Apoorva Javadekar -Role of Reputation For Mutual Fund Flows

Role of Reputation For Mutual Fund Flows
Apoorva Javadekar1
September2, 2015
1
Boston University,Departmentof Economics

Broad Question
1. Question:
What causesinvestors to invest or withdraw moneyfrom
mutual funds?
) In particular: what is the link between fund performanceand
fund flows?
2. Litarature:
Narrow focus on ”Winner Chasing” phenomenon
) link between recent-most performanceand fund flows ignoring
role for reputation of fund
3. This paper: Role of Fund Reputation
) Investor’s choices
) Risk Choices by fund managers

Why Study Fund Flows?
1. Important Vehicle of Investment
) Large: Manage 15Tr $ (ICI, 2014)
) Dominant way to equities: (ICI -2014, French (2008))
) HH through MF: owns 30% US equities
) Direct holdings of HH: 20% of US equities
) Participation: 46% of US HH invest
2. Understand Behavioral Patterns:
) Investors learn about managerialability through returns
) =⇒ fund flows shedlight on learning, information processing
capacities etc.
3. Fund Flows Affect Managerial Risk Taking
) Compensation≈ flows: 90% MF managerspaid asa% of
AUM
)
)
=⇒ flow patterns canaffect risk taking
=⇒ impacts on asset prices

Literature Snapshot
1. Seminal Paper: Chevallier & Ellison (JPE, 1997)
Flows(t+1)
Returns(t)
=⇒ Convex Fund Flows in Recent Performance!
2. Why Interesting? Non-Linear Flows (could) mean
) Bad and extremely bad returns carry same information !
) Non-Bayesian Learning
) Behavioral Biases
) Excess risk taking by managers given limited downside

Motivating Role of Reputation
1. No Role For Reputation: Literature links time t returns (rit )
to time t + 1 fund flows (FFi,t+1)
2. Why a Problem? The wayinvestor perceives current
performance depends upon historic performance
Why? History of Returns ≈ reputation
Manager 1: {rt−3,rt−2,rt−1,rt} = {G,G, G, B}
Manager 2: {rt−3,rt−2,rt−1,rt} = {B, B, B, B}
3. What it means for estimation?
FFi,t+1 = g(rit, ri,t−1, ...) + errori,t+1
where g(.) is non-separablein returns
4. Useful For Studying Investors Learning
FFi,t+1 = g (
=
s
de
¸
c
¸
isio
x
n =
s
s
¸
ig
¸
n
x
al
s x
=p
¸
r
¸
iors
rit , ri,t−1, ri,t−2, ...)

Data
1. Source: CRSPSurvivor-Bias freemutual fund dataset
2. Time Period: 1980-2012.
3. Include:
) Domestic, Open ended,equity funds
) Growth, Income,Growth&Income, Small and Mid-Cap, Capital
Appreciation funds (Pastor, Stambaugh (2002))
4. Exclude
) Sectoral, global and index or annuity funds
) Funds with sales restrictions
) young funds with less than 5 years
) small funds (Assets < 10Mn $)
5. Annual Frequency: Disclosuresof yearly returns, ratings are
based on annual performance

Performance Measures
1. Reputation: Aggregate performance of 3or 5 yearsprior to
current period
2. How to Measure Performance?
) Factor Adjusted: CAPM α or 3-factor α (Fama,French
(2010), Kosowski (2006))
) Peer Ranking (Within each investment style):
(Chevallier,Ellison (1997), Spiegel (2012))
3. Which Measure?
) Not easyfor naive investor to exploit factors like value,
premium or momentum =⇒ factor-mimicking is valued
(Berk, Binsbergen (2013))
) Flows more sensitive to raw returns (Clifford (2011))
) Peerranking within eachstyle control for bulk of risk
differentials across funds
) CAPM α wins the horse race amongst factor models (Barber
et.al 2014)
4.I useboth the measures:CAPM α and PeerRanking but not 3-
factor model.

Main Variables
1. Fund Flows:Main dependent variable is %growth in Assets
dueto fund flows
FFi,t+1 =
Ai,t+1 − (Ait × (1 + ri,t+1))
Ait
Ait : Assetswith fund iat time t rit :
Fund returns for period ended t

Empirical Methodology
FFi,t +1
1. Interact Reputation With Recent Performance: To
understandhow investors mix signalswith priors
K
k=1
= β0 +
.
βk
.
Zk
i,t −1 ×(rankit )
.
K
k=1
+
.
ψk
.
Zk
i,t −1 × (rankit)2
.
+ controls + εi,t+1
2. Variables:
) Zk
i,t −1: Dummy for reputation category (k ) at t − 1
) rankit ∈[0, 1]
3. Structure:
) Capture learning technology
) No independent effects of reputation(t-1) on flows(t+1):
) Reputation affect flows only through posteriors

Results 1: OLS Estimation
Table:Reputation And Fund Flows
Only Short Term Reputation
Dep Var:FFit+1
Peer CAPM Peer CAPM
Time Effects Yes Yes Yes Yes
Standard Errors Fund Clustered FundClustered Fund Clustered FundClustered
N 13512 13512 11468 11468
Adj R-sq 0.137 0.135 0.158 0.148
Constant -0.088*** -0.109***
(0.021) (0.021)
-0.098*** -0.126***
(0.022) (0.022)
Rank(t+1) 0.216*** 0.202***
(0.010) (0.010)
0.207*** 0.193***
(0.011) (0.011)
Risk(t) -0.894*** -0.808***
(0.183) (0.178)
-0.830*** -0.761***
(0.193) (0.188)
LogAge (t) -0.031*** -0.027*** -0.010 -0.006
(0.005) (0.005) (0.005) (0.005)
LogSize(t) -0.002 -0.002 -0.011*** -0.008***
(0.001) (0.001) (0.001) (0.001)
∆ Style(t+1) 0.045 0.039 0.039 0.035
(0.049) (0.038) (0.038) (0.033)

FFit +1 Peer CAPM Peer CAPM
Unconditional Estimates
Rank(t) 0.043 0.117**
(0.041) (0.041)
Rank-Sq(t) 0.296*** 0.223***
(0.043) (0.043)
Low Reputation (Bottom 20%)
Rank(t) -0.031 -0.031
(0.054) (0.060)
Rank-Sq(t) 0.210*** 0.250***
(0.062) (0.074)
Medium Reputation(Middle 60 %)
Rank(t) -0.023 0.077
(0.046) (0.044)
Rank-Sq(t) 0.374*** 0.260***
(0.052) (0.049)
TopReputation (Top 20%)
Rank(t) 0.308*** 0.285***
(0.059) (0.061)
Rank-Sq(t) 0.116 0.124
-0.0693 -0.0741

Mean Estimates Graph
-.20.2.4
0 .5 1 0 1 0 .5 1
95% ConfidenceInterval Mean FlowGrowth%(t+1)
FlowGrowth(%)
.5
Rank(t)
Flow Sensitivities In Response to Reputation
Low reputation (t-1) Med reputation (t-1) Top Reputation(t-1)

-.10.1.2.3
0 .
2
.
4
.
6
.
8
1
Rank(t)
95 % Confidence Interval Flow Growth %(t+1)
Flowgrowth(t+1)% Short Term Performance And Flow Growth

Piecewise Linear Specification
-.20.2.4
0 .5 1 0 1 0 .5 1
95 % CI Flow Growth %
.5
Rank ( t)
Reputation And Fund Flows (Piecewise Linear)
Low Reputation Medium Reputation Top Reputation

Implications
1. Shape:
) Convex Fund Flows For Low Reputation
) Linear Flows for Top Reputation
2. Level:
) Flows% increasing in reputation for a given short-term rank
) Break Even Rank: 0.90 for Low reputation funds Vs 0.40 for
Top repute funds
3. Slope:
) Flow sensitivity is lower for low reputation, evenat the extreme
high end of current performance.

Robustness Checks
1. Reputation: 3or 5or 7years of history
2. Performance Measure: CAPM or Peer Ranks
3. Standard Errors:
) Clustered SE(cluster by fund) with time effects controlled
using time dummies
) Cluster by fund-year (Veldkamp et.al (2014))
4. Institutional Vs Individual Investors
5. Fixed Effects Model: To control for fund family effects

Robustness With Fixed Effects
Only Short Term Reputation
Dep Var:FFit+1 Peer CAPM Peer CAPM
Rank(t) 0.0345 0.0871*
(0.0435) (0.0430)
Rank-Sq(t) 0.276*** 0.232***
(0.0453) (0.0448)
LowReputation
Rank(t) -0.0978 -0.140*
(0.0592) (0.0630)
Rank-Sq(t) 0.244*** 0.339***
(0.0682) (0.0776)
Medium Reputation
Rank(t) -0.0566 0.0270
(0.0496) (0.0491)
Rank-Sq(t) 0.389*** 0.308***
(0.0553) (0.0542)
Top Reputation
Rank(t) 0.323*** 0.359***
(0.0585) (0.0585)
Rank-Sq(t) 0.100 0.0528
(0.0671) (0.0691)

Evidence on Risk Shifting: Background
1. Do mid-year losing funds change portfoliorisk?
) Convexflows =⇒ limited downside in payoff
2. Previous Papers:
) Brown, Harlow, Starks (1996): Mid-Year losing funds
increasethe portfolio volatility
) Chevallier, Ellison (1997): marginal mid-year winners
benchmark but marginal losers ↑σ
) Busse (2001):
) Uses daily data =⇒ efficient estimates of σ
) No support for ∆σ(rit )
) Basak(2007):
) What is risk? σ or deviation from benchmark/peers?
) Shows that mid-year losers deviate from benchmark
) Portfolio risk can be up or down (σ ↓or ↑)
3. But Flows Are Not Convex For All Funds !

Measuring Risk Shifting
1.Consider a simplest factor model
Rit = αi + m
tβi
=
s
lo
¸
a
¸
d
x
ing =
s
p
¸
r
¸
ic
x
e
× R + st
2. Fact: Factors (e.g market) explain substantial σ(rit )
3. σ(rit ) Flawed meaure: Lot of exogenousvariation for
manager
4. Factor Loadings (β): Within managercontrol =⇒ good
measure of risk-shifting
5. Measure of Devitation:
∆Risk = | βi,2t
s¸¸x
β for 2nd half
−
s¸¸x
β2t
medianβ for 2nd half
|
) Median β for funds with same investment style

Some Statistics
Table:SummaryStatistics For Risk Change
Reputation Category
Variables Low Med Top
Annual Beta
Mean 1.04 1.02 1.02
Median 1.03 1.00 1.00
Dispersion 0.19 0.15 0.20
∆ Risk
Mean 0.12 0.09 0.12
Median 0.084 0.066 0.091
Dispersion 0.14 0.09 0.11

Regression Results
Table:Risk Shifting
Unconditional Control For Reputation
Dep: Beta Devitation Peer CAPM Peer CAPM
Time Effects Yes Yes Yes Yes
Style Effects Yes Yes Yes Yes
Standard Errors FundClustered FundClustered FundClustered FundClustered
Constant 0.298*
**
(0.015)
0.291*
**
(0.015)
0.304*
**
(0.015)
0.305*
**
(0.016)
∆Risk Rank(H1) 0.542*
**
(0.008)
0.543*
**
(0.008)
0.534*
**
(0.008)
0.532*
**
(0.008)
Log Age(t) -0.007 -0.007 -0.006 -0.006
(0.004) (0.004) (0.004) (0.004)
Log Size(t) -0.000 -0.000 -0.000 -0.002
(0.001) (0.001) (0.001) (0.001)
Unconditional Beta Deviation
Perf. Rank(H1) -0.243*** -0.228***
(0.029) (0.029)
Perf. Rank(H1)2 0.229*** 0.226***
(0.028) (0.028)

Result Continued
Peer CAPM Peer CAPM
LowReputation(t)
Perf. Rank(H1) -0.355*** -0.378***
(0.042) (0.043)
Perf. Rank(H1)2 0.377*** 0.410***
(0.048) (0.049)
Medium Reputation(t)
Perf. Rank(H1) -0.250*** -0.227***
(0.032) (0.034)
Perf. Rank(H1)2 0.219*** 0.208***
(0.033) (0.034)
Top Reputation(t)
Perf. Rank(H1) -0.0573 -0.0472
(0.042) (0.043)
Perf. Rank(H1)2 0.034 0.044
(0.046) (0.047)
Observations 15720 15720 14434 13406
Adj. R2 0.308 0.308 0.306 0.304

Discussion of Results
1. Low Reputation Funds
) Severe career concerns
) Low Mid-Year Rank: Gamble for resurrection
) High Mid-Year Rank: Exploit convexity of flows asrisk of
job-loss relatively low
2. Top Reputation Funds:
) No immediate careerconcerns=⇒ Level of deviation slightly
higher
) Flows Linear =⇒ No response to mid-yearrank

Section III
Model Of Fund Flows

Model Overview
1. Question: What explains the heterogenietyin observed
Fund-Flow schedules
2. Possible Answer:
) Investor-Baseis heterogenousfor funds with different
reputation or track record.
3. Basic Intuition:
) A model with loss-averse investors + partial visibility
) Rational investors shift out of poor perfoming funds but
loss-averse agents stick
)
)
=⇒ Bad fund performs poor again: Nooutflows
=⇒ Poor fund perform Good: Someinflows asfund
becomes’visible’

Model Outline
1. Basic Set-Up:
) Finite horizon model with T < ∞
) Two mutual funds indexed by i = 1, 2
) Two types of investors (N of each type)
) Rational Investors (R): 1 unit at t = 0
) Loss-Averse Investors (B): has η units at t = 0
22. At t = 0: Each fund has N of each type of investors
3. Partial Visibility:
) Fund is visible to fund insiders at year end
) Fund visibility at t to outsiders increases with performanceat
time t
) visible =⇒ entire history is known

Returns and Beliefs
1. Return Dynamics:
ri,t+1 = αi + εit+1
εit+1 ∼ N
.
0, (σε)2
.
where αi = unobserved ability of manageri
2. Beliefs:
) Iit = Set of investors to whom i is visible
) For every j ∈Iit , priors at end of t are
i tα ∼ N αit tˆ , (σ ) 2
. .
) All investors are Bayesian =⇒ Normal Posteriors with
αit+1 αit i,t +1 αitˆ = ˆ + (r − ˆ )
(σt )2
t ε(σ )2
+ (σ )2
. .

Loss-Averse Investors
1. Assumptions:
) Invest in only one of the visible funds at a time
) Solves Two period problem every t as if model ends at t + 1
2. Preferences: Following Barberis, Xiong (2009)
) πt = accumulated loss/gain for investor of B type with i
) Instantaneous Utility realized only upon liquidation
u(πt ) =
.
δπt 1 (πt < 0) + πt 1 (πt ≥ 0) If sell
0 If no sell
) Evolution of πt
πt+1+ ri,t+1
πt +1 = rj,t +1
0
If no sell
If shift to fund j ∈ Ii
If exit from industry
3. Trade-off: =⇒ B canmark-to-market losstoday andexit fund
i or carry forward losses in hope that rit+1 is large enough
4. Why? Loss hurts more: δ >1

Motivation For Loss-Averse Investors
1. Strong Empirical Support:
) Shefrin, Statman (1985), Odean(1998): Investors hold on
to losses for long but realize gains early
) Calvet,Cambell, Sodini(2009): Slightly weakerbut robust
tendency to hold on losing mutual funds
) Heath (1999): Disposition effect present in ESOP’s
) Brown (2006), Frazzini (2006): Institutional traders exhibit
tendency to hold losing investments
2. Why Realized Loss-Aversion?
) Barberis, Xiong (2009): Realization LossAversepreferences
cangenerate disposition effect
) Usual Prospect utility preferencesover terminal gain/loss need
not generate tendency to hold losses

Problem of Loss-Averse Investor
Keep Vs Sell Decision: B type invested in fund i = 1
t it
V π , {α }
ˆ i=1,2
. . ,
t t= max V ,V ,Vsell keep exit
t
,

t it
V π , {α }
ˆ i=1,2
. . ,
t
,
In turn
α , π ) = E [u (π + r α1t) |ˆ ]

t itV π , {ˆ }i=1,2
. . ,
t tα = max V ,V ,Vsell keep exit
t
,
In turn
α , π ) = E [u (π + r α1t) |ˆ ]
= P (πt + r1t+1 ≥ 0) Et [πt + r1t+1|πt + r1t+1 ≥ 0]

t it
V π , {α }
ˆ i=1,2
. . ,
t
,
In turn
α , π ) = E [u (π + r α1t) |ˆ ]
= P (πt + r1t+1 ≥ 0) Et [πt + r1t+1|πt + r1t+1 ≥ 0]
+P (πt + r1t+1 < 0)δEt [πt + r1t+1|πt + r1t+1 < 0]

t it
V π , {α }
ˆ i=1,2
. . ,
t
,
E [u (π + r α1t) |ˆ ]
In turn
α , π ) =
= P (πt + r1t+1 ≥ 0)Et [πt + r1t+1|πt + r1t+1 ≥ 0]
t α1t= Q (π + ˆ )

tV π ,{ it i=1,2
. . ,
t t
α } = max V ,V ,V
ˆ
sell keep exit
t
,
α1t) |ˆ ]
In turn
α , π ) = E [u (π + r
t α1t= Q (π + ˆ )
sell t α2t tV (π , ˆ ) = u (π ) + E [u(rt 2t+1 α2t) |ˆ ]

t it
V π , {α }
ˆ i=1,2
. . ,
t
,
α1t) |ˆ ]
In turn
α , π ) = E [u (π + r
t α1t= Q (π + ˆ )

t it
V π , {α }
ˆ i=1,2
. . ,
t
,
α1t) |ˆ ]
In turn
α , π ) = E [u (π + r
t α1t= Q (π + ˆ )
= u (πt ) + P (r2t+1 ≥ 0) Et [r2t+1|r2t+1 ≥ 0]

tV π ,{ it i=1,2
. . ,
t t
α } = max V ,V ,V
ˆ
sell keep exit
t
,
α1t) |ˆ ]
In turn
α , π ) = E [u (π + r
t α1t= Q (π + ˆ )
= u (πt ) + P (r2t+1 ≥ 0) Et [r2t+1|r2t+1 ≥ 0]
+δP (r2t+1 < 0) Et [r2t+1|r2t+1 <0]

t it
V π , {α }
ˆ i=1,2
. . ,
t
,
α1t) |ˆ ]
In turn
α , π ) = E [u (π + r
t α1t= Q (π + ˆ )
sell t α2t tu (π ) + E [u (rt 2t+1 α2t) |ˆ ]V (π , ˆ ) =
= u(πt) + P (r2t+1 ≥ 0)Et [r2t+1|r2t+1 ≥ 0]
+δP (r2t+1 < 0) Et [r2t+1|r2t+1 <0]
t α2t= u(π ) + Q ( ˆ )

Properties of Q(µ)
1.Expression for Q(µ), µ ∈ R
Q (µ) = µ + (δ − 1)
.
µΦ
.
−
µ .
− σφ
. µ. .
σ σ
2. Q(µ) is increasing in µ. In particular, one unit risein µ
changes Q(µ) by morethan 1 unit
∂Q (µ) µ
∂µ σ
= 1+ (δ − 1)Φ
.
−
.
∈(1,δ)
3. Q(µ) is concave,with lim
µ→∞ ∂µ
∂Q(µ)
= 1
∂2Q(µ)
∂µ2
= −
(δ −1)
σ
. µ .
φ −
σ
<0

Optimal Policy For Loss Averse Investor
1. Result 1: Participation Premium
) t α1tFor any π , liquidation of current fund is optimal if ˆ <0.
) In fact, break-even skill is positive. That is if
Vkeep(α1,min(πt ), πt) = Vexit (πt ), then α1,min(πt ) > 0, for any
πt
) Similarly, break-evenlevel for manager2 skill α2,min > 0. Else B
will exit but not shift to fund 2
2. How to interpret ”LOW reputation then?
) Relative: Low relative to Top, but still with positive expected
excessreturns.
) Replacement Theory: Bad managersarereplaced or bad funds
mergewith good funds.Henceexpectation about ”fund
returns” never go negative (e.g Lynch,Musto 2003)
α2t α1t t3. Assumption: ˆ > α and ˆ (π ) > α2,min 2,min t(π )

Optimal Policy For Loss-Averse Investor
1. Result 2: Hold Losses Unless Fund is ExtremelyBad
) α2t α1t t
∗
α1t α2tIf Q ( ˆ ) < δˆ , then B holds if π < π ( ˆ , ˆ ), for some
∗
α1t α2tπ ( ˆ , ˆ ) < 0
2. Understanding Why?
∂Q(µ)
∂µ
=Margi
s
nal
¸
v
¸
alu
x
e to skill
< δ= ut(π)
s ¸¸ x
=Marginal Loss
) =⇒ realizing lossis costly if ∆µ is small or πt < 0 is large in
magnitude.
) Note If shifted
Gain =
∂Q(µ)
∂µ
× (α2t − α1t )
ˆ ˆ
Loss = δπt

Optimal Policy
1. Result 3: Loss-Holding Region Increases in ˆα1t
) Why? Relative gain from shifting ( ˆ − ˆ ) decreases as ˆα2t α1t α1t
increases
2. Result 4: Policy For Gains
) α2t α1tIf Q ( ˆ ) < ˆ , hold gains if greater than some
∗ α1t α2tπ ( ˆ , ˆ ) >0
) α2t α1tIf Q ( ˆ ) > ˆ , liquidate any gain.
) Why? Hold large gainsin somecasesascurrent gains reduces
probability that πt+1 = πt + rit+1 < 0
3. Result 5: No Liquidation If Manager Is Better
) α1t α2t tNo liquidation is optimal if ˆ > ˆ for any given π ∈ R
) α1t α2tWhy? If ˆ > ˆ , then sticking with same manager is the
best chance to recover losses (given participation is satisfied)

Illustration Of Optimal Policy
Figure:Hold Losses Even if α1 < α2
ˆ ˆ

Illustration Of Optimal Policy
Figure:Loss-Holding Region

Optimal Policy For Rational Investor
1. Objective: Mean-Variance Optimization
V R
t
ω∈HR
t
.
t
ˆ= max ωαt −
γ
2
ωtΣω
.
2. Solution:
ωi =
ˆαit
γσ2
it
3. Discussion:
) Simplification: Generaltime consistent policy under learning is
complicated
) Lynch&Musto (2003): Similar simplification assumption
with exponential utility and one-period investors
) Alternative: Assumeexponential utility and one-period
agents,sothat policy of old and newagent coincide given
information

Dynamics Of Investor-Base
Figure: Dynamics Of Investor-Base
› Sequenceof poor performce=⇒ Higher fraction of
Loss-Averse Investorsin Fund

Equilibrium Fund Flows
Figure: Fund Flow Schedules

Alternative Theories
1. Lynch & Musto (JF,2003):
) Optimal replacementof managerby company below acut-off
performance
=⇒ Magnitude of shortfall has no information content)
) =⇒ asset demand similar belowcut-off
2. Berk & Green (JPE,2004)
) Decreasing returns to scale
) Quantities (size of fund) adjust sothat expected excessreturns
on all funds are equalized to zero
) Return chasing,differential abilities and lack of persistence are
all consistent with each other
3. Lynch & Musto For Current Evidence?
) P(firing) and hence convexity decreasing in reputation
) Consistent with empirics?Somemanagerfiring evenfor ’Top’
category
) =⇒ Someinsensitivity should havebeenobservedif firing
mechanismwas true

Conclusions
1. Lack of Flow Convexity for Reputed Funds(or for 40%of
Industry money)
2.No Risk Shifting ForTop funds in responseto Mid-Year rank
3.Some 2 nd half risk-sfiting for badrepute funds
4.Fund Flow heterogenietycould beexplained through presence
of loss-averse investors

Apoorva Javadekar -Role of Reputation For Mutual Fund Flows

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