gao feng (tsinghua sem) he ping (tsinghua sem) he xi (mit economics)
TRANSCRIPT
GAO Feng (Tsinghua SEM)GAO Feng (Tsinghua SEM)
HE Ping (Tsinghua SEM)HE Ping (Tsinghua SEM)
HE Xi (MITHE Xi (MIT Economics)Economics)
A long time ago, a visitor from out of town
came to a tour in Manhattan. At the end of the tour they took him to the financial district. When they arrived to Battery Park the guide showed him some nice yachts anchoring there, and said, "Here are the yachts of our bankers and stockbrokers." "And where are the yachts of the investors?" asked the naive visitor.
Preface
Investment decisions are intertemporal choices
involving tradeoffs among costs and benefits occurring at different times, which not only affect one's health, wealth, and happiness, but may also determine the economic prosperity of nations
Fisher (1930): investment is not an end in itself but rather a process for distributing consumption over time
Major concerns: return, risk, information acquisition, life-cycle, liquidity constraint, risk preference, background risk, etc.
Investment
Samuelson (1969, REStat), Merton (1969, REStat):
dynamic programming with uncertainty Ehrlich and Hamlen (1995, JEDC): precommitment
strategy with intermittent revision Campbell and Viceira (1999, QJE): time varying
investment opportunities Viceira (2001, JF): background risk, life-cycle Gollier (2002, JME): Liquidity constraint, decreasing
aversion to risk on wealth Chacko and Viceira (2005, RFS): incomplete
market with stochastic volatility
Related Studies
Investment behaviors are more complex than what
most standard theories could explain Barber and Odean (2002, RFS): online trading make
investors trade more actively but less profitable Barnea, Cronqvist and Siegel (2010, JFE): genetic
factor is critical for investor behavior He and Hu (2010, RBF): horizon effect Mastrobuoni and Weinberg (2009, AEJ-EP):
consumptions are not smoothed Meier and Sprenger (2010, AEJ-AE): individuals with
present-biased preference over-borrow on their credit cards
Empirical Facts
Barberis & Huang (2001, JF): mental accounting
and loss aversion Angeletos, Laibson, Repetto, Tobacman and
Weinberg (2001, JEP); Harris & Laibson (2001, Econometrica); Salanie and Treich (2006, EER): hyperbolic discounting
Grenadier & Wang (2007, JFE): real options investment model with hyperbolic discounting entrepreneurs
Munk (2008, JEDC): habit formation
Behavioral Theories and Investment
Frederick, Loewenstein and O’Donoghue (2002, JEL): given
two similar rewards, humans show a preference for one that arrives sooner rather than later, but valuations fall very rapidly for small delay periods, but then fall slowly for longer delay periods
Hyperbolic Discounting
Time inconsistent preferences, implying a
motive for consumers to constrain their own future choices (Laibson, QJE 1997) Under-saving (Laibson, EER 1998; Diamond and
Koszegi, JPubE 2003; Salanie and Treich, EER 2006)
Over-borrowing (Heidhues and Kőszegi, AER 2010)
Use of commitment device (Basu, AEJ-Micro 2011)
Facts Related to Hyperbolic Discounting
Information production: He (2007, RFS); Gorton
and He (2008, RES) Monitoring: Diamond (1984, RES) Screening: Bernanke and Blinder (1988, AER) Liquidity provider: Diamond and Dybvig (1983, JPE) Risk transformation: Diamond (1984, RES) Maturity transformation: Diamond and Dybvig
(1983, JPE) Payment methods: He, Huang and Wright (2005,
IER)
The Role of Intermediaries for Investors
Time inconsistent preference generates a
liquidity shortage for the investor who invests on his own
Financial intermediaries make investments on behalf of the investors and provide liquidity for unsophisticated investors
The financial intermediaries in our model can be interpreted as banks, pension funds, mutual funds, etc.
Goal of This Paper
DellaVigna and Malmendier (2004, QJE): contract
design with time inconsistency (monopoly firm) Heidhues and Kőszegi (2010, AER): credit contract
with time inconsistency (competitive firm) Basu (2011, AEJ-Micro): individuals join rotational
savings and credit associations (roscas) to fund repeated purchases of nondivisible goods without defect even when there is no punishment, roscas serves a commitment device
Related Works
Basic model Competitive equilibrium Linear contract and term premium Discussions Conclusion
Agenda
Three dates (t=0,1,2) Each agent is endowed with 1 unit of good at
date 0, and consumes at date 1 and 2 The good can be stored with 0 return, or
invested in a project at date 0 with a return R > 1 at date 2, if it is liquidated at date 1, one can get 1
Investment Technology
Self 0’s utility is u(c1) + u(c2)
Self 1’s utility is u(c1) + βu(c2) Self 0 believes that self 1’s utility
Time Inconsistent Preferences
1ˆ:naivety complete
ˆ:tionsophisticaperfect
1ˆ
)(ˆ)( 21
β
ββ
ββ
cuβcu
We measure welfare using long-run self-0
utility The first best solution does not depend on
degree of time-inconsistency
First Best
Rcu
cuFOC
Rcc
cucu
fb
fb
cc
)('
)(':
1/ s.t.
)()(max
2
1
21
21, 21
Diagram of Proof
R
1
c2
c1
)()( 21 cucu ),( 21fbfb cc
Investors cannot commit, and liquidation has
no cost, so they will liquidate some of the investment for consumption at date 1 based on their date 1 preference regardless what they believe at date 0
Autarky
fbatfbatat
at
cc
ccccRRβcu
cuFOC
Rcc
cuβcu
22112
1
21
21,
,)('
)(':
1/ s.t.
)()(max21
Diagram of Proof
R
1
c2
c1
)()( 21 cucu
),( 21atat cc
)()( 21 cuβcu ),( 21fbfb cc
In the autarky case, if we allow for trading at date
1, that is, an investor can trade his date 2 consumption from his investment for date 1 consumption, investors will have the same consumptions as in autarky case
Proof: The price of date 2 consumption, p, must be 1/R, otherwise either (1,0) or (0,R) will dominate all other points on the budget line and it cannot be equilibrium
Ineffective Market
1/ s.t.
)()(max
02
01
02
0121
21,,, 2102
01
Rcc
pccpcc
cuβcucccc
Diagram of Proof
R
1
c2
c1
p = 1/R
p > 1/R
p < 1/R
pR
1/p
At its own best interest, an intermediary can
improve the welfare of an investor with time inconsistent preference by offering a contract that punishes early withdraw
Role of Intermediary
Assume there are finite β’s among people,
with β1 < β2 < … < βN, and , and financial intermediaries offer a finite menu of repayment options C = {(c1s, c2s)} .
An incentive compatible map (c1(.), c2(.)): {β1, β2, … ,βN} R+ satisfies the following condition:
Incentive Compatible Contract
}ˆ,...,ˆ,ˆ{ˆ21 Nββββ
Ss
Cccβββββββ
cuβcuβcuββcu
NN
),( and }ˆ,...,ˆ,ˆ{},...,,{
)()())(())((
212121
2121
}ˆ,...,ˆ,ˆ{ 21 Nβββ
We define a competitive equilibrium as a
contract C offered by the financial intermediaries with an incentive compatible map (c1(.), c2(.)) that satisfies the following properties:1. Zero-profit2. No profitable deviation, there exists no contact C’
with incentive-compatible map (c1‘(.), c2‘(.)) such that for some β, u(c1‘(β)) + βu(c2‘(β)) > u(c1(β)) + βu(c2(β)), and C’ yields positive profits
3. Non-redundancy
Equilibrium Definition
The financial intermediary solves
u is the perceived utility from the perspective of date 0 if she accepts the contract
Observable Naïve Investors
IC) ,constraint compatible-(incentive
)ˆ()ˆ()()(
PCC) ,constraint choice-(perceived
)(ˆ)()ˆ(ˆ)ˆ(
PC) ,constraintion (paticipat
)ˆ()ˆ(
..
)1(max
2121
2121
21
21,,ˆ,ˆ 2121
cuβcucuβcu
cuβcucuβcu
ucucu
ts
cRccccc
)ˆ( ββ
PC must be binding IC must be binding PCC is equivalent to Perceived date 1 consumption is zero: Competitiveness will drive the financial
intermediary’s profits to zero The problem is equivalent to setting the profit
to be zero with PC binding through lifting u
Equilibrium Outcome
01̂ c2211 ˆ and ˆ cccc
For a naïve investor, the competitive-equilibrium
contract has two repayment options, with the investor expecting to choose , and actually choosing c1 and c2 satisfying
Equivalent to the autarky case
Equilibrium Contract
0ˆ and ,0ˆ 21 cc
Rβcu
cu
RcccRc
)('
)('
1/0)1(
2
1
2121
Diagram of the Result
R
1
c2
c1
0)1( 21 cRc
0ˆ with )ˆ()ˆ( where
)ˆ()ˆ()()(
121
2121
cucucu
cuβcucuβcu
)()( 21 cuβcu
)ˆ,0ˆ( 21 cc
),( 21 cc
At date 0, the intermediary will offer a perceived-
choice contract with very high date 2 consumption but zero date 1 consumption while expecting the investor with a need of immediate gratification at date 1 will switch to a contract with early withdraw of date 2 consumption despite of a high penalty
The more date 2 perceived-consumption, the greater drop in utility when date 1 comes, the more desperate the investor is, and the less the intermediary needs to offer in an alternative contract
Intuition
The financial intermediary solves
Observable Sophisticated Investors
(PC) )()(..
)1(max
21
21, 21
ucucuts
cRccc
)ˆ( ββ
PC must be binding Competitiveness will drive the financial
intermediary’s profits to zero The problem is equivalent to setting the profit
to be zero with PC binding through lifting u
Equilibrium Outcome
For a sophisticated investor, the competitive-
equilibrium contract has a single repayment option satisfying
Equivalent to the first best case
Equilibrium Contract
Rcu
cu
RcccRc
)('
)('
1/0)1(
2
1
2121
Diagram of the Result
R
1
c2
c1
0)1( 21 cRc)()( 21 cucu
slope)(smaller )()( 21 cuβcu
Equilibrium consumption for naïve investors
Equilibrium consumption for sophisticated investors
A sophisticated investor rationally expect his
own preference change and his choice at date 1, which is the only relevant choice for his utility at date 0
Intuition
For a naïve investor, the financial intermediary offers a
contract with a punishment for early withdraw, the welfare of a naïve investor is NOT improved However, if liquidation is costly, then the financial
intermediary can improve welfare as it avoids costly liquidation
For a sophisticated investor, the first best is achieved, and his welfare is strictly improved
If everyone else is as naïve as you are, or everyone knows that you are naïve, making investment through a zero-profit intermediary does not help nor hurt
Summary for Observable Preference
Again we study the most simple case: all investors
has the same at date 0, and investors are naïve ( ) with probability π, and investors are sophisticated ( ) with probability 1 – π
All investors choose the same contract (c1s, c2s) at date 0, but naïve investors will switch to (c1n, c2n) at date 1
Unobservable Preference
β̂ ββnˆ
ββsˆ
)(IC )()()()(
)(IC )()()()(
(PC) )()(
..
)1()1()1(max
2121
2121
21
2121,,, 2121
snsnsss
nsnsnnn
ss
ssnncccc
cuβcucuβcu
cuβcucuβcu
ucucu
ts
cRcπcRcπssnn
PC must be binding ICn must be binding
ICs implies c1s < c1n and c2s > c2n
Competitiveness will drive the financial intermediary’s profits to zero
The problem is equivalent to setting the profit to be zero with PC binding through lifting u
Equilibrium Outcome
Suppose all investors has the same at date 0,
and investors are naïve ( ) with probability π, and investors are sophisticated ( ) with probability 1 – π, the competitive-equilibrium contract has two repayment options. All investors choosing the same contract (c1s, c2s) at date 0, but naïve investors will switch to (c1n, c2n) at date 1. We have
Equilibrium Contract
)('
)('
1)1(1
)('
)(' ,
)('
)('
0)1()1()1(
1
1
2
1
2
1
2121
n
sn
s
sn
n
n
ssnn
cu
cu
π
πβR
cu
cuRβ
cu
cu
cRcπcRcπ
ββnˆ
β̂
ββsˆ
“Efficiency-at-the-top”: the repayment
schedule of naïve investors is similar to the case with known preference, but this is not the case for the sophisticated investors, who get a more back-loaded repayment schedule
There is a discontinuity at full sophistication
Interpretation of the Results
Suppose all investors has the same at date 0,
and investors are naïve with probability π, and investors are sophisticated with probability 1 – π. In a competitive equilibrium, the intermediary makes money on the naïve investors but loses money on the sophisticated investors. Moreover, the sophisticated investors’ welfare in the competitive equilibrium is strictly increasing in π
Cross-Subsidy Effect
β̂ββnˆ
ββsˆ
Diagram of the Result
c2
c1
nnn profitcRc 21 )1(
)()( 21 cuβcu n
)('
)('
1)1(1
)('
)(' ,
)('
)('
1
1
2
1
2
1
n
sn
s
sn
n
n
cu
cu
π
πβR
cu
cuRβ
cu
cu
sss profitcRc 21 )1((c1n,c2n)
(c1s,c2s)
)(IC )()()()( 2121 nsnsnnn cuβcucuβcu
The intermediary offers a contract with very
high long-term return and large penalty upon early withdraw, and it makes a profit from the naïve investors, who suffer from the need for immediate gratification, while losing money to the sophisticated investors, who enjoy the high long-term return
Intuition
The welfare of a naïve investor is LOWER than the
case of autarky For a sophisticated investor, the first best is NOT
achieved, and his welfare is strictly improved upon the autarky case
If you are naïve, do not pretend to be sophisticated, because that will hurt you
The sophisticated investors are happier if there are more naïve investors, but they always think their repayment structure is distorted with the existence of naïve investors
Summary for Unobservable Preference
Our earlier analyses focus on the case in which
investors can only liquidate a predetermined fixed portion of his investment contract
In practice, restricted linear contract corresponds to the case in which investors can liquidate any portion of his investment contract
But do more options bring welfare improvement to the investors? in particular, the naïve investors?
Restricted Linear Contracting
The financial intermediary solves
Observable Sophisticated Investors
TRccts
cuβcucc
ucucuts
cRc
cc
TR
~/..
)()(maxarg),(
(PC) )()(..
)1(max
21
21,*2
*1
*2
*1
*2
*1,
~
21
)ˆ( ββ
Diagram of the Result
R
1
c2
c1
0)1( 21 cRc )()( 21 cucu slope)(smaller )()( 21 cuβcu
TRcc ~/21
A perfectly sophisticated depositor is fully
aware of her time inconsistency, so it would be profit maximizing to offer her a contract with an interest rate of which aligns self 1's interest with the self 0’s welfare
The first best is still achieved
Intuition
βRR /~
The financial intermediary solves
Observable Naïve Investors
TRcc
cuβcucc
TRcc
cuβcucc
ucucu
ts
cRcTR
~/ˆˆ
(PCC) )ˆ(ˆ)ˆ(maxarg)ˆ,ˆ(
~/
(IC) )()(maxarg),(
(PC) )ˆ()ˆ(
..
)1(max
21
2121
21
2121
21
21,~
)ˆ( ββ
Diagram of the Result
c2
c1
0)1( 21 cRc
)()( 21 cuβcu )ˆ,ˆ( 21 cc
TRcc ~/21
)(ˆ)( 21 cuβcu
),( 21 cc
Diagram of the Result
c2
c1
0)1( 21 cRc
)()( 21 cuβcu )ˆ,ˆ( 21 cc
TRcc ~/21
)(ˆ)( 21 cuβcu
),( 21 cc)()( 21 cucu
Naïve investors will benefit from the linear contract The intermediary would set a very high interest
rate to attract the naïve investors, but that will also prevent the investors from liquidating too much, which lead to a low profit
As , the payoff of the investors gets to first best
For naïve investors, setting a upper limit for interest rate by regulation will help to improve their welfare
Equilibrium Outcome and Intuition
R~
ββ ˆ
Again we study the most simple case: all investors
has the same at date 0, and investors are naïve ( ) with probability π, and investors are sophisticated ( ) with probability 1 – π
All investors choose the same contract (c1s, c2s) at date 0, but naïve investors will switch to (c1n, c2n) at date 1
Unobservable Preference
β̂ ββnˆ
ββsˆ
)(IC ~
/ s.t. ),()(maxarg),(
)(IC ~
/ s.t. ),()(maxarg),(
(PC) )()(
..
)1()1()1(max
212121
212121
21
2121,,, 2121
nnnnnn
ssssss
ss
ssnncccc
TRcccuβcucc
TRcccuβcucc
ucucu
ts
cRcπcRcπssnn
Diagram of the Result
c2
c1
nnn profitcRc 21 )1(
)()( 21 cuβcu n),( 21 ss cc
TRcc ~/21
)()( 21 cuβcu s
),( 21 nn ccsss profitcRc 21 )1(
Both sophisticated investors and naïve investors
strictly prefer the unrestricted market, with a higher perceived u, to the restricted market with linear contract
When the naïve investors are sufficiently sophisticated, their welfare and the population-weighted sum of two types of investors’ welfare are greater in the restricted market with linear contract
Equilibrium Outcomes
In terms of the perceived date 0 utility, u, if u is
higher in restricted market with linear contract, we know that all the equilibrium outcomes in restricted market are also feasible in unrestricted market, but not vice versa
In terms of welfare, sophisticated investors correctly predict their future behavior, they are made worse off by the linear intervention; however, the benefit of this intervention to not-so-naïve investors outweighs the harm to sophisticated investors
Intuition
When preferences are observable, the welfare of a
naïve investor can be strictly improved with linear contract, while the sophisticated investors can always achieve first best
When preferences are unobservable, sophisticated investor welfare reduces while the naïve investors’ welfare improves, though nobody likes linear contract at the beginning
A welfare improving financial innovation might not be welcomed by anyone, even for those who benefit from it
Summary for Linear Contract
The restricted linear contract implies a term
structure of interest rates
Term Structure
2/1
2
1
22
2
1
121
~1
1
1)1(1
~/
TRi
Ti
i
c
i
cTRcc
For sophisticated investors, when they get
more impatient, financial intermediary would offer a lower one-period interest rate and a higher two-period interest rate such that people are committed to consume the first-best allocation
Term Premium and Impatience
2/1
212
211
21
/1
/1
~/,/
~
fbfb
fbfb
fbfb
cβRci
Rcβci
RccTβRR
Suppose all investors has the same at date 0, and
investors are naïve with probability π, and investors are sophisticated with probability 1 – π. In a competitive equilibrium, the term premium is increasing with the portion of naïve investors in the economy, π
The profit an intermediary can make from the naïve investors shrinks as π increases; the loss from sophisticated investors increases but is bounded
The more naïve investors in the economy, the happier the sophisticated ones and the naïve ones
Term Premium and Naivete
β̂ββnˆ
ββsˆ
Diagram of the Result
c2
c1
nnn profitcRc 21 )1(
)()( 21 cuβcu n),( 21 ss cc
TRcc ~/21
)()( 21 cuβcu s
),( 21 nn ccsss profitcRc 21 )1(
Suppose all investors has the same at date 0,
and investors are naïve with probability π, and investors are sophisticated with probability 1 – π. If contracts are divisible and can be traded on a secondary market at date 1, in competitive equilibrium all the depositors get the same allocations as when deposit contracts are restricted to be linear
Tradable Contract
β̂ββnˆ
ββsˆ
If loans can be sold (through securitization) at a
high price instead of being liquidated to get 1, the bank will invest all proceeds and sell the loan when there is early withdrawal; the results remain qualitatively the same
For open-end mutual funds, it requires all the liquidation value goes to the investor, this corresponds to the case of restricted linear contract with a slope R/P, with P being the liquidation value
Loan Securitization
Diagram of Expanded Budget Constraint
R
1
c2
c1
0)/1( 21 cRPc
P
If the financial intermediary has to disclose its
amount of investment at date 0 and needs to be able to satisfy all customers' needs according to the contract, the financial intermediary cannot remain solvent ex-ante when there is possibility that all depositors choose that expected repayment option
The financial intermediaries make positive profits, and the naïve investors are worse off
Transparency does not always benefit the investors
Transparency of Financial Intermediaries
Diagram of with Solvency at Date 0
R
1
c2
c1
0)1( 21 cRc )()( 21 cuβcu
),( 21 cc ),()ˆ,ˆ( 2121fbfb cccc
)()( 21 cucu
Small banks are more aggressive in attract
deposits For example, two-year term deposits, 10%
higher interest rate with individual deposits greater than RMB10,000, for firm deposits greater than RMB1,000,000
There is a much higher probability of early withdrawal for small banks For example, some regional branch of ABC, 1.08%;
Everbright (光大 ), 4%; CMBC (招商 ), 7.32%(in value); Minsheng, 9.1%
Empirical Evidence in China
Gilkeson, List and Ruff (1999, JFSR) found that
depositors withdraw a significant amount of their time deposits before maturity, 2.4% and 6.4% of the deposit base each year for shortest and longest maturity type, respectively
Withdrawals from pension funds for nonretirement purposes by account holders under 60 amount to $60 billion a year, or 40 percent of the $176 billion employees put into such accounts each year and nearly a quarter of the combined $294 billion that workers and employers contribute
Empirical Evidence in US
Naïve investors do suffer from time-inconsistent
preference Financial intermediaries subsidize the sophisticated
investors at the cost of naïve investors Competition among financial intermediaries might
not help the naïve investors, and regulation on interest rate might be needed
Financial innovation like negotiable CD and securitization help the naïve investors, but this might not necessarily be the case for regulation on transparency
Conclusion
