Diseconomies of Scope and Mutual Fund Manager Performance. Richard Evans, Javier Gil-Bazo and Marc Lipson*

Transcription

1 Diseconomies of Scope and Mutual Fund Manager Performance by Richard Evans, Javier Gil-Bazo and Marc Lipson* We examine the changes in performance of mutual fund managers that result from changes in the scope of their duties. While confirming that the scope of manager responsibilities is expanded in response to positive past performance, we demonstrate that this expanded scope attenuates subsequent performance after controlling for effects related to fund size. Conversely, reductions in scope enhance performance. Our results suggest a significant diseconomy of scope exists with respect to performance similar to the diseconomies of scale previously highlighted and that, together, these two effects may explain the observed attenuation over time in abnormal relative mutual fund returns. * Evans (evansr@darden.virginia.edu) is an Associate Professor at Darden Graduate School of Business. Gil-Bazo (javier.gil-bazo@upf.edu) is an Associate Professor of Finance at Universitat Pompeu Fabra. Lipson (mlipson@virginia.edu) is a Professor at the Darden Graduate School of Business. We thank seminar participants from the Darden School of Business and the McIntire School of Commerce at the University of Virginia and the Cologne Center for Research in Finance for their helpful comments and suggestions. 1

2 Diseconomies of Scope and Mutual Fund Manager Performance Substantial debate continues with respect to whether active mutual fund management provides value to investors results vary by sample, sample period, and definition of performance. 1 Even when beneficial performance is identified, whether in absolute terms or relative terms, there is strong evidence that beneficial fund performance declines over time. Much of the research on this topic has focused on identifying the drivers of performance attenuation as a way to generate insight into the underlying economics of fund management. Early research emphasized competitive use of information and market efficiency while recent work explores the characteristics and organization of funds themselves. Notable in this recent work is Berk and Green (2004), who offer an explanation for attenuated performance based on diseconomies of scale: that large flows into a manager s portfolio generate ongoing trade sizes too large to implement effectively. We explore a related explanation based on diseconomies of scope: that successful mutual fund managers are promoted to a broader range of responsibilities and this increase in scope also degrades performance. Much of the extant analysis of mutual fund performance focuses on fund level performance. To the extent one examines the relation of performance to fund characteristics such as fund size, as emphasized in Berk and Green (2004), this focus on the fund-level unit of observation is appropriate. At the same time, there is substantial evidence suggesting that fund 1 See, e.g., Carhart (1997), Fama and French (2010), Barras, Scaillet,Wermers (2010), Kacperczyk, Sialm and Zheng (2008), Kacperczyk, Van Nieuwerburgh, and Veldkamp (2014). 1

3 performance is determined in part by characteristics of individual managers. 2 In our analysis, we examine both fund-level and manager-level characteristics and, where Berk and Green (2004) emphasize the role of fund size, we emphasize the role of manager scope. We begin by examining whether or not there is cross sectional variation in fund performance that could be diminished by changes in scope. 3 Sorting our sample of U.S. equity fund managers based on four-factor alpha (henceforth simply alpha unless otherwise qualified), we find that funds in the top decile of performance significantly outperform funds in the bottom decile for four years. In a regression analysis with controls, better funds outperform worse funds for two years. These results suggest fund performance varies reliably in the cross-section while confirming that there is an attenuation over time the very effect we seek to explain. 4 Since we are exploring whether manager performance might explain this phenomenon, we confirm that identical effects are seen in individual manager performance. As for changes in scope resulting from better relative performance, we show that managers with higher relative alphas see an expansion in the scope of their responsibilities, defined as an increase in number of funds under control or an increase in total size of assets under management after a change in control (reallocation of funds) that that keeps the number of funds constant. Managers with lower relative alphas see a similarly defined contraction in the scope of responsibilities. These results hold with time fixed effects and robust to various lags in 2 See, for example, Wermers (2000), Baks (2003), Gottesman and Morey (2006), Hu and Chang (2008), Li, Zhang, and Zhao (2011), and Berk and van Binsbergen (2015). 3 Prior evidence suggests relative differences exist and are persistent over time, though the extent of the effect varies by sample and methodology. See, for example, Wermers (2000), Hu and Chang (2008), Li, Zhang, and Zhao (2011), and Berk and van Binsbergen (2015). Our objective is to establish that meaningful variations across managers is observed in our sample and using our measure of performance. 4 As with most studies, performance of funds and managers subsequent to the sorting year, particularly when returns are calculated net of fees as in our analysis, are negative on average our objective is to document that relative performance is persistent. 2

4 performance. These results are consistent with other studies exploring mutual fund manager professional advancement and compensation since many of the measures of advancement are, in effect, measures of scope (e.g. Khorana (1996), Chevalier and Ellison (1999), Drazin and Rao (2002), Fang, Kempf, and Trapp (2014), and Berk, van Binsbergen and Liu (2015)). As for our main hypothesis - that relative manager performance drives changes in scope that subsequently attenuates performance differences - we provide a number of tests. First, we examine the time series of alphas around manager scope changes. We document significantly rising cumulative alphas (adjusted for average manager performance) for four years prior to an expansion of scope, after which there is no perceptible change. Similarly, we see falling cumulative alphas in advance of a reduction in scope, after which, once again, there is no perceptible change. These results suggest that better performing managers experience increases in scope that eliminate outperformance. In these tests we also find that worse performing managers experience scope reductions that improve performance to a degree that offsets underperformance. This reinforces our interpretation that the results are driven by manager activity. In another univariate test we partition both by manager performance over a given year and again based on later changes in scope, and examine how performance changes as a result of the scope change. In this test, therefore, we are controlling for prior performance, can document resulting scope changes, and can look at performance changes. Consistent with scope changes being driven, in part, by performance, we find that managers in the best performing decile see more expansions in scope than reductions in scope and that managers in the worst performing decile see more reductions than expansions. In all but the bottom two deciles of initial performance, we find evidence of a larger reduction in performance for scope expansions than 3

5 scope reductions in either the first or second year subsequent to a scope change. Once again, the results are consistent with a performance driven scope changes that attenuate relative performance differences.our main objective is to draw attention to diseconomies of scope as a possible explanation for the lack of persistence in fund performance in a manner similar to diseconomies of scale. One distinction between these explanations is that scope changes impact performance at the individual manager level while scale impacts performance at the fund level. In our most comprehensive tests, which control for both scope and scale effects along with other fund performance drivers, we link fund level alphas to measures that reflect the scope of responsibilities of the fund s managers - where those measures are defined in a manner that acknowledges that there may be multiple managers of a fund. We complement this fund level analysis with a manager level analysis to establish once again, in this multivariate setting, the mechanism at work. We consider, in these tests, a broader set of scope measures than in our univariate tests. We find that fund alphas are negatively related to measures of the scope of manager responsibilities: the size of assets managers manage in other funds; the number of other funds managed; and the number of distinct fund investment objectives managed. These results control for possible scale effects by including: the size of the fund itself (assets under management, AUM), the size of the fund family, and the flow of funds into the fund. These results hold in a variety of specifications including ones with fixed effects related to time, fund, fund family, and fund style. The results are similar, if a bit stronger, when we look at manager performance. As to the relative importance of scale and scope, looking at one standard deviation shifts in scope measures relative to a similar change in fund size, the effect of scope on alpha is roughly half the effect of size. 4

6 Taken together, our results suggest that diseconomies of scope may play a role in determining fund performance in a manner similar to the diseconomies of scale emphasized by Berk and Green (2004). 5 As such, our results contribute to the ongoing debate on the value of active management by highlighting another economic force at play that would naturally diminish the value of active management: the expansion of manager responsibilities that might result from outstanding manager relative performance. One notable difference between scope (at the manager level) and size (at the fund level) as mechanisms that attenuate performance is that scope does not require outside fund flows to respond to abnormal performance as measured by a multi-factor model. In fact, while we document that changes in scope are related to prior multifactor alpha, most evidence on the drivers of fund flows find that flows are not driven by alpha, but by single-factor alpha, ranked returns, or absolute returns. 6 Put another way, the Berk and Green (2004) model assumes that investors respond perfectly to the manager s ability as measured by the true risk-adjusted alpha, but recent empirical evidence suggests that mutual fund investment decisions are made on the basis of less sophisticated performance measures. We show, however, that investment advisors make their decisions regarding changes in the scope of a manager based on multi-factor alphas, suggesting that it is an important additional equilibrating mechanism for the seminal Berk and Green (2004) argument. As such, our results extend the size argument in a useful direction. Note that we do not specifically address the question of why mutual funds allow this increase in scope to occur or whether this occurs to an extent that would 5 Our analysis of manager scope is consistent with a number of studies documenting the limitations associated with reduced attention in other contexts such as boards of director performance (Ferris, Jagannathan, Pritchard (2003), Fich and Shivdasani (2006) and Field, Lowry and Mkrtchyan (2013)). 6 See, for example, Sirri and Tufano (1998), Chevalier and Ellison (1997), Evans (2009), Berk and van Binsbergen (2016) and Barber, Huang, and Odean (2016). 5

7 fully eliminate the value of active management. 7 We simply highlight how this scope change drives relative performance across managers. Our work complements a growing literature that looks at the allocation of managerial talent. In respect to career advancement, Khorana (1996) and Chevalier and Ellison (1999) look at determinants of hiring and firing while Drazin and Rao (2002) look at allocation of current managers to new funds. Berk, van Binsbergen and Liu (2015) look at the Berk and van Binsbergen (2013) measure of value creation (alpha multiplied by assets under management) at the fund level and find that managers that create value are more likely to be promoted. As for allocating talent within a fund family, Fang, Kempf, and Trapp (2014) document more positive manager alphas in the high yield (as opposed to low yield) corporate debt markets and find that better managers (based on SAT scores) are allocated to the high yield market. These papers are consistent with our evidence that strong managers are promoted and suggest that firms allocate talent thoughtfully, but they do not examine the effects of expansions in scope on underlying performance. 8 We also contribute to the growing body of work documenting reliable and persistent variation in manager performance. For example, Chen, Hong, Jian and Kubic (2013) show that funds with outsourced management perform more poorly than funds managed within the fund 7 Berk and van Binsbergen (2013) suggest an interesting possibility specifically intended to address the Berk and Green (2004) observation on the diseconomies of scale that mutual funds are focused on the net value created by active management, which is the product of alpha and size. Thus, a decrease in alpha as a result of fund inflows may be more than offset by the increase in fund size. Our diseconomy of scope results control for changes is size, so represent an additional factor that would not be offset by an increase in size. 8 There are some unpublished papers that have examined scope in relation to mutual fund managers. Evans (2009) documents that mutual fund managers are promoted on the basis of raw returns rather than risk adjusted returns. Gerakos, Linnainmaa andmorse (2014) link compensation to performance and document a diminishing in performance tied to fund size. Most similar to our work, Agarwal and Ma (2012) look at open-end equity funds managers that move from one to more funds (existing or new) and show these managers were good past managers and they take over bad funds. They show that original fund performance gets worse and find more performance declines when the new fund is in different investment style. 6

8 family; both Gaspar, Massa and Matos (2006) and Bhattacharya, Lee and Pool (2013) provide evidence of performance transfers between funds through trading activities; Hu and Chang (2008) and Berk and van Binsbergen (2015) document long term persistence in cross-sectional variation in manager performance. 9 Berk and van Binsbergen (2015) attribute the majority of performance variation to differences in firm size, with a minor role for alpha. Wermers (2000) finds persistence in performance and persistence is explicitly tied to manager identity in Baks (2003), Gottesman and Morey (2006), and Li, Zhang, and Zhao (2011). Hu and Chang (2008) and Hoberg, Kumar and Prabhala (2014) suggest fund families recognize differences in compensation decisions. These papers suggest managerial ability may differ, but do not explore why this may be diminished over time or close the loop by illustrating how the outcomes of relatively strong performance degrade that same performance. The remainder of the paper is organized as follows. In the next section we describe our data with a focus on the relationship between managers, funds and firms. This is followed by sections presenting our results on: manager relative performance, drivers of manager scope changes, and the effects of scope changes on performance. Data and Summary Statistics Our data comprise the monthly observations in the Morningstar Direct mutual fund data base from 1997 to We restrict our performance analysis to actively managed diversified domestic (U.S.) equity mutual funds. Note that while our analysis of performance focuses on U.S. equity funds, when determining manager scope of activities, we consider all possible funds a manager might manage. This would include non-u.s. funds, index funds, and bond funds. 9 Unpublished work making similar points include Hoberg, Kumar and Prabhala (2014) who show manager persistence when there is weak competition. 7

9 Table 1 presents summary statistics on our sample partitioned in two ways. First, we consider the various levels of analysis, which is at the fund level, the manager level, and the fund family (firm) level. As discussed previously, studies of mutual fund performance typically view the funds from the point of view of possible investors, and therefore focus (for the most part) on the performance of individual funds. Since our focus is on how the actions of the fund families with respect to allocating manager talent affects manager performance, we also include information on individual managers and on firms that manage families of funds. In our sample, there are about 10,000 funds. Funds may have multiple managers while at the same time managers may manage more than one fund. In our sample, we have about 16,000 managers. Not surprisingly, there are far fewer firms in our sample about 1,000. Second, we distinguish between types of funds (the fund asset class) since differences is asset classes also reflects a difference in scope. We consider three partitions: diversified domestic equity funds (for which we calculate performance), other equity funds, and non-equity funds. Our sample is relatively balanced across fund types. In our sample, about 10,000 of the 16,000 managers will manage only one asset class, though they may manage more than one fund within a given asset class. The remainder will manage across asset classes. The roughly 5,000 managers who manage more than one asset class, by definition, will manage more than one fund. As for firms (fund families), in our sample about a third exclusively offer diversified domestic equity funds and a third offer funds in all three asset classes. The rest mostly offer other equity funds or some combination of asset classes. Table 2 presents summary statistics that describe the relationship between managers, funds and firms. Observations are monthly and at the fund-manager level. We examine only 8

10 funds that have at least 36 observations and this results in about 1.3 million fund-manager-month observations (we have slightly fewer observations for some variables). In Panel A, we describe the relations between funds, managers and firms and also provide descriptions of their sizes. Within our sample, the average number of managers in a fund is 4.6 with a median of 3 and a 99 th percentile of 26. The average fund size $1,746 million. The distribution is skewed due to the existence of a number of large funds the median is only 240 million with a 75 th and 99 th percentile of $924 million and $31,199 million, respectively. As for managers, the mean number of funds a manager manages is 6.2 and the mean dollar value of assets a manager manages (across all managed funds) is $9,203 million. As with the funds, the value of assets managed is skewed the median value of assets managed is $1,771 million with a 75 th and 99 th percentile of $6,805 and $47,551, respectively. As for firms, the average number of funds in a firm is 49 and the average number of managers is 64. On average, in our sample, a firm manages $83,373 million in assets. The firm size, like funds and manager assets, is also skewed while the median firm manages $15,528 million in assets, the 75 th and 95 th percentile firms manage $63,284 million and $1,186,207 million, respectively. Table 2 also provides descriptive information on funds and managers in Panel B. The average age of a fund is almost five years. The funds turnover their assets a little less than once a year (84%) though this varies greatly and is skewed - the 25 th percentile is about a 31% turnover while the 75 th and 95 th percentiles are 102% and 475%, respectively. Expense ratios average 1.1% of AUM. We know the year a manager first appears in the data set, so we can estimate the length of time a manager has been in this industry (career). The average is 8.1 years. Some managers, of course, newly appear in the data (a career of one month, or about 10% of a year) while some have been managing for a long time (the 99 th percentile is 20 years). As for the 9

11 length of time a manager has managed a given fund, on average they have been with a given fund in our sample nine years. We measure performance using the Carhart (1997) four-factor alpha calculated using the Fama and French factor data. This essentially evaluates manager performance by calculating the excess return (alpha) relative to an appropriate benchmark (factor model). In our case, this would be: = where r it is the period t return on fund i (in excess of the one month T-bill return), α i is our performance measure, the betas represent factor loadings for the value weighted market return (MKT t, in excess of the one month T-bill) and the zero-investment factor mimicking size (SMB t ), book-to-market (HML t ), and one-year momentum (UMD t ) portfolios. The returns we use are net of all operating expenses and (implicitly) net of transaction costs unless otherwise explicitly stated. We use a 3 year (36 month) rolling window prior to the month of analysis to establish factor loadings and apply those loadings to the realized data in the month of analysis. Since our focus is on relative performance, in some tests were report the alpha in a given month less the average alpha of all managers in that month. We calculate monthly alphas for each unit of analysis (fund or manager depending on the test) and aggregate as indicated. When managers manage more than one fund, we weight the individual fund alphas based on the following: the AUM in each fund divided by the number of managers. Thus, for a manager who manages a fund with two other managers, the weight on that manager s performance in that fund is one third of the AUM of that fund. 10

12 Fund and Manager Relative Performance and Persistence We establish at the start that there are variations in performance that can be meaningfully attributed to managers. Specifically, we consider whether managerial performance in the crosssection is persistent. Our initial analysis of persistence is presented in Table 3, looking at both funds and managers. We first annualize our monthly alphas by summing the constituent monthly alphas and then sort these alphas into deciles. In our sample the top decile fund earned 9.53% per year while the worst earned % per year. Even allowing for the possibility that the initial sorting variable included noise, which is confirmed by the strong mean reversion in alphas, we still see very significant differences between the top performing funds and the worst performing funds for two years after the sort. Years three and four are significant, but of smaller magnitude and inconsistent in sign. Results are quite similar in the columns looking at manager performance. The partitions suggest performance is persistent, but includes little in the way of controls. In a more formal analysis of persistence, we regress alpha in a given year on alpha lagged one through five years. This analysis includes time period fixed effects so all results reflect relative performance and these results are presented in Table 4. As suggested by the prior tables, performance is statistically significantly persistent for two years for both funds and managers. We still observe a slight reversal of this difference in year three for funds when all lags are included. Taken together, these results confirm what has been documented frequently in the literature that there is relative performance persistence but that the performance differences decline over time. 11

13 Performance Driven Changes in Scope Much of the recent research on mutual funds has focused on the internal organization and governance of funds. This literature spans decisions such as whether to co-manage or outsource funds to how managers are rewarded. As would be expected, there is ample evidence that managers are rewarded for strong performance, where performance is measured relative to appropriately established benchmarks. Typically, these studies identify events that would naturally be interpreted as a promotion and explore the relation between past performance and these events. As might be expected, events that expand the scope of manager responsibilities are often used to indicate a promotion. Our objective in this paper is not to provide evidence as to whether managers are rewarded, per se, for their performance. Rather, we believe these rewards often include (but may not be limited to) expansions of scope and these expansions in scope may degrade performance. Our objective, therefore, is to establish that managers who do well (relatively high alpha) experience expansions in scope not as indicators of reward, but as outcomes of interest with real economic consequences. In this regard, while our analysis of performance driven scope changes is quite similar to other studies of promotion and demotion, it differs in important respects. For example, what would not be counted as an expansion of scope in our analysis, but has been used as an indicator of promotion, would be an increase in the size of the fund a manager manages absent an actual change in responsibilities associated with new funds. 10 In our 10 For example, Chevalier and Ellison (1999), Hu, Hall and Harvey (2000) and Baks (2003) define a promotion as a change in manager activities where average monthly total of AUM in a year exceeds the prior year total AUM adjusted for the average growth of AUM for all domestic diversified equity funds. There is no distinction as to whether that growth is within, or outside of, a given fund a manager might be managing. 12

14 framing of the issues (scope versus scale), these changes in size would be considered changes in scale. To establish the link between performance and scope in this section, and to provide a preliminary insight into the effects of scope expansions on performance, we proceed as follows. We define an expansion of scope as occurring when there is either an increase in the number of funds under the manager s control or, if the number of funds stays constant after a change in fund oversight (one or more swaps into new funds), there is an increase in the AUM of the manager. A reduction in scope is analogously defined. (We consider other measures of scope in later tests.) We then estimate a multinomial logistic regression model with increases and decreases in scope as the outcome variable and past alpha as the explanatory variable to establish the link to the performance measure we previously documented as declining. We consider a variety of ranges for alpha from very recent to more distant performance. The results are shown in Table 5 along with a number of controls known to affect changes in manager activities. We see quite clearly that manager performance, as measured by alpha, is a determinant of later changes in scope of responsibilities. This result is seen both for expansions and reductions in scope. All the links to alpha, whether over three years or for each of the past three years, is significant. We also see significant links to other variables including the amount of assets under management a manager with more assets is more likely to see an expansion in scope. We also control for various measure of scope and note that managers with more funds are more likely to see a change in scope, of one form or another, while a manager of more asset classes is more likely to see a scope expansion. We also note that as managers stay longer in the profession, they are more likely to see (unconditionally) a reduction in scope (less likely to see an expansion). 13

15 Managers at firms employing a larger number of managers are more likely to see changes in scope, either an expansion or reduction. Diseconomies of Scope This section presents our principal tests exploring how diseconomies of scope can affect manager, and therefore fund performance. We begin with basic univariate tests that illustrate the central points of our analysis. These provide a clear view of the underlying dynamics, particularly with respect to the drivers of scope changes along with the effects of those changes on manager performance. We then present multivariate tests that focus on fund level performance and the effects at the fund level of manager level diseconomies of scope. Univariate Tests In our first analysis we partition managers based on a change in scope as defined in the prior section. We then document the time series of alphas prior to and subsequent to, the scope change. Since our concern is relative performance, we adjust these alphas for the average alpha in any given month, which we call relative alpha. 11 The results are presented in Figure 1 with related tests of significance in Table 7. Figure 1 graphs the cumulative relative alpha for both expansion and contractions in scope. In Figure 1 we observe a striking increase in cumulative alpha over four years prior to a scope expansion. We see a similar decrease in cumulative alpha prior to a scope reduction, though the drop is observed 11 Given that managers, on average, underperform their benchmarks and earn negative alphas, if we did not adjust for the average alpha in a given year, we would observe a drift in cumulative alphas. Adjusting for average alphas accomplishes two things: it makes the intuition more obvious by highlighting relative performance and it controls for any time period effects on the average level of fund manager performance. 14

16 only over the two years prior to the scope change. This pattern is entirely consistent with our earlier evidence that manager performance drives scope change. Most important for our study is that subsequent to the scope expansion or scope reduction the prior performance is attenuated: there is no further cumulative increase for scope expansions or decrease for scope contractions. Specifically, there is a change in performance that is consistent with a diseconomy of scope. Not too surprising, given the possible drivers of a diseconomy of scope, we observe that the effect is symmetric after a scope reduction, the poor performance of ostensibly worse managers is curtailed. Interestingly, the graph suggests that after the scope changes, manager performance is essentially indistinguishable between those managers with a scope expansion and those with a scope reduction (no positive or negative relative alpha). This is not an essential part of our argument we only seek to document that diseconomies of scope can adversely affect manager performance. However, it does seem that in this simple test the effects of scope changes do all but eliminate differences in performance, which suggests the may eliminate performance differences over time. We provide additional tests of these observations in Table 6. In particular, we look at the change in performance from before a scope change to after a scope change, conditional on the type of scope change. Looking at Panel A of Table 6, which reports the median alphas, we see that prior to a scope expansion, managers earn a relative alpha of about 8.6 basis points. This drops to 1.18 after the scope expansion and this change is statistically significant based on the simple time series standard deviation of the median alphas (we impose no independence assumption across manager observations). For a scope reduction, managers lose about 1.8 basis points relative to other managers prior to the reduction, and this improves to 1.0 basis points 15

17 thereafter. This change is also significant. As expected, the relative alphas of the managers with expansions and contractions are significantly different prior to the scope change. Once again, there is no evidence of a difference in performance across the two manager groups after the scope change. Panel B of Table 6 presents this same set of tests but looking at the mean, rather than median, relative alphas. The results are very similar. In the Table 6 analysis, we initially conditioned on whether a manager had experienced a change in scope. While the time series alpha prior to the change suggests the performance caused the scope change (and our earlier evidence is consistent with this interpretation), Table 7 provides a more comprehensive look at these effects. In particular, Table 7 combines these two effects in a double sort analysis: we first sort on alpha, then look at changes in scope (including no change) conditional on this alpha sort, then look at subsequent performance within each sort. As alluded to earlier, sorting on alpha presents a statistical problem we may be sorting on noise along with true alpha differences and we would expect some reversion in performance after the sort. Furthermore, firms are likely to have information on managers that would affect decisions on manager scope and also be related to future manager performance. To address these concerns, we conduct our analysis as shown in the time line diagram below where t indicates relative months. t-24 to t-13 t-12 to t-1 t t+1 to t+12 t+13 to t+24 Alpha for Sort based on Alpha for first year sorting scope change after scope change Alpha for benchmarking performance Performance Change Performance Change Alpha for second year after scope change 16

18 Given the structure of this test, we can examine whether scope changes are consistent with the first sort based on alpha (performance drives scope change), then we can see if performance is altered as a result of the scope change by comparing the performance in periods subsequent to the scope change with the alphas in a period that is free of sorting bias and unaffected by the scope change (the benchmark alpha). This does present a relatively weak test of whether scope changes are driven by alpha, but this link we have explored in greater detail already. The main advantage is that we can establish whether there are performance effects related scope changes conditional on the performance that might have driven the scope change. The results are presented in Table 7. Note that all alphas are cumulated over the 12 month windows and, therefore, are annual alphas. These are also relative alphas and, therefore, have had the average alpha in a given year subtracted. In the initial sorts, the best managers earn an alpha of about 10.47% over the sorting year. The worst lose about 9.75%. In the sort on scope change, looking at the benchmark alphas, we see that there is a performance difference between managers with scope expansions and those with scope reductions. For example, in the partition with the best managers, those with a reduction earned an alpha of 0.22% in the benchmark year while those managers with an expansion earned 1.78%. This difference is statistically significant in this partition and in every partition, and suggests, not surprisingly, that the managers with scope expansions perform better than those with reductions in the year prior to the change in scope. We also see that in the top partition about 500 managers see scope reductions and over 800 see expansions. In the remaining partitions this difference reverses (roughly monotonically) to the point where, in the partition with the worst managers, over 900 see scope reductions and a little over 500 see scope expansions. All told, these results confirm that scope changes are driven by performance differences. 17

19 Looking at the effect of the scope changes on performance (controlling for the performance that may have contributed to a scope change), we observe changes that are consistent with diseconomies of scope. Specifically, we observe a greater reduction in alpha for scope expansions than for scope reductions in either the first or second year after a scope change in all but the bottom two deciles (and a reduction both the first and second years for the top four deciles). Multivariate Tests Our tests so far have been univariate and focused simply on changes in scope and alpha. In addition, the focus has been on fund managers. Our ultimate objective is to add insight into the performance of funds by including the effects of manager scope, so we must look at fund performance, not just manager performance. Looking at fund level performance introduces some complications related to the fact that funds will often have multiple fund managers. This necessitates the calculation of measures of scope appropriate for multiple managers and are described below. Furthermore, in contrast to the simple expansion and contraction we explored in the last section, in this section we explore in more detail the various possible changes in scope. Broadly speaking, we explore three measures of manager scope: expansions in the size of assets managed outside of a given fund (both in total and on average for other funds managed), an increase in the number of funds managed, and an increase in the number of investment objectives (asset classes) being managed. These three categories can be viewed as increasingly significant increases in scope placing, as it were, increasing demands on manager time and effort. 18

20 For the analysis at the fund level, we construct our scope measures in a way that reflects the scope of activities for the managing team of managers. To be specific, looking at fund f which has n f managers, measures of scope are defined below. Total manager external assets is first calculated for fund f by summing the AUM managed by all managers of fund f that are outside of fund f, where the AUM of a fund included in this calculation is divided by the number of managers in that fund. We then take logs. For example, assume there are two managers of fund A, managers A1 and A2; assume manager A1 also manages fund B with three other managers and that manager A2 also manages fund C with one other manager; total manager external assets would be equal to the log of the sum of one quarter the AUM of fund B and one half the AUM of fund C: log( ¼AUM A + ½ AUM B ). Mean external assets per manager is first calculated for fund f by summing the AUM managed by all managers of fund f that are outside of fund f, where the AUM of a fund included in this calculation is divided by the number of managers in that fund. We then divide by the number of managers, n f, of fund f and take logs. For the example above, mean external assets per manager would be equal to the log of one half of the sum of one quarter the AUM of fund B and one half the AUM of fund C. Specifically, it would equal: log( ½ ( ¼ AUM A + ½ AUM B )). Mean number of funds is calculated as the log of the average number of funds managed by the n f managers of fund f. For the example above, mean number of funds would be equal to the log of the average of four and two: log(3). 19

21 Mean number of inv. objectives is calculated as the log of the average number of investment objectives spanned by the n f managers of fund f. Assuming funds A and B are in the same asset class and that fund C is a different asset class, then for the example above, the mean number of investment objectives would be equal to the log of the average of 1 and 2: log(1.5). The dependent variable in our analysis is the alpha of a given fund. Our unit of observation will be annual fund observations and the explanatory variables are calculated using year-end reports. We sum the calculated alphas from our prior monthly analysis (in percentage) to arrive at annual alphas. As control variables, we include those typically employed in fund performance regressions: log of total assets in the fund and log of firm assets (assets in the fund family); the reported turnover and expense ratio (both in percent); fund age, which is the number of years since fund inception; an indicator as to whether a fund s share class has a sales load; and the annual flow into the fund from new money (relative annual growth in assets). These are all defined as of the start of the year in which we measure firm performance (lag one year). The results of our analysis are presented in Tables 8 and 9, where Table 8 presents an analysis of scope changes and performance at the fund level and Table 9 presents a similar set of tests at the manager level. In these tests, the first column presents our analysis with only control variables (baseline) and the next four columns present the results with mean manager external assets as our variable of interest, but with different specifications. The final three columns consider other measures of scope, but with only one specification.consider the results in Table 8 (fund level). The baseline specification is consistent with the results of prior studies of fund performance. As expected from the Berk and Green (2004) observation regarding the size of funds, fund size is negatively related to firm performance. We also see that larger firms generate 20

22 better performance. Turnover, expenses and load tend to harm performance, though we do not see this in all the specifications. There is little effect from the flow of assets into a fund. Looking at mean external assets per manager, we see a consistent negative effect across four specifications. The first specification (model [1]) serves as our baseline. The second specification includes our first measure of manager scope, mean external assets per manager. There is little impact on the typical variables from adding mean external assets. The third specification considers gross alpha rather than net alpha as in all the other specifications. An important concern with the analysis is that neither fund assets nor the responsibilities of the fund s managers are exogenous to fund performance. In fact, we know that investors chase performance and that better-performing managers are rewarded with more responsibilities. To the extent that performance is driven by unobservable time-invariant variables, such as managerial skill, the estimated coefficients on both scale and scope variables will underestimate their true negative effect on fund subsequent performance. To deal with this concern, in our fourth specification, we allow for fund fixed effects. We are therefore exploring only the effects over time of variation of a given fund from its mean (and we drop, therefore, the load indicator and investment category fixed effects, which are unchanged for a fund over time). As expected, the size of the fund has a greater (more negative) impact on performance. 12 The fifth specification uses firm level fixed effects rather than fund level fixed effects. Across these various specifications, the effect of mean external assets per manager is similar in magnitude and 12 Pastor, Stambaugh, and Taylor (2015) argue that including fixed effects solves the problem of the endogeneity of fund assets, but leads to an overestimation of the effect of size on performance in small samples. We therefore view the coefficients on scale and scope with (without) fund fixed effects as lower (upper) bounds on the the true effects. 21

23 significance. The results indicate that the average level of scope faced by managers in a fund is negatively related to the fund s performance. The next three columns present our other measures of scope: total manager external assets, mean number of funds, and mean number of investment objectives. In these analyses, we return to the baseline specification (time and category fixed effects), but results are qualitatively similar with the other specifications. Here we see, again, the negative effect of scope on performance. The final specification includes all scope measures. 13 In this specification, external assets and investment objectives are both significant, while number funds is not. The effect of the number of outside funds, therefore, seems to be subsumed by the other two, suggesting it is the size of the outside assets that matters, not the specific number of outside funds unless those outside funds are a different fund style. This also suggests a distinct and potentially additive scope effect for the magnitude of requirements (assets) and the type of assets (investment objectives). In Table 9, we report the results of estimating the performance regressions of Table 9 at the fund-manager level. In this case, that managerial responsibilities need not be aggregated across all managers of a given fund. For instance, Total manager external assets is now calculated for fund f and manager m as the sum of the AUM managed by manager m that are outside of fund f, where the AUM of a fund included in this calculation is divided by the number of managers in that fund. The main advantage of changing the unit of observation to fundmanagers is we can include manager fixed effects in addition to the other fixed effects. The results are quite similar to those in Table 8. The only difference in results worth noting are the 13 We include only one of the two external assets measures (total assets and average assets) as the two are highly correlated. Results are similar with either variable. 22

24 following. First, the fund load is now a significant driver of alpha. Second, when all three measures of scope are included together, the number of funds has a significant positive effect. This suggests that, in the presence of the other diseconomies of scope, there may be some benefit to a manager from having other funds. Given that our analysis in Table 8 includes both measures of scope and measures of scale (size), we can draw some conclusions as to the relative importance of each. Consider the second specification with external assets per manager (column 2). The standard deviation of fund assets is such that a one standard deviation increase in assets (not reported) would reduce alpha by 41 basis points. In contrast, a one standard deviation increase in external assets per manager would reduce alpha by 18 basis points. The effect of scope is roughly half that of scale. The magnitudes of the effects for other variables is similar. In the case where a manager sees a scope increase in both outside assets and a new style, the magnitude of the two effects might very well be similar. For column 2 of Table 9 (managers), the comparable effects are 30 basis points (scale) and 16 basis points (scope). Once again, results for managers and funds are quite consistent. Conclusion The difficulty that funds and managers face with respect to generating abnormal returns from active management has historically be framed as a question related to market efficiency. In this framing of the challenge, managers compete away profits by trading on their information. Recent work on mutual funds has begun to explore the myriad ways in which the organization of funds, and the compensation of fund managers, might affect fund and manager performance. We contribute to this strand of literature by highlighting the potential effects on fund performance from diseconomies of scope. We position this as a natural extension of Berk and 23

25 Green (2004) who posit that the lack of persistence in fund performance can be attributed to increased fund size as a result of fund inflows a diseconomy of scale. Interestingly, the agents behind the Berk and Green (2004) effect investors who channel their resources to a fund, presumably by observing and responding to fund performance. The agent behind our effect are the fund families themselves, who presumably observe and respond to manager performance. 24

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