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)

Strategy	Risk Budget	Best Use Case
Equal risk contribution	Each asset 1/N	When you do not know which asset is best
Equity-tilted risk budget	Stocks 60%, bonds 30%, commodities 10%	When you want equities to contribute more risk
Dynamic risk budget	Adjust dynamically by signal strength	When you have market-timing ability

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:

optimizer	Display Name	Core Idea	Best Use Case
equal_volatility	Equal Volatility	Allocate weights by inverse volatility	Simple and effective baseline
risk_parity	Risk Parity	Equalize risk contribution while accounting for correlation	Long-term robust allocation
mean_variance	Mean-Variance	Maximize Sharpe ratio or minimize variance	When return forecasts are available
max_diversification	Maximum Diversification	Maximize the diversification ratio	When pursuing a low-correlation portfolio
turnover_aware	Turnover-Aware	Mean-variance utility with an L1 penalty on weight changes vs the previous rebalance	When trading costs matter; tune turnover_penalty to your data frequency

1. equal_volatility

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

Principle: w_i = (1/σ_i) / Σ(1/σ_j)

Parameter	Default	Description
lookback	60	Volatility calculation window (trading days)

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.

Parameter	Default	Description
lookback	60	Covariance-matrix estimation window

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.

Parameter	Default	Description
lookback	60	Window for estimating means and covariances
risk_free	0.0	Risk-free rate (annualized)

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).

Parameter	Default	Description
lookback	60	Calculation window

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.

Parameter	Default	Description
lookback	60	Calculation window
risk_aversion	1.0	Weight on the variance term (λ)
turnover_penalty	0.0	Weight on the L1 turnover term (γ); 0 reduces to the mean-variance baseline

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

Method	Trigger Condition	Advantages	Disadvantages
Periodic rebalancing	Fixed monthly / quarterly date	Simple, predictable trading cost	May miss or delay adjustments
Threshold trigger	Deviation from target weight > X%	Trades only when needed	Frequent trading in high-volatility markets
Volatility trigger	VIX / volatility breaks a threshold	Adapts to market regime	Parameter selection is difficult

Suggested Rebalancing Frequency

Asset Class	Suggested Frequency	Threshold
Equity portfolio	Monthly	±5%
Stock-bond mix	Quarterly	±10%
Global macro	Quarterly / semiannual	±10%
Cryptocurrency	Weekly / biweekly	±15% (high volatility)

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)

	CSI 300	CSI 500	Government Bonds	Gold	BTC
CSI 300	1.00	0.85	-0.15	0.05	0.10
CSI 500	0.85	1.00	-0.10	0.03	0.12
Government Bonds	-0.15	-0.10	1.00	0.20	-0.05
Gold	0.05	0.03	0.20	1.00	0.15
BTC	0.10	0.12	-0.05	0.15	1.00

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

Metric	Value
Expected annualized return	7.2%
Expected annualized volatility	8.5%
Expected Sharpe	0.85
Expected maximum drawdown	-12%

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