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Lecture Notes for ECN 200E - Macro Theory with Salyer at UC Davis (UCD)

Notes Information

Material Type:Note
Professor:Salyer
Class:ECN 200E - Macro Theory
Subject:Economics
University:University of California - Davis
Term:--
Keywords:
  • Consumption
  • Implications
  • Substitution
  • Risk Premium
  • Random Variable
  • Risk-Free Rate
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1 Derivation of eq. (10.79) in Ljungqvist & Sar- gent - p. 262 First, L&S make the assumption that the returns and consumption growth follow the following process: c t+1 c t =c ? exp ? c,t+1 ?? 2 c /2 (1) 1+r i t+1 = 1+r i exp ? i,t+1 ?? 2 i /2 ; i = s,b (2) It is assumed that the means of the innovations (? t+1 ) are 0. And also that they are normally distributed. The basic asset pricing equation is: 1=?E " 1+r i t+1 c t+1 c t ?? !# (3) Using the assumed processes for the returns and consumption growth (eqs. (1) and (2) yields: 1=? 1+r i c ?? ? E exp ? i,t+1 ?? 2 i /2?? ? c,t+1 ?? 2 c /2 (4) Note that eq.(1) has simply been raised to the power of ??.Thetermin braces can be written as: ? i,t+1 ??? c,t+1 ?? 2 i /2+?? 2 c /2 (5) That last two terms are constants. Define the variable x as: x t+1 = ? i,t+1 ??? c,t+1 (6) Since ? i and ? c are jointly normally distributed...
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