1. Department of Economics
Does fund size matter?
Authors: Christian Marina & Oskar Jonjons
Supervisor: Roine Vestman
EC6902 Bachelor thesis in Economics
Autumn 2016
2. Table of contents
1 INTRODUCTION ........................................................................................................................ 3
2 A THEORY BY BERK AND GREEN (2004).......................................................................... 5
3.0 EARLIER RESEARCH........................................................................................................ 6
3.1 Flow-performance relationship.................................................................................................................6
3.2 Decreasing returns to scale?......................................................................................................................8
4 DATA..........................................................................................................................................11
5.0 ECONOMETRIC METHODOLOGY....................................................................................13
5.1 Flow performance regression....................................................................................................................13
5.2 Regression of returns to scale ...................................................................................................................14
6.0 RESULTS.................................................................................................................................15
6.1 Flow-performance results .........................................................................................................................16
6.2 Returns to scale results (non-small cap) ...................................................................................................18
6.3 Return to scale results (small cap) ............................................................................................................20
7 CONCLUSION.........................................................................................................................24
8 ACKNOWLEDGEMENTS...................................................................................................25
9 REFERENCES.........................................................................................................................25
10 SOURCES ...............................................................................................................................27
11 APPENDIX...............................................................................................................................32
3. 3
Abstract
When investors choose mutual funds, they try to estimate the sustainability of the
funds by looking at historic performances, management fees, managerial skills,
risk profiles etc. But should the fund size also be taken under consideration and
serve as decision basis? This paper investigates if fund size erodes mutual fund
performance in the Swedish active mutual fund industry. Mutual funds attract new
capital by good performance. But does it come to a point where there is too much
money in the fund and hence, performance is hindered? If that is the case, at what
levels does Swedish active funds start to perform worse? We apply a quadratic
regression to estimate the effect of scale on performance and a potential
performance-maximum point. 132 actively managed equity funds are observed
over the 2002-2015 period. A distinction is made between small cap funds and
funds in general. Neither showed hindrances in performance due to fund size.
1 Introduction
Since the first Swedish mutual fund was started in 1958, fund savings have
increased sharply. At the end of 2015, total assets invested in Swedish mutual
funds amounted to approximately 3,246 BSEK. Outside of the premium pension
plan, 8 out of 10 swedes have savings in funds through different channels, private
and collective pension savings. Around 58 percent of the total fund savings were
placed in equity funds and 88 percent of those were actively managed.
But can the mutual fund industry handle all this capital in line with the best
interest of the investors? Earlier studies performed on U.S. funds suggest that the
increase in fund size can serve as a detriment to sustaining a good performance.
As mutual funds accumulate more capital from investors, they will at some point
exhibit decreasing returns to scale. From the fund companies’ standpoint, a larger
fund size is preferable since their main source of income is the management fee in
which a fixed percentage is charged of the funds’ total assets. The main goal of
this paper is to answer whether a relatively large fund size should scare away
potential investors. The hypothesis is based on a theory by Berk and Green
(2004), using two intuitions. The first is called the flow-performance relationship
4. 4
where investors behave rationally by reacting to historic returns. The intuition is
that investors withdraw capital from poor-performing funds and invest in mutual
funds who performed well historically. But as the fund experience large net
inflows of capital, it will reach a point where supply of invested capital become
too competitive and create difficulties for the fund manager to sustain a positive
abnormal return. In trading with larger assets, fund managers move prices against
them originating from a higher illiquidity. This second relationship is known as
decreasing returns to scale. The major focus of this paper will be on the latter
relationship since there is no clear consensus how funds’ performances are
affected by their fund size. There has not been a study done on Swedish mutual
funds returns to scale yet.
In July of 2016, Vanguard closed their Dividend Growth Fund to new investors
which had seen a large inflow-increase, lending support to Berk and Green’s
theory. CEO Bill McNabb explained why:
“Vanguard is proactively taking steps to slow strong cash flows to help ensure
that the advisor’s ability to produce competitive long-term results for investors is
not compromised, … We have long been committed to protecting the interests of
our funds’ shareholders, and demonstrate this conviction by closing or restricting
funds to stem further growth.”
Carnegie Sverige Select is the most recent Swedish case (September 2013) where
an equity mutual fund chose to close for new investors. Fund manager Simon
Blecher pointed to same reasons as Bill McNabb for the decision. But is it
justified?
We try to answer that question by applying a quadratic regression on panel data
observed 2002-2015, consisting of 1,186 fund-years in total, for Swedish equity
funds. There are two line of demarcation that need to be highlighted. First, all
mutual funds in the sample are actively managed, which means there are no index
funds included. Why? Since the goal of an actively managed fund is to generate
5. 5
positive excess returns1
by beating the market, while an index fund does its best to
follow the market and therefore it is safe to assume that there are no significant
abnormal returns. Second, we are only interested in mutual funds that have their
holdings in Swedish based corporations since controlling for currency risk,
geopolitical risk et al. can be complex. Consequently in the following sections,
actively managed equity funds will exclusively be referred to as “mutual funds”.
The paper is organized as follows. Section 2 describes the theory that the
hypothesis is based upon. Section 3 summarizes research in relation to
the topic, which will be useful to construct the regression. In Section 4, the
dataset is described, what sources are used and eventual problems. Section 5
specifies the regressions, the first one describes the flow-performance
relationship while the second regression determines whether there are returns to
scale. The regression for funds in general (non-small cap) and small cap funds,
are the same for both samples. In Section 6, results are presented and discussed.
Finally, our conclusions are summarized in Section 7.
2 A theory by Berk and Green (2004)
If you search through the mutual fund literature, you are likely to come across two
central facts that are well-known. The first is, the lack of persistency to
outperform the benchmark for an actively managed fund, based on more than
thirty years of research, (Jensen 1968) and (Carhart 1997). Second, Chevalier and
Ellison (1997), Sirri and Tufano (1998), showed an asymmetric relationship
between mutual funds’ net flow and past performance. Mutual fund investors
chase performance but fails to flee from poor-performing funds. The traditional
interpretation of the two facts have been that active managers who performed well
in the past have been lucky and are no more skilled than the average manager.
Also, investors behave irrationally by rewarding lucky managers and not
punishing them when they are not so lucky.
In 2004, Jonathan B. Berk and Richard C. Green came to another conclusion,
1
In this paper, the term excess return refers to the difference between a fund’s return and the
return of the market. It should not be confused with the return over the risk-free rate.
6. 6
starting from the same facts. In their model, investors rationally chase
performance based on past returns. They do so until expected risk-adjusted returns
are equal across mutual funds. Mutual funds generate inflow and enjoy growth in
fund size by beating the market (alpha > 0). As fund size grow it will eventually
reach a level where the fund will exhibit decreasing returns to scale (alpha
regresses towards an equilibrium equal to zero). By accumulating more capital,
managers in trades, move the prices against them, whether by buying or selling.
Berk and Green argue that active manager with superior abilities exist and
investors are rational by identifying and investing in them. But simply due to the
competitiveness of capital, managers fail to outperform their benchmark
persistently.
3.0 Earlier research
3.1 Flow-performance relationship
Extensive research has shown that fund flows are, to a large extent, affected by
historic returns. The impact of past performance has been well-documented by
researchers such as Ippolito (1992), Gruber (1996), Chevalier and Ellison (1997)
and Sirri and Tufano (1998).
Gruber (1996) explains why performance and fund flows of capital are positively
correlated and why investors choose actively managed funds. Mutual funds are
priced according to their net asset value, but the perception of the manager’s
ability is not incorporated in the price. This means, given the same underlying
assets of two different mutual funds, one manager with superior ability compared
to the other manger, are priced at the same level. Hence, a greater net inflow can
be expected for the higher skilled manager. In his research, on 188 American
equity funds over the period 1977-1993, Gruber found a non-linear relationship
between returns and fund flows. Good performance generates inflow of capital but
bad performance does not lead to outflows symmetrically. Meaning, investors are
more reactive to good performance than bad. This is also what Chevalier and
Ellison (1997) and Sirri and Tufano (1998) found in the years to follow.
Chevalier and Ellison (1997) showed how mutual funds alter their portfolio’s risk
7. 7
profile derived from the non-linear relationship between expected net fund flow
and return. The non-linear flow-performance relationship provided an incentive
scheme for the manager to either gamble by increasing the risk late in the year or
decreasing the risk by indexing the portfolio, in order to achieve a higher expected
net flow of capital. This created a conflict of interest between the fund company
and their investors, since the highest risk-adjusted return was no longer the main
goal of the manager. Chevalier and Ellison (1997) also found how the flow-
performance relationship looked different depending on the age of the fund. For a
given level of return, fund flows attenuated based on the fund’s age. This was
consistent with Berk and Green’s (2004) findings.
Figure 1. Flow-performance relationship (taken from Berk and Green (2004) page 1287).
Berk and Green (2004) reason as follows: As the fund’s age increases, investors
learn more about past performance with a bigger sample size and therefore
become less flow-sensitive to performance.
In the same research, it was also concluded that flows respond much more to
extreme performances than to average performances. The lowest performance
levels result in a perfect steeply sloped line. These funds that perform poorly are
very likely to shut down and will therefore experience a withdrawal of all capital.
8. 8
Per Chevalier and Ellison (1997), the reason for a sharp increase in fund flows for
excellent performance is due to the appearance of the annual “best fund” lists, by
which the fund can grab the attention of uniformed potential investors.
Consistent with the explanation above, Sirri and Tufano (1998) argued, a big
factor for consumers’ decisions depends on the cost of searching. The time and
effort expended by a consumer to search for information about a product is costly.
This can be directly applied to the mutual fund industry. Mutual funds who
receive more attention, by media or acquaintances, are less costly and therefore
are more likely to draw capital from investors. The responsiveness is greater for
recent performance than performance extending five years back. The fund flow
respond, in the largest extent, to last year’s performance. Another important
implication by Sirri and Tufano (1998), is how investors relate to funds’ portfolio
risk. They found a negative relationship between fund flows but this effect was
“marginally significant”.
This marginal effect can be directly tied to the incentive scheme drawn by
Chevalier and Ellison (1997). Both studies suggest investors are marginally
indifferent between risk adjusted return and raw performance (simple linear
difference between return and return on the market).
3.2 Decreasing returns to scale?
The effect of fund size on performance are divided into two different opposed
ideas and intuitions. There is one party agreeing with Berk and Green (2004) and
conjecture that small-asset funds have an advantage over big-asset funds because
securities are traded more easily without prices being altered. But some argue that
there are increasing returns to scale on performance, because of lower expense
ratio (operating expenses divided by assets under management) for large-asset
funds. In addition, one must be aware of the survivorship bias occurring within
smaller funds. This is what Elton, Gruber and Blake (1996) pointed out when one
is making inferences about fund characteristics. They compared the alphas
between large and small funds, but did so separately for a survivorship biased and
unbiased sample. In the biased sample, small funds perform slightly better than
9. 9
large funds. However, when controlled for bias, small funds performed much
worse than large funds.
Grinblatt and Titman (1989) highlighted the advantages and disadvantages to
scale by comparing the gross returns difference, between small and large fund, to
the actual return difference. Small funds performed significantly better when
measuring the gross return, but after adjusting for fees and expenses, the abnormal
performance diminished.
Returns to scale for mutual funds was investigated further by Pastor, Stambaugh
and Taylor (2014), using a panel data regression across funds. They distinguished
between the effect on a fund’s performance caused by the size of the fund and the
mutual fund industry. Before reaching their conclusion, they highlighted a
problem in estimating fund size effect on performance, which was the
endogeneity of fund size. They argued that a bias is likely to occur because fund
size is likely to be correlated with managerial skills and performance,
simultaneously. The growth in fund size can be a result of a skilled manager or
large-asset funds can afford to hire higher skilled managers. This would not be a
problem if fund size was randomly assigned across funds and then, a negative
coefficient (estimating fund size effect on performance) would indicate decreasing
returns to scale. In a reference to Berk and Green (2004) where managerial skill is
constant and investors update their beliefs and reallocates capital across funds,
based on those beliefs, Pastor, Stambaugh and Taylor (2014) differ between
perceived skill and true skill. Because perceived skill, measured in performance,
induces change in fund size (if one believes it to be true) then one cannot observe
true skill of managers that is time in-variant, where fund size is not. It is
illustrated by this equation:
𝑝𝑒𝑟𝑐𝑒𝑖𝑣𝑒𝑑 𝑠𝑘𝑖𝑙𝑙it= true skilli + noiseit
Berk and Green’s investors allocate their money based on how they perceive skill.
If an investor’s perceived skill exceeds true skill, the fund size would exceed its
optimal size and thus generating lower expected returns. Similarly, if perceived
skill were below the true skill, then fund size would be smaller than its optimal
10. 10
size and expected return is higher. Hence, in the context of Berk and Green
(2004), the size-performance relation is negative. By using fund fixed effects
(OLS FE), Pastor, Stambaugh and Taylor absorb all the heterogeneity-variation in
performance that is induced by skill across funds. After controlling for total bias,
the estimates indicated that a mutual fund increase of $100 million depresses the
marked-adjusted year return by 0.025 percent2
. However, this result was non-
significant. But on an industry-level, results showed significant decreasing returns
to scale for mutual funds.
In the theory by Berk and Green (2004) of an alpha equilibrium, performance
must be eroded with an increasing fund size on the mutual fund level. Chen,
Hong, Huang and Kubik (2004) supported the theory by finding a negative effect
that fund size has on return, which was more pronounced among small cap funds,
suggesting liquidity as the reason to why performance is eroded by fund size.
Thus, given the same fund assets, small cap funds need new stock ideas whereas
funds that invest in larger corporations can simply increase their holdings without
driving the share price against them.
Along the same conclusion, Yan (2008) found an inverse relation between fund
size and performance directly tied to illiquidity by looking at bid-ask spread,
stock’s market capitalization and relative holding size. Results showed decreasing
performance with higher fund size. This study was more effective, Yan argued in
contrast to Chen, Hong, Huang and Kubik (2004), by using direct measures of
illiquidity and even though same conclusion was reached, there were less margin
of errors.
Bessler, Blake, Luckoff and Tonks (2010) documents fund adversity from the
impact of large inflow in the medium and long run, consistent with Berk and
Green’s (2004) theory. The lack of positive persistence was much more noticeable
2
This result is estimated after controlling for finite sample bias which was caused by the OLS FE. In the
paper, this procedure is referred to as the bias-free RD procedure.
11. 11
with skilled mangers (sorted by alpha) compared to “lucky” manager (sorted by
return). Managerial turnover is also an important factor, in the research.
The “winner funds” who achieved a high alpha in one period, will significantly
experience an underperformance when the manager is changed.
Limited research has been done on returns to scale outside of U.S. mutual funds
and one cannot simply conclude the results as externally valid by applying the
findings on the Swedish fund market. As a matter of fact, Ferreira et al. (2013)
found increasing returns to scale when studying funds across 27 different
countries, while U.S. funds exhibited decreasing returns to scale.
4 Data
Our panel data contains 132 actively managed equity funds that almost
exclusively have their holdings in corporations listed on the Stockholm
Stock Exchange3
. The equity funds can be registered domestically
and in foreign countries. The measured timespan is between 2002-2015.
We started from the same dataset that was used in Flam and Vestman
(2014), which include returns of Swedish equity mutual funds and
SIXPRX4
between 2002-2013. Small cap funds were denoted and
the benchmark MSCI Sweden Small cap was added5
. The monthly return
was converted into yearly return. Yearly returns on the last two missing
years were later added from Morningstar. Returns are strict adjusted for
expenses and dividends (net returns). Data of mutual fund assets were also
expanded to 2015, collected from each fund’s annual report. All continuous
variables are measured at the end of year t.
Index-funds were excluded since they track the benchmark and have no
significant abnormal returns. Closed-end funds were deleted from the dataset,
although only one was found (Carnegie Sverige Select). Funds whose assets
3
The funds can have holdings outside of Sweden but according to Morningstar are classified as
Swedish equity funds.
4
SIX Portfolio Return Index. Average returns on the Stockholm Stock Exchange including ‘
dividends with share restrictions.
5
Classifying a mutual fund as a small cap fund was based on Morningstar categorization.
12. 12
have been boosted by mergers are denoted and being controlled for.
Mergers were detected by going through each fund’s history, using their
ISIN code6
. Länsförsäkringar’s fund archive was also used. In addition,
we searched for outliers in asset growth between two years to detect
possibilities of mergers.
Throughout the paper, references to two types of performance-measure are being
made. In this paper, performance is mainly measured by the excess return which
does not account for any risk behavior. The other is alpha, where risk taken by
funds relative the market is adjusted for. If funds take excessive risk to achieve
high excess returns, then returns will be proportionally adjusted. In the flow-
performance regression, performance is approximated by the excess return since
studies suggest investors are marginally sensitive to risk. In the regression
estimating potential returns to scale, monthly returns on MSCI Sweden Small cap
are missing. Hence, yearly values of alpha cannot be produced and used in the
regression. Excess return is used instead.
Funds with less than three years of observations are excluded, either data was
missing or their existence did not exceed three years. The issue of survivorship
bias has partially been addressed by including 49 “dead” funds. These funds
ceased to exist at some point between 2002-2015 and are accounted for. However,
10 “dead” funds are dropped from the dataset since data are missing. Because they
are not missing at random, one cannot reject the existence of survivorship bias. It
is very likely that mutual funds who still existed by the end of 2015 are still alive
because of their past performance. 83 percent of non-surviving funds are still
accounted for in the sample.
6
Financial securities and instruments are formally identified by their Identification Securities Identification
Number (ISIN).
13. 13
Summary statistics (2002-2015)
Number
of funds
observed
Survivorship
bias (“dead”
funds
missing)
Asset under
management
(average
MSEK)
Industry
asset
compound
growth %
Index
CAGR7
%
Fund
average
CAGR
%
Small
cap
25 0 1,841 14.6 16.17 15.13
Non-
small
cap
107 10 1,910 14.6 9.51 7.83
Table 1. Summary statistics of the dataset.
5.0 Econometric methodology
The regression models are constructed to answer the question if there is support
for Berk and Green’s theory in the Swedish equity fund market. Regression 5.1 is
used to estimate the flow-performance relationship, while regression 5.2 answers
the issue regarding returns to scale as funds accumulates more capital. If there are
decreasing returns to scale, one can find a maximum point at which the mutual
fund start performing worse with larger fund size. Two separate quadratic
regressions (Stock and Watson 2015) are being ran to see if there are differences
between Swedish small cap funds and non-small funds. Previous research links
these differences to liquidity or lack thereof, Chen, Hong, Huang and Kubik
(2004) and Yan (2008). The Ordinary Least-Square method and clustered standard
errors are used in all regressions to follow. This allows for correlation between
year-observations within funds, during the sample period, but not across funds.
5.1 Flow performance regression
Since investors form their decision on historic returns of funds (discussed in
section 3.1) and since last year’s return are more weighted, Sirri and Tufano
(1998), we set up the main variable of interest as the excess return (𝑟𝑖,𝑡 − 𝑟𝑚𝑖,𝑡),
and estimate the effect it has on fund flow in year t+1. The simple linear
difference is the excess return for a mutual fund over the SIXPRX in year t. The
dependent variable 𝑓𝑙𝑜𝑤𝑖,𝑡+1 denotes the external asset growth (i.e. growth in
assets under management, AUM, from period t to t+1). Returns from underlying
securities are deducted in year t+1, to only capture net inflows.
7
Compund Annual Growth Rate (CAGR)
14. 14
𝑓𝑙𝑜𝑤𝑖,𝑡+1 =
𝐴𝑈𝑀𝑖,𝑡+1 − 𝐴𝑈𝑀𝑖,𝑡
𝐴𝑈𝑀𝑖,𝑡
− 𝑟𝑖,𝑡+1
Since we are only interested in capturing variation in fund flow by excess return,
we added several control variables to adjust for variation that is not explained by
excess return. The age of the fund affects flow-sensitivity as was seen by
Chevalier and Ellison (1997) and Berk and Green (2004). Three dummy age
categories were created, young represents mutual funds that have been existing for
seven years or less, old stands for funds whose age are 17 or older and the
baseline dummy includes funds with an age of 8-16. Asset-boosts stemming from
mergers are accounted for, otherwise misleading outliers in fund flows create bias.
Time fixed effects are captured in 𝐼𝑛𝑑𝑢𝑠𝑡𝑟𝑦𝑓𝑙𝑜𝑤𝑡 since there is variation over
time but not across funds. This variable measures the flow of all Swedish equity
funds and is important to include because investors willingness to invest in equity
funds also depends on risk appetite and not simply on a given funds past
performance and this variation needs to be explained. For instance, in a time of
financial crisis, investors become more pessimistic and withdraw their money
from mutual funds leading to funds experiencing huge outflows. But this is not
due to their excess return but simply because the market is more risk-averse.
𝑓𝑙𝑜𝑤i,t+1 = β0 + β1(𝑟𝑖,𝑡 − 𝑟𝑚𝑖,𝑡) + β2 𝑦𝑜𝑢𝑛𝑔𝑖,𝑡+1 + β3 𝑜𝑙𝑑𝑖,𝑡+1 + β4 𝑀𝑒𝑟𝑔𝑒𝑖,𝑡+1 + β5 𝐼𝑛𝑑𝑢𝑠𝑡𝑟𝑦𝑓𝑙𝑜𝑤𝑡+1
+𝜀𝑖,𝑡+1
5.2 Regression of returns to scale
With assets under management (AUM) being our main variable of interest, we are
trying to estimate the effect of assets under management in period t, on excess
return in period t+1. This quadratic regression allows us to determine whether
there are decreasing or increasing returns to scale, by formally testing if β2 is
significantly different from zero. If β2 < 0, then we could conclude for decreasing
returns to scale and vice versa if β2 > 0. Control variables are included for the
same reason as in regression 5.1, to control for variation in excess return that is
15. 15
not explained by Assets under management. The time a fund has spent and existed
on the market, is to be accounted for. If we believe that experience is related to
skill and performance, while time and assets are positively correlated, then
introducing 𝑇𝑖𝑚𝑒𝑖,𝑡 is justified. However, time of existence for the fund does not
say anything about the experience of the manager but rather the experience of the
fund itself and fund company.
As Pastor, Stambaugh and Taylor (2014) explained in their research: The growth
in industry asset size has made it harder for fund manager to keep up with the rest
of the pack with the increase of competition. With higher resource being spent to
analyze securities, fund managers are less likely to come across mispriced ones.
Their results showed significantly decreasing returns to scale on an industry-level
for a given mutual fund. Also, discussed in the paper; if funds were to follow the
exact same strategy, then the size of industry assets is a better explaining variable
of a fund’s performance than the assets of the same fund. However, there is no
reason to believe this is true since each fund manager operate on their own and are
all trying to beat the market at once by using different analyzing methods and
information.
ri,t+1 − rmi,t+1 = β0 + β1 𝐴𝑈𝑀𝑖,𝑡 + β2
𝐴𝑈𝑀𝑖,𝑡
2
1000
+ β3 𝑇𝑖𝑚𝑒𝑖,𝑡 + β4 𝑇𝑜𝑡𝐼𝑛𝑑𝑢𝑠𝑡𝑟𝑦𝑎𝑠𝑠𝑒𝑡𝑠𝑡 + εi,t+1
Because we are also investigating possible differences between small cap funds
and non-small cap funds, the same regression specification is being used for both
samples.
6.0 Results
The following three sub-sections will include tables showing estimations produced from
regressions 5.1 and 5.2. The estimations are divided into three columns. Column 1 shows the
results from a simple regression where only the main variable interest is included as an
explanatory variable. Column 2 and 3 display the function of the controls respectively. As
more control variables are included in the regression, the coefficient of the main variable is
16. 16
different because the controls adjust for omitted variable bias. The focus will be on
estimations in column 3 since these regression results include all control variables.
6.1 Flow-performance results
In estimating the flow-performance relationship, we are only interested in the
causal effect that Excess return has on flow. The control variables are in place to
control for variation in flow not explained by Excess return from period t.
Table 2. *=p<0.05, **=p<0.01, ***=p<0.001. Standard error in parentheses.
The results seem to indicate a significant effect on a five percent level. The fund
can expect a net flow of 819,100 SEK for every unit percentage of excess return it
yielded the year prior. The fund’s asset will grow differently from 819,100 since
the dependent variable is specified to discount the return of the underlying
securities.
The intuition of the results is very logical. Investors chase performance and do so
by identifying the mutual fund with best sustainability by looking at historic
returns. If a fund has a track record of beating the market consistently, then an
investor would be justified to invest in it. Conversely, capital outflow is likely to
occur as result of poor past performance as this positive relationship suggests.
𝑭𝒍𝒐𝒘𝒊,𝒕+𝟏
(1) (2) (3)
𝐸𝑥𝑐𝑒𝑠𝑠 𝑟𝑒𝑡𝑢𝑟𝑛𝑖,𝑡 1.035*
(.4074)
.9640*
(.3807)
.8191*
(.4062)
𝑦𝑜𝑢𝑛𝑔𝑖,𝑡+1 _ .2692**
(.0793)
.2653**
(.0766)
𝑜𝑙𝑑𝑖,𝑡+1 _ .0200
(.1516)
.0282
(.1825)
𝑀𝑒𝑟𝑔𝑒𝑖,𝑡+1 _ _ .6293
(.5497)
𝑖𝑛𝑑𝑢𝑠𝑡𝑟𝑦𝑓𝑙𝑜𝑤𝑖,𝑡+1 _ _ 2.755
(1.7461)
𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 .2028***
(.0482)
.1110
(.0575)
-.0014
(.0713)
𝑅2
0.0022 0.0080 0.0379
Observations/
Fund-years
1186 1186 1186
17. 17
If an investor believe that this poor performance will repeat itself in the future and
see its investment shrink, then there would be no reason to keep the money in the
fund. From the fund company and the manager’s standpoint, the positive
relationship provides incentive to beat the market since the fund profits off a
larger fund size.
Figure 2. Flow-performance relationship.
Figure 2 plots 1,186 fund-years and draws the fitted line based on these fund-
years. The positive relationship is stronger as more fund-years are allocated in the
first and third quadrants. Since 10 “dead” funds and roughly 70 fund-years are
missing from the dataset there is reason to believe a stronger positive flow-
performance relationship would be achieved if survivorship bias was at zero8
.
“Dead” funds are likely to have been the outcome of sequentially poor
performances and large outflows, indicating fund-year observations allocated in
the third quadrant. But since data is missing on these funds, the relationship is
relatively weaker than in a scenario when all funds, during the period, are
included in the sample.
8
70 fund-years is an estimation since we have no information about fund-years on 4 out of the 10
“dead” funds.
-1
-0,8
-0,6
-0,4
-0,2
0
0,2
0,4
0,6
0,8
1
-0,3 -0,2 -0,1 0 0,1 0,2 0,3
Flowt+1%
Excess returnt %
Fund-year Fitted line
18. 18
We estimated a linear regression but we do not determine a linear relationship
between flow and performance. Instead, we concluded for overall positive
relationship for the average equity fund. From earlier studies (Chevalier and
Ellison 1997, Sirri and Tufano 1998), we know that net flow differentiate
asymmetrically for good and bad performers respectively.
6.2 Returns to scale results (non-small cap)
The causal effect of returns to scale is represented by exponential term, 𝐴𝑈𝑀𝑖,𝑡
2
in
column 3. A significant negative coefficient would support Berk and Green’s
theory of decreasing returns to scale. In this case, this would apply to equity
mutual funds who invest in all Swedish securities.
Table 3. *=p<0.05, **=p<0.01, ***=p<0.001. Standard error in parentheses.
Despite a negative coefficient, the results does not show decreasing returns to
scale on any relevant significance level (p-value=0.199). Neither does it show
increasing returns to scale. The implication from the results is that performance is
not dependent on fund size for funds in general. There can still be effects going
both ways, meaning that there are advantages and disadvantages of a larger fund
size but we expect a net effect equal to zero. Since the sample consist of 107
mutual funds who hold big and small corporations, measured by their market cap,
we would expect a less effect of decreasing returns to scale compared to funds
who only hold small corporations. Of course, this assumption is based on earlier
𝑬𝒙𝒄𝒆𝒔𝒔 𝒓𝒆𝒕𝒖𝒓𝒏𝒊,𝒕+𝟏 (1) (2) (3)
𝐴𝑈𝑀𝑖,𝑡 -4.03e-08
(8.83e-07)
6.76e-07
(8.68e-07)
6.20e-07
(8.81e-07)
𝐴𝑈𝑀𝑖,𝑡
2
-1.09e-09
(3.29e-08)
-2.54e-08
(3.03e-08)
-4.06e-08
(3.14e-08)
𝑇𝑖𝑚𝑒𝑖,𝑡 _ -.0003
(.0002)
-.0006*
(.0002)
𝑇𝑜𝑡𝐼𝑛𝑑𝑢𝑠𝑡𝑟𝑦𝑎𝑠𝑠𝑒𝑡𝑠𝑡 _ _ 8.64e-08*
(2.44e-08)
𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 -.0154***
(.0023)
-.0128***
(.0031)
-.0303***
(.0061)
𝑅2
0.000 0.0015 0.0220
Observations/
Fund-years
967 967 967
19. 19
studies where decreasing returns to scale is linked to illiquidity. But if larger
corporations are targeted more extensive by these 107 funds, then this effect is not
as observable. Figure 3 support the results from Table 3. No pattern of returns to
scale seem to be in existence and the relatively high p-value suggests a linear
fitted line, or close to linear, which Figure 3 can confirm.
Figure 3. Returns to scale (non-small cap).
In our sample, out of 117 funds, 10 funds are missing. Based upon Elton, Gruber
and Blake (1996), we should not consider survivorship bias as a problem to our
result findings. In a survivorship bias-free sample, small-asset funds who perform
poorly are included which would not indicate decreasing returns to scale. If data
was available on the 10 funds, the likelihood would have that our results would
have gotten even stronger by a higher p-value.
Johan Ståhl, manager of Lannebo Småbolag, provided the answer to why Asset
under management, in an absolute sense, is perhaps not the best explaining
variable9
:
9
Ståhl, Johan; fund manager Lannebo Småbolag. 2016. Telephone interview December 14th
.
-0,6
-0,4
-0,2
0
0,2
0,4
0,6
0,8
0 5000 10000 15000 20000 25000 30000 35000
Excessreturnt+1%
AUMt MSEK
Fund-year Fitted line
20. 20
“Asset under management must be put in relation to the total market
capitalization. If my fund net assets increased from 10 BSEK to 15 BSEK, and
during that same period, the total market capitalization is doubled. Then my fund
has shrunken in size relative to the market. Looking at the absolute number is
meaningless, so you must put it in some relation to the market.
It is a big difference. Between 2009–2012, there were a lot of companies who was
bought out from the market and that is not good when the market shrinks. But in
recent years, we have seen the opposite, a lot of IPOs which makes the pond
bigger and there are more fishes to catch. Usually when the stock market is
valued lower, we see a lot of companies being bought out. It is not the worst
companies that are taken private, instead they buy the best. That is what I would
do. In these scenarios, our investment universe is shrinking. But now, we have
seen an active IPO-market which is good. Even though you are not a participating
in an IPO, there are others who do and to finance its new investments they must
sell off some stocks which creates liquidity. This creates opportunities.”
6.3 Return to scale results (small cap)
Table 4. *=p<0.05, **=p<0.01, ***=p<0.001. Standard error in parentheses.
𝑬𝒙𝒄𝒆𝒔𝒔 𝒓𝒆𝒕𝒖𝒓𝒏𝒊,𝒕+𝟏
(1) (2) (3)
𝐴𝑈𝑀𝑖,𝑡 .0000121
(8.74e-06)
.00001
(.00001)
.00001*
(5.09e-06)
𝐴𝑈𝑀𝑖,𝑡
2
8.73e-08
(6.35e-07)
1.14e-07
(6.99e-07)
-7.21e-07*
(3.41e-07)
𝑇𝑖𝑚𝑒𝑖,𝑡 _ .0001817
(.0025)
-.0011
(.0013)
𝑇𝑜𝑡𝐼𝑛𝑑𝑢𝑠𝑡𝑟𝑦𝑎𝑠𝑠𝑒𝑡𝑠𝑡 _ _ 9.99e-07***
(6.22e-08)
𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 -.0506807**
(.0171722)
-.0518959
(.0272)
-.2937***
(.0210)
𝑅2
0.0299 0.0299 0.3083
Observations/
Fund-years
219 219 219
21. 21
The results (from column 3) indicate decreasing returns to scale on a five percent
significance level. Meaning, as small cap funds grow they tend to perform worse
compared to their benchmark. Why is that the case? As Yan (2008) and Chen,
Hong, Huang and Kubik (2004) explained in their study, holding high assets in
small cap stocks can be costly due to stocks’ illiquidity. The buying pressure will
push up the price making the stocks more expensive until the last stock is bought.
Conversely, selling pressure will cause a drop in the stock price and therefore,
trying to get out of the position can greatly reduce the return of the investment. If
the fund manager deemed the stock as attractive and chose to invest in it, in both
his private and fund portfolio, a greater return can be expected in the private
portfolio. This assumes that the private portfolio is smaller in asset size and the
manager has the same investment period for both portfolios. This can lead to the
fund manager settling for stocks with lower expected return, but because of lower
liquidity risk are more suitable.
Figure 4. Returns to scale (small cap).
If we were to plot the panel data, consisting of 219 total observations, and draw
the fitted line, we can see that a small cap fund should be expected to perform
worse after its assets under management exceed 8,800 MSEK.
-0,6
-0,4
-0,2
0
0,2
0,4
0,6
0,8
0 2000 4000 6000 8000 10000 12000 14000 16000 18000
Excessreturnt+1%
AUMt MSEK
Fund-year Fitted line
22. 22
What is also noticeable by the graph is the large number of observations before
the maximum point, relative to the number of observations after 8,800 MSEK.
This raises a problematic issue in interpreting the results. If the regression
outcome is determined by the observations that are below 8,800 MSEK, we
cannot be confident that Swedish small cap funds exhibit decreasing returns to
scale. How can we test this? We run the exact same regression but we drop all 7
observations taking values of AUM larger than 8,800 MSEK. We then obtain a p-
value equal to 0.047, which would still be significant at a five percent level.
This led us another question: if the regression outcome expects small cap funds to
perform worse after 8,800 MSEK. Have they performed worse since they passed
this level? First, we identified the funds that exceeded 8,800 MSEK at one point
between 2002-2015. Lannebo Småbolagsfond passed this level in 2010, Swedbank
Robur Småbolagsfond Sverige passed it in 2013 and Handelsbanken Svenska
Småbolag asset exceeded 8,800 MSEK in 2014. By simply observing the plot in
Figure 4, we see that five out of the seven fund-years, the funds beat the market
by raw return when assets has surpassed 8,800 MSEK. But did they take their
more risk to achieve this? Two periods are set up. Period 1 represents the
timespan when the funds’ assets were below 8,800 MSEK. Period 2 is the
timespan when funds have exceeded 8,800 MSEK. Notice that the periods are
specific for each fund since they pass the line at different years. Their
performance is measured by alpha and accounts for risk behavior relative to the
market10
. If any of these funds take excessive risk to keep a positive excessive
return, then alpha would show a relative lower value.
Table 5. Alpha in period 1 vs alpha in period 2.
10
The 10-year Swedish government bond is used as the risk-free rate.
Handelsbanken
Svenska
Småbolag
Lannebo
Småbolag
Swedbank Robur
Småbolagsfond
Sverige
𝜶 𝟏 -0,0403 -0,0308 -0,0345
𝜶 𝟐 0,2692 0,1060 0,2356
23. 23
Interpreting Table 5, all three small cap funds have performed better after their
assets exceeded 8,800 MSEK, since the difference in alpha ( 𝛼2 − 𝛼1 ) is positive
for each fund. While the regression results (Table 4) show decreasing returns to
scale when funds’ assets exceed 8,800 MSEK and the only observations we have,
over 8,800 MSEK, show the opposite. Why? As Figure 5 show, there is a huge
unbalance in observations on the two sides of the maximum point. The left side
contains 212 observed fund-years while the right side contains 7 observed fund-
years. Our goal is to draw conclusions about the right side of the maximum point
and if the regression outcome is largely determined by the 212 fund-years, there
need to be substantial evidence from the observations on the right side. Neither
can we say that small cap funds exhibits increasing returns by just looking at
Table 5. First, there are too few observations over 8,800 MSEK. Second, since the
maximum point stems from regression results showing decreasing returns to scale,
it cannot be used as a reference point to draw the opposite conclusion. Either we
can say that Asset under management in no way affects a fund’s performance or
that there are both positive and negative effects but they cancel out each other.
Johan Ståhl, manager of the largest Swedish small cap fund, pointed as to several
reasons to why a large fund size can work to his advantage:
“I always say, there are several advantages being a big player. It is obvious that a
club like Barcelona has a bigger following than Club Brügge when it comes to
people who follow you, people who want to talk to you and it is the same thing
here. We get to be included in more discussions, the stock brokers find it
interesting to call us in an early stage if they have a considerable number of
shares to buy or sell. If we say “yes”, they have completed the deal by calling one
portfolio manager instead of having to call five portfolio managers. We get to be
an attractive owner in many companies, in conjunctions with IPO as the previous
owners know that Lannebo Fonder takes their share ownership seriously.
Over the years, I have learned that there are tendencies of selling way too early
which is common mistake. A good company is not only good one year but longer
than that and one gets long term commitments in its investments. That is our
24. 24
philosophy, the company should do the work for us by developing, increase its
profit, leading to an increase in the share price.
If you look at Lannebo Småbolag, we have had a turnover ratio of 0.2x and 0.3x
the last couple of years so we are looking long term and I believe that it is an
advantage.
Of course, if things do not develop as planned, then it can be hard to get out of a
position. But because the stock market tends to go up and good companies tend to
be good over a longer period, I believe that long term investing is the right way to
do investing.”
The definition of small cap can have different meanings. If the 25 small cap funds
in our sample exclusively invested in companies listed on Nasdaq OMX Small
Cap Sweden (companies with market cap below 150 million euros), then liquidity
risk would certainly be a bigger issue for the funds. While most fund companies
define a small cap company as a market capitalization that is under 1 percent of
the total Swedish market capitalization11
. By the end of 2015, this would include
all companies with a market cap under 58 BSEK, which most Large Cap-listed
companies would fall under. While one definition draws the line at an absolute
number, the other puts it in relation to the market. This is what Johan Ståhl
pointed out, in the interview. All components need to be put in relations to the
market. If funds’ assets were to grow in the same proportion as the total market
cap, then fund assets are relatively the same, which is a more important factor.
This also means that the 1 percent-line would follow the total market cap, so there
should not be a higher liquidity risk in this case.
7 Conclusion
A positive flow-performance relationship is found in the Swedish equity fund
market. Mutual funds who manage large assets today have likely performed well
historically. We cannot however find evidence of mutual funds exhibiting
decreasing returns to scale on a general or small cap level. Does this mean we
11
Lannebo Småbolag, Monthly report December 2015
25. 25
should determine Berk and Green’s theory as non-valid? No, all we can say is that
there is no such pattern, looking at the Swedish equity fund market. If we imagine
an extreme scenario where one active equity fund grew so large that it would eat
up all share capital existing on the market. This fund would converge to an alpha
equal to zero since this fund is also equal to index. Point being, if we want to test
Berk and Green’s theory, active mutual funds need to outgrow the total market
cap to the extent that active mutual funds have a larger share of total share capital
existing on the market.
8 Acknowledgements
Special thanks to our tutor Roine Vestman for his input, constructive feedback
and providing the main dataset. Our greatest appreciation to Johan Ståhl, at
Lannebo Fonder, for taking time for an interview where we gained deep insight to
fund managing. Third, we like to thank the following people and organizations for
helping us collecting data: Lars-Erik Lundgren (Aktie-ansvar), Fredrik Hård
(Fondbolagens förening), Emma Saxeby (Finansinspektionen) , Ghina Zeidan
(SEB), Christer Speiner (Cicero), Mikaela Fahlberg (Agenta), Lillan Röjlar
(Ålandsbanken), Jessica Almgren (Nordic Equties), Emelie Magnusson
(Folksam), Shyam Sollerhag (Handelsbanken) and Ann Marie Karlsson (Cliens).
26. 26
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32. 32
11 Appendix
Figure 1
Table 1
Summary statistics (2002-2015)
Number
of funds
observed
Survivorship
bias (“dead”
funds
missing)
Asset under
management
(average
MSEK)
Industry
assets
compound
growth %
Index
CAGR
%
Fund
average
CAGR
%
Small
cap
25 0 1,841 14.6 16.17 15.13
Non-
small-
cap
107 10 1,910 14.6 9.51 7.83
