Merge remote-tracking branch 'origin/dev' into dev

app/pypfopt/__init__.py

+from .black_litterman import (
+    market_implied_prior_returns,
+    market_implied_risk_aversion,
+    BlackLittermanModel,
+)
+from .cla import CLA
+from .discrete_allocation import get_latest_prices, DiscreteAllocation
+from .efficient_frontier import EfficientFrontier
+from .hierarchical_portfolio import HRPOpt
+from .risk_models import CovarianceShrinkage
+
+
+__version__ = "1.2.6"
+
+__all__ = [
+    "market_implied_prior_returns",
+    "market_implied_risk_aversion",
+    "BlackLittermanModel",
+    "CLA",
+    "get_latest_prices",
+    "DiscreteAllocation",
+    "EfficientFrontier",
+    "HRPOpt",
+    "CovarianceShrinkage",
+]

app/pypfopt/exceptions.py

+"""
+The ``exceptions`` module houses custom exceptions. Currently implemented:
+
+- OptimizationError
+"""
+
+
+class OptimizationError(Exception):
+    """
+    When an optimization routine fails – usually, this means
+    that cvxpy has not returned the "optimal" flag.
+    """
+
+    def __init__(self, *args, **kwargs):
+        default_message = (
+            "Please check your objectives/constraints or use a different solver."
+        )
+        super().__init__(default_message, *args, **kwargs)

app/pypfopt/hierarchical_portfolio.py

+"""
+The ``hierarchical_portfolio`` module seeks to implement one of the recent advances in
+portfolio optimisation – the application of hierarchical clustering models in allocation.
+
+All of the hierarchical classes have a similar API to ``EfficientFrontier``, though since
+many hierarchical models currently don't support different objectives, the actual allocation
+happens with a call to `optimize()`.
+
+Currently implemented:
+
+- ``HRPOpt`` implements the Hierarchical Risk Parity (HRP) portfolio. Code reproduced with
+  permission from Marcos Lopez de Prado (2016).
+"""
+
+import collections
+import numpy as np
+import pandas as pd
+import scipy.cluster.hierarchy as sch
+import scipy.spatial.distance as ssd
+
+from . import base_optimizer, risk_models
+
+
+class HRPOpt(base_optimizer.BaseOptimizer):
+    """
+    A HRPOpt object (inheriting from BaseOptimizer) constructs a hierarchical
+    risk parity portfolio.
+
+    Instance variables:
+
+    - Inputs
+
+        - ``n_assets`` - int
+        - ``tickers`` - str list
+        - ``returns`` - pd.Series
+
+    - Output:
+
+        - ``weights`` - np.ndarray
+        - ``clusters`` - linkage matrix corresponding to clustered assets.
+
+    Public methods:
+
+    - ``optimize()`` calculates weights using HRP
+    - ``portfolio_performance()`` calculates the expected return, volatility and Sharpe ratio for
+      the optimised portfolio.
+    - ``set_weights()`` creates self.weights (np.ndarray) from a weights dict
+    - ``clean_weights()`` rounds the weights and clips near-zeros.
+    - ``save_weights_to_file()`` saves the weights to csv, json, or txt.
+    """
+
+    def __init__(self, returns=None, cov_matrix=None):
+        """
+        :param returns: asset historical returns
+        :type returns: pd.DataFrame
+        :param cov_matrix: covariance of asset returns
+        :type cov_matrix: pd.DataFrame.
+        :raises TypeError: if ``returns`` is not a dataframe
+        """
+        if returns is None and cov_matrix is None:
+            raise ValueError("Either returns or cov_matrix must be provided")
+
+        if returns is not None and not isinstance(returns, pd.DataFrame):
+            raise TypeError("returns are not a dataframe")
+
+        self.returns = returns
+        self.cov_matrix = cov_matrix
+        self.clusters = None
+
+        if returns is None:
+            tickers = list(cov_matrix.columns)
+        else:
+            tickers = list(returns.columns)
+        super().__init__(len(tickers), tickers)
+
+    @staticmethod
+    def _get_cluster_var(cov, cluster_items):
+        """
+        Compute the variance per cluster
+
+        :param cov: covariance matrix
+        :type cov: np.ndarray
+        :param cluster_items: tickers in the cluster
+        :type cluster_items: list
+        :return: the variance per cluster
+        :rtype: float
+        """
+        # Compute variance per cluster
+        cov_slice = cov.loc[cluster_items, cluster_items]
+        weights = 1 / np.diag(cov_slice)  # Inverse variance weights
+        weights /= weights.sum()
+        return np.linalg.multi_dot((weights, cov_slice, weights))
+
+    @staticmethod
+    def _get_quasi_diag(link):
+        """
+        Sort clustered items by distance
+
+        :param link: linkage matrix after clustering
+        :type link: np.ndarray
+        :return: sorted list of indices
+        :rtype: list
+        """
+        return sch.to_tree(link, rd=False).pre_order()
+
+    @staticmethod
+    def _raw_hrp_allocation(cov, ordered_tickers):
+        """
+        Given the clusters, compute the portfolio that minimises risk by
+        recursively traversing the hierarchical tree from the top.
+
+        :param cov: covariance matrix
+        :type cov: np.ndarray
+        :param ordered_tickers: list of tickers ordered by distance
+        :type ordered_tickers: str list
+        :return: raw portfolio weights
+        :rtype: pd.Series
+        """
+        w = pd.Series(1, index=ordered_tickers)
+        cluster_items = [ordered_tickers]  # initialize all items in one cluster
+
+        while len(cluster_items) > 0:
+            cluster_items = [
+                i[j:k]
+                for i in cluster_items
+                for j, k in ((0, len(i) // 2), (len(i) // 2, len(i)))
+                if len(i) > 1
+            ]  # bi-section
+            # For each pair, optimise locally.
+            for i in range(0, len(cluster_items), 2):
+                first_cluster = cluster_items[i]
+                second_cluster = cluster_items[i + 1]
+                # Form the inverse variance portfolio for this pair
+                first_variance = HRPOpt._get_cluster_var(cov, first_cluster)
+                second_variance = HRPOpt._get_cluster_var(cov, second_cluster)
+                alpha = 1 - first_variance / (first_variance + second_variance)
+                w[first_cluster] *= alpha  # weight 1
+                w[second_cluster] *= 1 - alpha  # weight 2
+        return w
+
+    def optimize(self, linkage_method="single"):
+        """
+        Construct a hierarchical risk parity portfolio, using Scipy hierarchical clustering
+        (see `here <https://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.hierarchy.linkage.html>`_)
+
+        :param linkage_method: which scipy linkage method to use
+        :type linkage_method: str
+        :return: weights for the HRP portfolio
+        :rtype: OrderedDict
+        """
+        if linkage_method not in sch._LINKAGE_METHODS:
+            raise ValueError("linkage_method must be one recognised by scipy")
+
+        if self.returns is None:
+            cov = self.cov_matrix
+            corr = risk_models.cov_to_corr(self.cov_matrix).round(6)
+        else:
+            corr, cov = self.returns.corr(), self.returns.cov()
+
+        # Compute distance matrix, with ClusterWarning fix as
+        # per https://stackoverflow.com/questions/18952587/
+
+        # this can avoid some nasty floating point issues
+        matrix = np.sqrt(np.clip((1.0 - corr) / 2.0, a_min=0.0, a_max=1.0))
+        dist = ssd.squareform(matrix, checks=False)
+
+        self.clusters = sch.linkage(dist, linkage_method)
+        sort_ix = HRPOpt._get_quasi_diag(self.clusters)
+        ordered_tickers = corr.index[sort_ix].tolist()
+        hrp = HRPOpt._raw_hrp_allocation(cov, ordered_tickers)
+        weights = collections.OrderedDict(hrp.sort_index())
+        self.set_weights(weights)
+        return weights
+
+    def portfolio_performance(self, verbose=False, risk_free_rate=0.02, frequency=252):
+        """
+        After optimising, calculate (and optionally print) the performance of the optimal
+        portfolio. Currently calculates expected return, volatility, and the Sharpe ratio
+        assuming returns are daily
+
+        :param verbose: whether performance should be printed, defaults to False
+        :type verbose: bool, optional
+        :param risk_free_rate: risk-free rate of borrowing/lending, defaults to 0.02.
+                               The period of the risk-free rate should correspond to the
+                               frequency of expected returns.
+        :type risk_free_rate: float, optional
+        :param frequency: number of time periods in a year, defaults to 252 (the number
+                            of trading days in a year)
+        :type frequency: int, optional
+        :raises ValueError: if weights have not been calculated yet
+        :return: expected return, volatility, Sharpe ratio.
+        :rtype: (float, float, float)
+        """
+        if self.returns is None:
+            cov = self.cov_matrix
+            mu = None
+        else:
+            cov = self.returns.cov() * frequency
+            mu = self.returns.mean() * frequency
+
+        return base_optimizer.portfolio_performance(
+            self.weights, mu, cov, verbose, risk_free_rate
+        )

app/pypfopt/objective_functions.py

+"""
+The ``objective_functions`` module provides optimisation objectives, including the actual
+objective functions called by the ``EfficientFrontier`` object's optimisation methods.
+These methods are primarily designed for internal use during optimisation and each requires
+a different signature (which is why they have not been factored into a class).
+For obvious reasons, any objective function must accept ``weights``
+as an argument, and must also have at least one of ``expected_returns`` or ``cov_matrix``.
+
+The objective functions either compute the objective given a numpy array of weights, or they
+return a cvxpy *expression* when weights are a ``cp.Variable``. In this way, the same objective
+function can be used both internally for optimisation and externally for computing the objective
+given weights. ``_objective_value()`` automatically chooses between the two behaviours.
+
+``objective_functions`` defaults to objectives for minimisation. In the cases of objectives
+that clearly should be maximised (e.g Sharpe Ratio, portfolio return), the objective function
+actually returns the negative quantity, since minimising the negative is equivalent to maximising
+the positive. This behaviour is controlled by the ``negative=True`` optional argument.
+
+Currently implemented:
+
+- Portfolio variance (i.e square of volatility)
+- Portfolio return
+- Sharpe ratio
+- L2 regularisation (minimising this reduces nonzero weights)
+- Quadratic utility
+- Transaction cost model (a simple one)
+"""
+
+import numpy as np
+import cvxpy as cp
+
+
+def _objective_value(w, obj):
+    """
+    Helper method to return either the value of the objective function
+    or the objective function as a cvxpy object depending on whether
+    w is a cvxpy variable or np array.
+
+    :param w: weights
+    :type w: np.ndarray OR cp.Variable
+    :param obj: objective function expression
+    :type obj: cp.Expression
+    :return: value of the objective function OR objective function expression
+    :rtype: float OR cp.Expression
+    """
+    if isinstance(w, np.ndarray):
+        if np.isscalar(obj):
+            return obj
+        elif np.isscalar(obj.value):
+            return obj.value
+        else:
+            return obj.value.item()
+    else:
+        return obj
+
+
+def portfolio_variance(w, cov_matrix):
+    """
+    Calculate the total portfolio variance (i.e square volatility).
+
+    :param w: asset weights in the portfolio
+    :type w: np.ndarray OR cp.Variable
+    :param cov_matrix: covariance matrix
+    :type cov_matrix: np.ndarray
+    :return: value of the objective function OR objective function expression
+    :rtype: float OR cp.Expression
+    """
+    variance = cp.quad_form(w, cov_matrix)
+    return _objective_value(w, variance)
+
+
+def portfolio_return(w, expected_returns, negative=True):
+    """
+    Calculate the (negative) mean return of a portfolio
+
+    :param w: asset weights in the portfolio
+    :type w: np.ndarray OR cp.Variable
+    :param expected_returns: expected return of each asset
+    :type expected_returns: np.ndarray
+    :param negative: whether quantity should be made negative (so we can minimise) 
+    :type negative: boolean
+    :return: negative mean return
+    :rtype: float
+    """
+    sign = -1 if negative else 1
+    mu = w @ expected_returns
+    return _objective_value(w, sign * mu)
+
+
+def sharpe_ratio(w, expected_returns, cov_matrix, risk_free_rate=0.02, negative=True):
+    """
+    Calculate the (negative) Sharpe ratio of a portfolio
+
+    :param w: asset weights in the portfolio
+    :type w: np.ndarray OR cp.Variable
+    :param expected_returns: expected return of each asset
+    :type expected_returns: np.ndarray
+    :param cov_matrix: covariance matrix
+    :type cov_matrix: np.ndarray
+    :param risk_free_rate: risk-free rate of borrowing/lending, defaults to 0.02.
+                           The period of the risk-free rate should correspond to the
+                           frequency of expected returns.
+    :type risk_free_rate: float, optional
+    :param negative: whether quantity should be made negative (so we can minimise) 
+    :type negative: boolean
+    :return: (negative) Sharpe ratio
+    :rtype: float
+    """
+    mu = w @ expected_returns
+    sigma = cp.sqrt(cp.quad_form(w, cov_matrix))
+    sign = -1 if negative else 1
+    sharpe = (mu - risk_free_rate) / sigma
+    return _objective_value(w, sign * sharpe)
+
+
+def L2_reg(w, gamma=1):
+    r"""
+    L2 regularisation, i.e :math:`\gamma ||w||^2`, to increase the number of nonzero weights.
+
+    Example::
+
+        ef = EfficientFrontier(mu, S)
+        ef.add_objective(objective_functions.L2_reg, gamma=2)
+        ef.min_volatility()
+
+    :param w: asset weights in the portfolio
+    :type w: np.ndarray OR cp.Variable
+    :param gamma: L2 regularisation parameter, defaults to 1. Increase if you want more
+                    non-negligible weights
+    :type gamma: float, optional
+    :return: value of the objective function OR objective function expression
+    :rtype: float OR cp.Expression
+    """
+    L2_reg = gamma * cp.sum_squares(w)
+    return _objective_value(w, L2_reg)
+
+
+def quadratic_utility(w, expected_returns, cov_matrix, risk_aversion, negative=True):
+    r"""
+    Quadratic utility function, i.e :math:`\mu - \frac 1 2 \delta  w^T \Sigma w`.
+
+    :param w: asset weights in the portfolio
+    :type w: np.ndarray OR cp.Variable
+    :param expected_returns: expected return of each asset
+    :type expected_returns: np.ndarray
+    :param cov_matrix: covariance matrix
+    :type cov_matrix: np.ndarray
+    :param risk_aversion: risk aversion coefficient. Increase to reduce risk.
+    :type risk_aversion: float
+    :param negative: whether quantity should be made negative (so we can minimise).
+    :type negative: boolean
+    :return: value of the objective function OR objective function expression
+    :rtype: float OR cp.Expression
+    """
+    sign = -1 if negative else 1
+    mu = w @ expected_returns
+    variance = cp.quad_form(w, cov_matrix)
+
+    utility = mu - 0.5 * risk_aversion * variance
+    return _objective_value(w, sign * utility)
+
+
+def transaction_cost(w, w_prev, k=0.001):
+    """
+    A very simple transaction cost model: sum all the weight changes
+    and multiply by a given fraction (default to 10bps). This simulates
+    a fixed percentage commission from your broker.
+
+    :param w: asset weights in the portfolio
+    :type w: np.ndarray OR cp.Variable
+    :param w_prev: previous weights
+    :type w_prev: np.ndarray
+    :param k: fractional cost per unit weight exchanged
+    :type k: float
+    :return: value of the objective function OR objective function expression
+    :rtype: float OR cp.Expression
+    """
+    return _objective_value(w, k * cp.norm(w - w_prev, 1))

app/pypfopt/plotting.py

+"""
+The ``plotting`` module houses all the functions to generate various plots.
+
+Currently implemented:
+
+  - ``plot_covariance`` - plot a correlation matrix
+  - ``plot_dendrogram`` - plot the hierarchical clusters in a portfolio
+  - ``plot_efficient_frontier`` – plot the efficient frontier, using the CLA algorithm.
+  - ``plot_weights`` - bar chart of weights
+"""
+
+import numpy as np
+from . import risk_models
+import scipy.cluster.hierarchy as sch
+
+try:
+    import matplotlib.pyplot as plt
+
+    plt.style.use("seaborn-deep")
+except (ModuleNotFoundError, ImportError):
+    raise ImportError("Please install matplotlib via pip or poetry")
+
+
+def _plot_io(**kwargs):
+    """
+    Helper method to optionally save the figure to file.
+
+    :param filename: name of the file to save to, defaults to None (doesn't save)
+    :type filename: str, optional
+    :param dpi: dpi of figure to save or plot, defaults to 300
+    :type dpi: int (between 50-500)
+    :param showfig: whether to plt.show() the figure, defaults to True
+    :type showfig: bool, optional
+    """
+    filename = kwargs.get("filename", None)
+    showfig = kwargs.get("showfig", True)
+    dpi = kwargs.get("dpi", 300)
+
+    plt.tight_layout()
+    if filename:
+        plt.savefig(fname=filename, dpi=dpi)
+    if showfig:
+        plt.show()
+
+
+def plot_covariance(cov_matrix, plot_correlation=False, show_tickers=True, **kwargs):
+    """
+    Generate a basic plot of the covariance (or correlation) matrix, given a
+    covariance matrix.
+
+    :param cov_matrix: covariance matrix
+    :type cov_matrix: pd.DataFrame or np.ndarray
+    :param plot_correlation: whether to plot the correlation matrix instead, defaults to False.
+    :type plot_correlation: bool, optional
+    :param show_tickers: whether to use tickers as labels (not recommended for large portfolios),
+                        defaults to True
+    :type show_tickers: bool, optional
+
+    :return: matplotlib axis
+    :rtype: matplotlib.axes object
+    """
+    if plot_correlation:
+        matrix = risk_models.cov_to_corr(cov_matrix)
+    else:
+        matrix = cov_matrix
+    fig, ax = plt.subplots()
+
+    cax = ax.imshow(matrix)
+    fig.colorbar(cax)
+
+    if show_tickers:
+        ax.set_xticks(np.arange(0, matrix.shape[0], 1))
+        ax.set_xticklabels(matrix.index)
+        ax.set_yticks(np.arange(0, matrix.shape[0], 1))
+        ax.set_yticklabels(matrix.index)
+        plt.xticks(rotation=90)
+
+    _plot_io(**kwargs)
+
+    return ax
+
+
+def plot_dendrogram(hrp, show_tickers=True, **kwargs):
+    """
+    Plot the clusters in the form of a dendrogram.
+
+    :param hrp: HRPpt object that has already been optimized.
+    :type hrp: object
+    :param show_tickers: whether to use tickers as labels (not recommended for large portfolios),
+                        defaults to True
+    :type show_tickers: bool, optional
+    :param filename: name of the file to save to, defaults to None (doesn't save)
+    :type filename: str, optional
+    :param showfig: whether to plt.show() the figure, defaults to True
+    :type showfig: bool, optional
+    :return: matplotlib axis
+    :rtype: matplotlib.axes object
+    """
+    if hrp.clusters is None:
+        hrp.optimize()
+
+    fig, ax = plt.subplots()
+    if show_tickers:
+        sch.dendrogram(hrp.clusters, labels=hrp.tickers, ax=ax, orientation="top")
+        plt.xticks(rotation=90)
+        plt.tight_layout()
+    else:
+        sch.dendrogram(hrp.clusters, no_labels=True, ax=ax)
+
+    _plot_io(**kwargs)
+
+    return ax
+
+
+def plot_efficient_frontier(cla, points=100, show_assets=True, **kwargs):
+    """
+    Plot the efficient frontier based on a CLA object
+
+    :param points: number of points to plot, defaults to 100
+    :type points: int, optional
+    :param show_assets: whether we should plot the asset risks/returns also, defaults to True
+    :type show_assets: bool, optional
+    :param filename: name of the file to save to, defaults to None (doesn't save)
+    :type filename: str, optional
+    :param showfig: whether to plt.show() the figure, defaults to True
+    :type showfig: bool, optional
+    :return: matplotlib axis
+    :rtype: matplotlib.axes object
+    """
+    if cla.weights is None:
+        cla.max_sharpe()
+    optimal_ret, optimal_risk, _ = cla.portfolio_performance()
+
+    if cla.frontier_values is None:
+        cla.efficient_frontier(points=points)
+
+    mus, sigmas, _ = cla.frontier_values
+
+    fig, ax = plt.subplots()
+    ax.plot(sigmas, mus, label="Efficient frontier")
+
+    if show_assets:
+        ax.scatter(
+            np.sqrt(np.diag(cla.cov_matrix)),
+            cla.expected_returns,
+            s=30,
+            color="k",
+            label="assets",
+        )
+
+    ax.scatter(optimal_risk, optimal_ret, marker="x", s=100, color="r", label="optimal")
+    ax.legend()
+    ax.set_xlabel("Volatility")
+    ax.set_ylabel("Return")
+
+    _plot_io(**kwargs)
+    return ax
+
+
+def plot_weights(weights, **kwargs):
+    """
+    Plot the portfolio weights as a horizontal bar chart
+
+    :param weights: the weights outputted by any PyPortfolioOpt optimiser
+    :type weights: {ticker: weight} dict
+    :return: matplotlib axis
+    :rtype: matplotlib.axes object
+    """
+    desc = sorted(weights.items(), key=lambda x: x[1], reverse=True)
+    labels = [i[0] for i in desc]
+    vals = [i[1] for i in desc]
+
+    y_pos = np.arange(len(labels))
+
+    fig, ax = plt.subplots()
+    ax.barh(y_pos, vals)
+    ax.set_xlabel("Weight")
+    ax.set_yticks(y_pos)
+    ax.set_yticklabels(labels)
+    ax.invert_yaxis()
+
+    _plot_io(**kwargs)
+    return ax

app/utils/draw.py

@@ -6,6 +6,10 @@
 # @Email      : acepengxiong@163.com
 # @Software   : PyCharm
 # -----------------------------------------------------------------------------
+import base64
+from urllib import parse
+
+from io import BytesIO
 
 import numpy as np
 import matplotlib.pyplot as plt
@@ -14,11 +18,11 @@ from matplotlib.ticker import FuncFormatter
 from matplotlib.font_manager import FontProperties
 
 # 中文字体初始化
-plt.rcParams['font.sans-serif']=['simsunb.ttf']
+plt.rcParams['font.sans-serif']=['Heiti TC']
 
 
 def to_percent(temp, position):
-    return '%1.0f' % temp + '%'
+    return '%.2f' % temp + '%'
 
 
 def draw_month_return_chart(xlabels, product_list, cumulative):
@@ -26,9 +30,9 @@ def draw_month_return_chart(xlabels, product_list, cumulative):
 
     # plt.title('Scores by group and gender')
     # plt.ylabel('Scores')
-    figsize = (20, 12)
+    figsize = (24, 12)
     # 标签文字大小
-    fontsize = 20
+    fontsize = 15
     # 初始化
     fig = plt.figure(figsize=figsize)
     ax1 = fig.add_subplot(111)
@@ -41,16 +45,17 @@ def draw_month_return_chart(xlabels, product_list, cumulative):
     # 坐标轴
     ax1.tick_params(labelsize=fontsize)
     ax2.tick_params(labelsize=fontsize)
+
     # 坐标轴颜色
     ax2.tick_params(axis='y', colors='#C6A774')
     ax1.set_xticks(loc)
     ax1.set_xticklabels(xlabels)
     # ax1.yaxis.set_major_formatter(FuncFormatter(to_percent))
     ax2.yaxis.set_major_formatter(FuncFormatter(to_percent))
-    temp_rate = np.zeros(max_x_count)
-    for i in range(len(product_list)):
-        temp_rate += product_list[i]['data']
-    max_rate = np.max(np.hstack((temp_rate, cumulative['data'])))
+    # temp_rate = np.zeros(max_x_count)
+    # for i in range(len(product_list)):
+    #     temp_rate += product_list[i]['data']
+    # max_rate = np.max(np.hstack((temp_rate, cumulative['data'])))
     # ax2.set_ylim(0, max_rate + 15)
 
     # 柱状图
@@ -67,15 +72,27 @@ def draw_month_return_chart(xlabels, product_list, cumulative):
                 ax = ax1.bar(loc, product_list[i]['data'], width, bottom=bottom, color=color_list[i], alpha=0.8)
             else:
                 ax = ax1.bar(loc, product_list[i]['data'], width, bottom=bottom, alpha=0.8)
+        for a, b in zip(range(len(xlabels)), product_list[0]['data']):
+            if b > 0:
+                ax1.text(a, b+0.2, '%.0f万' % b, ha='center', va='bottom', fontsize=fontsize)
+            elif b < 0:
+                ax1.text(a, b-0.5, '%.0f万' % b, ha='center', va='top', fontsize=fontsize)
         prod_legend.append(ax[0])
     ax1.legend(prod_legend, [prod['name'] for prod in product_list], loc='upper left', fontsize=fontsize)
 
     # 画折线图
     ax2.plot(loc, cumulative['data'], color='#C6A774', marker='', linewidth=3, label=cumulative['name'])
+    # 添加数字标签
+    for a, b in zip(range(len(xlabels)), cumulative['data']):
+        ax2.text(a, b + 0.1, '%.2f' % b + '%', ha='center', va='bottom', fontsize=fontsize)
     ax2.legend(loc='upper center', fontsize=fontsize)
 
-    plt.show()
-    plt.savefig("")
+    # plt.show()
+    imgdata = BytesIO()
+    fig.savefig(imgdata, format='png')
+    imgdata.seek(0)  # rewind the data
+    month_return_img = 'data:image/png;base64,' + base64.b64encode(imgdata.getvalue()).decode('utf-8')
+    return month_return_img
 
 
 def draw_contribution_chart(xlabels, product_list, cumulative):

app/utils/risk_parity.py

+import numpy as np
+import pandas as pd
+from scipy.optimize import minimize
+
+
+# 风险预算优化
+def calculate_portfolio_var(w, S):
+    # 计算组合风险的函数
+    w = np.mat(w)
+    return w * S * w.T
+
+
+def calculate_risk_contribution(w, S):
+    # 计算单个资产对总体风险贡献度的函数
+    w = np.mat(w)
+    sigma = np.sqrt(calculate_portfolio_var(w, S))
+    # 边际风险贡献
+    MRC = S * w.T / sigma
+    # 风险贡献
+    RC = np.multiply(MRC, w.T)
+    return RC
+
+
+def risk_budget_objective(w, pars):
+    # 计算组合风险
+    S = pars[0]  # 协方差矩阵
+    risk_target = pars[1]  # 组合中资产预期风险贡献度的目标向量
+    sig_p = np.sqrt(calculate_portfolio_var(w, S))  # portfolio sigma
+    risk_target = np.asmatrix(np.multiply(sig_p, risk_target))
+    asset_RC = calculate_risk_contribution(w, S)
+    J = sum(np.square(asset_RC - risk_target.T))[0, 0]  # sum of squared error
+    return J
+
+
+def total_weight_constraint(x):
+    return np.sum(x) - 1.0
+
+
+def long_only_constraint(x):
+    return x
+
+
+# 根据资产预期目标风险贡献度来计算各资产的权重
+def calcu_w(w_origin, S, risk_target):
+    # w0 = [0.2, 0.2, 0.2, 0.6]
+    #     x_t = [0.25, 0.25, 0.25, 0.25] # 目标是让四个资产风险贡献度相等，即都为25%
+    cons = ({'type': 'eq', 'fun': total_weight_constraint},)
+            # {'type': 'ineq', 'fun': long_only_constraint})
+    res = minimize(risk_budget_objective, w_origin, args=[S, risk_target], method='SLSQP',
+                   bounds=[[0,1]] * len(w_origin),
+                   constraints=cons, options={'disp': True})
+    w_rb = np.asmatrix(res.x)
+    return w_rb
+    # return res.x
+
+
+# 将各资产风险贡献度绘制成柱状图
+def plot_rc(w, S):
+    rc = calculate_risk_contribution(w, S)
+    print(rc)
+
+
+if __name__ == '__main__':
+    P = pd.read_csv("tests/resources/stock_prices.csv", parse_dates=True, index_col="date")
+    w_origin, S, mu = optim_drawdown(P, 0.6, [0.001, 1])
+    S = np.asmatrix(S)
+    w_origin = np.asarray([i for i in w_origin.values()])
+    risk_target = np.asarray([1/len(w_origin)] * len(w_origin))
+    print(risk_target)
+    w_rb = calcu_w(w_origin, S, risk_target)
+    print('各资产权重：', w_rb)
+    print(w_rb @ mu)
+    plot_rc(w_rb)
\ No newline at end of file