Risk-Return Optimization Flashcards
(10 cards)
1
Q
Portfolio expected return formula
A
E[r] = wᵀ·μ (weighted average of asset returns)
2
Q
Portfolio variance formula
A
Var(r) = wᵀ·V·w (weights and asset covariances)
3
Q
Mean-variance optimization goal
A
Minimize ½ wᵀ·V·w subject to E[r] ≥ α and Σw = 1
4
Q
First-order condition in MV
A
V·w* = λ₁·μ + λ₂·1 (trade-off of risk and return)
5
Q
Closed-form MV weights
A
w* = λ₁ V⁻¹μ + λ₂ V⁻¹1 with λ from a 2×2 system
6
Q
Coherent risk measure axioms
A
Monotonicity, Subadditivity, Homogeneity, Certainty invariance
7
Q
Capital Market Line (CML)
A
Return = r_f + θ(α − r_f), Risk = θ·σ*
8
Q
Sharpe ratio
A
(E[r] − r_f) / σ(r) (reward per unit risk)
9
Q
Value-at-Risk (VaR)
A
Loss quantile at confidence β; not subadditive
10
Q
Expected Shortfall (ES)
A
Average loss beyond VaR at confidence β; coherent
