1. Behavioral Finance Law Of One Price Feb 4-9 2016 Behavioral Finance Economics 437

2. 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? 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)

3. 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

4. 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

5. 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

6. 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

7. 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 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

8. 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

9. 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

10. 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)

11. 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

12. 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)

13. Behavioral Finance Law Of One Price Feb 4-9 2016 Question Can s and u trade at different prices? If yes, EMH is false

14. Behavioral Finance Law Of One Price Feb 4-9 2016 The players Arbitrageurs Noise Traders

15. Behavioral Finance Law Of One Price Feb 4-9 2016 Utility Functions “Expected Utility”, not “Expected Value” U = -e -(2λ)w wealth Utility

16. 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” t1t1 t2t2 t3t3 t4t4

17. Behavioral Finance Law Of One Price Feb 4-9 2016 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

18. Behavioral Finance Law Of One Price Feb 4-9 2016 What is a noise trader? P t+1 is the price of the risky asset at time t+1 Ρ t+1 is the “mean misperception” of p t+! Ρ t+!

19. Behavioral Finance Law Of One Price Feb 4-9 2016 What is an “arbitrage trader” Arbitrage traders “correctly” perceive the true distribution of p t+1. There is “systematic” error in estimation of future price, p t+1 But, arbitrageurs face risk unrelated to the “true” distribution of p t+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

20. Behavioral Finance Law Of One Price Feb 4-9 2016 Arbitrageurs expectations are “correct;” noise traders expectations are “biased” Correct mean of p t+1 Difference is ρ t+1

21. Behavioral Finance Law Of One Price Feb 4-9 2016 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?

22. 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

23. 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 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)

24. Behavioral Finance Law Of One Price Feb 4-9 2016 The End