1. Behavioral Finance “Shleifer on Noise Trading”
Economics 437

2. Black on “Noise”
Black strong believer in noise and noise traders in particular
They lose money according to him (though they may make money for a short while)
Prices are “efficient” if they are within a factor of 2 of “correct” value
Actual prices should have higher volatility than values because of noise

3. The Law of One Price Identical things should have identical prices
But, what if two identical things have different names?
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)

4. 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

5. 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

6. Decifering Shleifer Chapter 2
The assets
The players
Their behavior
Equilibrium
Profitability of the players

7. 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)

8. 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

9. 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)

10. The players
Arbitrageurs
Noise Traders

11. Utility Functions “Expected Utility”, not “Expected Value”
U = -e-(2λ)w
Utility
wealth

12. 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 t2 t3 t4

13. How many are arbitrageurs? How many are noise traders?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

14. What is a noise trader? Ρt+1 is the “mean misperception” of pt+!
Pt+1 is the price of the risky asset at time t+1
Ρt+1 is the “mean misperception” of pt+!
Ρt+!

15. 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

16. Arbitrageurs expectations are “correct;” noise traders expectations are “biased”
Difference is ρt+1
Correct mean of pt+1

17. The Price of the Risky Asset
Taken from equation 2.9 on page 37 in Shleifer’s “Inefficient Markets”

18. 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?

19. 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

20. What Does Shleifer Accomplish?
Given two assets that are “fundamentally” identical, he shows a logic where the market fails to price them identically
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)

21. The End