Week #1 Exercise 1, 2:

$r_t = \mu_{t-1} +\epsilon_t,$ $\mu_{t-1}=E[r_t|F_{t-1}]$

$r_{t,t+j} = \mu_{t,t+j} +\epsilon_{t,t+j},$ $\mu_{t,t+j}=E[r_{t,t+j}|F_{t-1}]$

Week #2 Exercise 1:

Markowitz Preferences: $E[U_i^{MV}]=E[r_W]-\frac{\gamma_i}{2}*Var(r_W)$

Week #2 A2:

Risk Decomposition for an equal weight portfolio:

$\sigma_p^2=\frac{1}{N^2}\sum_{i = 1}^{N}\sigma_i^2+\sum_{i = 1}^{N}\sum_{m = 1}^{N}\frac{1}{N}\frac{1}{N}\sigma_{i,m}$, i≠m

Week #2 Prof Cafe:

Certainty Equivalent: risk-free payoff that has same utility as E[U(w_T)]:

U(w_CE) ! = E[U(w_t)]

Risk premium: RP = E[w_t] - w_CE

Realtive risk premium: RRP = RP/inital wealth

Week#3 A2:

Sharpe Ratio: $SR=\frac{E[r_p]-r_f}{\sigma_p}$

Optimal Complete Portfolio: $y^=\frac{SR_{TP}}{\gamma_i\sigma_{TP}}$, $w_{CP}= y^**w_{TP}$, $w_{rf}= 1-y^*$

Models: