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Optimization API

PortfolioOptimizer

Portfolio optimization using various strategies.

Supports Maximum Sharpe Ratio, Minimum Volatility, Risk Parity, and Target Return optimization strategies.

Parameters:

Name Type Description Default
data DataFrame

Historical price data with datetime index

 required
risk_free_rate float

Annual risk-free rate

 0.02

Examples:

>>> optimizer = PortfolioOptimizer(data, risk_free_rate=0.02)
>>> optimal = optimizer.optimize_max_sharpe()
>>> print(f"Optimal weights: {optimal['weights']}")
>>> optimizer.plot_efficient_frontier()
Source code in portfolio_analysis/analysis/optimization.py 
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class PortfolioOptimizer:
    """
    Portfolio optimization using various strategies.

    Supports Maximum Sharpe Ratio, Minimum Volatility, Risk Parity,
    and Target Return optimization strategies.

    Parameters
    ----------
    data : pd.DataFrame
        Historical price data with datetime index
    risk_free_rate : float, default 0.02
        Annual risk-free rate

    Examples
    --------
    >>> optimizer = PortfolioOptimizer(data, risk_free_rate=0.02)
    >>> optimal = optimizer.optimize_max_sharpe()
    >>> print(f"Optimal weights: {optimal['weights']}")
    >>> optimizer.plot_efficient_frontier()
    """

    TRADING_DAYS = TRADING_DAYS_PER_YEAR

    def __init__(
        self, data: pd.DataFrame, risk_free_rate: float = DEFAULT_RISK_FREE_RATE
    ):
        self.data = data
        self.risk_free_rate = risk_free_rate
        self.n_assets = len(data.columns)
        self.tickers = list(data.columns)

        # Calculate returns and covariance
        self.returns = data.pct_change().dropna()
        self.mean_returns = self.returns.mean() * self.TRADING_DAYS
        self.cov_matrix = self.returns.cov() * self.TRADING_DAYS

    def _portfolio_return(self, weights: np.ndarray) -> float:
        """Calculate portfolio expected return."""
        return np.dot(weights, self.mean_returns)

    def _portfolio_volatility(self, weights: np.ndarray) -> float:
        """Calculate portfolio volatility."""
        return np.sqrt(np.dot(weights.T, np.dot(self.cov_matrix, weights)))

    def _portfolio_sharpe(self, weights: np.ndarray) -> float:
        """Calculate portfolio Sharpe ratio."""
        ret = self._portfolio_return(weights)
        vol = self._portfolio_volatility(weights)
        return (ret - self.risk_free_rate) / vol

    def _neg_sharpe(self, weights: np.ndarray) -> float:
        """Negative Sharpe for minimization."""
        return -self._portfolio_sharpe(weights)

    def optimize_max_sharpe(self, weight_bounds: tuple[float, float] = (0, 1)) -> dict:
        """
        Find the portfolio with maximum Sharpe ratio.

        Parameters
        ----------
        weight_bounds : tuple, default (0, 1)
            Min and max weight for each asset

        Returns
        -------
        dict
            Optimal weights, return, volatility, and Sharpe ratio
        """
        constraints = {"type": "eq", "fun": lambda x: np.sum(x) - 1}
        bounds = tuple(weight_bounds for _ in range(self.n_assets))
        initial_weights = np.array([1 / self.n_assets] * self.n_assets)

        result = minimize(
            self._neg_sharpe,
            initial_weights,
            method="SLSQP",
            bounds=bounds,
            constraints=constraints,
        )

        optimal_weights = result.x
        return {
            "weights": dict(zip(self.tickers, optimal_weights)),
            "return": self._portfolio_return(optimal_weights),
            "volatility": self._portfolio_volatility(optimal_weights),
            "sharpe_ratio": self._portfolio_sharpe(optimal_weights),
        }

    def optimize_min_volatility(
        self, weight_bounds: tuple[float, float] = (0, 1)
    ) -> dict:
        """
        Find the minimum volatility portfolio.

        Parameters
        ----------
        weight_bounds : tuple, default (0, 1)
            Min and max weight for each asset

        Returns
        -------
        dict
            Optimal weights, return, volatility, and Sharpe ratio
        """
        constraints = {"type": "eq", "fun": lambda x: np.sum(x) - 1}
        bounds = tuple(weight_bounds for _ in range(self.n_assets))
        initial_weights = np.array([1 / self.n_assets] * self.n_assets)

        result = minimize(
            self._portfolio_volatility,
            initial_weights,
            method="SLSQP",
            bounds=bounds,
            constraints=constraints,
        )

        optimal_weights = result.x
        return {
            "weights": dict(zip(self.tickers, optimal_weights)),
            "return": self._portfolio_return(optimal_weights),
            "volatility": self._portfolio_volatility(optimal_weights),
            "sharpe_ratio": self._portfolio_sharpe(optimal_weights),
        }

    def optimize_target_return(
        self, target_return: float, weight_bounds: tuple[float, float] = (0, 1)
    ) -> dict:
        """
        Find minimum volatility portfolio for a target return.

        Parameters
        ----------
        target_return : float
            Target annual return
        weight_bounds : tuple, default (0, 1)
            Min and max weight for each asset

        Returns
        -------
        dict
            Optimal weights, return, volatility, and Sharpe ratio
        """
        constraints = [
            {"type": "eq", "fun": lambda x: np.sum(x) - 1},
            {"type": "eq", "fun": lambda x: self._portfolio_return(x) - target_return},
        ]
        bounds = tuple(weight_bounds for _ in range(self.n_assets))
        initial_weights = np.array([1 / self.n_assets] * self.n_assets)

        result = minimize(
            self._portfolio_volatility,
            initial_weights,
            method="SLSQP",
            bounds=bounds,
            constraints=constraints,
        )

        optimal_weights = result.x
        return {
            "weights": dict(zip(self.tickers, optimal_weights)),
            "return": self._portfolio_return(optimal_weights),
            "volatility": self._portfolio_volatility(optimal_weights),
            "sharpe_ratio": self._portfolio_sharpe(optimal_weights),
        }

    def optimize_risk_parity(self) -> dict:
        """
        Find the risk parity portfolio (equal risk contribution).

        Each asset contributes equally to total portfolio risk.

        Returns
        -------
        dict
            Optimal weights, return, volatility, and Sharpe ratio
        """

        def risk_contribution(weights):
            """Calculate risk contribution of each asset."""
            port_vol = self._portfolio_volatility(weights)
            marginal_contrib = np.dot(self.cov_matrix, weights)
            risk_contrib = weights * marginal_contrib / port_vol
            return risk_contrib

        def risk_parity_objective(weights):
            """Objective: minimize deviation from equal risk contribution."""
            rc = risk_contribution(weights)
            target_rc = np.mean(rc)
            return np.sum((rc - target_rc) ** 2)

        constraints = {"type": "eq", "fun": lambda x: np.sum(x) - 1}
        bounds = tuple((0.01, 1) for _ in range(self.n_assets))  # Min 1% per asset
        initial_weights = np.array([1 / self.n_assets] * self.n_assets)

        result = minimize(
            risk_parity_objective,
            initial_weights,
            method="SLSQP",
            bounds=bounds,
            constraints=constraints,
        )

        optimal_weights = result.x
        return {
            "weights": dict(zip(self.tickers, optimal_weights)),
            "return": self._portfolio_return(optimal_weights),
            "volatility": self._portfolio_volatility(optimal_weights),
            "sharpe_ratio": self._portfolio_sharpe(optimal_weights),
            "risk_contributions": dict(
                zip(self.tickers, risk_contribution(optimal_weights))
            ),
        }

    def generate_efficient_frontier(
        self, n_points: int = 50, weight_bounds: tuple[float, float] = (0, 1)
    ) -> pd.DataFrame:
        """
        Generate points on the efficient frontier.

        Parameters
        ----------
        n_points : int, default 50
            Number of points to generate
        weight_bounds : tuple, default (0, 1)
            Min and max weight for each asset

        Returns
        -------
        pd.DataFrame
            DataFrame with return, volatility, and Sharpe for each point
        """
        # Find return range
        min_vol = self.optimize_min_volatility(weight_bounds)
        _max_sharpe = self.optimize_max_sharpe(weight_bounds)  # noqa: F841

        min_ret = min_vol["return"]
        max_ret = max(self.mean_returns)

        target_returns = np.linspace(min_ret, max_ret, n_points)

        frontier = []
        failed_count = 0
        for target in target_returns:
            try:
                portfolio = self.optimize_target_return(target, weight_bounds)
                frontier.append(
                    {
                        "return": portfolio["return"],
                        "volatility": portfolio["volatility"],
                        "sharpe_ratio": portfolio["sharpe_ratio"],
                    }
                )
            except (ValueError, RuntimeError) as e:
                # Optimization may fail for extreme target returns
                failed_count += 1
                logger.debug(f"Optimization failed for target return {target:.4f}: {e}")
                continue

        if failed_count > 0:
            warnings.warn(
                f"Optimization failed for {failed_count}/{n_points} target returns. "
                "This is normal for extreme values at the frontier edges.",
                stacklevel=2,
            )

        if len(frontier) == 0:
            raise OptimizationError(
                "Failed to generate any points on the efficient frontier. "
                "Check that your data is valid and has sufficient history."
            )

        return pd.DataFrame(frontier)

    def plot_efficient_frontier(
        self,
        n_points: int = 50,
        show_assets: bool = True,
        show_optimal: bool = True,
        weight_bounds: tuple[float, float] = (0, 1),
        show: bool = True,
    ) -> plt.Figure:
        """
        Plot the efficient frontier with optimal portfolios marked.

        Parameters
        ----------
        n_points : int, default 50
            Number of points on the frontier
        show_assets : bool, default True
            Show individual assets
        show_optimal : bool, default True
            Mark optimal portfolios (max Sharpe, min vol)
        weight_bounds : tuple, default (0, 1)
            Min and max weight for each asset
        show : bool, default True
            Whether to display the plot. Set to False for automated/server contexts.

        Returns
        -------
        plt.Figure
            The matplotlib figure object
        """
        frontier = self.generate_efficient_frontier(n_points, weight_bounds)

        fig, ax = plt.subplots(figsize=(12, 8))

        # Plot efficient frontier
        ax.plot(
            frontier["volatility"] * 100,
            frontier["return"] * 100,
            "b-",
            linewidth=2,
            label="Efficient Frontier",
        )

        if show_assets:
            # Plot individual assets
            for i, ticker in enumerate(self.tickers):
                ax.scatter(
                    np.sqrt(self.cov_matrix.iloc[i, i]) * 100,
                    self.mean_returns.iloc[i] * 100,
                    s=100,
                    marker="o",
                    label=ticker,
                )

        if show_optimal:
            # Mark max Sharpe portfolio
            max_sharpe = self.optimize_max_sharpe(weight_bounds)
            ax.scatter(
                max_sharpe["volatility"] * 100,
                max_sharpe["return"] * 100,
                s=200,
                marker="*",
                c="red",
                label="Max Sharpe",
            )

            # Mark min volatility portfolio
            min_vol = self.optimize_min_volatility(weight_bounds)
            ax.scatter(
                min_vol["volatility"] * 100,
                min_vol["return"] * 100,
                s=200,
                marker="*",
                c="green",
                label="Min Volatility",
            )

        ax.set_xlabel("Volatility (%)")
        ax.set_ylabel("Expected Return (%)")
        ax.set_title("Efficient Frontier")
        ax.legend()
        ax.grid(True, alpha=0.3)
        fig.tight_layout()

        if show:
            plt.show()

        return fig

    def print_comparison(self, weight_bounds: tuple[float, float] = (0, 1)) -> None:
        """Print comparison of optimization strategies."""
        equal_weight = np.array([1 / self.n_assets] * self.n_assets)
        max_sharpe = self.optimize_max_sharpe(weight_bounds)
        min_vol = self.optimize_min_volatility(weight_bounds)
        risk_parity = self.optimize_risk_parity()

        print("\n" + "=" * 70)
        print("PORTFOLIO OPTIMIZATION COMPARISON")
        print("=" * 70)
        print(f"{'Strategy':<20} {'Return':>12} {'Volatility':>12} {'Sharpe':>10}")
        print("-" * 70)

        # Equal weight
        print(
            f"{'Equal Weight':<20} "
            f"{self._portfolio_return(equal_weight)*100:>11.2f}% "
            f"{self._portfolio_volatility(equal_weight)*100:>11.2f}% "
            f"{self._portfolio_sharpe(equal_weight):>10.2f}"
        )

        # Max Sharpe
        print(
            f"{'Max Sharpe':<20} "
            f"{max_sharpe['return']*100:>11.2f}% "
            f"{max_sharpe['volatility']*100:>11.2f}% "
            f"{max_sharpe['sharpe_ratio']:>10.2f}"
        )

        # Min Volatility
        print(
            f"{'Min Volatility':<20} "
            f"{min_vol['return']*100:>11.2f}% "
            f"{min_vol['volatility']*100:>11.2f}% "
            f"{min_vol['sharpe_ratio']:>10.2f}"
        )

        # Risk Parity
        print(
            f"{'Risk Parity':<20} "
            f"{risk_parity['return']*100:>11.2f}% "
            f"{risk_parity['volatility']*100:>11.2f}% "
            f"{risk_parity['sharpe_ratio']:>10.2f}"
        )

        print("=" * 70)

        print("\nOptimal Weights (Max Sharpe):")
        for ticker, weight in max_sharpe["weights"].items():
            if weight > 0.01:
                print(f"  {ticker}: {weight*100:.1f}%")

optimize_max_sharpe(weight_bounds=(0, 1))

Find the portfolio with maximum Sharpe ratio.

Parameters:

Name Type Description Default
weight_bounds tuple

Min and max weight for each asset

 (0, 1)

Returns:

Type Description
dict

Optimal weights, return, volatility, and Sharpe ratio
Source code in portfolio_analysis/analysis/optimization.py 
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def optimize_max_sharpe(self, weight_bounds: tuple[float, float] = (0, 1)) -> dict:
    """
    Find the portfolio with maximum Sharpe ratio.

    Parameters
    ----------
    weight_bounds : tuple, default (0, 1)
        Min and max weight for each asset

    Returns
    -------
    dict
        Optimal weights, return, volatility, and Sharpe ratio
    """
    constraints = {"type": "eq", "fun": lambda x: np.sum(x) - 1}
    bounds = tuple(weight_bounds for _ in range(self.n_assets))
    initial_weights = np.array([1 / self.n_assets] * self.n_assets)

    result = minimize(
        self._neg_sharpe,
        initial_weights,
        method="SLSQP",
        bounds=bounds,
        constraints=constraints,
    )

    optimal_weights = result.x
    return {
        "weights": dict(zip(self.tickers, optimal_weights)),
        "return": self._portfolio_return(optimal_weights),
        "volatility": self._portfolio_volatility(optimal_weights),
        "sharpe_ratio": self._portfolio_sharpe(optimal_weights),
    }

optimize_min_volatility(weight_bounds=(0, 1))

Find the minimum volatility portfolio.

Parameters:

Name Type Description Default
weight_bounds tuple

Min and max weight for each asset

 (0, 1)

Returns:

Type Description
dict

Optimal weights, return, volatility, and Sharpe ratio
Source code in portfolio_analysis/analysis/optimization.py 
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def optimize_min_volatility(
    self, weight_bounds: tuple[float, float] = (0, 1)
) -> dict:
    """
    Find the minimum volatility portfolio.

    Parameters
    ----------
    weight_bounds : tuple, default (0, 1)
        Min and max weight for each asset

    Returns
    -------
    dict
        Optimal weights, return, volatility, and Sharpe ratio
    """
    constraints = {"type": "eq", "fun": lambda x: np.sum(x) - 1}
    bounds = tuple(weight_bounds for _ in range(self.n_assets))
    initial_weights = np.array([1 / self.n_assets] * self.n_assets)

    result = minimize(
        self._portfolio_volatility,
        initial_weights,
        method="SLSQP",
        bounds=bounds,
        constraints=constraints,
    )

    optimal_weights = result.x
    return {
        "weights": dict(zip(self.tickers, optimal_weights)),
        "return": self._portfolio_return(optimal_weights),
        "volatility": self._portfolio_volatility(optimal_weights),
        "sharpe_ratio": self._portfolio_sharpe(optimal_weights),
    }

optimize_target_return(target_return, weight_bounds=(0, 1))

Find minimum volatility portfolio for a target return.

Parameters:

Name Type Description Default
target_return float

Target annual return

 required
weight_bounds tuple

Min and max weight for each asset

 (0, 1)

Returns:

Type Description
dict

Optimal weights, return, volatility, and Sharpe ratio
Source code in portfolio_analysis/analysis/optimization.py 
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def optimize_target_return(
    self, target_return: float, weight_bounds: tuple[float, float] = (0, 1)
) -> dict:
    """
    Find minimum volatility portfolio for a target return.

    Parameters
    ----------
    target_return : float
        Target annual return
    weight_bounds : tuple, default (0, 1)
        Min and max weight for each asset

    Returns
    -------
    dict
        Optimal weights, return, volatility, and Sharpe ratio
    """
    constraints = [
        {"type": "eq", "fun": lambda x: np.sum(x) - 1},
        {"type": "eq", "fun": lambda x: self._portfolio_return(x) - target_return},
    ]
    bounds = tuple(weight_bounds for _ in range(self.n_assets))
    initial_weights = np.array([1 / self.n_assets] * self.n_assets)

    result = minimize(
        self._portfolio_volatility,
        initial_weights,
        method="SLSQP",
        bounds=bounds,
        constraints=constraints,
    )

    optimal_weights = result.x
    return {
        "weights": dict(zip(self.tickers, optimal_weights)),
        "return": self._portfolio_return(optimal_weights),
        "volatility": self._portfolio_volatility(optimal_weights),
        "sharpe_ratio": self._portfolio_sharpe(optimal_weights),
    }

optimize_risk_parity()

Find the risk parity portfolio (equal risk contribution).

Each asset contributes equally to total portfolio risk.

Returns:

Type Description
dict

Optimal weights, return, volatility, and Sharpe ratio
Source code in portfolio_analysis/analysis/optimization.py 
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def optimize_risk_parity(self) -> dict:
    """
    Find the risk parity portfolio (equal risk contribution).

    Each asset contributes equally to total portfolio risk.

    Returns
    -------
    dict
        Optimal weights, return, volatility, and Sharpe ratio
    """

    def risk_contribution(weights):
        """Calculate risk contribution of each asset."""
        port_vol = self._portfolio_volatility(weights)
        marginal_contrib = np.dot(self.cov_matrix, weights)
        risk_contrib = weights * marginal_contrib / port_vol
        return risk_contrib

    def risk_parity_objective(weights):
        """Objective: minimize deviation from equal risk contribution."""
        rc = risk_contribution(weights)
        target_rc = np.mean(rc)
        return np.sum((rc - target_rc) ** 2)

    constraints = {"type": "eq", "fun": lambda x: np.sum(x) - 1}
    bounds = tuple((0.01, 1) for _ in range(self.n_assets))  # Min 1% per asset
    initial_weights = np.array([1 / self.n_assets] * self.n_assets)

    result = minimize(
        risk_parity_objective,
        initial_weights,
        method="SLSQP",
        bounds=bounds,
        constraints=constraints,
    )

    optimal_weights = result.x
    return {
        "weights": dict(zip(self.tickers, optimal_weights)),
        "return": self._portfolio_return(optimal_weights),
        "volatility": self._portfolio_volatility(optimal_weights),
        "sharpe_ratio": self._portfolio_sharpe(optimal_weights),
        "risk_contributions": dict(
            zip(self.tickers, risk_contribution(optimal_weights))
        ),
    }

generate_efficient_frontier(n_points=50, weight_bounds=(0, 1))

Generate points on the efficient frontier.

Parameters:

Name Type Description Default
n_points int

Number of points to generate

 50
weight_bounds tuple

Min and max weight for each asset

 (0, 1)

Returns:

Type Description
DataFrame

DataFrame with return, volatility, and Sharpe for each point
Source code in portfolio_analysis/analysis/optimization.py 
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def generate_efficient_frontier(
    self, n_points: int = 50, weight_bounds: tuple[float, float] = (0, 1)
) -> pd.DataFrame:
    """
    Generate points on the efficient frontier.

    Parameters
    ----------
    n_points : int, default 50
        Number of points to generate
    weight_bounds : tuple, default (0, 1)
        Min and max weight for each asset

    Returns
    -------
    pd.DataFrame
        DataFrame with return, volatility, and Sharpe for each point
    """
    # Find return range
    min_vol = self.optimize_min_volatility(weight_bounds)
    _max_sharpe = self.optimize_max_sharpe(weight_bounds)  # noqa: F841

    min_ret = min_vol["return"]
    max_ret = max(self.mean_returns)

    target_returns = np.linspace(min_ret, max_ret, n_points)

    frontier = []
    failed_count = 0
    for target in target_returns:
        try:
            portfolio = self.optimize_target_return(target, weight_bounds)
            frontier.append(
                {
                    "return": portfolio["return"],
                    "volatility": portfolio["volatility"],
                    "sharpe_ratio": portfolio["sharpe_ratio"],
                }
            )
        except (ValueError, RuntimeError) as e:
            # Optimization may fail for extreme target returns
            failed_count += 1
            logger.debug(f"Optimization failed for target return {target:.4f}: {e}")
            continue

    if failed_count > 0:
        warnings.warn(
            f"Optimization failed for {failed_count}/{n_points} target returns. "
            "This is normal for extreme values at the frontier edges.",
            stacklevel=2,
        )

    if len(frontier) == 0:
        raise OptimizationError(
            "Failed to generate any points on the efficient frontier. "
            "Check that your data is valid and has sufficient history."
        )

    return pd.DataFrame(frontier)

plot_efficient_frontier(n_points=50, show_assets=True, show_optimal=True, weight_bounds=(0, 1), show=True)

Plot the efficient frontier with optimal portfolios marked.

Parameters:

Name Type Description Default
n_points int

Number of points on the frontier

 50
show_assets bool

Show individual assets

 True
show_optimal bool

Mark optimal portfolios (max Sharpe, min vol)

 True
weight_bounds tuple

Min and max weight for each asset

 (0, 1)
show bool

Whether to display the plot. Set to False for automated/server contexts.

 True

Returns:

Type Description
Figure

The matplotlib figure object
Source code in portfolio_analysis/analysis/optimization.py 
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def plot_efficient_frontier(
    self,
    n_points: int = 50,
    show_assets: bool = True,
    show_optimal: bool = True,
    weight_bounds: tuple[float, float] = (0, 1),
    show: bool = True,
) -> plt.Figure:
    """
    Plot the efficient frontier with optimal portfolios marked.

    Parameters
    ----------
    n_points : int, default 50
        Number of points on the frontier
    show_assets : bool, default True
        Show individual assets
    show_optimal : bool, default True
        Mark optimal portfolios (max Sharpe, min vol)
    weight_bounds : tuple, default (0, 1)
        Min and max weight for each asset
    show : bool, default True
        Whether to display the plot. Set to False for automated/server contexts.

    Returns
    -------
    plt.Figure
        The matplotlib figure object
    """
    frontier = self.generate_efficient_frontier(n_points, weight_bounds)

    fig, ax = plt.subplots(figsize=(12, 8))

    # Plot efficient frontier
    ax.plot(
        frontier["volatility"] * 100,
        frontier["return"] * 100,
        "b-",
        linewidth=2,
        label="Efficient Frontier",
    )

    if show_assets:
        # Plot individual assets
        for i, ticker in enumerate(self.tickers):
            ax.scatter(
                np.sqrt(self.cov_matrix.iloc[i, i]) * 100,
                self.mean_returns.iloc[i] * 100,
                s=100,
                marker="o",
                label=ticker,
            )

    if show_optimal:
        # Mark max Sharpe portfolio
        max_sharpe = self.optimize_max_sharpe(weight_bounds)
        ax.scatter(
            max_sharpe["volatility"] * 100,
            max_sharpe["return"] * 100,
            s=200,
            marker="*",
            c="red",
            label="Max Sharpe",
        )

        # Mark min volatility portfolio
        min_vol = self.optimize_min_volatility(weight_bounds)
        ax.scatter(
            min_vol["volatility"] * 100,
            min_vol["return"] * 100,
            s=200,
            marker="*",
            c="green",
            label="Min Volatility",
        )

    ax.set_xlabel("Volatility (%)")
    ax.set_ylabel("Expected Return (%)")
    ax.set_title("Efficient Frontier")
    ax.legend()
    ax.grid(True, alpha=0.3)
    fig.tight_layout()

    if show:
        plt.show()

    return fig

print_comparison(weight_bounds=(0, 1))

Print comparison of optimization strategies.

Source code in portfolio_analysis/analysis/optimization.py 
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def print_comparison(self, weight_bounds: tuple[float, float] = (0, 1)) -> None:
    """Print comparison of optimization strategies."""
    equal_weight = np.array([1 / self.n_assets] * self.n_assets)
    max_sharpe = self.optimize_max_sharpe(weight_bounds)
    min_vol = self.optimize_min_volatility(weight_bounds)
    risk_parity = self.optimize_risk_parity()

    print("\n" + "=" * 70)
    print("PORTFOLIO OPTIMIZATION COMPARISON")
    print("=" * 70)
    print(f"{'Strategy':<20} {'Return':>12} {'Volatility':>12} {'Sharpe':>10}")
    print("-" * 70)

    # Equal weight
    print(
        f"{'Equal Weight':<20} "
        f"{self._portfolio_return(equal_weight)*100:>11.2f}% "
        f"{self._portfolio_volatility(equal_weight)*100:>11.2f}% "
        f"{self._portfolio_sharpe(equal_weight):>10.2f}"
    )

    # Max Sharpe
    print(
        f"{'Max Sharpe':<20} "
        f"{max_sharpe['return']*100:>11.2f}% "
        f"{max_sharpe['volatility']*100:>11.2f}% "
        f"{max_sharpe['sharpe_ratio']:>10.2f}"
    )

    # Min Volatility
    print(
        f"{'Min Volatility':<20} "
        f"{min_vol['return']*100:>11.2f}% "
        f"{min_vol['volatility']*100:>11.2f}% "
        f"{min_vol['sharpe_ratio']:>10.2f}"
    )

    # Risk Parity
    print(
        f"{'Risk Parity':<20} "
        f"{risk_parity['return']*100:>11.2f}% "
        f"{risk_parity['volatility']*100:>11.2f}% "
        f"{risk_parity['sharpe_ratio']:>10.2f}"
    )

    print("=" * 70)

    print("\nOptimal Weights (Max Sharpe):")
    for ticker, weight in max_sharpe["weights"].items():
        if weight > 0.01:
            print(f"  {ticker}: {weight*100:.1f}%")