ml-finance-python

python scripts for finance machine learning

git clone https://9o.is/git/ml-finance-python.git

How To - Computing Risk Ratios.ipynb

(160285B)


      1 {
      2  "cells": [
      3   {
      4    "cell_type": "markdown",
      5    "metadata": {},
      6    "source": [
      7     "# How to compute $\\alpha$ and $\\beta$ for a given asset\n",
      8     "By Evgenia \"Jenny\" Nitishinskaya and Delaney Granizo-Mackenzie\n",
      9     "\n",
     10     "Notebook released under the Creative Commons Attribution 4.0 License.\n",
     11     "\n",
     12     "---\n",
     13     "\n",
     14     "A fundamental concept in portfolio management and risk allocation is computing the $\\beta$ of an asset. $\\beta$ is a measurement of the covariance of the asset with the market in general, and is expressed in this model.\n",
     15     "\n",
     16     "$$r_a \\approx \\alpha + \\beta r_b$$\n",
     17     "\n",
     18     "$r_a$ are the returns of the asset, and $r_b$ are the returns of the benchmark, usually a proxy for the market like the S&P 500.\n",
     19     "\n",
     20     "$\\beta$ can be defined as\n",
     21     "\n",
     22     "$$\\beta = \\frac{Cov(r_a, r_b)}{Var(r_b)}$$\n",
     23     "\n",
     24     "To actually compute $\\beta$, we can use linear regression. We find the OLS best fit line for all points $(r_{a, t}, r_{b, t})$, where $r_{a, t}$ is the asset's returns for time $t$, and $r_{b, t}$ the same for the benchmark. The slope of this line is $\\beta$, and the y-intercept is $\\alpha$."
     25    ]
     26   },
     27   {
     28    "cell_type": "markdown",
     29    "metadata": {},
     30    "source": [
     31     "We'll start by getting data for a specific time range."
     32    ]
     33   },
     34   {
     35    "cell_type": "code",
     36    "execution_count": 2,
     37    "metadata": {
     38     "collapsed": true
     39    },
     40    "outputs": [],
     41    "source": [
     42     "# Import libraries\n",
     43     "import numpy as np\n",
     44     "from statsmodels import regression\n",
     45     "import statsmodels.api as sm\n",
     46     "import matplotlib.pyplot as plt\n",
     47     "import math"
     48    ]
     49   },
     50   {
     51    "cell_type": "code",
     52    "execution_count": 3,
     53    "metadata": {
     54     "collapsed": false
     55    },
     56    "outputs": [
     57     {
     58      "data": {
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UCgx+YJe9SZIERWHmpxnZgm7/N6dXfZy3z48d/LDhAVH/EMEPABR0Bj9E1HlsdU2twOAH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q7B56V3hvIq6NQwnXyobeB+OFBz/DMFhKjpZyb6NAoIPYRUutjPVZwC+AE6LevKSQ/gUNAFDV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\nzjnXEP4/lIuoX1O67AYAAAAASUVORK5CYII=\n",
     60       "text/plain": [
     61        "<matplotlib.figure.Figure at 0x7f7a2ecd25d0>"
     62       ]
     63      },
     64      "metadata": {},
     65      "output_type": "display_data"
     66     }
     67    ],
     68    "source": [
     69     "# Get data for the specified period and stocks\n",
     70     "start = '2014-01-01'\n",
     71     "end = '2015-01-01'\n",
     72     "asset = get_pricing('TSLA', fields='price', start_date=start, end_date=end)\n",
     73     "benchmark = get_pricing('SPY', fields='price', start_date=start, end_date=end)\n",
     74     "\n",
     75     "# We have to take the percent changes to get to returns\n",
     76     "# Get rid of the first (0th) element because it is NAN\n",
     77     "r_a = asset.pct_change()[1:]\n",
     78     "r_b = benchmark.pct_change()[1:]\n",
     79     "\n",
     80     "# Let's plot them just for fun\n",
     81     "r_a.plot()\n",
     82     "r_b.plot();"
     83    ]
     84   },
     85   {
     86    "cell_type": "markdown",
     87    "metadata": {},
     88    "source": [
     89     "Now we have to fit a line to the data to determine the slope. We use Ordinary Least Squares (OLS) for this."
     90    ]
     91   },
     92   {
     93    "cell_type": "code",
     94    "execution_count": 4,
     95    "metadata": {
     96     "collapsed": false
     97    },
     98    "outputs": [
     99     {
    100      "name": "stdout",
    101      "output_type": "stream",
    102      "text": [
    103       "alpha: 0.00108062811902\n",
    104       "beta: 1.92705010047\n"
    105      ]
    106     }
    107    ],
    108    "source": [
    109     "# Let's define everything in familiar regression terms\n",
    110     "X = r_b.values # Get just the values, ignore the timestamps\n",
    111     "Y = r_a.values\n",
    112     "\n",
    113     "# We add a constant so that we can also fit an intercept (alpha) to the model\n",
    114     "# This just adds a column of 1s to our data\n",
    115     "X = sm.add_constant(X)\n",
    116     "model = regression.linear_model.OLS(Y, X)\n",
    117     "model = model.fit()\n",
    118     "# Remove the constant now that we're done\n",
    119     "X = X[:, 1]\n",
    120     "alpha = model.params[0]\n",
    121     "beta = model.params[1]\n",
    122     "print 'alpha: ' + str(alpha)\n",
    123     "print 'beta: ' + str(beta)"
    124    ]
    125   },
    126   {
    127    "cell_type": "markdown",
    128    "metadata": {
    129     "collapsed": false
    130    },
    131    "source": [
    132     "We can plot the line of best fit to visualize this."
    133    ]
    134   },
    135   {
    136    "cell_type": "code",
    137    "execution_count": 5,
    138    "metadata": {
    139     "collapsed": false
    140    },
    141    "outputs": [
    142     {
    143      "data": {
    144       "image/png": 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mLlyoViAQHwxLynhfLK+WXmW6R5d7TdWpHc1QJC6feuutq3r06Nza8z58eEbv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\nB4lDyPFoBOOgAAAAAElFTkSuQmCC\n",
    145       "text/plain": [
    146        "<matplotlib.figure.Figure at 0x7f7a2ece4090>"
    147       ]
    148      },
    149      "metadata": {},
    150      "output_type": "display_data"
    151     }
    152    ],
    153    "source": [
    154     "X2 = np.linspace(X.min(), X.max(), 100)\n",
    155     "Y_hat = X2 * beta + alpha\n",
    156     "\n",
    157     "plt.scatter(X, Y, alpha=0.3) # Plot the raw data\n",
    158     "plt.xlabel(\"r_b\")\n",
    159     "plt.ylabel(\"r_a\")\n",
    160     "\n",
    161     "# Add the regression line, colored in red\n",
    162     "plt.plot(X2, Y_hat, 'r', alpha=0.9);"
    163    ]
    164   },
    165   {
    166    "cell_type": "markdown",
    167    "metadata": {},
    168    "source": [
    169     "# How to compute the volatility for a given asset\n",
    170     "\n",
    171     "The volatility $\\sigma$ of an asset is the standard deviation of its returns. A low volatility means that the returns are generally close to the mean, while a high volatility corresponds to returns that are often much higher and often much lower than expected.\n",
    172     "\n",
    173     "We'll go ahead and continue using the stock from before:"
    174    ]
    175   },
    176   {
    177    "cell_type": "code",
    178    "execution_count": 5,
    179    "metadata": {
    180     "collapsed": false
    181    },
    182    "outputs": [
    183     {
    184      "name": "stdout",
    185      "output_type": "stream",
    186      "text": [
    187       "0.0304267478169\n",
    188       "0.00710144477583\n"
    189      ]
    190     }
    191    ],
    192    "source": [
    193     "# Use numpy to find the standard deviation of the returns\n",
    194     "SD = np.std(Y)\n",
    195     "print SD\n",
    196     "\n",
    197     "# Let's compute the volatility for our benchmark, as well\n",
    198     "benchSD = np.std(X)\n",
    199     "print benchSD"
    200    ]
    201   },
    202   {
    203    "cell_type": "markdown",
    204    "metadata": {},
    205    "source": [
    206     "This gives the daily volatility. As expected, the benchmark has a much lower volatility than the stock - a volatile asset would not make a good benchmark.\n",
    207     "\n",
    208     "We generally compute the annualized volatility so that we can compare volatilities for daily, weekly, or monthly samples. To get it we normalize the standard deviation of the daily returns by multiplying by the square root of the number of trading days in a year:\n",
    209     "\n",
    210     "$$\\sigma_{\\text{annual}} = SD \\cdot \\sqrt{252}$$"
    211    ]
    212   },
    213   {
    214    "cell_type": "code",
    215    "execution_count": 6,
    216    "metadata": {
    217     "collapsed": false
    218    },
    219    "outputs": [
    220     {
    221      "name": "stdout",
    222      "output_type": "stream",
    223      "text": [
    224       "0.483009647568\n",
    225       "0.112731940957\n"
    226      ]
    227     }
    228    ],
    229    "source": [
    230     "vol = SD*(252**.5)\n",
    231     "print vol\n",
    232     "\n",
    233     "benchvol = benchSD*(252**.5)\n",
    234     "print benchvol"
    235    ]
    236   },
    237   {
    238    "cell_type": "markdown",
    239    "metadata": {},
    240    "source": [
    241     "This tells us that we should expect the returns of a benchmark to cluster more closely around their mean than those of the stock. We can plot histograms of the returns to see this:"
    242    ]
    243   },
    244   {
    245    "cell_type": "code",
    246    "execution_count": 7,
    247    "metadata": {
    248     "collapsed": false
    249    },
    250    "outputs": [
    251     {
    252      "data": {
    253       "image/png": 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A0ByhAwAANEfoAAAAzRE6AABAc4QOAADQHKEDAAA0R+gAAADNEToAAEBzhA4AANAcoQMA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\n",
    254       "text/plain": [
    255        "<matplotlib.figure.Figure at 0x7f0453a17d50>"
    256       ]
    257      },
    258      "metadata": {},
    259      "output_type": "display_data"
    260     }
    261    ],
    262    "source": [
    263     "# Since we have many distinct values, we'll lump them into buckets of size .02\n",
    264     "x_min = int(math.floor(X.min()))\n",
    265     "x_max = int(math.ceil(X.max()))\n",
    266     "plt.hist(X, bins=[0.02*i for i in range(x_min*50, x_max*50)], alpha=0.5, label='S&P')\n",
    267     "plt.hist(Y, bins=[0.02*i for i in range(x_min*50, x_max*50)], alpha=0.5, label='Stock')\n",
    268     "plt.legend(loc='upper right');"
    269    ]
    270   },
    271   {
    272    "cell_type": "markdown",
    273    "metadata": {},
    274    "source": [
    275     "# How to compute the Sharpe and information ratios for an asset\n",
    276     "\n",
    277     "The Sharpe and information ratios are used to calculate how well the historic returns of an asset compensate for its risk, relative to some benchmark or risk-free asset. An asset with a higher ratio has either higher returns, lower risk, or both. As when computing volatility, the standard deviation of the returns is used to measure risk.\n",
    278     "\n",
    279     "$$R = \\frac{E[r_a - r_b]}{\\sqrt{Var(r_a - r_b)}}$$\n",
    280     "\n",
    281     "$r_a$ are the returns of the asset, and $r_b$ are the returns of the benchmark; generally, Treasury bills are used when computing the Sharpe ratio, while the S&P 500 index is commonly used for the information ratio. We subtract the returns of the benchmark from the returns of the asset becasue we would like to get higher returns through our investment than we would, say, simply buying Treasury bills."
    282    ]
    283   },
    284   {
    285    "cell_type": "code",
    286    "execution_count": 8,
    287    "metadata": {
    288     "collapsed": false
    289    },
    290    "outputs": [
    291     {
    292      "name": "stdout",
    293      "output_type": "stream",
    294      "text": [
    295       "Sharpe ratio: 0.0665469573483\n",
    296       "Information ratio: 0.0548536005258\n"
    297      ]
    298     }
    299    ],
    300    "source": [
    301     "# Get the returns for a treasury-tracking ETF to be used in the Sharpe ratio\n",
    302     "# Note that BIL is only being used in place of risk free rate,\n",
    303     "# and should not be used in such a fashion for strategy development\n",
    304     "riskfree = get_pricing('BIL', fields='price', start_date=start, end_date=end)\n",
    305     "r_b_S = riskfree.pct_change()[1:]\n",
    306     "X_S = r_b_S.values\n",
    307     "\n",
    308     "# Compute the Sharpe ratio for the asset we've been working with\n",
    309     "SR = np.mean(Y - X_S)/np.std(Y - X_S)\n",
    310     "\n",
    311     "# Compute the information ratio for the asset we've been working with, using the S&P index\n",
    312     "IR = np.mean(Y - X)/np.std(Y - X)\n",
    313     "\n",
    314     "# Print results\n",
    315     "print 'Sharpe ratio: ' + str(SR)\n",
    316     "print 'Information ratio: ' + str(IR)"
    317    ]
    318   },
    319   {
    320    "cell_type": "markdown",
    321    "metadata": {},
    322    "source": [
    323     "# How to compute the Sortino ratio for an asset\n",
    324     "\n",
    325     "The Sharpe and information ratios are useful, but they penalize stocks for going above the expected return as well as for going below it. The Sortino ratio is modified to take into account only returns that fall below the mean.\n",
    326     "\n",
    327     "$$S = \\frac{E[r_a - r_b]}{\\sqrt{Semivar(r_a - r_b)}}$$\n",
    328     "\n",
    329     "The semivariance is the variance below the mean, and so quantifies the downside risk of our asset. Here as in the Sharpe ratio returns on Treasury bills can be used for $r_b$. The more skewed the distribution of returns is, the more the Sortino ratio will differ from the Sharpe ratio."
    330    ]
    331   },
    332   {
    333    "cell_type": "code",
    334    "execution_count": 11,
    335    "metadata": {
    336     "collapsed": false
    337    },
    338    "outputs": [
    339     {
    340      "name": "stdout",
    341      "output_type": "stream",
    342      "text": [
    343       "Sortino ratio: 0.0738307139237\n"
    344      ]
    345     }
    346    ],
    347    "source": [
    348     "# To compute the semideviation, we want to filter out values which fall above the mean\n",
    349     "meandif = np.mean(Y - X_S)\n",
    350     "lows = [e for e in Y - X_S if e <= meandif]\n",
    351     "\n",
    352     "# Because there is no built-in semideviation, we'll compute it ourselves\n",
    353     "def dist(x):\n",
    354     "    return (x - meandif)**2\n",
    355     "semidev = math.sqrt(sum(map(dist,lows))/len(lows))\n",
    356     "\n",
    357     "Sortino = meandif/semidev\n",
    358     "print 'Sortino ratio: ' + str(Sortino)"
    359    ]
    360   }
    361  ],
    362  "metadata": {
    363   "kernelspec": {
    364    "display_name": "Python 2",
    365    "language": "python",
    366    "name": "python2"
    367   },
    368   "language_info": {
    369    "codemirror_mode": {
    370     "name": "ipython",
    371     "version": 2
    372    },
    373    "file_extension": ".py",
    374    "mimetype": "text/x-python",
    375    "name": "python",
    376    "nbconvert_exporter": "python",
    377    "pygments_lexer": "ipython2",
    378    "version": "2.7.6"
    379   }
    380  },
    381  "nbformat": 4,
    382  "nbformat_minor": 0
    383 }