efficient frontier and tangent portfolio.ipynb

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     "text": [
      "                 MMM       ABT      ABBV       ACN      ATVI       AYI  \\\n",
      "Date                                                                     \n",
      "2016-01-04       NaN       NaN       NaN       NaN       NaN       NaN   \n",
      "2016-01-05 -0.004340  0.000233  0.004183 -0.005178  0.012924 -0.012533   \n",
      "2016-01-06  0.020555  0.008459 -0.000174  0.001958  0.009513  0.027094   \n",
      "2016-01-07  0.024970  0.024555  0.002972  0.030254  0.014337  0.027252   \n",
      "2016-01-08  0.003417  0.021392  0.028032  0.009776  0.015682  0.038797   \n",
      "2016-01-11  0.000214 -0.001473  0.032851 -0.010380 -0.013808  0.044346   \n",
      "2016-01-12 -0.002840 -0.017607 -0.017505 -0.017622 -0.024515 -0.013294   \n",
      "2016-01-13  0.015427  0.029295  0.071512  0.017630  0.064831  0.047803   \n",
      "2016-01-14 -0.017425 -0.019951 -0.061950 -0.025717 -0.015254 -0.035894   \n",
      "2016-01-15  0.017954  0.013814 -0.048483  0.026292  0.014036  0.019403   \n",
      "\n",
      "                ADBE       AMD       AAP       AES    ...         WYNN  \\\n",
      "Date                                                  ...                \n",
      "2016-01-04       NaN       NaN       NaN       NaN    ...          NaN   \n",
      "2016-01-05 -0.004007  0.007273  0.006878 -0.013598    ...    -0.018553   \n",
      "2016-01-06  0.014502  0.100000  0.027174  0.035753    ...     0.054636   \n",
      "2016-01-07  0.021434  0.096491 -0.010952  0.025556    ...     0.103838   \n",
      "2016-01-08  0.014343  0.065421  0.022465 -0.014239    ...     0.042432   \n",
      "2016-01-11 -0.017118 -0.085470 -0.010133  0.011074    ...     0.016728   \n",
      "2016-01-12 -0.004899 -0.020921 -0.006889  0.032000    ...     0.021036   \n",
      "2016-01-13  0.017214  0.062222  0.041573  0.012731    ...     0.060034   \n",
      "2016-01-14 -0.016704  0.018100  0.005944 -0.023729    ...     0.018835   \n",
      "2016-01-15  0.007065  0.088670 -0.020584  0.036300    ...    -0.117697   \n",
      "\n",
      "                 XEL       XRX      XLNX  XL       XYL       YUM       ZBH  \\\n",
      "Date                                                                         \n",
      "2016-01-04       NaN       NaN       NaN NaN       NaN       NaN       NaN   \n",
      "2016-01-05 -0.009983  0.001946 -0.014630 NaN  0.000277  0.002499 -0.020398   \n",
      "2016-01-06 -0.010428  0.012808  0.018628 NaN  0.012633  0.007131 -0.004311   \n",
      "2016-01-07 -0.003827  0.028369  0.041068 NaN  0.026513  0.035321  0.023534   \n",
      "2016-01-08  0.011056  0.029197  0.020964 NaN  0.009601  0.013795  0.004234   \n",
      "2016-01-11 -0.007952  0.020213 -0.004406 NaN  0.008509  0.001764  0.017535   \n",
      "2016-01-12  0.003854 -0.013641 -0.005535 NaN -0.005544 -0.022280 -0.029843   \n",
      "2016-01-13  0.006092  0.033623  0.034598 NaN  0.026663  0.007823  0.016502   \n",
      "2016-01-14 -0.016344  0.004357 -0.011790 NaN -0.005660 -0.013998 -0.014606   \n",
      "2016-01-15  0.005753  0.008791 -0.009344 NaN  0.017890  0.043524  0.016027   \n",
      "\n",
      "                ZION       ZTS  \n",
      "Date                            \n",
      "2016-01-04       NaN       NaN  \n",
      "2016-01-05  0.010977 -0.015413  \n",
      "2016-01-06  0.030019 -0.000208  \n",
      "2016-01-07  0.030949  0.031357  \n",
      "2016-01-08  0.011382  0.014821  \n",
      "2016-01-11  0.020324  0.029161  \n",
      "2016-01-12  0.004165 -0.008672  \n",
      "2016-01-13  0.048930  0.039769  \n",
      "2016-01-14 -0.004350 -0.019941  \n",
      "2016-01-15  0.029096  0.017289  \n",
      "\n",
      "[10 rows x 502 columns]\n"
     ]
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   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import cvxopt as opt\n",
    "from cvxopt import blas, solvers\n",
    "import pandas as pd\n",
    "import os\n",
    "import get_stock_data as gd\n",
    "import pickle\n",
    "import get_market_data as gmd\n",
    "data = gmd.Rate_return_compile()\n",
    "with open(\"sp500tickers.pickle\", \"rb\") as f:\n",
    "    tickers = pickle.load(f)\n",
    "# there might be tickers that the web can not reach\n",
    "tickers = [t for t in tickers if os.path.exists('stock_dfs/{}.csv'.format(t))]\n",
    "data = data.fillna(method='ffill')\n",
    "data = data.fillna(0)\n",
    "np.random.seed(123)\n",
    "# Turn off progress printing \n",
    "solvers.options['show_progress'] = False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "return_vec = data.values.T\n",
    "## NUMBER OF ASSETS\n",
    "n_assets = return_vec.shape[0]\n",
    "## NUMBER OF OBSERVATIONS\n",
    "n_obs = return_vec.shape[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# random portfolio\n",
    "def rand_weights(n):\n",
    "    ''' Produces n random weights that sum to 1 '''\n",
    "    k = np.random.rand(n)\n",
    "    return k / sum(k)\n",
    "\n",
    "def random_portfolio(returns):\n",
    "    ''' \n",
    "    Returns the mean and standard deviation of returns for a random portfolio, and a filter that only allows\n",
    "    the portfolio with a standard deviation smaller that 2.\n",
    "    '''\n",
    "\n",
    "    p = np.asmatrix(np.mean(returns, axis=1))\n",
    "    w = np.asmatrix(rand_weights(returns.shape[0]))\n",
    "    C = np.asmatrix(np.cov(returns))\n",
    "    \n",
    "    mu = w * p.T\n",
    "    sigma = np.sqrt(w * C * w.T)\n",
    "    \n",
    "    # This recursion reduces outliers to keep plots pretty\n",
    "#     if sigma > 2:\n",
    "#         return random_portfolio(returns)\n",
    "    return mu, sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
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       "       [-0.00029195],\n",
       "       [-0.00028819],\n",
       "       [-0.00029191],\n",
       "       [-0.00029782],\n",
       "       [-0.00030831],\n",
       "       [-0.00029792],\n",
       "       [-0.0002451 ],\n",
       "       [-0.00029022],\n",
       "       [-0.00028121],\n",
       "       [-0.00028231],\n",
       "       [-0.00025623],\n",
       "       [-0.00028772],\n",
       "       [-0.00029112],\n",
       "       [-0.00031025],\n",
       "       [-0.0002678 ],\n",
       "       [-0.00031661],\n",
       "       [-0.00028679],\n",
       "       [-0.00030208],\n",
       "       [-0.00026841],\n",
       "       [-0.00031606],\n",
       "       [-0.00028553],\n",
       "       [-0.00028094],\n",
       "       [-0.00028345],\n",
       "       [-0.00028907],\n",
       "       [-0.00025022],\n",
       "       [-0.00030532],\n",
       "       [-0.00025698],\n",
       "       [-0.00032989],\n",
       "       [-0.00025589],\n",
       "       [-0.0003351 ],\n",
       "       [-0.00028584],\n",
       "       [-0.00026402],\n",
       "       [-0.00028882]])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x118dc4da0>"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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FHQmz6+uPu5USRapSotFo8ou2aDX9htnlgykujCQtWoDiwgizygf3YKsy01OWZSalRFv/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\nn0zI8lkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1193350b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_portfolios = 1000\n",
    "means, stds = np.column_stack([\n",
    "    random_portfolio(return_vec) \n",
    "    for i in range(n_portfolios)\n",
    "])\n",
    "\n",
    "plt.plot(stds, means, 'o', markersize=5)\n",
    "plt.xlabel('std')\n",
    "plt.ylabel('mean')\n",
    "plt.title('Mean and standard deviation of returns of randomly generated portfolios')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1192fdef0>]"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x119ab62b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def optimal_portfolio(returns):\n",
    "    n = len(returns)\n",
    "    returns = np.asmatrix(returns)\n",
    "    \n",
    "    N = 1000\n",
    "    mus = [10**(5.0 * t/N - 1.0) for t in range(N)]\n",
    "    \n",
    "    # Convert to cvxopt matrices\n",
    "    S = opt.matrix(np.cov(returns))\n",
    "    pbar = opt.matrix(np.mean(returns, axis=1))\n",
    "    \n",
    "    # Create constraint matrices\n",
    "    G = -opt.matrix(np.eye(n))   # negative n x n identity matrix\n",
    "    h = opt.matrix(0.0, (n ,1))\n",
    "    A = opt.matrix(1.0, (1, n))\n",
    "    b = opt.matrix(1.0)\n",
    "    \n",
    "    # Calculate efficient frontier weights using quadratic programming\n",
    "    portfolios = [solvers.qp(mu*S, -pbar, G, h, A, b)['x'] \n",
    "                  for mu in mus]\n",
    "    ## CALCULATE RISKS AND RETURNS FOR FRONTIER\n",
    "    returns = [blas.dot(pbar, x) for x in portfolios]\n",
    "    risks = [np.sqrt(blas.dot(x, S*x)) for x in portfolios]\n",
    "    ## CALCULATE THE 2ND DEGREE POLYNOMIAL OF THE FRONTIER CURVE\n",
    "    m1 = np.polyfit(returns, risks, 2)\n",
    "    x1 = np.sqrt(m1[2] / m1[0])\n",
    "    # CALCULATE THE OPTIMAL PORTFOLIO\n",
    "    wt = solvers.qp(opt.matrix(x1 * S), -pbar, G, h, A, b)['x']\n",
    "    return np.asarray(wt), returns, risks\n",
    "\n",
    "weights, returns, risks = optimal_portfolio(return_vec)\n",
    "\n",
    "plt.plot(stds, means, 'o')\n",
    "plt.ylabel('mean')\n",
    "plt.xlabel('std')\n",
    "plt.plot(risks, returns, 'y-o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.519950782211\n",
      "1.92603448276\n"
     ]
    }
   ],
   "source": [
    "print(np.min(return_vec))\n",
    "print(np.max(return_vec))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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