Portfolio Optimization GuideSAFE

🔬 A curated collection of 23,000+ agent skills for empirical research across 8 social science disciplines. | 精选 23,000+ AI Agent 技能库,覆盖8大社会科学学科的实证研究。CoPaper.AI 20分钟完成一篇可复现的规范实证论文,并支持用户上传 Skills。-- Maintained by CoPaper.AI from Stanford REAP.

The instruction file, verbatim from the audited commit — this is the text the model reads, and the surface the audit's instruction layer examines. Quoted here so you can judge it without cloning anything.

---
name: portfolio-optimization-guide
description: "Portfolio theory, optimization algorithms, and asset allocation methods"
metadata:
  openclaw:
    emoji: "💼"
    category: "domains"
    subcategory: "finance"
    keywords: ["portfolio", "optimization", "markowitz", "asset-allocation", "mean-variance", "black-litterman"]
    source: "wentor"
---

# Portfolio Optimization Guide

A skill for implementing and researching portfolio optimization methods, from classical mean-variance optimization to modern robust and factor-based approaches. Covers Markowitz theory, Black-Litterman, risk parity, and machine learning-enhanced portfolio construction.

## Mean-Variance Optimization

### Classical Markowitz Portfolio

```python
import numpy as np
from scipy.optimize import minimize

def mean_variance_optimize(expected_returns: np.ndarray,
                             cov_matrix: np.ndarray,
                             target_return: float = None,
                             risk_free_rate: float = 0.02) -> dict:
    """
    Markowitz mean-variance optimization.
    expected_returns: array of expected returns for each asset
    cov_matrix: covariance matrix of asset returns
    target_return: target portfolio return (None for max Sharpe)
    """
    n_assets = len(expected_returns)

    def portfolio_volatility(weights):
        return np.sqrt(weights @ cov_matrix @ weights)

    def neg_sharpe(weights):
        ret = weights @ expected_returns
        vol = portfolio_volatility(weights)
        return -(ret - risk_free_rate) / vol

    # Constraints
    constraints = [
        {"type": "eq", "fun": lambda w: np.sum(w) - 1},  # weights sum to 1
    ]
    if target_return is not None:
        constraints.append(
            {"type": "eq", "fun": lambda w: w @ expected_returns - target_return}
        )

    # Bounds: no short selling (0 to 1 per asset)
    bounds = [(0, 1) for _ in range(n_assets)]

    # Initial guess: equal weight
    w0 = np.ones(n_assets) / n_assets

    if target_return is not None:
        # Minimize volatility for given return
        result = minimize(portfolio_volatility, w0,
                         bounds=bounds, constraints=constraints)
    else:
        # Maximize Sharpe ratio
        result = minimize(neg_sharpe, w0,
                         bounds=bounds, constraints=constraints)

    weights = result.x
    ret = weights @ expected_returns
    vol = portfolio_volatility(weights)

    return {
        "weights": {f"asset_{i}": round(w, 4) for i, w in enumerate(weights)},
        "expected_return": round(ret, 4),
        "volatility": round(vol, 4),
        "sharpe_ratio": round((ret - risk_free_rate) / vol, 4),
    }
```

### Efficient Frontier

```python
def compute_efficient_frontier(expected_returns: np.ndarray,
                                 cov_matrix: np.ndarray,
                                 n_points: int = 50) -> list[dict]:
    """
    Compute the efficient frontier by solving for minimum variance
    portfolios at each target return level.
    """
    min_ret = expected_returns.min() * 0.8
    max_ret = expected_returns.max() * 1.1
    target_returns = np.linspace(min_ret, max_ret, n_points)

    frontier = []
    for target in target_returns:
        try:
            result = mean_variance_optimize(
                expected_returns, cov_matrix, target_return=target
            )
            frontier.append({
                "return": result["expected_return"],
                "volatility": result["volatility"],
                "sharpe": result["sharpe_ratio"],
            })
        except Exception:
            continue

    return frontier
```

## Black-Litterman Model

### Incorporating Investor Views

```python
def black_litterman(market_cap_weights: np.ndarray,
                      cov_matrix: np.ndarray,
                      P: np.ndarray,
                      Q: np.ndarray,
                      omega: np.ndarray = None,
                      risk_aversion: float = 2.5,
                      tau: float = 0.05) -> dict:
    """
    Black-Litterman model for combining market equilibrium with
    investor views.
    market_cap_weights: market-cap weighted portfolio
    cov_matrix: covariance matrix
    P: pick matrix (k views x n assets), identifies assets in each view
    Q: view returns (k x 1), expected returns for each view
    omega: view uncertainty (k x k), diagonal matrix
    """
    # Step 1: Implied equilibrium returns (reverse optimization)
    pi = risk_aversion * cov_matrix @ market_cap_weights

    # Step 2: View uncertainty (if not provided, use He-Litterman)
    if omega is None:
        omega = np.diag(np.diag(tau * P @ cov_matrix @ P.T))

    # Step 3: Posterior expected returns
    tau_sigma = tau * cov_matrix
    inv_tau_sigma = np.linalg.inv(tau_sigma)
    inv_omega = np.linalg.inv(omega)

    posterior_precision = inv_tau_sigma + P.T @ inv_omega @ P
    posterior_cov = np.linalg.inv(posterior_precision)
    posterior_mean = posterior_cov @ (inv_tau_sigma @ pi + P.T @ inv_omega @ Q)

    return {
        "equilibrium_returns": pi.round(4).tolist(),
        "posterior_returns": posterior_mean.round(4).tolist(),
        "posterior_covariance": posterior_cov.round(6).tolist(),
    }
```

## Risk Parity

### Equal Risk Contribution Portfolio

```python
def risk_parity(cov_matrix: np.ndarray, budget: np.ndarray = None) -> dict:
    """
    Risk parity: each asset contributes equally to total portfolio risk.
    budget: risk budget (default: equal, 1/n each)
    """
    n = cov_matrix.shape[0]
    if budget is None:
        budget = np.ones(n) / n

    def objective(weights):
        portfolio_vol = np.sqrt(weights @ cov_matrix @ weights)
        marginal_risk = cov_matrix @ weights
        risk_contribution = weights * marginal_risk / portfolio_vol
        target_risk = budget * portfolio_vol
        return np.sum((risk_contribution - target_risk) ** 2)

    constraints = [{"type": "eq", "fun": lambda w: np.sum(w) - 1}]
    

SAFEgrade B · trust 89/100 Nothing in the source contradicts what it says it does. Grade A is reserved for packages that have also passed the behavioural sandbox.

What the source does

Filesystem

none-observed

Network

none-observed

Shell

none-observed

Dependencies

pinned

Secrets in source

none-found

Findings (0)

No findings outside the package's declared scope.

Gates applied: no_behavioural_pass.