asset-allocation

name	asset-allocation
description	Asset allocation theory and optimizer usage — MPT / Black-Litterman / risk budgeting / all-weather strategy, including guides for 4 optimizers and rebalancing rules.
category	asset-class

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 4 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

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.

Optimizer Selection Decision Tree

Do you have return forecasts?
├── Yes → 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