Epstein-Zin Preferences Flashcards
Definition of EIS (write algebra)
elasticity of change in consumption w.r.t gross risk free
No risk Euler for EZ preferences
1=\beta R_f,t (C_{t+1}/C_t)^{-\psi^-1}
Euler equation for EZ
q_s= \beta \pi(s) (C_{s}/C_0)^{-\psi^-1} E[V_(w,s’)^{1-\gamma}]^((1-\theta)/\theta)/(V_w,0)^{etc.})
When is there early resolution for uncertainty?
theta>1 (note that 1-psi^-1 < 0, so adjust ineq twice)
When does EZ reduce to risk sensitive recursion?
psi=1 and theta\rightarrow +\infty
What happens when psi=1?
c-w constant
What happens when gamma=1?
Myopic portfolio choice (growth optimal, not sensitive to future investment options)
Relationship between psi and gamma under power?
psi = 1/gamma
Relationship between psi and gamma under log?
psi=gamma=1
When is EZ returns CCAPM? Write it down
theta = 1. RP equals theta sigma_ic / psi + (1-\theta)*sigma_iw
When is EZ returns static CAPM?
theta = 0. RP equals sigma_iw
Write down ICAPM and the takeaway (only depends on gamma). What is sigma_ih?
gamma sigma_iw + (gamma-1)\sigma_ih. Depends on changes to investment opportunity (higher than 1 loads on investments) ih.
sigma_ih: covariation with future returns on wealth
CCAPM+ (what does it depend on?) When is it CCAPM? What is sigma_ig?
\gamma\sigma_ic + (gamma - psi^-1)\sigma_ig;
becomes CCAPM when gamma = 1/psi (as in power util)
What is sigma_ig: covariation with future consumption growth.
Flow budget constraint (eat the pie)
W_t+1=R_w,t+1(W_t-C_t)
Flow budget constraint (eat the pie)
W_t+1=R_w,t+1(W_t-C_t)
