apoorva Javadekar - Role of Reputation For Mutual Fund Flows

1. Role of Reputation For Mutual FundFlows ApoorvaJavadekar1 September 2,2015 1 Boston University, Department ofEconomics

2. Broad Question Question: What causes investors to invest or withdraw money from mutualfunds? ) In particular: what is the link between fund performance and fundflows? Litarature: Narrow focus on ”Winner Chasing” phenomenon ) link between recent-most performance and fund flows ignoring role for reputation offund This paper: Role of Fund Reputation ) Investor’schoices ) Risk Choices by fundmanagers

3. Why Study FundFlows? Important Vehicle of Investment ) Large: Manage 15 Tr $ (ICI,2014) ) Dominant way to equities: (ICI -2014, French (2008)) ) HH through MF: owns 30% USequities ) Direct holdings of HH: 20% of US equities ) Participation: 46% of US HHinvest Understand BehavioralPatterns: ) Investors learn about managerial ability through returns =⇒ fund flows shed light on learning, information processing capacities etc. ) 3. Fund Flows Affect Managerial RiskTaking ) Compensation ≈ flows: 90% MF managers paid as a % of AUM =⇒ flow patterns can affect risk taking =⇒ impacts on assetprices ) )

4. LiteratureSnapshot 1. Seminal Paper: Chevallier & Ellison (JPE,1997) Flows(t+1) Returns(t) =⇒ Convex Fund Flows in RecentPerformance! 2. Why Interesting? Non-Linear Flows (could)mean ) Bad and extremely bad returns carry same information ! ) Non-BayesianLearning ) BehavioralBiases ) Excess risk taking by managers given limiteddownside

5. Motivating Role ofReputation No Role For Reputation: Literature links time t returns (rit ) to time t + 1 fund flows(FFi,t+1) Why a Problem? The way investor perceives current performance depends upon historicperformance Why? History of Returns ≈reputation Manager1:{rt−3,rt−2,rt−1,rt}={G,G,G,B} Manager2:{rt−3,rt−2,rt−1,rt}={B,B,B,B} What it means forestimation? FFi,t+1=g(rit,ri,t−1,...)+errori,t+1 where g(.) is non-separable in returns Useful For Studying Investors Learning FFi,t+1 =g ( =sde¸c¸isioxn rit, ri,t−1, ri,t−2, ...) x =ss¸ig¸nxal s =p¸r¸iors

6. Data 1. Source: CRSP Survivor-Bias free mutual fund dataset 2. Time Period:1980-2012. Include: ) Domestic, Open ended, equity funds ) Growth, Income, Growth&Income, Small and Mid-Cap, Capital Appreciation funds (Pastor, Stambaugh (2002)) Exclude ) Sectoral, global and index or annuity funds ) Funds with salesrestrictions ) young funds with less than 5 years ) small funds (Assets < 10 Mn $) Annual Frequency: Disclosures of yearly returns, ratings are based on annualperformance

7. PerformanceMeasures Reputation: Aggregate performance of 3 or 5 years prior to current period How to Measure Performance? ) Factor Adjusted: CAPM α or 3-factor α (Fama,French (2010), Kosowski(2006)) ) Peer Ranking (Within each investmentstyle): (Chevallier,Ellison (1997), Spiegel (2012)) WhichMeasure? ) Not easy for 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)) ) Peer ranking within each style control for bulk of risk differentials acrossfunds ) CAPM α wins the horse race amongst factor models (Barber et.al2014) 4.I use both the measures: CAPM α and Peer Ranking but not 3-factormodel.

8. MainVariables 1. Fund Flows: Main dependent variable is % growth in Assets due to fundflows Ai,t+1−(Ait×(1+ri,t+1)) FFi,t+1= A it Ait : Assets with fund i at time t rit : Fund returns for period ended t

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

10. Results 1: OLSEstimation Table:Reputation And Fund Flows

11. PeerCAPM Peer CAPM FFit+1 UnconditionalEstimates Top Reputation (Top20%)

12. Mean EstimatesGraph Flow Sensitivities In Response toReputation Lowreputation(t-1) Medreputation(t-1) TopReputation(t-1) .4 FlowGrowth(%) .2 0 -.2 0 .5 1 0 .5 Rank(t) 1 0 .5 1 95% ConfidenceInterval Mean FlowGrowth%(t+1)

13. UnconditionalEstimates Short Term Performance And FlowGrowth .3 .2 Flow growth(t+1)% .1 0 -.1 0 .2 .4 .6 .8 1 Rank(t) 95 %Confidence Interval Flow Growth %(t+1)

14. Mean EstimatesGraph Flow Sensitivities In Response toReputation Lowreputation(t-1) Medreputation(t-1) TopReputation(t-1) .4 FlowGrowth(%) .2 0 -.2 0 .5 1 0 .5 Rank(t) 1 0 .5 1 95% ConfidenceInterval Mean FlowGrowth%(t+1)

15. Piecewise LinearSpecification Reputation And Fund Flows (PiecewiseLinear) LowReputation MediumReputation TopReputation .4 .2 0 -.2 0 .5 1 0 .5 Rank (t) 1 0 .5 1 95 % CI Flow Growth%

16. Implications Shape: ) Convex Fund Flows For LowReputation ) Linear Flows for Top Reputation 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 reputefunds Slope: ) Flow sensitivity is lower for low reputation, even at the extreme high end of currentperformance.

17. RobustnessChecks Reputation: 3 or 5 or 7 years of history Performance Measure: CAPM or PeerRanks StandardErrors: ) Clustered SE (cluster by fund) with time effects controlled using timedummies ) Cluster by fund-year (Veldkamp et.al (2014)) Institutional Vs Individual Investors Fixed Effects Model: To control for fund family effects

18. Robustness With FixedEffects

19. Section II: RiskShifting

20. Evidence on Risk Shifting:Background Do mid-year losing funds change portfoliorisk? ) Convex flows =⇒ limited downside in payoff PreviousPapers: ) Brown, Harlow, Starks (1996): Mid-Year losing funds increase the portfoliovolatility ) 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 frombenchmark/peers? ) Shows that mid-year losers deviate from benchmark ) Portfolio risk can be up or down (σ ↓or ↑) But Flows Are Not Convex For All Funds !

21. Measuring RiskShifting 1.Consider a simplest factormodel m Rit = αi+ βi =slo¸a¸dxing=sp¸r¸icxe ×R +s t t Fact: Factors (e.g market) explain substantialσ(rit ) σ(rit ) Flawed meaure: Lot of exogenous variation for manager Factor Loadings (β): Within manager control =⇒ good measure ofrisk-shifting Measure ofDevitation: ∆Risk =| − | βi,2t s¸¸x β2t median β for 2nd half s¸¸x β for 2ndhalf ) Median β for funds with same investment style

22. SomeStatistics Table:Summary Statistics For Risk Change ReputationCategory

23. First Pass: PolynomialSmooth

24. RegressionResults Table:RiskShifting Unconditional Control ForReputation

25. ResultContinued Peer CAPMPeer CAPM LowReputation(t) Medium Reputation(t)

26. Mean Estimates ForRisk-Shift

27. Discussion ofResults Low ReputationFunds ) Severe careerconcerns ) Low Mid-Year Rank: Gamble forresurrection ) High Mid-Year Rank: Exploit convexity of flows as risk of job-loss relativelylow Top ReputationFunds: ) No immediate career concerns =⇒ Level of deviation slightly higher ) Flows Linear =⇒ No response to mid-yearrank

28. SectionIII Model Of Fund Flows

29. ModelOverview Question: What explains the heterogeniety in observed Fund-Flowschedules PossibleAnswer: ) Investor-Base is heterogenous for funds with different reputation or trackrecord. BasicIntuition: ) A model with loss-averse investors + partialvisibility ) Rational investors shift out of poor perfoming funds but loss-averse agentsstick =⇒ Bad fund performs poor again: Nooutflows =⇒ Poor fund perform Good: Some inflows as fund becomes’visible’ ) )

30. ModelOutline 1. BasicSet-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 2. At t = 0: Each fund has N of each type ofinvestors 2 3. PartialVisibility: ) Fund is visible to fund insiders at year end ) Fund visibility at t to outsiders increases with performance at timet ) visible =⇒ entire history isknown

31. Returns andBeliefs ReturnDynamics: ri,t+1 = αi +εit+1 εit+1 ∼ N .0, (σε)2. where αi = unobserved ability of manageri Beliefs: ) Iit = Set of investors to whom i is visible ) For every j ∈ Iit , priors at end of t are . . 2 α ∼ Nα ˆ , (σ) i t it t ) All investors are Bayesian =⇒ Normal Posteriorswith . . (σt)2 ˆ = ˆ+(r − ˆ) αit+1αiti,t+1αit (σ )2 + (σ)2 t ε

32. Loss-AverseInvestors 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 Preferences: Following Barberis, Xiong (2009) ) πt = accumulated loss/gain for investor of B type with i ) Instantaneous Utility realized only upon liquidation .δπt 1 (πt < 0) + πt 1 (πt ≥ 0)If sell u(πt)= 0 If nosell ) Evolution ofπt  If nosell If shift to fund j ∈ Ii If exit fromindustry πt+1 +ri,t+1 πt+1=rj,t+1 0 Trade-off: =⇒ B can mark-to-market loss today and exit fund i or carry forward losses in hope that rit+1 is large enough Why? Loss hurts more: δ >1

33. Motivation For Loss-AverseInvestors Strong EmpiricalSupport: ) Shefrin, Statman (1985), Odean(1998): Investors hold on to losses for long but realize gains early ) Calvet,Cambell, Sodini(2009): Slightly weaker but 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 Why RealizedLoss-Aversion? ) Barberis, Xiong (2009): Realization Loss Averse preferences can generate dispositioneffect ) Usual Prospect utility preferences over terminal gain/loss need not generate tendency to hold losses

34. Problem of Loss-AverseInvestor Keep Vs Sell Decision: B type invested in fund i =1 . . , , V π , {α} ˆ =max V ,V ,V sell keepexit t t it t t i=1,2

35. Problem of Loss-AverseInvestor Keep Vs Sell Decision: B type invested in fund i =1 . . , , V π , {α} ˆ =max V ,V ,V sell keepexit t t it t t i=1,2 Inturn α , π ) = E [u (π +r ) | ˆ] α1t

36. Problem of Loss-AverseInvestor Keep Vs Sell Decision: B type invested in fund i =1 . . , , V π , { ˆ} α =max V ,V ,V sell keepexit t t it t t i=1,2 Inturn α , π ) = E [u (π +r ) | ˆ] α1t = P (πt + r1t+1 ≥ 0) Et [πt + r1t+1|πt + r1t+1 ≥0]

37. Problem of Loss-AverseInvestor Keep Vs Sell Decision: B type invested in fund i =1 . . , , V π , {α} ˆ =max V ,V ,V sell keepexit t t it t t i=1,2 Inturn α , π ) = E [u (π +r ) | ˆ] α1t = 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]

38. Problem of Loss-AverseInvestor Keep Vs Sell Decision: B type invested in fund i =1 . . , , V π , {α} ˆ =max V ,V ,V sell keepexit t t it t t i=1,2 Inturn α , π ) = = E [u (π +r ) | ˆ] α1t 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] = Q (π + ˆ) t α1t

39. Problem of Loss-AverseInvestor Keep Vs Sell Decision: B type invested in fund i =1 . . , , V π ,{ α} =max V ,V ,V ˆ sell keepexit t t it t t i=1,2 Inturn α , π ) = E [u (π +r = ) | ˆ] α1t 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] = Q (π + ˆ) t α1t V (π , ˆ ) = u (π ) + E [u(r ) | ˆ] tα2t t 2t+1 α2t t sell

40. Problem of Loss-AverseInvestor Keep Vs Sell Decision: B type invested in fund i =1 . . , , V π , {α} ˆ =max V ,V ,V sell keepexit t t it t t i=1,2 Inturn α , π ) = E [u (π +r = ) | ˆ] α1t 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] = Q (π + ˆ) t α1t V (π , ˆ ) = u (π ) + E [u(r ) | ˆ] tα2t t 2t+1 α2t t sell

41. Problem of Loss-AverseInvestor Keep Vs Sell Decision: B type invested in fund i =1 . . , , V π , {α} ˆ =max V ,V ,V sell keepexit t t it t t i=1,2 Inturn α , π ) = E [u (π +r = ) | ˆ] α1t 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] = Q (π + ˆ) t α1t V (π , ˆ ) = u (π ) + E [u(r ) | ˆ] tα2t t 2t+1 α2t t sell = u (πt ) + P(r2t+1 ≥ 0) Et [r2t+1|r2t+1 ≥ 0]

42. Problem of Loss-AverseInvestor Keep Vs Sell Decision: B type invested in fund i =1 . . , , V π ,{ α} =max V ,V ,V ˆ sell keepexit t t it t t i=1,2 Inturn α , π ) = E [u (π +r = ) | ˆ] α1t 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] = Q (π + ˆ) t α1t V (π , ˆ ) = u (π ) + E [u(r ) | ˆ] tα2t t 2t+1 α2t t sell = u (πt ) + P(r2t+1 ≥ 0) Et [r2t+1|r2t+1 ≥ 0] +δP (r2t+1 < 0) Et [r2t+1|r2t+1 <0]

43. Problem of Loss-AverseInvestor Keep Vs Sell Decision: B type invested in fund i =1 . . , , V π , {α} ˆ =max V ,V ,V sell keepexit t t it t t i=1,2 Inturn α , π ) = E [u (π +r = ) | ˆ] α1t 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] = Q (π + ˆ) t α1t V (π , ˆ )= = u (π ) +E [u (r ) | ˆ] tα2t t 2t+1 α2t t sell u(πt)+P(r2t+1≥0)Et[r2t+1|r2t+1≥0] +δP (r2t+1 < 0) Et [r2t+1|r2t+1 <0] = u(π ) + Q (ˆ) α2t t

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

45. Optimal Policy For Loss AverseInvestor 1. Result 1: ParticipationPremium For any π , liquidation of current fund is optimal ifˆ <0. α1t ) t ) In fact, break-even skill is positive. That is if Vkeep(α1,min(πt),πt)=Vexit(πt),thenα1,min(πt)>0,forany πt ) Similarly, break-even level for manager 2 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 managers are replaced or bad funds merge with good funds. Hence expectation about ”fund returns” never go negative (e.g Lynch,Musto2003) 3. Assumption: ˆ >α and ˆ (π ) >α (π) α2t α1t t t 2,min 2,min

46. Optimal Policy For Loss-AverseInvestor 1. Result 2: Hold Losses Unless Fund is ExtremelyBad ∗ If Q (ˆ ) < δ ˆ , then B holds if π < π (ˆ , ˆ ), for some α2t α1t α1t α2t ) t ∗ π (ˆ , ˆ ) < 0 α1t α2t 2. UnderstandingWhy? ∂Q(µ) ∂µ =Margisnal¸v¸aluxe toskill <δ=ut(π) s ¸¸x =MarginalLoss =⇒ realizing loss is costly if ∆µ is small or πt < 0 is large in magnitude. ) Note Ifshifted ) ∂Q(µ) ∂µ ×(α2t−α1t) ˆ ˆ Gain= Loss =δπt

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

48. Illustration Of OptimalPolicy Figure:Hold Losses Even if α1 <α2 ˆ ˆ

49. Illustration Of OptimalPolicy Figure:Loss-HoldingRegion

50. Optimal Policy For RationalInvestor 1. Objective: Mean-VarianceOptimization . γ 2 VR t = max ω αt− ˆ ωtΣω. t ω∈HR t 2.Solution: ˆ αit ωi = γσ2 it 3.Discussion: ) Simplification: General time consistent policy under learning iscomplicated ) Lynch&Musto (2003): Similar simplification assumption with exponential utility and one-period investors ) Alternative: Assume exponential utility and one-period agents, so that policy of old and new agent coincide given information