Behavioral Finance Shleifer on Noise Trading Economics 437

Behavioral Finance “Shleifer on Noise Trading” Economics 437 Behavioral Finance Shleifer Jan 24 & 29, 2019

Black on “Noise” n Black strong believer in noise and noise traders in particular n They lose money according to him (though they make money for a short while) n Prices are “efficient” if they are within a factor of 2 of “correct” value n Actual prices should have higher volatility than values because of noise Behavioral Finance Shleifer Jan 24 & 29, 2019

The Law of One Price n Identical things should have identical prices n But, what if two identical things have different names? Example: baseball, hardball n 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) n Behavioral Finance Shleifer Jan 24 & 29, 2019

Fungibility (convertibility from one form to another) n Imagine two “different” products n Product A n Product B n Imagine a machine that you can plug A into and out comes B and you can plus B into and out comes A n This is called “fungibility” n You can easily turn one thing into another and vice versa costlessly Behavioral Finance Shleifer Jan 24 & 29, 2019

The Mysterious Case of Royal Dutch and Shell (stocks) n Royal Dutch – incorporated in Netherlands n Shell – incorporated in England n Royal Dutch Trades primarily in Netherlands and US n Entitled to 60% of company economics n Shell n Trades predominantly in the UK n Entitled to 40% of company economics n n Royal Dutch should trade at 1. 5 times Shell n But it doesn’t Behavioral Finance Shleifer Jan 24 & 29, 2019

Decifering Shleifer Chapter 2 n The assets n The players n Their behavior n Equilibrium n Profitability of the players Behavioral Finance Shleifer Jan 24 & 29, 2019

Imagine an economy with two assets (financial assets) n A Safe Asset, s n An Unsafe Asset, u n Assume a single consumption good n Suppose that s is always convertible (back and forth between the consumption good and itself) n 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 Shleifer Jan 24 & 29, 2019

Safe asset, s, and unsafe asset, u n Why is u an unsafe asset? n Because it’s price is not fixed because u is not convertible back and forth into the consumption good n You buy u on the open market and sell it on the open market Behavioral Finance Shleifer Jan 24 & 29, 2019

Now imagine n Both s and u pay the same dividend, d n d is constant, period after period n d is paid with complete certainty, no uncertainty at all n This implies that neither s or u have “fundamental” risk n (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 Shleifer Jan 24 & 29, 2019

The players n Arbitrageurs n Noise Traders Behavioral Finance Shleifer Jan 24 & 29, 2019

Utility Functions n “Expected Utility”, not Utility “Expected Value” n U = -e-(2λ)w wealth Behavioral Finance Shleifer Jan 24 & 29, 2019

Overlapping Generations Structure n All agents live two periods Born in period 1 and buy a portfolio (s, u) n Live (and die) in period 2 and consume n At time t n The (t-1) generation is in period 2 of their life n The (t) generation is in period 1 of their life n So, they “overlap” n t 1 Behavioral Finance t 2 Shleifer t 3 t 4 Jan 24 & 29, 2019

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 Shleifer Jan 24 & 29, 2019

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 Shleifer Jan 24 & 29, 2019

What is an “arbitrage trader” n Arbitrage traders “correctly” perceive the true distribution of pt+1. There is “systematic” error in estimation of future price, pt+1 n But, arbitrageurs face risk unrelated to the “true” distribution of pt+1 n 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 Shleifer Jan 24 & 29, 2019

Arbitrageurs expectations are “correct; ” noise traders expectations are “biased” Difference is ρt+1 Correct mean of pt+1 Behavioral Finance Shleifer Jan 24 & 29, 2019

The Price of the Risky Asset Taken from equation 2. 9 on page 37 in Shleifer’s “Inefficient Markets” Behavioral Finance Shleifer Jan 24 & 29, 2019

The Main Issues n What happens in equilbrium n Undetermined n Some forces make pt > 1, some forces push pt < 1, result is indeterminant n Who makes more profit, arbitrageurs or noise traders? Depends n But, it is perfectly possible for arbitrageurs to make more! n n Survival? Behavioral Finance Shleifer Jan 24 & 29, 2019

When Do Noise Traders Profit More Than Arbitrageurs? n Noise traders can earn more than arbitrageurs when ρ* is positive. (Meaning when noise traders are systematically too optimistic) n Why? n Because they relatively more of the risky asset than the arbitrageurs n But, if ρ* is too large, noise traders will not earn more than arbitrageurs n 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 Shleifer Jan 24 & 29, 2019

What Does Shleifer Accomplish? n Given two assets that are “fundamentally” identical, he shows a logic where the market fails to price them identically Assumes “systematic” noise trader activity n Shows conditions that lead to noise traders actually profiting from their noise trading n Shows why arbitrageurs could have trouble (even when there is no fundamental risk) n Behavioral Finance Shleifer Jan 24 & 29, 2019

The End Behavioral Finance Shleifer Jan 24 & 29, 2019