Behavioral Finance Noise Traders and the Limits to Arbitrage January 24, 2008 Behavioral Finance “Noise Traders and the Limits to Arbitrage” – Part I Economics 437

Behavioral Finance Noise Traders and the Limits to Arbitrage January 24, 2008 Make-Up Class There is no class on Tuesday, Jan 28 th This class will be made up on Sunday, Feb 10, 2007 at 3:00 PM in the big Wilson Auditorium (Wilson 402)

Behavioral Finance Noise Traders and the Limits to Arbitrage January 24, 2008 By now, you should have read Malkiel and Shiller – “The Great Debate” Now, on to Shleifer’s article on noise traders

Behavioral Finance Noise Traders and the Limits to Arbitrage January 24, 2008 Why Shleifer’s Article Previous view was: “Noise” was random and cancelled out Smart “arbitrageurs” took noise traders money But, in the real world 1987 Bubbles Are their analytical models that could account for 1987 and bubbles?

Behavioral Finance Noise Traders and the Limits to Arbitrage January 24, 2008 “Noise Traders” Models distinguish two types of traders Arbitrage traders – “the smart guys” Use fundamentals – earnings, balance sheet Discounted cash flow or dividend methods Noise traders – “the dumb guys” Follow price trends, charts, hunches Usually, they are “momentum” players Sometimes just random buyers and sellers (but that might mean they are irrelevant if they are truly “random” players

Behavioral Finance Noise Traders and the Limits to Arbitrage January 24, 2008 The Milton Friedman argument for market efficiency in the presence of “noise traders” If noise traders are truly “random,” then their effects will “cancel out.” (Kind of a law of large numbers result) Noise traders are “systematic,” then arbitrage traders will “trade against them” and take all of their money Thus prices will be efficient in either case

Behavioral Finance Noise Traders and the Limits to Arbitrage January 24, 2008 Limits to Arbitrage Argument Arbitrageurs can not take “arbitrarily large” positions, because of risk Thus, arbitrageurs might lose money, not make money Noise traders might, for extended periods, make lots of money, while arbitrageurs are losing money Thus prices can remain “inefficient” for extended periods of time

Behavioral Finance Noise Traders and the Limits to Arbitrage January 24, 2008 Casual Empirical Evidence The “tech bubble” of Money Ball

Behavioral Finance Noise Traders and the Limits to Arbitrage January 24, 2008 Decifering Shleifer’s Article The players The assets Their behavior Equilibrium Profitability of the players

Behavioral Finance Noise Traders and the Limits to Arbitrage January 24, 2008 The players Arbitrageurs Noise Traders

Behavioral Finance Noise Traders and the Limits to Arbitrage January 24, 2008 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” t1t1 t2t2 t3t3 t4t4

Behavioral Finance Noise Traders and the Limits to Arbitrage January 24, 2008 How many are arbitrageurs? How many are noise traders? 01 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 Noise Traders and the Limits to Arbitrage January 24, 2008 The Assets s,….the “safe asset” Pays a constant dividend, r Perfectly elastic supply u, the “unsafe asset” (the “risky” asset) Pays a constant dividend, r Fixed in supply (supply equals one unit) s is convertible (reversibly) into the consumption good on a one-to-one basis Thus price of s is 1 Price of u determined by market place

Behavioral Finance Noise Traders and the Limits to Arbitrage January 24, 2008 What is a noise trader? P t is the price of the risky asset at time t ρ t is the “mean misperception” of p t ρtρt

Behavioral Finance Noise Traders and the Limits to Arbitrage January 24, 2008 Arbitrageurs expectations are “correct;” noise traders expectations are “biased” Correct mean of p t Difference is ρ t

Behavioral Finance Noise Traders and the Limits to Arbitrage January 24, 2008 What is an “arbitrage trader” Arbitrage traders “correctly” perceive the true distribution of p t. There is “systematic” error in estimation of future price, p t But, arbitrageurs face risk unrelated to the “true” distribution of p t 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 Noise Traders and the Limits to Arbitrage January 24, 2008 The Main Issues What happens in equilbrium Undetermined Some forces make p t > 1, some forces push p t < 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 Noise Traders and the Limits to Arbitrage January 24, 2008 End