coefficient values range from 0.05 to 0.08 and do not increase monotonically across size partitions. However, when the sample is further partitioned by funds with and without a within-family competitor (as described in Section 6), substantial differences across partitions emerge (reported in Panel B and C). In the pre-regulatory environment, the coefficient on family size for funds with smaller competitors in -28-

the same management objective is negative and statistically different from zero (reversing from a positive value in the aggregate model specification in Panel A). The family size coefficient remains insignificant and of a similar magnitude for the other partitions relative to Panel A. For funds without a within-family competitor, the coefficient on family size is insignificant across all five partitions. In particular, the family size coefficient is positive but insignificant for the large family partition (t-statistic 1.59). Our results are largely similar in the post-regulatory environment. For funds in the large family partition with within-family competitors, the coefficient on family size is -0.33 (t-statistic 4.12), while being insignificant in the other partitions. For funds without withinfamily competitors, there is no statistically significant relation between fund performance and family size. In sum, we find results broadly consistent with preferential allocation of superior strategies to smaller funds within fund families driving the relation between size and performance. Our evidence is also consistent with a structural shift in the relation between family size and performance coincidental with establishment of fair disclosure regulation by the SEC. However, our analysis suggests the magnitude of the competitive advantage enjoyed by large fund families is smaller than previously documented. Additionally, preferential allocation of investment strategies derived from non-public information to smaller funds results in a persistent negative relation between family size and fund performance across regulatory regimes for large funds with within-family competitors.

8.

Conclusions The academic literature has found mixed evidence that fund size is negatively related to

performance. One reason for the lack of evidence may be that the fund size and performance relation is likely to be endogenous, i.e. fund size is only indirectly related to performance via other fund characteristics. In this paper, we identify a set of instrumental variables (IVs) that influence fund size but are unrelated to fund performance. These variables are based on the stale return chasing behavior identified by Phillips, Pukthuanthong, and Rau (2014) who show that investors strongly react to lagged returns which relate to the end of commonly reported and advertised holding periods (1, 3 and 5 year HPRs). Since these changes in HPRs resulting from end-returns dropping from the sample are mechanical and only give the perception of changed fund -29-

performance, they are nearly ideal instrumental variables as they directly influence fund size but have no perceivable relation with future fund performance. Using the instrument variable specification, we find little evidence that fund size affects fund performance. We also find little evidence of a relation when we examine illiquid funds specifically or when we examine the period after the SEC established fair disclosure regulation, levelling the playing field for small and large families. Overall, we conclude that fund size does not appear to affect fund performance directly through liquidity or trading costs. The effect documented in prior literature appears to be driven by an endogenous relation between size and performance. In particular, the relation between size and performance appears to be non-linear. The significant negative relation between size and performance in the sub-sample of large funds with a smaller within-family competitor in the same management objective suggests that fund families preferentially allocate their best investment strategies to smaller funds, resulting in a negative size-performance relationship in the largest fund families.

-30-

References Amihud, A., 2002, Illiquidity and stock returns: Cross-section and time-series effects, Journal of Financial Markets 5, 31-56. Bennedsen, M., K. Nielsen, F. Perez-Gonzalez and D. Wolfenzon, 2007, Inside the family firm: The role of families in succession decisions and performance, Quarterly Journal of Economics 122, 647-691. Berk, J. and R. Green, 2004, Mutual fund flows and performance in rational markets, Journal of Political Economy 112, 1269-1295. Bhojraj, S., Y. Cho and N. Yehuda, 2012, Mutual fund family size and mutual fund performance: The role of regulatory changes, Journal of Accounting Research 50, 647-684. Carhart, M., 1997, On persistence in mutual fund performance, Journal of Finance 52, 57-82. Chen, J., H. Hong, M. Huang and J. Kubik, 2004, Does fund size erode mutual fund performance? The role of liquidity and organization, American Economic Review 94, 1276-1302. Chen, J., S. Hanson, H. Hong, and J. Stein, 2007, Do hedge funds profit from mutual-fund distress, University of California at Davis working paper. Cremers, M. and A. Petajisto, 2009, How active is your fund manager? A new measure that predicts performance, Review of Financial Studies 22, 3329-3365. Cohen, R., C. Polk and B. Silli, 2010, Best ideas, Harvard Business School working paper. Coval, J. and E. Stafford, 2007, Asset firesales (and purchases) in equity markets, Journal of Financial Economics 86, 479-512. Dong, X., S. Feng and R. Sadka, 2011, Liquidity risk and mutual-fund performance, INSEAD working paper. Edelen, R., R. Evans, and G. B. Kadlec, 2007, Scale effects in mutual fund performance: The role of trading costs, University of California - Davis working paper. Elton, E., M. Gruber and C. Blake, 2012, Does mutual fund size matter? The relationship between size and performance, Review of Asset Pricing Studies 2, 31-55. Fama, E. and K. French, 1993, Common risk factors in the returns of stocks and bonds, Journal of Financial Economics 33, 3-56. Fama, E. and J. Macbeth, 1973, Risk return, and equilibrium: Empirical tests, Journal of Political Economy 81, 607-636.

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Ferreira, M., A. Keswani, A. Miguel and S. Ramos, 2013, The determinants of mutual fund performance: A cross-country study, Review of Finance 17, 483-525. Frazzini, A., R. Israel and T. Moskowitz, 2012, Trading costs of asset pricing anomalies, University of Chicago working paper. Frazzini, A. and O. Lamont, 2008, Dumb money: Mutual fund flows and the cross-section of stock returns, Journal of Financial Economics 88, 299-322. 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. Guedj, I. and J. Papastaikoudi, 2004, Can mutual fund families affect the performance of their funds?, MIT working paper. Kacperczyk, M., C. Sialm and L. Zheng, 2005, On the industry concentration of actively managed mutual funds, Journal of Finance 60, 1983-2011. Keim, D. and A. Madhavan, 1988, Execution costs and investment performance: An empirical analysis of institutional equity trades, University of Pennsylvania working paper. Khan, M., L. Kogan and G. Serafeim, 2012, Mutual fund trading pressure: Firm-level stock price impact and the timing of SEOs, Journal of Finance 67, 1371-1395. Lou, D., 2012, A flow-based explanation for return predictability, Review of Financial Studies 25, 3457-3489. Lynch, A. and X. Yan, 2012, Liquidity, liquidity risk and the cross section of mutual fund returns, University of Missouri working paper. Ma, L., Y. Tang and J. Gomez, 2012, Portfolio manager compensation in the U.S. mutual fund industry, Georgia State University working paper. Pastor, L., R. Stambaugh and L. Taylor, 2014, Scale and skill in active management, Journal of Financial Economics, forthcoming. Petajisto, A., 2013, Active share and mutual fund performance, Financial Analysts Journal 69, 7393. Petersen, M., 2009, Estimating standard errors in finance panel data sets: Comparing approaches, Review of Financial Studies 22, 435-480. Phillips, B., K. Pukthuanthong and P. R. Rau, 2014, Past performance may be an illusion: Performance, flows, and fees in mutual funds, Critical Finance Review, forthcoming.

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Pollet, J. and M. Wilson, 2008, How does fund size affect mutual fund behavior?, Journal of Finance 63, 2941-2969. Pomorski, L. 2009, Acting on the most valuable information: “Best idea” trades of mutual fund managers, University of Toronto working paper. Reuter, J. and E. Zitzewitz, 2013, How much does size erode mutual fund performance? A regression discontinuity approach, Boston College working paper. Roberts, M. and T. Whited, 2012, Endogeneity in empirical corporate finance, Handbook of the Economics of Finance, Vol. 2, Forthcoming. Stock, J. and M. Yogo, 2005, Testing for weak instruments in linear IV regression, identification and inference for econometric models: Essays in honor of Thomas Rothenberg, 80-108. Cambridge University Press, Cambridge. Wermers, R., 2000, Mutual fund performance: An empirical decomposition into stock-picking talent, style, transactions costs, and expenses, Journal of Finance 55, 1655-1695. Yan, X., 2008, Liquidity, investment style, and the relation between fund size and fund performance, Journal of Financial and Quantitative Analysis 43, 741-768.

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Table I Summary Statistics This table reports descriptive statistics for the mutual fund sample. Fund size is total net assets (TNA) under management by the fund in million USD, and family size is TNA under management by all funds in the fund family, excluding the assets of the fund of interest, also in million USD. Expense ratio is the total annual management fees and expenses charged by the fund scaled by year-end TNA. Turnover is the minimum of annual aggregate sales or purchases of securities scaled by average monthly TNA in each year. Total load is the total front, deferred and rearend load fees charged by the fund as a percentage of investment. Gross and net fund return, is the monthly marketadjusted fund return before (gross) and after (net) expenses and fees. Fund age is the number of years the fund was in operation at the beginning of the year. Fund flow is calculated as (TNAi,t – TNAi,t-1 × (1+Ri,t))/TNAi,t-1) where TNA is total net assets to fund i at the end of month t and R is fund return. Family flow is calculated in the same manner utilizing aggregate TNA and the TNA-weighted average return for all funds in the family, excluding the fund of interest. Panel A reports time-series averages of monthly cross-sectional values with standard deviations of monthly values reported in brackets. Panel B reports the correlation matrix of the time-series averages of the monthly values and Panel C reports the same correlation matrix excluding funds in the smallest size quintile. In Panels B and C, statistically significant correlation coefficients (α=0.05) appear in bold face.

Panel A: Time-series Averages of Cross-sectional Averages and Standard Deviations

Number of funds Log fund size Expense ratio (%) Turnover Total load (%) Gross fund return (%) Net fund return (%) Log age Fund flow Log family size Family flow Funds in family

1

2

847 1.64 [1.52] 1.55 [1.31] 0.67 [2.80] 2.34 [1.80] 0.12 [2.08] -0.09 [3.25] 1.61 [0.60] 0.35 [1.16] 7.48 [2.54] 1.54 [13.71] 2.03 [3.31]

849 4.10 [0.79] 1.46 [0.64] 1.06 [1.91] 2.89 [2.31] 0.05 [2.36] -0.03 [2.26] 2.14 [0.89] 0.34 [1.18] 7.66 [2.55] 1.36 [9.86] 3.19 [4.71]

Size quintile 3 849 5.52 [0.73] 1.17 [0.39] 1.05 [1.70] 3.04 [2.57] 0.04 [2.40] -0.08 [3.47] 2.44 [0.92] 0.32 [1.15] 9.02 [2.20] 1.33 [8.45] 4.04 [7.70]

4

5

All funds

848 6.22 [0.83] 0.86 [0.37] 1.16 [0.66] 3.13 [2.76] -0.09 [2.18] -0.13 [2.33] 3.02 [1.17] 0.27 [0.88] 10.93 [2.20] 0.98 [5.08] 4.60 [8.35]

848 9.22 [0.73] 0.75 [0.30] 0.99 [0.52] 4.00 [3.18] -0.03 [1.80] -0.10 [2.06] 3.57 [1.11] 0.15 [0.52] 11.82 [1.98] 0.72 [3.94] 4.62 [9.36]

4240 5.34 [2.08] 1.16 [1.11] 0.99 [1.93] 3.08 [2.59] 0.02 [2.75] -0.09 [2.67] 2.56 [0.82] 0.29 [1.07] 9.38 [2.50] 1.19 [10.26] 3.70 [6.75]

Quintiles 2-5 3394 6.27 [1.81] 1.06 [0.51] 1.07 [0.68] 3.27 [2.38] -0.01 [2.06] -0.09 [2.33] 2.79 [1.04] 0.27 [0.94] 9.86 [2.48] 1.10 [7.17] 4.11 [5.11]

Panel B: Correlation Matrix of Time-series Averages

Log fund size Expense ratio Turnover Total load Age fund flow Log family size Family flow Funds in family

Log fund size 1

Exp. ratio

Turn over

Total load

Age

fund flow

-0.34 1

0.05 0.15 1

0.21 -0.05 0.06 1

0.40 -0.12 0.01 0.20 1

-0.06 0.09 -0.01 -0.04 -0.17 1

Log family size 0.43 -0.17 0.09 0.27 0.09 -0.01 1

Family flow

Funds in family

-0.02 0.06 -0.02 -0.03 -0.07 0.23 -0.09 1

0.12 -0.11 0.07 0.31 -0.12 -0.02 0.27 0.10 1

Panel C: Correlation Matrix of Time-series Averages Excluding Funds in the Smallest Size Quintile

Log fund size Expense ratio Turnover Total load Age fund flow Log family size Family flow Funds in family

Log fund size 1

Exp. ratio

Turn over

Total load

Age

fund flow

-0.37 1

-0.04 0.23 1

0.14 0.01 0.03 1.00

0.38 -0.20 -0.04 0.18 1

-0.07 0.10 0.01 -0.05 -0.20 1

Log family size 0.40 -0.16 0.08 0.20 0.03 -0.01 1

Family flow

Funds in family

-0.02 0.07 -0.02 -0.03 -0.07 0.21 -0.09 1

0.14 -0.10 0.06 0.27 -0.10 -0.02 0.19 0.14 1

Table II Fund Size and Performance: Base Line Regression Models This table reports OLS panel regression results of fund return related to fund characteristics lagged one month. Fund returns are calculated before (gross) and after (net) expenses and fees and are adjusted using: 1) the market model (Market-adj.), 2) the Capital Asset Pricing Model (Beta-adj.), 3) the Fama-French 3 factor model and 4) the Fama and French (1993) 3-factor model augmented with the Carhart (1997) momentum factor (4-factor). Fund size is total net assets (TNA) under management by the fund in million USD and family size is TNA under management by all funds in the fund family, excluding the assets of the fund of interest, also in million USD. Expense ratio is the total annual management fees and expenses charged by the fund scaled by year-end TNA. Turnover is the minimum of annual aggregate sales or purchases of securities scaled by average monthly TNA in each year. Total load is the total front, deferred and rear-end load fees charged by the fund as a percentage of investment. Gross and net fund return, is the monthly market-adjusted fund return before (gross) and after (net) expenses and fees. Fund age is the number of years the fund was in operation at the beginning of the year. Fund flow is calculated as (TNAi,t – TNAi,t-1 × (1+Ri,t))/TNAi,t-1) where TNA is total net assets to fund i at the end of month t and R is fund return. Family flow is calculated in the same manner utilizing aggregate TNA and the TNA-weighted average return for all funds in the family, excluding the fund of interest. Number of funds in the fund family is measured at the end of the year. The table reports standardized regression coefficients with t-statistics reported in brackets. The regressions include year fixed effects and standard errors are clustered by fund. Significance at the 10%, 5% and 1% levels is indicated by *, **, ***, respectively.

Panel A: Full Sample 1992-2010 Dependent Variable

Log fund size t-1 Expense ratio t-1

Gross fund returnt Marketadj. -0.19*** (3.19) -0.04 (0.09)

Beta-adj.

3-factor

4-factor

-0.17***

-0.15***

-0.13**

Marketadj. -0.17***

(2.82) -0.05 (0.11)

(2.71) -0.07 (0.16)

(2.38) -0.07 (0.12)

(2.69) -0.06 (1.63)

Net fund returnt Beta3-factor adj. -0.18*** -0.13** (2.74) -0.04 (1.36)

(2.44) -0.06 (1.57)

4-factor -0.12** (2.18) -0.03 (1.18)

Turnover t-1

0.03

0.06

0.04

0.02

0.03

0.03

0.05

0.05

Total load t-1

(0.60) 0.16 (1.24)

(1.24) 0.13 (1.15)

(1.11) 0.13 (1.25)

(1.04) 0.12 (1.19)

(0.82) 0.09 (1.16)

(0.60) 0.14 (1.09)

(0.93) 0.10 (1.32)

(1.11) 0.08 (0.88)

0.36*** (5.11) -0.01

0.36*** (4.93) -0.01

0.33*** (4.33) -0.01

0.26*** (3.70) -0.01

0.33*** (5.19) -0.01

0.30*** (5.03) -0.01

0.28*** (4.84) 0.01

0.25*** (3.69) 0.01

(0.59) 0.02 (0.72) -0.15*** (2.66)

(0.66) 0.02 (0.63) -0.12** (2.37)

(0.54) 0.01 (0.52) -0.14** (2.15)

(0.86) 0.01 (0.58) -0.10** (2.12)

(0.55) 0.02 (0.44) -0.12** (2.59)

(0.51) 0.05 (0.43) -0.11** (2.13)

(0.47) 0.05 (0.75) -0.11** (2.25)

(0.47) 0.04 (0.46) -0.09* (1.86)

0.09** (2.09) -0.07 (1.49) 12.77

0.12** (2.37) -0.03 (0.72) 13.08

0.06 (1.56) -0.04 (0.96) 11.85

0.04 (1.11) -0.15** (2.34) 14.20

0.09 (1.61) -0.12* (1.75) 13.11

0.14** (2.19) -0.10 (1.57) 13.35

0.07** (2.00) -0.14*** (2.64) 12.44

0.04 (1.11) -0.14*** (2.75) 12.79

Gross fund return t-1 Log age t-1 Fund flow t-1 Log family size t-1 Family flow t-1 Funds in family t-1 Adjusted R2

Panel B: Gross Return Subsamples Dependent variable: Gross fund returnt Before FD: 1992-1999 Market-adj.

Beta-adj.

3-factor

4-factor

***

***

**

Market-adj.

3-factor

4-factor

***

***

-0.20 (3.12)

-0.19 (3.06)

-0.17 (2.83)

-0.13 (2.49)

-0.18 (3.16)

-0.16 (2.65)

-0.15 (2.78)

-0.13** (2.46)

Expense ratio t-1

-0.05 (0.12) 0.03 (0.54)

-0.05 (0.10) 0.07 (1.53)

-0.07 (0.14) 0.04 (1.00)

-0.08 (0.14) 0.02 (1.29)

-0.05 (0.11) 0.03 (0.55)

-0.04 (0.10) 0.06 (1.55)

-0.06 (0.14) 0.03 (0.92)

-0.07 (0.14) 0.02 (1.32)

0.16 (1.10) 0.43***

0.15 (1.37) 0.36***

0.13 (1.08) 0.35***

0.13 (1.45) 0.31***

0.15 (1.08) 0.38***

0.13 (0.96) 0.29***

0.13 (1.07) 0.23***

0.10 (1.06) 0.26***

(5.79) -0.01 (0.44)

(4.43) -0.01 (0.52)

(4.29) -0.01 (0.47)

(3.95) -0.01 (0.66)

(4.33) -0.01 (0.51)

(3.27) -0.01 (0.59)

(3.30) -0.01 (0.45)

(3.83) -0.01 (0.73)

0.02 (0.60) 0.18***

0.02 (0.73) 0.17***

0.01 (0.43) 0.12**

0.01 (0.73) 0.09*

0.02 (0.85) -0.12**

0.02 (0.55) -0.12**

0.01 (0.47) -0.12*

0.01 (0.51) -0.11*

(3.21) 0.11** (2.14) 0.07 (1.49) 12.25

(3.05) 0.10* (1.99) 0.03 (0.72) 13.49

(2.39) 0.06 (1.55) 0.04 (0.96) 12.25

(1.78) 0.03 (1.01) -0.10* (1.86) 13.84

(2.38) 0.09** (2.08) 0.07 (1.49) 12.74

(2.26) 0.12** (2.15) 0.03 (0.72) 13.61

(1.96) 0.06 (1.61) 0.04 (0.96) 12.98

(1.92) 0.03 (0.84) -0.10* (1.79) 14.27

Total load t-1 Gross fund return t-1 Log age t-1 Fund flow t-1 Log family size t-1 Family flow t-1 Funds in family t-1 Adjusted R2

***

Beta-adj.

Log fund size t-1

Turnover t-1

***

After FD: 2001-2010

Panel C: Net Return Subsamples Dependent variable: Net fund returnt Before FD: 1992-1999 Market-adj.

Beta-adj.

4-factor

**

**

Market-adj.

3-factor

4-factor

***

**

-0.15 (2.38)

-0.14 (2.23)

-0.13 (2.25)

-0.16 (2.74)

-0.17 (2.81)

-0.11 (2.09)

-0.12** (2.12)

Expense ratio t-1

-0.07* (1.90) 0.03 (0.69)

-0.05 (1.63) 0.03 (0.46)

-0.07* (1.86) 0.05 (0.76)

-0.04 (1.56) 0.05 (0.96)

-0.05 (1.35) 0.02 (0.75)

-0.04* (1.81) 0.03 (0.77)

-0.05 (1.41) 0.04 (0.71)

-0.02 (1.03) 0.06 (1.47)

0.08 (1.02) 0.35***

0.15 (1.30) 0.33***

0.09 (1.05) 0.26***

0.09 (1.03) 0.26***

0.10 (1.48) 0.38***

0.16 (1.42) 0.29***

0.11* (1.68) 0.27***

0.07 (0.69) 0.28***

(6.35) -0.01 (0.66)

(5.91) -0.01 (0.63)

(4.87) 0.01 (0.42)

(3.94) 0.01 (0.60)

(6.57) -0.01 (0.63)

(6.49) -0.01 (0.66)

(3.91) 0.01 (0.38)

(4.41) 0.01 (0.42)

0.02 (0.38) 0.09*

0.05 (0.55) 0.10**

0.06 (1.01) 0.11**

0.03 (0.37) 0.07*

0.02 (0.34) -0.11**

0.04 (0.36) -0.09

0.06 (0.89) -0.12***

0.04 (0.61) -0.08*

(1.93) 0.09* (1.85) 0.07 (1.49) 12.83

(2.27) 0.13* (1.97) 0.03 (0.72) 13.74

(2.26) 0.07 (1.56) 0.04 (0.96) 12.65

(1.71) 0.03 (0.98) -0.12* (1.86) 12.62

(2.17) 0.11* (1.86) 0.07 (1.49) 13.42

(1.62) 0.07 (1.59) 0.03 (0.72) 14.06

(2.84) 0.06 (1.54) 0.04 (0.96) 12.93

(1.66) 0.03 (0.95) -0.12* (1.82) 12.51

Gross fund return t-1 Log age t-1 Fund flow t-1 Log family size t-1 Family flow t-1 Funds in family t-1 Adjusted R2

***

Beta-adj.

-0.19 (2.86)

Total load t-1

**

3-factor

Log fund size t-1

Turnover t-1

***

After FD: 2001-2010

Table III Instrument Variable Falsification Tests This table reports fund characteristics sorted by lagged instrument variables. Three instrument variables are considered: the three return chasing coefficients (n=13, 37, and 61) obtained from the regression Flowi,t = αi + βi,1Ri,t1 + βnRi,t-n + εi,t where Flowi,t is net asset flow to fund i in month t, calculated as (TNAi,t – TNAi,t-1 × (1+Ri,t))/TNAi,t-1) where TNA is total net assets and R is fund return. The regression is estimated by year utilizing monthly frequency fund flow and returns. Fund size is total net assets (TNA) under management by the fund in million USD at year end, and family size is TNA under management by all funds in the fund family, excluding the assets of the fund of interest, also in million USD at year end. Expense ratio is the total annual management fees and expenses charged by the fund scaled by year-end TNA. Turnover is the minimum of annual aggregate sales or purchases of securities scaled by average monthly TNA in each year. Total load is the total front, deferred and rear-end load fees charged by the fund as a percentage of investment. Gross and net fund return, is the monthly market-adjusted fund return before (gross) and after (net) expenses and fees. Fund age is the number of years the fund was in operation at the beginning of the year. Family flow is calculated in the same manner as fund flow, utilizing aggregate TNA and the TNA-weighted average return for all funds in the family, excluding the fund of interest. Significance at the 10%, 5% and 1% levels is indicated by *, **, ***, respectively.

Panel A: Return Chasing Instrument Variables Coefficient

Fund size

Family size

-0.29 -0.31 -0.31 -0.36 -0.41 Q5-Q1 t-stat

246.68 292.33 261.24 318.77 298.57 51.89 (1.12)

255.27 402.11 263.02 465.28 439.86 184.59** (2.44)

-0.31 -0.36 -0.39 -0.43 -0.47 Q5-Q1 t-stat

222.21 240.95 305.05 333.64 315.75 93.54* (1.81)

-0.26 -0.29 -0.30 -0.31 -0.36 Q5-Q1 t-stat

152.79 259.90 217.85 405.83 381.23 228.44*** (2.61)

Expense ratio

Total load

Turnover

Fund Flow

Family Flow

Fund return (gross)

Fund return (net)

Return Chasing Coefficient β13 1.19 2.47 35.20 0.97 4.44 71.25 1.01 4.33 63.75 0.56 5.81 47.25 0.91 4.50 46.80 -0.28* 2.03*** 11.6 (1.69) (2.78) (1.43)

35.06 24.44 31.97 17.52 20.47 -14.59 (1.50)

101.36 85.78 86.58 48.68 69.69 -31.67 (1.41)

0.08 -0.04 0.04 -0.04 0.05 -0.03 (0.02)

-0.03 -0.12 -0.07 -0.13 -0.05 -0.02 (0.01)

158.79 308.16 344.33 542.11 472.16 313.37*** (3.29)

Return Chasing Coefficient β37 1.34 2.96 38.80 1.30 3.63 63.64 0.78 4.65 55.92 0.54 5.28 52.97 0.69 5.03 53.04 -0.65* 2.07* 14.24 (1.72) (1.87) (1.44)

36.36 32.51 25.38 10.12 25.09 -11.27 (1.38)

89.53 87.7 80.18 61.74 72.95 -16.58 (1.16)

0.03 0.10 0.02 -0.06 -0.07 -0.10 (0.04)

-0.06 -0.01 -0.03 -0.13 -0.14 -0.08 (0.02)

140.62 369.54 252.43 588.30 474.67 334.05*** (3.72)

Return Chasing Coefficient β61 1.11 3.70 46.75 0.95 4.29 65.94 1.06 4.13 49.93 0.79 4.95 56.38 0.73 4.47 45.25 -0.38 0.77 -1.50 (1.57) (1.44) (0.75)

32.55 26.1 31.77 15.35 23.67 -8.88 (1.51)

98.22 91.08 92.41 50.43 59.95 -38.27* (1.69)

0.00 -0.09 0.01 -0.07 0.09 0.09 (0.05)

-0.05 -0.11 -0.07 -0.14 -0.02 0.03 (0.01)

Table IV Instrument Variable Regression Analysis This table reports coefficients for instrument variable 2SLS regressions relating fund size to performance. β13, β 37, and β61 are stale performance chasing coefficient estimates from the regression: Flowi,t = αi + βi,1Ri,t-1 + βnRi,t-n + εi,t where Flowi,t is net asset flow to fund i in month t, calculated as (TNAi,t – TNAi,t-1 × (1+Ri,t))/TNAi,t-1, TNA is total net assets and R is fund return. The instrument variables are estimated by year utilizing monthly frequency fund flow and returns. The remaining variables are as defined in Table II with the addition of the number of funds in the fund family. In Panels B, residual Fund βn are calculated from the regression of Fund βn on fund marketing (proxied by fund 12b-1 fee). In the second stage reported in Panel C, fund returns are calculated before (gross) and after (net) expenses and fees and are adjusted using: 1) the market model (Market-adj.), 2) the Capital Asset Pricing Model (Beta-adj.), 3) the Fama-French 3 factor model and 4) the Fama and French (1993) 3-factor model augmented with the Carhart (1997) momentum factor (4-factor). The table reports standardized regression coefficients with t-statistics reported in brackets. For comparative ease, the bottom rows of Panel B report the OLS coefficient estimate on fund size from Table 2 and the t-statistic testing the difference between the IV and OLS fund size coefficient estimates. The regressions include year fixed effects and standard errors are clustered by fund. Significance at the 10%, 5% and 1% levels is indicated by *, **, ***, respectively.

Panel A: Unadjusted First Stage Fund Size Quintile Mean log fund size Fund β13, t-1 Fund β 37, t-1 Fund β61,t-1 Expense ratiot-1 Turnover t-1 Total load t-1 Fund return t-1 Log age t-1 Fund flow t-1 Log family size t-1 Family flow t-1 Funds in family t-1 Adjusted R2

Dependent Variable: Log Fund Sizet Full Small 2 Sample 1.64 4.10 -0.19** -0.10** -0.15** (2.54) (2.27) (2.38) -0.58*** -0.51*** -0.48*** (3.19) (2.92) (2.77) -0.40*** -0.40*** -0.33*** (3.12) (3.07) (2.88) -0.14*** -0.17** -0.15** (2.32) (2.47) (2.48) 0.02 0.05 0.04 (0.98) (1.12) (1.15) 0.03 0.03 0.01 (0.85) (0.71) (0.76) 0.26*** 0.34*** 0.30*** (3.13) (3.75) (3.32) 0.05 0.08 0.05 (1.14) (1.25) (0.92) 0.19** 0.26*** 0.23*** (2.47) (3.77) (3.41) 0.16*** 0.16*** 0.16*** (2.64) (2.92) (2.70) 0.09 0.15*** 0.14** (1.49) (2.60) (2.54) 0.09** 0.05* 0.04* (2.10) (1.77) (1.68) 18.03 18.40 17.19

3 5.52 -0.19*** (3.12) -0.59*** (3.49) -0.39*** (2.93) -0.10** (2.08) 0.01 (0.81) 0.01 (0.72) 0.25*** (2.76) 0.05 (0.98) 0.18** (2.19) 0.16*** (2.74) 0.04* (1.72) 0.09** (2.05) 18.65

4 6.22 -0.22*** (2.77) -0.63*** (3.72) -0.43*** (3.58) -0.14** (2.17) 0.01 (0.88) 0.05 (0.92) 0.27*** (2.81) 0.05 (1.20) 0.10** (2.04) 0.16*** (2.73) 0.05* (1.75) 0.13** (2.22) 17.79

Large 9.22 -0.25*** (3.51) -0.67*** (3.79) -0.44*** (3.62) -0.18** (2.54) 0.01 (0.90) 0.05 (0.89) 0.20*** (2.63) 0.03 (0.92) 0.12** (2.20) 0.17*** (2.95) 0.07* (1.83) 0.16* (2.50) 18.71

Panel B: Marketing Adjusted First Stage Fund Size Quintile Mean log fund size Residual Fund β13, t-1 Residual Fund β 37, t-1 Residual Fund β61,t-1 Controls Adjusted R2

Dependent Variable: Log Fund Sizet Small 2 1.64 4.10 -0.12** -0.14* (2.37) (2.51) -0.45*** -0.50*** (2.73) (3.10) -0.42*** -0.41*** (3.34) (3.25) Yes Yes 17.78 17.72

3 5.52 -0.19*** (2.61) -0.52*** (3.24) -0.39*** (3.05) Yes 19.21

4 6.22 -0.17** (2.48) -0.47*** (2.84) -0.36*** (2.84) Yes 17.43

Large 9.22 -0.15** (2.40) -0.49*** (2.93) -0.39*** (3.09) Yes 19.15

Panel C: Second Stage Dependent variable Fund size from 1st stage t-1 Expense ratio t-1 Turnover t-1 Total load t-11 Gross fund return t-1 Log age t-1 Fund flow t-1 Log family size t-1 Family flow t-1 No. of funds in family t-1 Adjusted R2 Fund Size OLS Coefficient (Table II) Difference (OLS – IV) Difference t-stat

Market-adj -0.09 (0.98) -0.06 (0.18) 0.03 (1.12) 0.19** (2.27) 0.37*** (5.43) -0.01 (1.27) 0.02 (0.49) -0.12** (2.43) 0.10** (2.09) -0.06 (1.11) 12.92 -0.19 -0.10*** (2.81)

Gross returnt Beta-adj 3-factor -0.11* -0.08 (1.75) (0.71) -0.03 -0.06 (0.08) (0.15) 0.04 0.03 (1.04) (0.50) 0.13 0.11 (1.01) (0.72) 0.39*** 0.27*** (5.40) (3.73) -0.01 -0.01 (0.66) (0.69) 0.02 0.01 (0.27) (0.27) -0.14** -0.10** (2.14) (2.05) 0.12** 0.05 (2.04) (0.95) -0.03 -0.04 (0.48) (0.63) 14.19 12.34 -0.17 -0.15 -0.06* -0.07* (1.86) (1.92)

4-factor -0.10 (1.61) -0.07 (0.14) 0.02 (0.90) 0.12 (0.74) 0.52*** (3.20) -0.01 (0.66) 0.01 (0.51) -0.08* (1.71) 0.05 (1.09) -0.07* (1.92) 13.44 -0.13 -0.03 (1.25)

Market-adj -0.12* (1.71) -0.05 (0.80) 0.02 (0.35) 0.09 (1.44) 0.24*** (3.39) 0.01 (0.68) 0.02 (0.56) -0.09 (1.61) 0.08 (1.52) -0.17*** (3.05) 12.23 -0.17 -0.05 (1.41)

Net returnt Beta-adj 3-factor -0.10 -0.06 (1.56) (1.43) -0.03 -0.05 (0.92) (1.27) 0.03 0.05 (0.74) (0.68) 0.13 0.09 (0.73) (1.19) 0.23*** 0.27*** (3.22) (3.06) -0.01 -0.01 (0.42) (0.67) 0.04 0.06 (0.30) (0.96) -0.15** -0.10* (2.55) (1.85) 0.09 0.07 (1.05) (1.53) -0.15*** -0.14** (2.71) (2.09) 10.63 14.75 -0.18 -0.13 -0.08** -0.07** (2.40) (2.28)

4-factor -0.05 (1.24) -0.03 (0.85) 0.04 (0.50) 0.11 (1.30) 0.38*** (6.68) 0.01 (0.39) 0.05 (0.54) -0.10** (2.18) 0.05 (1.38) -0.11* (1.82) 9.62 -0.12 -0.07* (1.95)

Table V Fund Liquidity Cross-sectional Analysis This table reports the second stage estimates of instrument variable 2SLS regressions relating fund size to performance while partitioning by fund portfolio liquidity. The fund size first stage estimates are obtained from the model in Panel A of Table IV. The small cap indicator variable is set to 1 (and otherwise 0) for funds which selfdeclare small market capitalization stocks as part of its investment style. SMB loading is the loading of fund return on the Fama and French (1993) SMB factor, estimated by year using monthly frequency returns. Amihud is the asset-weighted average Amihud Illiquidity Ratio (Amihud, 2002) of the stocks held by the fund. The stock level Amihud Illiquidity Ratio is estimated as the mean annual value of daily absolute return divided by trading volume. All other variables are as defined in Table IV. The table reports standardized regression coefficients with t-statistics reported in brackets. The regressions include year fixed effects and standard errors are clustered by fund. Significance at the 10%, 5% and 1% levels is indicated by *, **, ***, respectively.

Panel A: Small Market Cap Style Dependent variable Small cap. indicator (SCI) 1st stage fund size × SCI t-1 1st stage fund size t-1 Expense ratio t-1 Turnover t-1 Total load t-1 Gross fund return t-1 Log age t-1 Fund flow t-1 Log family size t-1 Family flow t-1 Number of funds in family t-1 Adjusted R2

Market-adj -0.07 (1.48) -0.05 (1.15) -0.04 (1.22) -0.07 (0.22) 0.03 (0.45) 0.14 (1.10) 0.55*** (6.14) -0.01 (0.72) 0.02 (0.52) -0.12** (2.03) 0.06* (1.80) -0.09* (1.97) 13.73

Gross returnt Beta-adj 3-factor -0.06* -0.06 (1.69) (1.38) -0.03 -0.05 (1.24) (1.05) -0.08 -0.06 (1.09) (0.63) -0.05 -0.08 (0.15) (0.13) 0.05 0.04 (0.72) (0.93) 0.17 0.15* (1.24) (1.81) 0.26*** 0.31*** (3.96) (4.18) -0.01 -0.01 (0.27) (0.75) 0.02 0.01 (0.22) (0.64) -0.10 -0.10** (1.63) (2.30) 0.13** 0.07 (2.01) (1.22) -0.02 -0.04 (0.40) (1.14) 14.56 12.65

4-factor -0.06* (1.76) -0.02 (0.88) -0.10 (1.23) -0.10 (0.24) 0.02 (1.18) 0.09 (0.73) 0.27*** (3.01) -0.01 (0.31) 0.01 (0.56) -0.05 (1.29) 0.03 (0.31) -0.04 (0.76) 13.15

Market-adj -0.07 (1.12) -0.03 (0.82) -0.06 (1.15) -0.07* (1.78) 0.02 (0.48) 0.09 (1.55) 0.38*** (4.73) 0.01 (0.81) 0.02 (0.31) -0.09* (1.82) 0.09 (1.22) -0.18** (2.35) 12.50

Net returnt Beta-adj 3-factor -0.03 -0.05 (1.03) (1.41) -0.04 -0.03 (0.81) (0.85) -0.06 -0.07 (1.54) (1.36) -0.02 -0.06 (0.40) (0.73) 0.02 0.04 (0.53) (1.18) 0.14 0.08 (1.27) (0.81) 0.38*** 0.23*** (4.54) (3.33) -0.01 -0.01 (0.54) (0.44) 0.06 0.06 (0.75) (0.93) -0.14** -0.13** (2.33) (2.33) 0.07 0.07 (0.86) (1.37) -0.13*** -0.14** (2.73) (2.08) 12.73 16.07

4-factor -0.06 (1.53) -0.03 (1.26) -0.06 (0.86) -0.02 (0.42) 0.06 (0.52) 0.07 (0.55) 0.18*** (2.93) 0.01 (0.79) 0.04 (0.36) -0.06 (1.59) 0.05 (1.33) -0.14*** (2.73) 11.67

Panel B: SMB Factor Loading Dependent variable SMB loading (SMBL) t-1 1st stage fund size × SMBL t-1 1st stage fund size t-1 Expense ratio t-1 Turnover t-1 Total load t-1 Gross fund return t-1 Log age t-1 Fund flow t-1 Log family size t-1 Family flow t-1 Number of funds in family t-1 Adjusted R2

Market-adj -0.08 (1.43) -0.03 (0.76) -0.02 (0.89) -0.03 (0.08) 0.03 (0.75) 0.16* (1.68) 0.41*** (4.92) -0.01 (1.45) 0.02 (0.74) -0.12** (2.04) 0.12* (1.90) -0.07* (1.75) 14.49

Gross returnt Beta-adj 3-factor -0.08* -0.04 (1.89) (1.05) -0.04 -0.03 (1.12) (1.65) -0.08 -0.07 (0.69) (0.82) -0.03 -0.08 (0.09) (0.22) 0.05 0.03 (1.22) (0.55) 0.13 0.15* (0.90) (1.72) 0.30*** 0.33*** (3.81) (4.51) -0.01 -0.01 (0.25) (0.77) 0.01 0.01 (0.49) (0.53) -0.17*** -0.14** (2.97) (2.01) 0.14** 0.09** (2.07) (2.12) -0.03 -0.03 (0.86) (0.57) 14.87 13.54

4-factor -0.06 (1.43) -0.05* (1.68) -0.04 (0.46) -0.10 (0.29) 0.02 (0.48) 0.10 (1.35) 0.37*** (4.48) -0.01 (0.39) 0.01 (0.53) -0.10** (2.45) 0.05 (1.03) -0.06 (1.45) 13.16

Market-adj -0.08 (0.91) -0.05 (1.14) -0.07* (1.74) -0.07 (0.96) 0.01 (0.59) 0.10 (1.48) 0.48*** (5.29) 0.01 (0.71) 0.02 (0.43) -0.17** (2.32) 0.09 (1.23) -0.19*** (3.04) 12.31

Net returnt Beta-adj 3-factor -0.09** -0.07 (2.03) (1.62) -0.03 -0.04 (1.31) (1.13) -0.08 -0.08 (1.64) (1.63) -0.03 -0.05 (0.61) (0.55) 0.03 0.05 (0.30) (1.23) 0.18 0.10 (1.35) (1.34) 0.39*** 0.24*** (5.15) (3.52) -0.01 -0.01 (0.41) (0.28) 0.04 0.06 (0.42) (0.79) -0.10** -0.10** (2.44) (2.13) 0.07 0.05 (0.99) (0.74) -0.11** -0.14** (1.99) (2.17) 11.83 15.69

4-factor -0.08* (1.73) -0.05 (1.36) -0.04 (0.93) -0.05 (0.88) 0.05 (0.57) 0.07 (0.57) 0.25*** (3.63) 0.01 (0.61) 0.06 (1.02) -0.12** (2.48) 0.05 (0.58) -0.07* (1.76) 10.67

Panel C: Portfolio Amihud Illiquidity Dependent variable Amihud t-1 1st stage fund size × Amihud t-1 1st stage fund size t-1 Expense ratio t-1 Turnover t-1 Total load t-1 Gross fund return t-1 Log age t-1 Fund flow t-1 Log family size t-1 Family flow t-1 Number of funds in family t-1 Adjusted R2

Market-adj 0.17*** (3.11) -0.17** (2.42) -0.08 (1.47) -0.02 (0.07) 0.05 (1.45) 0.08 (0.50) 0.45*** (5.34) -0.01 (1.27) 0.02 (0.39) -0.08* (1.78) 0.12** (2.18) -0.04 (0.61) 16.27

Gross returnt Beta-adj 3-factor 0.13* 0.16*** (1.99) (2.90) -0.09* -0.08 (1.95) (1.63) -0.07 -0.09 (0.85) (1.34) -0.01 -0.01 (0.08) (0.21) 0.02 0.02 (0.82) (0.67) 0.06 0.12 (0.47) (0.99) 0.24*** 0.27*** (2.99) (3.55) -0.01 -0.01 (0.57) (0.65) 0.02 0.01 (0.76) (0.43) -0.08* -0.10* (1.81) (1.84) 0.07* 0.06 (1.88) (1.16) -0.04 -0.04 (0.74) (1.30) 16.05 13.08

4-factor 0.05 (0.93) -0.08* (1.79) -0.12 (1.64) -0.02 (0.36) 0.02 (0.92) 0.12 (1.13) 0.55*** (5.67) -0.01 (0.51) 0.01 (0.65) -0.07 (1.42) 0.06* (1.69) -0.06 (0.81) 13.86

Market-adj 0.13* (1.96) -0.21*** (3.00) -0.06 (1.26) -0.04 (0.48) 0.02 (0.55) 0.10** (2.12) 0.46*** (5.47) -0.01 (0.47) 0.02 (0.23) -0.15** (2.32) 0.06 (0.68) -0.15** (2.48) 14.96

Net returnt Beta-adj 3-factor 0.13*** 0.09** (2.60) (2.25) -0.18*** -0.08* (2.68) (1.87) -0.08** -0.07* (2.28) (1.88) -0.04 -0.05 (0.95) (0.62) 0.02 0.03 (0.51) (0.60) 0.09 0.09 (0.97) (1.16) 0.28*** 0.19*** (3.40) (3.15) -0.01 -0.01 (0.57) (0.50) 0.02 0.06 (0.26) (0.99) -0.08* -0.12** (1.85) (2.13) 0.12 0.06 (1.43) (1.24) -0.10 -0.09* (1.09) (1.70) 13.72 12.54

4-factor 0.07* (1.83) -0.07* (1.70) -0.05 (1.02) -0.04 (0.45) 0.05 (0.59) 0.08 (0.77) 0.12*** (2.69) -0.01 (0.62) 0.06 (0.87) -0.12** (2.37) (0.03 0.57) -0.14*** (2.65) 12.51

Table VI Fund Size and Performance across Size Partitions This table reports instrument variable 2SLS regression output relating fund size to performance, which replicate the regression models in Table IV, with the sample partitioned by fund size in month t-1. The full sample and two subsamples are considered, including and excluding funds with overlapping management objectives in the same fund family. For example, if two or more funds in the same management objective are offered in the same fund family, these funds have overlapping management objectives. The variables are as previously defined. Net fund returns are fund returns net of management and marketing fees adjusted using the 4-factor model. The table reports standardized regression coefficients with t-statistics reported in brackets. The regressions include year fixed effects and standard errors are clustered by fund. In Panel B, coefficient values for the control variables are suppressed in the interest of brevity. Significance at the 10%, 5% and 1% levels is indicated by *, **, ***, respectively.

Panel A: Full Sample Fund Size Quintile Mean log fund size Fund size from 1st stage t-1

Dependent variable: Net fund returnt 3 4 5.52 6.22 -0.08* -0.06* (1.94) (1.76)

Small 1.64 -0.03 (0.95)

2 4.10 -0.03 (1.16)

-0.03 (0.54) 0.05 (0.75) 0.11 (1.84) 0.41*** (5.20) 0.01 (0.18) 0.06 (0.63) -0.09 (1.36) 0.05 (0.65) -0.10 (1.09) 8.64

-0.03 (0.73) 0.05 (0.45) 0.09 (0.50) 0.42** (5.51) 0.01 (0.28) 0.05 (1.21) -0.11** (2.04) 0.05 (1.06) -0.10* (1.71) 9.58

Large 9.22 -0.12*** (2.80)

LargeSmall -0.08*** (2.62)

-0.02 (0.28) 0.05 (0.26) 0.08 (0.60) 0.37*** (5.23) 0.01 (0.52) 0.05 (0.43) -0.09** (2.11) 0.05 (1.48) -0.16*** (2.63) 8.69

0.02 (1.52) 0.00 (1.04) -0.02 (1.65) -0.04* (1.89) 0.00 (0.78) -0.01 (1.47) 0.00 (1.20) 0.00 (1.16) -0.05** (2.01)

Fund size from 1st stage2 t-1 Expense ratio t-1 Turnover t-1 Total load t-1 Gross fund return t-1 Log age t-1 Fund flow t-1 Log family size t-1 Family flow t-1 Number of funds in family t-1 Adjusted R2

-0.03 (1.14) 0.06 (0.64) 0.08 (0.77) 0.30*** (5.03) 0.01 (0.13) 0.05 (0.27) -0.08 (1.45) 0.05 (0.87) -0.14** (2.25) 10.60

-0.02 (0.43) 0.05 (0.53) 0.06 (0.38) 0.35*** (4.47) 0.01 (0.16) 0.03 (0.25) -0.10** (2.08) 0.04 (0.37) -0.14** (2.40) 8.51

Full Sample -0.06 (1.47) -0.11** (2.40) -0.04 (0.85) 0.06 (1.04) 0.08 (0.47) 0.40*** (5.25) 0.01 (0.46) 0.03 (0.53) -0.09 (1.15) 0.04 (1.18) -0.11* (1.84) 10.01

Panel B: Subsamples Fund Size Quintile

Dependent variable: Net fund returnt Small 2

3

4

Large

Large-Small

458 5.39

458 6.22

458 8.88

459 9.70

-0.03 (0.60)

-0.07 (1.36)

-0.08* (1.73)

-0.21*** (2.86)

-0.19*** (3.39)

-0.03 (0.68) 0.07* (1.72)

-0.05 (1.13) 0.09** (2.20)

-0.08* (1.71) 0.07 (1.51)

-0.20*** (3.10) 0.06 (1.47)

-0.18*** (3.27) -0.11*** (2.88)

Partition 1: Funds with overlapping management objectives in the same family Number of funds Mean log fund size

458 2.13 Model 1

Fund size from 1st stage t-1

-0.03 (0.43) Model 2

Fund size from 1st stage t-1 Active share t-1

-0.03 (0.57) 0.17*** (2.80)

Partition 2: Funds without overlapping management objectives in the same family Number of funds Mean log fund size Fund size from 1st stage t-1

208 1.85

209 4.68

209 6.19

209 7.67

209 8.51

-0.02 (0.63)

-0.02 (0.49)

-0.05 (1.11)

-0.06 (1.60)

-0.06 (1.45)

-0.04 (1.39)

Panel C: Robustness Test, Adjustment for Advertising

Fund Size Quintile

Dependent variable: Net fund returnt Small 2

3

4

Large

Large-Small

342 5.48

342 6.03

342 8.75

343 9.81

-0.03 (0.53)

-0.08 (1.46)

-0.07 (1.40)

-0.24*** (2.54)

-0.20*** (3.47)

-0.04 (0.77) 0.08* (1.92)

-0.05 (1.07) 0.11** (2.59)

-0.09* (1.87) 0.08 (1.61)

-0.19** (2.47) 0.05 (1.36)

-0.16*** (2.95) -0.13*** (3.03)

Partition 1: Funds with overlapping management objectives in the same family Number of funds Mean log fund size

342 2.07 Model 1

Fund size from 1st stage t-1

-0.04 (0.47) Model 2

Fund size from 1st stage t-1 Active share t-1

-0.03 (0.60) 0.18** (3.35)

Partition 2: Funds without overlapping management objectives in the same family Number of funds Mean log fund size Fund size from 1st stage t-1

112 1.75

112 4.92

113 6.24

113 7.18

113 8.17

-0.02 (0.59)

-0.02 (0.43)

-0.06 (1.22)

-0.06 (1.80)

-0.06 (1.60)

-0.04 (1.41)

Table VII Large Relative to Small Fund Holdings and Return Comparison This table summarizes holdings in common and performance for small – large fund pairs. Fund pairs are formed between funds which share a common family and detailed Lipper investment objective, matching funds in the large fund size quintile in Table VI with the smallest fund in either of the bottom two quintiles. The holdings comparisons considers the proportion of asset held in common between the fund pairs based on the holdings declaration most proximal to calendar yearend from 2004 - 2012. Returns are calculated over the subsequent year (T). Average returns are reported for the small and large fund as well as the subset of the large fund portfolio not held by the small fund. T-test statistics are reported (H0: average return = 0), calculated with standard errors clustered by fund pair. Significance at the 10%, 5% and 1% levels is indicated by *, **, ***, respectively.

Holdings Ave.% of small fund Ave.% of large fund holdings held by large holdings held by small fund fund 73.10% 33.89%

Average return T+1 Small fund

Large fund

5.48%

3.92%

Small Large 2.07%** (2.51)

Unique holdings of large fund -2.37%*** (2.78)

Actual – unique holdings for large fund 5.98%*** (4.04)

Table VIII Family Size and Fund Performance This table reports coefficients for instrument variable 2SLS regressions relating fund performance to family size. β13, β 37, and β61 are obtained from the regression: Flowj,t = αi + βj,1Rj,t-1 + βnRj,t-n + εi,t where Flowj,t is net asset flow to family j in month t, calculated as (TNAj,t – TNAj,t-1 × (1+Rj,t))/TNAj,t-1), TNA is total net assets and R is family return calculated as the TNA-weighted average return to all funds in the family. The regression is estimated by year utilizing monthly frequency family flow and returns. All other variables are as defined in Table IV. The second stage estimates in Panel B are partitioned before (1992-1999) and after (20012010) introduction of the Fair Disclosure (FD) regulation. The table reports standardized regression coefficients with t-statistics reported in brackets. The regressions include year fixed effects and standard errors are clustered by family. Significance at the 10%, 5% and 1% levels is indicated by *, **, ***, respectively.

Panel A: First Stage Dependent variable: Family sizet Family β13, t-1 Family β 37, t-1 Family β61, t-1 Expense ratio t-1 Turnover t-1 Total load t-1 Gross fund return t-1 Log age t-1 Family flow t-1 Number of funds in family t-1 Adjusted R2

-0.12** (2.53) -0.38*** (4.30) -0.34*** (4.30) -0.21*** (2.67) 0.02 (1.09) 0.03 (1.06) 0.26*** (3.96) 0.06 (1.29) 0.15** (2.13) 0.22*** (3.51) 15.17

Panel B: Gross Fund Return 2nd Stage

Family size from 1st stage t-1 Log fund size t-1 Expense ratio t-1 Turnover t-1 Total load t-1 Fund return t-1 Log age t-1 Fund flow t-1 Family flow t-1 Funds in family t-1 Adjusted R2 Fund Size OLS Coefficient (Table II) Difference (OLS – IV) Difference t-stat

Dependent variable: Gross fund returnt Before FD 1992-1999 Market-adj Beta- adj 3-factor 4-factor 0.06* 0.08 0.06 0.08 (1.68) (1.39) (1.39) (1.31) -0.22*** -0.25*** -0.18*** -0.14*** (3.04) (3.34) (2.85) (2.81) -0.05 -0.06 -0.08 -0.11 (0.12) (0.13) (0.12) (0.15) 0.03 0.06 0.03 0.02 (0.88) (1.27) (0.73) (0.89) 0.15* 0.16 0.12 0.17 (1.96) (1.42) (0.54) (1.40) 0.46*** 0.37*** 0.47*** 0.40*** (3.86) (5.09) (3.98) (5.15) -0.01 -0.01 -0.01 -0.01 (0.41) (0.29) (0.23) (1.18) 0.02 0.02 0.01 0.01 (0.78) (0.76) (0.35) (0.72) 0.08* 0.12* 0.06* 0.03 (1.74) (1.77) (1.83) (0.80) 0.06 0.02 0.04 -0.08 (0.76) (0.61) (0.77) (1.54) 11.90 12.56 12.99 14.82 0.18 0.12*** (2.85)

0.17 0.09*** (2.66)

0.12 0.06* (1.70)

0.09 -0.01 (1.21

Market-adj -0.02 (0.77) -0.22*** (3.06) -0.04 (0.19) 0.02 (0.27) 0.17 (1.00) 0.44*** (5.68) -0.01 (0.31) 0.02 (0.65) 0.07 (1.12) 0.09** (2.19) 14.20 -0.12 -0.10*** (2.82)

After FD 2001-2010 Beta adj 3-factor -0.02 -0.03 (1.14) (1.41) -0.17** -0.13** (2.24) (2.37) -0.03 -0.05 (0.16) (0.06) 0.07 0.03 (1.52) (0.54) 0.12 0.14 (0.91) (0.68) 0.31*** 0.19*** (4.38) (3.11) -0.01 -0.01 (0.54) (0.83) 0.02 0.01 (0.44) (0.42) 0.15** 0.06* (2.15) (1.96) 0.03 0.05* (0.38) (1.66) 12.06 10.86 -0.12 -0.10*** (2.73)

-0.12 -0.09** (2.59)

4-factor -0.04 (1.38) -0.12** (2.12) -0.08 (0.11) 0.02 (1.35) 0.10 (1.23) 0.22*** (3.51) -0.01 (0.41) 0.01 (0.97) 0.02 (0.43) -0.13*** (2.61) 13.59 -0.11 -0.07* (1.90)

Panel C: Net Fund Return 2nd Stage Dependent variable: Net fund returnt Before FD: 1992-1999

st

Family size from 1 stage t-1 Log fund size t-1 Expense ratio t-1 Turnover t-1 Total load t-1 Fund return t-1 Log age t-1 Fund flow t-1 Family flow t-1 Funds in family t-1 Adjusted R2 Fund Size OLS Coefficient (Table II) Difference (OLS – IV) Difference t-stat

Marketadj 0.04 (0.85) -0.17*** (3.15) -0.07 (0.88) 0.03 (0.41) 0.06* (1.75) 0.30*** (4.17) -0.01 (0.31) 0.02 (0.33) 0.06* (1.96) 0.07* (1.98) 13.09 0.09 0.05 (1.34)

After FD: 2001-2010

Beta- adj

3-factor

4-factor

Market-adj

Beta adj

3-factor

4-factor

0.07 (1.28) -0.17*** (2.92) -0.07 (1.32) 0.03 (0.47) 0.14 (1.14) 0.41*** (5.00) -0.01 (0.52) 0.04 (0.49) 0.14** (2.07) 0.03 (0.59) 15.39

0.01 (0.97) -0.16*** (2.99) -0.07 (0.94) 0.04 (0.71) 0.07 (0.93) 0.22*** (2.99) 0.01 (0.34) 0.06* (1.66) 0.07 (1.12) 0.03 (0.89) 16.28

0.08 (1.30) -0.13 (1.54) -0.03 (0.81) 0.05* (1.89) 0.11 (0.89) 0.31*** (4.30) 0.01 (0.44) 0.03 (0.36) 0.03 (1.29) -0.14* (1.83) 17.62

-0.02 (1.22) -0.13** (2.17) -0.04 (1.42) 0.02 (1.23) 0.12 (1.60) 0.36*** (4.13) -0.01 (0.64) 0.02 (0.34) 0.11** (2.38) 0.06 (1.35) 11.40

-0.02 (0.57) -0.15** (2.50) -0.03* (1.71) 0.03 (1.43) 0.11 (0.66) 0.29*** (4.06) -0.01 (0.54) 0.05 (0.55) 0.09** (2.41) 0.03 (0.73) 10.58

-0.02 (0.51) -0.17** (2.33) -0.05 (1.21) 0.04 (1.43) 0.10 (0.72) 0.27*** (3.20) 0.01 (0.20) 0.06 (0.84) 0.06* (1.79) 0.04 (0.92) 13.84

-0.07 (1.47) -0.09 (1.39) -0.02 (1.64) 0.07 (1.51) 0.08 (0.61) 0.32*** (4.46) 0.01 (0.44) 0.03 (0.61) 0.04 (0.98) -0.13** (2.37) 16.54

0.10 0.03 (1.26)

0.11 0.10*** (2.77)

0.07 -0.01 (1.18)

-0.11 -0.09** (2.57)

-0.09 -0.07** (2.24)

-0.12 -0.10*** (2.76)

-0.08 -0.01 (1.05)

Table IX Fund Family Size and Performance across Size Partitions This table reports coefficients for instrument variable 2SLS regressions relating fund performance to family size, which replicate the regression models in Table VIII, with the sample partitioned by fund family size in month t-1. The full sample and two subsamples are considered, including and excluding funds with overlapping management objectives in the same fund family. The variables are as previously defined. Net fund returns are fund returns net of management and marketing fees adjusted using the 4factor model. The table reports standardized regression coefficients with t-statistics reported in brackets. The regressions include year fixed effects and standard errors are clustered by fund. In Panel B, coefficient values for the control variables are suppressed in the interest of brevity. Significance at the 10%, 5% and 1% levels is indicated by *, **, ***, respectively.

Panel A: Full Sample Family size quintile Mean log family size Number of families Number of funds Family size 1st stage t-1 Log fund size t-1 Expense ratio t-1 Turnover t-1 Total load t-1 Fund return t-1 Log age t-1 Fund flow t-1 Family flow t-1 Funds in family t-1 Adjusted R2

Small 3.09 74 102 0.05 (1.05) -0.17*** (2.56) -0.04 (1.46) 0.05 (1.24) 0.11 (0.97) 0.35*** (4.46) 0.01 (0.49) 0.05 (0.66) 0.04** (2.09) -0.12 (0.75) 15.27

2 6.30 74 156 0.08 (1.09) -0.12** (2.41) -0.03** (2.28) 0.03 (1.58) 0.11 (0.85) 0.36*** (4.70) 0.01 (0.27) 0.03 (0.70) 0.04* (1.93) -0.11 (0.46) 14.92

Dependent variable: Net fund returnt Before FD 3 4 Large L-S Small 8.85 10.63 13.79 3.07 74 74 75 101 251 369 492 151 0.06 0.07 0.08 0.03 -0.07* (1.04) (1.16) (1.35) (1.20) (1.68) -0.18*** -0.16** -0.15* 0.02 -0.14* (2.83) (2.35) (1.90) (1.27) (1.84) -0.03 -0.02 -0.03 0.01 -0.02 (0.85) (1.05) (1.09) (0.85) (0.63) 0.05 0.04 0.06** 0.01 0.07 (1.04) (1.11) (2.23) (0.86) (0.84) 0.09 0.09 0.11 0.00 0.10 (0.95) (0.63) (1.15) (0.83) (0.64) 0.39*** 0.29*** 0.22*** -0.13*** 0.41*** (5.07) (3.91) (3.02) (2.65) (5.24) 0.01 0.01 0.01 0.00 0.01 (0.19) (0.35) (0.64) (0.53) (0.33) 0.03 0.03 0.03 -0.02 0.04 (0.17) (0.25) (0.26) (0.97) (0.44) 0.03* 0.03 0.05* 0.01 0.07* (1.94) (0.58) (1.75) (0.94) (1.74) -0.13 -0.12** -0.14 -0.01 -0.13** (1.56) (2.20) (0.97) (0.88) (2.02) 16.06 12.34 12.20 17.58

2 6.47 101 214 -0.06 (1.18) -0.17* (2.65) -0.02 (1.64) 0.04 (1.11) 0.06 (0.67) 0.34*** (4.43) 0.01 (0.23) 0.03 (0.36) 0.05* (1.95) -0.12 (1.17) 18.11

After FD 3 4 7.06 9.65 101 102 322 581 -0.05 -0.06 (1.03) (1.54) -0.13 -0.11 (1.18) (1.58) -0.02 -0.02 (1.12) (1.28) 0.05 0.06* (1.08) (1.91) 0.04 0.06 (0.60) (0.78) 0.28*** 0.30*** (3.33) (3.92) 0.01 0.01 (0.21) (0.13) 0.04 0.03 (0.33) (0.29) 0.06 0.03 (1.14) (0.38) -0.16** -0.13* (2.59) (1.99) 11.92 14.61

Large 14.45 102 696 -0.08 (1.61) -0.21** (2.35) -0.01 (0.63) 0.06 (1.49) 0.11 (1.03) 0.33*** (4.58) 0.01 (0.46) 0.03 (0.11) 0.03 (0.92) -0.19*** (2.97) 10.69

L-S

-0.01 (0.82) -0.07** (2.35) 0.01 (0.98) 0.00 (0.74) 0.00 (0.77) -0.08*** (2.53) 0.00 (0.35) -0.02 (1.24) -0.04 (1.61) -0.06** (2.30)

Panel B: Subsamples before FD Family size quintile

Dependent variable: Net fund returnt Small 2 3

4

Large

Large - Small

Partition 1: Funds with overlapping management objectives in the same family Mean log family size Number of families Number of funds Family size from 1st stage t-1 Active share t-1

3.33 53 77

6.00 53 97

8.87 53 183

8.91 53 250

11.71 54 351

0.06 (1.31) 0.17** (2.55)

0.05 (1.24) 0.07** (2.16)

0.05 (0.92) 0.09* (1.84)

0.04 (0.87) 0.08* (1.96)

-0.11** (2.07) 0.13** (2.39)

-0.17*** (3.42) -0.04* (1.85)

Partition 2: Funds without overlapping management objectives in the same family Mean log family size Number of families Number of funds Family size from 1st stage t-1 Active share t-1

2.98 21 25

5.57 21 59

8.84 21 68

10.87 21 119

14.09 21 141

0.03 (0.69) 0.19*** (3.12)

-0.03 (1.57) 0.07* (1.85)

0.03 (0.98) 0.08** (2.20)

-0.06 (1.54) 0.07* (1.87)

0.05 (1.59) 0.14*** (2.85)

0.03 (1.23) -0.05 (1.32)

Panel C: Subsamples after FD Family size quintile

Dependent variable: Net fund returnt Small 2 3

4

Large

Large - Small

Partition 1: Funds with overlapping management objectives in the same family Mean log family size Number of families Number of funds Family size from 1st stage t-1 Active share t-1

2.92 69 112

6.09 69 153

7.80 69 253

10.73 69 499

12.99 70 566

0.03 (0.62) 0.27*** (3.30)

0.04 (0.90) 0.08* (1.92)

0.04* (1.92) 0.10** (2.20)

-0.07* (1.66) 0.10** (2.43)

-0.33*** (4.12) 0.12** (2.58)

-0.36*** (5.81) -0.15*** (2.88)

Partition 2: Funds without overlapping management objectives in the same family Mean log family size Number of families Number of funds Family size from 1st stage t-1 Active share t-1

3.07 32 39

6.42 32 60

7.80 32 69

10.55 33 82

13.85 32 130

-0.02 (0.66) 0.19*** (2.76)

-0.02 (0.87) 0.06 (1.08)

-0.05 (1.57) 0.08* (1.84)

-0.07* (1.68) 0.12** (2.26)

-0.07 (1.18) 0.15** (2.29)

-0.05 (1.27) -0.04 (1.36)

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