Market Frictions and Persistence in Mutual Fund Performance

Market Frictions, Investor Sophistication and
Persistence in Mutual Fund Performance
Ariadna Dumitrescu1 Javier Gil-Bazo2
1Department of Finance
ESADE Business School
2Department of Economics and Business
University Pompeu Fabra and Barcelona GSE
UC3M, March 31, 2014

Motivation
“Our system of investor protection is predicated on the notion that
investors who are armed with complete and accurate information will
be able to look out for their own interests. This concept may be overly
optimistic in its assumptions about the ﬁnancial sophistication of
average retail investors.” (Barbara Roper, Consumer Federation of
America)
Dumitrescu & Gil-Bazo Persistence in Mutual Fund Performance 2 / 34

Motivation
Investor protection focused on information disclosure
Too optimistic about retail investors’ ﬁnancial sophistication:
Biases (e.g., Barber and Odean, 2000; Bailey, Kumar, and Ng,
2011)
Financial illiteracy (e.g., Lusardi and Tufano, 2009; van Rooij et al.
2011)
Frictions: search costs, switching costs, information processing
costs (Hortaçsu and Syverson, 2004; Brunnermeier and Oehmke,
2009)
Some investors more sophisticated than others
This paper: Consequences of frictions for equilibrium in the
mutual fund market.

Berk and Green (2004)
Berk and Green (BG) (2004): If investors compete for the best mutual funds
in a friction-less market with increasing marginal trading costs, all funds
should deliver zero net expected risk-adjusted return in equilibrium

Empirical evidence favorable to diseconomies of scale hypothesis (Chen et
al., 2004; Yan et al., 2008; Turtle and Wang, 2013)

Empirical evidence favorable to diseconomies of scale hypothesis (Chen et
al., 2004; Yan et al., 2008; Turtle and Wang, 2013)
...but not to BG’s model implications:
Average fund earns negative net alpha (e.g., Jensen, 1968; Gruber,
1996; Wermers, 2000)
Underperformers persist (Carhart, 1997) and some evidence of
short-term persistence in outperformance (Bollen and Busse, 2004)
Performance predictable from fees and trading costs (e.g., Gil-Bazo and
Ruiz-Verdu, 2009; Edelen, Evans & Kadlec, 2007)

Possible explanations:
No diseconomies of scale: Reuter and Zitzewitz (2013)

Investor irrationality: What type of irrationality? How does it impact
fund performance?

Investor irrationality: What type of irrationality? How does it impact
fund performance?
Frictions

What we do
We develop a BG-type model (an active manager competes against a
passive investment) with investors characterized by frictions: search costs
and ﬁnancial constraints

What we do
We develop a BG-type model (an active manager competes against a
passive investment) with investors characterized by frictions: search costs
and ﬁnancial constraints
Findings:
Negative expected (net) performance in equilibrium
Expected performance increasing in expected managerial skill ⇒ Persistence
New prediction: Persistence more prevalent among more visible funds (higher
fraction of unsophisticated investors)
We then test the model’s new prediction with the data

Related literature
Studies on conditional persistence:
Berk and Tonks (2007): Past fund performance affects investor composition:
performance more persistent after poor returns
Glode et al. (2009): Past market performance affects investor composition:
performance more persistent after high market returns
Elton, Gruber and Blake (2011): Persistence does not depend on fund size
Ferreira et al. (2010): Increasing returns to scale and competition among
funds (both at the country level) are associated with less persistence.

The model
Model retains BG’s main features: rationality and diseconomies of scale
Frictions:
Search costs: Each investor i has a specific search cost γi that reflects
her ability to find an alternative investment: an index fund with zero
performance
i-th investor’s reservation return = −γi
Financial constraints: Investor i endowed with m dollars and subject to
a liquidity shock with probability γi , expected investment = m (1 − γi ) .
We also consider an entry cost, K, borne by new investors

Timeline
Investors
enter the fund
t − 1
Fund’s return at date t is realized
Current Investors decide whether to re-invest or not
New Investors decide whether to invest and pay entry cost K
t
Fund return at date
t + 1 is realized
t + 1

The model
0 γSup

The model
0 γMAX γSup

The model
0 γ γMAX γSup

The model: Equilibrium
Equilibrium: an amount of assets q∗
t+1 and the associated expected
risk-adjusted net return, TPt+1 q∗
t+1 = φt+1 −
C q∗
t+1
q∗
t+1
− f, such that:
All current investors that (re)invest in the fund have reservation
returns lower than TPt+1 q∗
t+1
All new investors that invest in the fund have reservation returns
lower than TPt+1 q∗
t+1 − K
Holding f constant, depending on φt+1: (i) nobody invests; (ii) some
current investors reinvest; (iii) all current but no new investors invest;
(iv) new investors invest; (v) all target investors invest

0 γ γ∗ γMAX γSup
γ∗ = γC obtained from TPt+1 qC
t+1 = −γC

0 γ∗ γ γMAX γSup
γ∗ = γN obtained from TPt+1 qN
t+1 − K = −γN

Proposition 1: Expected net performance

Proposition 2: Comparative statics, K = 0

Proposition 2: Comparative statics, K > 0

Endogenous Fee
When the manager chooses f to maximize fq∗
t+1(f):
f increases with φ,

Endogenous Fee
t+1(f):
however, f increases less that one-to-one with φ, so TP still
increasing in phi,

Endogenous Fee
t+1(f):
however, f increases less that one-to-one with φ, so TP still
increasing in phi,
except when there is no entry of investors

Testing the Model
Difﬁcult to base our test on investor sophistication

Testing the Model
Instead, test the prediction that performance of high-visibility funds
more sensitive to managerial skill

Testing the Model
Since managerial skill persistent (by deﬁnition?), performance of
high-visibility funds

Testing the Model
high-visibility funds should persist longer
Unexpected result!

Testing the Model
high-visibility funds should persist longer
Unexpected result!
Test: regress future performance on past performance, compare
coefﬁcient between high- and low-visibility funds

Empirical Strategy
We construct a panel of monthly risk-adjusted portfolio alphas using Carhart’s
(1997) model:
rit = αi + βrm,i rmt + βsmb,i smbt + βhml,i hmlt + βpr1y,i pr1yt + εit
Compute past and future 12-month alphas and estimate by pooled OLS:
ˆαi,t:t+11 = θ0,t + θ1 ˆαi,t−12:t−1 + θ2 ˆαi,t−12:t−1LOi,t−1 + θ3 ˆαi,t−12:t−1HIi,t−1 +
+θ4LOi,t−1 + θ5HIi,t−1 + ΘXi,t−1 + εi,t:t+11,
LO, HI, dummy variables for low- and high-visibility funds, respectively
We are interested in θ2 and θ3

Empirical strategy
Proxies for fund visibility:
1 Number of different investment categories in which the family
offers mutual funds;
2 Family size, as proxied by the natural logarithm of total family
assets;
3 Family age, computed as the age of the oldest fund in the family;
4 Average advertising expenditure over the previous 12 months
For each one of these proxies: deﬁne LO (bottom 25%) and HI (top
25%) dummies

Data
CRSP MFDB, July ’11 version, 1993-2010
Advertising data from Kantar Media, 1995-2009
We aggregate class-level monthly observations at the portfolio level
Data: TNA; return; investment category; exp. ratio; 12b-1 fee; front-end
load; back-end load
We exclude index, non-domestic, non-diversiﬁed, non-equity funds
Portfolios and fund families identiﬁed by CRSP or name
We exclude funds with TNA<$15M and age<3yr
Average: 1,251 funds and 327 families (m.co.)
Fee and return data winsorized at 1% of each tail each month

Summary Statistics
1993-2000
variable Obs. mean sd p25 p50 p75
Total net assets 84287 1333.59 4040.44 93.31 278.9 921.88
Annual ﬂow (in %) 63369 12.24 63.35 -11.43 -0.02 18.18
Age 84144 15.13 14.82 5.42 9.08 17.5
Family total net assets 26998 10981.68 40743.85 228.6 1428.47 5611.1
Family age 26987 25.86 20.68 9.67 16.25 40.5
Front-end load (in %) 37433 3.36 1.96 1.73 3.76 4.75
Back-end load (in %) 28188 1.43 1.37 0.32 1 2.17
Management fee (in %) 37991 0.74 0.24 0.6 0.75 0.9
Expense ratio (in %) 71040 1.21 0.39 0.94 1.16 1.44
12b-1 fee (in %) 22914 0.33 0.25 0.12 0.25 0.5
Turnover ratio (in %) 70452 82.28 64.63 36.2 67 109
Return (in %) 83929 15.17 66.71 -22.03 17.44 51.83
Carhart’s 4-factor alpha (in %) 51181 -0.41 26.99 -13.38 -0.73 11.96

Summary Statistics
2001-2010
variable Obs. mean sd p25 p50 p75
Total net assets 186114 1256.74 4946.26 80 242.7 838.8
Annual ﬂow (in %) 145663 6.31 58.90 -15.26 -4.73 11.26
Age 185881 14.10 12.87 6.5 10.17 16.08
Family total net assets 43703 20925.18 91580.15 201.1 1265.4 7738.7
Family age 43703 28.74 21.84 12.58 20.67 38.58
Front-end load (in %) 97186 2.62 1.73 1.09 2.65 4.00
Back-end load (in %) 75535 0.76 0.89 0.10 0.43 1.09
Management fee (in %) 171168 0.72 0.25 0.59 0.75 0.89
Expense ratio (in %) 170249 1.23 0.38 0.99 1.21 1.47
12b-1 fee (in %) 127940 0.29 0.23 0.09 0.25 0.44
Turnover ratio (in %) 173993 82.15 64.48 35 66 110
Return (in %) 185859 4.56 65.30 -29.18 11.98 45.30
Carhart’s 4-factor alpha (in %) 130793 -2.17 21.14 -12.01 -1.99 7.86

Performance persistence and fund visibility
#Inv Cat Family Size Family Age Family Adv.
α 0.071*** 0.085*** 0.088*** 0.090*** 0.113***
size -0.003*** -0.003*** -0.003*** -0.002*** -0.002***
ﬂow -0.005** -0.005** -0.005** -0.004** -0.004**
age 0.000 0.000 0.000 0.000 0.001
fam_size 0.001** 0.001** 0.003*** 0.001** 0.001
fam_age -0.000 -0.000 -0.000 -0.001 -0.001
F-load 0.021 0.026 0.021 0.024 0.032
B-load -0.329*** -0.317*** -0.335*** -0.328*** -0.315***
exp -0.619** -0.615** -0.554** -0.637** -0.551*
turnover -0.003* -0.003* -0.003* -0.003* -0.003
α x LO -0.076** -0.059* -0.078*** -0.052**
α x HI -0.015 -0.018 -0.021 -0.048
LO 0.003 0.006** -0.003 -0.005***
HI 0.001 -0.004* -0.001 -0.001
Time Fixed Effects Yes Yes Yes Yes Yes
Observations 108,524 108,524 108,524 108,524 101,098
Adjusted R-squared 0.074 0.075 0.075 0.074 0.076

Endogeneity issues
Fund visibility not exogenous

Endogeneity issues
So what?
Reverse causality: persistence ⇒ visibility?
Third variable causes both persistence and visibility

Endogeneity issues
So what?
Reverse causality: persistence ⇒ visibility?
Third variable causes both persistence and visibility
More on this later...

Role of fund size and investment categories
α 0.171*** 0.186*** 0.181*** 0.185*** 0.221***
size -0.003*** -0.003*** -0.003*** -0.003*** -0.002***
ﬂow -0.005** -0.005** -0.005** -0.005** -0.004**
age 0.001 0.001 0.001 0.001 0.001
fam_size 0.001*** 0.002*** 0.003*** 0.001*** 0.001*
fam_age -0.000 -0.000 -0.000 -0.000 -0.001
F-load 0.025 0.029 0.026 0.027 0.036
B-load -0.339*** -0.328*** -0.349*** -0.340*** -0.324***
exp -0.622** -0.618** -0.552** -0.626** -0.567**
turnover -0.002 -0.002 -0.002 -0.002 -0.001
α x LO -0.096*** -0.089*** -0.088*** -0.058**
α x HI 0.005 0.019 -0.004 -0.028
LO 0.002 0.005* -0.003 -0.006***
HI 0.000 -0.003 -0.001 -0.001
α x size -0.003 -0.008 -0.016* -0.007 -0.005
Inv. Cat. Fixed Effects Yes Yes Yes Yes Yes
Inv. Cat. Interactions Yes Yes Yes Yes Yes
Observations 108,524 108,524 108,524 108,524 101,098

Performance persistence among winners and losers
To distinguish between persistence in poor and good performance, we
estimate:
ˆαi,t:t+11 = δ0,t +
n
δ1,ndec_ni,t−1
+
n
δ2,ndec_ni,t−1LOi,t−1 +
n
δ3,ndec_ni,t−1HIi,t−1
+δ4LOi,t−1 + δ5HIi,t−1 + ∆Xi,t−1 + ξi,t:t+11,
where dec_ni,t−1 = 1 if fund i’s past performance in n − th decile
(1st=bottom, 10th=top)
We consider n = 1, 2, 3, 8, 9, 10

Performance persistence among winners and losers
dec_1(α)(bottom) -0.008*** -0.012*** -0.010*** -0.009*** -0.009*
dec_2(α) -0.004*** -0.005*** -0.003* -0.005** -0.006*
dec_3(α) -0.003*** -0.003*** -0.003** -0.003*** -0.001
dec_8(α) 0.003*** 0.003** 0.003** 0.003** 0.001
dec_9(α) 0.006*** 0.006*** 0.008*** 0.007*** 0.008***
dec_10(α)(top) 0.010*** 0.014*** 0.015*** 0.014*** 0.020***
dec_1(α) x LO 0.012** 0.010** 0.009* 0.000
dec_2(α) x LO 0.003 -0.000 0.002 0.003
dec_3(α) x LO 0.006*** 0.003 0.007** -0.001
dec_1(α) x HI 0.006 -0.003 -0.001 0.017**
dec_2(α) x HI 0.002 -0.003 0.001 -0.002
dec_3(α) x HI -0.001 -0.001 -0.001 -0.003
dec_8(α) x LO -0.004* -0.004* -0.004 0.001
dec_9(α) x LO -0.001 -0.004 -0.004 -0.003
dec_10(α) x LO -0.016*** -0.014*** -0.011** -0.013**
dec_8(α) x HI 0.003 0.001 0.002 0.011**
dec_9(α) x HI 0.003 -0.004 -0.000 0.004
dec_10(α) x HI -0.005 -0.008 -0.007 -0.001
LO 0.004* 0.008*** -0.002 -0.003*
HI -0.000 -0.002 -0.001 -0.002
Controls Yes Yes Yes Yes Yes
Observations 108,524 108,524 108,524 108,524 101,098

Ranking on returns
dec_1(ret)(bottom) -0.009*** -0.013*** -0.012*** -0.012*** -0.009
dec_2(ret) -0.004*** -0.006*** -0.007*** -0.004** -0.004
dec_3(ret) -0.003** -0.004** -0.003** -0.003* 0.000
dec_8(ret) 0.000 -0.000 -0.001 0.001 0.002
dec_9(ret) 0.002 0.001 0.002 0.003 0.007*
dec_10(ret)(top) 0.003 0.003 0.003 0.005 0.006
dec_1(ret) x LO 0.012*** 0.010** 0.012*** -0.001
dec_2(ret) x LO 0.009*** 0.008** 0.005* -0.000
dec_3(ret) x LO 0.005 0.003 0.005* -0.003
dec_1(ret) x HI 0.011** 0.001 0.003 -0.002
dec_2(ret) x HI 0.003 0.003 -0.004 -0.001
dec_3(ret) x HI 0.002 0.001 -0.003 -0.001
dec_8(ret) x LO 0.000 0.002 -0.001 -0.002
dec_9(ret) x LO 0.000 0.002 -0.003 -0.006
dec_10(ret) x LO -0.002 0.001 -0.002 -0.004
dec_8(ret) x HI 0.002 0.002 -0.003 -0.003
dec_9(ret) x HI 0.002 -0.004 -0.003 -0.004
dec_10(ret) x HI 0.002 -0.003 -0.004 -0.000
LO 0.001 0.004 -0.003 -0.003
HI -0.001 -0.004* 0.000 0.001
Observations 108,524 108,524 108,524 108,524 101,098

Retail funds only
dec_1(α)(bottom) -0.011*** -0.012*** -0.017*** -0.012** -0.009
dec_2(α) -0.006*** -0.007*** -0.006** -0.008*** -0.008
dec_3(α) -0.003** -0.004** -0.003* -0.005** -0.000
dec_8(α) 0.003** 0.005** 0.004 0.004** -0.002
dec_9(α) 0.006*** 0.005* 0.007** 0.007*** 0.004
dec_10(α)(top) 0.010*** 0.012** 0.015*** 0.012*** 0.018**
dec_1(α) x LO 0.013** 0.017*** 0.015* -0.001
dec_2(α) x LO 0.004 0.001 0.008* 0.004
dec_3(α) x LO 0.006** 0.002 0.008* -0.002
dec_1(α) x HI -0.015* 0.002 -0.007 -0.003
dec_2(α) x HI -0.004 -0.004 0.002 -0.014
dec_3(α) x HI -0.002 -0.001 0.001 -0.005
dec_8(α) x LO -0.005* -0.005 -0.003 0.005
dec_9(α) x LO 0.001 -0.002 -0.003 0.001
dec_10(α) x LO -0.013** -0.014** -0.008 -0.010
dec_8(α) x HI -0.000 0.002 -0.001 0.018***
dec_9(α) x HI 0.002 -0.003 -0.001 0.008
dec_10(α) x HI 0.007 -0.003 -0.004 0.014
LO 0.006** 0.005 -0.001 -0.000
HI 0.001 -0.001 0.006** -0.002
Observations 55,214 55,214 55,214 55,214 48,643

Conclusions
Interaction of market frictions can generate both negative and positive
expected performance in equilibrium as well as cross-sectional
differences in performance

Conclusions
Less visible funds exhibit a substantially lower degree of persistence in
performance

Conclusions
performance
However, more visible funds’ performance does not persist more

Conclusions
performance
Institutional investors not necessarily more sophisticated (James and
Karceski, 2006; Phillips et al., 2012))

Conclusions
performance
Institutional investors not necessarily more sophisticated (James and
Karceski, 2006; Phillips et al., 2012))
More information disclosure should be accompanied by policies: (i)
aimed at reducing participation costs and (2) especially targeted to the
least sophisticated investors

To-do list
Competition among two active funds: Cournot-type duopoly
Exogenous source of variation in visibility:
“Star” in the family
Non-performance related news about family/fund
Merger into a larger fund/family
Any ideas?

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