When Finance Meets Statistics - Chapter 1 .ipynb

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   "source": [
    "# Fundamentals of Statistical Finance"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27f84dea",
   "metadata": {},
   "source": [
    "## Idea\n",
    "\n",
    "When we speak about some mathematics in Finance, we know that it has something to do with data. That is correct. Although a lot of people are very interested in quatitative finace, they seem to know a little about it. There are few miscenceptions as well. First, they think it's just some basic number crunching but it's not true. Second, they think it's a lot of deep mathematics but unfortunately, that is not a proper idea as well. Third, they think it's related to machine learning but trust me, ML is just 0.01% of quantitative finance. \n",
    "\n",
    "I am starting to write this series of notebooks with pyhton codes and some dummy data to show example of most diffcult concepts of quantitative finance aiming to help best finance professionals. That is why my series is named as \"When Finance meets Statistics\". "
   ]
  },
  {
   "cell_type": "markdown",
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   "metadata": {},
   "source": [
    "## What are the problems? \n",
    "\n",
    "I have hired and trained more than 30 data analysts and scientists in my short career span of 6 years. In my opnion, the biggest problem in any analysts job is interpretation of data and analysis. The interpretation is the first stage of communicaton. If you are not being able to interpret data and analysis well, you won't be able to communicate it better. As a result, all of your tools, ML magic, analysis and skills will seem pretty useless. So, this is the problem definition I am trying to solve for here. I will largely focus on right interpretation of data and statistical analysis.  \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1612c9f",
   "metadata": {},
   "source": [
    "## How do we do it? \n",
    "\n",
    "First, I will go through some very fundamental ideas of statistics and how they can be used in finance. Second, I will take an example dataset to apply those ideas. Third, we will interpret data in very detailed format - actually this is the oart where I will put 80% efforts so that when you use any tool, you know what the results are telling is. We need to understand the story behind these financial data and only then we can make informed decisions. \n",
    "\n",
    "For every chapter, I will take a dataset and use Python as a coding language. Although I don't use Python for statistics a lot, I hope I can do it for financial statitics but if you find any issues with my codes, please contact me at amon163c@gmail.com - that would help me to improve as well. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5ce6f9c",
   "metadata": {},
   "source": [
    "## Contents \n",
    "\n",
    "Chapter 1: Fundamentals of Statistical Finance\n",
    "\n",
    "Chapter 2: Martingales, Random Walks and Time Series models for Statistical Finance \n",
    "\n",
    "Chapter 3: Capital Asset Pricing Models and Hedge Models\n",
    "\n",
    "Chapter 4: Brownian Motion, Black Scholes Model and Some Advanced applications\n",
    "\n",
    "Chapter 5: Machine Learning Applications (Case studies) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe9e1a63",
   "metadata": {},
   "source": [
    "## Chapter 1:  Fundamentals of Statistical Finance\n",
    "\n",
    "In the first secion, we will use the bitcoin's daily price data of 4 years from 2019 to 2022. We can use 2 types of daily returns (1) discrete returns (2) continuous returns. I have used dicrete returns for my analysis but I am sure you will find similar results for continuous returns also. \n",
    "\n",
    "First, I will analyze the distribution of daily returns and try to interpret what it means - in this part, we try to build story for each and every detail of the data. \n",
    "\n",
    "So, I am loading all necessary packages first and then let's have look at the data first. \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
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   "id": "36c2a882",
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   "source": [
    "#import all necessary libraries\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import statsmodels.api as sm\n",
    "from scipy import stats as ss\n",
    "from scipy.stats import shapiro,t\n",
    "from sklearn.model_selection import train_test_split\n",
    "import numpy as np\n",
    "\n",
    "sns.set_style('whitegrid')\n",
    "np.random.seed(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7b1932b3",
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>price</th>\n",
       "      <th>open</th>\n",
       "      <th>high</th>\n",
       "      <th>low</th>\n",
       "      <th>change_pct</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12/31/2022</td>\n",
       "      <td>16537.4</td>\n",
       "      <td>16607.2</td>\n",
       "      <td>16635.9</td>\n",
       "      <td>16487.3</td>\n",
       "      <td>-0.0042</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12/30/2022</td>\n",
       "      <td>16607.2</td>\n",
       "      <td>16636.4</td>\n",
       "      <td>16644.4</td>\n",
       "      <td>16360.0</td>\n",
       "      <td>-0.0018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12/29/2022</td>\n",
       "      <td>16636.4</td>\n",
       "      <td>16546.2</td>\n",
       "      <td>16659.1</td>\n",
       "      <td>16496.6</td>\n",
       "      <td>0.0055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12/28/2022</td>\n",
       "      <td>16546.2</td>\n",
       "      <td>16705.9</td>\n",
       "      <td>16781.1</td>\n",
       "      <td>16474.2</td>\n",
       "      <td>-0.0096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12/27/2022</td>\n",
       "      <td>16706.1</td>\n",
       "      <td>16918.2</td>\n",
       "      <td>16964.0</td>\n",
       "      <td>16610.1</td>\n",
       "      <td>-0.0125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1456</th>\n",
       "      <td>1/5/2019</td>\n",
       "      <td>3785.4</td>\n",
       "      <td>3802.8</td>\n",
       "      <td>3846.7</td>\n",
       "      <td>3769.0</td>\n",
       "      <td>-0.0046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1457</th>\n",
       "      <td>1/4/2019</td>\n",
       "      <td>3802.7</td>\n",
       "      <td>3780.5</td>\n",
       "      <td>3823.9</td>\n",
       "      <td>3720.0</td>\n",
       "      <td>0.0060</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1458</th>\n",
       "      <td>1/3/2019</td>\n",
       "      <td>3780.1</td>\n",
       "      <td>3874.1</td>\n",
       "      <td>3875.8</td>\n",
       "      <td>3753.0</td>\n",
       "      <td>-0.0242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1459</th>\n",
       "      <td>1/2/2019</td>\n",
       "      <td>3873.8</td>\n",
       "      <td>3809.7</td>\n",
       "      <td>3894.8</td>\n",
       "      <td>3768.1</td>\n",
       "      <td>0.0169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1460</th>\n",
       "      <td>1/1/2019</td>\n",
       "      <td>3809.4</td>\n",
       "      <td>3709.5</td>\n",
       "      <td>3814.3</td>\n",
       "      <td>3664.4</td>\n",
       "      <td>0.0269</td>\n",
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       "<p>1461 rows × 6 columns</p>\n",
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      "text/plain": [
       "            Date    price     open     high      low  change_pct\n",
       "0     12/31/2022  16537.4  16607.2  16635.9  16487.3     -0.0042\n",
       "1     12/30/2022  16607.2  16636.4  16644.4  16360.0     -0.0018\n",
       "2     12/29/2022  16636.4  16546.2  16659.1  16496.6      0.0055\n",
       "3     12/28/2022  16546.2  16705.9  16781.1  16474.2     -0.0096\n",
       "4     12/27/2022  16706.1  16918.2  16964.0  16610.1     -0.0125\n",
       "...          ...      ...      ...      ...      ...         ...\n",
       "1456    1/5/2019   3785.4   3802.8   3846.7   3769.0     -0.0046\n",
       "1457    1/4/2019   3802.7   3780.5   3823.9   3720.0      0.0060\n",
       "1458    1/3/2019   3780.1   3874.1   3875.8   3753.0     -0.0242\n",
       "1459    1/2/2019   3873.8   3809.7   3894.8   3768.1      0.0169\n",
       "1460    1/1/2019   3809.4   3709.5   3814.3   3664.4      0.0269\n",
       "\n",
       "[1461 rows x 6 columns]"
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     "output_type": "execute_result"
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   ],
   "source": [
    "#read the csv and save if needed\n",
    "BCX = pd.read_csv(\"BCX1822V.csv\")\n",
    "BCX"
   ]
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    "The first step of our analysis would be doing descriptive analysis of daily returns. This will include: \n",
    "\n",
    "1. Mean\n",
    "2. Median\n",
    "3. Percentiles\n",
    "4. Variance and volatility of returns\n",
    "5. Skewness and Kurtosis\n",
    "6. Low and high expected shortfalls "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3ba9e4e4",
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Summary statistics:\n",
      "count    1461.000000\n",
      "mean        0.001763\n",
      "std         0.038003\n",
      "min        -0.391800\n",
      "25%        -0.014900\n",
      "50%         0.000700\n",
      "75%         0.018500\n",
      "max         0.194100\n",
      "Name: change_pct, dtype: float64\n",
      "DescribeResult(nobs=1461, minmax=(-0.3918, 0.1941), mean=0.0017625598904859687, variance=0.0014442624671411023, skewness=-0.5176255603243027, kurtosis=10.243963228110324)\n",
      "Expected Shortfall for lower Q: -0.086\n",
      "Expected Shortfall for Higher Q: 0.094\n",
      "volatility: 0.603\n"
     ]
    }
   ],
   "source": [
    "#function for all key summary statistics\n",
    "def summary_statistics(df):\n",
    "    five_pctl = df.quantile(0.05)\n",
    "    nintyfive_pctl = df.quantile(0.95)\n",
    "    esfL = (df[df <= five_pctl]).mean()\n",
    "    esfH = (df[df >= nintyfive_pctl]).mean()\n",
    "    print(\"Summary statistics:\")\n",
    "    print(df.describe())\n",
    "    print(ss.describe(df))\n",
    "    print(\"Expected Shortfall for lower Q:\",round(esfL,3))\n",
    "    print(\"Expected Shortfall for Higher Q:\",round(esfH,3))\n",
    "    volatility = (df.std())*np.sqrt(252)\n",
    "    print(\"volatility:\", round(volatility,3))\n",
    "    \n",
    "#we run this fnction over our dataset for daily returns of bitcoins\n",
    "summary_statistics(BCX[\"change_pct\"])  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8e80dbe",
   "metadata": {},
   "source": [
    "### Interpretations \n",
    "\n",
    "1. Average daily return is 0.17% and median daily return is 0.07% with daily standart deviation of 3.8% whiic already indicates a low daily return and high volatility. \n",
    "2. The skewness (=-0.517) of returns is left-skewed and the curve is LeptoKurtic because Kurtosis is 10.24 which is greater than Kurtosis of a Normal distribution. A leptokurtic distribution indicates that the data have more outliers or extreme values than a normal distribution. So, this data is highly peaked and has heavier tails. This is very common in financial data. \n",
    "3. Expected shortfall is defined as mean value of extreme gains or losses beyond a certain level. We have used 5% as the threshold for both sides. So, there is a 5% probability that your daily losses will be more than 8.6% and also there is a 5% probability that your daily gains will be more than 9.4%. So this stock is almost equally likely for extreme gains or losses. \n",
    "4. The yearly volatility of the stock is 0.603 or 60.3% - this is insanely big for stock market and just looking at this data we can say this is a very very risky stock to add in your portfolio. \n",
    "\n",
    "\n",
    "Theoretically, we model daily returns as normally distributed data. In books they use: Return ~ N(Mu, Sigma) to indicate this. But, when you are an analyst if you believe such stupid thing, it will be a mistake. So, we need to check this. We already have seen that return distribution is slightly left-skewed and Leptokurtic which indicates it might fit well actually but we will dig it deeper and check. \n",
    "\n",
    "First, we first plot a histogram of daily returns. Then, we plot Kernel density of returns along with a normal distribution. To plot the sample normal distrbution, we use metrics from emphirical data which means: number of samples = 1461, mean = 0.0017, sigma = 0.001444. The comparison between these two will be interesting. "
   ]
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\n",
      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#visual inspection of normality of returns\n",
    "def visual_inspection_of_normality(df):\n",
    "    plt.rcParams[\"figure.figsize\"] = (20,6)\n",
    "    plt.hist(BCX[\"change_pct\"], bins = 100)\n",
    "    plt.title(\"hisogram of daily returns\")\n",
    "    mu = df.mean()\n",
    "    var = df.std()\n",
    "    nd = np.random.normal(loc=mu, scale= var, size=1471)\n",
    "    plt.show()\n",
    "    sns.kdeplot(np.array(nd), label = \"Normal Dist\").set(title = \"Normal Dist. vs True Returns\")\n",
    "    sns.kdeplot(np.array(df), label = \"True Returns\")\n",
    "    plt.rcParams[\"figure.figsize\"] = (20,6)\n",
    "    plt.legend()\n",
    "    \n",
    "#we run this function for our dataset for daily returns of bitcoins\n",
    "visual_inspection_of_normality(BCX['change_pct'])   "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f32654fe",
   "metadata": {},
   "source": [
    "The first figure shows that daily returns indeed has a bell-shape which indicates some kind of unknown randomness. The second figure however potrays what we have already interpreted from the descriptive statistics. But still it is not convincing to belive that daily returns are not normally distributed. \n",
    "\n",
    "That being said, we will apply two statistical theory to know more about this. \n",
    "\n",
    "1. QQ plot - this plots emphical data comparing a nomral distribution also but in a better way. \n",
    "2. Shapiro Test - this is a very strong test to check normality of data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "id": "24314cf9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test-1: QQ plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test-2: Shapiro Test\n",
      "Shapiro-Wilk test statistic:  0.9163883328437805\n",
      "p-value:  1.1488818267766204e-27\n",
      "Sample does not look Gaussian (reject H0)\n"
     ]
    }
   ],
   "source": [
    "#is the daily returns are truly random? \n",
    "def check_normality_of_returns(df): \n",
    "    print(\"test-1: QQ plot\")\n",
    "    sm.qqplot(df, line = '45', fit = True)\n",
    "    plt.title(\"QQ plot of daily returns\")\n",
    "    plt.show()\n",
    "    print(\"Test-2: Shapiro Test\")\n",
    "    stat, p = shapiro(df)\n",
    "    print('Shapiro-Wilk test statistic: ', stat)\n",
    "    print('p-value: ', p)\n",
    "    alpha = 0.05\n",
    "    if p > alpha:\n",
    "        print('Sample looks Gaussian (fail to reject H0)')\n",
    "    else:\n",
    "        print('Sample does not look Gaussian (reject H0)')\n",
    "\n",
    "#we run this fnction over our dataset for daily returns of bitcoins\n",
    "check_normality_of_returns(BCX['change_pct'])    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83c92528",
   "metadata": {},
   "source": [
    "Both QQ plot and Shapiro test provides enough evidence to say that daily return is not normally distributed. From QQ plot we can see that, ~70% of data follows a normal distribution but then it starts to deviate. Moreover, Shapiro test strongly rejects normality. \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "0fd9cb42",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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idhrzVI7CYiQSADQpFJEAAACApiJtlSTDV0AKCTU7jXm6DJcsNunAeslVaHYaAECFWhWRNmzY0Ng5AAAAABy+qHZL5oyQOp0oGZ6KwhoAoCmoVRHpjTfe0OTJk/Xuu+8qPz+/sTMBAAAALVNlEaklr4dUiXWRAKDJqVURae7cuXr99ddlsVj0pz/9SXfccYdWrlzZ2NkAAACAlsNdJu1b7dtu6SORJNZFAoAmqNZrImVlZWn//v3Kzc1VmzZt9MUXX+jOO+9szGwAAABAy3FwveQulWISpPB2ZqcxX2URKW2V5Ck3NwsAQJJkr02jSZMmKTQ0VJMnT9af/vQnORwOSdI111xzzHN++eUXzZkzR/Pnz1dKSoruueceWSwW9enTR3/+859ltf5avyotLdXMmTOVnZ2t8PBwPfXUU2rbtu1xfmkAAABAEKkccVNZPGnpItpL7XpL2Tt8BbYuw8xOBAAtXq1GIt1///2aP3++LrzwQjkcDv3000+SpHnz5h21/euvv67Zs2fL5XJJkp544gnddttteu+992QYhpYuXVql/YIFC5SQkKD33ntPEyZM0CuvvHI8XxMAAAAQfPyLalNE8vNPaWNdJABoCqotIq1evVoLFy7UXXfdpUWLFmnRokV677339PDDD1d70fj4eL344ov+15s2bdJJJ50kSRo7dqx+/PHHKu3XrFmjMWPG+I8vX868ZwAAALQghnHYotoUkfz8i2vz+wEANAXVTmeLiopSVlaWysrKlJmZKUmyWCyaOXNmtRcdP3680tLS/K8Nw5DFYpEkhYeHq6CgoEr7wsJCRUZGHvP4sbhcLiUnJ9eqbSCUlpY2qTxATeizCEb0WwQb+ixqw1GwV72Ks+QObavt6S4p48g+4wltrayszDpfu6ysXZ3Oc7vd/vZ1Pbe+9zxcXl6kCtNTJEkh5bHqLcm963tt37xZqvidAjgc32cRbIK5z1ZbREpISFBCQoImT56s9u3b1/smh69/VFRUpKioqCrHIyIiVFRUdMzjx+J0OpWYmFjvXA0tOTm5SeUBakKfRTCi3yLY0GdRKz+vkSTZe4xWYv/+R22SmlOsmJjYOl/a4Qip03lZWZn+9nU9t773PFx0dLS69ujke2H0k75tL3tRhhLbO6SY3vW6Jpo3vs8i2ARDnz1Wkava6Wy33nqrJOnSSy/VqaeeWuVRF/3799fKlSslScuWLdPw4cOrHB86dKi+/fZb//Fhw1g0DwAAAC2If1HtU8zN0dRYLIeti8SUNgAwW7VFpBdeeEGS9P333x/xqIu7775bL774oqZMmaLy8nKNHz9ekjR9+nSVlZXp8ssv1/bt23X55Zdr0aJFuvnmm+v55QAAAABBKKVizVDWQzqSf10kFtcGALNVO52t0o8//ii32y3DMPTII4/oT3/6ky688MJqz4mLi9PixYslST169NC77757RJs33njDv11ZsAIAAABalPwDUs4uyREpdTzR7DRNj38k0o/VtwMANLpqRyJVmjt3rrp376533nlHCxYs0MKFCxs7FwAAANAypPzge44/WbLV6m+8LUvHQVJIuK/QVpBudhoAaNFqVUQKDQ1Vu3btZLfbFRsb6/+kNQAAAADHqbKI1G2UuTmaKptd6jrCt53KlDYAMFOtikgRERH6wx/+oHPPPVf/+Mc/1LZt28bOBQAAALQMleshdavbh9e0KKyLBABNQq3Gyz7//PPau3evevfurW3btmnSpEmNnQsAAABo/oqypMwtkj1M6jzE7DRNV+W6SCmsiwQAZqpVESk7O1vffPONPv/8c/8+PkENAAAAOE6VRZGuIyS7w9wsTVncCMlikw6ul1wFkjPS7EQA0CLVajrbn/70JxUWFiomJsb/AAAAAHCc/OshMZWtWo5wqdOJkuGV0labnQYAWqxajUQKDw/XjBkzGjsLAAAA0LLsYVHtWos/Rdq/1rcuUq9xZqcBgBapViOR+vTpo08++US7du3S7t27tXv37sbOBQAAADRvJblS+kbJ5pDihpudpumrXBdpL+siAYBZajUSKTk5WcnJyf7XFotF77zzTqOFAgAAAJq9vSskGVKXYVJImNlpmr7KT2hLWy15yiVbiLl5AKAFqlURaf78+SooKNC+ffvUtWtXhYeHN3YuAAAAoHnzr4c02twcwSIiVmrXW8re4Vtgu8swsxMBQItTqyLSF198ob/+9a/yeDw655xzZLFYdOONNzZ2NgAAAKD5qlwPqTtFpFqLH+krIu1dQREJAExQqzWR3nzzTS1evFitW7fWjTfeqK+++qqxcwEAAADNl6tAOvCL72Pr404yO03wqJzSlsK6SABghloVkaxWqxwOhywWiywWi8LCmLMNAAAA1FvqSsnwSJ2HSM4Is9MEj8oi0t4VkmGYmwUAWqBaFZGGDx+uO+64Q+np6XrggQd0wgknNHYuAAAAoPliKlv9tO0phbeXirOk7J1mpwGAFqfGItKWLVtktVq1adMmXXTRRerTp4/uueeeQGQDAAAAmicW1a4fi8W3LpIk7WVKGwAEWrVFpM8++0z33nuvunTpopkzZyoqKkqLFy9mTSQAAACgvlwF0r41vvWQKqdnofYqC2+7vzM3BwC0QNV+Ots777yjd999V61atfLvu+SSS3TDDTfozDPPbPRwAAAAQLOTslzyuqW4EVJolNlpgk/P03zPu7/1rYtksZibBwBakGpHItnt9ioFJEmKiIiQzWZr1FAAAABAs7X7W99zj9PMzRGsYvtJER2kwnQpc6vZaQCgRam2iGQ5RlXf6/U2ShgAAACg2dtVUUTqSRGpXiwWqcdY33ZlQQ4AEBDVTmfbsWOH7rjjjir7DMPQzp18EgIAAABQZ0XZUvoGyR4qxZ1kdprg1eM0acP70u5l0snXm50GAFqMaotIzz333FH3T506tTGyAAAAAM3bnmW+564nSyGh5mYJZpUjkfZ8J3k9kpXlNgAgEKotIp10En8dAQAAABoMU9kaRptuUpvuUu4e6cA6qcswkwMBQMtQbREJAAAAQMPx7PpWNknp7U5WWU5xnc4tc7eMdUm9hqHUWrw3bTqPVkTuHh3a9JUKwhIV4bSrTbgjAAkBoOWiiAQAAAAEQl6abLm75LKFa0FaWxn70up0+nkndGykYE1LablHn244WGO7hPL+Ol9S3qavtMRyiSYOi6OIBACNrNpPZwMAAADQQCqmsqVFD5Nh4W+5xys1ergkqUvBL7J5XSanAYCWgSISAAAAEAgVH0dfWfzA8SlxtFVmq96ye13qVLDR7DgA0CJQRAIAAAAam2H4Po5e0t7oESaHaT5SK97Lrod+MjkJALQMFJEAAACAxpa1XSo4IE9YjLJb9TI7TbOxt7WviBSft8rkJADQMlBEAgAAABpbxVS20q6nShaLyWGaj31RQ+SVTR0LNsviKjA7DgA0exSRAAAAgMZWUURyxZ1qcpDmpcweoYOR/WWVR879K8yOAwDNHkUkAAAAoDF53NIu33pIpV3HmBym+alcYyo0dZnJSQCg+aOIBAAAADSmfWskV57Utpc80fFmp2l29rYeKUkKTfmfuUEAoAWgiAQAAAA0pp1Lfc+9zzQ3RzN1IPIEuWzhCsndIR3aa3YcAGjWKCIBAAAAjWnHV77n3meYm6OZ8lrt/ilt2rHU3DAA0MxRRAIAAAAaS3GOtG+tZHNI3VlUu7GktDnFt1FZsAMANAp7oG60ZMkSffTRR5Ikl8ul5ORk/fDDD4qKipIkPfroo1q7dq3Cw8MlSa+88ooiIyMDFQ8AAABoeDu/lmRI8adIjnBJxWYnapb2tK4oIu1eJnnKJVuIuYEAoJkKWBHp0ksv1aWXXipJeuihh3TZZZf5C0iStGnTJv39739X27ZtAxUJAAAAaFw7v/Y9M5WtURWEdlJ5m96+dZHSVkndRpkdCQCapYAVkSpt2LBBO3bs0J///Gf/Pq/Xq5SUFD3wwAPKysrSxIkTNXHixBqvVTmiqakoLS1tUnmAmtBnEYzotwg29NkWzDDUe8sXCpG0y9pDruRkeUJbKysrs16XKytrV69z63qe2+32tw/UPRvi3LyOoxSTu0NZKxcps7hNve6N4MT3WQSbYO6zAS8i/e1vf9NNN91UZV9xcbH+7//+T7///e/l8Xg0bdo0DRw4UP369av2Wk6nU4mJiY0Zt06Sk5ObVB6gJvRZBCP6LYINfbYFO7hRKs2SIjqq58gLJYtFqTnFiomJrdflHI6Qep1b1/OysjL97QN1z4Y412g3Xkp+RzG56xTDf3MtCt9nEWyCoc8eq8gV0IW18/PztXv3bo0cObLK/rCwME2bNk1hYWGKiIjQyJEjtWXLlkBGAwAAABrWzopPCut9hmSxmJulBXB1GSnZnNKBdVJh/UZBAQCqF9Ai0qpVq3TKKaccsX/Pnj26/PLL5fF4VF5errVr12rAgAGBjAYAAAA0rMpPCut1urk5WggjpJXUfbTvxa5vzA0DAM1UQKez7d69W3Fxcf7Xb775puLj43XGGWfo4osv1uTJkxUSEqKLL75Yffr0CWQ0AAAAoOGU5kspyyWLlSJSIPU+07eY+fb/SoMmm50GAJqdgBaR/vCHP1R5/fvf/77Ksd8eBwAAAILSrm8kb7kUf4rUik8fDpg+46Uv7vWNAvO4JVvAl4AFgGYtoNPZAAAAgBZh6+e+54Tx5uZoaWJ6S217SSW5UtpPZqcBgGaHIhIAAADQkLwe33QqSUo4x9wsLVHfc33P2z43NwcANEMUkQAAAICGtG+tVJwlte4mxfYzO03LUzn6aytFJABoaBSRAAAAgIZUOQIm4RzJYjE3S0sUf4rkjJaytko5u8xOAwDNCkUkAAAAoCFtYz0kU9lCpN5n+La3/dfcLADQzFBEAgAAABrKoVQpfaPkiJC6n2p2mparci2qbZ+ZmwMAmhmKSAAAAEBD2f6F77nXOMnuNDdLS9bnLMlilfb8IJXmm50GAJoNikgAAABAQ9lWUUTiU9nM1aqt1PVkyVsu7fza7DQA0GxQRAIAAAAagqtA2vWtJIvU52yz06CykLeVKW0A0FAoIgEAAAANYft/JY9Lih8pRbQ3Ow36XeB73vaZ5Ck3NwsANBMUkQAAAICGkPxv33PihebmgE9Mbyk2USrNk3YvMzsNADQLFJEAAACA41Ve+uvHyVeOgIH5Kgt6lQU+AMBxoYgEAAAAHK9d30jlRVKnE6U23cxOg0qVRaQtn0hej7lZAKAZoIgEAAAAHC+msjVNHU+Q2nSXijKk1J/MTgMAQY8iEgAAAHA8POXS1k9924kXmZsFVVksTGkDgAZkNzsAAAAAEGxyi8pU6HJLkpyp36l9Sa7K2/TWQVtXKaf4mOeVub2BiohKiRdJP77oKyKNf8xXWAIA1AtFJAAAAKCOCl1ufbAmTZI0buditZe0NnyMfqzYdyznndAxAOlQRZfhUmQnKW+vdGCd1HmI2YkAIGgxnQ0AAACoJ4vhUe/s/0mSdrQ73dwwODqr9ddPzNv8sblZACDIUUQCAAAA6qlL/jpFlGcpz9lZGeF9zY6DY+lfsVbVpiWSYZibBQCCGEUkAAAAoJ76Zn4hSdoaezZr7TRl3UZLER2l3D3S/rVmpwGAoEURCQAAAKgHq7dcfbK/liRtiRlvchpUy2qTBlzi297woblZACCIsbA2AAAAUA/xh35SmDtPWa16Kju8t9lxWjyvYSi1mk/Gc3S7QB1W/lXuDR/qwPBZvsJShQinXW3CHYGICQBBjSISAAAAUA/9siqmssWcbXISSFJpuUefbjh47AZGrH4f2kWti/Zpxf/+o7ToYf5DE4fFUUQCgFpgOhsAAABQRxZ3iXplfyuJIlLQsFj8/1aVa1kBAOqGIhIAAABQR6G7l8rhLdbBiP7KC+tqdhzUUmURqU/217J6y01OAwDBhyISAAAAUEettn0kiQW1g012eG9lteqpMHeeuh1aaXYcAAg6FJEAAACAuig5pLA9S2XIom0xZ5qdBnW0taLw1zfzc5OTAEDwoYgEAAAA1MWmJbJ4XEqNHq4iZ3uz06COtsT6iki9c/4nh7vQ5DQAEFwoIgEAAAB1se49SdKm9heaHAT1kR/aRalRwxTidSkh60uz4wBAUKGIBAAAANRW5lYpbZW8IRHa0W6c2WlQT5s7XCBJGpDxH5OTAEBwoYgEAAAA1FbFKKTihIvktoWaHAb1ta3dGSqztlLngvVqU7zH7DgAEDQoIgEAAAC14XFLvyyUJBUlTjE5DI6H2xambTFnSJL6Z35ichoACB4UkQAAAIDa2PWNVHhQattLZZ1GmJ0Gx2lzxZpWiRmfSl6PyWkAIDhQRAIAAABqY90/fM+Dr5AsFnOz4LjtixqsQ6FxiizLUOjeb82OAwBBwR7Im11yySWKiIiQJMXFxemJJ57wH1u8eLEWLlwou92uG264QePGsVAhAAAAmojiHGnLJ5Is0olTJQauBD+LRZvaX6DRe19V+OaF0tALzE4EAE1ewIpILpdLhmFo/vz5RxzLzMzU/Pnz9eGHH8rlcumKK67Q6NGj5XA4AhUPAAAAOLaf35U8ZVLvM6XoOCmn2OxEaACb25+vU/a+prBdn0uFGVJEe7MjAUCTFrDpbFu2bFFJSYmmT5+uadOmad26df5j69ev15AhQ+RwOBQZGan4+Hht2bIlUNEAAACAY/N6pdVv+LaHX2NuFjSoQmdH7W57qizecmntO2bHAYAmL2AjkUJDQ3XNNddo0qRJ2rNnj6699lp9/vnnstvtKiwsVGRkpL9teHi4CgsLa7ymy+VScnJyY8auk9LS0iaVB6gJfRbBiH6LYEOfDX7hB1cqPne3ylt10A5PvJScLE9oa2VlZdb5WmVl7ep13vGcW9fz3G63v32g7tkQ59b3vO9analeOctUvuJ17Wh3jmS11fkaMBffZxFsgrnPBqyI1KNHD3Xr1k0Wi0U9evRQ69atlZmZqU6dOikiIkJFRUX+tkVFRVWKSsfidDqVmJjYmLHrJDk5uUnlAWpCn0Uwot8i2NBnm4FfHpUkhZx8rRIHDJQkpeYUKyYmts6XcjhC6nXe8Zxb1/OysjL97QN1z4Y4t77n5bYbL3f+PIXkpyjRnib1PafO14C5+D6LYBMMffZYRa6ATWf74IMP9OSTT0qS0tPTVVhYqNhY3zf5QYMGac2aNXK5XCooKNDOnTuVkJAQqGgAAADA0eXtk7Z+Jlnt0tBpZqdBY7BYVXhCkm979TxzswBAExewkUgTJ07UrFmzdPnll8tisejxxx/X/PnzFR8frzPOOENJSUm64oorZBiGZsyYIafTGahoAAAAwNGtfUcyPFLiBCmyg9lp0EiKEqeo9Yqnpe1fSrl7pDbdzY4EAE1SwIpIDodDzzzzTJV9Q4cO9W9PnjxZkydPDlQcAAAAoHqecmnt277tESyo3Zx5W8VI/SdIGxZLa96SznzQ5EQA0DQFbDobAAAAEFQ2/0sqOCDFJEjdx5idBo1txB98z2velsqKzc0CAE0URSQAAADgtwxDWv6Sb3vkjZLFYm4eNL6uJ0mdh0olOdIvC8xOAwBNEkUkAAAA4LdSfpT2/yy1aiedONXsNAgEi0UadbNve8Urktdrbh4AaIIoIgEAAAC/tfxl3/OIP0ghYeZmQeAkXixFx0vZO6Rtn5udBgCaHIpIAAAAwOGyd0pbP5Vszl/XyUHLYLNLI//o264sJAIA/CgiAQAAAIdb8YokQxo0WYpob3YaBNqQJMkZJaV875vSCADwo4gEAAAAVCrKln7+h2/7lJvMzQJzhEZJw67ybf/4orlZAKCJoYgEAAAAVFrxiuQukfqcLbVPNDsNzHLyHyWrXdr0kW96IwBAEkUkAAAAwKckV1r5N9/22JnmZoG5ouOkwVdIhlf67hmz0wBAk0ERCQAAAJB8BaSyAqnn76SuJ5mdBmY79XbJYpN+WSjl7jE7DQA0CRSRAAAAgNL8igW1JY29y9wsaBra9pAGTZEMj/Tds2anAYAmgSISAAAA8NNrUmme1O1Uqftos9OgqRhzh2SxSuvekw7tNTsNAJjObnYAAAAAwAy5RWUqdLllKStSpx9fkk1SxtBb5coprvHcMre38QPCfDG9pYGXSRvel75/TrqAEUkAWjaKSAAAAGiRCl1ufbAmTSfvfV1xpbnaHzlIi9K7SxlpNZ573gkdGz8gmoaxM6UNH0hr35FG3yq16W52IgAwDdPZAAAA0GKFledq+L53JUnfd7tJslhMToQmJ7avdOJUyVsuff2Y2WkAwFSMRAIAAECLdXLqPDm8xdrVZrT2RQ81Ow5M4jUMpVYzjdE2ZIY6bfhQlg2LdXDgtSqPHShJinDa1SbcEaiYAGA6ikgAAABokWx5ezXo4IcyZNEP3W4yOw5MVFru0acbDlbTwqKxHSdq2P73VPLZA/rngBckSROHxVFEAtCiMJ0NAAAALVL0iqdkM9xKjj1XWeF9zI6DJu6nuN/LZQtXj0PL1fXQKrPjAIApKCIBAACg5dm/Tq22fiS3JUTL4683Ow2CQGlIa63qcpUk6dSUFyWDT+gD0PJQRAIAAEDLYhjSZ3fJIkO/dJqk/NDOZidCkPi581QVOmLVsTBZAzL+Y3YcAAg4ikgAAABoWdYvklJXytMqViu6Xmt2GgQRty1My7rfKkk6NeUlWVx5JicCgMBiYW0AAAC0HKX50pcPSJIOjbpPZSURJgdCsNkaM16DDi5RXP7Pcq/4i1JPe7Re1+GT3QAEI4pIAAAAaDmW/UUqTJfiRqg4cZK0dr/ZiRBsLBZ90/NOXbkuSZHr39I/LWcqO7x3nS/DJ7sBCEZMZwMAAEDLkLlVWvFXSRbp3KclCz8Ko36ywhO0vuNlshgejdv1F986WwDQAvB/TgAAADR/Xq/08S2St1waOk3qMtTsRAhyP3b7o9yhbdU1f60GZHxsdhwACAiKSAAAAGj+Vv1dSl0pRXSUznrY7DRoBlz2KGWMfkiSNHb3cwp3ZZqcCAAaH0UkAAAANG+H9kpfPejbPv8ZKay1mWnQjBT0vli72pyqUE+hTt/1FNPaADR7FJEAAADQfBmG9J8ZUnmR1H+ClHiB2YnQnFgsWtrrHrls4eqd860Ssr8yOxEANCqKSAAAAGi+fp4v7fhKCm0tnfcXs9OgGSp0dtB33W+VJI3b9Re1Kss2OREANB6KSAAAAGiesndKn93j2z73aSmivbl50Gxt6DBBe6OHq1V5rs7a8QjT2gA0WxSRAAAA0Px4yqUP/+CbxjZwojRostmJ0JxZrPqiz4MqtUepZ+4PGnxgsdmJAKBRUEQCAABA8/O/J6T9a6XoeN9i2haL2YnQzBU6O+jLXvdJksbseUHtinaYnAgAGh5FJAAAADQvu5dJ3z0rWazSpX/j09gQMDtiTteG9hfLbpTpvG2zZfeUmh0JABqU3ewAAAAAwPHILSpTocstSbIV7FeHxVfLJkN5w/+k/MjBUk7xUc8rc3sDmBItxbc9b1eX/J8VU7xTZ+x8Ql/0eZCRcACaDYpIAAAACGqFLrc+WJMmm7dMkzZcL1tJtlKiT9JHIVNlrEk75nnnndAxgCnRUpTbWuk//Z7S5et/r/6Zn+pg5AD90ok1uQA0DwGbzlZeXq6ZM2fqiiuu0MSJE7V06dIqx9966y2df/75SkpKUlJSknbt2hWoaAAAAGgGxu6eq06FG5Xv7KhP+z4mw2IzOxJaqOzw3vpv7/slSaftflad8n8xOREANIyAjUT6+OOP1bp1a/3lL3/RoUOHNGHCBJ1xxhn+4xs3btRTTz2lgQMHBioSAAAAGtjhU8vqIsJpV5twR73vOyD9Xxp88AO5LSH6T98nVRrSut7XAhrCttiz1algo4YeWKALttyjBSe+pUJnB7NjAcBxCVgR6ZxzztH48eMlSYZhyGar+pehTZs26bXXXlNmZqZ+97vf6frrrw9UNAAAADSQyqlldTVxWFy9i0jOvct0xs4nJElf97pb6ZED6nUdoKF91/1WxRZtVdf8tbo4eYYWD3xd5fZws2MBQL0FrIgUHu77ZllYWKhbb71Vt912W5Xj559/vq644gpFRETo5ptv1jfffKNx48ZVe02Xy6Xk5OTGilxnpaWlTSoPUBP6LIIR/RbBpqX1WU9oa2VlZdb5vLy8SBWmp9T5PEfeLnVfep1shkfL2k7Ut7ZRUi3vX1bWrl5Zj+fcYLin2+32t2/OX2eg7vl2+7v0x5Lb1b5ou87aeKfe7fJneS22evd5HKmlfZ9F8AvmPhvQhbUPHDigm266SVdccYUuvPBC/37DMHTVVVcpMjJSknTaaadp8+bNNRaRnE6nEhMTGzVzXSQnJzepPEBN6LMIRvRbBJuW1mdTc4oVExNb5/Oio6PVtUenup1UkC59PlkqL9S2dmdoTd+ZirHUfslPhyOkXlmP59xguGdWVqa/fXP+OgN3z1h9HPWSLl//e/UtWq2J+W/p655316/P46ha2vdZBL9g6LPHKnIFbGHtrKwsTZ8+XTNnztTEiROrHCssLNQFF1ygoqIiGYahlStXsjYSAAAAjq04R5p/iZS3V64OQ/V5nwelOhSQgEDKC+uqjxOfkdvi0IkHP9TI1NfNjgQA9RKwkUivvvqq8vPz9corr+iVV16RJE2aNEklJSWaMmWKZsyYoWnTpsnhcOiUU07RaaedFqhoAAAACCauAukfE6WMTVJMgrIufFue5FKzUwHV2h91oj7r+4jO3zJLp6S+rkNrO0tn3m52LACok4AVkWbPnq3Zs2cf8/iECRM0YcKEQMUBAABAMCovkd6bKu1bI7WOl5L+Ka+njaS6L+YNBNqOdqfryz73a/z2h9T6+4ek1q2l4dPNjgUAtcaYXwAAAASHsiLpvclSyvdSREdp2sdSdBezUwF1srn9BVra8y7fi//cLq1+09xAAFAHFJEAAADQ9JXmS/MvlXYvk8LbS9P+JbXtYXYqoF7Wd5qkQ6c+IMmQ/nObtPwVsyMBQK1QRAIAAEDTVpwjvXOxlLpCiuoi/f4zqX0/s1MBx6Vg6A3SuU/7XnwxS1r2F3MDAUAtBGxNJAAAAKDOclOkf0ySsrZKrbtJV/1batPN7FTAcfMahlL7JCm8zK42S++Q5etHVZB9QIfGPCRZbcc8L8JpV5twRwCTAsCvKCIBAACgadq3VnpvilSUIbXvL135AWsgodkoLffo0w0HJY1RQsKjGr/9QUX+Mk/pqTv0WcKjcttCj3rexGFxFJEAmIbpbAAAAGh6tnwivXW+r4DU4zRp+ucUkNBsbYs9W0sGvKhSW6R653yriRv/qPCyLLNjAcARGIkEAAAA03kNQ6k5xZLhVdTKZxT907OSpKJ+k5RzxhypOEQqLj7quWVubyCjAo1iX/QwLRo0TxM2/0mdCjfpinVJ+k+/p3QgapDZ0QDAjyISAAAATFda7tFXP+/QudvuV3Tu9/LKqh+63ajVbadJ6zKqPfe8EzoGKCXQuHJa9dDCQW/q/K2zFJf/syZtvF7f9JypDR0ukSwWs+MBANPZAAAAYL7Q9LX6v3VXqmfu9yq1R+mj/s9rddxV/OKMFqfY0U4fDnhFP3eaIpvh1pk7n9C522bL6S4wOxoAMBIJAAAA5rEYHg3f947if/ybLIZH6eH99Em/J5QXGmd2NMA0Xqtd/+t5pw5G9NcZO59Uv6z/qlPBBn2e8LAk/tsAYB6KSAAAADBF65IUnbXjMcXl/yxJWt35Sv3Q7SZ5rSEmJwOahi3tz9PByIE6d9v96li4WZM2XK+C0Fulc2ZLtrr/d5JbVKZCl7vO50U47XwiHABJFJEAAAAQYBbDrWH73tMpqa/J7nWpKKStcs56Tt/lJZodDWhyDoXFa9EJ8zQy9TWdlPaWolc9J6V8KV34vNR1RJ2uVehy64M1aXXOMHFYHEUkAJJYEwkAAAABFFu4VVPXT9eYlBdl97q0qf35envIYhXHjzM7GtBkea12/djtRr0/8K9yR3WTMjZJ886SPrlTKs03Ox6AFoSRSAAAAGh0YeW5GpXyqgam/1NWeZXv7Kives1SSptRZkcDgsa+6GE6eOXXitvwkvTji9Kq16Ut/5HOelgaOFGyMkYAQOPiuwwAAAAajdXr1pD97+nqNZdqUPoSGRaL1naaqncGL6SABNSDEdJKOvNB6fplUtwIqeCAtORa6e9nSCk/mh0PQDPHSCQAAAA0OIvhUd/MLzQy9e9qU5oqSdrTeqS+7XG7clr1MDkd0Ax0GCBN/0L6ZYG09BFp/1rpzXOlfhdIZzwgxfY1OyGAZogiEgAAABqO4VVC1pcaufc1tSvZI0nKCY3Xsh4ztLvNaMliMTcf0JxYbdKQ/5MGXCL98IL04wu+6W1bPpEGXiqNvUtq38/slACaEYpIAAAAOH5ul7ThfXX87nl1zdkmScpzdtaKrn9QcvtzZVj4sRNoNI5wadwsadhV0rK/SGvnSxs/lDYukfpfLI25Xep0otkpATQD/N8cAAAA9VeSK61+U1r5N6nwoEIkFTjaa2XXa7Sp/YXyWkPMTgi0HFGdpQvmSmPukL6fK619R9r8T9+j26kKHXiNLEaiDIutTpf1GoZSc4rrFSnCaVebcEe9zgXQ9FBEAgAAQN0YhpS2ylc82vSR5C7x7W8/QNknXq93C4dTPALMFB0nnf+MdOrt0vKXfcWklO8Vm/K9rg6N0/qOl2pz7PkqcbSt1eVKyz36dMPBekWZOCyOIhLQjFBEAgAAQO2U5ErrF0tr3pIyNv+6v+c4adQtUq/TVZxbIu+aNNMiAjhMdBfpnMel390j/fyu3Mv/qtb5ezV2zwsanfKydrUdq43tL1ZKm5F1Hp0EoGWiiAQAAIBjKyuWtn0mbfhQ2vGl5Cnz7Q+PlQZfKQ2dJrXrZW5GANULjZJOuVEH+iRp7VcLNTD9X+qR+6P6ZH+jPtnfqMDRXltiz9G2mDOVEd6vSSyAn1tUpkKXu1ZtPaGtq0y3Ywod0HgoIgEAAKCqsmJp1ze+RXm3fiaVF1UcsEg9fycNu1rqe75k55c0IKhYbdrV7jTtaneawl2Z6p/5iQakf6w2pakase8djdj3jg6FdtG2dmdqe8yZygjva1pBqdDl1ge1HNWYlZWpmJhY/2um0AGNhyISAAAApLx90rbPfY/dyyR36a/H4kZIAy/zfYx4ZEfzMgJoMEXOWK2Ku1qrulylLvnr1Cf7KyVkLVXr0n06ad/bOmnf28pzdtLuNqMVHnWhbJ6e8thCzY4NwGQUkQAAAFoiV6G0d7m0+1tp1/+kgxuqHu8yTOp3vq941Ka7GQkBBILFon3RQ7Qveoi+7XG7OuevU0LWV+qT/bWiXQc0+OAH0mcf6EarU3ujhyul9UilRg9XdqueksVqdnoAAUYRCQAAoCUoK5L2rZF2f+cbabRvteQ9bL0Re5jU63Sp7zlSn/FSZAfzsgIwhWGxaV/0MO2LHqZves5Uh8Jk9cz9XoNLVyo0c4N65v6gnrk/SJKK7a21L3qoUqOHKS16mLLDejaJtZQANC6KSAAAAM2NYUg5u6TUn6S0VVLaT1L6Zsnw/NrGYvWNNuoxVupxmhQ/UgoJMy8zgKbFYlV65AClRw5QmxP+rP+t2ajuuT8qPm+14vLWKLIsQ32yv1af7K8lSSX2aB2M6K+DkQN1MGKADkYOUGlIa3O/BgANjiISAABAMPOUS5lbpfSNvilpBzdIB9dLJblV21lsUsdBUvdTfYWjbqOk0GhzMgOoN69hVPkksrooc3vrfd9iR4w2d7hImztcJBmGokvT1DVvjeLyVqtr/lpFlGWqx6Hl6nFouf+cQ6FxCskcLnUdJHU4QeowQIrqzIglIIhRRAIAAGjC/B9z7SmXPT9F9pwdCjm0UyE52xWStUkh2dtk8ZYdcZ6nVaw8nUfI0f0kKe4kqfNgyRFet3vWw/H8kgqgZqXlHn264WC9zj3vhAZaGN9iUV5YV+WFddXGjhMkw1Ck66A6FW5Ux4KN6li4We0Lk9W6NE3aliZt++ev54a1kToM9BWU2veXYvpI7XpL4bEUl4AgQBEJAAAgAGpVmPG6ZSs8IHt+qux5e2TP3SlHzg6FH9yiaNc+2Q6fjnaYQ6FxygxPUEZ4grLC+ygzPEEFjg6aOLyrurZtVeesdflo7d9qsF9SAQQPi0UFoZ1UENpJ22LOkiRZvW61K96p82LS1bZwu5S+yTdSsiRX2vOd73E4Z7TUrpe/qBTm7KrYwgjlh3aSyxZZpwJTfUdrRTjtahPuqPN5QEtCEQkAACAACl1u/fOnHQovy1JEWbqiXQcUVXpAUa59Fc8HFOnKkFVHForCJRmyKM/ZSblh3ZQb1k05Yd19BaNWvVVur90IIwAIFK/VrsyIvioacIbaVhazDUPK3+8rKKVvkDK2SNk7fA9XnrR/re8hKUbS/1Vcy2ULV4Gzo/KdnfyPgtDK1x1lMaqOgKzvaK2Jw+IoIgE1oIgEAABQS0cdTWR4ZXXlyVqSI2txpmxF6Yc9Dqpr3n6V/zdLnYsydEtZfrXXN2RRgaO97xejUF/BqHvCiVqa1Vq5oV3lsYXWKW99/xrPlDQAjcJikaK7+B4JZ/+63zCkosxfC0pZ21V8cKtKDmxTpOugnJ4iOYt3KqZ451Ev65FVJXvaqSgkRkWOdmqbE69TClupKCRGhY4YFTl8+0tC2shjdR4z3vGsN8UoJrQUFJEAAAAk3y8x5SWSK18qzZNK833TLoqz/Y+Q3HSVHtinMHeewsoPKcx9SKHlebKqdkUXtyVERY5YFTlilBfaWfnOzv6CUZ6zswqdHeSxVv0lpF3vjsoqqd/6J/X9azxT0gAElMUiRbT3PbqNkiRl5xT7ptUahkLdeYpyHVSkfwTngV9fuw4qzJ2niLJMRZRlSkWScqWRx7hVmTVMJSGtVWpvrZKQaJXYo1Ua0lolIa0Vao3X6gyLSuytVWqPUpk9XC5bhFz2CBmW6n91ZhQTWgqKSAAAIHgZhlR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      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The data does not come from a t-distribution.\n",
      "Test statistic: 0.9163883328437805\n",
      "p-value: 1.1488818267766204e-27\n"
     ]
    }
   ],
   "source": [
    "def checking_t_fit(df):\n",
    "    df1, loc, scale = t.fit(df)\n",
    "    plt.hist(returns, bins=70, density=True, alpha=0.5)\n",
    "    x = np.linspace(returns.min(), returns.max(), 1000)\n",
    "    pdf = t.pdf(x, df1, loc, scale)\n",
    "    plt.plot(x, pdf, linewidth=2)\n",
    "    plt.xlabel('Daily returns')\n",
    "    plt.ylabel('Density')\n",
    "    plt.title('Histogram of daily returns with fitted t-dist.')\n",
    "    plt.legend(['t-distribution', 'Returns'])\n",
    "    plt.show()\n",
    "    stat, p_value = shapiro(df)\n",
    "    crit_val = t.ppf(0.975, df)\n",
    "    if p_value < 0.05:\n",
    "        print('The data does not come from a t-distribution.')\n",
    "    else:\n",
    "        print('The data comes from a t-distribution.')\n",
    "    print('Test statistic:', stat)\n",
    "    print('p-value:', p_value)\n",
    "\n",
    "#we run this fnction over our dataset for daily returns of bitcoins\n",
    "checking_t_fit(BCX[\"change_pct\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "9c090ec6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gaussian AIC: -633.1011633239889, Gaussian BIC: -622.9202806849318\n",
      "t-distribution AIC: -792.5817451647672, t-distribution BIC: -779.0072349793578\n",
      "Conclusion: The t-distribution fits better.\n"
     ]
    }
   ],
   "source": [
    "def gaussianVSt(df):\n",
    "    train_data, test_data = train_test_split(df, test_size=0.15, random_state=42)\n",
    "    mu, std = norm.fit(train_data)\n",
    "    df, loc, scale = t.fit(train_data)\n",
    "    # Calculate AIC and BIC for both models on the test data\n",
    "    gaussian_aic = -2*np.log(norm.pdf(test_data, mu, std)).sum() + 2*3\n",
    "    gaussian_bic = -2*np.log(norm.pdf(test_data, mu, std)).sum() + np.log(len(test_data))*3\n",
    "    t_aic = -2*np.log(t.pdf(test_data, df, loc, scale)).sum() + 2*4\n",
    "    t_bic = -2*np.log(t.pdf(test_data, df, loc, scale)).sum() + np.log(len(test_data))*4\n",
    "    print(f'Gaussian AIC: {gaussian_aic}, Gaussian BIC: {gaussian_bic}')\n",
    "    print(f't-distribution AIC: {t_aic}, t-distribution BIC: {t_bic}')\n",
    "    if gaussian_aic < t_aic and gaussian_bic < t_bic:\n",
    "        print('Conclusion: The Gaussian distribution fits better.')\n",
    "    else:\n",
    "        print('Conclusion: The t-distribution fits better.')\n",
    "\n",
    "#we run this fnction over our dataset for daily returns of bitcoins\n",
    "gaussianVSt(BCX[\"change_pct\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c25f48f",
   "metadata": {},
   "source": [
    "In summary, if the data is generated from a t-distribution, it is still a random variable like the Gaussian distribution, but with slightly different properties due to the shape of the distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9de007f5",
   "metadata": {},
   "source": [
    "But, I think we are left with some interesting questions: \n",
    "\n",
    "1. If this is not normally distributed, what kind of distribution is it following? Can we ever understand its true nature? \n",
    "2. Are daily returns random? If they are random, it means we can't really predict stock prices. \n",
    "3. If it is not random, what factors are actually influencing it? Can we ever solve this puzzle using data? \n",
    "\n",
    "Yes - these are valid questions and we will go through them one by one in future. \n",
    "\n",
    "Thanks for reading this document."
   ]
  }
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