asset-allocation

Asset Allocation and Portfolio Optimization

Overview

From asset allocation theory to practical implementation, this skill covers classical frameworks (MPT, BL, risk budgeting, all-weather) and the usage of the four optimizers built into this system. The output can be written directly into config.json.

Asset Allocation Theory

1. Modern Portfolio Theory (MPT, Markowitz)

Core idea: maximize expected return for a given level of risk (the efficient frontier).

Optimization problem:
min  w'Σw              (portfolio variance)
s.t. w'μ = target_return
     Σw = 1
     w ≥ 0              (no shorting)

Advantages	Disadvantages
Mathematically rigorous	Extremely sensitive to inputs (garbage in, garbage out)
Efficient frontier is visualizable	Concentrated-allocation problem (often produces extreme weights)
Foundational framework	Assumes normality and ignores fat tails

Practical advice: do not use raw MPT directly. Add constraints (upper/lower bounds, sector limits) or use a regularized version.

2. Black-Litterman Model

Core idea: start from market equilibrium and incorporate investor views.

Steps:
1. Reverse-imply market equilibrium returns: π = δΣw_mkt
2. Build the view matrices: P (selection matrix), Q (view returns), Ω (view uncertainty)
3. Blend the posterior: μ_BL = [(τΣ)^-1 + P'Ω^-1 P]^-1 [(τΣ)^-1 π + P'Ω^-1 Q]
4. Run Markowitz optimization using posterior μ_BL

Example views:

• Absolute view: "China A-shares will return 10% over the next year" → P=[1,0,0], Q=[0.10]
• Relative view: "China A-shares will outperform US equities by 5%" → P=[1,-1,0], Q=[0.05]

Parameter guidance:

• τ (uncertainty scaling): 0.025-0.05
• Ω: set according to view confidence, where higher confidence = smaller variance

3. Risk Budgeting

Core idea: allocate by risk contribution rather than by capital share.

Risk contribution: RC_i = w_i × (Σw)_i / σ_p
Target: RC_i / σ_p = budget_i  (for all i)