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Behavioral Finance
Economics 437
Behavioral Finance
Law Of One Price
Feb 4-9 2016
The Law of One Price
 Identical things should have identical prices
 But, what if two identical things have different
names?

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Example: baseball, hardball
Another example: two companies with exact
same cash flow but they are different
companies in name, but in every other way
they are different (think of two bonds, if it
makes any easier to imagine)
Behavioral Finance
Law Of One Price
Feb 4-9 2016
Fungibility (convertibility from
one form to another)
 Imagine two “different” products


Product A
Product B
 Imagine a machine that you can plug A into
and out comes B and you can plus B into and
out comes A
 This is called “fungibility”
 You can easily turn one thing into another
and vice versa costlessly
Behavioral Finance
Law Of One Price
Feb 4-9 2016
The Mysterious Case of Royal Dutch
and Shell (stocks)
 Royal Dutch – incorporated in Netherlands
 Shell – incorporated in England
 Royal Dutch
Trades primarily in Netherlands and US
 Entitled to 60% of company economics
 Shell
 Trades predominantly in the UK
 Entitled to 40% of company economics

 Royal Dutch should trade at 1.5 times Shell
 But it doesn’t
Behavioral Finance
Law Of One Price
Feb 4-9 2016
Open End Funds are the Typical
 An investors sends cash to the mutual fund to
buy a unit interest in the fund
 The fund takes the investor’s cash and buys
securities in exactly the same proportions as
exist in the current fund
 When an investor sells his unit interest, the
fund liquidates shares in the funds to redeem
the investor’s interest
Behavioral Finance
Law Of One Price
Feb 4-9 2016
Closed End Funds
 They begin by purchasing securities
 Then they do an IPO to the public selling
shares in the fund
 After that, the fund shares are fixed in number
and the shares trade in the open market
Behavioral Finance
Law Of One Price
Feb 4-9 2016
Problem
 No problem with open end fund. The investor
buys and sells at NAV (net asset value)
 Problem arises with closed end fund


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Price of a share can diverge from the stock
values in the fund
Begin at a premium and, over time, trade at a
discount
Discount only goes away when fund is
terminated
Behavioral Finance
Law Of One Price
Feb 4-9 2016
ETFs (Exchange Traded Funds)
 Created much like closed end funds:
securities pooled together to create a fund
 Then shares in the pool sold to the public
 But (“creation units”)


Shares can be created
Shares can be destroyed
 Permits arbitrage to solve the closed end
puzzle
Behavioral Finance
Law Of One Price
Feb 4-9 2016
Decifering Shleifer Chapter 2
 The assets
 The players
 Their behavior
 Equilibrium
 Profitability of the players
Behavioral Finance
Law Of One Price
Feb 4-9 2016
Imagine an economy with two
assets (financial assets)
 A Safe Asset, s
 An Unsafe Asset, u
 Assume a single consumption good
 Suppose that s is always convertible (back and forth between
the consumption good and itself)
 That means the price of s is always 1 in terms of the
consumption good (that is why it is called the “safe” asset – it’s
price is always 1, regardless of anything)
Behavioral Finance
Law Of One Price
Feb 4-9 2016
Safe asset, s, and unsafe asset, u
 Why is u an unsafe asset?
 Because it’s price is not fixed because u is
not convertible back and forth into the
consumption good
 You buy u on the open market and sell it on
the open market
Behavioral Finance
Law Of One Price
Feb 4-9 2016
Now imagine
 Both s and u pay the same dividend, d


d is constant, period after period
d is paid with complete certainty, no
uncertainty at all
 This implies that neither s or u have
“fundamental” risk
 (If someone gave you 10 units of s and you
never sold it, your outcome would be the
same as if someone gave you 10 units of u)
Behavioral Finance
Law Of One Price
Feb 4-9 2016
Question
 Can s and u trade at different prices?

If yes, EMH is false
Behavioral Finance
Law Of One Price
Feb 4-9 2016
The players
 Arbitrageurs
 Noise Traders
Behavioral Finance
Law Of One Price
Feb 4-9 2016
Utility Functions
 “Expected Utility”, not
Utility
“Expected Value”
 U = -e-(2λ)w
wealth
Behavioral Finance
Law Of One Price
Feb 4-9 2016
Overlapping Generations Structure
 All agents live two periods
Born in period 1 and buy a portfolio (s, u)
 Live (and die) in period 2 and consume
 At time t
 The (t-1) generation is in period 2 of their life
 The (t) generation is in period 1 of their life
 So, they “overlap”

t1
Behavioral Finance
t2
Law Of One Price
t3
t4
Feb 4-9 2016
How many are arbitrageurs? How
many are noise traders?
0
1
The total number of traders are the same as the number of real numbers
Between zero and one (an infinite number)
The term “measure” means the size of any interval. For example the
“measure” of the interval between 0 and ½ is ½. Interestingly, the
measure of a single point (a single number) is zero. The measure of
the entire interval between zero and one is 1. You can think of it as
a fraction of the entire interval.
The measure of noise traders is µ and the measure of arbitrage traders
is 1 - µ. That is, the fraction of noise traders is µ and everybody else
is an arbitrage traders
Behavioral Finance
Law Of One Price
Feb 4-9 2016
What is a noise trader?
Pt+1 is the price of the risky asset at time t+1
Ρt+1 is the “mean misperception” of pt+!
Ρt+!
Behavioral Finance
Law Of One Price
Feb 4-9 2016
What is an “arbitrage trader”
 Arbitrage traders “correctly” perceive the true
distribution of pt+1. There is “systematic” error
in estimation of future price, pt+1
 But, arbitrageurs face risk unrelated to the
“true” distribution of pt+1
 If there were no “noise traders,” then there
would be no variance in the price of the risky
asset…..but, there are noise traders, hence
the risky asset is a risky asset
Behavioral Finance
Law Of One Price
Feb 4-9 2016
Arbitrageurs expectations are “correct;” noise
traders expectations are “biased”
Difference is ρt+1
Correct mean of pt+1
Behavioral Finance
Law Of One Price
Feb 4-9 2016
The Main Issues
 What happens in equilbrium
 Undetermined
 Some forces make pt > 1, some forces push pt
< 1, result is indeterminant
 Who makes more profit, arbitrageurs or noise
traders?


Depends
But, it is perfectly possible for arbitrageurs to
make more!
 Survival?
Behavioral Finance
Law Of One Price
Feb 4-9 2016
When Do Noise Traders Profit
More Than Arbitrageurs?
 Noise traders can earn more than arbitrageurs when
ρ* is positive. (Meaning when noise traders are
systematically too optimistic)
 Why?
 Because they relatively more of the risky asset
than the arbitrageurs
 But, if ρ* is too large, noise traders will not earn
more than arbitrageurs
 The more risk averse everyone is (higher λ in the
utility function, the wider the range of values of ρ
for which noise traders do better than arbitrageurs
Behavioral Finance
Law Of One Price
Feb 4-9 2016
What Does Shleifer Accomplish?
 Given two assets that are “fundamentally”
identical, he shows a logic where the market
fails to price them identically

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Assumes “systematic” noise trader activity
Shows conditions that lead to noise traders
actually profiting from their noise trading
Shows why arbitrageurs could have trouble
(even when there is no fundamental risk)
Behavioral Finance
Law Of One Price
Feb 4-9 2016
The End
Behavioral Finance
Law Of One Price
Feb 4-9 2016