# 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: ConsumptionImplicationsSubstitutionRisk PremiumRandom VariableRisk-Free Rate

## Sample Document Text

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 ª (1) 1+r i t+1 = ¡ 1+¯r i ¢ exp © ? i,t+1 ?? 2 i /2 ª ; 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 "Ã 1+r i t+1 µ 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 ¢¤ª (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...