1. Behavioral Finance Other Noise Trader Models Feb 3, 2015 Behavioral Finance Economics 437

2. Behavioral Finance Other Noise Trader Models Feb 3, 2015 US Oil Production Doubled in 5 Years

3. Behavioral Finance Other Noise Trader Models Feb 3, 2015 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)

4. Behavioral Finance Other Noise Trader Models Feb 3, 2015 Are There Other Noise Trader Models? Yes Broadly, two kinds NT models Momentum models (whatever the stock price has been, it will continue to do Feedback models (exhibiting the effect of a higher {than efficient} stock price on economic behavior, including work effort, investment, etc. Problem: most interesting thing is “turning points”; not really addressed well in this literature

5. Behavioral Finance Other Noise Trader Models Feb 3, 2015 Choices When Alternatives are Uncertain Lotteries Choices Among Lotteries Maximize Expected Value Maximize Expected Utility Allais Paradox

6. Behavioral Finance Other Noise Trader Models Feb 3, 2015 What happens with uncertainty Suppose you know all the relevant probabilities Which do you prefer? 50 % chance of $ 100 or 50 % chance of $ 200 25 % chance of $ 800 or 75 % chance of zero

7. Behavioral Finance Other Noise Trader Models Feb 3, 2015 Lotteries A lottery has two things: A set of (dollar) outcomes: X 1, X 2, X 3,…..X N A set of probabilities: p 1, p 2, p 3,…..p N X 1 with p 1 X 2 with p 2 Etc. p’s are all positive and sum to one (that’s required for the p’s to be probabilities)

8. Behavioral Finance Other Noise Trader Models Feb 3, 2015 For any lottery We can define “expected value” p 1 X 1 + p 2 X 2 + p 3 X 3 +……..p N X N But “Bernoulli paradox” is a big, big weakness of using expected value to order lotteries So, how do we order lotteries?

9. Behavioral Finance Other Noise Trader Models Feb 3, 2015 For any two lotteries, calculate Expected Utility II p U(X) + (1 – p) U(Y) q U(S) + (1 – q) U(T) U(X) is the utility of X when X is known for certain; similar with U(Y), U(S), U(T)

10. Behavioral Finance Other Noise Trader Models Feb 3, 2015 Allais Paradox Choice of lotteries Lottery A: sure $ 1 million Or, Lottery B: 89 % chance of $ 1 million 1 % chance of zero 10 % chance of $ 5 million Which would you prefer? A or B

11. Behavioral Finance Other Noise Trader Models Feb 3, 2015 Now, try this: Choice of lotteries Lottery C 89 % chance of zero 11 % chance of $ 1 million Or, Lottery D: 90 % chance of zero 10 % chance of $ 5 million Which would you prefer? C or D

12. Behavioral Finance Other Noise Trader Models Feb 3, 2015 Back to A and B Choice of lotteries Lottery A: sure $ 1 million Or, Lottery B: 89 % chance of $ 1 million 1 % chance of zero 10 % chance of $ 5 million If you prefer B to A, then.89 (U ($ 1M)) +.10 (U($ 5M)) > U($ 1 M) Or.10 *U($ 5M) >.11*U($ 1 M)

13. Behavioral Finance Other Noise Trader Models Feb 3, 2015 And for C and D Choice of lotteries Lottery C 89 % chance of zero 11 % chance of $ 1 million Or, Lottery D: 90 % chance of zero 10 % chance of $ 5 million If you prefer C to D: Then.10*U($ 5 M) <.11*U($ 1M)

14. Behavioral Finance Other Noise Trader Models Feb 3, 2015 So, if you prefer B to A and C to D It must be the case that:.10 *U($ 5M) >.11*U($ 1 M) And.10*U($ 5 M) <.11*U($ 1M)

15. Behavioral Finance Other Noise Trader Models Feb 3, 2015 The End