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) ``` | 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` ```json { "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` ```json { "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` ```json { "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` ```json { "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` ```json { "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`: ```python # 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 ```markdown ## 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