behavioral finance other noise trader models feb 3, 2015 behavioral finance economics 437

Behavioral Finance Other Noise Trader Models Feb 3, 2015

Behavioral Finance

Economics 437


US Oil Production Doubled in 5 Years


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)


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


Choices When Alternatives are Uncertain

Lotteries Choices Among Lotteries Maximize Expected Value Maximize Expected Utility Allais Paradox


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


Lotteries

A lottery has two things: A set of (dollar) outcomes: X1, X2, X3,…..XN

A set of probabilities: p1, p2, p3,…..pN

X1 with p1

X2 with p2

Etc. p’s are all positive and sum to one (that’s

required for the p’s to be probabilities)


For any lottery

We can define “expected value” p1X1 + p2X2 + p3X3 +……..pNXN

But “Bernoulli paradox” is a big, big weakness of using expected value to order lotteries

So, how do we order lotteries?


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)


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


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


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)


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)


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)


The End

behavioral finance other noise trader models feb 3, 2015 behavioral finance economics 437

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