优化投资组合.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 优化投资组合\n",
    "\n",
    "**References:**     \n",
    "[Portfolio optimization, CVXPY](https://nbviewer.jupyter.org/github/cvxgrp/cvx_short_course/blob/master/applications/portfolio_optimization.ipynb)    \n",
    "Barra risk model handbook, chp 3., pp.27\n",
    "\n",
    "\n",
    "### 1. 什么是投资组合？\n",
    "投资组合是由不同投资产品（包括股票、债券等）组成的集合，目的是为了分散风险。  \n",
    "我们给不同标的不同的权重 $w_i$, $i=1, \\ldots, n$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. 投资组合的收益及风险\n",
    "\n",
    "把标的的价格变化看做随机变量，以它的期望值/均值来衡量收益，以它的方差来衡量风险。  \n",
    "\n",
    "对于单支股票：  \n",
    "- 收益率是一个随机变量\n",
    "- 期望值（均值）： ${\\bf E}(r) = \\mu$ \n",
    "- 方差：${\\bf (r_1-\\mu)^2 + (r_2-\\mu)^2 + \\ldots + (r_n-\\mu)^2} = {\\bf E{(r-\\mu)(r-\\mu)^T}} = \\Sigma$\n",
    "\n",
    "两支股票的协方差：  \n",
    "$ Cov(r_1, r_2) = {\\bf E}[(r_1 - \\mu_1)(r_2 - \\mu_2)] $\n",
    "\n",
    "对于投资组合：  \n",
    "- 收益率是一个随机变量\n",
    "- 期望值（均值）： ${\\bf E}(R) = w_1\\mu_1 + w_2\\mu_2 + \\ldots + w_n\\mu_n = \\mu^T w$  \n",
    "- 方差：${\\bf Var}(R) = w^T\\Sigma w$\n",
    "\n",
    "以两支股票组成的投资组合为例：  \n",
    "$$ {\\bf E}(R) = w_1\\mu_1 + w_2\\mu_2 $$ \n",
    "\n",
    "$$ \\begin{equation}\n",
    "{\\bf E}(R)=\\left[\n",
    "\\begin{matrix}\n",
    "\\mu_1&\\mu_2&\n",
    "\\end{matrix}\\right]\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "w_1&\\\\\n",
    "w_2&\n",
    "\\end{matrix}\\right]\n",
    "\\end{equation} $$\n",
    "\n",
    "$${\\bf Var}(R) = w_1^2 Cov(r_1, r_1) + w_2^2 Cov(r_2, r_2) + 2w_1 w_2 Cov(r_1, r_2)$$\n",
    "\n",
    "$$\\begin{equation}\n",
    "{\\bf Var}(R)=\\left[\n",
    "\\begin{matrix}\n",
    "w_1&w_2&\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "Cov(r_1, r_1)&Cov(r_2, r_1)&\\\\\n",
    "Cov(r_1, r_2)&Cov(r_2, r_2)&\n",
    "\\end{matrix}\\right]\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "w_1&\\\\\n",
    "w_2&\n",
    "\\end{matrix}\\right]\n",
    "\\end{equation}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. 马科维茨投资组合理论\n",
    "**终极问题**：如何确定w，使得投资组合在收益率一定时，风险最小；也就是使得收益-风险最大化。  \n",
    "\\begin{array}{ll} \\mbox{maximize} & \\mu^T w - \\gamma w^T\\Sigma w\\\\\n",
    "\\mbox{subject to} & {\\bf 1}^T w = 1, \\quad w \\in {\\cal W},\n",
    "\\end{array}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tushare as ts\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "stock_list = ts.get_hs300s()\n",
    "return_dict = {}\n",
    "for symbol in stock_list['code']:\n",
    "    data = ts.get_hist_data(symbol, start='2017-01-01')\n",
    "    if data is not None:\n",
    "        return_dict[symbol] = data['p_change']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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       "      <td>0.00</td>\n",
       "      <td>0.26</td>\n",
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       "      <td>-0.44</td>\n",
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       "      <td>0.74</td>\n",
       "      <td>-1.22</td>\n",
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       "            000001  000002  000008  000060  000063  000069  000100  000157  \\\n",
       "2017-01-03    0.66    0.88    0.21    1.26    1.57    0.29    3.94    0.00   \n",
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       "2017-01-09    0.39    0.93    0.40    0.18    0.64  \n",
       "\n",
       "[5 rows x 286 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "return_df = pd.DataFrame(return_dict)\n",
    "return_df.dropna(how='all', axis=1, inplace=True)\n",
    "return_df = return_df.replace([np.inf, -np.inf], np.nan)\n",
    "return_df.fillna(0, inplace=True)\n",
    "return_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((286, 1), (286, 286))"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "symbols = return_df.columns.values\n",
    "mu = return_df.mean().values\n",
    "mu.shape = (len(mu),1)\n",
    "Sigma = return_df.cov().values\n",
    "mu.shape, Sigma.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.030808687756599062"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import cvxpy as cvx\n",
    "w = cvx.Variable(len(symbols))\n",
    "gamma = 0.5\n",
    "ret = mu.T*w \n",
    "risk = cvx.quad_form(w, Sigma)\n",
    "prob = cvx.Problem(cvx.Maximize(ret - gamma*risk), \n",
    "               [cvx.sum(w) == 1, \n",
    "                w >= 0])\n",
    "prob.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "000001    3.424403e-11\n",
       "000002    2.912290e-10\n",
       "000008    3.864077e-11\n",
       "000060    1.825174e-11\n",
       "000063    1.008711e-10\n",
       "dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(w.value, index=symbols).head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999999997032"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(w.value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.14432115])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ret.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.22702491925342172"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "risk.value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. 市场中性的投资组合\n",
    "市场中性的投资组合，是不随市场的波动而波动的投资组合，也就是使得组合与市场之间相关系数为0，即两者协方差为0。  \n",
    "- ${\\bf Cov}(M, R) = m^T\\Sigma w$ = 0 (m为市场中各股的权重)\n",
    "\n",
    "以两支股票组成的投资组合为例：\n",
    "\n",
    "$${\\bf Cov}(M, R) = Cov(m_1 r_1+m_2 r_2, w_1 r_1+w_2 r_2)\\\\\n",
    "            = Cov(m_1 r_1, w_1 r_1+w_2 r_2) + Cov(m_2 r_2, w_1 r_1+w_2 r_2)\\\\\n",
    "            = Cov(m_1 r_1, w_1 r_1) + Cov(m_1 r_1, w_2 r_2) + Cov(m_2 r_2, w_1 r_1) + Cov(m_2 r_2, w_2 r_2)\\\\\n",
    "            = m_1 w_1 Cov(r_1, r_1) + m_1 w_2 Cov(r_1, r_2) + m_2 w_1 Cov(r_2, r_1) + m_2 w_2 Cov(r_2, r_2)$$\n",
    "\n",
    "$$\\begin{equation}\n",
    "{\\bf Cov}(M, R)=\\left[\n",
    "\\begin{matrix}\n",
    "m_1&m_2&\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "Cov(r_1, r_1)&Cov(r_2, r_1)&\\\\\n",
    "Cov(r_1, r_2)&Cov(r_2, r_2)&\n",
    "\\end{matrix}\\right]\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "w_1&\\\\\n",
    "w_2&\n",
    "\\end{matrix}\\right]\n",
    "\\end{equation}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(286,)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stock_list.set_index('code', inplace=True)\n",
    "market_weight = pd.Series(stock_list['weight'], index=symbols)\n",
    "m = market_weight.values\n",
    "m.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.3683343916091525e-11"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import cvxpy as cvx\n",
    "w = cvx.Variable(len(symbols))\n",
    "gamma = 0.5\n",
    "ret = mu.T*w \n",
    "risk = cvx.quad_form(w, Sigma)\n",
    "cov_MR = m.T*Sigma*w\n",
    "prob = cvx.Problem(cvx.Maximize(ret - gamma*risk), \n",
    "               [cvx.sum(w) <= 1, cov_MR == 0, w >= 0])\n",
    "prob.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "000001   -5.188573e-14\n",
       "000002    3.747884e-14\n",
       "000008    2.164068e-13\n",
       "000060    6.144296e-14\n",
       "000063   -1.532397e-14\n",
       "dtype: float64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(w.value, index=symbols).head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.89615857e-13])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ret.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0391530516688176e-21"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "risk.value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. 多因子模型\n",
    "#### 5.1 单支股票的多因子模型\n",
    "单支股票的收益率：  \n",
    "- $ r_j = x_{j1} f_1 + x_{j2} f_2 + \\ldots + x_{jk} f_k + u_j = X_jf+u_j$ （X为因子值，f为因子的权重，u为特质因子值）    \n",
    "\n",
    "股票的收益由两部分组成，一部分是可以共有因子的收益率$X_jf$, 一部分是各股特有的收益率$u_j$。我们需清晰的切分这两部分收益，因此$X_jf$和$u_j$的相关系数为0。    \n",
    "    \n",
    "单支股票的方差：  \n",
    "- $ {\\bf Var}(r_j) = Var(X_jf+u_j) = Var(X_jf) + Var(u_j) + 2Cov(X_jf, u) $ (其中f和u为随机变量)     \n",
    "\n",
    "因 $ Cov(X_jf, u) = 0$，所以 $ {\\bf Var}(r_j) = Var(X_jf) + Var(u_j) $。 也就是说股票的风险也由两部分组成，一部分是共有因子的风险，一部分是特异风险。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 5.2 投资组合的多因子模型：    \n",
    "- 收益率： $ R_p = \\sum_{j=1}^N w_j * (\\sum_{k=1}^K f_kX_{jk} + u_j) = w^T (Xf + u)$     \n",
    "\n",
    "$$\\begin{equation}\n",
    "Xf + u =\n",
    "\\left[\\begin{matrix}\n",
    "r_1&\\\\\n",
    "r_2&\\\\\n",
    "\\ldots&\\\\\n",
    "r_j&\n",
    "\\end{matrix}\\right]_{N*1} = \n",
    "\\left[\\begin{matrix}\n",
    "X_{11}&X_{12}&\\ldots&X_{1k}&\\\\\n",
    "X_{21}&X_{22}&\\ldots&X_{2k}&\\\\\n",
    "\\ldots&\\ldots&\\ldots&\\ldots&\\\\\n",
    "X_{j1}&X_{j2}&\\ldots&X_{jk}&\n",
    "\\end{matrix}\\right]_{N*K} *  \n",
    "\\left[\\begin{matrix}\n",
    "f_1&\\\\\n",
    "f_2&\\\\\n",
    "\\ldots&\\\\\n",
    "f_k&\n",
    "\\end{matrix}\\right]_{K*1} + \n",
    "\\left[\\begin{matrix}\n",
    "u_1&\\\\\n",
    "u_2&\\\\\n",
    "\\ldots&\\\\\n",
    "u_j&\n",
    "\\end{matrix}\\right]_{N*1}\n",
    "\\end{equation}$$ \n",
    "    \n",
    "- 方差： ${\\bf Var}(R_p) = w^T\\Sigma w$, 其中 $\\Sigma = XFX^T + \\Delta$   \n",
    "\n",
    "$$\\begin{equation}\n",
    "\\Sigma =\n",
    "\\left[\\begin{matrix}\n",
    "Cov(r_1,r_1)&Cov(r_2,r_1)&\\ldots&Cov(r_j,r_1)&\\\\\n",
    "Cov(r_1,r_2)&Cov(r_2,r_2)&\\ldots&Cov(r_j,r_2)&\\\\\n",
    "\\ldots&\\ldots&\\ldots&\\ldots&\\\\\n",
    "Cov(r_1,r_j)&Cov(r_2,r_j)&\\ldots&Cov(r_j,r_j)&&\n",
    "\\end{matrix}\\right]_{N*N}\\\\ = \n",
    "\\left[\\begin{matrix}\n",
    "X_{11}&X_{12}&\\ldots&X_{1k}&\\\\\n",
    "X_{21}&X_{22}&\\ldots&X_{2k}&\\\\\n",
    "\\ldots&\\ldots&\\ldots&\\ldots&\\\\\n",
    "X_{j1}&X_{j2}&\\ldots&X_{jk}&\n",
    "\\end{matrix}\\right]_{N*K} *  \n",
    "\\left[\\begin{matrix}\n",
    "Cov(f_1,f_1)&Cov(f_2,f_1)&\\ldots&Cov(f_k,f_1)&\\\\\n",
    "Cov(f_1,f_2)&Cov(f_2,f_2)&\\ldots&Cov(f_k,f_2)&\\\\\n",
    "\\ldots&\\ldots&\\ldots&\\ldots&\\\\\n",
    "Cov(f_1,f_k)&Cov(f_2,f_k)&\\ldots&Cov(f_k,f_k)&&\n",
    "\\end{matrix}\\right]_{K*K} * \n",
    "\\left[\\begin{matrix}\n",
    "X_{11}&X_{21}&\\ldots&X_{j1}&\\\\\n",
    "X_{12}&X_{22}&\\ldots&X_{j2}&\\\\\n",
    "\\ldots&\\ldots&\\ldots&\\ldots&\\\\\n",
    "X_{1k}&X_{2k}&\\ldots&X_{jk}&\n",
    "\\end{matrix}\\right]_{K*N} + \n",
    "\\left[\\begin{matrix}\n",
    "Var(u_1)&0&\\ldots&0&\\\\\n",
    "0&Var(u_2)&\\ldots&0&\\\\\n",
    "\\ldots&\\ldots&\\ldots&\\ldots&\\\\\n",
    ".&0&\\ldots&Var(u_j)&\n",
    "\\end{matrix}\\right]_{N*N}\n",
    "\\end{equation}$$ \n",
    "   \n",
    "以两支股票组成的投资组合,两个因子的模型为例：    \n",
    "    \n",
    "$$\\begin{equation}\n",
    "XFX^T =\n",
    "\\left[\\begin{matrix}\n",
    "X_{11}&X_{12}&\\\\\n",
    "X_{21}&X_{22}&\n",
    "\\end{matrix}\\right] *  \n",
    "\\left[\\begin{matrix}\n",
    "Cov(f_1,f_1)&Cov(f_2,f_1)&\\\\\n",
    "Cov(f_1,f_2)&Cov(f_2,f_2)&\n",
    "\\end{matrix}\\right] * \n",
    "\\left[\\begin{matrix}\n",
    "X_{11}&X_{21}&\\\\\n",
    "X_{12}&X_{22}&\n",
    "\\end{matrix}\\right]\\\\\n",
    "=\\left[\\begin{matrix}\n",
    "X_{11}Cov(f_1,f_1)+X_{12}Cov(f_1,f_2),&X_{11}Cov(f_2,f_1)+X_{12}Cov(f_2,f_2)&\\\\\n",
    "X_{21}Cov(f_1,f_1)+X_{22}Cov(f_1,f_2),&X_{21}Cov(f_1,f_1)+X_{22}Cov(f_1,f_2)&\n",
    "\\end{matrix}\\right] * \n",
    "\\left[\\begin{matrix}\n",
    "X_{11}&X_{21}&\\\\\n",
    "X_{12}&X_{22}&\n",
    "\\end{matrix}\\right]\n",
    "\\end{equation}$$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\begin{equation}\n",
    "\\begin{matrix}\n",
    "X_{11}^2Cov(f_1,f_1)+2X_{12}X_{11}Cov(f_1,f_2)+X_{12}^2Cov(f_2,f_2),&X_{11}X_{21}Cov(f_1,f_1)+X_{12}X_{21}Cov(f_1,f_2)+X_{11}X_{22}Cov(f_2,f_1)+X_{12}X_{22}Cov(f_2,f_2)&\\\\\n",
    "X_{21}X_{11}Cov(f_1,f_1)+X_{22}X_{11}Cov(f_1,f_2)+X_{21}X_{12}Cov(f_2,f_1)+X_{22}X_{12}Cov(f_2,f_2),&X_{21}^2Cov(f_1,f_1)+2X_{22}X_{21}Cov(f_1,f_2)+X_{22}^2Cov(f_2,f_2)&\n",
    "\\end{matrix}\n",
    "\\end{equation}$$  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "分解开来看:  \n",
    "左上: $ X_{11}^2Cov(f_1,f_1)+2X_{12}X_{11}Cov(f_1,f_2)+X_{12}^2Cov(f_2,f_2) = Var(X_{11}f_1+X_{12}f_2)$    \n",
    "右下: $ X_{21}^2Cov(f_1,f_1)+2X_{22}X_{21}Cov(f_1,f_2)+X_{22}^2Cov(f_2,f_2) = Var(X_{21}f_1+X_{22}f_2)$    \n",
    "右上: $ X_{11}X_{21}Cov(f_1,f_1)+X_{12}X_{21}Cov(f_1,f_2)+X_{11}X_{22}Cov(f_2,f_1)+X_{12}X_{22}Cov(f_2,f_2)\\\\ \n",
    "    = Cov(X_{11}f_1,X_{21}f_1)+Cov(X_{21}f_1,X_{12}f_2)+Cov(X_{22}f_2,X_{11}f_1)+Cov(X_{12}f_2,X_{22}f_2)\\\\\n",
    "    = Cov(X_{11}f_1 + X_{12}f_2, X_{21}f_1 + X_{22}f_2)\\\\\n",
    "    = Cov(r_1, r_2)$    \n",
    "  \n",
    "因此:    \n",
    "$$\\begin{equation}\n",
    "XFX^T =\n",
    "\\left[\\begin{matrix}\n",
    "Var(X_{11}f_1+X_{12}f_2)&Cov(r_1, r_2)&\\\\\n",
    "Cov(r_1, r_2)&Var(X_{21}f_1+X_{22}f_2)&\n",
    "\\end{matrix}\\right]\n",
    "\\end{equation}$$    \n",
    "   \n",
    "$$\\begin{equation}\n",
    "XFX^T + \\Delta =\n",
    "\\left[\\begin{matrix}\n",
    "Var(X_{11}f_1+X_{12}f_2)&Cov(r_1, r_2)&\\\\\n",
    "Cov(r_1, r_2)&Var(X_{21}f_1+X_{22}f_2)&\n",
    "\\end{matrix}\\right] + \n",
    "\\left[\\begin{matrix}\n",
    "Var(u_1)&0&\\\\\n",
    "0&Var(u_2)&\n",
    "\\end{matrix}\\right]\\\\\n",
    "=\\left[\\begin{matrix}\n",
    "Var(X_{11}f_1+X_{12}f_2)+Var(u_1)&Cov(r_1, r_2)&\\\\\n",
    "Cov(r_1, r_2)&Var(X_{21}f_1+X_{22}f_2)+Var(u_2)&\n",
    "\\end{matrix}\\right]\\\\\n",
    "=\\left[\\begin{matrix}\n",
    "Var(r_1)&Cov(r_2, r_1)&\\\\\n",
    "Cov(r_1, r_2)&Var(r_2)&\n",
    "\\end{matrix}\\right]\n",
    "\\end{equation}$$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/user/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:16: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  app.launch_new_instance()\n"
     ]
    }
   ],
   "source": [
    "data_dict = {}\n",
    "basic_data = ts.get_stock_basics()\n",
    "for symbol in stock_list.index.values:\n",
    "    data = ts.get_hist_data(symbol, start='2018-05-01')\n",
    "    if data is not None:\n",
    "        data['eps'] = basic_data.loc[symbol,'esp']\n",
    "        data['pe'] = data['close']/data['eps']\n",
    "        data['shares']=basic_data.loc[symbol,'outstanding']\n",
    "        data['market_cap'] = data['shares']*data['close']\n",
    "        data.sort_index(inplace=True)\n",
    "        data['high_low'] = (data['high'] - data['low'])/data['low']\n",
    "        data['turnover_mean_5'] = data['turnover'].rolling(window=5).mean()\n",
    "        data['p_std_5'] = data['p_change'].rolling(window=5).std()\n",
    "        data['ma5_10'] = (data['ma5'] - data['ma10'])/data['ma10']\n",
    "        hist_data = data[['p_change','high_low','turnover_mean_5','p_std_5','ma5_10','eps','market_cap']]\n",
    "        hist_data['p_change'] = hist_data['p_change'].shift(-1)\n",
    "        data_dict[symbol] = hist_data[4:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/user/anaconda3/lib/python3.6/site-packages/pandas/core/panel.py:728: FutureWarning: '.reindex_axis' is deprecated and will be removed in a future version. Use '.reindex' instead.\n",
      "  result = self.reindex_axis(new_ax, axis=axis)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<class 'pandas.core.panel.Panel'>\n",
       "Dimensions: 12 (items) x 287 (major_axis) x 7 (minor_axis)\n",
       "Items axis: 2018-05-08 to 2018-05-23\n",
       "Major_axis axis: 000001 to 601958\n",
       "Minor_axis axis: p_change to market_cap"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "panel = pd.Panel(data_dict)\n",
    "panel = panel.transpose(1,0,2)\n",
    "panel.dropna(how='all',inplace=True)\n",
    "panel.fillna(0,inplace=True)\n",
    "panel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "factor_return = {}\n",
    "special_factor = {}\n",
    "model = LinearRegression()\n",
    "for dt in panel.items.values[:-1]:\n",
    "    daily_data = panel[dt]\n",
    "    daily_data['large_marketcap'] = daily_data['market_cap'].apply(lambda x:int(x > daily_data['market_cap'].quantile(.7)))\n",
    "    daily_data['small_marketcap'] = daily_data['market_cap'].apply(lambda x:int(x < daily_data['market_cap'].quantile(.3)))\n",
    "    y = np.array(daily_data[['p_change']])\n",
    "    x_data = daily_data.drop(columns=['p_change','market_cap'])\n",
    "    X = np.array(x_data)\n",
    "    model.fit(X, y)\n",
    "\n",
    "    coef = model.coef_\n",
    "    factor_return[dt] = pd.Series(coef[0], index=x_data.columns)\n",
    "    \n",
    "    Xf = np.dot(X, coef.T)\n",
    "    sf = y - Xf\n",
    "    special_factor[dt] = pd.Series(sf.T[0], index=x_data.index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>high_low</th>\n",
       "      <th>turnover_mean_5</th>\n",
       "      <th>p_std_5</th>\n",
       "      <th>ma5_10</th>\n",
       "      <th>eps</th>\n",
       "      <th>large_marketcap</th>\n",
       "      <th>small_marketcap</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2018-05-08</th>\n",
       "      <td>6.670470</td>\n",
       "      <td>-0.182490</td>\n",
       "      <td>-0.028127</td>\n",
       "      <td>8.420476</td>\n",
       "      <td>0.112217</td>\n",
       "      <td>-0.153569</td>\n",
       "      <td>0.050132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-05-09</th>\n",
       "      <td>5.777776</td>\n",
       "      <td>0.010403</td>\n",
       "      <td>-0.217403</td>\n",
       "      <td>17.511872</td>\n",
       "      <td>0.230607</td>\n",
       "      <td>-0.079605</td>\n",
       "      <td>-0.258813</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-05-10</th>\n",
       "      <td>-26.209500</td>\n",
       "      <td>0.052642</td>\n",
       "      <td>0.091407</td>\n",
       "      <td>-8.853087</td>\n",
       "      <td>0.142846</td>\n",
       "      <td>0.020659</td>\n",
       "      <td>0.034860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-05-11</th>\n",
       "      <td>16.744839</td>\n",
       "      <td>-0.307259</td>\n",
       "      <td>-0.226117</td>\n",
       "      <td>25.175268</td>\n",
       "      <td>0.386079</td>\n",
       "      <td>0.643401</td>\n",
       "      <td>-0.712759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-05-14</th>\n",
       "      <td>20.059912</td>\n",
       "      <td>-0.034315</td>\n",
       "      <td>0.356477</td>\n",
       "      <td>-13.544423</td>\n",
       "      <td>0.002269</td>\n",
       "      <td>-0.609350</td>\n",
       "      <td>0.001860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-05-15</th>\n",
       "      <td>-17.227617</td>\n",
       "      <td>-0.182684</td>\n",
       "      <td>0.662731</td>\n",
       "      <td>0.936921</td>\n",
       "      <td>0.052209</td>\n",
       "      <td>-0.110553</td>\n",
       "      <td>0.598854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-05-16</th>\n",
       "      <td>8.686961</td>\n",
       "      <td>-0.251627</td>\n",
       "      <td>-0.310518</td>\n",
       "      <td>5.221918</td>\n",
       "      <td>-0.084423</td>\n",
       "      <td>-0.614749</td>\n",
       "      <td>0.249073</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-05-17</th>\n",
       "      <td>2.270676</td>\n",
       "      <td>0.032830</td>\n",
       "      <td>-0.218502</td>\n",
       "      <td>8.057830</td>\n",
       "      <td>0.040464</td>\n",
       "      <td>0.195925</td>\n",
       "      <td>-0.195881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-05-18</th>\n",
       "      <td>-27.659419</td>\n",
       "      <td>0.084165</td>\n",
       "      <td>0.545749</td>\n",
       "      <td>-12.145739</td>\n",
       "      <td>-0.382981</td>\n",
       "      <td>-0.259181</td>\n",
       "      <td>0.031443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-05-21</th>\n",
       "      <td>-6.493047</td>\n",
       "      <td>0.280076</td>\n",
       "      <td>0.177590</td>\n",
       "      <td>16.129936</td>\n",
       "      <td>0.160302</td>\n",
       "      <td>-0.173893</td>\n",
       "      <td>0.233640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-05-22</th>\n",
       "      <td>16.051949</td>\n",
       "      <td>-0.444841</td>\n",
       "      <td>-0.380561</td>\n",
       "      <td>12.639575</td>\n",
       "      <td>-0.296151</td>\n",
       "      <td>-0.238412</td>\n",
       "      <td>0.201259</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             high_low  turnover_mean_5   p_std_5     ma5_10       eps  \\\n",
       "2018-05-08   6.670470        -0.182490 -0.028127   8.420476  0.112217   \n",
       "2018-05-09   5.777776         0.010403 -0.217403  17.511872  0.230607   \n",
       "2018-05-10 -26.209500         0.052642  0.091407  -8.853087  0.142846   \n",
       "2018-05-11  16.744839        -0.307259 -0.226117  25.175268  0.386079   \n",
       "2018-05-14  20.059912        -0.034315  0.356477 -13.544423  0.002269   \n",
       "2018-05-15 -17.227617        -0.182684  0.662731   0.936921  0.052209   \n",
       "2018-05-16   8.686961        -0.251627 -0.310518   5.221918 -0.084423   \n",
       "2018-05-17   2.270676         0.032830 -0.218502   8.057830  0.040464   \n",
       "2018-05-18 -27.659419         0.084165  0.545749 -12.145739 -0.382981   \n",
       "2018-05-21  -6.493047         0.280076  0.177590  16.129936  0.160302   \n",
       "2018-05-22  16.051949        -0.444841 -0.380561  12.639575 -0.296151   \n",
       "\n",
       "            large_marketcap  small_marketcap  \n",
       "2018-05-08        -0.153569         0.050132  \n",
       "2018-05-09        -0.079605        -0.258813  \n",
       "2018-05-10         0.020659         0.034860  \n",
       "2018-05-11         0.643401        -0.712759  \n",
       "2018-05-14        -0.609350         0.001860  \n",
       "2018-05-15        -0.110553         0.598854  \n",
       "2018-05-16        -0.614749         0.249073  \n",
       "2018-05-17         0.195925        -0.195881  \n",
       "2018-05-18        -0.259181         0.031443  \n",
       "2018-05-21        -0.173893         0.233640  \n",
       "2018-05-22        -0.238412         0.201259  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factor_df = pd.DataFrame(factor_return)\n",
    "factor_df = factor_df.unstack().unstack()\n",
    "factor_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>000001</th>\n",
       "      <th>000002</th>\n",
       "      <th>000008</th>\n",
       "      <th>000060</th>\n",
       "      <th>000063</th>\n",
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       "      <th>000157</th>\n",
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       "      <th>...</th>\n",
       "      <th>601878</th>\n",
       "      <th>601881</th>\n",
       "      <th>601888</th>\n",
       "      <th>601898</th>\n",
       "      <th>601899</th>\n",
       "      <th>601901</th>\n",
       "      <th>601919</th>\n",
       "      <th>601933</th>\n",
       "      <th>601939</th>\n",
       "      <th>601958</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2018-05-08</th>\n",
       "      <td>-0.059286</td>\n",
       "      <td>-1.472061</td>\n",
       "      <td>-0.229883</td>\n",
       "      <td>1.101778</td>\n",
       "      <td>-0.050132</td>\n",
       "      <td>0.270870</td>\n",
       "      <td>-1.224212</td>\n",
       "      <td>0.206938</td>\n",
       "      <td>-1.278765</td>\n",
       "      <td>0.054897</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.751201</td>\n",
       "      <td>-1.874375</td>\n",
       "      <td>1.404167</td>\n",
       "      <td>-0.142913</td>\n",
       "      <td>0.027944</td>\n",
       "      <td>-0.817671</td>\n",
       "      <td>-0.546739</td>\n",
       "      <td>-1.451425</td>\n",
       "      <td>0.581975</td>\n",
       "      <td>-0.306112</td>\n",
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       "    <tr>\n",
       "      <th>2018-05-09</th>\n",
       "      <td>0.950246</td>\n",
       "      <td>0.546861</td>\n",
       "      <td>1.191029</td>\n",
       "      <td>0.730996</td>\n",
       "      <td>0.258813</td>\n",
       "      <td>2.387547</td>\n",
       "      <td>-0.245818</td>\n",
       "      <td>0.396568</td>\n",
       "      <td>0.675540</td>\n",
       "      <td>0.972523</td>\n",
       "      <td>...</td>\n",
       "      <td>0.738674</td>\n",
       "      <td>2.309294</td>\n",
       "      <td>2.588358</td>\n",
       "      <td>0.598448</td>\n",
       "      <td>1.391091</td>\n",
       "      <td>0.901906</td>\n",
       "      <td>0.084679</td>\n",
       "      <td>0.883015</td>\n",
       "      <td>0.067882</td>\n",
       "      <td>0.010356</td>\n",
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       "    <tr>\n",
       "      <th>2018-05-10</th>\n",
       "      <td>0.153613</td>\n",
       "      <td>-0.069618</td>\n",
       "      <td>-1.368612</td>\n",
       "      <td>0.155284</td>\n",
       "      <td>-0.034860</td>\n",
       "      <td>-0.763678</td>\n",
       "      <td>-0.575772</td>\n",
       "      <td>-0.585538</td>\n",
       "      <td>-0.015335</td>\n",
       "      <td>-1.042799</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.643917</td>\n",
       "      <td>-1.295082</td>\n",
       "      <td>0.348122</td>\n",
       "      <td>0.230631</td>\n",
       "      <td>0.569495</td>\n",
       "      <td>0.083519</td>\n",
       "      <td>-1.747156</td>\n",
       "      <td>-0.460490</td>\n",
       "      <td>2.512539</td>\n",
       "      <td>0.709699</td>\n",
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       "    <tr>\n",
       "      <th>2018-05-11</th>\n",
       "      <td>0.818151</td>\n",
       "      <td>-0.363652</td>\n",
       "      <td>0.226496</td>\n",
       "      <td>0.201412</td>\n",
       "      <td>0.712759</td>\n",
       "      <td>-2.034786</td>\n",
       "      <td>0.172314</td>\n",
       "      <td>-0.073208</td>\n",
       "      <td>-0.595293</td>\n",
       "      <td>1.448765</td>\n",
       "      <td>...</td>\n",
       "      <td>1.154940</td>\n",
       "      <td>1.110111</td>\n",
       "      <td>0.528873</td>\n",
       "      <td>-1.677850</td>\n",
       "      <td>-1.137885</td>\n",
       "      <td>-0.535872</td>\n",
       "      <td>1.108647</td>\n",
       "      <td>-0.369676</td>\n",
       "      <td>-0.640447</td>\n",
       "      <td>-0.697768</td>\n",
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       "    <tr>\n",
       "      <th>2018-05-14</th>\n",
       "      <td>-0.472658</td>\n",
       "      <td>-1.102699</td>\n",
       "      <td>2.251026</td>\n",
       "      <td>-0.167316</td>\n",
       "      <td>-0.001860</td>\n",
       "      <td>0.075015</td>\n",
       "      <td>-0.774158</td>\n",
       "      <td>1.619828</td>\n",
       "      <td>0.080224</td>\n",
       "      <td>-0.352993</td>\n",
       "      <td>...</td>\n",
       "      <td>0.034604</td>\n",
       "      <td>-1.716444</td>\n",
       "      <td>0.507375</td>\n",
       "      <td>-0.330888</td>\n",
       "      <td>-1.087403</td>\n",
       "      <td>1.107431</td>\n",
       "      <td>0.748992</td>\n",
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       "      <td>-0.073251</td>\n",
       "      <td>1.174885</td>\n",
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       "    <tr>\n",
       "      <th>2018-05-15</th>\n",
       "      <td>-2.098305</td>\n",
       "      <td>-1.609298</td>\n",
       "      <td>1.220258</td>\n",
       "      <td>-1.517399</td>\n",
       "      <td>-0.598854</td>\n",
       "      <td>-1.183377</td>\n",
       "      <td>-0.997101</td>\n",
       "      <td>-1.129961</td>\n",
       "      <td>-1.440367</td>\n",
       "      <td>-1.957959</td>\n",
       "      <td>...</td>\n",
       "      <td>-2.280235</td>\n",
       "      <td>-2.751720</td>\n",
       "      <td>-1.761161</td>\n",
       "      <td>0.201605</td>\n",
       "      <td>-2.051436</td>\n",
       "      <td>-1.703267</td>\n",
       "      <td>-0.433072</td>\n",
       "      <td>1.075916</td>\n",
       "      <td>-1.616268</td>\n",
       "      <td>1.294926</td>\n",
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       "    <tr>\n",
       "      <th>2018-05-16</th>\n",
       "      <td>0.232994</td>\n",
       "      <td>-0.863433</td>\n",
       "      <td>0.535039</td>\n",
       "      <td>0.053974</td>\n",
       "      <td>-0.249073</td>\n",
       "      <td>0.239898</td>\n",
       "      <td>-1.018629</td>\n",
       "      <td>-0.114746</td>\n",
       "      <td>-0.037548</td>\n",
       "      <td>-1.298458</td>\n",
       "      <td>...</td>\n",
       "      <td>0.422410</td>\n",
       "      <td>0.650741</td>\n",
       "      <td>-0.643161</td>\n",
       "      <td>-0.912160</td>\n",
       "      <td>0.035610</td>\n",
       "      <td>-0.049099</td>\n",
       "      <td>-0.762980</td>\n",
       "      <td>-1.731088</td>\n",
       "      <td>0.656864</td>\n",
       "      <td>-1.416382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-05-17</th>\n",
       "      <td>1.271057</td>\n",
       "      <td>1.309399</td>\n",
       "      <td>6.925819</td>\n",
       "      <td>2.159487</td>\n",
       "      <td>0.195881</td>\n",
       "      <td>1.136581</td>\n",
       "      <td>0.766485</td>\n",
       "      <td>0.894522</td>\n",
       "      <td>0.559096</td>\n",
       "      <td>1.497391</td>\n",
       "      <td>...</td>\n",
       "      <td>1.631922</td>\n",
       "      <td>1.121977</td>\n",
       "      <td>0.843902</td>\n",
       "      <td>3.611940</td>\n",
       "      <td>0.981306</td>\n",
       "      <td>1.330316</td>\n",
       "      <td>4.108377</td>\n",
       "      <td>-1.412592</td>\n",
       "      <td>1.750585</td>\n",
       "      <td>2.221059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-05-18</th>\n",
       "      <td>0.011548</td>\n",
       "      <td>-0.248018</td>\n",
       "      <td>0.554499</td>\n",
       "      <td>-0.921647</td>\n",
       "      <td>-0.031443</td>\n",
       "      <td>0.089691</td>\n",
       "      <td>1.007226</td>\n",
       "      <td>0.216973</td>\n",
       "      <td>1.104379</td>\n",
       "      <td>0.401072</td>\n",
       "      <td>...</td>\n",
       "      <td>0.585833</td>\n",
       "      <td>0.227036</td>\n",
       "      <td>1.737826</td>\n",
       "      <td>-0.151262</td>\n",
       "      <td>0.721585</td>\n",
       "      <td>0.106805</td>\n",
       "      <td>8.126613</td>\n",
       "      <td>1.843074</td>\n",
       "      <td>-0.696727</td>\n",
       "      <td>0.255897</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-05-21</th>\n",
       "      <td>-0.847900</td>\n",
       "      <td>-1.071388</td>\n",
       "      <td>-2.987661</td>\n",
       "      <td>1.765085</td>\n",
       "      <td>-0.233640</td>\n",
       "      <td>-0.487653</td>\n",
       "      <td>-0.363361</td>\n",
       "      <td>-0.336066</td>\n",
       "      <td>-0.270700</td>\n",
       "      <td>-2.625310</td>\n",
       "      <td>...</td>\n",
       "      <td>0.039039</td>\n",
       "      <td>-0.789154</td>\n",
       "      <td>0.093966</td>\n",
       "      <td>-0.900448</td>\n",
       "      <td>-0.963191</td>\n",
       "      <td>-1.187135</td>\n",
       "      <td>-0.727904</td>\n",
       "      <td>2.511030</td>\n",
       "      <td>-2.253618</td>\n",
       "      <td>-1.714377</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-05-22</th>\n",
       "      <td>-1.161486</td>\n",
       "      <td>1.195315</td>\n",
       "      <td>-1.021039</td>\n",
       "      <td>-0.259584</td>\n",
       "      <td>-0.201259</td>\n",
       "      <td>-1.345574</td>\n",
       "      <td>-0.050303</td>\n",
       "      <td>-0.717356</td>\n",
       "      <td>-0.061063</td>\n",
       "      <td>-0.769255</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.082251</td>\n",
       "      <td>-0.811254</td>\n",
       "      <td>-0.184318</td>\n",
       "      <td>-1.942532</td>\n",
       "      <td>0.371445</td>\n",
       "      <td>-0.612087</td>\n",
       "      <td>-2.159458</td>\n",
       "      <td>-0.320409</td>\n",
       "      <td>-0.366556</td>\n",
       "      <td>-2.366439</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>11 rows × 287 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              000001    000002    000008    000060    000063    000069  \\\n",
       "2018-05-08 -0.059286 -1.472061 -0.229883  1.101778 -0.050132  0.270870   \n",
       "2018-05-09  0.950246  0.546861  1.191029  0.730996  0.258813  2.387547   \n",
       "2018-05-10  0.153613 -0.069618 -1.368612  0.155284 -0.034860 -0.763678   \n",
       "2018-05-11  0.818151 -0.363652  0.226496  0.201412  0.712759 -2.034786   \n",
       "2018-05-14 -0.472658 -1.102699  2.251026 -0.167316 -0.001860  0.075015   \n",
       "2018-05-15 -2.098305 -1.609298  1.220258 -1.517399 -0.598854 -1.183377   \n",
       "2018-05-16  0.232994 -0.863433  0.535039  0.053974 -0.249073  0.239898   \n",
       "2018-05-17  1.271057  1.309399  6.925819  2.159487  0.195881  1.136581   \n",
       "2018-05-18  0.011548 -0.248018  0.554499 -0.921647 -0.031443  0.089691   \n",
       "2018-05-21 -0.847900 -1.071388 -2.987661  1.765085 -0.233640 -0.487653   \n",
       "2018-05-22 -1.161486  1.195315 -1.021039 -0.259584 -0.201259 -1.345574   \n",
       "\n",
       "              000100    000157    000166    000333    ...       601878  \\\n",
       "2018-05-08 -1.224212  0.206938 -1.278765  0.054897    ...    -0.751201   \n",
       "2018-05-09 -0.245818  0.396568  0.675540  0.972523    ...     0.738674   \n",
       "2018-05-10 -0.575772 -0.585538 -0.015335 -1.042799    ...    -1.643917   \n",
       "2018-05-11  0.172314 -0.073208 -0.595293  1.448765    ...     1.154940   \n",
       "2018-05-14 -0.774158  1.619828  0.080224 -0.352993    ...     0.034604   \n",
       "2018-05-15 -0.997101 -1.129961 -1.440367 -1.957959    ...    -2.280235   \n",
       "2018-05-16 -1.018629 -0.114746 -0.037548 -1.298458    ...     0.422410   \n",
       "2018-05-17  0.766485  0.894522  0.559096  1.497391    ...     1.631922   \n",
       "2018-05-18  1.007226  0.216973  1.104379  0.401072    ...     0.585833   \n",
       "2018-05-21 -0.363361 -0.336066 -0.270700 -2.625310    ...     0.039039   \n",
       "2018-05-22 -0.050303 -0.717356 -0.061063 -0.769255    ...    -1.082251   \n",
       "\n",
       "              601881    601888    601898    601899    601901    601919  \\\n",
       "2018-05-08 -1.874375  1.404167 -0.142913  0.027944 -0.817671 -0.546739   \n",
       "2018-05-09  2.309294  2.588358  0.598448  1.391091  0.901906  0.084679   \n",
       "2018-05-10 -1.295082  0.348122  0.230631  0.569495  0.083519 -1.747156   \n",
       "2018-05-11  1.110111  0.528873 -1.677850 -1.137885 -0.535872  1.108647   \n",
       "2018-05-14 -1.716444  0.507375 -0.330888 -1.087403  1.107431  0.748992   \n",
       "2018-05-15 -2.751720 -1.761161  0.201605 -2.051436 -1.703267 -0.433072   \n",
       "2018-05-16  0.650741 -0.643161 -0.912160  0.035610 -0.049099 -0.762980   \n",
       "2018-05-17  1.121977  0.843902  3.611940  0.981306  1.330316  4.108377   \n",
       "2018-05-18  0.227036  1.737826 -0.151262  0.721585  0.106805  8.126613   \n",
       "2018-05-21 -0.789154  0.093966 -0.900448 -0.963191 -1.187135 -0.727904   \n",
       "2018-05-22 -0.811254 -0.184318 -1.942532  0.371445 -0.612087 -2.159458   \n",
       "\n",
       "              601933    601939    601958  \n",
       "2018-05-08 -1.451425  0.581975 -0.306112  \n",
       "2018-05-09  0.883015  0.067882  0.010356  \n",
       "2018-05-10 -0.460490  2.512539  0.709699  \n",
       "2018-05-11 -0.369676 -0.640447 -0.697768  \n",
       "2018-05-14 -0.090416 -0.073251  1.174885  \n",
       "2018-05-15  1.075916 -1.616268  1.294926  \n",
       "2018-05-16 -1.731088  0.656864 -1.416382  \n",
       "2018-05-17 -1.412592  1.750585  2.221059  \n",
       "2018-05-18  1.843074 -0.696727  0.255897  \n",
       "2018-05-21  2.511030 -2.253618 -1.714377  \n",
       "2018-05-22 -0.320409 -0.366556 -2.366439  \n",
       "\n",
       "[11 rows x 287 columns]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp_factor_df = pd.DataFrame(special_factor)\n",
    "sp_factor_df = sp_factor_df.unstack().unstack()\n",
    "sp_factor_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>high_low</th>\n",
       "      <th>turnover_mean_5</th>\n",
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       "      <th>turnover_mean_5</th>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>p_std_5</th>\n",
       "      <td>-3.738807</td>\n",
       "      <td>0.031859</td>\n",
       "      <td>0.127357</td>\n",
       "      <td>-2.916032</td>\n",
       "      <td>-0.015755</td>\n",
       "      <td>-0.028921</td>\n",
       "      <td>0.055465</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ma5_10</th>\n",
       "      <td>102.804290</td>\n",
       "      <td>-0.733326</td>\n",
       "      <td>-2.916032</td>\n",
       "      <td>161.133231</td>\n",
       "      <td>1.486816</td>\n",
       "      <td>2.464291</td>\n",
       "      <td>-1.743899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>eps</th>\n",
       "      <td>0.814864</td>\n",
       "      <td>0.005933</td>\n",
       "      <td>-0.015755</td>\n",
       "      <td>1.486816</td>\n",
       "      <td>0.049480</td>\n",
       "      <td>0.045600</td>\n",
       "      <td>-0.036386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>large_marketcap</th>\n",
       "      <td>-0.216198</td>\n",
       "      <td>-0.004990</td>\n",
       "      <td>-0.028921</td>\n",
       "      <td>2.464291</td>\n",
       "      <td>0.045600</td>\n",
       "      <td>0.122544</td>\n",
       "      <td>-0.077126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>small_marketcap</th>\n",
       "      <td>-2.169820</td>\n",
       "      <td>0.002902</td>\n",
       "      <td>0.055465</td>\n",
       "      <td>-1.743899</td>\n",
       "      <td>-0.036386</td>\n",
       "      <td>-0.077126</td>\n",
       "      <td>0.112889</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   high_low  turnover_mean_5   p_std_5      ma5_10       eps  \\\n",
       "high_low         288.972362        -1.873522 -3.738807  102.804290  0.814864   \n",
       "turnover_mean_5   -1.873522         0.043209  0.031859   -0.733326  0.005933   \n",
       "p_std_5           -3.738807         0.031859  0.127357   -2.916032 -0.015755   \n",
       "ma5_10           102.804290        -0.733326 -2.916032  161.133231  1.486816   \n",
       "eps                0.814864         0.005933 -0.015755    1.486816  0.049480   \n",
       "large_marketcap   -0.216198        -0.004990 -0.028921    2.464291  0.045600   \n",
       "small_marketcap   -2.169820         0.002902  0.055465   -1.743899 -0.036386   \n",
       "\n",
       "                 large_marketcap  small_marketcap  \n",
       "high_low               -0.216198        -2.169820  \n",
       "turnover_mean_5        -0.004990         0.002902  \n",
       "p_std_5                -0.028921         0.055465  \n",
       "ma5_10                  2.464291        -1.743899  \n",
       "eps                     0.045600        -0.036386  \n",
       "large_marketcap         0.122544        -0.077126  \n",
       "small_marketcap        -0.077126         0.112889  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factor_cov = factor_df.cov()\n",
    "factor_cov"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.98323782, 0.        , 0.        , ..., 0.        , 0.        ,\n",
       "        0.        ],\n",
       "       [0.        , 1.02296505, 0.        , ..., 0.        , 0.        ,\n",
       "        0.        ],\n",
       "       [0.        , 0.        , 6.36407643, ..., 0.        , 0.        ,\n",
       "        0.        ],\n",
       "       ...,\n",
       "       [0.        , 0.        , 0.        , ..., 1.91770948, 0.        ,\n",
       "        0.        ],\n",
       "       [0.        , 0.        , 0.        , ..., 0.        , 1.88780763,\n",
       "        0.        ],\n",
       "       [0.        , 0.        , 0.        , ..., 0.        , 0.        ,\n",
       "        1.9622128 ]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp_factor_var = sp_factor_df.var()\n",
    "sp_factor_diag_cov = np.diag(sp_factor_var)\n",
    "sp_factor_diag_cov"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(287, 7)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "last_dt = panel.items.values[-1]\n",
    "last_data = panel[last_dt]\n",
    "last_data['large_marketcap'] = last_data['market_cap'].apply(lambda x:int(x > last_data['market_cap'].quantile(.7)))\n",
    "last_data['small_marketcap'] = last_data['market_cap'].apply(lambda x:int(x < last_data['market_cap'].quantile(.3)))\n",
    "x_data = last_data.drop(columns=['p_change','market_cap'])\n",
    "X = np.array(x_data)\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.17526094, 0.18231485, 0.23108995, ..., 0.26413624, 0.23972436,\n",
       "        0.08273511],\n",
       "       [0.18231485, 1.20962809, 0.24934152, ..., 0.26749794, 0.23169761,\n",
       "        0.10812575],\n",
       "       [0.23108995, 0.24934152, 7.3792011 , ..., 0.51885377, 0.39183531,\n",
       "        0.5539212 ],\n",
       "       ...,\n",
       "       [0.26413624, 0.26749794, 0.51885377, ..., 2.35609101, 0.37507993,\n",
       "        0.23029667],\n",
       "       [0.23972436, 0.23169761, 0.39183531, ..., 0.37507993, 2.24859302,\n",
       "        0.14822129],\n",
       "       [0.08273511, 0.10812575, 0.5539212 , ..., 0.23029667, 0.14822129,\n",
       "        2.30601552]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Sigma = np.dot(np.dot(X, np.array(factor_cov)), X.T) + sp_factor_diag_cov\n",
    "Sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.12063623, -0.08573641,  0.04115681,  5.41368611,  0.03303983,\n",
       "       -0.12539334,  0.02124268])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factor_mu = np.array(factor_df.mean())\n",
    "factor_mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(287,)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp_factor_mu = np.array(sp_factor_df.mean())\n",
    "sp_factor_mu.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(287,)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu = np.dot(X,factor_mu)+sp_factor_mu\n",
    "mu.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9041807938696902"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import cvxpy as cvx\n",
    "w = cvx.Variable(len(X))\n",
    "gamma = 0.5\n",
    "ret = mu.T*w \n",
    "risk = cvx.quad_form(w, Sigma)\n",
    "prob = cvx.Problem(cvx.Maximize(ret - gamma*risk), \n",
    "               [cvx.sum(w) <= 1, w >= 0])\n",
    "prob.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "000001    2.469138e-12\n",
       "000002    1.750725e-12\n",
       "000008    5.689806e-03\n",
       "000060    2.268313e-12\n",
       "000063    5.746878e-12\n",
       "dtype: float64"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(w.value, index=panel.major_axis).head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 因子中性 —— eg. 市值中性"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.485969147081809"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import cvxpy as cvx\n",
    "w = cvx.Variable(len(X))\n",
    "gamma = 0.5\n",
    "ret = mu.T*w \n",
    "risk = cvx.quad_form(w, Sigma)\n",
    "\n",
    "large_weight = np.array(x_data['large_marketcap']).T*w\n",
    "small_weight = np.array(x_data['small_marketcap']).T*w\n",
    "prob = cvx.Problem(cvx.Maximize(ret - gamma*risk), \n",
    "               [cvx.sum(w) <= 1,\n",
    "               large_weight == 0, small_weight == 0])\n",
    "prob.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "000001   -0.082440\n",
       "000002   -0.286741\n",
       "000008    0.125836\n",
       "000060    1.004990\n",
       "000063    0.168340\n",
       "dtype: float64"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(w.value, index=panel.major_axis).head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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