Present Value Relations

Question 1

Three types of efficiency:

Answer 1

1) Weak form: past returns
2) Semi-strong form: past publicly available information
3) Strong form efficiency: past information, even if only private

Question 2

Shiller critique of EMH

Answer 2

returns are not the same as prices.

Question 3

Write price as present value for K periods

Answer 3

P_t = E_t [\sum _k=1^K R^-k D_t+k]+E_t[R^-KP_t+K]

Question 4

GG model

Answer 4

D/P=R-G

Question 5

Bubble is a stochastic process satisfying

Answer 5

B_t = E_t[B_t+1/R]

Question 6

When do bubbles not exist

Answer 6

finite periods and limits on price

Question 7

Write down CS approximation for returns

Answer 7

r_t+1 \approx k + \rho p_t+1 + (1-\rho)d_t+1 - p_t

Question 8

Write down CS approximation for prices

Answer 8

p_t = \frac{k}{1-\rho}+\sum_j=0^\infty \rho^j[(1-\rho)d_t+1+j-r_t+1+j]

Question 9

When does CS hold?

Answer 9

All expectations that respect identities

Question 10

Write down GG CS approximation

Answer 10

d_t - p_t = -k(1-\rho)_E_t[\sum_j=0^\infty -\Delta d_t+1+j + r_t+1+j

Question 11

Write down innovation to returns

Answer 11

r_t+1-E_tr_t+1 = (E_t+1-E_t)\sum_j=0^\infty \rho^j\Delta d_t+1+j - (E_t+1-E_t)\sum_j=1^\infty \rho^j r_t+1+j

Question 12

Drifting SS GG model

Answer 12

E_t (R_t+1)=D_t+1/P_t + \exp(E_t g_t+1)+1/2Var_t(r_t+1)