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 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`

```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.

### Optimizer Selection Decision Tree

```
Do you have return forecasts?
├── Yes → mean_variance (reme