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Macro Theory

by: Madie Schinner

Macro Theory ECN 200E

Madie Schinner
GPA 3.57

Kevin Salyer

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Kevin Salyer
Class Notes
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This 2 page Class Notes was uploaded by Madie Schinner on Tuesday September 8, 2015. The Class Notes belongs to ECN 200E at University of California - Davis taught by Kevin Salyer in Fall. Since its upload, it has received 43 views. For similar materials see /class/191858/ecn-200e-university-of-california-davis in Economcs at University of California - Davis.

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Date Created: 09/08/15
1 Derivation of eq 1079 in Ljungqvist amp Sar gent p 262 First7 LampS make the assumption that the returns and consumption growth follow the following process C 2 H Q P Emu 032 1 t 1r 1 1 exp Ei t1 70222 isb 2 It is assumed that the means of the innovations 6H1 are 0 And also that they are normally distributed The basic asset pricing equation is 18E lt1r 1 3 Using the assumed processes for the returns and consumption growth eqs 1 and 2 yields 1 1 FiElEexp6m1 7 0222 7 7ac1 7 TE2H 4 Note that eq1 has simply been raised to the power of 77 The term in braces can be written as Ezkt1 76c 1 0222 7032 5 That last two terms are constants De ne the variable as as t1 5it1 75w 6 Since 6239 and so are jointly normally distributed7 the mean and variance of ac Ext1 0 7 Z 7 27Cov Shea 8 This implies that the random variable expx1 is log normally distributed so using the formulas given in LampS we have 0U720 02 20272 C01 86 Eexpxt1 exp W 9 First re7writing eq4 as 1 1 772 EAWE exp ac1 exp 70222 7032 10 And using eq9 we have v 2 2 272 C v 1 1772E YeXp 027 79 27 0U5275c702227032 1 1 W EAW exp 7 1 7 032 7 7Cov 62569 11 which is eq1079 in LampS For i b ie riskless bonds7 C01 61769 0 Then7 taking logs and rearranging terms we have 0 Fb7ln 7lnEA7717 2 Notice the implications that this expression has for how risk aversion or intertemporal substitution and the variance of consumption have on the risk7 free rate For the risk premium7 we have rs 7 77b 7001 6569 Since 775 7 77b m 006 and C01 65 ac 0002197 this requires 7 m 27 which is too high 7 this is the equity premium puzzle


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