Homework2.ipynb

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     "source": [
      "# Homework Set 2"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Problem 1:\n",
      "\n",
      "Prove the following inequalities for the matrix norm, where $A, B$ are matrices, $\\boldsymbol u$ is a vector and $b$ is a scaler.\n",
      "\n",
      "* $\\Vert A \\boldsymbol u \\Vert  \\le \\Vert A\\Vert \\; \\Vert \\boldsymbol u\\Vert $\n",
      "* $\\Vert b A\\Vert  = \\vert b\\vert \\; \\Vert A\\Vert $ \n",
      "* $\\Vert A + B\\Vert  \\le \\Vert A\\Vert  + \\Vert B\\Vert $\n",
      "* $\\Vert AB\\Vert  \\le \\Vert A\\Vert \\Vert B\\Vert$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Problem 2\n",
      "\n",
      "For a symmetric positive definite matrix, we can compute its inversion using either LU or Cholesky decomposition.\n",
      "\n",
      "1. Estimate the complexity of these two different methods, verify that both of them are of $O(n^3)$ complexity. \n",
      "  * you can use external reference to answer this question, feel free to state the conclusion and give a reference. However, you are responsible for the accuracy of your conclusion, i.e., you lose points if your conclusion is incorrect.\n",
      "2. Which method is relatively faster? (ie, has a smaller constant before $n^3$). \n",
      "3. Use Python's scipy/numpy LU and cholesky functions, and check if their relative speed matches your estimate."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Problem 3\n",
      "\n",
      "Implement the recursive cholesky decomposition algorithm discussed in the class in Python, with the following requirements:\n",
      "\n",
      "1. use vector/matrix calculation whenever possible, but you obviously should not just call the buildin numpy/scipy functions for Cholesky decomposition \n",
      "2. detect and throw exception if the input matrix is not semi-positive definite\n",
      "3. test your program against the version provided in scipy.linalg, and compare their performance\n",
      "\n",
      "Hint: for #2, if you don't know what conditoin to catch, you can create a non-SPD matrix and observe how your program can fail. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Problem 4\n",
      "\n",
      "Implement the correlated Brownian motion simulation using cholesky decomposition on the covariance matrix and correlation matrix, and show that they are indeed equivalent. You can use the covariance matrix between the three assets (SPY, OIL, GLD) given in the class."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pandas as pd\n",
      "import fmt\n",
      "\n",
      "f3url = \"https://raw.githubusercontent.com/yadongli/nyumath2048/master/data/f3.csv\"\n",
      "f3 = pd.read_csv(f3url, parse_dates=[0], index_col=[0])\n",
      "\n",
      "r = np.log(f3).diff()\n",
      "cm = r.corr()\n",
      "cv = r.cov()\n",
      "    \n",
      "fmt.displayDFs(cm, cv*1e4, headers=['Correlation', 'Covariance'])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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       "html": [
        "<center><table style=\"border-style:hidden; border-collapse:collapse; text-align:center;\"><tr style=\"border:none\"><th style=\"border:none; text-align:center\">Correlation</th><th style=\"border:none; text-align:center\">Covariance</th></tr><tr style=\"border:none\"><td style=\"border:none; padding:20px; text-align:center\"><table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>SPY</th>\n",
        "      <th>GLD</th>\n",
        "      <th>OIL</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>SPY</th>\n",
        "      <td>      1</td>\n",
        "      <td>0.03215</td>\n",
        "      <td>0.4191</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>GLD</th>\n",
        "      <td>0.03215</td>\n",
        "      <td>      1</td>\n",
        "      <td>0.3011</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>OIL</th>\n",
        "      <td> 0.4191</td>\n",
        "      <td> 0.3011</td>\n",
        "      <td>     1</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table></td><td style=\"border:none; padding:20px; text-align:center\"><table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>SPY</th>\n",
        "      <th>GLD</th>\n",
        "      <th>OIL</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>SPY</th>\n",
        "      <td> 8.043</td>\n",
        "      <td>0.2461</td>\n",
        "      <td>5.611</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>GLD</th>\n",
        "      <td>0.2461</td>\n",
        "      <td> 7.288</td>\n",
        "      <td>3.838</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>OIL</th>\n",
        "      <td> 5.611</td>\n",
        "      <td> 3.838</td>\n",
        "      <td>22.28</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table></td></tr></table></center>"
       ],
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       "output_type": "display_data",
       "text": [
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     "prompt_number": 84
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Hint: think about how to present the equivalence. It is an important skill to present your evidence and conclusions in a clear and concise way, (think about how you can convice your future clients, coworkers and supervisors in a very limited amount of time, like in a few seconds)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Problem 5\n",
      "\n",
      "Take the portfolio and historical stock time series of the Dow Jones industrial average (DJIA) index:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "djiaurl = \"https://raw.githubusercontent.com/yadongli/nyumath2048/master/data/djia.csv\"\n",
      "djia = pd.read_csv(djiaurl, index_col=[0])\n",
      "\n",
      "fmt.displayDF(djia)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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       "html": [
        "<center><font size=2><table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Name</th>\n",
        "      <th>Sector</th>\n",
        "      <th>Weights</th>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>Ticker</th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>MMM</th>\n",
        "      <td>                                3M Co.</td>\n",
        "      <td>                  Diversified Industrials</td>\n",
        "      <td>0.0539</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>AXP</th>\n",
        "      <td>                  American Express Co.</td>\n",
        "      <td>                         Consumer Finance</td>\n",
        "      <td>0.0324</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>T</th>\n",
        "      <td>                             AT&amp;T Inc.</td>\n",
        "      <td>            Fixed Line Telecommunications</td>\n",
        "      <td>0.0134</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>BA</th>\n",
        "      <td>                            Boeing Co.</td>\n",
        "      <td>    Aerospace/Defense Products &amp; Services</td>\n",
        "      <td>0.0483</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>CAT</th>\n",
        "      <td>                      Caterpillar Inc.</td>\n",
        "      <td>             Commercial Vehicles &amp; Trucks</td>\n",
        "      <td>0.0373</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>CVX</th>\n",
        "      <td>                         Chevron Corp.</td>\n",
        "      <td>                     Integrated Oil &amp; Gas</td>\n",
        "      <td>0.0438</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>CSCO</th>\n",
        "      <td>                    Cisco Systems, Inc</td>\n",
        "      <td>               Networking &amp; Communication</td>\n",
        "      <td>0.0091</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>KO</th>\n",
        "      <td>                         Coca-Cola Co.</td>\n",
        "      <td>                              Soft Drinks</td>\n",
        "      <td>0.0168</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>DD</th>\n",
        "      <td>          E.I. DuPont de Nemours &amp; Co.</td>\n",
        "      <td>                      Commodity Chemicals</td>\n",
        "      <td>0.0263</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>XOM</th>\n",
        "      <td>                     Exxon Mobil Corp.</td>\n",
        "      <td>                     Integrated Oil &amp; Gas</td>\n",
        "      <td>0.0358</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>GE</th>\n",
        "      <td>                  General Electric Co.</td>\n",
        "      <td>                  Diversified Industrials</td>\n",
        "      <td>0.0097</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>GS</th>\n",
        "      <td>              Goldman Sachs Group Inc </td>\n",
        "      <td>          Investment Brokerage - National</td>\n",
        "      <td>0.0694</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>HD</th>\n",
        "      <td>                       Home Depot Inc.</td>\n",
        "      <td>               Home Improvement Retailers</td>\n",
        "      <td>0.0354</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>INTC</th>\n",
        "      <td>                           Intel Corp.</td>\n",
        "      <td>                           Semiconductors</td>\n",
        "      <td>0.0123</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>IBM</th>\n",
        "      <td> International Business Machines Corp.</td>\n",
        "      <td>                        Computer Services</td>\n",
        "      <td>0.0714</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>JNJ</th>\n",
        "      <td>                     Johnson &amp; Johnson</td>\n",
        "      <td>                          Pharmaceuticals</td>\n",
        "      <td>0.0387</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>JPM</th>\n",
        "      <td>                  JPMorgan Chase &amp; Co.</td>\n",
        "      <td>                                    Banks</td>\n",
        "      <td>0.0220</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>MCD</th>\n",
        "      <td>                      McDonald's Corp.</td>\n",
        "      <td>                       Restaurants &amp; Bars</td>\n",
        "      <td>0.0357</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>MRK</th>\n",
        "      <td>                      Merck &amp; Co. Inc.</td>\n",
        "      <td>                          Pharmaceuticals</td>\n",
        "      <td>0.0212</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>MSFT</th>\n",
        "      <td>                       Microsoft Corp.</td>\n",
        "      <td>                                 Software</td>\n",
        "      <td>0.0171</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>NKE</th>\n",
        "      <td>                              NIKE Inc</td>\n",
        "      <td> Textile - Apparel Footwear &amp; Accessories</td>\n",
        "      <td>0.0342</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>PFE</th>\n",
        "      <td>                           Pfizer Inc.</td>\n",
        "      <td>                          Pharmaceuticals</td>\n",
        "      <td>0.0109</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>PG</th>\n",
        "      <td>                  Procter &amp; Gamble Co.</td>\n",
        "      <td>            Nondurable Household Products</td>\n",
        "      <td>0.0326</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>TRV</th>\n",
        "      <td>         The Travelers Companies, Inc.</td>\n",
        "      <td>            Property &amp; Casualty Insurance</td>\n",
        "      <td>0.0366</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>UTX</th>\n",
        "      <td>             United Technologies Corp.</td>\n",
        "      <td>                                Aerospace</td>\n",
        "      <td>0.0398</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>UNH</th>\n",
        "      <td>                    UnitedHealth Group</td>\n",
        "      <td>                               Healthcare</td>\n",
        "      <td>0.0346</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>VZ</th>\n",
        "      <td>           Verizon Communications Inc.</td>\n",
        "      <td>            Fixed Line Telecommunications</td>\n",
        "      <td>0.0188</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>V</th>\n",
        "      <td>                              Visa Inc</td>\n",
        "      <td>                          Credit Services</td>\n",
        "      <td>0.0808</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>WMT</th>\n",
        "      <td>                  Wal-Mart Stores Inc.</td>\n",
        "      <td>                      Broadline Retailers</td>\n",
        "      <td>0.0291</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>DIS</th>\n",
        "      <td>                       Walt Disney Co.</td>\n",
        "      <td>             Broadcasting &amp; Entertainment</td>\n",
        "      <td>0.0329</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table></font></center>"
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     "input": [
      "def download_hist_prices(tickers) : # we download the stock prices from Yahoo!Finance\n",
      "    base_url = \"http://ichart.finance.yahoo.com/table.csv?s=\"\n",
      "    closeKey = 'Adj Close'\n",
      "    dfs = []\n",
      "\n",
      "    for ticker in tickers:\n",
      "        try :\n",
      "            url = base_url + ticker\n",
      "            dfs.append(pd.read_csv(url, parse_dates=[0], index_col=[0]).rename(columns={closeKey:ticker})[ticker])\n",
      "        except Error:\n",
      "            print \"error in \" + ticker\n",
      "            continue\n",
      "\n",
      "    return pd.concat(dfs, axis=1, join='inner')\n",
      "\n",
      "histprice = download_hist_prices(djia.index).sort()\n",
      "histprice.plot(legend=False, title='Historical Prices');"
     ],
     "language": "python",
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Ra+Wuu9WKT9q7aQXAENquutMukA5J6fLStu6Gjh/UDdWane2eKJw9W/lhX3pp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psQKYwpMjp1TjF1FpOLF2XUJ0sErVZqDwyTKOu21RrybkgldFNvMMjR9HRBq5W0f+ifBoNB0Gol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tQ5gV7c7XV7/j/T/Ao5TaoLTpuu0aQ0P7wN81+Lv9YGi42Ib41QsYijb2cgNwr6/tMTQYGgz7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\nw5EbGBgY+Dn/ByGcRSZIEcvAAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1720b208>"
       ]
      }
     ],
     "prompt_number": 86
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This problem explores the practical problems in estimating the mean and volatility from the stock price time series. We assume that stock prices follow Geometric Brownian motion, thus their log returns are normally distributed. It is common practice to estimate the mean and variance of the log returns $r(t; \\Delta) = \\log\\left(\\frac{s(t+\\Delta)}{s(t)}\\right)$ from historical data, where $\\Delta$ is the period of returns. Suppose we are interested in estimating the annualized returns with $\\Delta = 1$, and we have more frequent data samples of $\\delta < \\Delta$ (such as daily data, $\\delta = 1/250$), then we could estimate annualized return mean and variance using the more frequent observations as:\n",
      "\n",
      "$$ \\mathbb{E}[r(t; \\Delta)] = \\frac{\\Delta}{\\delta} \\mathbb{E}[r(t; \\delta)] \\approx \\frac{\\Delta}{\\delta} \\frac{1}{n}\\sum_{k=0}^{n-1} r(t + k\\delta; \\delta) := \\frac{\\Delta}{\\delta} \\mu $$\n",
      "$$ \\sigma^2\\left(r(t; \\Delta)\\right) = \\frac{\\Delta}{\\delta} \\sigma^2\\left(r(t; \\delta)\\right) \\approx \\frac{\\Delta}{\\delta} \\frac{1}{n-1} \\sum_{k=0}^{n-1}  \\left(r(t + k\\delta; \\delta) - \\mu\\right)^2$$\n",
      "\n",
      "where $\\mu$ is the average daily historical log returns. These expressions directly follow the Geometric Brownian motions. For the following questions, assume that we estimate expected returns by averaging the log returns over consecutive, non-overlapping windows. \n",
      "\n",
      "1. are they the same if we estimate the annualized returns using daily or yearly windows? explain your conclusion.\n",
      "2. are they the same if we estimate the annualized vol using daily or yearly windows? explain your conclusion.\n",
      "3. for the 30 DJIA sstocks, how many years of data we'd need so that the annualized return estimate is accurate within 1%?\n",
      "4. take the daily return time series from the 30 DJIA stocks, divide them to consecutive monthly intervals (you can assume each month has 20 business days), estimate the volatility for each monthly interval, and take their averages as an estimator of the annualized vol. Estimate the error of the volatility estimate for the 30 stocks from this procedure. \n",
      "5. comments on the implication of your results\n",
      "\n",
      "Hint: \n",
      "* It is well known that if we average $n$ independent samples, the error of of the average estimator is about $\\frac{\\sigma}{\\sqrt{n}}$, where $\\sigma$ is the std dev of the population we are sampling (i.e, the underlying random variable). You can use this fact to answer the last 3 questions.\n",
      "* numpy's std and mean functions are useful, they can take an axis as parameter to compute statistic along a given axis."
     ]
    },
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     "source": [
      "## Problem 6\n",
      "\n",
      "This problem uses the same data set as in the previous problem.\n",
      "\n",
      "1. estimate the historical correlation and covariance matrix of the DJIA constiuents' daily returns, \n",
      "2. estimate historical excess return of individual stocks (assume the historical risk free rate is 0%)\n",
      "3. compute the optimal portfolio using the estimated historical excess return and covariance matrix, comment on whether the portfolio looks reasonable.\n",
      "4. compute the implied return forecast from the actual DJIA portfolio, compare this to the historical estimate, comment on which may be a better forecast for the future returns\n",
      "5. compute the condition number of the covariance matrix, and comments the numerical stability of the optimal portfolio\n",
      "6. does the result change if you use daily returns or weekly returns for the historical estimate? \n",
      "7. use numerical simulation to show that the optimal portfolio from #3 indeed has the largest Sharp ratio for the historical excess return and covariance; the best way to illustrate this is to introduce many random perturbations around the optimal portfolio, \n",
      "8. [open question] comment on what practical implication you might infer from your results in 7\n",
      "\n",
      "Hints: \n",
      "* you may run into singular matrix when reverting the covariance matrix, try to find a work around if you do, (imagine what you would do if your future boss needs some results fast, and he doesn't understand what is a singular matrix that can't be inverted)."
     ]
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