Ambiguity Aversion, Puzzles, and LRR Flashcards
Define relative entropy (two definitions, for ambiguity aversion not AJ bounds)
=\hatE[log(\hatpi/pi)]
=E[\hat pi / pi log \hat pi / pi]
What is the ambiguity problem? Define g_t+1
expected martingale consumption, minimizing g_s subject to relative entropy. Take c as random walk.
What is malevolent demon’s first order condition (write down minimization problem, be, lagrange, then foc)
Radon Nikodym derivative is CARA value function over expected CARA of value function.
Distort relative to average.
When is the ambiguity model more pessimistic?
Higher consumption volatility or when entropy penalty is smaller.
Name the three puzzles of CBAP
1) Equity premium puzzle–high curvature; 2) Equity volatility puzzle–consumption not volatile enough (think power utility); 3) Riskfree rate puzzle (high aversion leads to high risk free)
Describe LRR solution–what type of RP and time series?
Use CCAPM+ approach to equity premium with persistent consumption growth changes.
\Delta c_t+1 = x_t + eps_t+1
x_t random walk
sigma_t+1 depends on previous sigma.
When does higher volatility lead to lower consumption in CCAPM+? What is the exact algebra?
gamma and psi > 1. (1-gamma)(1-psi^-1)sigma^2/2f
What does gamma > 1 imply about an increase in volatility?
Deterioration in investment opportunities.
What does psi > 1 imply about an increase in volatility?
Improvement in investment opportunities leads to lower consumption relative to wealth (elastic!)
What is the risk premium of the rare disasters model? (relative to lambda and gamma)
er(lambda) = time rate of preference - cumulant(lambda - \gamma)+c(\lambda)
Define c(\theta), the CGF both ways. What is X?
=\log E \exp(\theta X)
=\sum moment_n * \theta ^n / n!
X is log consumption growth
How to get time-varying RP in rare disasters?
changing perceived probability of disaster (Wachter) or consequences of disaster “resilience rate” (Gabaix)
