19_capm.ipynb

{
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CAPM Notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Security market line\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pandas_datareader import DataReader as pdr\n",
    "import plotly.graph_objects as go\n",
    "import statsmodels.api as sm\n",
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "betas = norm.rvs(loc=1, scale=0.5, size=10,random_state=10)\n",
    "mrp = 0.05\n",
    "rf  = 0.02\n",
    "expret = rf + betas*mrp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
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           "showland": true,
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           "style": "light"
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           "bgcolor": "#E5ECF6",
           "radialaxis": {
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          "scene": {
           "xaxis": {
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           "line": {
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           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
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          },
          "title": {
           "x": 0.05
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          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
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           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
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           "ticks": "",
           "title": {
            "standoff": 15
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           "zerolinewidth": 2
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        },
        "title": {
         "text": "Security Market Line"
        },
        "xaxis": {
         "range": [
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         "tickformat": ".2f",
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          "text": "Beta"
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        },
        "yaxis": {
         "range": [
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         "tickformat": ".1%",
         "title": {
          "text": "Expected Return"
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     },
     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "# Plot SML with no alpha\n",
    "trace  = go.Scatter(x=betas, y=expret, mode=\"markers\", name='Assets', marker=dict(size=10),)\n",
    "minval = 0.0\n",
    "maxval = 2.0\n",
    "trace_sml = go.Scatter(x= np.linspace(minval,maxval,100), y = rf+mrp*np.linspace(minval,maxval,100), mode='lines',name='SML',\n",
    "    hovertemplate=\"SML<br>y-intercept: risk-free rate<br>slope: market risk premium<extra></extra>\")\n",
    "\n",
    "fig = go.Figure()\n",
    "fig.add_trace(trace)\n",
    "fig.add_trace(trace_sml)\n",
    "fig.update_xaxes(title='Beta',tickformat=\".2f\", range=[minval,maxval])\n",
    "fig.update_yaxes(title='Expected Return',tickformat=\".1%\", range=[0, 0.2])\n",
    "fig.update_layout(title='Security Market Line (no alpha)')\n",
    "fig.update_layout(legend=dict(yanchor=\"top\", y =0.99, xanchor=\"left\", x=0.01))\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Add alphas to some assets\n",
    "\n",
    "alphas = np.zeros(len(betas))\n",
    "alphas[0]=0.02\n",
    "alphas[3]=-0.02\n",
    "alphas[6]= 0.01\n",
    "alphas[9]= -0.03\n",
    "expret += alphas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
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          "scene": {
           "xaxis": {
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            "ticks": ""
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            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
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        },
        "title": {
         "text": "Security Market Line (with alpha)"
        },
        "xaxis": {
         "range": [
          0,
          2
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         "tickformat": ".2f",
         "title": {
          "text": "Beta"
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         "range": [
          0,
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         "tickformat": ".1%",
         "title": {
          "text": "Expected Return"
         }
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot SML with no alpha\n",
    "trace  = go.Scatter(x=betas, y=expret, mode=\"markers\", name='Assets', marker=dict(size=10),customdata=alphas,\n",
    "    hovertemplate=\"<br>beta: %{x:.2f}<br>alpha: %{customdata:.1%}<extra></extra>\")\n",
    "minval = 0.0\n",
    "maxval = 2.0\n",
    "trace_sml = go.Scatter(x= np.linspace(minval,maxval,100), y = rf+mrp*np.linspace(minval,maxval,100), mode='lines',name='SML',\n",
    "    hovertemplate=\"SML<br>y-intercept: risk-free rate<br>slope: market risk premium<extra></extra>\")\n",
    "\n",
    "fig = go.Figure()\n",
    "fig.add_trace(trace)\n",
    "fig.add_trace(trace_sml)\n",
    "fig.update_xaxes(title='Beta',tickformat=\".2f\", range=[minval,maxval])\n",
    "fig.update_yaxes(title='Expected Return',tickformat=\".1%\", range=[0, 0.2])\n",
    "fig.update_layout(title='Security Market Line (with alpha)')\n",
    "fig.update_layout(legend=dict(yanchor=\"top\", y =0.99, xanchor=\"left\", x=0.01))\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Industries SML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Read industry and clean-up missing data (coded -99.99)\n",
    "ff48 = pdr(\"48_Industry_Portfolios\", \"famafrench\", start=1900)[0]\n",
    "\n",
    "# Clean-up missings\n",
    "for c in ff48.columns:\n",
    "    ff48[c] = np.where(ff48[c]==-99.99, np.nan, ff48[c])\n",
    "ff48 = ff48/100\n",
    "\n",
    "# Pull and merge market returns\n",
    "ff3 = pdr('F-F_Research_Data_Factors','famafrench', start=1900)[0]/100\n",
    "df = ff48.join(ff3[['Mkt-RF','RF']])\n",
    "df = df.loc['1970-01':].copy()  # There is missing data prior to 1970"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.5158115967503908, 0.005413902053712481]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Estimate betas and take average return\n",
    "def params(varname):\n",
    "    y = df[varname]-df['RF']\n",
    "    X = sm.add_constant(df['Mkt-RF'])\n",
    "    mm = sm.OLS(y, X, missing='drop').fit()\n",
    "    return [mm.params['Mkt-RF'], y.mean()]\n",
    "params('Util ')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>beta</th>\n",
       "      <th>avg_ret</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Agric</th>\n",
       "      <td>0.844771</td>\n",
       "      <td>0.006379</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Food</th>\n",
       "      <td>0.650510</td>\n",
       "      <td>0.006962</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Soda</th>\n",
       "      <td>0.799203</td>\n",
       "      <td>0.007330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beer</th>\n",
       "      <td>0.722205</td>\n",
       "      <td>0.007446</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Smoke</th>\n",
       "      <td>0.635587</td>\n",
       "      <td>0.009831</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Toys</th>\n",
       "      <td>1.178129</td>\n",
       "      <td>0.003612</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fun</th>\n",
       "      <td>1.338614</td>\n",
       "      <td>0.008741</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Books</th>\n",
       "      <td>1.081942</td>\n",
       "      <td>0.004824</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hshld</th>\n",
       "      <td>0.773439</td>\n",
       "      <td>0.004763</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Clths</th>\n",
       "      <td>1.114118</td>\n",
       "      <td>0.006841</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hlth</th>\n",
       "      <td>1.125943</td>\n",
       "      <td>0.005756</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MedEq</th>\n",
       "      <td>0.906563</td>\n",
       "      <td>0.006354</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Drugs</th>\n",
       "      <td>0.767770</td>\n",
       "      <td>0.006894</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Chems</th>\n",
       "      <td>1.052284</td>\n",
       "      <td>0.006423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rubbr</th>\n",
       "      <td>1.068038</td>\n",
       "      <td>0.006806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Txtls</th>\n",
       "      <td>1.150030</td>\n",
       "      <td>0.005446</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BldMt</th>\n",
       "      <td>1.191047</td>\n",
       "      <td>0.006462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cnstr</th>\n",
       "      <td>1.277505</td>\n",
       "      <td>0.005755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Steel</th>\n",
       "      <td>1.328546</td>\n",
       "      <td>0.004370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FabPr</th>\n",
       "      <td>1.106557</td>\n",
       "      <td>0.004715</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mach</th>\n",
       "      <td>1.224780</td>\n",
       "      <td>0.006500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ElcEq</th>\n",
       "      <td>1.228995</td>\n",
       "      <td>0.007620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Autos</th>\n",
       "      <td>1.239019</td>\n",
       "      <td>0.007076</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aero</th>\n",
       "      <td>1.133451</td>\n",
       "      <td>0.008106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ships</th>\n",
       "      <td>1.100845</td>\n",
       "      <td>0.006873</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Guns</th>\n",
       "      <td>0.782415</td>\n",
       "      <td>0.009333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Gold</th>\n",
       "      <td>0.564163</td>\n",
       "      <td>0.005510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mines</th>\n",
       "      <td>1.118807</td>\n",
       "      <td>0.006732</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Coal</th>\n",
       "      <td>1.153815</td>\n",
       "      <td>0.007276</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oil</th>\n",
       "      <td>0.858441</td>\n",
       "      <td>0.007124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Util</th>\n",
       "      <td>0.515812</td>\n",
       "      <td>0.005414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Telcm</th>\n",
       "      <td>0.792798</td>\n",
       "      <td>0.005214</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PerSv</th>\n",
       "      <td>1.087760</td>\n",
       "      <td>0.002404</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BusSv</th>\n",
       "      <td>1.261318</td>\n",
       "      <td>0.007307</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Comps</th>\n",
       "      <td>1.198053</td>\n",
       "      <td>0.005134</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Chips</th>\n",
       "      <td>1.387478</td>\n",
       "      <td>0.007842</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LabEq</th>\n",
       "      <td>1.264037</td>\n",
       "      <td>0.007073</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Paper</th>\n",
       "      <td>0.957084</td>\n",
       "      <td>0.005038</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Boxes</th>\n",
       "      <td>0.956197</td>\n",
       "      <td>0.005857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Trans</th>\n",
       "      <td>1.062852</td>\n",
       "      <td>0.006058</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Whlsl</th>\n",
       "      <td>1.037250</td>\n",
       "      <td>0.005945</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rtail</th>\n",
       "      <td>1.001465</td>\n",
       "      <td>0.007137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Meals</th>\n",
       "      <td>1.026546</td>\n",
       "      <td>0.006905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Banks</th>\n",
       "      <td>1.073443</td>\n",
       "      <td>0.005979</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Insur</th>\n",
       "      <td>0.942057</td>\n",
       "      <td>0.007149</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RlEst</th>\n",
       "      <td>1.232069</td>\n",
       "      <td>0.002512</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fin</th>\n",
       "      <td>1.225120</td>\n",
       "      <td>0.007457</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Other</th>\n",
       "      <td>1.130517</td>\n",
       "      <td>0.001578</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           beta   avg_ret\n",
       "Agric  0.844771  0.006379\n",
       "Food   0.650510  0.006962\n",
       "Soda   0.799203  0.007330\n",
       "Beer   0.722205  0.007446\n",
       "Smoke  0.635587  0.009831\n",
       "Toys   1.178129  0.003612\n",
       "Fun    1.338614  0.008741\n",
       "Books  1.081942  0.004824\n",
       "Hshld  0.773439  0.004763\n",
       "Clths  1.114118  0.006841\n",
       "Hlth   1.125943  0.005756\n",
       "MedEq  0.906563  0.006354\n",
       "Drugs  0.767770  0.006894\n",
       "Chems  1.052284  0.006423\n",
       "Rubbr  1.068038  0.006806\n",
       "Txtls  1.150030  0.005446\n",
       "BldMt  1.191047  0.006462\n",
       "Cnstr  1.277505  0.005755\n",
       "Steel  1.328546  0.004370\n",
       "FabPr  1.106557  0.004715\n",
       "Mach   1.224780  0.006500\n",
       "ElcEq  1.228995  0.007620\n",
       "Autos  1.239019  0.007076\n",
       "Aero   1.133451  0.008106\n",
       "Ships  1.100845  0.006873\n",
       "Guns   0.782415  0.009333\n",
       "Gold   0.564163  0.005510\n",
       "Mines  1.118807  0.006732\n",
       "Coal   1.153815  0.007276\n",
       "Oil    0.858441  0.007124\n",
       "Util   0.515812  0.005414\n",
       "Telcm  0.792798  0.005214\n",
       "PerSv  1.087760  0.002404\n",
       "BusSv  1.261318  0.007307\n",
       "Comps  1.198053  0.005134\n",
       "Chips  1.387478  0.007842\n",
       "LabEq  1.264037  0.007073\n",
       "Paper  0.957084  0.005038\n",
       "Boxes  0.956197  0.005857\n",
       "Trans  1.062852  0.006058\n",
       "Whlsl  1.037250  0.005945\n",
       "Rtail  1.001465  0.007137\n",
       "Meals  1.026546  0.006905\n",
       "Banks  1.073443  0.005979\n",
       "Insur  0.942057  0.007149\n",
       "RlEst  1.232069  0.002512\n",
       "Fin    1.225120  0.007457\n",
       "Other  1.130517  0.001578"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_beta = pd.DataFrame(index=ff48.columns, columns = ['beta','avg_ret'],dtype=float)\n",
    "for c in ff48.columns:\n",
    "    df_beta.loc[c,:] = params(c)\n",
    "df_beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Under CAPM, slope of empirical CAPM should be  0.0056 per month.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.0677004739336493"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theory_slope = df['Mkt-RF'].mean()\n",
    "print(f'Under CAPM, slope of empirical CAPM should be {theory_slope: .4f} per month.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                avg_ret   R-squared:                       0.016\n",
      "Model:                            OLS   Adj. R-squared:                 -0.005\n",
      "Method:                 Least Squares   F-statistic:                    0.7473\n",
      "Date:                Tue, 15 Nov 2022   Prob (F-statistic):              0.392\n",
      "Time:                        14:05:58   Log-Likelihood:                 241.20\n",
      "No. Observations:                  48   AIC:                            -478.4\n",
      "Df Residuals:                      46   BIC:                            -474.7\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0072      0.001      6.166      0.000       0.005       0.010\n",
      "beta          -0.0010      0.001     -0.864      0.392      -0.003       0.001\n",
      "==============================================================================\n",
      "Omnibus:                        5.799   Durbin-Watson:                   2.199\n",
      "Prob(Omnibus):                  0.055   Jarque-Bera (JB):                4.618\n",
      "Skew:                          -0.655   Prob(JB):                       0.0994\n",
      "Kurtosis:                       3.769   Cond. No.                         9.93\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# Empirical SML\n",
    "y = df_beta.avg_ret\n",
    "X = sm.add_constant(df_beta.beta)\n",
    "emp_sml = sm.OLS(y, X, missing='drop').fit()\n",
    "print(emp_sml.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
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   "source": [
    "# Plot SML \n",
    "trace  = go.Scatter(x=df_beta.beta, y=df_beta.avg_ret, mode=\"markers\", name='Industries', marker=dict(size=10),text=df_beta.index,\n",
    "    hovertemplate=\"<br>industry: %{text}<br>beta: %{x:.2f}<br>avg excess return: %{y:.2%}<extra></extra>\")\n",
    "minval = 0.0\n",
    "maxval = 2.0\n",
    "trace_sml = go.Scatter(x= np.linspace(minval,maxval,100), y = theory_slope*np.linspace(minval,maxval,100), mode='lines',name='Theoretical SML',\n",
    "    hovertemplate=f'Theoretical SML<br>slope: realized market risk premium of {theory_slope:.2%}<extra></extra>')\n",
    "\n",
    "xvals = np.linspace(minval,maxval,100)\n",
    "yvals = emp_sml.params['const'] + emp_sml.params['beta']*xvals\n",
    "trace_emp_sml = go.Scatter(x=xvals, y=yvals , mode='lines',name='Empirical SML', hovertemplate=\"Empirical SML<extra></extra>\")\n",
    "\n",
    "fig = go.Figure()\n",
    "fig.add_trace(trace)\n",
    "fig.add_trace(trace_sml)\n",
    "fig.add_trace(trace_emp_sml)\n",
    "fig.update_xaxes(title='Beta',tickformat=\".2f\", range=[minval,maxval])\n",
    "fig.update_yaxes(title='Expected Excess Return',tickformat=\".1%\")\n",
    "fig.update_layout(title='Theoretical and Empirical Security Market Lines')\n",
    "fig.update_layout(legend=dict(yanchor=\"top\", y =0.99, xanchor=\"left\", x=0.01))\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Note that the location of the industry relative to the theoretical SML is related to their in-sample alpha."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.587\n",
      "Model:                            OLS   Adj. R-squared:                  0.587\n",
      "Method:                 Least Squares   F-statistic:                     897.9\n",
      "Date:                Tue, 15 Nov 2022   Prob (F-statistic):          2.28e-123\n",
      "Time:                        14:31:18   Log-Likelihood:                 981.19\n",
      "No. Observations:                 633   AIC:                            -1958.\n",
      "Df Residuals:                     631   BIC:                            -1949.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         -0.0031      0.002     -1.517      0.130      -0.007       0.001\n",
      "Mkt-RF         1.3285      0.044     29.964      0.000       1.241       1.416\n",
      "==============================================================================\n",
      "Omnibus:                       78.415   Durbin-Watson:                   1.926\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              185.607\n",
      "Skew:                           0.669   Prob(JB):                     4.97e-41\n",
      "Kurtosis:                       5.290   Cond. No.                         21.7\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "varname = 'Steel'\n",
    "y = df[varname]-df['RF']\n",
    "X = sm.add_constant(df['Mkt-RF'])\n",
    "mm = sm.OLS(y, X, missing='drop').fit()\n",
    "print(mm.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Other portfolios"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 100 portfolios formed on size and book-to-market ratios\n",
    "d = pdr('100_Portfolios_10x10','famafrench',start=1900)[1]\n",
    "\n",
    "\n",
    "# Clean-up missings\n",
    "for c in d.columns:\n",
    "    d[c] = np.where(d[c]==-99.99, np.nan, d[c])\n",
    "d = d/100\n",
    "\n",
    "# Pull and merge market returns\n",
    "ff3 = pdr('F-F_Research_Data_Factors','famafrench', start=1900)[0]/100\n",
    "df = d.join(ff3[['Mkt-RF','RF']])\n",
    "df = df.loc['1970-01':].copy()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>beta</th>\n",
       "      <th>avg_ret</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>SMALL LoBM</th>\n",
       "      <td>1.344637</td>\n",
       "      <td>0.001540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ME1 BM2</th>\n",
       "      <td>1.263685</td>\n",
       "      <td>0.005086</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ME1 BM3</th>\n",
       "      <td>1.226589</td>\n",
       "      <td>0.007074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ME1 BM4</th>\n",
       "      <td>1.157218</td>\n",
       "      <td>0.007460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ME1 BM5</th>\n",
       "      <td>1.117289</td>\n",
       "      <td>0.008839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ME10 BM6</th>\n",
       "      <td>0.892037</td>\n",
       "      <td>0.007338</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ME10 BM7</th>\n",
       "      <td>0.876677</td>\n",
       "      <td>0.003850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ME10 BM8</th>\n",
       "      <td>0.972414</td>\n",
       "      <td>0.007004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ME10 BM9</th>\n",
       "      <td>0.959974</td>\n",
       "      <td>0.005089</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BIG HiBM</th>\n",
       "      <td>1.038104</td>\n",
       "      <td>0.006665</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                beta   avg_ret\n",
       "SMALL LoBM  1.344637  0.001540\n",
       "ME1 BM2     1.263685  0.005086\n",
       "ME1 BM3     1.226589  0.007074\n",
       "ME1 BM4     1.157218  0.007460\n",
       "ME1 BM5     1.117289  0.008839\n",
       "...              ...       ...\n",
       "ME10 BM6    0.892037  0.007338\n",
       "ME10 BM7    0.876677  0.003850\n",
       "ME10 BM8    0.972414  0.007004\n",
       "ME10 BM9    0.959974  0.005089\n",
       "BIG HiBM    1.038104  0.006665\n",
       "\n",
       "[100 rows x 2 columns]"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_beta = pd.DataFrame(index=d.columns, columns = ['beta','avg_ret'],dtype=float)\n",
    "for c in d.columns:\n",
    "    df_beta.loc[c,:] = params(c)\n",
    "df_beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Under CAPM, slope of empirical CAPM should be  0.56% per month.\n"
     ]
    }
   ],
   "source": [
    "theory_slope = df['Mkt-RF'].mean()\n",
    "print(f'Under CAPM, slope of empirical CAPM should be {theory_slope: .2%} per month.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                avg_ret   R-squared:                       0.161\n",
      "Model:                            OLS   Adj. R-squared:                  0.152\n",
      "Method:                 Least Squares   F-statistic:                     18.81\n",
      "Date:                Tue, 15 Nov 2022   Prob (F-statistic):           3.50e-05\n",
      "Time:                        14:49:44   Log-Likelihood:                 479.34\n",
      "No. Observations:                 100   AIC:                            -954.7\n",
      "Df Residuals:                      98   BIC:                            -949.5\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0143      0.002      9.150      0.000       0.011       0.017\n",
      "beta          -0.0060      0.001     -4.337      0.000      -0.009      -0.003\n",
      "==============================================================================\n",
      "Omnibus:                        3.974   Durbin-Watson:                   1.455\n",
      "Prob(Omnibus):                  0.137   Jarque-Bera (JB):                3.520\n",
      "Skew:                           0.302   Prob(JB):                        0.172\n",
      "Kurtosis:                       3.694   Cond. No.                         15.5\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# Empirical SML\n",
    "y = df_beta.avg_ret\n",
    "X = sm.add_constant(df_beta.beta)\n",
    "emp_sml = sm.OLS(y, X, missing='drop').fit()\n",
    "print(emp_sml.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
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            "showbackground": true,
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           "bgcolor": "#E5ECF6",
           "caxis": {
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          "title": {
           "x": 0.05
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          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
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        },
        "title": {
         "text": "Theoretical and Empirical Security Market Lines"
        },
        "xaxis": {
         "range": [
          0,
          2
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         "tickformat": ".2f",
         "title": {
          "text": "Beta"
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         "tickformat": ".1%",
         "title": {
          "text": "Expected Excess Return"
         }
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       }
      }
     },
     "metadata": {},
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   ],
   "source": [
    "# Plot SML \n",
    "trace  = go.Scatter(x=df_beta.beta, y=df_beta.avg_ret, mode=\"markers\", name='Portfolios', marker=dict(size=10),text=df_beta.index,\n",
    "    hovertemplate=\"<br>portfolio: %{text}<br>beta: %{x:.2f}<br>avg excess return: %{y:.2%}<extra></extra>\")\n",
    "minval = 0.0\n",
    "maxval = 2.0\n",
    "trace_sml = go.Scatter(x= np.linspace(minval,maxval,100), y = theory_slope*np.linspace(minval,maxval,100), mode='lines',name='Theoretical SML',\n",
    "    hovertemplate=f'Theoretical SML<br>slope: realized market risk premium of {theory_slope:.2%}<extra></extra>')\n",
    "\n",
    "xvals = np.linspace(minval,maxval,100)\n",
    "yvals = emp_sml.params['const'] + emp_sml.params['beta']*xvals\n",
    "trace_emp_sml = go.Scatter(x=xvals, y=yvals , mode='lines',name='Empirical SML', hovertemplate=\"Empirical SML<extra></extra>\")\n",
    "\n",
    "fig = go.Figure()\n",
    "fig.add_trace(trace)\n",
    "fig.add_trace(trace_sml)\n",
    "fig.add_trace(trace_emp_sml)\n",
    "fig.update_xaxes(title='Beta',tickformat=\".2f\", range=[minval,maxval])\n",
    "fig.update_yaxes(title='Expected Excess Return',tickformat=\".1%\")\n",
    "fig.update_layout(title='Theoretical and Empirical Security Market Lines')\n",
    "fig.update_layout(legend=dict(yanchor=\"top\", y =0.99, xanchor=\"left\", x=0.01))\n",
    "fig.show()"
   ]
  }
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