market frictions, investor sophistication and persistence in mutual fund performance

Market Frictions, Investor Sophistication andPersistence in Mutual Fund Performance

Ariadna Dumitrescu1 Javier Gil-Bazo2

1Department of FinanceESADE Business School

2Department of Economics and BusinessUniversity Pompeu Fabra and Barcelona GSE

UC3M, March 31, 2014

Motivation

“Our system of investor protection is predicated on the notion thatinvestors who are armed with complete and accurate information willbe able to look out for their own interests. This concept may be overlyoptimistic in its assumptions about the financial sophistication ofaverage retail investors.” (Barbara Roper, Consumer Federation ofAmerica)

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 processingcosts (Hortaçsu and Syverson, 2004; Brunnermeier and Oehmke,2009)Some investors more sophisticated than others

This paper: Consequences of frictions for equilibrium in themutual fund market.


Berk and Green (2004)

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

Empirical evidence favorable to diseconomies of scale hypothesis (Chen etal., 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 ofshort-term persistence in outperformance (Bollen and Busse, 2004)

Performance predictable from fees and trading costs (e.g., Gil-Bazo andRuiz-Verdu, 2009; Edelen, Evans & Kadlec, 2007)


Berk and Green (2004)

Possible explanations:

No diseconomies of scale: Reuter and Zitzewitz (2013)

Investor irrationality: What type of irrationality? How does it impactfund performance?

Frictions


What we do

We develop a BG-type model (an active manager competes against apassive investment) with investors characterized by frictions: search costsand 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 (higherfraction 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 amongfunds (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 reflectsher ability to find an alternative investment: an index fund with zeroperformance

i-th investor’s reservation return = −γi

Financial constraints: Investor i endowed with m dollars and subject toa 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 reservationreturns lower than TPt+1

(q∗

t+1)

All new investors that invest in the fund have reservation returnslower than TPt+1

(q∗

t+1)− K

Holding f constant, depending on φt+1: (i) nobody invests; (ii) somecurrent 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,

however, f increases less that one-to-one with φ, so TP stillincreasing in phi ,

except when there is no entry of investors


Testing the Model

Difficult to base our test on investor sophistication

Instead, test the prediction that performance of high-visibility fundsmore sensitive to managerial skill

Since managerial skill persistent (by definition?), performance ofhigh-visibility funds should persist longer

Unexpected result!

Test: regress future performance on past performance, comparecoefficient between high- and low-visibility funds


Testing the Model



Since managerial skill persistent (by definition?), performance ofhigh-visibility funds

should persist longer

Unexpected result!



Testing the Model



Since managerial skill persistent (by definition?), performance ofhigh-visibility funds should persist longer

Unexpected result!



Empirical Strategy

We construct a panel of monthly risk-adjusted portfolio alphas using Carhart’s(1997) model:

rit = αi + βrm,i rmt + βsmb,ismbt + βhml,ihmlt + βpr1y,ipr1yt + εit

Compute past and future 12-month alphas and estimate by pooled OLS:

α̂i,t :t+11 = θ0,t + θ1α̂i,t−12:t−1 + θ2α̂i,t−12:t−1LOi,t−1 + θ3α̂i,t−12:t−1HIi,t−1 +

+θ4LOi,t−1 + θ5HIi,t−1 + ΘX ′i,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 (top25%) 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-endload; 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 p75Total net assets 84287 1333.59 4040.44 93.31 278.9 921.88Annual flow (in %) 63369 12.24 63.35 -11.43 -0.02 18.18Age 84144 15.13 14.82 5.42 9.08 17.5Family total net assets 26998 10981.68 40743.85 228.6 1428.47 5611.1Family age 26987 25.86 20.68 9.67 16.25 40.5Front-end load (in %) 37433 3.36 1.96 1.73 3.76 4.75Back-end load (in %) 28188 1.43 1.37 0.32 1 2.17Management fee (in %) 37991 0.74 0.24 0.6 0.75 0.9Expense ratio (in %) 71040 1.21 0.39 0.94 1.16 1.4412b-1 fee (in %) 22914 0.33 0.25 0.12 0.25 0.5Turnover ratio (in %) 70452 82.28 64.63 36.2 67 109Return (in %) 83929 15.17 66.71 -22.03 17.44 51.83Carhart’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 p75Total net assets 186114 1256.74 4946.26 80 242.7 838.8Annual flow (in %) 145663 6.31 58.90 -15.26 -4.73 11.26Age 185881 14.10 12.87 6.5 10.17 16.08Family total net assets 43703 20925.18 91580.15 201.1 1265.4 7738.7Family age 43703 28.74 21.84 12.58 20.67 38.58Front-end load (in %) 97186 2.62 1.73 1.09 2.65 4.00Back-end load (in %) 75535 0.76 0.89 0.10 0.43 1.09Management fee (in %) 171168 0.72 0.25 0.59 0.75 0.89Expense ratio (in %) 170249 1.23 0.38 0.99 1.21 1.4712b-1 fee (in %) 127940 0.29 0.23 0.09 0.25 0.44Turnover ratio (in %) 173993 82.15 64.48 35 66 110Return (in %) 185859 4.56 65.30 -29.18 11.98 45.30Carhart’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 0.001fam_size 0.001** 0.001** 0.003*** 0.001** 0.001fam_age -0.000 -0.000 -0.000 -0.001 -0.001F-load 0.021 0.026 0.021 0.024 0.032B-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* -0.003α x LO -0.076** -0.059* -0.078*** -0.052**α x HI -0.015 -0.018 -0.021 -0.048LO 0.003 0.006** -0.003 -0.005***HI 0.001 -0.004* -0.001 -0.001Time Fixed Effects Yes Yes Yes Yes YesObservations 108,524 108,524 108,524 108,524 101,098Adjusted R-squared 0.074 0.075 0.075 0.074 0.076


Endogeneity issues

Fund visibility not exogenous

So what?Reverse causality: persistence⇒ visibility?

Third variable causes both persistence and visibility

More on this later...


Role of fund size and investment categories

#Inv Cat Family Size Family Age Family Adv.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 0.001fam_size 0.001*** 0.002*** 0.003*** 0.001*** 0.001*fam_age -0.000 -0.000 -0.000 -0.000 -0.001F-load 0.025 0.029 0.026 0.027 0.036B-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 -0.001α x LO -0.096*** -0.089*** -0.088*** -0.058**α x HI 0.005 0.019 -0.004 -0.028LO 0.002 0.005* -0.003 -0.006***HI 0.000 -0.003 -0.001 -0.001α x size -0.003 -0.008 -0.016* -0.007 -0.005Time Fixed Effects Yes Yes Yes Yes YesInv. Cat. Fixed Effects Yes Yes Yes Yes YesInv. Cat. Interactions Yes Yes Yes Yes YesObservations 108,524 108,524 108,524 108,524 101,098Adjusted R-squared 0.090 0.091 0.091 0.091 0.094


Performance persistence among winners and losers

To distinguish between persistence in poor and good performance, weestimate:

α̂i,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 + ∆X ′i,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

#Inv Cat Family Size Family Age Family Adv.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*** -0.001dec_8(α) 0.003*** 0.003** 0.003** 0.003** 0.001dec_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* 0.000dec_2(α) x LO 0.003 -0.000 0.002 0.003dec_3(α) x LO 0.006*** 0.003 0.007** -0.001dec_1(α) x HI 0.006 -0.003 -0.001 0.017**dec_2(α) x HI 0.002 -0.003 0.001 -0.002dec_3(α) x HI -0.001 -0.001 -0.001 -0.003dec_8(α) x LO -0.004* -0.004* -0.004 0.001dec_9(α) x LO -0.001 -0.004 -0.004 -0.003dec_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 0.004dec_10(α) x HI -0.005 -0.008 -0.007 -0.001LO 0.004* 0.008*** -0.002 -0.003*HI -0.000 -0.002 -0.001 -0.002Time Fixed Effects Yes Yes Yes Yes YesControls Yes Yes Yes Yes YesObservations 108,524 108,524 108,524 108,524 101,098Adjusted R-squared 0.076 0.077 0.078 0.077 0.079


Ranking on returns

#Inv Cat Family Size Family Age Family Adv.dec_1(ret)(bottom) -0.009*** -0.013*** -0.012*** -0.012*** -0.009dec_2(ret) -0.004*** -0.006*** -0.007*** -0.004** -0.004dec_3(ret) -0.003** -0.004** -0.003** -0.003* 0.000dec_8(ret) 0.000 -0.000 -0.001 0.001 0.002dec_9(ret) 0.002 0.001 0.002 0.003 0.007*dec_10(ret)(top) 0.003 0.003 0.003 0.005 0.006dec_1(ret) x LO 0.012*** 0.010** 0.012*** -0.001dec_2(ret) x LO 0.009*** 0.008** 0.005* -0.000dec_3(ret) x LO 0.005 0.003 0.005* -0.003dec_1(ret) x HI 0.011** 0.001 0.003 -0.002dec_2(ret) x HI 0.003 0.003 -0.004 -0.001dec_3(ret) x HI 0.002 0.001 -0.003 -0.001dec_8(ret) x LO 0.000 0.002 -0.001 -0.002dec_9(ret) x LO 0.000 0.002 -0.003 -0.006dec_10(ret) x LO -0.002 0.001 -0.002 -0.004dec_8(ret) x HI 0.002 0.002 -0.003 -0.003dec_9(ret) x HI 0.002 -0.004 -0.003 -0.004dec_10(ret) x HI 0.002 -0.003 -0.004 -0.000LO 0.001 0.004 -0.003 -0.003HI -0.001 -0.004* 0.000 0.001Time Fixed Effects Yes Yes Yes Yes YesControls Yes Yes Yes Yes YesObservations 108,524 108,524 108,524 108,524 101,098Adjusted R-squared 0.073 0.074 0.074 0.074 0.075


Retail funds only

#Inv Cat Family Size Family Age Family Adv.dec_1(α)(bottom) -0.011*** -0.012*** -0.017*** -0.012** -0.009dec_2(α) -0.006*** -0.007*** -0.006** -0.008*** -0.008dec_3(α) -0.003** -0.004** -0.003* -0.005** -0.000dec_8(α) 0.003** 0.005** 0.004 0.004** -0.002dec_9(α) 0.006*** 0.005* 0.007** 0.007*** 0.004dec_10(α)(top) 0.010*** 0.012** 0.015*** 0.012*** 0.018**dec_1(α) x LO 0.013** 0.017*** 0.015* -0.001dec_2(α) x LO 0.004 0.001 0.008* 0.004dec_3(α) x LO 0.006** 0.002 0.008* -0.002dec_1(α) x HI -0.015* 0.002 -0.007 -0.003dec_2(α) x HI -0.004 -0.004 0.002 -0.014dec_3(α) x HI -0.002 -0.001 0.001 -0.005dec_8(α) x LO -0.005* -0.005 -0.003 0.005dec_9(α) x LO 0.001 -0.002 -0.003 0.001dec_10(α) x LO -0.013** -0.014** -0.008 -0.010dec_8(α) x HI -0.000 0.002 -0.001 0.018***dec_9(α) x HI 0.002 -0.003 -0.001 0.008dec_10(α) x HI 0.007 -0.003 -0.004 0.014LO 0.006** 0.005 -0.001 -0.000HI 0.001 -0.001 0.006** -0.002Time Fixed Effects Yes Yes Yes Yes YesControls Yes Yes Yes Yes YesObservations 55,214 55,214 55,214 55,214 48,643Adjusted R-squared 0.068 0.071 0.070 0.070 0.069


Conclusions

Interaction of market frictions can generate both negative and positiveexpected performance in equilibrium as well as cross-sectionaldifferences in performance

Less visible funds exhibit a substantially lower degree of persistence inperformance

However, more visible funds’ performance does not persist more

Institutional investors not necessarily more sophisticated (James andKarceski, 2006; Phillips et al., 2012))

More information disclosure should be accompanied by policies: (i)aimed at reducing participation costs and (2) especially targeted to theleast sophisticated investors


To-do list

Competition among two active funds: Cournot-type duopoly

Exogenous source of variation in visibility:

“Star” in the familyNon-performance related news about family/fundMerger into a larger fund/family

Any ideas?


market frictions, investor sophistication and persistence in mutual fund performance

Economy & Finance