As per apoorva javadekar From this ppt
we can conclude that 3.Some 2 nd half risk-sfiting for bad repute funds .Fund Flow heterogeniety could be explained through presence of loss-averse investors
qCIO Global Macro Hedge Fund Strategy - November 2014BCV
qCIO seeks to exploit evolving economic conditions and the temporary mispricings that result among individual geographies and asset classes, opportunistically adjusting our investment views in response to the changing patterns of risk and reward in the markets.
Leveraged and inverse ETFs seek a daily return equal to a multiple of an index' return, an objective that requires continuous portfolio rebalancing. The resulting trading costs create a tradeoff between tracking error, which controls the short-term correlation with the index, and excess return (or tracking difference) -- the long-term deviation from the levered index' performance. With proportional trading costs, the optimal replication policy is robust to the index' dynamics. A summary of a fund's performance is the \emph{implied spread}, equal to the product of tracking error and excess return, rescaled for leverage and average volatility. The implies spread is insensitive to the benchmark's risk premium, and offers a tool to compare the performance of funds on the same benchmark, but with different multiples and tracking errors.
qCIO Global Macro Hedge Fund Strategy - November 2014BCV
qCIO seeks to exploit evolving economic conditions and the temporary mispricings that result among individual geographies and asset classes, opportunistically adjusting our investment views in response to the changing patterns of risk and reward in the markets.
Leveraged and inverse ETFs seek a daily return equal to a multiple of an index' return, an objective that requires continuous portfolio rebalancing. The resulting trading costs create a tradeoff between tracking error, which controls the short-term correlation with the index, and excess return (or tracking difference) -- the long-term deviation from the levered index' performance. With proportional trading costs, the optimal replication policy is robust to the index' dynamics. A summary of a fund's performance is the \emph{implied spread}, equal to the product of tracking error and excess return, rescaled for leverage and average volatility. The implies spread is insensitive to the benchmark's risk premium, and offers a tool to compare the performance of funds on the same benchmark, but with different multiples and tracking errors.
Investment management performance is easily measured at any frequency and easily
compared to publicly traded benchmarks such as S&P500 and Barclays Agg indices. In
contrast, wealth management is concerned with custom portfolios evolving over multi-decade
horizons. Such long horizons make it impractical to assess the quality of employed strategies
ex-post, while singularly personalized nature of the objective - funding a set of goals specific to
each individual - makes it impossible to create a single observable benchmark similar to an
index. We suggest that indexing should be done not at the level of portfolios but strategies, in a
way reminiscent of target date funds, and evaluation should be done using Monte-Carlo
simulations. We propose a simple methodology for building personalized benchmarks based on
a combination of user starting financial state and arbitrary list of goals. Such benchmarks can
be used to realistically evaluate a client’s current financial situation and serve as a point of
departure for providing nuanced advice.
Risk Return Trade Off PowerPoint Presentation SlidesSlideTeam
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While investment management can be readily measured against known benchmarks like the S&P500, wealth management, with its personalized, multi-decade scope, lacks such straightforward comparisons. This study recommends a shift in focus from portfolio to strategy indexing, much like target date funds, using Monte Carlo simulations for evaluation. A proposed methodology enables the construction of personalized benchmarks, combining a client's initial financial status with a selection of specific goals. These benchmarks facilitate a realistic appraisal of a client's financial situation, providing a foundation for tailored financial advice.
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Apoorva Javadekar -Role of Reputation For Mutual Fund Flows
1. Role of Reputation For Mutual Fund Flows
Apoorva Javadekar1
September2, 2015
1
Boston University,Departmentof Economics
2. 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
3. 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
4. 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
5. 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, ...)
6. 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
7. 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.
8. 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
9. 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
10. 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)
14. 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)
15. 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
16. 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.
17. 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
18. Robustness With Fixed Effects
Only Short Term Reputation
Dep Var:FFit+1 Peer CAPM Peer CAPM
Unconditional Estimates
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)
20. 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 !
21. 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
22. 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
27. 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
29. 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’
30. 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
31. 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
. .
32. 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
33. 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
34. 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
,
35. 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
,
In turn
α , π ) = E [u (π + r α1t) |ˆ ]
36. Problem of Loss-Averse Investor
Keep Vs Sell Decision: B type invested in fund i = 1
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]
37. 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
,
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]
38. 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
,
E [u (π + r α1t) |ˆ ]
In turn
α , π ) =
= 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 α1t= Q (π + ˆ )
39. Problem of Loss-Averse Investor
Keep Vs Sell Decision: B type invested in fund i = 1
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
= 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 α1t= Q (π + ˆ )
sell t α2t tV (π , ˆ ) = u (π ) + E [u(rt 2t+1 α2t) |ˆ ]
40. 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
,
α1t) |ˆ ]
In turn
α , π ) = E [u (π + r
= 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 α1t= Q (π + ˆ )
sell t α2t tV (π , ˆ ) = u (π ) + E [u(rt 2t+1 α2t) |ˆ ]
41. 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
,
α1t) |ˆ ]
In turn
α , π ) = E [u (π + r
= 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 α1t= Q (π + ˆ )
sell t α2t tV (π , ˆ ) = u (π ) + E [u(rt 2t+1 α2t) |ˆ ]
= u (πt ) + P (r2t+1 ≥ 0) Et [r2t+1|r2t+1 ≥ 0]
42. Problem of Loss-Averse Investor
Keep Vs Sell Decision: B type invested in fund i = 1
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
= 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 α1t= Q (π + ˆ )
sell t α2t tV (π , ˆ ) = u (π ) + E [u(rt 2t+1 α2t) |ˆ ]
= 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-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
,
α1t) |ˆ ]
In turn
α , π ) = E [u (π + r
= 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 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 )
44. 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
45. 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 )
46. 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
47. 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)
50. 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
51. Dynamics Of Investor-Base
Figure: Dynamics Of Investor-Base
› Sequenceof poor performce=⇒ Higher fraction of
Loss-Averse Investorsin Fund
53. 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
54. 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