ml-finance-python

notebook.ipynb

(188243B)

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  "cells": [
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    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "# Estimation of Covariance Matrices\n",
     "By Christopher van Hoecke and Max Margenot\n",
     "\n",
     "Part of the Quantopian Lecture Series:\n",
     "\n",
     "* [www.quantopian.com/lectures](https://www.quantopian.com/lectures)\n",
     "* [github.com/quantopian/research_public](https://github.com/quantopian/research_public)\n",
     "\n",
     "\n",
     "---\n",
     "\n",
     "Volatility has long been a thorn in the side of investors in the market. Successfully measuring volatility would allow for more accurate modeling of the returns and more stable investments leading to greater returns, but forecasting volatility accurately is a difficult problem. \n",
     "\n",
     "## Measuring Volatility\n",
     "\n",
     "Volatility needs to be forward-looking and predictive in order to make smart decisions. Unfortunately, simply taking the historical standard deviation of an individual asset's returns falls short when we take into account need for robustness to the future. When we scale the problem up to the point where we need to forecast the volatility for many assets, it gets even harder.\n",
     "\n",
     "To model how a portfolio overall changes, it is important to look not only at the volatility of each asset in the portfolio, but also at the pairwise covariances of every asset involved. The relationship between two or more assets provides valuable insights and a path towards reduction of overall portfolio volatility. A large number of assets with low covariance would assure they decrease or increase independently of each other. Indepedent assets have less of an impact on our portfolio's volatility as they give us true diversity and help us avoid [position concentration risk](https://www.quantopian.com/lectures/position-concentration-risk).\n",
     "\n",
     "## Covariance\n",
     "\n",
     "In statistics and probability, the covariance is a measure of the joint variability of two random variables. When random variables exhibit similar behavior, there tends to be a high covariance between them. Mathematically, we express the covariance of X with respect to Y as:\n",
     "\n",
     "$$ COV(X, Y) = E[(X - E[X])(Y - E[Y])]$$\n",
     "\n",
     "Notice that if we take the covariance of $X$ with itself, we get:\n",
     "\n",
     "$$ COV(X, X) = E[(X - E[X])(X - E[X])] = E[(X - E[X])^2] = VAR(X) $$\n",
     "\n",
     "We can use covariance to quantify the similarities between different assets in much the same way. If two assets have a high covariance, they will generally behave the same way. Assets with particularly high covariance can essentially replace each other.\n",
     "\n",
     "Covariance matrices form the backbone of Modern Portfolio theory (MPT). MPT focuses on maximizing return for a given level of risk, making essential the methods with which we estimate that risk. We use covariances to quantify the joint risk of assets, forming how we view the risk of an entire portfolio. What is key is that investing in assets that have high pairwise covariances provides little diversification because of how closely their fluctuations are related."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 1,
    "metadata": {
     "collapsed": false
    },
    "outputs": [],
    "source": [
     "import numpy as np \n",
     "import pandas as pd\n",
     "import matplotlib.pyplot as plt\n",
     "import seaborn as sns\n",
     "import scipy.stats as stats\n",
     "from sklearn import covariance"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Let's take the covariance of two closely related variables, $X$ and $Y$. Say that $X$ is some randomly drawn set and that $Y =  5X + \\epsilon$, where $\\epsilon$ is some extra noise. We can compute the covariance using the formula above to get a clearer picture of how $X$ evolves with respect to asset $Y$."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 2,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Value of the covariance between X and Y: 5.50710185158\n"
      ]
     }
    ],
    "source": [
     "# Generate random values of x\n",
     "X = np.random.normal(size = 1000)\n",
     "epsilon = np.random.normal(0, 3, size = len(X))\n",
     "Y = 5*X + epsilon\n",
     "\n",
     "product = (X - np.mean(X))*(Y - np.mean(Y))\n",
     "expected_value = np.mean(product)\n",
     "\n",
     "print 'Value of the covariance between X and Y:', expected_value"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "We can also compute the covariance between $X$ and $Y$ with a single function."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 3,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
        "array([[  1.08671434,   5.51261447],\n",
        "       [  5.51261447,  36.24846599]])"
       ]
      },
      "execution_count": 3,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "np.cov([X, Y])"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "This gives us the covariance matrix between $X$ and $Y$. The diagonals are their respective variances and the indices $(i, j)$ refer to the covariance between assets indexed $i$ and $j$."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 4,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "1.08562762864 36.2122175246\n"
      ]
     }
    ],
    "source": [
     "print np.var(X), np.var(Y)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "In this case, we only have two assets so we only have indices $(0, 1)$ and $(1, 0)$. Covariance matrices are symmetric, since $COV(X, Y) = COV(Y, X)$, which is why the off-diagonals mirror each other."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "We can intuitively think of this as how much $Y$ changes when $X$ changes and vice-versa. As such, our covariance value of about 5 could have been anticipated from the definition of the relationship between $X$ and $Y$.\n",
     "\n",
     "Here is a scatterplot between $X$ and $Y$ with a line of best fit down the middle."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 5,
    "metadata": {
     "collapsed": false,
     "scrolled": false
    },
    "outputs": [
     {
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jAfj+++/p3LmzzT5rEo0UiYiIiIhUMVdXVwYM8CM9PR1XV89KByKAkSNHcuTI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+rVmSYj6JSo/qiY8X3D4FZQUNrgPUnhzV53SfUaZvipuc+5pYDx4Yf3aty4tdfWFOXrww8THP4M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\nAAAASUVORK5CYII=\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7f52380857d0>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# scatter plot of X and y\n",
     "from statsmodels import regression\n",
     "import statsmodels.api as sm\n",
     "def linreg(X,Y):\n",
     "    # Running the linear regression\n",
     "    X = sm.add_constant(X)\n",
     "    model = regression.linear_model.OLS(Y, X).fit()\n",
     "    a = model.params[0]\n",
     "    b = model.params[1]\n",
     "    X = X[:, 1]\n",
     "\n",
     "    # Return summary of the regression and plot results\n",
     "    X2 = np.linspace(X.min(), X.max(), 100)\n",
     "    Y_hat = X2 * b + a\n",
     "    plt.scatter(X, Y, alpha=0.3) # Plot the raw data\n",
     "    plt.plot(X2, Y_hat, 'r', alpha=0.9);  # Add the regression line, colored in red\n",
     "    plt.xlabel('X Value')\n",
     "    plt.ylabel('Y Value')\n",
     "    return model.summary()\n",
     "\n",
     "linreg(X, Y)\n",
     "plt.scatter(X, Y)\n",
     "plt.title('Scatter plot and linear equation of x as a function of y')\n",
     "plt.xlabel('X')\n",
     "plt.ylabel('Y')\n",
     "plt.legend(['Linear equation', 'Scatter Plot']);"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Between the covariance, the linear regression, and our knowledge of how $X$ and $Y$ are related, we can easily assess the relationship between our toy variables. With real data, there are two main complicating factors. The first is that we are exmaining significantly more relationships. The second is that we do not know any of their underlying relationships. These hindrances speak to the benefit of having accurate estimates of covariance matrices."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## The Covariance Matrix\n",
     "\n",
     "As the number of assets we are curious about increases, so too do the dimensions of the covariance matrix that describes their relationships. If we take the covariance between $N$ assets, we will get out a $N \\times N$ covariance matrix. This allows us to efficiently express the relationships between many arrays at once. As with the simple $2\\times 2$ case, the $i$-th diagonal is the variance of the $i$-th asset and the values at $(i, j)$ and $(j, i)$ refer to the covariance between asset $i$ and asset $j$. We display this with the following notation:\n",
     "\n",
     "$$ \\Sigma = \\left[\\begin{matrix}\n",
     "VAR(X_1) & COV(X_1, X_2) & \\cdots & COV(X_1, X_N) \\\\\n",
     "COV(X_2, X_0) & VAR(X_2) & \\cdots & COV(X_2, X_N) \\\\\n",
     "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
     "COV(X_N, X_1) & COV(X_N, X_2) & \\cdots & VAR(X_N)\n",
     "\\end{matrix}\\right] $$  \n",
     "\n",
     "When trying to find the covariance of many assets, it quickly becomes apparent why the matrix notation is more favorable. "
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 6,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Covariance matrix:\n",
       "          SBUX      AAPL        GS      GILD\n",
       "SBUX  0.000453  0.000330  0.000331  0.000075\n",
       "AAPL  0.000330  0.000739  0.000463  0.000237\n",
       "GS    0.000331  0.000463  0.000533  0.000130\n",
       "GILD  0.000075  0.000237  0.000130  0.000569\n"
      ]
     }
    ],
    "source": [
     "# Four asset example of the covariance matrix.\n",
     "start_date = '2016-01-01'\n",
     "end_date = '2016-02-01'\n",
     "\n",
     "returns = get_pricing(\n",
     "    ['SBUX', 'AAPL', 'GS', 'GILD'],\n",
     "    start_date=start_date,\n",
     "    end_date=end_date,\n",
     "    fields='price'\n",
     ").pct_change()[1:]\n",
     "returns.columns = map(lambda x: x.symbol, returns.columns)\n",
     "\n",
     "print 'Covariance matrix:'\n",
     "print returns.cov()"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Why does all this matter?  \n",
     "\n",
     "We measure the covariance of the assets in our portfolio to make sure we have an accurate picture of the risks involved in holding those assets togther. We want to apportion our capital amongst these assets in such a way as to minimize our exposure to the risks associated with each individual asset and to neutralize exposure to systematic risk. This is done through the process of portfolio optimization. Portfolio optimization routines go through exactly this process, finding the appropriate weights for each asset given its risks. Mean-variance optimization, a staple of MPT, does exactly this. \n",
     "\n",
     "Estimating the covariance matrix becomes critical when using methods that rely on it, as we cannot know the true statistical relationships underlying our chosen assets. The stability and accuracy of these estimates are essential to getting stable weights that encapsulate our risks and intentions.\n",
     "\n",
     "Unfortunately, the most obvious way to calculate a covariance matrix estimate, the sample covariance, is notoriously unstable. If we have fewer time observations of our assets than the number of assets ($T < N$), the estimate becomes especially unreliable. The extreme values react more strongly to changes, and as the extreme values of the covariance jump around, our optimizers are perturbed, giving us inconsistent weights. This is a problem when we are trying to make many independent bets on many assets to improve our risk exposures through diversification. Even if we have more time elements than assets that we are trading, we can run into issues, as the time component may span multiple regimes, giving us covariance matrices that are still inaccurate.\n",
     "\n",
     "The solution in many cases is to use a robust formulation of the covariance matrix. If we can estimate a covariance matrix that still captures the relationships between assets and is simultaneously more stable, then we can have more faith in the output of our optimizers. A main way that we handle this is by using some form of a shrinkage estimator."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "# Shrinkage Estimators\n",
     "\n",
     "The concept of shrinkage stems from the need for stable covariance matrices. The basic way we \"shrink\" a matrix is to reduce the extreme values of the sample covariance matrix by pulling them closer to the center. Practically, we take a linear combination of the sample covariance covariance matrix a constant array representing the center.\n",
     "\n",
     "Given a sample covariance matrix, $\\textbf{S}$, the mean variance, $\\mu$, and the shrinkage constant $\\delta$, the shrunk estimated covariance is mathematically defined as:   \n",
     "\n",
     "$$(1 - \\delta)\\textbf{S} + \\delta\\mu\\textbf{1}$$  \n",
     " \n",
     "We restrict $\\delta$ such that $0 \\leq \\delta \\leq 1$ making this a weighted average between the sample covariance and the mean variance matrix. The optimal value of $\\delta$ has been tackled several times. For our purposes, we will use the formulation by Ledoit and Wolf.\n",
     "\n",
     "## Ledoit-Wolf Estimator.\n",
     "\n",
     "In [their paper](http://ledoit.net/honey.pdf), Ledoit and Wolf  proposed an optimal $\\delta$: \n",
     "\n",
     "$$\\hat\\delta^* \\max\\{0, \\min\\{\\frac{\\hat\\kappa}{T},1\\}\\}$$\n",
     "\n",
     "$\\hat\\kappa$ has a mathematical formulation that is beyond the scope of this lecture, but you can find its definition in the paper.\n",
     "\n",
     "The Ledoit-Wolf Estimator is the robust covariance estimate that uses this optimal $\\hat\\delta^*$ to shrink the sample covariance matrix. We can draw an implementation of it directly from `scikit-learn` for easy use."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 7,
    "metadata": {
     "collapsed": false
    },
    "outputs": [],
    "source": [
     "# Getting the return data of assets. \n",
     "start = '2016-01-01'\n",
     "end = '2016-02-01'\n",
     "\n",
     "symbols = ['AAPL', 'MSFT', 'BRK-A', 'GE', 'FDX', 'SBUX']\n",
     "\n",
     "prices = get_pricing(symbols, start_date = start, end_date = end, fields = 'price')\n",
     "prices.columns = map(lambda x: x.symbol, prices.columns)\n",
     "returns = prices.pct_change()[1:]"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 8,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
       "text/html": [
        "<div>\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>AAPL</th>\n",
        "      <th>MSFT</th>\n",
        "      <th>BRK_A</th>\n",
        "      <th>GE</th>\n",
        "      <th>FDX</th>\n",
        "      <th>SBUX</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>2016-01-05 00:00:00+00:00</th>\n",
        "      <td>-0.024969</td>\n",
        "      <td>0.004745</td>\n",
        "      <td>0.001934</td>\n",
        "      <td>0.000651</td>\n",
        "      <td>0.008526</td>\n",
        "      <td>0.006522</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2016-01-06 00:00:00+00:00</th>\n",
        "      <td>-0.019474</td>\n",
        "      <td>-0.017711</td>\n",
        "      <td>0.003365</td>\n",
        "      <td>-0.015935</td>\n",
        "      <td>-0.026958</td>\n",
        "      <td>-0.008697</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2016-01-07 00:00:00+00:00</th>\n",
        "      <td>-0.041311</td>\n",
        "      <td>-0.034674</td>\n",
        "      <td>-0.011251</td>\n",
        "      <td>-0.041970</td>\n",
        "      <td>-0.044043</td>\n",
        "      <td>-0.024772</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2016-01-08 00:00:00+00:00</th>\n",
        "      <td>0.004558</td>\n",
        "      <td>0.002682</td>\n",
        "      <td>-0.008396</td>\n",
        "      <td>-0.018972</td>\n",
        "      <td>0.000817</td>\n",
        "      <td>-0.000882</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2016-01-11 00:00:00+00:00</th>\n",
        "      <td>0.015983</td>\n",
        "      <td>-0.000764</td>\n",
        "      <td>-0.003227</td>\n",
        "      <td>0.004923</td>\n",
        "      <td>-0.012697</td>\n",
        "      <td>0.020833</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "text/plain": [
        "                               AAPL      MSFT     BRK_A        GE       FDX  \\\n",
        "2016-01-05 00:00:00+00:00 -0.024969  0.004745  0.001934  0.000651  0.008526   \n",
        "2016-01-06 00:00:00+00:00 -0.019474 -0.017711  0.003365 -0.015935 -0.026958   \n",
        "2016-01-07 00:00:00+00:00 -0.041311 -0.034674 -0.011251 -0.041970 -0.044043   \n",
        "2016-01-08 00:00:00+00:00  0.004558  0.002682 -0.008396 -0.018972  0.000817   \n",
        "2016-01-11 00:00:00+00:00  0.015983 -0.000764 -0.003227  0.004923 -0.012697   \n",
        "\n",
        "                               SBUX  \n",
        "2016-01-05 00:00:00+00:00  0.006522  \n",
        "2016-01-06 00:00:00+00:00 -0.008697  \n",
        "2016-01-07 00:00:00+00:00 -0.024772  \n",
        "2016-01-08 00:00:00+00:00 -0.000882  \n",
        "2016-01-11 00:00:00+00:00  0.020833  "
       ]
      },
      "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "returns.head()"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Here we calculate the in-sample Ledoit-Wolf estimator."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 9,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "[[ 0.00065499  0.00041175  0.00014706  0.0001944   0.00028022  0.00026144]\n",
       " [ 0.00041175  0.00050599  0.00016123  0.00022653  0.00033813  0.00022635]\n",
       " [ 0.00014706  0.00016123  0.00019215  0.00012305  0.00016825  0.0001618 ]\n",
       " [ 0.0001944   0.00022653  0.00012305  0.00032382  0.00021071  0.00023099]\n",
       " [ 0.00028022  0.00033813  0.00016825  0.00021071  0.00045808  0.00024686]\n",
       " [ 0.00026144  0.00022635  0.0001618   0.00023099  0.00024686  0.00042922]]\n"
      ]
     }
    ],
    "source": [
     "in_sample_lw = covariance.ledoit_wolf(returns)[0]\n",
     "print in_sample_lw"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "### Calculating Errors\n",
     "\n",
     "We can quantify the difference between the in and out-of-sample estimates by taking the absolute difference element-by-element for the two matrices. We represent this mathematically as: \n",
     "\n",
     "$$ \\frac{1}{n} \\sum_{i=1}^{n} |a_i - b_i| $$\n",
     "\n",
     "First, we calculate the out-of-sample estimate and then we compare."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 10,
    "metadata": {
     "collapsed": false
    },
    "outputs": [],
    "source": [
     "oos_start = '2016-02-01'\n",
     "oos_end = '2016-03-01'\n",
     "oos_prices = get_pricing(symbols, start_date = oos_start, end_date = oos_end, fields = 'price')\n",
     "oos_prices.columns = map(lambda x: x.symbol, oos_prices.columns)\n",
     "oos_returns = oos_prices.pct_change()[1:]\n",
     "out_sample_lw = covariance.ledoit_wolf(oos_returns)[0]"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 11,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Average Ledoit-Wolf error:  0.000543690949796\n"
      ]
     }
    ],
    "source": [
     "lw_errors = sum(abs(np.subtract(in_sample_lw, out_sample_lw)))\n",
     "print \"Average Ledoit-Wolf error: \", np.mean(lw_errors)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "### Comparing to Sample Matrix\n",
     "\n",
     "We can check how much of an improvement this is by comparing the errors with the erros of the sample covariance."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 12,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Average sample covariance error:  0.000646608903348\n"
      ]
     }
    ],
    "source": [
     "sample_errors = sum(abs(np.subtract(returns.cov().values, oos_returns.cov().values)))\n",
     "print 'Average sample covariance error: ', np.mean(sample_errors)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 13,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Error improvement of LW over sample: 18.21%\n"
      ]
     }
    ],
    "source": [
     "print 'Error improvement of LW over sample: {0:.2f}%'.format((np.mean(sample_errors/lw_errors)-1)*100)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "We can see that the improvement of Ledoit-Wolf over the sample covariance is pretty solid. This translates into decreased volatility and turnover rate in our portfolio, and thus increased returns when using the shrunk covariance matrix. "
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 14,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
       "image/png": 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cmpqaTJgwIW1tbfus2bZtW1auXJmJEycmSSZOnJgVK1bsca6FCxfmL//yL6s5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\nASUiIiIiIlIiLaBERERERERK9A/15TfyIFUUHQAAAABJRU5ErkJggg==\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7f5220fef890>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "sns.boxplot(\n",
     "    data = pd.DataFrame({\n",
     "        'Sample Covariance Error': sample_errors,\n",
     "        'Ledoit-Wolf Error': lw_errors\n",
     "    })\n",
     ")\n",
     "plt.title('Box Plot of Errors')\n",
     "plt.ylabel('Error');"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "### Adding More Assets\n",
     "\n",
     "Now we bring this to more assets over a longer time period. Let's see how the errors change over a series of months."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 15,
    "metadata": {
     "collapsed": false
    },
    "outputs": [],
    "source": [
     "start_date = '2016-01-01'\n",
     "end_date = '2017-06-01'\n",
     "\n",
     "symbols = [\n",
     "    'SPY', 'XLF', 'XLE', 'XLU','XLK', 'XLI', 'XLB', 'GE', 'GS', 'BRK-A', 'JPM', 'AAPL', 'MMM', 'BA',\n",
     "    'CSCO','KO', 'DIS','DD', 'XOM', 'INTC', 'IBM', 'NKE', 'MSFT', 'PG', 'UTX', 'HD', 'MCD', 'CVX', \n",
     "    'AXP','JNJ', 'MRK', 'CAT', 'PFE', 'TRV', 'UNH', 'WMT', 'VZ', 'QQQ', 'BAC', 'F', 'C', 'CMCSA',\n",
     "    'MS', 'ORCL', 'PEP', 'HON', 'GILD', 'LMT', 'UPS', 'HP', 'FDX', 'GD', 'SBUX'\n",
     "]\n",
     "\n",
     "prices = get_pricing(symbols, start_date=start_date, end_date=end_date, fields='price')\n",
     "prices.columns = map(lambda x: x.symbol, prices.columns)\n",
     "returns = prices.pct_change()[1:]"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 16,
    "metadata": {
     "collapsed": false
    },
    "outputs": [],
    "source": [
     "dates = returns.resample('M').first().index"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Here we calculate our different covariance estimates."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 17,
    "metadata": {
     "collapsed": false
    },
    "outputs": [],
    "source": [
     "sample_covs = []\n",
     "lw_covs = []\n",
     "\n",
     "for i in range(1, len(dates)):\n",
     "    sample_cov = returns[dates[i-1]:dates[i]].cov().values\n",
     "    sample_covs.append(sample_cov)\n",
     "    \n",
     "    lw_cov = covariance.ledoit_wolf(returns[dates[i-1]:dates[i]])[0]\n",
     "    lw_covs.append(lw_cov)      "
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Here we calculate the error for each time period."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 18,
    "metadata": {
     "collapsed": false
    },
    "outputs": [],
    "source": [
     "lw_diffs = []\n",
     "for pair in zip(lw_covs[:-1], lw_covs[1:]):\n",
     "    diff = np.mean(np.sum(np.abs(pair[0] - pair[1])))\n",
     "    lw_diffs.append(diff)\n",
     "    \n",
     "sample_diffs = []\n",
     "for pair in zip(sample_covs[:-1], sample_covs[1:]):\n",
     "    diff = np.mean(np.sum(np.abs(pair[0] - pair[1])))\n",
     "    sample_diffs.append(diff)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "And here we plot the errors over time!"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 19,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
       "image/png": 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G6KzhA74eJZ6KnqKoiEURAMCozUW5tQoNHc0J32NFRERE0hHRj3q3bt2KWbNm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\nETmLC+oAAAAASUVORK5CYII=\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7f52380581d0>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "plt.plot(dates[2:], lw_diffs)\n",
     "plt.plot(dates[2:], sample_diffs)\n",
     "plt.xlabel('Time')\n",
     "plt.ylabel('Mean Error')\n",
     "plt.legend(['Ledoit-Wolf Errors', 'Sample Covariance Errors']);"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "We can see that the mean errors of Ledoit-Wolf are lower than those of the sample covariance matrix. This shows us that the sample sample covariance matrix is less robust. This example only used 50 assets, but as we add more, the Ledoit-Wolf estimator would likely perform even better as the number of assets outpaces the number of observations."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "*This presentation is for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation for any security; nor does it constitute an offer to provide investment advisory or other services by Quantopian, Inc. (\"Quantopian\"). Nothing contained herein constitutes investment advice or offers any opinion with respect to the suitability of any security, and any views expressed herein should not be taken as advice to buy, sell, or hold any security or as an endorsement of any security or company.  In preparing the information contained herein, Quantopian, Inc. has not taken into account the investment needs, objectives, and financial circumstances of any particular investor. Any views expressed and data illustrated herein were prepared based upon information, believed to be reliable, available to Quantopian, Inc. at the time of publication. Quantopian makes no guarantees as to their accuracy or completeness. All information is subject to change and may quickly become unreliable for various reasons, including changes in market conditions or economic circumstances.*"
    ]
   }
  ],
  "metadata": {
   "kernelspec": {
    "display_name": "Python 2",
    "language": "python",
    "name": "python2"
   },
   "language_info": {
    "codemirror_mode": {
     "name": "ipython",
     "version": 2
    },
    "file_extension": ".py",
    "mimetype": "text/x-python",
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython2",
    "version": "2.7.12"
   }
  },
  "nbformat": 4,
  "nbformat_minor": 2
 }