# lecture12 - Lecture 12 Equity-Premium Puzzle Preferences...

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ECN/APEC 7240 XII - 2 Preferences Consider a representative-agent model where the consumer maximizes The period utility function u has the usual probabilities and β (0, 1). E t is the expectation operator conditional on all information available at t . . ) ~ ( 0 = + j j t t t c u E
ECN/APEC 7240 XII - 3 Return Condition If R j is the return on asset j , we have shown it must satisfy This condition imposes strong testable conditions on the comovements of consumption and asset returns. . ~ ) ( ' ) ~ ( ' 1 1 1 = + + t j t t t R c u c u E β

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ECN/APEC 7240 XII - 4 Two Assets We focus on two assets: 1. Risk-free bond—purchased at t for the price R t -1 it pays one unit of consumption at t + 1 with certainty. 2. Equity—purchased at t for the price p t , a unit of equity confers ownership of a future stream of dividends { y s } t=s +1 .
ECN/APEC 7240 XII - 5 Budget Constraint • Let L t represent purchases of the bond, which are negative if you issue the bond. • Let N t represent holdings of the equity, which are negative if selling short. 1 1 1 ) ( - - - + + = + + t t t t t t t t t N y p L N p L R c

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ECN/APEC 7240 XII - 6 Asset Returns The return on the equity is The return conditions imply . 1 1 1 t t t t e p y p R + + + + = = + t t t t R c u c u E ) ( ' ) ~ ( ' 1 1 β + = + + + t t t t t t p y p c u c u E 1 1 1 ~ ~ ) ( ' ) ~ ( '
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lecture12 - Lecture 12 Equity-Premium Puzzle Preferences...

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