Bayesian_Analysis_of_Regression_Model_with_R.ipynb

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      "name": "Bayesian Analysis of Regression Model with R.ipynb",
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        "# **Bayesian Analysis of Regression Models**\n",
        "    \n",
        "### **Introduction**\n",
        "\n",
        "* Many studies concern the relationship between two or more observable quantities.\n",
        "\n",
        "* How do changes in quantity y (the dependent variable) vary as a function of another quantity x (the independent variable)?\n",
        "\n",
        "* Regression models allow us to examine the conditional distribution of $y$ given $x$, parameterized as $p(y|\\beta,x)$ when the $n$ observations $(y_i, x_i)$ are exchangeable.\n",
        "\n",
        "### **Multiple Linear Regression**\n",
        "\n",
        "* The normal linear model occurs when a distribution of $y$ given $x$ is normal with a mean equal to a linear function of $X$:\n",
        "$$\n",
        "\\mathbb{E}(y_i|\\beta,X)=\\beta_1 X_{1i}+\\beta_2 X_{2i}+...+\\beta_k X_{ki}\n",
        "$$\n",
        "for $i = 1,2,...,n$ and $X_1$ is a vector of one's.\n",
        "\n",
        "* The ordinary linear regression model occurs when the variance of $y$ given $X$, $\\beta$ is assumed to be constant over all observations.\n",
        "\n",
        "* In other words, we have an ordinary linear regression model when:\n",
        "$$\n",
        "y_i\\sim N(\\beta_1+\\beta_{2i} X_{2i}+\\cdots+\\beta_{ki} X_{ki}, \\sigma^2)\n",
        "$$\n",
        "for $i = 1,2,\\cdots,n$.\n",
        "\n",
        "* If $$y_i\\sim N(X_i^T\\beta, \\sigma^2)$$ \n",
        "$$\n",
        "y\\sim N_n(X^T\\beta,\\sigma^2I)\n",
        "$$\n",
        "then it is well known that the ordinary least squares estimates and the maximum likelihood estimates of the parameters $\\beta=(\\beta_1,...,\\beta_k)$ are equivalent.\n",
        "\n",
        "* If $\\beta=[\\beta_1,...,\\beta_k]^T$  then the frequentist estimate of $\\beta$ is\n",
        "$$\n",
        "\\hat{\\beta}=(X^TX)^{-1}X^Ty\n",
        "$$\n",
        "\n",
        "* The frequentist estimate of $\\sigma^2$ is \n",
        "$$s^2=\\frac{(y-X\\beta)^T(y-X\\beta)}{(n-k)}$$\n",
        "\n",
        "* The sampling distribution of $\\hat{\\beta}$ is\n",
        "$$\n",
        "\\hat{\\beta}\\sim N_k(\\beta,\\sigma^2(X^TX)^{-1})\n",
        "$$\n",
        "\n",
        "$$\n",
        "\\hat{\\beta}\\sim t_{n-k}(\\beta,s^2(X^TX)^{-1})\n",
        "$$\n",
        "\n",
        "Ref: Multivariate Statistics, by T. W. Anderson (1984) Wiley Second Ed \n",
        "\n",
        "### **Bayesian Regression with Noninformative Flat Prior**\n",
        "\n",
        "* By Bayes Rule, the posterior distribution is:\n",
        "$$\n",
        "p(\\beta_1,...,\\beta_k,\\sigma^2|y,X)\\propto \\prod_{i=1}^n p(y_i|\\mu_i,\\sigma^2)p(\\beta_1,...,\\beta_k,\\sigma^2)\n",
        "$$\n",
        "\n",
        "* The standard non-informative prior distribution is uniform on $(\\beta,\\log \\sigma^2)$ which is equivalent to :\n",
        "$$\n",
        "p(\\beta,\\log(\\sigma^2))\\propto p(\\beta) p(\\log(\\sigma^2)) = \\sigma^{-2}\n",
        "$$\n",
        "\n",
        "* This prior is a good choice for statistical models when you have a lot of data points and only a few parameters.\n",
        "\n",
        "* The Bayesian solution is equivalent to OLS or MLE and you enjoy the advantage of direct Bayesian probabilistic statement.\n",
        "\n",
        "* The posterior distribution of $\\sigma^2$ can be written as:\n",
        "$$\n",
        "p(\\sigma^2|y,X)\\sim Scaled-Inv \\chi^2(n-k,s^2)\n",
        "$$\n",
        "where $s^2=(y-X\\hat{\\beta})^T(y-X\\hat{\\beta})/(n-k)$\n",
        "\n",
        "* The marginal posteror distribution of $\\beta$ follow Multivariate t-distribution, i.e.,\n",
        "$$\n",
        "p(\\beta|y,X)\\sim t_{n-k}(\\hat{\\beta},s^2(X^TX)^{-1})\n",
        "$$\n",
        "\n",
        "* Notice the close comparison with the classical results. The key difference would be interpretation of the standard errors.\n",
        "\n",
        "### **Conjugate priors and the Gaussian linear model**\n",
        "\n",
        "* Suppose that instead of an improper prior, we decide to use the conjugate prior.\n",
        "\n",
        "* For the normal regression model, the conjugate prior distribution for $p(\\beta_0,...,\\beta_k,\\sigma^2)$ is the normal-inverse-gamma distribution,\n",
        "$$\n",
        "p(\\beta_0,...,\\beta_k,\\sigma^2)=p(\\beta_0,...,\\beta_k|\\sigma^2)p(\\sigma^2)\n",
        "$$\n",
        "where $$p(\\beta_0,...,\\beta_k|\\sigma^2)\\sim N_k(\\beta_0,\\Lambda_0)$$\n",
        "and $$p(\\sigma^2)\\sim \\text{Inv-Gamma}(a_0,b_0)$$\n",
        "\n",
        "* **Posterior Distribution**\n",
        "$$\n",
        "p(\\beta_0,...,\\beta_k,\\sigma^2|y,X)=p(\\beta_0,...,\\beta_k|\\sigma^2,y,X)p(\\sigma^2|y,X)\n",
        "$$\n",
        "where $$p(\\beta_0,...,\\beta_k|\\sigma^2,y,X)\\sim N_k(\\beta_n,\\Lambda_n)$$\n",
        "and $$p(\\sigma^2|y,X)\\sim \\text{Inv-Gamma}(a_n,b_n)$$\n",
        "\n",
        "* **Posterior mean**:\n",
        "$$\n",
        "\\mathbb{E}(\\beta|y,X)=(X^TX+\\Lambda_0^{-1})^{-1}(X^TX\\hat{\\beta}+\\Lambda_0^{-1}\\beta_0)\n",
        "$$\n",
        "\n",
        "* Notice that the coefficients are essentially a weighted average of the prior coefficients described by $\\beta_0$ and standard OLS estimate $\\hat{\\beta}$.\n",
        "\n",
        "* The weights are provided by the conditional prior precision $\\Lambda_0^{-1}$ and the data $X^TX$. \n",
        "\n",
        "* This should make clear that as we increase our prior precision (decrease our prior variance) for $\\beta$ we place greater posterior weight on our prior beliefs relative to the data.\n",
        "\n",
        "* **Posterior mean**:\n",
        "$$\n",
        "\\mathbb{E}(\\beta|y,X)=(X^TX+\\Lambda_0^{-1})^{-1}(X^TX\\hat{\\beta}+\\Lambda_0^{-1}\\beta_0)\n",
        "$$\n",
        "\n",
        "* If you choose $\\beta_0 = 0$ and $\\Lambda_0^{-1}=\\lambda I$, then\n",
        "$$\n",
        "\\mathbb{E}(\\beta|y,X)=(X^TX+\\lambda I)^{-1} X^Ty\n",
        "$$\n",
        "this is \"**Ridge Solution**\" of the Ridge Regression.\n",
        "\n",
        "* Ridge Regression is a special case of Bayesian Regression with Conjugate prior\n",
        "\n",
        "* Bayesian Regression with Conjugate prior automatically takes care of multicollinearity issue of the data.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0VGHuVwkvAIm"
      },
      "source": [
        "# **Application : Capital Asset Pricing Model**\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 392
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        "id": "V7FMtboCyvsl",
        "outputId": "393b41d7-194f-4bbd-af9b-f7e7ed22dc75"
      },
      "source": [
        "data = read.csv(file='https://www.cmi.ac.in/~sourish/StatFin2016/Program/R_Workshop/stock_treasury.csv')\n",
        "head(data)"
      ],
      "execution_count": null,
      "outputs": [
        {
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            "text/plain": [
              "  Date       IBM_Volume IBM_AdjClose Apple_Volume Apple_AdjClose MSFT_Volume\n",
              "1 2015-01-02 5525500    156.9353     53204600     106.9182       27913900   \n",
              "2 2015-01-05 4880400    154.4659     64285500     103.9062       39673900   \n",
              "3 2015-01-06 6146700    151.1347     65797100     103.9160       36447900   \n",
              "4 2015-01-07 4701800    150.1469     40105900     105.3731       29114100   \n",
              "5 2015-01-08 4236800    153.4104     59364500     109.4218       29645200   \n",
              "6 2015-01-09 4484800    154.0785     53699500     109.5391       23942800   \n",
              "  MSFT_AdjClose Intel_Volume Intel_AdjClose SnP500  ⋯ UST_Mo_3 UST_Mo_6\n",
              "1 45.52076      23605600     34.98996       2058.20 ⋯ 0.02     0.11    \n",
              "2 45.10216      32785000     34.59541       2020.58 ⋯ 0.03     0.10    \n",
              "3 44.44018      30847600     33.95066       2002.61 ⋯ 0.03     0.10    \n",
              "4 45.00480      27725200     34.66277       2025.90 ⋯ 0.03     0.09    \n",
              "5 46.32876      31765400     35.30753       2062.14 ⋯ 0.03     0.08    \n",
              "6 45.93936      22846000     35.37489       2044.81 ⋯ 0.02     0.08    \n",
              "  UST_Yr_1 UST_Yr_2 UST_Yr_3 UST_Yr_5 UST_Yr_7 UST_Yr_10 UST_Yr_20 UST_Yr_30\n",
              "1 0.25     0.66     1.07     1.61     1.92     2.12      2.41      2.69     \n",
              "2 0.26     0.68     1.06     1.57     1.85     2.04      2.32      2.60     \n",
              "3 0.25     0.65     1.02     1.50     1.78     1.97      2.25      2.52     \n",
              "4 0.25     0.62     1.00     1.47     1.76     1.96      2.25      2.52     \n",
              "5 0.23     0.62     1.00     1.50     1.81     2.03      2.33      2.59     \n",
              "6 0.22     0.59     0.96     1.45     1.75     1.98      2.29      2.55     "
            ],
            "text/latex": "A data.frame: 6 × 21\n\\begin{tabular}{r|lllllllllllllllllllll}\n  & Date & IBM\\_Volume & IBM\\_AdjClose & Apple\\_Volume & Apple\\_AdjClose & MSFT\\_Volume & MSFT\\_AdjClose & Intel\\_Volume & Intel\\_AdjClose & SnP500 & ⋯ & UST\\_Mo\\_3 & UST\\_Mo\\_6 & UST\\_Yr\\_1 & UST\\_Yr\\_2 & UST\\_Yr\\_3 & UST\\_Yr\\_5 & UST\\_Yr\\_7 & UST\\_Yr\\_10 & UST\\_Yr\\_20 & UST\\_Yr\\_30\\\\\n  & <chr> & <int> & <dbl> & <int> & <dbl> & <int> & <dbl> & <int> & <dbl> & <dbl> & ⋯ & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n\\hline\n\t1 & 2015-01-02 & 5525500 & 156.9353 & 53204600 & 106.9182 & 27913900 & 45.52076 & 23605600 & 34.98996 & 2058.20 & ⋯ & 0.02 & 0.11 & 0.25 & 0.66 & 1.07 & 1.61 & 1.92 & 2.12 & 2.41 & 2.69\\\\\n\t2 & 2015-01-05 & 4880400 & 154.4659 & 64285500 & 103.9062 & 39673900 & 45.10216 & 32785000 & 34.59541 & 2020.58 & ⋯ & 0.03 & 0.10 & 0.26 & 0.68 & 1.06 & 1.57 & 1.85 & 2.04 & 2.32 & 2.60\\\\\n\t3 & 2015-01-06 & 6146700 & 151.1347 & 65797100 & 103.9160 & 36447900 & 44.44018 & 30847600 & 33.95066 & 2002.61 & ⋯ & 0.03 & 0.10 & 0.25 & 0.65 & 1.02 & 1.50 & 1.78 & 1.97 & 2.25 & 2.52\\\\\n\t4 & 2015-01-07 & 4701800 & 150.1469 & 40105900 & 105.3731 & 29114100 & 45.00480 & 27725200 & 34.66277 & 2025.90 & ⋯ & 0.03 & 0.09 & 0.25 & 0.62 & 1.00 & 1.47 & 1.76 & 1.96 & 2.25 & 2.52\\\\\n\t5 & 2015-01-08 & 4236800 & 153.4104 & 59364500 & 109.4218 & 29645200 & 46.32876 & 31765400 & 35.30753 & 2062.14 & ⋯ & 0.03 & 0.08 & 0.23 & 0.62 & 1.00 & 1.50 & 1.81 & 2.03 & 2.33 & 2.59\\\\\n\t6 & 2015-01-09 & 4484800 & 154.0785 & 53699500 & 109.5391 & 23942800 & 45.93936 & 22846000 & 35.37489 & 2044.81 & ⋯ & 0.02 & 0.08 & 0.22 & 0.59 & 0.96 & 1.45 & 1.75 & 1.98 & 2.29 & 2.55\\\\\n\\end{tabular}\n",
            "text/markdown": "\nA data.frame: 6 × 21\n\n| <!--/--> | Date &lt;chr&gt; | IBM_Volume &lt;int&gt; | IBM_AdjClose &lt;dbl&gt; | Apple_Volume &lt;int&gt; | Apple_AdjClose &lt;dbl&gt; | MSFT_Volume &lt;int&gt; | MSFT_AdjClose &lt;dbl&gt; | Intel_Volume &lt;int&gt; | Intel_AdjClose &lt;dbl&gt; | SnP500 &lt;dbl&gt; | ⋯ ⋯ | UST_Mo_3 &lt;dbl&gt; | UST_Mo_6 &lt;dbl&gt; | UST_Yr_1 &lt;dbl&gt; | UST_Yr_2 &lt;dbl&gt; | UST_Yr_3 &lt;dbl&gt; | UST_Yr_5 &lt;dbl&gt; | UST_Yr_7 &lt;dbl&gt; | UST_Yr_10 &lt;dbl&gt; | UST_Yr_20 &lt;dbl&gt; | UST_Yr_30 &lt;dbl&gt; |\n|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n| 1 | 2015-01-02 | 5525500 | 156.9353 | 53204600 | 106.9182 | 27913900 | 45.52076 | 23605600 | 34.98996 | 2058.20 | ⋯ | 0.02 | 0.11 | 0.25 | 0.66 | 1.07 | 1.61 | 1.92 | 2.12 | 2.41 | 2.69 |\n| 2 | 2015-01-05 | 4880400 | 154.4659 | 64285500 | 103.9062 | 39673900 | 45.10216 | 32785000 | 34.59541 | 2020.58 | ⋯ | 0.03 | 0.10 | 0.26 | 0.68 | 1.06 | 1.57 | 1.85 | 2.04 | 2.32 | 2.60 |\n| 3 | 2015-01-06 | 6146700 | 151.1347 | 65797100 | 103.9160 | 36447900 | 44.44018 | 30847600 | 33.95066 | 2002.61 | ⋯ | 0.03 | 0.10 | 0.25 | 0.65 | 1.02 | 1.50 | 1.78 | 1.97 | 2.25 | 2.52 |\n| 4 | 2015-01-07 | 4701800 | 150.1469 | 40105900 | 105.3731 | 29114100 | 45.00480 | 27725200 | 34.66277 | 2025.90 | ⋯ | 0.03 | 0.09 | 0.25 | 0.62 | 1.00 | 1.47 | 1.76 | 1.96 | 2.25 | 2.52 |\n| 5 | 2015-01-08 | 4236800 | 153.4104 | 59364500 | 109.4218 | 29645200 | 46.32876 | 31765400 | 35.30753 | 2062.14 | ⋯ | 0.03 | 0.08 | 0.23 | 0.62 | 1.00 | 1.50 | 1.81 | 2.03 | 2.33 | 2.59 |\n| 6 | 2015-01-09 | 4484800 | 154.0785 | 53699500 | 109.5391 | 23942800 | 45.93936 | 22846000 | 35.37489 | 2044.81 | ⋯ | 0.02 | 0.08 | 0.22 | 0.59 | 0.96 | 1.45 | 1.75 | 1.98 | 2.29 | 2.55 |\n\n",
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A data.frame: 6 × 21</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>Date</th><th scope=col>IBM_Volume</th><th scope=col>IBM_AdjClose</th><th scope=col>Apple_Volume</th><th scope=col>Apple_AdjClose</th><th scope=col>MSFT_Volume</th><th scope=col>MSFT_AdjClose</th><th scope=col>Intel_Volume</th><th scope=col>Intel_AdjClose</th><th scope=col>SnP500</th><th scope=col>⋯</th><th scope=col>UST_Mo_3</th><th scope=col>UST_Mo_6</th><th scope=col>UST_Yr_1</th><th scope=col>UST_Yr_2</th><th scope=col>UST_Yr_3</th><th scope=col>UST_Yr_5</th><th scope=col>UST_Yr_7</th><th scope=col>UST_Yr_10</th><th scope=col>UST_Yr_20</th><th scope=col>UST_Yr_30</th></tr>\n",
              "\t<tr><th></th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>⋯</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>1</th><td>2015-01-02</td><td>5525500</td><td>156.9353</td><td>53204600</td><td>106.9182</td><td>27913900</td><td>45.52076</td><td>23605600</td><td>34.98996</td><td>2058.20</td><td>⋯</td><td>0.02</td><td>0.11</td><td>0.25</td><td>0.66</td><td>1.07</td><td>1.61</td><td>1.92</td><td>2.12</td><td>2.41</td><td>2.69</td></tr>\n",
              "\t<tr><th scope=row>2</th><td>2015-01-05</td><td>4880400</td><td>154.4659</td><td>64285500</td><td>103.9062</td><td>39673900</td><td>45.10216</td><td>32785000</td><td>34.59541</td><td>2020.58</td><td>⋯</td><td>0.03</td><td>0.10</td><td>0.26</td><td>0.68</td><td>1.06</td><td>1.57</td><td>1.85</td><td>2.04</td><td>2.32</td><td>2.60</td></tr>\n",
              "\t<tr><th scope=row>3</th><td>2015-01-06</td><td>6146700</td><td>151.1347</td><td>65797100</td><td>103.9160</td><td>36447900</td><td>44.44018</td><td>30847600</td><td>33.95066</td><td>2002.61</td><td>⋯</td><td>0.03</td><td>0.10</td><td>0.25</td><td>0.65</td><td>1.02</td><td>1.50</td><td>1.78</td><td>1.97</td><td>2.25</td><td>2.52</td></tr>\n",
              "\t<tr><th scope=row>4</th><td>2015-01-07</td><td>4701800</td><td>150.1469</td><td>40105900</td><td>105.3731</td><td>29114100</td><td>45.00480</td><td>27725200</td><td>34.66277</td><td>2025.90</td><td>⋯</td><td>0.03</td><td>0.09</td><td>0.25</td><td>0.62</td><td>1.00</td><td>1.47</td><td>1.76</td><td>1.96</td><td>2.25</td><td>2.52</td></tr>\n",
              "\t<tr><th scope=row>5</th><td>2015-01-08</td><td>4236800</td><td>153.4104</td><td>59364500</td><td>109.4218</td><td>29645200</td><td>46.32876</td><td>31765400</td><td>35.30753</td><td>2062.14</td><td>⋯</td><td>0.03</td><td>0.08</td><td>0.23</td><td>0.62</td><td>1.00</td><td>1.50</td><td>1.81</td><td>2.03</td><td>2.33</td><td>2.59</td></tr>\n",
              "\t<tr><th scope=row>6</th><td>2015-01-09</td><td>4484800</td><td>154.0785</td><td>53699500</td><td>109.5391</td><td>23942800</td><td>45.93936</td><td>22846000</td><td>35.37489</td><td>2044.81</td><td>⋯</td><td>0.02</td><td>0.08</td><td>0.22</td><td>0.59</td><td>0.96</td><td>1.45</td><td>1.75</td><td>1.98</td><td>2.29</td><td>2.55</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "hxtzBtJ5zdCu",
        "outputId": "aa48d5c9-75c5-485f-e71f-088b3d863652"
      },
      "source": [
        "n = nrow(data)\n",
        "cat('Sample size = ',n,'\\n')\n",
        "\n",
        "# Risk Free Rate is in percentage and annualised. \n",
        "# So the following conversion is required.\n",
        "Rf = data$UST_Yr_1/(250)\n",
        "\n",
        "## Compute log-return in percentage\n",
        "ln_rt_snp500 = diff(log(data$SnP500))*100-Rf[2:n]\n",
        "ln_rt_ibm = diff(log(data$IBM_AdjClose))*100-Rf[2:n]\n",
        "ln_rt_apple = diff(log(data$Apple_AdjClose))*100-Rf[2:n]\n",
        "ln_rt_msft = diff(log(data$MSFT_AdjClose))*100-Rf[2:n]\n",
        "ln_rt_intel = diff(log(data$Intel_AdjClose))*100-Rf[2:n]\n",
        "\n",
        "## log-return of the portfolio\n",
        "ln_r = cbind(ln_rt_ibm,ln_rt_apple,ln_rt_msft,ln_rt_intel)\n",
        "\n",
        "plot(ln_rt_snp500,ln_rt_ibm,pch=20,xlab = 'log return of S&P 500',ylab='log return of IBM')\n",
        "grid(col=\"red\")\n",
        "hist(ln_rt_snp500,main='',nclass=15,col='red',xlim = c(-6,6))\n",
        "hist(ln_rt_ibm,main='',nclass=15,col='red',xlim = c(-6,6))\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Sample size =  250 \n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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CcogfAEJRCeALUhPEEJhCcogfAEJRCe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            "text/plain": [
              "plot without title"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3Zt2rRZsmTJlClTpk+fPn/+/Orq6v27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\nGvT4449PmjRp165dh+7dsWPH+PHj58yZM3To0MafDQCgKUiZkyc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            "text/plain": [
              "Plot with title “”"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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id7AICDV0kIixYtqlOnTkJWW7RoUULW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\nRELYAQBEQtgBAERC2AEAROL/A//YzA/PuexLAAAAAElFTkSuQmCC",
            "text/plain": [
              "Plot with title “”"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uiTMMudv1eqU"
      },
      "source": [
        "* **Portfolio Allocation**:\n",
        "\n",
        "Company | IBM  | Apple | Microsoft | Intel \n",
        "--------|------|-------|-----------|-------\n",
        "Weights | 20%  | 30%   |  25%      | 25%  \n",
        "--------|------|-------|-----------|-------\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Vqm-NsOd1jT3"
      },
      "source": [
        "w = c(0.2,0.3,0.25,0.25)\n",
        "ln_rt_portf = ln_r%*%w"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qn5cFjAG9LWd"
      },
      "source": [
        "$$\n",
        "r_t^{\\text{IBM}}=\\alpha + \\beta r_t^{\\text{S&P 500}}+\\epsilon_t\n",
        "$$\n",
        "$\\epsilon_t \\sim N(0,\\sigma^2)$\n",
        "\n",
        "$$\n",
        "r_t^{\\text{IBM}}\\sim N(\\alpha + \\beta r_t^{\\text{S&P 500}},\\sigma^2)\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 123
        },
        "id": "Ioq1XtbV1r_-",
        "outputId": "ad9b2dae-2cda-4f24-b014-0e118781e3e9"
      },
      "source": [
        "capm_ibm = lm(ln_rt_ibm~ln_rt_snp500)\n",
        "capm_ibm_analysis = coefficients(summary(capm_ibm))\n",
        "capm_ibm_analysis = round(capm_ibm_analysis,digits = 5)\n",
        "rownames(capm_ibm_analysis) = c(\"alpha\",\"beta\")\n",
        "## Result of capm using lm() for IBM\n",
        "capm_ibm_analysis\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "      Estimate Std. Error t value  Pr(>|t|)\n",
              "alpha -0.04989 0.05760    -0.86605 0.3873  \n",
              "beta   1.01601 0.05863    17.32801 0.0000  "
            ],
            "text/latex": "A matrix: 2 × 4 of type dbl\n\\begin{tabular}{r|llll}\n  & Estimate & Std. Error & t value & Pr(>\\textbar{}t\\textbar{})\\\\\n\\hline\n\talpha & -0.04989 & 0.05760 & -0.86605 & 0.3873\\\\\n\tbeta &  1.01601 & 0.05863 & 17.32801 & 0.0000\\\\\n\\end{tabular}\n",
            "text/markdown": "\nA matrix: 2 × 4 of type dbl\n\n| <!--/--> | Estimate | Std. Error | t value | Pr(&gt;|t|) |\n|---|---|---|---|---|\n| alpha | -0.04989 | 0.05760 | -0.86605 | 0.3873 |\n| beta |  1.01601 | 0.05863 | 17.32801 | 0.0000 |\n\n",
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A matrix: 2 × 4 of type dbl</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>Estimate</th><th scope=col>Std. Error</th><th scope=col>t value</th><th scope=col>Pr(&gt;|t|)</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>alpha</th><td>-0.04989</td><td>0.05760</td><td>-0.86605</td><td>0.3873</td></tr>\n",
              "\t<tr><th scope=row>beta</th><td> 1.01601</td><td>0.05863</td><td>17.32801</td><td>0.0000</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fKqLpfU01wiq",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "cbca7ef0-384b-41d0-ef32-00171c58555b"
      },
      "source": [
        "plot(ln_rt_snp500\n",
        "     ,ln_rt_ibm\n",
        "     ,xlab=\"S&P 500\"\n",
        "     ,ylab=\"IBM\"\n",
        "     ,pch=20)\n",
        "abline(capm_ibm\n",
        "       ,col=\"blue\"\n",
        "       ,lwd=2)\n",
        "grid(col=\"red\")\n",
        "## lower bound and upper bound\n",
        "rse = summary(capm_ibm)$sigma\n",
        "al = capm_ibm$coefficients[1]-2*rse\n",
        "b = capm_ibm$coefficients[2]\n",
        "abline(a= al,b= b,col=3,lty=2,lwd=2)\n",
        "au = capm_ibm$coefficients[1]+2*rse\n",
        "abline(a=au,b=b,col=3,lty=2,lwd=2)\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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PPPy5Yt69Sp0+uvvz537tyTJ0/a2toarkCDEiAsvzdP29XVdKjzmc8K8+zqYD7h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\nAAAAgEygsQMAAACQif8HRxR5GFUgWEkAAAAASUVORK5CYII=",
            "text/plain": [
              "plot without title"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_sn-NCCp2rSW"
      },
      "source": [
        "### Bayesian CAPM"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zw8dwsZ62n4y",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 242
        },
        "outputId": "657dbc7d-6822-41b2-8249-c16fe0047bdb"
      },
      "source": [
        "rP = ln_rt_ibm\n",
        "n = length(ln_rt_snp500)\n",
        "Intercept = rep(1,n)\n",
        "X = cbind(Intercept,ln_rt_snp500)\n",
        "head(X)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "     Intercept ln_rt_snp500\n",
              "[1,] 1         -1.8457613  \n",
              "[2,] 1         -0.8943255  \n",
              "[3,] 1          1.1552736  \n",
              "[4,] 1          1.7720969  \n",
              "[5,] 1         -0.8448122  \n",
              "[6,] 1         -0.8134217  "
            ],
            "text/latex": "A matrix: 6 × 2 of type dbl\n\\begin{tabular}{ll}\n Intercept & ln\\_rt\\_snp500\\\\\n\\hline\n\t 1 & -1.8457613\\\\\n\t 1 & -0.8943255\\\\\n\t 1 &  1.1552736\\\\\n\t 1 &  1.7720969\\\\\n\t 1 & -0.8448122\\\\\n\t 1 & -0.8134217\\\\\n\\end{tabular}\n",
            "text/markdown": "\nA matrix: 6 × 2 of type dbl\n\n| Intercept | ln_rt_snp500 |\n|---|---|\n| 1 | -1.8457613 |\n| 1 | -0.8943255 |\n| 1 |  1.1552736 |\n| 1 |  1.7720969 |\n| 1 | -0.8448122 |\n| 1 | -0.8134217 |\n\n",
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A matrix: 6 × 2 of type dbl</caption>\n",
              "<thead>\n",
              "\t<tr><th scope=col>Intercept</th><th scope=col>ln_rt_snp500</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><td>1</td><td>-1.8457613</td></tr>\n",
              "\t<tr><td>1</td><td>-0.8943255</td></tr>\n",
              "\t<tr><td>1</td><td> 1.1552736</td></tr>\n",
              "\t<tr><td>1</td><td> 1.7720969</td></tr>\n",
              "\t<tr><td>1</td><td>-0.8448122</td></tr>\n",
              "\t<tr><td>1</td><td>-0.8134217</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "emM9ute729Mk"
      },
      "source": [
        "**parameters of prior distribution**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lkF99gXc2_bN",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "bdb13082-f079-4acd-bc93-c4c5c4607216"
      },
      "source": [
        "nms = c(\"alpha\",\"beta\")\n",
        "k = length(nms)\n",
        "beta_0 = rep(0,k)\n",
        "cat('prior mean of beta_0 = ',beta_0,'\\n')\n",
        "\n",
        "Lambda_0 = diag(1,nrow=length(beta_0))\n",
        "\n",
        "a_0 = 0.1\n",
        "b_0 = 0.01"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "prior mean of beta_0 =  0 0 \n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2VcUEDKo3vP8"
      },
      "source": [
        "**parameters of posterior distribution**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5VgK3VHS3ooQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "754324a9-e5fe-4ad1-b9db-1ca872f9ae02"
      },
      "source": [
        "## parameters of posterior distribution\n",
        "Lambda_pi = t(X)%*%X+Lambda_0\n",
        "Lambda_pi_inv = solve(Lambda_pi)\n",
        "beta_pi = Lambda_pi_inv%*%(t(X)%*%rP\n",
        "                          +Lambda_0%*%beta_0)\n",
        "rownames(beta_pi) = nms\n",
        "\n",
        "cat('posterior mean of beta_pi = ',beta_pi,'\\n')\n",
        "\n",
        "\n",
        "a_pi = a_0+n/2\n",
        "err = (rP-f%*%beta_pi)\n",
        "b_pi = b_0+0.5*t(err)%*%(err)\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "posterior mean of beta_pi =  -0.04970582 1.011796 \n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "quXFQGMR4LLE"
      },
      "source": [
        "* Compare posterior mean and MLE of $\\beta$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QHYVF3YG4P9y",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 123
        },
        "outputId": "5c2bfdc3-ef95-4792-d174-ceb089abdc5c"
      },
      "source": [
        "beta_estimates = cbind(beta_pi,capm_ibm_analysis[,'Estimate'])\n",
        "colnames(beta_estimates) = c('Posterior mean','MLE')\n",
        "round(beta_estimates,5)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "      Posterior mean MLE     \n",
              "alpha -0.04971       -0.04989\n",
              "beta   1.01180        1.01601"
            ],
            "text/latex": "A matrix: 2 × 2 of type dbl\n\\begin{tabular}{r|ll}\n  & Posterior mean & MLE\\\\\n\\hline\n\talpha & -0.04971 & -0.04989\\\\\n\tbeta &  1.01180 &  1.01601\\\\\n\\end{tabular}\n",
            "text/markdown": "\nA matrix: 2 × 2 of type dbl\n\n| <!--/--> | Posterior mean | MLE |\n|---|---|---|\n| alpha | -0.04971 | -0.04989 |\n| beta |  1.01180 |  1.01601 |\n\n",
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A matrix: 2 × 2 of type dbl</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>Posterior mean</th><th scope=col>MLE</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>alpha</th><td>-0.04971</td><td>-0.04989</td></tr>\n",
              "\t<tr><th scope=row>beta</th><td> 1.01180</td><td> 1.01601</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5SsUX1AkQpbT"
      },
      "source": [
        "**Simulate from Posterior distribution**\n",
        "\n",
        "$$p(\\beta_0,...,\\beta_k|\\sigma^2,y,x)\\sim N_k(\\beta_n,\\Lambda_n |\\sigma^2,y,x)$$\n",
        "and $$p(\\sigma^2|y,x)\\sim \\text{Inv-Gamma}(a_n,b_n|y,x)$$\n",
        "\n",
        "\n",
        "* We simulate in the following way:\n",
        "  - Simulate $\\sigma_i^{2}$ from $\\text{Inv-Gamma}(a_n,b_n)$\n",
        "  - Simulate $\\beta_{0i},\\cdots,\\beta_{ki}$ from $N(\\beta_n,\\Lambda_n|\\sigma_i^{2},y,x)$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7pUCT5kKQ7qo",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "38008727-2109-4299-92ec-2cb1eccaf1bf"
      },
      "source": [
        "install.packages('mvtnorm')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Installing package into ‘/usr/local/lib/R/site-library’\n",
            "(as ‘lib’ is unspecified)\n",
            "\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RpSh5mIFQf8T",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 342
        },
        "outputId": "aa7f099d-a74c-4a89-e3f3-fab89a0bc58a"
      },
      "source": [
        "## Simulate from Posterior distribution\n",
        "set.seed(1)\n",
        "library(mvtnorm)\n",
        "N.sim = 30000\n",
        "burnin = 0\n",
        "sigma = rep(NA,N.sim)\n",
        "beta.draws = matrix(NA\n",
        "                     , nrow=N.sim\n",
        "                     , ncol=k)\n",
        "colnames(beta.draws) = nms\n",
        "\n",
        "for(i in 1:(N.sim+burnin)){\n",
        "  if(i %% 5000 ==0) cat('i=',i,'\\n')\n",
        "  sigma_2_star = 1/rgamma(1,a_pi,b_pi)\n",
        "  S = sigma_2_star*Lambda_pi_inv\n",
        "  beta_star = rmvnorm(1,mean = beta_pi\n",
        "                     ,sigma = S)\n",
        "  if(i >burnin){\n",
        "    sigma[i-burnin] = sqrt(sigma_2_star)\n",
        "    beta.draws[i-burnin,] = beta_star\n",
        "  }\n",
        "}\n",
        "theta = cbind(beta.draws,sigma)\n",
        "head(theta)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "i= 5000 \n",
            "i= 10000 \n",
            "i= 15000 \n",
            "i= 20000 \n",
            "i= 25000 \n",
            "i= 30000 \n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "     alpha         beta      sigma    \n",
              "[1,]  0.0289259397 1.0883857 0.9330648\n",
              "[2,] -0.1365226150 0.9584015 0.8902614\n",
              "[3,] -0.0162772626 0.9938006 0.9189859\n",
              "[4,] -0.0288374629 0.9778802 0.8492077\n",
              "[5,] -0.0758787729 1.0280899 1.0069203\n",
              "[6,] -0.0005678017 1.0480128 0.9446459"
            ],
            "text/latex": "A matrix: 6 × 3 of type dbl\n\\begin{tabular}{lll}\n alpha & beta & sigma\\\\\n\\hline\n\t  0.0289259397 & 1.0883857 & 0.9330648\\\\\n\t -0.1365226150 & 0.9584015 & 0.8902614\\\\\n\t -0.0162772626 & 0.9938006 & 0.9189859\\\\\n\t -0.0288374629 & 0.9778802 & 0.8492077\\\\\n\t -0.0758787729 & 1.0280899 & 1.0069203\\\\\n\t -0.0005678017 & 1.0480128 & 0.9446459\\\\\n\\end{tabular}\n",
            "text/markdown": "\nA matrix: 6 × 3 of type dbl\n\n| alpha | beta | sigma |\n|---|---|---|\n|  0.0289259397 | 1.0883857 | 0.9330648 |\n| -0.1365226150 | 0.9584015 | 0.8902614 |\n| -0.0162772626 | 0.9938006 | 0.9189859 |\n| -0.0288374629 | 0.9778802 | 0.8492077 |\n| -0.0758787729 | 1.0280899 | 1.0069203 |\n| -0.0005678017 | 1.0480128 | 0.9446459 |\n\n",
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A matrix: 6 × 3 of type dbl</caption>\n",
              "<thead>\n",
              "\t<tr><th scope=col>alpha</th><th scope=col>beta</th><th scope=col>sigma</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><td> 0.0289259397</td><td>1.0883857</td><td>0.9330648</td></tr>\n",
              "\t<tr><td>-0.1365226150</td><td>0.9584015</td><td>0.8902614</td></tr>\n",
              "\t<tr><td>-0.0162772626</td><td>0.9938006</td><td>0.9189859</td></tr>\n",
              "\t<tr><td>-0.0288374629</td><td>0.9778802</td><td>0.8492077</td></tr>\n",
              "\t<tr><td>-0.0758787729</td><td>1.0280899</td><td>1.0069203</td></tr>\n",
              "\t<tr><td>-0.0005678017</td><td>1.0480128</td><td>0.9446459</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QihGM2FKYdYK",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "aaf4ba98-ba47-4653-c61b-27d17a19ce70"
      },
      "source": [
        "par(mfrow=c(3,2))\n",
        "plot(ts(theta[,\"alpha\"])\n",
        "     ,ylab = \"alpha\",type='b')\n",
        "plot(density(theta[,\"alpha\"])\n",
        "     ,main = \"\"\n",
        "     ,xlab = \"alpha\")\n",
        "plot(ts(theta[,\"beta\"])\n",
        "     ,ylab = \"beta\")\n",
        "plot(density(theta[,\"beta\"])\n",
        "     ,main = \"\"\n",
        "     ,xlab = \"beta\")\n",
        "plot(ts(theta[,\"sigma\"])\n",
        "     ,ylab = \"sigma\")\n",
        "plot(density(theta[,\"sigma\"])\n",
        "     ,main = \"\"\n",
        "     ,xlab = \"sigma\")\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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FtuphxY2eOn8hDBt9tICk86aimGdbRnoxgaSGkkl5Cfu9FlL0I7TScRo68MD7cv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\nwAAQCQAY8H87Fn1gzUM3KQAAAABJRU5ErkJggg==",
            "text/plain": [
              "Plot with title “”"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KNtQFDC6Rt9j",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 212
        },
        "outputId": "145265ac-827f-41f2-de5f-e179ffda695b"
      },
      "source": [
        "post_median = apply(theta,2,median)\n",
        "post_mean = apply(theta,2,mean)\n",
        "post_sd   = apply(theta,2,sd)\n",
        "post_band = apply(theta,2,quantile\n",
        "                   ,prob=c(0.025,0.975))\n",
        "post_sumry = rbind( post_median     \n",
        "                   ,post_mean\n",
        "                   ,post_sd\n",
        "                   ,post_band)\n",
        "rownames(post_sumry) = c(\"median\"\n",
        "                        ,\"mean\"\n",
        "                        ,\"sd\"\n",
        "                        ,\"2.5%\"\n",
        "                        ,\"97.5%\")\n",
        "round(post_sumry,digits = 4)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "       alpha   beta   sigma \n",
              "median -0.0497 1.0122 0.9062\n",
              "mean   -0.0499 1.0115 0.9079\n",
              "sd      0.0573 0.0583 0.0409\n",
              "2.5%   -0.1631 0.8966 0.8331\n",
              "97.5%   0.0625 1.1266 0.9927"
            ],
            "text/latex": "A matrix: 5 × 3 of type dbl\n\\begin{tabular}{r|lll}\n  & alpha & beta & sigma\\\\\n\\hline\n\tmedian & -0.0497 & 1.0122 & 0.9062\\\\\n\tmean & -0.0499 & 1.0115 & 0.9079\\\\\n\tsd &  0.0573 & 0.0583 & 0.0409\\\\\n\t2.5\\% & -0.1631 & 0.8966 & 0.8331\\\\\n\t97.5\\% &  0.0625 & 1.1266 & 0.9927\\\\\n\\end{tabular}\n",
            "text/markdown": "\nA matrix: 5 × 3 of type dbl\n\n| <!--/--> | alpha | beta | sigma |\n|---|---|---|---|\n| median | -0.0497 | 1.0122 | 0.9062 |\n| mean | -0.0499 | 1.0115 | 0.9079 |\n| sd |  0.0573 | 0.0583 | 0.0409 |\n| 2.5% | -0.1631 | 0.8966 | 0.8331 |\n| 97.5% |  0.0625 | 1.1266 | 0.9927 |\n\n",
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A matrix: 5 × 3 of type dbl</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>alpha</th><th scope=col>beta</th><th scope=col>sigma</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>median</th><td>-0.0497</td><td>1.0122</td><td>0.9062</td></tr>\n",
              "\t<tr><th scope=row>mean</th><td>-0.0499</td><td>1.0115</td><td>0.9079</td></tr>\n",
              "\t<tr><th scope=row>sd</th><td> 0.0573</td><td>0.0583</td><td>0.0409</td></tr>\n",
              "\t<tr><th scope=row>2.5%</th><td>-0.1631</td><td>0.8966</td><td>0.8331</td></tr>\n",
              "\t<tr><th scope=row>97.5%</th><td> 0.0625</td><td>1.1266</td><td>0.9927</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "A_WmpsGaSLpI",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 123
        },
        "outputId": "16b8ef0b-3981-4a55-9b54-39b50e26a112"
      },
      "source": [
        "beta_estimates = cbind(beta_pi,post_mean[1:2],capm_ibm_analysis[,'Estimate'])\n",
        "colnames(beta_estimates) = c('Posterior mean (Analytical)','Posterior Mean (Numerical)','MLE')\n",
        "round(beta_estimates,5)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "      Posterior mean (Analytical) Posterior Mean (Numerical) MLE     \n",
              "alpha -0.04971                    -0.04988                   -0.04989\n",
              "beta   1.01180                     1.01148                    1.01601"
            ],
            "text/latex": "A matrix: 2 × 3 of type dbl\n\\begin{tabular}{r|lll}\n  & Posterior mean (Analytical) & Posterior Mean (Numerical) & MLE\\\\\n\\hline\n\talpha & -0.04971 & -0.04988 & -0.04989\\\\\n\tbeta &  1.01180 &  1.01148 &  1.01601\\\\\n\\end{tabular}\n",
            "text/markdown": "\nA matrix: 2 × 3 of type dbl\n\n| <!--/--> | Posterior mean (Analytical) | Posterior Mean (Numerical) | MLE |\n|---|---|---|---|\n| alpha | -0.04971 | -0.04988 | -0.04989 |\n| beta |  1.01180 |  1.01148 |  1.01601 |\n\n",
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A matrix: 2 × 3 of type dbl</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>Posterior mean (Analytical)</th><th scope=col>Posterior Mean (Numerical)</th><th scope=col>MLE</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>alpha</th><td>-0.04971</td><td>-0.04988</td><td>-0.04989</td></tr>\n",
              "\t<tr><th scope=row>beta</th><td> 1.01180</td><td> 1.01148</td><td> 1.01601</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T5AR8OOlVj9p"
      },
      "source": [
        "We simulate\n",
        "$$\n",
        "\\{\\beta_1^*,\\beta_2^*,\\cdots,\\beta_{N_s}^*\\} \\leftarrow N\\Big(\\mathbb{E}(\\beta|y,X),\\mathbb{V}ar(\\beta|y,X)\\Big)\n",
        "$$\n",
        "as simulation size $N_s$ increases, i.e.,\n",
        "$$\n",
        "N_s \\rightarrow \\infty\n",
        "$$\n",
        "$$\n",
        "\\hat{\\beta}^*\\longrightarrow \\mathbb{E}(\\beta|y,X),\n",
        "$$\n",
        "where $=\\frac{1}{N_{s}}\\sum_{i=1}^{N_{s}}\\beta_i^*$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KuJKte0uXtqs"
      },
      "source": [
        "**What about portfolio $\\alpha$ and $\\beta$**?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Qsd6IN11ghvb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 140
        },
        "outputId": "f4f17f69-e80c-40b1-921e-a3511da2eff0"
      },
      "source": [
        "rP = ln_rt_portf\n",
        "## parameters of posterior distribution\n",
        "Lambda_pi = t(X)%*%X+Lambda_0\n",
        "Lambda_pi_inv = solve(Lambda_pi)\n",
        "beta_pi = Lambda_pi_inv%*%(t(X)%*%rP\n",
        "                          +Lambda_0%*%beta_0)\n",
        "rownames(beta_pi) = nms\n",
        "\n",
        "cat('posterior mean of beta_pi = ',beta_pi,'\\n')\n",
        "\n",
        "\n",
        "a_pi = a_0+n/2\n",
        "err = (rP-f%*%beta_pi)\n",
        "b_pi = b_0+0.5*t(err)%*%(err)\n",
        "\n",
        "capm_portf = lm(rP~ln_rt_snp500)\n",
        "capm_portf_coef = coefficients(summary(capm_portf))\n",
        "capm_portf_coef = round(capm_portf_coef,digits = 5)\n",
        "rownames(capm_portf_coef)=c(\"alpha\",\"beta\")\n",
        "## Result of capm using lm() for IBM\n",
        "capm_portf_coef\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "posterior mean of beta_pi =  0.007532961 1.105694 \n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "      Estimate Std. Error t value  Pr(>|t|)\n",
              "alpha 0.00758  0.04356     0.17406 0.86196 \n",
              "beta  1.11029  0.04434    25.04207 0.00000 "
            ],
            "text/latex": "A matrix: 2 × 4 of type dbl\n\\begin{tabular}{r|llll}\n  & Estimate & Std. Error & t value & Pr(>\\textbar{}t\\textbar{})\\\\\n\\hline\n\talpha & 0.00758 & 0.04356 &  0.17406 & 0.86196\\\\\n\tbeta & 1.11029 & 0.04434 & 25.04207 & 0.00000\\\\\n\\end{tabular}\n",
            "text/markdown": "\nA matrix: 2 × 4 of type dbl\n\n| <!--/--> | Estimate | Std. Error | t value | Pr(&gt;|t|) |\n|---|---|---|---|---|\n| alpha | 0.00758 | 0.04356 |  0.17406 | 0.86196 |\n| beta | 1.11029 | 0.04434 | 25.04207 | 0.00000 |\n\n",
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A matrix: 2 × 4 of type dbl</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>Estimate</th><th scope=col>Std. Error</th><th scope=col>t value</th><th scope=col>Pr(&gt;|t|)</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>alpha</th><td>0.00758</td><td>0.04356</td><td> 0.17406</td><td>0.86196</td></tr>\n",
              "\t<tr><th scope=row>beta</th><td>1.11029</td><td>0.04434</td><td>25.04207</td><td>0.00000</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cukMtEejrN_o",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "014c714f-4a3f-4eb5-e42e-d412607d2e41"
      },
      "source": [
        "## parameters of posterior distribution\n",
        "Lambda_pi = t(X)%*%X+Lambda_0\n",
        "Lambda_pi_inv = solve(Lambda_pi)\n",
        "beta_pi = Lambda_pi_inv%*%(t(X)%*%rP\n",
        "                          +Lambda_0%*%beta_0)\n",
        "rownames(beta_pi) = nms\n",
        "\n",
        "cat('posterior mean of beta_pi = ',beta_pi,'\\n')\n",
        "\n",
        "\n",
        "a_pi = a_0+n/2\n",
        "err = (rP-f%*%beta_pi)\n",
        "b_pi = b_0+0.5*t(err)%*%(err)\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "posterior mean of beta_pi =  0.007532961 1.105694 \n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SQsexn17qQSL",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 123
        },
        "outputId": "485e59f3-fdb8-467c-84fe-03e672338e24"
      },
      "source": [
        "## Simulate from Posterior distribution\n",
        "set.seed(1)\n",
        "library(mvtnorm)\n",
        "N.sim = 3000\n",
        "burnin = 0\n",
        "sigma = rep(NA,N.sim)\n",
        "beta.draws = matrix(NA\n",
        "                     , nrow=N.sim\n",
        "                     , ncol=k)\n",
        "colnames(beta.draws) = nms\n",
        "\n",
        "for(i in 1:(N.sim+burnin)){\n",
        "  if(i %% 5000 ==0) cat('i=',i,'\\n')\n",
        "  sigma_2_star = 1/rgamma(1,a_pi,b_pi)\n",
        "  S = sigma_2_star*Lambda_pi_inv\n",
        "  beta_star = rmvnorm(1,mean = beta_pi\n",
        "                     ,sigma = S)\n",
        "  if(i >burnin){\n",
        "    sigma[i-burnin] = sqrt(sigma_2_star)\n",
        "    beta.draws[i-burnin,] = beta_star\n",
        "  }\n",
        "}\n",
        "theta = cbind(beta.draws,sigma)\n",
        "#head(theta)\n",
        "post_mean = apply(theta,2,mean)\n",
        "\n",
        "beta_estimates = cbind(beta_pi,post_mean[1:2],capm_portf_coef[,'Estimate'])\n",
        "colnames(beta_estimates) = c('Posterior mean (Analytical)','Posterior Mean (Numerical)','MLE')\n",
        "beta_estimates"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "      Posterior mean (Analytical) Posterior Mean (Numerical) MLE    \n",
              "alpha 0.007532961                 0.007698012                0.00758\n",
              "beta  1.105694103                 1.104816021                1.11029"
            ],
            "text/latex": "A matrix: 2 × 3 of type dbl\n\\begin{tabular}{r|lll}\n  & Posterior mean (Analytical) & Posterior Mean (Numerical) & MLE\\\\\n\\hline\n\talpha & 0.007532961 & 0.007698012 & 0.00758\\\\\n\tbeta & 1.105694103 & 1.104816021 & 1.11029\\\\\n\\end{tabular}\n",
            "text/markdown": "\nA matrix: 2 × 3 of type dbl\n\n| <!--/--> | Posterior mean (Analytical) | Posterior Mean (Numerical) | MLE |\n|---|---|---|---|\n| alpha | 0.007532961 | 0.007698012 | 0.00758 |\n| beta | 1.105694103 | 1.104816021 | 1.11029 |\n\n",
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A matrix: 2 × 3 of type dbl</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>Posterior mean (Analytical)</th><th scope=col>Posterior Mean (Numerical)</th><th scope=col>MLE</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>alpha</th><td>0.007532961</td><td>0.007698012</td><td>0.00758</td></tr>\n",
              "\t<tr><th scope=row>beta</th><td>1.105694103</td><td>1.104816021</td><td>1.11029</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MZ2lemjnRDrs",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 123
        },
        "outputId": "86ad6989-9643-4964-fc55-ba4bfa016290"
      },
      "source": [
        "apply(theta,2,quantile,prob=c(0.025,0.975))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "      alpha       beta     sigma    \n",
              "2.5%  -0.07788178 1.018352 0.6301433\n",
              "97.5%  0.09636173 1.190734 0.7499379"
            ],
            "text/latex": "A matrix: 2 × 3 of type dbl\n\\begin{tabular}{r|lll}\n  & alpha & beta & sigma\\\\\n\\hline\n\t2.5\\% & -0.07788178 & 1.018352 & 0.6301433\\\\\n\t97.5\\% &  0.09636173 & 1.190734 & 0.7499379\\\\\n\\end{tabular}\n",
            "text/markdown": "\nA matrix: 2 × 3 of type dbl\n\n| <!--/--> | alpha | beta | sigma |\n|---|---|---|---|\n| 2.5% | -0.07788178 | 1.018352 | 0.6301433 |\n| 97.5% |  0.09636173 | 1.190734 | 0.7499379 |\n\n",
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A matrix: 2 × 3 of type dbl</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>alpha</th><th scope=col>beta</th><th scope=col>sigma</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>2.5%</th><td>-0.07788178</td><td>1.018352</td><td>0.6301433</td></tr>\n",
              "\t<tr><th scope=row>97.5%</th><td> 0.09636173</td><td>1.190734</td><td>0.7499379</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Yn0iIq0qP3J4"
      },
      "source": [
        "**What is the $\\mathbb{P}(\\alpha >0|y,x)$?**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uiw4UxoCP-Re",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "31e8db11-c893-4979-b5c9-d3f990bab64d"
      },
      "source": [
        "alpha_star = theta[,'alpha']\n",
        "no.of.alpha.gt.zero = length(alpha_star[alpha_star>0])\n",
        "total.no.of.alpha = length(alpha_star)\n",
        "\n",
        "prob_a_gt_zero = (no.of.alpha.gt.zero/total.no.of.alpha)*100\n",
        "\n",
        "round(prob_a_gt_zero,4)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "[1] 56.7333"
            ],
            "text/latex": "56.7333",
            "text/markdown": "56.7333",
            "text/html": [
              "56.7333"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-_Hb5NKsplcE"
      },
      "source": [
        "## **Stress Testing: If S&P 500 drops by 3%, the portfolio return vary**\n",
        "\n",
        "*  What happens to the portfolio if S&P 500 drops by 3% in a day?\n",
        "\n",
        "* We can simulate from posterior predictive distribution \n",
        "$$\n",
        "  p(\\tilde{y}|y,x)=\\int_{\\beta,\\sigma}p(\\tilde{y}|\\beta,\\sigma,x)p(\\beta, \\sigma|y,x)d\\beta d\\sigma\n",
        "$$\n",
        "\n",
        "* We simulate in the following way:\n",
        "\n",
        "  - Simulate $\\beta_i^*$ and $\\sigma_i^*$ from $p(\\beta,\\sigma|y,x)$\n",
        "  - Simulate $\\tilde{y}_i^*$ from $N(x^T\\beta_i^*,\\sigma_i^*)$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4f6TgLG-qOQ0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 454
        },
        "outputId": "ca99d910-a63b-4229-943c-058f6e03fb23"
      },
      "source": [
        "market_drop=-3\n",
        "rP.sim = rep(NA,N.sim)\n",
        "x0 = matrix(c(1,market_drop),nrow=1,ncol = k)\n",
        "for(i in 1:N.sim){\n",
        "  ErP = x0%*%theta[i,1:k]\n",
        "  rP.sim[i] = rnorm(1,mean = ErP, sd= theta[i,(k+1)])\n",
        "}\n",
        "\n",
        "round(quantile(rP.sim,prob = c(0.025,0.975)),3)\n",
        "hist(rP.sim,probability = TRUE,col=\"orange\",main=\"\")\n",
        "lines(density(rP.sim),lwd=2,col=\"red\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  2.5%  97.5% \n",
              "-4.701 -1.881 "
            ],
            "text/latex": "\\begin{description*}\n\\item[2.5\\textbackslash{}\\%] -4.701\n\\item[97.5\\textbackslash{}\\%] -1.881\n\\end{description*}\n",
            "text/markdown": "2.5%\n:   -4.70197.5%\n:   -1.881\n\n",
            "text/html": [
              "<style>\n",
              ".dl-inline {width: auto; margin:0; padding: 0}\n",
              ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
              ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
              ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
              "</style><dl class=dl-inline><dt>2.5%</dt><dd>-4.701</dd><dt>97.5%</dt><dd>-1.881</dd></dl>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Ro40HCS4Lv5ZiUlSdI//mE6CgCHcczm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\nRK5CYII=",
            "text/plain": [
              "Plot with title “”"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EJ2R8a1ylNLJ"
      },
      "source": [
        "**Test the Assumpution**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ud4C7CemlPL9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 101
        },
        "outputId": "3882f418-5099-40ba-d260-e3849da49e08"
      },
      "source": [
        "### Test the assumption\n",
        "shapiro.test(capm_portf$residuals)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "\tShapiro-Wilk normality test\n",
              "\n",
              "data:  capm_portf$residuals\n",
              "W = 0.94758, p-value = 8.468e-08\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kHtUBM_Wqu3a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "5968d960-e131-479a-d850-c6016a8ed7c4"
      },
      "source": [
        "qqnorm(capm_portf$residuals\n",
        "       ,cex=0.3\n",
        "       ,pch=20\n",
        "       ,xlim=c(-3,3)\n",
        "       ,ylim=c(-3,3)\n",
        "       ,xlab=\"idiosyncratic return with fitted Gaussian distribution\"\n",
        "       ,ylab=\"observed residual or idiosyncratic return\"\n",
        "       ,main=\"Gaussian Q-Q Plot\")\n",
        "abline(a=0,b=1,col=\"blue\")\n",
        "grid(col=\"red\")\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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EBemzdvHj58+AOXBrx79261+zCb7xAA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",
            "text/plain": [
              "Plot with title “Gaussian Q-Q Plot”"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "id": "y_1QfHGeThc6",
        "outputId": "f104b911-f40d-4be6-ffa9-594f573f19fd"
      },
      "source": [
        "hist(capm_portf$residuals)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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KKCkIwipKggJKMIKSoIyShCigpCMoqQ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\n+P+PVoUeh/t44QAAAABJRU5ErkJggg==",
            "text/plain": [
              "Plot with title “Histogram of capm_portf$residuals”"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5kTfYcFLq6w0"
      },
      "source": [
        "- Assumption the $\\epsilon \\sim N(0,\\sigma^2)$ is not correct.\n",
        "\n",
        "- Does $\\epsilon \\sim Laplace(\\mu,\\lambda)$?\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FZOHlrZ9rGZi"
      },
      "source": [
        "## density of Laplace distribution \n",
        "dlaplace = function(x,mu,lambda){\n",
        "  exp(-abs(x-mu)/lambda)/(2*lambda)\n",
        "}\n",
        "## The negative log-likelihood function\n",
        "neg_log_likelihood = function(data,para){\n",
        "  mu = para[1]\n",
        "  lambda =(para[2])\n",
        "  f = dlaplace(x=data\n",
        "              ,mu=mu\n",
        "              ,lambda=lambda)\n",
        "  return(-sum(log(f)))\n",
        "}\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Hvtyq_mzrJ8v"
      },
      "source": [
        "## initial parameters\n",
        "para.init = c(0,1)\n",
        "\n",
        "## residual or idiosyncratic return \n",
        "## from capm_portf\n",
        "e = summary(capm_portf)$residual\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iXHJAlUOrU9W",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "013b24bb-d6b3-4955-cee7-ae613e29e7d0"
      },
      "source": [
        "\n",
        "mle = optim(para.init\n",
        "           ,neg_log_likelihood\n",
        "           ,data=e)\n",
        "mle$par"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "[1] 0.04755216 0.48957078"
            ],
            "text/latex": "\\begin{enumerate*}\n\\item 0.0475521634267527\n\\item 0.489570779979881\n\\end{enumerate*}\n",
            "text/markdown": "1. 0.0475521634267527\n2. 0.489570779979881\n\n\n",
            "text/html": [
              "<style>\n",
              ".list-inline {list-style: none; margin:0; padding: 0}\n",
              ".list-inline>li {display: inline-block}\n",
              ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
              "</style>\n",
              "<ol class=list-inline><li>0.0475521634267527</li><li>0.489570779979881</li></ol>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HNZU0Xixrdw-"
      },
      "source": [
        "- The following function simulate from  the fitted Laplace distribution\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mpCHC1W1rgV9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "10327717-3e70-4ef4-e463-cbb6deb93ffd"
      },
      "source": [
        "rlaplace = function(n,mu,lmbda){\n",
        "  # n : sample size\n",
        "  # mu: location parameter\n",
        "  # lambda : scale parameter\n",
        "  u = runif(n,-0.5,0.5)\n",
        "  sgn = rep(NA,n)\n",
        "  for(i in 1:n){\n",
        "    if(u[i]<0) sgn[i]<--1\n",
        "    if(u[i]>0) sgn[i]<-1\n",
        "    if(u[i]==0) sgn[i]<-0\n",
        "  }\n",
        "  r = mu-lmbda*sgn*log(1-2*abs(u))\n",
        "  return(r)\n",
        "}\n",
        "\n",
        "## simulate the result\n",
        "set.seed(4155)\n",
        "r.sim = rlaplace(n=1000\n",
        "                ,mu=mle$par[1]\n",
        "                ,lmbda=mle$par[2])\n",
        "qqplot(r.sim,e\n",
        "       ,xlim=c(-3,3)\n",
        "       ,ylim=c(-3,3)\n",
        "       ,cex=0.5\n",
        "       ,pch=20\n",
        "       ,xlab=\"idiosyncratic return with fitted Laplace distribution\"\n",
        "       ,ylab=\"observed residual or idiosyncratic return\"\n",
        "       ,main=\"Laplace Q-Q Plot\")\n",
        "abline(a=0,b=1,col=\"blue\")\n",
        "grid(col=\"red\")\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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FAJFHYAAAAAKoHCDgAAAEAlUNgBAAAA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\n/iLP0TMgsj0CDQKPHpEYo1efkyeqzJkzp6Cg4Jt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+Li7GyJE4dQp796JrVykLkwvOLxHnl4JPniDikzKl4SIAACAASURBVCfU7Ozs0tLS\ngoODL126BCA9PT09Pd3a2jokJOTo0aNGP6vTPjGaNyXEzdcUNTVfq1SqX3/99dSpUw9tz83F\nSy/h8mUcOcKzur9xfok4vxR88gSRGPmtVcBsbW1XrVp18+bN3Nzcixcv5ubm3rx5c9WqVba2\ntlLXZ4TEaN6UEDdfU1Rrvr5///61a9cqKytHjhzp5ub2wgsvqC8Upvb77+jXD+bmSExE27Z6\nqtYAcX6JOL8UfPIEkRj51Tyx27VrV0ZGBgCFQtGqVStnZ2f+lo5EjOZNCXHzNcXfzdcXLlxw\ndnZ2cHBwdXXdsWOH+sEVK1ZUVFQASE1Fnz5wdUVcHJ56Sp/1GhzOLxHnl4JPniASI7+aJ3aB\ngYG7d+/WQSmi4O5XIh5Air9Hb+7cuZcvXwZw/vx59Rp1AJo1a2ZqahoTg4ED4eeH7dvRqJE+\nizVEfPgR8QBS8OgRiTGAmk+eGDp0qJmZ2e7du00EGI4a8ckThoWbrykqK1WXLq3cs+f//u//\nqrI/evToI0eOWFparlix4sqVwcHBmDEDX3yh30INFeeXiPNLwSdPEIlx8oTm5U42btw4ffr0\nYcOGvfnmmx06dLCxsXnoCc7OztLUZqT4LYGI/1Grl3v37qWnp7u4uLz/ySfr1q2r2m5ra/vN\nN9+oc714MebNQ1gY3n5bf4UaOM4vEeeXgk+eIBIjv5ondnZ2duob+/fvr/EJGr/z05nbt2/n\n5+cb+kRT3bnJfYr1lpEBFxeYaj50WZWrV6/26dPn6tWrzaytHUpKqj80Z84cGxsbpRLTpiE8\nHFu24NVX9VWmHHB+iTi/FBUVOH8enTvruw7ZEiO/mtMVGBhobm5uZmamUCh0UBDFkiVLFi9e\nbDgTzZqpOzdXr9Z3HbLl4YHISHh56bsOOdm0adPVq1cB9Coq2qpQqL91b9Cgwfvvvz9t2rSy\nMowdi7g4HDzIndmacH6JOL8UsbEIDERBgb7rkC0x8qt5YrdlyxYd1CEQbi4hEqP7Vbua/f0D\nRCXQwMysT48e5eXlCxcu9PX1zc+Hvz+uXkVyMjp21G+ZcsDHHhHnl4JHj0iM0ePvw3WOm9KJ\njh+Ho6O+i5CZcePGxcfH7927V9WjR+mXXx7u0UO9/do1+PhApcKhQ3Bw0G+NMsH5JeL8Ugwe\njOPH9V2EnImRX9lM7Hr27KnxOdeuXdNBJVRiNG9KiHuH687CwiIiIuKhjRkZ8PZG+/aIisIj\n50Sxx+D8EnF+KfjkCSIx8iubid2JEycAmJmZPeE5FbJY0FyM5k0JcfM1xd/N1/HxGDECQ4Zg\n40Y0bKjvqmSE80vE+aXgkyeIxMivbH5vfv/9962srM6cOVP6eDNnztR3mbUgxsrXEuKV6yli\nY+HhERUFHx+MG4etW3lWV0ecXyLOLwVfeYJIjPzK5mPTJ5988vPPP48ePfrw4cNP/t6uroqK\nip78Vd+9e/caAYriYlQtUFxUBADW1vW5q1Q+9PL135WYd6vahw2qKrncNTEpu28yYVTRR7Mw\n5zODqUpGdzm/xLucX8pd9ejpvQz53tVqfg33ujwq+Th79qylpeXMmTMf94TZs2fX9b8oMzOz\nNsu4fAeoANXJk+q/USkUfFdvd/ftUymV+i9Dhncr00/O/0g52DTeoKriu2Ld5fxS7iqVqnjO\nr6Hc/RZITk5WGR7NlxQzKHfv3q2oqGjevHmNjyYkJBw5ciQ0NLRO+8zIyCgtLX3CE3bs2LHp\ns8/OpqQ06t276m9QWYnnn+e7fFcud5X3K98Oez4yEj/+CO82hlIV3+W7fJfvyvHu/fR0527d\nNhvkJcVqnti5ubnV8u/Ly8uPG/vZ11q+VqwYzZsSyuDm6zorKcGoUThxAnt3VXRrxM3XBJxf\nIs4vBZ88QaS9/MrvWrFpaWnV75qYmNy/f199W6H4Zy5oY2PTpEkTSeszQmKsfC0hXrlek5Ur\nV27btu35559ftGiRtbV1Xh6GDUN+PhIT0f6PWAzllesJOL9EnF8KvvIEkRj5rXliV/1kgvz8\n/OHDh3fp0iU4ONjFxaVhw4ZFRUWnTp0KCwu7cePGjh07dFVqDb766qudO3cmJSXpsYY6E2Pl\nawnx2utPdPDgwWnTpgGIj483NTWdNu0/3t5o2hRHjsDWFsjm0aPh0SPi/FLw6BGJMXqavw+f\nOXOmvb19WFhY1RZra2sPDw8PDw8/P78ZM2asWbNGygqfJDMzMzk5WV+vXk9irHwtIV65/ol+\n++23qtu//qrctAkvvIDt2/8+l4tXrifi/BJxfik4v0Ri5Ffz7DUmJsbrMV+bDxgwYNeuXdou\nydg1aybI4tdScXIS5FNXLd27d+9///vf6tWrS0pKAHh7e//dDDrk+PGvvL2xZ88/Z+jzyvVU\nnF8izi8F55dIjPxqDtjdu3dv3rxZ40O3b9++e/eutksydnl5f/VvsvrJyIAsLjGiK35+fpMm\nTXrrrbfUH8CcnZ1PnTo1blysqenPb71lFh6OB5Z9rKhARoa+SjUGnF8izi8F55dIjPxqnti5\nurquWLHi6NGjD21PTU1du3Ztx44dpSnMeImx8rWEeOX6agoLC3/55Rf17eTkZPVnsF27ntm0\nadCyZYply/DwKo28cj0R55eI80vB+SUSI7+ae+wWLlw4YsSIXr16OTs7P/PMMw0bNiwtLc3K\nylIv7Vu99073vvjii3my+5/EP0MQcftwNU2aNHF0dLx8+TIAe3v7Zs2az5yJsDBs2oTXXqvp\nD3j0iHj0iPgIpODRIxJj9Gq1QHFSUtKiRYvi4+OrFvI1Nzd3d3cPDQ19XPudMdHyOnb5+QBE\n+JlfKtnZcHQ0+nzGxcUlJib269dv8ODBj3vO1q1bFy1a1KBBg6eeesrGxmbWrA+//rrLzz8j\nOhr9+j3mbyorcfkyt+nUH+eXSIz8SoXzS6S9/MpvHbuH9O3bd9++fZWVlTk5Offu3bO0tLSz\nszPlFSbrh98SiAT4R23//v0+Pj7q2zExMX5+fo8+5+bNm2+88UZ5eTmAjh07bt368/DhyMzE\nL7/ghRcev2tuvibi/BLx4UfB+SUSI791+NhUUlJSUFDQsmVLBwcHntXVnxjNmxISoPl6//79\nNd6uLi8vTz2rA3DlinLAANy6hZSUJ87qwM3XZJxfIgHyKyHOL5EY+a3VxC4hIaFnz55NmjR5\n7rnnUlJS1Bv9/f1juQe2HsRo3pSQAM3XPXr0qPF2dZ06derbty8AwNXE5NdGjZCYiDZtNO2a\nm6+JOL9EAuRXQpxfIjHyq3lil5qa6unpeeHChertdDdv3jx69Kivr++xY8ekLM8YcfcrkdEN\n4PXr19evX1/9On5jx44NCwt77bXXli9fPn78+Br/qkGDBnFxcf/5z2Ebm/TBg5vFxqJFi1q8\nmNGNnq7xABLxAFLw6BGJMYCaT57w8/M7ffp0cnKyqampvb39vn37vL29Ady4cePFF1/s1q3b\nzp07dVKq3vDJE4ZF/s3XOTk58fHxL7zwgqur66VLl7p27VpQUABgw4YNb7zxRu33Ex2N0aMx\nYQKWL6/1eHDzNRHnl0j++dUnzi+RGCdPaE5XSkpKSEiIg4PDQ9ttbW0nT56cmJgoTWHGS4yV\nryUk85XrMzMzO3bsOGbMmC5duuzatWvPnj0Ff1/SOyIiovb7WbsWo0Zh1iyEhdVlPLj5mojz\nSyTz/OoZ55dIjPxqDlhhYWGbx3Tu2NvbFxcXa7skYydG86aE5Nl8XVFRsX379oiIiK1bt6qv\n16JUKn/44QdnZ+eq5zz77LO12ZVKhfnz8fbbWLkS8+fXuQ5uvibh/BLJM7+GgvNLJEZ+NZ/c\namdnd+7cuRofSkxMfPrpp7VdkrFTd26uXq3vOmTLwwORkZDbAopBQUHbt28H4OLiUrXRycnJ\n09NzyZIl27dvd3V1/eSTTzTuR6lESAgiIhAdDV/futcRG4vAQPz9HSGrM84vkTzzayg4v0Ri\n5FfzxM7X13fVqlUBAQHV53D5+flfffXVunXrpkyZImV5xoh/hiCSYfdrWVlZVFSU+vb58+f/\n7//+LyEhoVu3bh9++CGAmTNnzpw5szb7KSlBYCBSUnDgAPr0qVcpMhw9w8KjR8RHIAWPHpEY\no6f55Inc3NxevXrl5OR06dLl+PHjXbt2BXDu3LmysjJHR8fU1NRWrVrppFS94ZMnDIs8m6/b\ntWuXlZUFoGnTpjk5OQ0bNqzrHu7cwcsvIycH+/ejQ4f61sHN10ScXyJ55tdQcH6J+OQJNTs7\nu7S0tODg4EuXLgFIT09PT0+3trYOCQk5evSo0c/qtE+M5k0JGXzz9bVr1z788MOFCxfeunWr\namNUVJSfn9/QoUN37dpVj1ldVhbc3VFcjKQkwqwO3HxNxvklMvj8GjTOL5EY+a3VtWLVVCrV\njRs3ioqKrK2thZrPafkbO3XnpkgDqGUZGXBxgaFe+6SysrJTp04XLlwA0Lt376oFvSlOn4aP\nDzp2xI4daNKEtq+KCpw/j86d6VUJivNLZNj5NXScXyLt5Vfe39j1799/9erVBQUFCoWiVatW\nzs7OQs3qtE+Mla8lZNgr11+7dk09qwPw66+//vnnn8QdxsWhb18MHIh9+8izOvDK9WScXyLD\nzq+h4/wSiZFfzRO7Q4cOvfXWW3Z2dq+++mpUVFTV5SlZPXH3K5FhD+DTTz/9zDPPqG9369bN\n0tKSsrdt2zBsGMaPx/r1MDPTRn2GPXoywANIxANIwaNHJMYAav4p9urVq9u2bdu6dWtKSopK\npWrWrNmoUaPGjh3bt29fhUKhmyr1i0+eMCwG33ydlZW1fPlyMzOz9957j7Ie0LJlmDEDn3+O\n99/XXnHcfE3E+SUy+PwaNM4vkRgnT9Shx+6hGV7btm1ff/31sWPHdurUSdIS9U7LEzvGNFGp\nEBqKpUuxfj2CgvRdDWOMsQcZ8sSuDh+bHBwc3nvvvcOHD1++fPm///1v27Ztv/zyS1dXV+mK\nM05irHwtIWNfub68HK+/jm++QUyMBLM6XrmeiPNLZOz5lRbnl0iM/Nbn+3ArK6sWLVo4ODg0\n0UIvt3jEaN6UkFE3XxcXw98f8fFITISnpwQvwM3XRJxfIqPOr+Q4v0Ri5LcO55zfuHFj586d\n27dvj4uLq6iosLGxCQgIGD16tHTFGSduLiEy3u7X3Fz4+qK0FEeOoG1baV7DeEdPR3j0iPgI\npODRIxJj9DRP7K5duxYVFbV9+/ZDhw4plUpLS8sRI0aMGTPG19fXwsJCByUamy++0HcFMnf8\nOBwd9V3EX5RK5c2bN+3s7Oi7+v13eHujRQv8/DOeeoq+v8cYPBjHj0u2dwFwfokMKb/yw/kl\nEiO/mid2bdq0UalUpqamQ4cOHT169CuvvGJtba2DyowWn09HZDBnhF28eNHT0zM7O7tHjx4H\nDx5s2rRpvXeVmgo/P/Tpg82b0aiRFmt8BK9cT8T5JeLDj4LzSyRGfjV/Lenh4bFy5crr16/v\n27fvzTff5FkdlRjNmxIymObrJUuWZGdnAzh27NjatWvrvZ+YGAwcCD8/bN8u8awO3HxNxvkl\nMpj8yhLnl0iM/Gqe2L3//vv9+/dv2bKlDqoRghjNmxIymObr6us41ntNx/BwBATgnXewdq1O\nLrPEzddEnF8ig8mvLHF+icTIr+aJXWBg4O7du3VQiii4+5XIYAZw1qxZzz77LIBevXpNmDCh\nHntYvBjBwQgL02Hjh8GMnlzxABLxAFLw6BGJMYCaFygeOnSomZnZ7t27TQQYjhrxlScMiyGt\nXK9Sqe7cudOiRYu6/qFSiWnTEB6OjRvx6qtSlPYYvHI9EeeXyJDyKz+cXyIxrjyh+befjRs3\nTp8+fdiwYW+++WaHDh1sbGweeoKzs7M0tRkpfksgMqR/1BQKRT1mdWVlGDsWcXE4eFDnv6tw\n8zUR55eIDz8Kzi+RGPnVPLGrWsph//79NT6h9hclYwD+6txs1UrfdchWRgZcXHTSjyaJ/Hz4\n++PqVSQno2NHnb98RQXOn0fnzjp/YWPB+SWSeX71jPNLJEZ+NacrMDDQ3NzczMys3u3h7AHq\nzs3Vq/Vdh2x5eCAyEl5e+q6jPq5dg48PVCocOgQHB31UEBuLwEAUFOjjtY0C55dIzvnVP84v\nkRj51Tyx27Jliw7qEAg3lxDJtvs1IwPe3mjfHlFReKSjQVdkO3qGgkePiI9ACh49IjFGrw7f\nhxcVFV2+fLl169aUhViZICtfS0ieK9fHx2PECAwZgo0b0bCh/urgleuJOL9E8syvoeD8EomR\n31rNXhMSEnr27NmkSZPnnnsuJSVFvdHf3z+WlyOqh2bNBOnflIqTk+w+dUVFwccH48Zh61a9\nzurAzddknF8iGebXgHB+icTIr+aApaamenp6XrhwwataV8TNmzePHj3q6+t77NgxKcszRmKs\nfC0hua1cv2IFRo3C7NlYtswA3tF45Xoizi+R3PJrWDi/RGLkV/P7zMKFC+3s7M6ePRseHl61\nsWXLlidPnrSzs/vkk08krM4oibHytYTks3K9SoX58zFzJjZswPz5+q5GjVeuJ+L8Esknv4aI\n80skRn41T+xSUlJCQkIcHjmFz9bWdvLkyYmJidIUZry4+5VIJgNYUYHgYHz9NaKjMWaMvqup\nIpPRM1w8gEQ8gBQ8ekRiDKDmkycKCwvbtGlT40P29vbFxcXaLsnYidG8KSE5NF+XlGDUKJw4\ngYQEdO+u72qq4+ZrIs4vkRzya7g4v0Ri5LdWCxSfO3euxocSExOffvppbZdk7ATo3JSWwfcO\n5+Vh2DDk5yMxEe3b67uah3DzNRHnl4gPPwrOL5EY+dX8naSvr++qVauOP/gpIT8/f+7cuevW\nrRs2bJhktRkpMZo3JWTYzdd//IF+/WBigiNHDG9WB26+JuP8Ehl2fg0d55dIjPxqntgtWLCg\ncePGvXv3Vs/h5syZ061bN3t7+88++8zR0fGjjz6SvkjjIkbzpoT00Xy9YcMGR0fHDh06PO7C\nemppaejTB05OiI2Fra3OqqsLbr4m4vwS8ckTFJxfIjHyq3liZ2dnl5aWFhwcfOnSJQDp6enp\n6enW1tYhISFHjx5tZezXXNM+MZo3JaTzASwoKJg0adKVK1cuXrw4bty4x10c+eBBDBoEb2/s\n2QNra10WWBd8+BHxABLxAFLw6BGJMYCKx71LPUqlUt24caOoqMja2lqo+dx33303efLkoqKi\nxo0ba2F3+fmAKL/0SyI7G46OugznlStXHP9u97awsCguLjZ95BLmGzZg0iSEhGDpUhj0RZUr\nK3H5Mrfp1B/nl0jn+TUqnF8i7eW3vLzcwsIiOTnZ3d2dvjftqm26lEqlQqFo1aqVs7Nz06ZN\nf/311xMnTtR+Usj+IcbK1xLS+cr1bdq0CQwMVN9+7733Hp3VLVuGiROxdCmWLTPsWR24+ZqM\n80vEV56g4PwSiZFfzQFTKpVTp04NCgpS383OznZ1dXVzc+vevftLL73Ey53UmRjNmxLSR/P1\nli1b0tLSzpw588WDZ8urVJg5E7NnY9MmTJmi46LqhZuviTi/RHzyBAXnl0iM/Gqe2C1ZsmTV\nqlVVP0VNnTo1KysrJCRkypQphw8fDgsLk7hCoyNG86aE9NR83aNHj86dO1ffUlaG0aOxdi0O\nHMBrr+m+onrh5msizi8RnzxBwfklEiO/mtex27RpU0BAwNdffw3g2rVr+/btmzBhwqpVqwCU\nlpZGRkaGhoZKXqYx4Z8hiAyj+7WgAMOHIzMTv/yCF17QdzW1ZxijJ2M8ekR8BFLw6BGJMXqa\nJ3bZ2dnTpk1T3/7pp59UKtXo0aPVd3v06LFjxw4JqzNKYqx8LSEDWLn++nX4+uL+faSk4DGX\nZTFUvHI9EeeXyADyK2OcXyIx8qt5Yqeo1g1+8OBBKyurfv36qe+qVKr79+9LVZqxEqBzU1r6\n7h0+exY+PmjdGjExaNFCv7XUHTdfE3F+ifjwo+D8EomRX81fS7Zt2zYxMRFAXl5eTEyMp6en\nubm5+qGTJ086ODhIW6DxEaN5U0J6bb5OSUH//ujeHbGxMpzVgZuvyTi/RHzyBAXnl0iM/Gqe\n2I0ZMyYiIsLd3b179+7FxcXvvvuuevuGDRvWr1/v7+8vcYVGR4zmTQnpr/k6OhqDBiEwENu3\nw9JSLyWQcfM1EeeXiE+eoOD8EomRX80/xU6fPv3ChQuRkZHm5ubLly/v37+/entoaKiLi8uc\nOXMkrtDoiNG8KSE9tQ+vXYvJk/HBB5g/X/cvrj3cfE3Eo0fERyAFjx6RGKNXhytPPCQlJaVn\nz56PLtZqfPjKE4ZF5yvXq1RYsACLFmHVKgQH6+xlpcEr1xNxfon4yhMUnF8iMa48UYdp2ZUr\nVy5dulRaWtqoUaN27dq5ublJV5Yx47cEIt3+o6ZUIiQEERGIjoavry5fWRrcfE3E+SXiw4+C\n80skRn5r9bFpzZo17dq1c3R07Nev39ChQz08POzt7Tt37hwZGSl1fUZIjOZNCemw+bqkBMOH\nY8cOHDhgFLM6cPM1GeeXiE+eoOD8EomRX83f2K1cuXLatGnm5uYDBw5s165do0aN7t27l5mZ\neeTIkaCgoLKysjfffFMHhRoPdefm6tX6rkO2PDwQGQkvL6lf584dvPwycnJw+DA6dJD61XQl\nNhaBgSgo0HcdssX5JdJVfo0T55dIjPxqntgtW7asXbt2cXFxbdu2rb796tWrQ4YMWbx4MU/s\n6oabS4h00j6clQUfH1hYICkJTz8t9avpEDdfE/HoEfERSMGjRyTG6NXqyhMffPDBQ7M6AA4O\nDsHBwXPnzpWmMOMlxsrXEpJ+5frTp+Hjg44dsWMHmjSR9KV0jleuJ+L8EvGVJyg4v0Ri5Ffz\nxK5ly5YNGzas8SErK6unnnpK2yUZOzGaNyUkce9wXBxeeQX+/li7FmZmkr6UPnDzNRHnl4gP\nPwrOL5EY+dX8tWRQUNDevXsrKysffWjfvn1BQUESVGXUxGjelJCUzdfbtmHYMIwfj/XrjXFW\nB26+JuP8EvHJExScXyIx8lvzxO5qNVOnTm3SpMmgQYM2b9585syZy5cvnz9/fufOnf7+/mVl\nZfMEWMRZy8RY+VpCkq1cv2wZgoKwcCGWLTPeTgxeuZ6I80vEV56g4PwSiZHfmn+KbdOmzaMb\nExISHt3YrFmzei9xLCijnTLoigTtwyoVQkOxdCk2boSRfwfNzddEPHpEfARS8OgRiTF6NU/s\nAgMDa/n3paWl2itGDGI0b0pI283X5eUYPx67dyMmBp6eWtyxQeLmayLOLxGfPEHB+SUSI781\nT+y2bNmi4zoEIkbzpoQ09Q6fOnUqPT194MCBNX7x/JDiYowciVOnkJiIrl21U6BB4+ZrIs4v\nER9+FJxfIjHyW4dLit26devixYslJSXW1tYuLi5NmzaVrixjpu7cbNVK33XIVkYGXFzwmIsU\nR0VFjRo1SqlUWltbp6WldXjiysK5ufD1RWkpjhzBI+v5GKmKCpw/j86d9V2HbHF+iZ6YX6YB\n55dIjPzW6vfmpKQkNze3li1buru7Dx061M3NrXnz5kOGDDlz5ozU9RkhMZo3JfTE5uuIiAil\nUgmgqKgoOjr6Cbv5/Xf06wdzcyQmCjOrAzdfk3F+ifjkCQrOL5EY+dX8sSk1NXXIkCEVFRV9\n+/Z1cXGxtLQsKSk5e/ZsXFych4dHamqqi4uLDgo1HmI0b0roie3D7dq1q/H2Q1JT4eeHPn2w\neTMaNdJygQaNm6+JePSI+Aik4NEjEmP0NE/sPv3005YtWx44cKBjx47Vt584ccLb23vBggUR\nERGSlWeMxGjelNATm6/nzZuXn5+fnp7u5+cXEBBQ43NiYhAUhMBAfP+9eL8IcfM1EeeXiE+e\noOD8EomRX81va4cPH54xY8ZDszoA3bp1mzJlyjfffCNNYcZLjOZNCT2xd9ja2vr7779/whPC\nwxEcjBkzBAn4I7j5mojzS8SHHwXnl0iM/Gr+WrKwsNDBwaHGh5ycnO7cuaPtkoydGCtfS4iw\ncv3ixQgORliYqLM68Mr1ZJxfIr7yBAXnl0iM/Gqe2Nna2p47d67Gh86ePWtra6vtkoydGM2b\nEqpX87VSiZAQzJ+PLVvw9ttSlCUT3HxNxPkl4pMnKDi/RGLkV/PEztPTc8WKFdHR0dWvMKFS\nqaKiolauXOnj4yNlecaIu1+J6j6AZWUICsLWrTh4EK++KlFZMsGHHxEPIBEPIAWPHpEYA6jQ\neEGw7Ozs3r1737hxw87OztXV1crKSn1WbG5urr29fWpq6uN+qDUa33333eTJk4uKiho3bqyF\n3eXnA6L80i+J7Gw4OtY+nPn58PfH1avYtw+PdIqKp7ISly9zm079cX6J6phf9gDOL5H28lte\nXm5hYZGcnOzu7k7fm3ZpPnnCyckpLS3tww8/3LlzZ1xcnHpj8+bNJ02atHDhQnt7e4krNDr8\nlkBUl3/Url2Djw9UKhw6BGP/AFI73HxNxPkl4sOPgvNLJEZ+a7XYQ5s2bcLDw1UqVW5ubklJ\nSePGje3s7KSuzGiJsfK1hGq9cn1GBry90b49oqJgY6ODyuSAV64n4vwS8ZUnKDi/RGLktw7f\nhysUCnt7e2dnZ57VkYjRvCmh2jVfx8fDwwO9e2PvXp7VVcPN10ScXyI+eYKC80skRn650UHn\nxGjelFAtBjAqCj4+GDcOW7eiYUPdlCUTfPgR8QAS8QBS8OgRiTGA/H24zom7hJqWaFq5fsUK\nTJ+OefMwf76uSpIRXrmeiPNLxFeeoOD8EomRX57Y6ZwYzZsSenzvsEqFBQvw+efYsAFjxuiw\nJBnh5msizi8RH34UnF8iMfJrVN9J5ufnZ2dn67sKTcRY+VpCj1m5vqICwcH4+mtER/Os7vF4\n5Xoizi8RX3mCgvNLJEZ+5TSxO3Xq1LBhw5ycnPr12xTX8AAAIABJREFU67dq1SqlUvnQExYv\nXvzMM8/opbY6EKN5U0I1NV+XlMDfH3v2ICEB3t56KUsmuPmaiPNLxCdPUHB+icTIr2x+ik1O\nTh48eHBZWVmjRo2uX7+elJS0devWqKioZrL7ZlWAzk1pPdL9mpeHYcOQn4/ERLRvr6+yZEKM\n3mEJ8egR8RFIwaNHJMboyWZi9/nnn1dWVkZFRQ0fPry8vHzVqlWzZ8/28vL65ZdfrKys9F1d\nXYjRvCmhB5uv//gD3t5o2hRHjoAvXKwZN18TcX6J+OQJCs4vkRj5lc3s9dSpU4GBgSNGjFAo\nFBYWFtOnT9+/f//Jkydfe+21R3+TNWjNmgnSvykVJ6eqT11paejTB05OiI3lWV3tcPM1EeeX\nqFp+WZ1xfonEyK9sApabm9uuXbvqWwYNGrRmzZq9e/f++9//1ldV9SFG86aE/m6+PngQgwbB\n2xt79sDaWt9VyQU3XxNxfon45AkKzi+RGPmVzcSuVatW6enpD21844035syZs3z58iVLluil\nqvoQo3lTQh4eiI3dsAG+vvjXvxAeDjMzfZckI9x8TcT5JeKTJyg4v0Ri5Fc2PXYBAQErVqwI\nCwt7++23zaq9ky9atOj69euzZs26fv26PH6T5Z8hiExMoqJNJq7GsmWYMkXfxcgON18T8egR\n8RFIwaNHJMboyWZi99FHH+3cufOdd96Jjo4+cOBA1XaFQrFu3TobG5ulS5fWY7clJSVLliwp\nLS19wnPS09MDAPNPP0VoKJo2RUkJlixBZSX+/e/63G3WDJWVKCjQwq6EvPsf//h5a5+LXFsS\n8PsSfGQoVcnm7uDBSErC/PmGVZWM7nJ+iXfj4/Hcc/ovQ6Z3Ob8Gk98GX3zxSj3mHDohm4ld\nixYtjh079vHHH5ubmz/0kEKhWLZsWf/+/WfNmvX777/XabfFxcVHjx4tLy9/wnOuXbvmBZgc\nO4a7d9G0KYqLcfQoKivreff06fr/rdh3K389evpkZfi9ST8dMOnXoRgTDKIq+d1t0cIgypDp\nXc4v8e6kSTAx0X8Z8r3L+TWM/CrS0trWeSKjIwqVSqXvGgzdd999N3ny5KKiosaNG2thd+rO\nzVattLArkRQUYPhwZGYibkWGi78LTGXzmcSwVFTg/Hl07qzvOmSL80uUkQEXzm99cX6JtJff\n8vJyCwuL5ORkd3d3+t60S4jfmw2LGM2b2nX9OgYMwK1bSEmBywRuvibg5msizi8RnzxBwfkl\nEiO/8p7YffXVV3379tV3FXXE3a91dPYs+vRBo0ZITESbNjyANDx6RDyARDyAFDx6RGIMoLy/\nD8/MzExOTtZ3FXUkxsrX2pKSgpdfRt++iIiApSUAXrmehleuJ+L8EnF+KTi/RGLkV94TO1kS\nYNlrbYmOxujRmDABy5dX+5TFC69T8Mr1RJxfIj78KDi/RGLk1/i/kzQ4Yqx8Tbd2LUaNwqxZ\nCAt78LtzXrmegleuJ+L8EnF+KTi/RGLklyd2OidG8yaFSoX58/H221i5EvPnP/IwN19TcPM1\nEeeXiPNLwfklEiO/8p7YffHFF1euXNF3FXUkRvNmvSmVePttfPUVoqMRHFzTM3gAKXj0iHgA\niXgAKXj0iMQYQHn32DVt2rRp06b6rqKOxGjerJ+SEgQGIiUFBw6gT5/HPImbrym4+ZqI80vE\n+aXg/BKJkV95T+xkSYzmzXq4cwcvv4ycHBw+jA4dHv887h2m4OZrIs4vER9+FJxfIjHya/zf\nSRocMZo36yorC+7uKC5GUtITZ3Xg5msabr4m4vwScX4pOL9EYuSXJ3Y6J0bzZp2cPo1+/eDg\ngEOH8PTTmp7NzdcU3HxNxPkl4vxScH6JxMgvT+x0TozmzdqLi0Pfvhg4EPv2oUmTWvwBDyAF\njx4RDyARDyAFjx6RGAPIPXY6J0bzZi1t24Y33sBbb+G//6113Lj5moKbr4k4v0ScXwrOL5EY\n+eWJnc6J0bxZG8uWYcYMfP453n+/Ln/GvcMU3HxNxPkl4sOPgvNLJEZ+jf87SYMjRvPmk6lU\nmD0bs2Zh48Y6zurAzdc03HxNxPkl4vxScH6JxMgvT+x0TozmzScoL8frr+ObbxATg6Cguv89\nN19TcPM1kfD5peL8UnB+icTIL/8Uq3MCdG4+QXExRo7EqVNITETXrvXahRjdr1Lh0SPi0SPi\nI5CCR49IjNHjiZ3OidG8WaPcXPj6orQUR46gbdv67oWbrym4+ZpI4PxqB+eXgvNLJEZ+eWKn\nc2I0bz7q99/h7Y0WLfDzz3jqKcKOuHeYgpuviUTNr9bw4UfB+SUSI79CfC1pWMRo3nxIair6\n9IGrK+LiaLM6cPM1DTdfEwmZX23i/FJwfonEyC9P7HROjObN6mJiMHAg/PywfTsaNSLvjpuv\nKbj5mki8/GoZ55eC80skRn55YqdzgnW/hocjIADvvIO1a2GqlV/+BRtALePRI+IBJOIBpODR\nIxJjALnHTufEaN5UW7wY8+YhLAxvv629nXLzNQU3XxOJlF9JcH4pOL9EYuSXJ3Y6J0bzplKJ\nadMQHo4tW/Dqq1rdNfcOU3DzNZEY+ZUQH34UnF8iMfJr/N9JGhwBmjfLyhAUhK1bcfCgtmd1\n4OZrGm6+JhIgv9Li/FJwfonEyC9P7HTO2Js38/MxZAjS0pCcLE2bLzdfU3DzNZGx51dynF8K\nzi+RGPnln2J1zqg7N69dg48PVCocOgQHB2leQ4zuV6nw6BHx6BHxEUjBo0ckxujxxE7njLd5\nMyMD3t5o3x5RUbCxkexluPmagpuviYw3vzrC+aXg/BKJkV+e2OmckTZvxsdjxAgMGYKNG9Gw\noZSvxL3DFNx8TWSk+dUdPvwoOL9EYuRXiK8lDYsxNm9GRcHHB+PGYetWiWd14OZrGm6+JjLG\n/OoU55eC80skRn55YqdzRte8uWIFRo3C7NlYtkwnDQzcfE3BzddERpdfXeP8UnB+icTIL/8U\nq3NG1LypUmHBAnz+OTZswJgxunpVbh+m4NEj4tEj4iOQgkePSIzR44mdzhlL82ZFBSZPRmQk\noqPh7a3DF+bmawpuviYylvzqDeeXgvNLJEZ+eWKnc0bRvFlSglGjcOIEEhLQvbtuX5t7hym4\n+ZrIKPKrT3z4UXB+icTIrxBfSxoW+Tdv5uWhf3+cP4/ERJ3P6sDN1zTcfE0k//zqGeeXgvNL\nJEZ+eWKnczJv3vzjD/TrBxMTHDmC9u31UcHfzdc//PBDq1at7O3tIyMj9VGHPHHzNZHM86t/\nfPIEBeeXSIz88sRO5+Tc/ZqWhj594OSE2FjY2uqpCBMTmJj8+eefwf/f3p3HRVV//wM/I8wg\ni4ELasjirrkgomUmi3uu4FKKfdQ0wMTM3LXy41aZpbmifVoeSkomlRallWYirrh+aFE/Cgiu\nkKagILLP94/7a34Tyyycmblz7309/3Iul3sPx/e5c7hzZoiOvn37dk5OTmRkZGlpqUjRSI2U\nl59dQAKZkEAOZI9JGQnEjJ3NSXZ488ABGjWKRo6kTz8ltVq8OM6dI1/fovv3S0pKhA1FRUUl\nJSVqMWOSDgxfM0m2fu0F3jzBgfplUkb9yr91tTv160txfnPbNhoyhCZPprg4Ubs6ImrenOrU\nqV+//vTp04UNs2bNcnV1FTUm6cDwNZM069eONG+uhFsm1oL6ZVJG/aLAbE6Cw5vr11NkJK1b\nR+vXk0oldjR/D19v2LDh0qVLaWlpq1atEjsm6cDwNZME69e+4M0THKhfJmXULxo7m5PU8KZW\nS3Pn0oIF9PnnNG2a2NEI9Iav27Zt27p1a3HDkRgMXzNJqn7tEd48wYH6ZVJG/WLGzuak8zJE\ncTG9+CLt308//0zBwWJHo6OM6VdrQfaYkD0mrEAOZI9JGdlDY2dzEhnezMuj8HBKT6ekJOrS\nRexo9GH4mgPD10wSqV/7hfrlQP0yKaN+0djZnBQmN2/doiFDqLSUUlLIx4d7tNzc3NLS0saW\n+nwUzA5zYPiaSQr1a9ew/DhQv0zKqF9F3Ja0L3Y/vHnhAvXsSS4udPiwBbq6jRs3Nm7cuGnT\npnPnzrVEdBi+5sHwNZPd16+9Q/1yoH6ZlFG/aOxszr6HN1NSKDSUAgPpl1+oYUPu0crLy19/\n/fWysjKtVvvBBx9kZ2dbIEQMX3Ng+JrJvutXAlC/HKhfJmXULxo7m7Pj6dfEROrbl8aOpV27\nyNnZAgdUqVSOjo66fzs4OFjgoHacQAlA9piQQCYkkAPZY1JGAjFjZ3P2Ory5ZQtNnUpvvEFL\nl1rsmHXq1Nm4cWNMTExJScmyZcssM2aH4WsODF8z2Wv9SgbqlwP1y6SM+kVjZ3P2N7yp1dKy\nZfTOO7R5M0VHW/jgEyZMGDduXEVFhUajscwRMTvMgeFrJvurX4nB8uNA/TIpo37lf0/S7tjZ\n8GZ5Ob38Mq1eTYmJlu/qBI6Ojhbr6gjD1zwYvmays/qVHtQvB+qXSRn1i8bO5uxpePPhQwoP\np9276eefacgQsaMxEYavOTB8zWRP9StJqF8O1C+TMuoXL8XanN1Mbt67R8OHU3Y2HT9ObduK\nHY3plDH9ai3IHhOyx4QVyIHsMSkje2jsbM4+hjczM2nwYHJyoqNHyctL7GjMguFrDgxfM9lH\n/UoY6pcD9cukjPpFY2dzdjC8+fvvNHgwtW9Pu3fTY4+JHY25MDvMgeFrJjuoX2nD8uNA/TIp\no34VcVvSvog9vHnwIAUFUZ8+9OOPEuzqCMPXPBi+ZhK7fiUP9cuB+mVSRv2isbM5UYc3v/6a\nhg6lSZPos89IrRYrCh4MX3Ng+JpJGcPXVoT65UD9MimjftHY2Zx406/r11NEBC1fTuvXS3mE\nFOPDHMgeExLIhARyIHtMykggZuxsTozhTa2WFi6kdesoPp4iImx/fovC8DUHhq+ZlDF8bUWo\nXw7UL5My6heNnc3ZfHizpIQmTaI9e+j772ngQBuf3AowO8yB4WsmZQxfWxGWHwfql0kZ9Sv/\ne5J2x7bDmwUFFBZGhw7R4cOy6OoIw9c8GL5mUsbwtRWhfjlQv0zKqF80djZnw+HNnBwKCaFr\n1+jECQoIsM05rQ/D1xwYvmZSxvC1FaF+OVC/TMqoXzR2Nmer4c2MDAoOJo2GDh8mPz8bnNBW\nlDH9ai3IHhMSyIQEciB7TMpIIGbsbM4mw5unTtGwYdSzJ33xBbm42OCENoThaw4MXzMpY/ja\nilC/HKhfJmXULxo7m7P+8Ob331NEBI0dSx9/TI7y+x/G7DAHhq+ZlDF8bUVYfhyoXyZl1K/8\n70naHSsPb8bF0ahR9OqrtGWLHLs6wvA1D4avmZQxfG1FqF8O1C+TMuoXjZ3NWXN48733KDqa\nYmNlfb8Zw9ccGL5mUsbwtRWhfjlQv0zKqF9Z3tKxb9aZ3Cwvp+nTKS6Odu6k0aOtcQa7oYzp\nV2tB9piQPSasQA5kj0kZ2UNjZ3NWuJlWXEzjx9PBg3TggAJ+ncPwNQeGr5nkfDPcJlC/HKhf\nJmXULxo7m7P08GZuLoWF0Y0bdOwYtW9v2WPbJcwOc2D4mkkZw9dWhOXHgfplUkb9KuK2pH2x\n6PDmzZsUGkp5eXTkiDK6OsLwNQ+Gr5mUMXxtRahfDtQvkzLqF42dzVluePP8eXr6aWrUiI4e\nJW9vixxSCjB8zYHhayZlDF9bEeqXA/XLpIz6RWNncxaafj10iHr1oqeeoh9+IHd3/vGkA+PD\nHMgeExLIhARyIHtMykggZuxszhLDm998Qy+8QFOm0Nq1Slil/4Thaw4MXzMpY/jailC/HKhf\nJmXULxo7m2MPb27cSLNm0aJFtHSpJeKRHMwOc2D4mkkZw9dWhOXHgfplUkb9Ku1ujx1gDG9q\ntbR0Kc2dS9u2KbWrIwxf82D4mkkZw9dWhPrlQP0yKaN+0djZXG2HN8vKKDqaPviAEhPphRcs\nHpZ0YPiaA8PXTMoYvrYi1C8H6pdJGfWLl2JtrlYzcQ8f0vPP03//S8nJFBho8ZgkRRnTr9aC\n7DEhe0xYgRzIHpMysofGzubMH978808aOpRyc+nwYWrTxhoxSQqGrzkwfM2kjOFrK0L9cqB+\nmZRRv2jsbM7M4c0rV2jQIPLwoBMnqHFjK8UkKZgd5sDwNZMyhq+tCMuPA/XLpIz6VcRtSfti\nzvDmmTPUsyc1b06//IKu7m8YvubA8DWTMoavrQj1y4H6ZVJG/aKxszmThzcPHKC+fWnQINq7\nl+rVs3ZY0oHhaw4MXzMpY/jailC/HKhfJmXULxo7mzNt+nXbNhoyhCZPprg4UqttEJZ0YHyY\nA9ljQgKZkEAOZI9JGQnEjJ3NmTC8uX49zZ1L69fTtGk2CEhqMHzNgeFrJmUMX1sR6pcD9cuk\njPpFY2dzBoc3tVqaN49iY+nzz2nMGJvFJCmYHebA8DWTMoavrQjLjwP1y6SM+pX/PUm7U/Pw\nZnExjRtHW7bQzz+jq6sZhq85MHzNpIzhaytC/XKgfpmUUb+Sb+zKy8svXrx45syZoqIisWMx\nTQ3Dm3l5NHAgHTlCSUkUHGz7sKQDw9ccGL5mUsbwtRWhfjlQv0zKqF8pNXbHjx8fM2ZMQEDA\nyJEjz507R0Tp6ekBAQEdOnR48sknGzduvHnzZrFjNEF1w5u3blHv3vTXX5SSQl26iBKWdChj\n+tVakD0mJJAJCeRA9piUkUCVVqsVOwaTnDx5Mjg4uLS0VK1Wl5aWPvbYY//9738nTpyYmpo6\nYsSIR48e7d+/v6Cg4Lvvvhs+fLhlT/3RRx9NnTo1Pz/fzc3NAofLzSX6xyv9Fy7Q4MHUrBl9\n/z01bGiBM8hcVhb5+iqhOK2iooKuXcOYTu1VqV8wD+qXA/XLZLn6LSkpcXJyOnbs2DPPPMM/\nmmVJprrefvttItq9e/ejR49u3Ljh5+e3ZMmSlJSUn376KT4+fteuXWfPnnV1dd2wYYPYkRpT\nv77+qkpJodBQCgykX35BV2ea5s3xrFB7GL5m+mf9gtlQvxyoXyZl1K9kCuzEiRNjx44dOXKk\ng4NDs2bN1q1bFx8f36tXr6CgIGGHtm3bPv/882fPnhU3TuP0hjcTE6lvXxo7lnbtImdnccOS\nDgxfc2D4mkkZw9dWhPrlQP0yKaN+JdPYPXjwoFWrVrqHPXr0IKIOHTro7+Pl5ZWfn2/ryMz1\n9/Dmli30/PM0fz7FxuI3WHNg+JoDw9dMyhi+tiLULwfql0kZ9SuZz7Hz9vbOzMzUPXR1dXV3\nd/fw8NDfJyMjo6H9v5xZpw4RLV1K77xDmzdTdLTY8UiOMqZfrQXZY0L2mLACOZA9JmVkTzKN\nXd++fePj46Ojo3Wvvebl5envkJKSsnv37rCwMDGiM0P5OyvnzKFPV1NiIg0ZInY0UoRPrufA\nJ9czKeOT660I9cuB+mVSRv1KpntduHChi4tLSEjIG2+8UfWrEyZMCAkJ0Wq1CxYsMOuwmZmZ\njRs3bmDQ7Nmz1xK5+vn9v+GGzExq3JgaNarFw8LzmQXN2i3e3ubYx+eHDGEdSrkPHz6kOnXE\nD0OiD+vUIa1W/DCk+7BdO2rTRvwwpPsQ9Yv6lUX9ary915CdkszHnRDRxYsXZ8yY8fTTT7/1\n1luVvuTv75+XlxcbG2vuHbuKiorDhw+XGRzmPX/+/EczZ/62b59j377k6EgVFXT4MFVUUEiI\nWQ/vPXAMH17RKT3x34sqvGLCOYdS9MNGjahDB6pTx76ikspDIrp4ke7eta+oJPQwMZEqKigc\n9Yv6Rf1K8KHl6rfs4EH/AQM+tcuPO5FSY2fArVu3vLy8rHTw48eP9+rVq7i4WKPR1PogmZk0\neDA5OdGJTtEuLkSffGLBCJXFw4MSEujZZ8WOQ5r27aOxY+mfYwxgBmEqFvVba6hfDtQvk+Xq\nF59jZ3XW6+os4vffKTiYvL3pyBFyccP0Kw/GhzmQPSYkkAkJ5ED2mJSRQGnfsVu9evW33357\n9OhRq56Fecfu4EEaOZLCwmjLFlKr8cn1bPjkeo4KfHI9D+qXCfXLgfplUsZfnpDMu2KrlZ6e\nfuzYMbGjMOTrr2nCBJoyhdau/ftShqcEJlzUOPDJ9UyoXyYsPw7UL5My6he/NlnR+vUUEUHL\nl9P69Xq/oCrjk6+t6Dw+uZ4Bn1zPhPplQv1yoH6ZlFG/aOysQqulBQto/nyKj6d58/75NWV8\n8rUV4ZPrOfDJ9UyoXybULwfql0kZ9Svtl2LtU0kJTZpEe/bQ99/TwIFVvozhEiZlTL9aC7LH\nhOwxYQVyIHtMysietN88kZeXV1BQ4O3tbdWzmPXmiYICeu45+u03+uEHCgiobg8MXzNh+JoD\nw9dMqF8m1C8H6pcJb56wfx4eHpX+XKy4cnJoyBAqKqITJ8jPr4ad8JTAhIsaB4avmVC/TFh+\nHKhfJmXUL35tspiMDAoOJo2GDh+uuasjpQxvWhGGrzkwfM2E+mVC/XKgfpmUUb9o7Czj1Cnq\n2ZM6dKCDB6lRI4O7KmN404owfM2B4Wsm1C8T6pcD9cukjPpFY2cB339PffrQsGG0axe5uBjb\nG9OvTEggB7LHhAQyIYEcyB6TMhIo7TdP2IbhN0/ExVF0NM2ZQytXmnY4DF8zYfiaA8PXTKhf\nJtQvB+qXCW+eAKPee48WLaLYWHr5ZZO/B08JTLiocWD4mgn1y4Tlx4H6ZVJG/eLXploqL6eY\nGFq6lHbuNKerI6UMb1oRhq85MHzNhPplQv1yoH6ZlFG/aOxqo7iYIiLoyy/pwAEaPdrMb1bG\n8KYVYfiaA8PXTKhfJtQvB+qXSRn1i5dizZabS2FhdOMGHTtG7dub//0YLmFSxvSrtSB7TMge\nE1YgB7LHpIzsobEzz82bNHgwabV05AjV8g9emPomC6jBuXPk6yt2EJLVrx+dOyd2EFKG+mVC\n/XKgfpmUUb9o7Mxw/jwNGkRt2tA335C7e22PoozhTSvC7DAHhq+ZUL9MWH4cqF8mZdSvIm5L\nWsThw3V69aKnnqIffmB0daSU4U0rwvA1B4avmVC/TKhfDtQvkzLqF42dicKGDXN86SX66iuq\nW5d3JGUMb1oRhq85MHzNhPplQv1yoH6ZFFK/WjDm9OnTROOJzPpQkxpNIppkkQMp1QaizmLH\nIF2diTaIHYOkTUL98qB+OVC/TJMsXb+nT58Wu0OpBv7yhEl+/fXXMgu9fLBo0aLCwsLo6GiL\nHE2BoqKipk+fHhAQIHYgkpSamhobG/vpp5+KHYhUffLJJ0SE+q011C8H6pfpk08+cXFxefvt\nty1yNEdHxy5duljkUJaFxs7WJk+eTERbt24VOxCpcnNzS0hIGDp0qNiBSNLevXvHjh1bUFAg\ndiBShfplQv1yoH6ZFFK/mLEDAAAAkAk0dgAAAAAygcYOAAAAQCbQ2AEAAADIBBo7AAAAAJlA\nYwcAAAAgE2jsAAAAAGQCjR0AAACATKCxAwAAAJAJR7EDUByNRiN2CNKm0WiQw1pD9piQPSas\nQA5kj0kh2cOfFLO13NxcIqpfv77YgUhVVlaWr69vnTq42VwbFRUV165da968udiBSBXqlwn1\ny4H6ZVJI/aKxAwAAAJAJ/NoEAAAAIBNo7AAAAABkAo0dAAAAgEygsQMAAACQCTR2AAAAADKB\nxg4AAABAJtDYAQAAAMgEGjsAAAAAmUBjBwAAACATaOwAAAAAZAKNHQAAAIBMoLEDAAAAkAk0\ndgAAAAAygcYOAAAAQCbQ2AEAAADIBBo7EVy5cmXKlCmtWrVycnLy9PQcMWLEqVOnxA5KSnJz\nc+fOnevn5+fk5NSiRYsRI0akpKSIHZSUlJaWvv766w4ODt27dxc7FsnIy8ubOXNm8+bNNRqN\nl5dXVFRUdna22EFJCVYdBy56TIp62lVptVqxY1CWS5cu9erVKz8/f8yYMa1atUpPT//yyy+J\nKDk5uWfPnmJHJwH37t3r1q1bVlbW0KFDAwMDr1y5kpCQ4OjoeOrUqc6dO4sdnQRcvHhx/Pjx\naWlpDx8+7Nq165kzZ8SOSAJKSkp69ux57ty50aNHBwYGZmRkbN++3dvb++zZs/Xr1xc7OgnA\nquPARY9JcU+7WrCtAQMGqFSq5ORk3Zbdu3cT0ZgxY0SMSkJeeeUVItq4caNuy65du4hoyJAh\nIkYlFffv33d2du7evXtaWpqTk1O3bt3Ejkga1qxZQ0TvvfeebktCQgIRzZkzR8SopAKrjgkX\nPSalPe3ipVhb69Gjx8KFC0NCQnRbwsLC1Gr1pUuXRIxKQtRqdb9+/V5++WXdlpEjRzo7O58/\nf17EqKSirKxs2rRpx48fb926tdixSMm2bdvq1av32muv6baMGTOmdevW27dv1+JFD2Ow6phw\n0WNS2tOuo9gBKM5bb71VaUtOTk5paWmLFi1EiUdy1q5dW2lLSUlJWVmZt7e3KPFIS4MGDVav\nXi12FBJTVFT0+++/9+7d28nJSX97UFBQXFxcZmZmy5YtxYpNErDqmHDRY1La0y7u2ImpsLDw\n0KFDQ4YMqVev3ptvvil2OFL10UcflZaWRkREiB0IyNP169fLy8t9fHwqbffz8yOiK1euiBEU\nKBouerWmhKddNHai8fDwcHV17dOnj7+/f2pqKt4pVjvJycnz5s0LCgqaOnWq2LGAPOXn5xOR\nq6trpe1ubm66rwLYDC56taaQp128FGsteXl5Cxcu1D1s3br13Llz9XeIiYm5d+/eH3/8sWPH\njqysrM8++wwv6OgzmkAi+uKLLyZPntypU6fExERHRyzm/8+U7IFZVCpVpS3CdF3V7QDWg4se\nh1KedsV+94ZsXb9+XT/PvXr1qmnPpKQkV1dXf3//8vJyW0Zo5wwnsKKiYvHixUQ0aNCgBw8e\niBWk3TJl+eH9iSZKS0sjohdffLHS9kWLFhHRgQMHxAhKqrDqag0XPQuS99Mu+n1r8fb21pr2\ndrnevXuHh4fv2LHj0qVLTzzxhLUDkwoDCdSFq9hOAAAUHklEQVRqtVFRUVu2bHn11VfXrl3r\n4OBg49jsn+nLD4zy9fV1dHS8evVqpe0ZGRlE1KZNGzGCAmXBRc+y5P20ixk7m7p582aXLl0m\nTpxYaXtRURERPXz4UIygpGfWrFlbtmxZsWLFhg0bcIEDa9NoNN26dTt16lRhYaFuY0VFRXJy\nso+Pj6+vr4ixgULgoldrCnzaRWNnU82aNbt3715CQsLJkyd1Gy9fvrx//343N7dOnTqJGJtU\n7N69e/369a+99trrr78udiygFJGRkYWFhatWrdJt+fjjj2/duhUVFSViVKAQuOhxKPBpF39S\nzNa+/fbb5557rk6dOqNHj27VqtXNmze/+uqrhw8fxsbGCh8vDoa1bt06IyPj1VdfdXFxqfSl\nBQsW4O87GZacnPzjjz8K/169erWnp+eLL74oPJw3b17Dhg3FC82ulZeX9+nT58iRI+Hh4YGB\ngRcvXkxISOjUqVNKSkrVdQiVYNUx4aLHpLinXTEH/JQqJSVlxIgRnp6eDg4OHh4e/fv3/+67\n78QOSjIMLObMzEyxo7N37777bk3ZS0tLEzs6u5afny/8FXa1Wt2sWbNXXnnl7t27YgclDVh1\nTLjo8SnqaRd37AAAAABkAjN2AAAAADKBxg4AAABAJtDYAQAAAMgEGjsAAAAAmUBjBwAAACAT\naOwAAAAAZAKNHQAAAIBMoLEDAAAAkAk0dgAAAAAygcYOAAAAQCbQ2AEAAADIBBo7AAAAAJlA\nYwcAAAAgE2jsAAAAAGQCjR0AAACATKCxAwAAAJAJNHYAAAAAMoHGDgAAAEAm0NgBAAAAyAQa\nOwAAAACZQGMHAAAAIBNo7AAAAABkAo0dAAAAgEygsQMAAACQCTR2AAAAADKBxg4AAABAJtDY\nAQAAAMgEGjsAAAAAmUBjBwAAACATaOwAAAAAZAKNHQAAAIBMoLEDAAAAkAk0diANERERKpUq\nJyenph0cHR2ffvppE3eWGaX9vCYynJaoqCiVSpWenm7WMXfs2OHt7e3o6Dhv3jyjp7AU/bUt\nCuHHvHHjhogxVGLVetc/oDV+dhQsWBUaO5CGgICAZ5991snJyeI7S9HKlSv1OxJRft5KMdih\nSmnhB3z//v2oqKiCgoK33nrr2WefNeUUNshSfHy8SqVaunSpVc9iz8xa/6b8j1i8oOyhYEFB\ntACy4ODg0KNHD7GjsIVbt24R0Y8//qjwGMxSNeDIyEgiSktLM/0gp0+fJqJp06aZeApLZcnw\n2t6+fTsRLVmyhHkWA8aOHUtE169ft94pzFW7eq/F/wj/Z5dcsYDU4Y4dgMQI7QViMItFAi4q\nKiKievXqmXgKyWVJ9kT5H8EyAFsTu7MEMInwe3N2drbwcO/evYGBgXXr1vX09IyMjMzNzdX/\nDb7SzllZWZMmTfLy8lKr1Q0bNhw+fPjJkyd1Ry4qKnr//ff9/f0fe+wxNze3zp07v//+++Xl\n5VqtNigoqE6dOteuXdOP5K+//hLme7Ra7bhx44goPz9//vz5fn5+Go3G29t7zZo1FRUVuv2z\ns7MjIyO9vLxcXFz8/f3XrVtXWlqqH+eff/7Zv3//unXrJiYmCttPnjw5YsSIhg0bqtVqPz+/\n8ePHZ2ZmCl8aOnSofv0eOXKk6s9r4Iw1JbZqDDk5OdOmTfP19VWr1Y0aNQoPDz916pSBGISN\nubm5uiOXlpYSUb9+/QycyJQE6vPy8urcubP+lg4dOhDR3r17dVt27NhBRNu3b9elpdqAhTt2\nGRkZK1eubNGihUaj8fHxWb58eU2nFl571Xn55Zf1M1/1FNWe1HBiBYbXdlWm3LEzsKK0Wu2I\nESOI6NatW5GRkY0bN9ZoNO3atdu8ebNuh0p3rQwfTWtsBRrNQFWm17uBcjZQO5WWpf4BhX9n\nZGTMnj3by8tLSM6mTZt0sRle+aYUrOELlLk1AuBYU8MHYLeOHj0aFhbWpEmTxYsXe3p6Jicn\nh4WF1alT/e3n69evP/XUU4WFhTExMR07drx58+bmzZtDQkIOHDgQFBRERDExMVu3bn3hhRdi\nYmJUKtW+ffvmz59/9erV2NjYqKioo0ePbtu27c0339QdcNeuXWVlZZMmTSIijUZDRM8991yL\nFi127txZUVGxbNmy2bNne3h4TJ48mYju3LnTvXv3goKCiRMn+vn5HTp0aObMmb///vunn36q\n+/ZZs2ap1erFixe3bNmSiM6ePRsaGtqgQYPXXnutadOmV65c2bRp0/79+y9cuNCwYcNFixY1\naNBg+/btixcv7tq1q9DW6DN8xqqqjeHOnTs9evTIy8ubOnVqp06drl+/vnnz5uDg4H379oWG\nhhqNwfQTGU1gJQMGDNi2bVtubm79+vWJ6Pbt2xcuXHBzc0tOTh4yZIiwz6FDh1Qq1YABA/bs\n2SNsMRDw22+/nZqaOmXKFAcHh40bNy5evLh169bCU2klS5YsCQ0NfeONN0aNGjVhwoQWLVro\nf7XqKao9qeHEkplr20SGVxQRCcNeI0aM6NOnzzfffFNRUbF8+fJp06ap1eqoqChzj2Z4BRrN\nQFVm5cRAOVf7P1LtsqxqxowZDx48mD59elFRUXx8/CuvvKLRaKompyqjxWL0AmVujQDgjh1I\ng/7vuIMGDSIi/d/yp02bRkTV/gb/4osvEtHu3bt1O1+4cMHBwUG45abVal1cXHr27Kl/rlmz\nZo0ePbqsrOzhw4fu7u5t2rTR/2q/fv3q1q2bl5en/fuuz7hx43RfzcjIIKJhw4YJD2NiYoho\n3759uh2E3+D/+OMPrVb70ksvEdHAgQOFOwqCzZs3BwYGJiUl6bZs3LiRiDZu3Cg8fPfdd+mf\nIzv6P6/hM1ZVbQwxMTGOjo6nT5/Wbbl27Vq9evW6d+9eUwxG79hVeyKjCawkPj6eiL777jvh\n4c6dOx0dHSdPnqz739RqtW3btg0ICKiUlqoBC6cOCgoqKSkRtpw9e5aIwsLCqj21Vqs9cuQI\nES1YsEC3xfApqm4xmlija7sqo3fsjK4o4afQ/1/Iy8tzcnJq3ry5/g7CHTujRzO8Ao1moCqz\n6t1AOWur+x+pdllWvWMXHBys2yErK0uj0bRo0UL/pzOw8g0XrNELlLk1AoAZO5CYioqK5OTk\nVq1aPfnkk7qN0dHR1e6s1Wq//fbbJk2aCC82CZ544omePXumpKTcvXuXiNRq9dWrV2/fvq3b\nYc2aNV9//bWDg4OLi8u4cePS0tKOHTsmfOnOnTuHDh0aOXKku7u7bn/h0ixo2bKli4uL8OEI\nWq32yy+/9PHxGTBggG6HDRs2HDx4sEmTJkSkUqmEb9e//RATE3P27NnevXsTUWlpaVFRkfBb\nflZWltHkGD1jVVVj0Gq1X331lb+/v7e3d87f1Gr1M888c+bMmYKCAqNhmHginZoSWFX//v1V\nKtXhw4eFh0lJSZ07d+7Tp8+ZM2cePnxIRNnZ2ZcvX670sqkBc+bMUavVwr+7du3q4OAgjLpb\ng9HEmrW2TWfiioqIiND9293dPTg4OCsrKzs726yjGV6BtVha5ubEQDlXu7+BZalv6tSpuh38\n/Px69eqVmZl5/fp1A99iClMuUALTawQAjR1ITHZ29qNHjyq9YtK+fftqd87Jybl//37Hjh2F\ny7dOu3btiOjy5ctEtHz58lu3brVp02bixIlbt269efOm/p7Cqy1xcXHCw127dpWXl1d6BcTX\n11f/oVqtFn5lz87Ovnv3bvv27fXP3rJlyz59+jRq1KhSMPq2b98eGhpav359jUbj7Ozcr18/\nIiorK6spJzomnrEq/Rhu3779119/nTt37vF/2rdvHxFdu3bNaBgmnkinpgRW1aRJk86dOwt3\nzogoKSkpJCQkJCSkrKzsxIkTwhYiGjhwoInxtGnTRvdvlUrl5ub26NEjE7/XXEYTa9baNosp\nK6pt27b6D5s1a0ZE1X7WmoGjGV6BtVha5ubEcDnXpNplqc/f31//oRDP1atXTTm4AaZcoASm\n1wgAZuxAYgoLC4mobt26+hvr1q1b6cooEO7iuLq6Vtru7Oys++qMGTM6deq0cePG3bt3b9++\nXaVSDR48ePPmzX5+fkTUrVu3rl27fvnllxs2bHB2dhbuRgjPZDq6Wz6VCC2C0U+r0r/5R0Rv\nvPHGu+++271797Vr17Zo0cLJyen8+fOmTPOYfkbDMeTn5xNRQECA8BJSJV5eXuYevKYT6dSU\nwGoNGDBg/fr1Dx8+vH///uXLl1euXOnn5+fj45OcnNy/f/9Dhw65uroKw0mmsOVniRlN7J07\nd8jktW06E1eUi4uL/kOhavLy8sw6muEVWIulZVa9k7Fyrkm1y1LfY489pv9QyJXwLmkOUy5Q\nArNqBBQOjR1IjHDJq3RJLSgo0Gq1VXd2c3Ojf14fBcIW3edW9O3bt2/fvsXFxUeOHImPj9+2\nbVv//v3Pnz8vjC1HRkZOnz597969QUFBycnJr7/+uonD7E2bNqXqnhoNKCoqWrdunY+PT1JS\nkhA8Ed2/f9/Eb6/FGavSpUWYbaq1kpISzrfXZMCAAR988MGJEyf+/PNPlUoVHBxMREFBQcLr\ns4cOHQoNDRX+4+yN0cQKr0WauLZNZPqKqlQmwj7C+yFMP5rhFViLpWVWvQsMl3PtVLqPK7Sb\nlVphHdNXvokXKACz4KVYkJimTZtqNJrMzEz9jb/99ltNOzdo0ODixYuVngYuXLigUqkqvf7i\n5OTUv3//uLi4qVOnpqenp6amCtv/9a9/OTs7JyQkJCQkVFRUCO+HNYWrq6unp+fFixf1XzS5\ndOlSbGzs+fPnq/2WnJycR48ede/eXfesSUTJycnWO2NVTZo0adSo0f/+979KT8/C/aSaCHcU\n9M9b6f/IUkJCQpycnI4ePZqUlNSxY0fhJebg4OCTJ09mZmampaWZPmBnY0YTa9baNpHpK+ri\nxYv6D9PS0ojo8ccfN+tohldgLZZWrXNSUznXTqXkCG9fEF6Q5ax8sy5QACZCYwcS4+jo+Mwz\nz6Snp+t/7OemTZtq2n/UqFHZ2dmJiYm6LampqadOnerbt6+Hh0dKSkqzZs22bdum/y3CDTnd\nax8eHh6jRo364Ycf4uLigoKCWrdubXq04eHhd+/e/eyzz3Rbli5d+uqrrxYXF1e7f5MmTVQq\nlf5Ue2pqqhCe7qaFMAZe0yiYuWes1vPPP19UVLRq1Srdljt37vj7+w8fPrymGIQOQP/5r1JW\nLcXZ2blXr14pKSlJSUm6D8gIDg4uLi5eu3Yt1TBgZzhpFlH1FFW3GE6suWvbFKasKMGWLVt0\n/758+fLp06fbtWvn6elp7tEMr0CjS6sSs3JitJxrvQz0k3Pjxo3jx4936NBBuD1pdOUbPqnh\nC5S5cQIQXooFKZo/f35ycvKwYcNeeumlhg0bJicnFxYW1jQls2zZsj179kyYMGHGjBnt2rXL\nysratGmTm5vbmjVriKh79+4NGjSIjo4+evRoQECASqU6c+aM0MAFBAToDhIVFfX555+npqbW\n9GlwNVmyZMmePXtiYmJ+/fVXPz+/5OTkPXv2TJw4MTAwsNr9nZ2dhw4dumfPnqlTp/bu3fvC\nhQuxsbGff/55WFjY3r17v/jii7CwMOE+wcqVKzMzM4ODg/XfLViLM1Zr6dKle/fuXbFiRXZ2\ndmho6K1bt/7zn//cvXt3xowZwg5VY5g4ceKHH344e/bsVatWubi4JCYmnjhxwkqvJQ0YMOCd\nd94pKCjQNXYdO3Zs0KDB1q1bfX19q52sN5w0i6h6iqpbjCbWrLWt76effqr6Amh4eHifPn2M\nrihh5+Li4uHDhw8bNqyiouL999/XarWLFy+udEBT1qfhFWg0A1WZnhOj5VzrZVBcXDxy5MjB\ngwcXFhZ+/PHHJSUl//73v4UvGV35hk9q+AIFUBtifMYKgNkqfVb7zp07O3furNFoPD09X3rp\npdzcXB8fn65du1a787Vr1yZPnvz44487Ojo2btw4IiLiwoULuiPfvXt35syZrVq1cnFxcXd3\n79Kly4oVK/Lz8ysF4Ovr6+Li8uDBA/2N1f69UXd3944dO+oeZmVljR8/vnHjxmq1umXLlh98\n8IHwkVo1ffvt27dfeOEFT09Pd3f3vn37Ch9Vv2zZMjc3t6ZNm2ZnZ5eUlIwePdrZ2bl+/fpf\nffVV1Z/XwBmrqulPpmZnZ8fExPj4+Dg6Onp4eISFhel/Gn7VGLRabVxcXIcOHZydnZs0aTJl\nypS8vDwvL6+goCADJzIlgVWdOXNGuHzl5OToNgq3fKKionRb9NNSNeBanNrw59hVPUW1WTKc\nWK2xtV2V8Dl21Vq1apXWhBUl/BRpaWkzZ84U/rhChw4d4uLiKv2YwufYGT2a1tgKNJqBqkyv\nd8PlbOIy0D9geHg4Ed27d2/mzJmPP/64RqN54okntm7dqr+/4ZVvtGANX6BqVyOgZCotYywX\nQCGuX7/eqlWryMjIDz/8UOxYACwsIiIiISHh+vXr3t7eYscCAFyYsQMwbs6cOUQ0a9YssQMB\nAAAwBDN2ADVKT0/fv39/YmLi/v37lyxZUukTXAEAAOwNGjuAGv3222/Tp09v1KjRihUrFi5c\nKHY4AAAARmDGDgAAAEAmMGMHAAAAIBNo7AAAAABkAo0dAAAAgEygsQMAAACQCTR2AAAAADKB\nxg4AAABAJtDYAQAAAMgEGjsAAAAAmUBjBwAAACATaOwAAAAAZAKNHQAAAIBMoLEDAAAAkAk0\ndgAAAAAygcYOAAAAQCbQ2AEAAADIBBo7AAAAAJlAYwcAAAAgE2jsAAAAAGQCjR0AAACATKCx\nAwAAAJAJNHYAAAAAMoHGDgAAAEAm0NgBAAAAyAQaOwAAAACZQGMHAAAAIBNo7AAAAABk4v8A\nmsle6FzwceAAAAAASUVORK5CYII=",
            "text/plain": [
              "Plot with title “Laplace Q-Q Plot”"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A9TpB3-L7XPB"
      },
      "source": [
        "**Bayesian CAPM where Idiosyncratic Return follows Laplace Distribution!**\n",
        "\n",
        "- We want to model the relationship as\n",
        "$$\n",
        "r_t^{\\text{portf}}=\\alpha+\\beta~r_t^{\\text{S&P 500}} + \\epsilon\n",
        "$$\n",
        "where \n",
        "  - $r_t^{\\text{portf}}$ is portfolio return\n",
        "  - $r_t^{\\text{S&P 500}}$ is market index return\n",
        "  - $\\epsilon \\sim Laplace(0,\\lambda)$\n",
        "\n",
        "- That is the idiosyncratic Return follows Laplace Distribution\n",
        "\n",
        "- $$\\alpha \\sim Cauchy(0,1)$$\n",
        "- $$\\beta \\sim Cauchy(0,1)$$\n",
        "- $$\\lambda \\sim \\text{Half-Cauchy}(0,1)$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MyOeOfdQ8VD9"
      },
      "source": [
        "**Write log-likelihood function**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QJhESFhD8Uiu"
      },
      "source": [
        "log_likelihood = function(param,y,x){\n",
        "  a = param[1]\n",
        "  b = param[2]\n",
        "  lambda = param[3]\n",
        "  pred = a + b*x \n",
        "  likelihoods = -log(2*lambda)-abs(y-pred)/lambda\n",
        "  sumll = sum(likelihoods)\n",
        "  return(sumll)   \n",
        "}\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XQ3k0Ib68cOT"
      },
      "source": [
        "**Write log-prior function**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mjF_DEyK8eyQ"
      },
      "source": [
        "dHalfCauchy = function(theta,log=FALSE){\n",
        "  if(log==FALSE){\n",
        "    return(2/(pi*(1+theta^2)))\n",
        "  }else{\n",
        "    return(log(2)-log(pi)-log(1+theta^2))\n",
        "  }\n",
        "}\n",
        "\n",
        "log_prior = function(param,x){\n",
        "  a = param[1]\n",
        "  b = param[2]\n",
        "  lambda = param[3]\n",
        "  a_prior = dcauchy(a,0,1,log = T) \n",
        "  b_prior = dcauchy(b,0,1,log = T) \n",
        "  scale_prior = dHalfCauchy(theta=lambda,log = T)\n",
        "  \n",
        "  return(a_prior+b_prior+scale_prior)\n",
        "}\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6s475ulx85cE"
      },
      "source": [
        "**Write log-posterior function**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KWEKjZzv87Uf"
      },
      "source": [
        "log_posterior = function(param,y,x){\n",
        "  like = log_likelihood(param=param,y=y,x=x)\n",
        "  prior = log_prior(param=param,x=x)\n",
        "  post  = like + prior\n",
        "  return ( post )\n",
        "}"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "t8qyRt5J9EJp"
      },
      "source": [
        "**Bayesian CAPM Model Fitting with Metropolis-Hastings Algorithm**\n",
        "\n",
        "- Use conjugate posterior or posterior with flat prior as **proposal function**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BaQ8_Pnp9Dn9"
      },
      "source": [
        "proposalfunction = function(param,x){\n",
        "  X=cbind(rep(1,length(x)),x)\n",
        "  S=param[3]*solve(t(X)%*%X)\n",
        "  prop = c(rmvnorm(1\n",
        "                  ,mean = param[1:2]\n",
        "                  ,sigma = S)\n",
        "          ,rgamma(1,param[3]*5,5))\n",
        "  return(prop)\n",
        "}\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hg0cLKUbNqjw"
      },
      "source": [
        "**Run Metropolis**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ymm-PYyaNoFk"
      },
      "source": [
        "run_metropolis = function(startvalue, N.sim, burnin){\n",
        "  iterations = N.sim + burnin\n",
        "  chain = array(dim = c(iterations+1,3))\n",
        "  chain[1,] = startvalue\n",
        "  for (i in 1:iterations){\n",
        "    proposal = proposalfunction(chain[i,],x=x)\n",
        "    \n",
        "    probab = exp(log_posterior(param=proposal\n",
        "                               ,y=y,x=x) \n",
        "                 - log_posterior(param=chain[i,]\n",
        "                                 ,y=y,x=x))\n",
        "    \n",
        "    if (runif(1) < probab){\n",
        "      chain[i+1,] = proposal\n",
        "    }else{\n",
        "      chain[i+1,] = chain[i,]\n",
        "    }\n",
        "  }\n",
        "  return(chain)\n",
        "}\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xvv9WjhKNyiZ"
      },
      "source": [
        "y=ln_rt_portf\n",
        "x=ln_rt_snp500\n",
        "startvalue = c(0,1,0.1)\n",
        "N.sim=30000\n",
        "burnin=1000\n",
        "\n",
        "set.seed(1)\n",
        "chain = run_metropolis(startvalue=startvalue\n",
        "                       ,N.sim=N.sim\n",
        "                       ,burnin=burnin)\n",
        "colnames(chain)=c(\"alpha\",\"beta\",\"lambda\")\n",
        "chain=chain[(burnin+1):nrow(chain),]\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "90vkszX1OXA0",
        "outputId": "83bbc92b-f237-43d5-c3e2-b29b4d509c1e"
      },
      "source": [
        "apply(chain,2,mean)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "     alpha       beta     lambda \n",
              "0.04064922 1.08443496 0.49318034 "
            ],
            "text/latex": "\\begin{description*}\n\\item[alpha] 0.0406492170285312\n\\item[beta] 1.08443495610286\n\\item[lambda] 0.493180338630617\n\\end{description*}\n",
            "text/markdown": "alpha\n:   0.0406492170285312beta\n:   1.08443495610286lambda\n:   0.493180338630617\n\n",
            "text/html": [
              "<style>\n",
              ".dl-inline {width: auto; margin:0; padding: 0}\n",
              ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
              ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
              ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
              "</style><dl class=dl-inline><dt>alpha</dt><dd>0.0406492170285312</dd><dt>beta</dt><dd>1.08443495610286</dd><dt>lambda</dt><dd>0.493180338630617</dd></dl>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "io72P_FzOgxk",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 123
        },
        "outputId": "c0f1f5fd-9634-4733-910f-ea6045eeab97"
      },
      "source": [
        "apply(chain,2,quantile,prob=c(0.025\n",
        "                              ,0.975))\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "      alpha       beta      lambda   \n",
              "2.5%  -0.03079133 0.9992101 0.4368567\n",
              "97.5%  0.10515674 1.1711139 0.5601301"
            ],
            "text/latex": "A matrix: 2 × 3 of type dbl\n\\begin{tabular}{r|lll}\n  & alpha & beta & lambda\\\\\n\\hline\n\t2.5\\% & -0.03079133 & 0.9992101 & 0.4368567\\\\\n\t97.5\\% &  0.10515674 & 1.1711139 & 0.5601301\\\\\n\\end{tabular}\n",
            "text/markdown": "\nA matrix: 2 × 3 of type dbl\n\n| <!--/--> | alpha | beta | lambda |\n|---|---|---|---|\n| 2.5% | -0.03079133 | 0.9992101 | 0.4368567 |\n| 97.5% |  0.10515674 | 1.1711139 | 0.5601301 |\n\n",
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A matrix: 2 × 3 of type dbl</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>alpha</th><th scope=col>beta</th><th scope=col>lambda</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>2.5%</th><td>-0.03079133</td><td>0.9992101</td><td>0.4368567</td></tr>\n",
              "\t<tr><th scope=row>97.5%</th><td> 0.10515674</td><td>1.1711139</td><td>0.5601301</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Rqk3N6cXOcla",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "da5e6db6-c5b5-450d-da5f-452c9f965b06"
      },
      "source": [
        "apply(chain,2,sd)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "     alpha       beta     lambda \n",
              "0.03448685 0.04442147 0.03143131 "
            ],
            "text/latex": "\\begin{description*}\n\\item[alpha] 0.0344868461158168\n\\item[beta] 0.0444214667709812\n\\item[lambda] 0.031431306222036\n\\end{description*}\n",
            "text/markdown": "alpha\n:   0.0344868461158168beta\n:   0.0444214667709812lambda\n:   0.031431306222036\n\n",
            "text/html": [
              "<style>\n",
              ".dl-inline {width: auto; margin:0; padding: 0}\n",
              ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
              ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
              ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
              "</style><dl class=dl-inline><dt>alpha</dt><dd>0.0344868461158168</dd><dt>beta</dt><dd>0.0444214667709812</dd><dt>lambda</dt><dd>0.031431306222036</dd></dl>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8xat6lOXOVB7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "917cfc47-b1b9-47ff-ea11-ee1a79476251"
      },
      "source": [
        "par(mfrow=c(3,2))\n",
        "plot(ts(chain[,\"alpha\"])\n",
        "     ,ylab = \"alpha\")\n",
        "plot(density(chain[,\"alpha\"])\n",
        "     ,main = \"\"\n",
        "     ,xlab = \"alpha\")\n",
        "plot(ts(chain[,\"beta\"])\n",
        "     ,ylab = \"beta\")\n",
        "plot(density(chain[,\"beta\"])\n",
        "     ,main = \"\"\n",
        "     ,xlab = \"beta\")\n",
        "plot(ts(chain[,\"lambda\"])\n",
        "     ,ylab = \"lambda\")\n",
        "plot(density(chain[,\"lambda\"])\n",
        "     ,main = \"\"\n",
        "     ,xlab = \"lambda\")\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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qBsEbwMSUpGOkb606ZWpZO0q/zIeSHP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LhjS/YlpZ383unjHH8upA2lbQ3TPFIs9lcAbCYS2FxYIgfR12HsIIBikrRQXS/dxb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\nhYVCGCQWFgr5P92Xkfsi2fvRAAAAAElFTkSuQmCC",
            "text/plain": [
              "Plot with title “”"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xSMM4Ca5Outl"
      },
      "source": [
        "**What is the $\\mathbb{P}(\\alpha >0|y,x)$?**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xGI7QQeKOuKU",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "0b0fd9db-53fb-465d-b08d-427a689b89a1"
      },
      "source": [
        "alpha_star = chain[,'alpha']\n",
        "no.of.alpha.gt.zero = length(alpha_star[alpha_star>0])\n",
        "total.no.of.alpha = length(alpha_star)\n",
        "\n",
        "prob_a_gt_zero = (no.of.alpha.gt.zero/total.no.of.alpha)*100\n",
        "\n",
        "round(prob_a_gt_zero,4)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "[1] 88.2804"
            ],
            "text/latex": "88.2804",
            "text/markdown": "88.2804",
            "text/html": [
              "88.2804"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}