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)

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)

4. All-Weather Strategy

Bridgewater framework: allocate risk equally across economic environments.

Economic environment   Asset allocation
─────────              ─────────
Growth rising          Equities + commodities + corporate bonds
Growth falling         Government bonds + inflation-protected bonds
Inflation rising       Commodities + inflation-protected bonds + EM debt
Inflation falling      Equities + government bonds

Simplified allocation example for China-focused portfolios:
- 30% CSI 300 / CSI 500
- 40% government bonds / credit bonds
- 15% gold
- 15% commodities / REITs

Guide to the 5 Optimizers

Overview of the Built-In Optimizers

Configure them in config.json through optimizer and optimizer_params:

1. equal_volatility

{
  "optimizer": "equal_volatility",
  "optimizer_params": {
    "lookback": 60
  }
}

Principle: w_i = (1/σ_i) / Σ(1/σ_j)

Advantages: simple and fast, no return forecast required, no correlation matrix required.
Disadvantages: ignores cross-asset correlation.

2. risk_parity

{
  "optimizer": "risk_parity",
  "optimizer_params": {
    "lookback": 60
  }
}

Principle: solve for weights such that each asset contributes the same amount of risk.

Advantages: accounts for correlation, spreads risk more evenly, and is robust over long horizons.
Disadvantages: requires iterative solving and is sensitive to covariance estimates.

3. mean_variance

{
  "optimizer": "mean_variance",
  "optimizer_params": {
    "lookback": 60,
    "risk_free": 0.0
  }
}

Principle: Markowitz optimization that maximizes the Sharpe ratio.

Advantages: theoretically optimal (if inputs are accurate).
Disadvantages: extremely sensitive to inputs, prone to extreme weights, and often performs poorly out of sample.
Recommendation: do not make lookback too short (<30 easily overfits), and add upper/lower weight constraints.

4. max_diversification

{
  "optimizer": "max_diversification",
  "optimizer_params": {
    "lookback": 60
  }
}

Principle: maximize DR = (w'σ) / σ_p (the diversification ratio).

Advantages: does not require return forecasts and seeks true diversification.
Disadvantages: effectiveness is limited in highly correlated environments.

5. turnover_aware

{
  "optimizer": "turnover_aware",
  "optimizer_params": {
    "lookback": 60,
    "risk_aversion": 1.0,
    "turnover_penalty": 0.5
  }
}

Principle: minimize -w'μ + λ·w'Σw + γ·||w - w_prev||₁ subject to long-only, fully-invested weights — mean-variance utility with an L1 penalty on weight changes versus the previous rebalance, so the optimizer only trades when the expected improvement outweighs the (implicit) cost.

Advantages: dampens rebalancing churn, which usually dominates realized costs; the first rebalance is unpenalized so the cold start is undistorted.
Disadvantages: turnover_penalty is scale-sensitive to the return frequency of the input window — for daily returns even γ ≈ 0.5 strongly prefers holding still, so tune it per data frequency.

Optimizer Selection Decision Tree

Do you have return forecasts?
├── Yes → Do trading costs / churn matter?
│   ├── Yes → turnover_aware (tune turnover_penalty to data frequency)
│   └── No → mean_variance (remember to add constraints)
└── No → Do you need to account for correlation?
    ├── Yes → risk_parity (recommended default)
    └── No → Are volatility differences across assets large?
        ├── Yes → equal_volatility
        └── No → max_diversification

Rebalancing Strategy

Three Rebalancing Triggers

Suggested Rebalancing Frequency

Rebalancing in Backtests

Implement rebalancing logic in signal_engine.py:

# Periodic rebalancing example (every 20 trading days)
if bar_count % rebalance_freq == 0:
    # Recompute weights
    new_weights = calculate_target_weights(data_map)
    for code, weight in new_weights.items():
        signals[code].iloc[i] = weight

Cross-Asset Correlation Analysis

Typical Correlation Matrix (China-Focused Portfolio Example)

Key patterns:

• Negative stock-bond correlation is the foundation of allocation (but it does not always hold; in 2022 both stocks and bonds sold off)
• Gold has low correlation with equities and serves as a hedge
• BTC's correlation with traditional assets is unstable and tends to become positive in crises
• Large-cap versus small-cap China A-shares have high correlation (0.85), so diversification benefits are limited

Output Format

## Asset Allocation Recommendation

### Allocation Plan
| Asset | Weight | Risk Contribution | Expected Return (Annualized) |
|------|------|---------|--------------|
| CSI 300 | 30% | 45% | 8% |
| Government Bond ETF | 40% | 15% | 3% |
| Gold | 15% | 20% | 5% |
| BTC | 15% | 20% | 15% |

### Optimizer Configuration
```json
{
  "optimizer": "risk_parity",
  "optimizer_params": {"lookback": 60}
}

Expected Risk / Return

Rebalancing Rules

• Frequency: quarterly (first trading day of March / June / September / December)
• Threshold: trigger when any asset deviates from target by ±10%
• Cost: estimated annual trading cost 0.15%

## Notes

1. **The optimizer needs enough instruments**: at least 3 instruments are needed for meaningful optimization; with 2 instruments, `equal_volatility` is usually enough
2. **`lookback` window**: too short (`<20`) is noisy, too long (`>120`) reacts slowly, and 60 is a reasonable default
3. **`mean_variance` trap**: it is the easiest to overfit, and out-of-sample Sharpe is often cut by half or more
4. **Rebalancing cost**: frequent rebalancing eats into returns; for China A-share portfolios, stamp duty of 0.05% plus commissions is material
5. **Cross-market allocation**: use `"source": "auto"` in `config.json`, and let `codes` mix instruments from different markets
6. **Leverage constraint**: the sum of weights must be ≤ 1.0, and leverage is not allowed unless explicitly specified
7. **Survivorship bias**: historical correlations may be distorted by delistings and new listings