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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Gold vs. SP500 returns :: XAU vs. SPX"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Long-term comparison of two asset classes: we boxplot their return distribution and also compute geometric mean returns. Correlation between the two is shown to be nil. We then look at the history of projected returns using Holt-Winters method, which also gives the latest forecasts. \n",
      "\n",
      "To conclude, we closely examine the relative value of the two assets in terms of gold troy ounces per equity share. **Analytically *short equities vs. long gold is favorable for an investor with log utility*, but hardly profitable over the long haul.** "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Dependencies:*\n",
      "\n",
      "    - Linux, bash [not crucial, cross-platform prefered]\n",
      "    - Python: matplotlib, pandas [recommend Anaconda distribution]\n",
      "    - Modules: yi_1tools, yi_plot, yi_timeseries, yi_fred\n",
      "\n",
      "\n",
      "*CHANGE LOG*\n",
      "\n",
      "    2015-02-23  Code review and revision.\n",
      "    2014-08-05  Uses new boxplot routine with paste of dataframes."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  NOTEBOOK settings and system details:   [00-tpl v14.09.28]\n",
      "\n",
      "#  Assume that the backend is LINUX (our particular distro is Ubuntu, running bash shell):\n",
      "print '\\n ::  TIMESTAMP of last notebook execution:'\n",
      "!date\n",
      "print '\\n ::  IPython version:'\n",
      "!ipython --version\n",
      "\n",
      "#  Automatically reload modified modules:\n",
      "%load_ext autoreload\n",
      "%autoreload 2   \n",
      "#           0 will disable autoreload.\n",
      "#  Generate plots inside notebook:\n",
      "%matplotlib inline\n",
      "\n",
      "#  DISPLAY options\n",
      "from IPython.display import Image \n",
      "#  e.g. Image(filename='holt-winters-equations.png', embed=True)\n",
      "from IPython.display import YouTubeVideo\n",
      "#  e.g. YouTubeVideo('1j_HxD4iLn8')\n",
      "from IPython.display import HTML # useful for snippets\n",
      "#  e.g. HTML('<iframe src=http://en.mobile.wikipedia.org/?useformat=mobile width=700 height=350></iframe>')\n",
      "import pandas as pd\n",
      "print '\\n ::  pandas version:'\n",
      "print pd.__version__\n",
      "#      pandas DataFrames are represented as text by default; enable HTML representation:\n",
      "#      [Deprecated: pd.core.format.set_printoptions( notebook_repr_html=True ) ]\n",
      "pd.set_option( 'display.notebook_repr_html', False )\n",
      "\n",
      "#  MATH display, use %%latex, rather than the following:\n",
      "#                from IPython.display import Math\n",
      "#                from IPython.display import Latex\n",
      "\n",
      "print '\\n ::  Working directory (set as $workd):'\n",
      "workd, = !pwd\n",
      "print workd + '\\n'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " ::  TIMESTAMP of last notebook execution:\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Fri Mar  6 08:29:39 PST 2015\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " ::  IPython version:\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "2.3.0\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " ::  pandas version:\n",
        "0.15.0\n",
        "\n",
        " ::  Working directory (set as $workd):\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "/home/yaya/Dropbox/ipy/fecon235/nb\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from yi_1tools import *\n",
      "from yi_fred import *\n",
      "from yi_plot import *\n",
      "from yi_timeseries import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Get SPX daily:\n",
      "sp = getfred( d4spx )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " ::  S&P 500 prepend successfully goes back to 1957.\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Get Gold daily:\n",
      "au = getfred( d4xau )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Create their dataframe:\n",
      "assets = paste( [au, sp])\n",
      "assets.columns = ['Au', 'SP']"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Compute returns as YoY percentage, assuming 256 days/year:\n",
      "returns = pcent( assets, 256 )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can explore returns as far back as 1968-04-01, or any sub-section in time. The gold bubble crashes to its low point around 1982-03-19."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "start = '1969-07-01'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Show subret distribution:\n",
      "boxplot( returns[start:] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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uZlYSrqGXhGuU1sl8fDZPEc8UtTZbvLjoCKzXaZdHbL3MWBFASJWMvoN86nHD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\nos0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xad1f41cc>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " ::  Finished: boxplot-tmp.png\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The red line within the box shows the *median*, while the red dot plots the most recent data point.\n",
      "\n",
      "Gold shows a wider range of returns to the upside. To best summarize performance, we compute geometric mean returns."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Geometric mean return for gold in chosen period:\n",
      "georet( au[start:] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "[7.2, 9.2, 20.02, 256]"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Geometric mean return for US equities in chosen period:\n",
      "georet( sp[start:] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "[6.59, 8.0, 16.78, 256]"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For start since 1970, gold's *geometric* return exceeds that of US equities by 65 bp. Note that dividends are not included in the SPX index, so we are not comparing total investment return. (Geometric mean returns implicitly penalizes volatility, and is compatible for an investor with logrithmic utility.) "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "stats( returns[start:] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                 Au            SP\n",
        "count  11918.000000  11918.000000\n",
        "mean      10.613677      7.976448\n",
        "std       28.282301     16.759750\n",
        "min      -41.473587    -48.779458\n",
        "25%       -6.891652     -2.075755\n",
        "50%        5.086154      9.821511\n",
        "75%       22.170530     19.348908\n",
        "max      261.010830     65.300874\n",
        "\n",
        " ::  Index on min:\n",
        "Au   1982-03-19\n",
        "SP   2008-11-20\n",
        "dtype: datetime64[ns]\n",
        "\n",
        " ::  Index on max:\n",
        "Au   1980-01-21\n",
        "SP   2010-03-02\n",
        "dtype: datetime64[ns]\n",
        "\n",
        " ::  Head:\n",
        "                  Au        SP\n",
        "T                             \n",
        "1969-07-01  0.734394 -3.786541\n",
        "1969-07-02  3.580402 -3.218233\n",
        "1969-07-03  3.615960 -2.562848\n",
        "1969-07-04  6.393862 -2.715109\n",
        "1969-07-07  6.488550 -3.234317\n",
        "1969-07-08  7.397959 -4.527675\n",
        "1969-07-09  8.636364 -4.739430"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        " ::  Tail:\n",
        "                   Au         SP\n",
        "T                               \n",
        "2015-02-25  -9.739652  12.804777\n",
        "2015-02-26  -9.629768  12.644292\n",
        "2015-02-27  -9.756551  12.118613\n",
        "2015-03-02  -9.193035  12.744670\n",
        "2015-03-03  -9.765625  12.284982\n",
        "2015-03-04 -10.900650  12.363263\n",
        "2015-03-05 -12.005857  12.463334\n",
        "\n",
        " ::  Correlation matrix:\n",
        "          Au        SP\n",
        "Au  1.000000 -0.103213\n",
        "SP -0.103213  1.000000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Without the effects of volatility, the *arithmetic* mean of gold is 260 bp greater than US equities -- which might compensate for its lack of dividends cash flow."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Correlation and regression fit"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "We expect practically zero correlation between gold and US equities in most periods."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  This also runs a linear regression: Au = f(SP)\n",
      "stat2( returns[start:]['Au'], returns[start:]['SP'] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " ::  FIRST variable:\n",
        "count    11918.000000\n",
        "mean        10.613677\n",
        "std         28.282301\n",
        "min        -41.473587\n",
        "25%         -6.891652\n",
        "50%          5.086154\n",
        "75%         22.170530\n",
        "max        261.010830\n",
        "Name: Au, dtype: float64"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        " ::  SECOND variable:\n",
        "count    11918.000000\n",
        "mean         7.976448\n",
        "std         16.759750\n",
        "min        -48.779458\n",
        "25%         -2.075755\n",
        "50%          9.821511\n",
        "75%         19.348908\n",
        "max         65.300874\n",
        "Name: SP, dtype: float64"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        " ::  CORRELATION\n",
        "-0.103213213575\n",
        "\n",
        "-------------------------Summary of Regression Analysis-------------------------\n",
        "\n",
        "Formula: Y ~ <x> + <intercept>\n",
        "\n",
        "Number of Observations:         11918\n",
        "Number of Degrees of Freedom:   2\n",
        "\n",
        "R-squared:         0.0107\n",
        "Adj R-squared:     0.0106\n",
        "\n",
        "Rmse:             28.1324\n",
        "\n",
        "F-stat (1, 11916):   128.3076, p-value:     0.0000\n",
        "\n",
        "Degrees of Freedom: model 1, resid 11916\n",
        "\n",
        "-----------------------Summary of Estimated Coefficients------------------------\n",
        "      Variable       Coef    Std Err     t-stat    p-value    CI 2.5%   CI 97.5%\n",
        "--------------------------------------------------------------------------------\n",
        "             x    -0.1742     0.0154     -11.33     0.0000    -0.2043    -0.1440\n",
        "     intercept    12.0030     0.2854      42.06     0.0000    11.4436    12.5623\n",
        "---------------------------------End of Summary---------------------------------\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "History of projected returns"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We use the Holt-Winters technique to plot projected annual returns. Resampled monthly data, rather than raw daily data, is used to see the broader trends.\n",
      "\n",
      "The projected annual returns gives the best linear slope forecasts, thus it is a compact representation of many point predictions using the Holt-Winters technique. It may not be accurate at major turning points, but its path very far away from the (seemingly stationary) mean could indicate overbought or oversold conditions in the market."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Forecasting gold"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Gold: projected annual returns using monthly data:\n",
      "aupro = holtpc( monthly(au), 12 )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Gold projections for the last 40 years:\n",
      "plotfred( aupro[-480:] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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juTxdyv0Z13S+63H11Sl23z3FuHHmQBWz/9dfT31u4NOXi0DHjin++9/828+f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\nefF1+POfx/Dmm/246iqoqqp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XMB3YAegPzAcky/aazi67qL7/vublwANVX3op/zpRmTRp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\nwHs8Hk8jxRt4j8fjaaT8fxhADShSMpm/AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xad051a2c>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Long-term arithmetic mean return is 10.6%.\n",
      "#  Latest forecast of gold return for the coming year:\n",
      "tailvalue( aupro )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "-4.884878533176684"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Forecasting SPX"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  SPX: projected annual returns using monthly data:\n",
      "sppro = holtpc( monthly(sp), 12 )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  US equities projections for the last 40 years:\n",
      "plotfred( sppro[-480:] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+hgwJdkH5178sjdPPD34QrAV6++2NK3f6ycXj98+zm4qgtVz277fA5x8g5NWt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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xacfd214c>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Long-term arithmetic mean return is 8.0%.\n",
      "#  Latest forecast of SPX return for the coming year:\n",
      "tailvalue( sppro )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "10.944655163915927"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Relative value between SPX and XAU"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  SPX priced in USD per share:\n",
      "plotfred( sp['1968-04-01':] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KwEcfQc+eLdMXh42TN4wqZciQ4pR7002pSJDLlrm9C0OcIts493TuvNPNGA37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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xacf2c74c>"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  XAU priced in USD per troy ounce:\n",
      "plotfred( au['1968-04-01':] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6/amnwksvueMlS/zqGzA9cfikBfzUk8tds8suqeNNN4UVKxrPU1NqLb6RaCNf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\nKC9xRr7qfvjohvnkm82cOU3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       "text": [
        "<matplotlib.figure.Figure at 0xace77d4c>"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The previous section on forecasting looked the assets separately. **Now we shall look at SPX priced in terms of XAU, which can be interpretated as troy ounces of gold required to buy an equity share in the US.**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "spau = todf( sp / au )\n",
      "#   Units are thus expressed in troy ounces per share."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  USD as common denominator drops out, and \n",
      "#  Y plots the US equity in terms of troy ounces of gold:\n",
      "plotfred( spau )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Ep4pqKl9/bcPnHn44eWRgQ4M9j/enUA2UJVfGo4+mr0uNX2zXzn4YH35o/cuL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\nDbOiKIpjqGFWFEVxjP8HWldqPLvbjKwAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xacfd206c>"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That spike to 5.6 ounces is very noteworthy indicating overvalued equities, and a signal to buy gold. In fact, it is the all-time high since 1880."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Longer view using monthly Schiller \"data,\" back to 1880, but in terms of grams:\n",
      "Image(url='http://pricedingold.com/charts/SP500-1880.png', embed=False)\n",
      "#  1 troy ounce = 31.1 grams"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<img src=\"http://pricedingold.com/charts/SP500-1880.png\"/>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 46,
       "text": [
        "<IPython.core.display.Image at 0xacffd2ec>"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "stats( spau )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                  Y\n",
        "count  12244.000000\n",
        "mean       1.565869\n",
        "std        1.217546\n",
        "min        0.131882\n",
        "25%        0.644588\n",
        "50%        1.163509\n",
        "75%        2.306488\n",
        "max        5.565022\n",
        "\n",
        " ::  Index on min:\n",
        "Y   1980-01-21\n",
        "dtype: datetime64[ns]\n",
        "\n",
        " ::  Index on max:\n",
        "Y   1999-07-15\n",
        "dtype: datetime64[ns]\n",
        "\n",
        " ::  Head:\n",
        "                   Y\n",
        "T                   \n",
        "1968-04-01  2.453050\n",
        "1968-04-02  2.483646\n",
        "1968-04-03  2.485904\n",
        "1968-04-04  2.539648\n",
        "1968-04-05  2.521351\n",
        "1968-04-08  2.562753\n",
        "1968-04-09  2.532000\n",
        "\n",
        " ::  Tail:\n",
        "                   Y\n",
        "T                   \n",
        "2015-02-25  1.754605\n",
        "2015-02-26  1.746940\n",
        "2015-02-27  1.733526\n",
        "2015-03-02  1.746301\n",
        "2015-03-03  1.738017\n",
        "2015-03-04  1.749504\n",
        "2015-03-05  1.747953\n",
        "\n",
        " ::  Correlation matrix:\n",
        "   Y\n",
        "Y  1"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Over the long haul, it took an *average of 1.57 troy ounces of gold to purchase one US equity share*."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  What is the long-term trend?\n",
      "plotfred( trend(spau) )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " ::  regresstime slope = 9.67148719065e-05\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2u6UFTj1VhVuIrkImi3ds2VNMPu5w4YVNbLRRyLefeQauvz4sRZYGMfUNyKcU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\nSpsRNnwlwN4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xad01802c>"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Simplistically, US equites has arithmetically doubled in value in terms of gold (from 1 oz. in the 70's to over 2 oz. recently). That trend looks good, going as far back as 1932."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Compute the geometric mean return:\n",
      "georet( spau )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 49,
       "text": [
        "[-0.7, 2.71, 26.12, 256]"
       ]
      }
     ],
     "prompt_number": 49
    },
    {
     "cell_type": "markdown",
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     "source": [
      "### Conclusion for relative value\n",
      "\n",
      "The arithmetic mean return for spau is approximately 2.7% per annum (which is the trend shown graphically above), however, due to high volatility the geometric mean return is sub-zero. **This analytically implies *short equities vs. long gold is favorable for an investor with log utility*, but at high risk with hardly any profit over the long haul.** \n",
      "\n",
      "Including dividends in our analysis would reverse this conclusion as to positions, but would still leave us indifferent as to a definitive choice between the two assets. A complete treatment should also account for the taxation on dividends and capital gains (financial vs. commodity assets).\n",
      "\n",
      "Notice that the spau volatility is greater than that of SPX, and also that of XAU. **Opposing the two assets in a portfolio does not diminish risk, but rather increases risk.** \n",
      "\n",
      "It is worth noting that dividends are reduced generally when industries are not doing well. Interest rates may decrease in order to induce economic activity (cf. Great Recession), which would decrease *real* interest rates. Since gold has no income stream, it thus becomes more preferable over equities in such situations.\n",
      "\n",
      "Real interest rates also become negative when monetary policy allows inflation to rise above nominal interest rates. This is the classic scenario where gold is preferable because financial instruments will have difficulty merely preserving wealth."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### TODO\n",
      "\n",
      "- [ ] - do a portfolio analysis with SPX and XAU jointly long.\n",
      "    - What allocation between the two assets has been risk minimal?\n",
      "    - Can the allocation be improved by using real interest rates as a factor?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 49
    }
   ],
   "metadata": {}
  }
 ]
}