Econ 215 Chapter 6

Econ 215 Chapter 6 - Chapter 6 The Efficient Market...

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Chapter 6 The Efficient Market Hypothesis
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Conditional Probability Conditional probability allows the probability distribution to change according to the available information. Let Ω denote the available information. Then the co nditional probability distribution of a random variable X given the information Ω is denoted by ( ) : ( ) Ω = = p x P X x
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Conditional probability distributions have the same mathematical properties as unconditional probability distributions: (1) (2) 0 ( ) 1 p x Ω ≤ ( ) 1 x p x Ω =
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Example Suppose the information is the outcome of a coin toss, say Ω =1 or Ω = 0. Then there are two conditional probability distributions for X, say the distributions in the following table: x 4% 5% 6% 7% p(x|1) 0.25 0.25 0.25 0.25 p(x|0) 0.1 0.2 0.3 0.4
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Independence If the conditional probability distribution of X does not depend on the value of the information Ω, then we say that X is independent of Ω. In the previous example, X is not independent of Ω. In the next example, X is independent of Ω.
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Example x 4% 5% 6% 7% p(x|1) 0.25 0.25 0.25 0.25 p(x|0) 0.25 0.25 0..25 0.25 In this example, knowing the information about Ω is irrelevant to the probability distribution of X.
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Conditional Expectation The expectation of a random variable with respect to a conditional probability distribution is called its conditional expectation . Thus, we write The conditional variance can be defined in a similar way, but we do not need it here. ( | ) : ( | ) Ω = x E X xp x
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Example (continued): ( | 1) (4 .25) (5 .25) (6 .25) (7 .25) 5.5% Ω = = + + + = E X ( | 0) (4 .1) (5 .2) (6 .3) (7 .4) 6% Ω = = + + + = E X
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Rational Expectations An agent has rational beliefs provided that his degree of belief is measured by a probability distribution. An agent has rational expectations provided that his expectations are calculated as mathematical expectation.
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Rational Expectations Hypothesis REH was originally proposed by John Muth (1961) REH asserts that market expectations are rational and they are fulfilled in market equilibrium. Any deviations from equilibrium are caused by random shocks (e.g. the news).
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Robert Lucas Jr. University of Chicago Economist 1995 Nobel Laureate in Economics Champion of REH
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Allocative efficiency refers the ability of market prices to achieve maximal output with minimal input (e.g. price = marginal cost). Informational efficiency
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Econ 215 Chapter 6 - Chapter 6 The Efficient Market...

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