{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sharpe Ratio\n",
    "\n",
    "## Primer \n",
    "\n",
    "Sharpe Ratio is the most common metric used to measure risk in finance.\n",
    "\n",
    "The formula is \n",
    "\n",
    "> (return on portfolio - risk free rate)/standard deviation of the excess return on the portfolio\n",
    "\n",
    "There are tons of resources on the internet about sharpe ratio.\n",
    "\n",
    "[This investopedia page](https://www.investopedia.com/terms/s/sharperatio.asp) is a good introduction.\n",
    "\n",
    "\n",
    "We assume the risk free rate to be zero, then the formula simply becomes mean returns divided by the standard deviation of returns. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import empyrical as ep\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Single stock\n",
    "\n",
    "Let us create a set of 5 stocks with same monthly returns but with different standard deviation for a period of 20 years. Stocks are named a to e with *a* being the stock with least volatility *e* with the highest volatility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>a</th>\n",
       "      <th>b</th>\n",
       "      <th>c</th>\n",
       "      <th>d</th>\n",
       "      <th>e</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>240.000000</td>\n",
       "      <td>240.000000</td>\n",
       "      <td>240.000000</td>\n",
       "      <td>240.000000</td>\n",
       "      <td>240.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.010000</td>\n",
       "      <td>0.010500</td>\n",
       "      <td>0.010000</td>\n",
       "      <td>0.008800</td>\n",
       "      <td>0.007300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.004900</td>\n",
       "      <td>0.010200</td>\n",
       "      <td>0.019400</td>\n",
       "      <td>0.044800</td>\n",
       "      <td>0.098500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-0.003200</td>\n",
       "      <td>-0.014600</td>\n",
       "      <td>-0.042700</td>\n",
       "      <td>-0.106500</td>\n",
       "      <td>-0.264700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.006600</td>\n",
       "      <td>0.003400</td>\n",
       "      <td>-0.002800</td>\n",
       "      <td>-0.022400</td>\n",
       "      <td>-0.063300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.010400</td>\n",
       "      <td>0.010100</td>\n",
       "      <td>0.009500</td>\n",
       "      <td>0.009100</td>\n",
       "      <td>0.002000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.013100</td>\n",
       "      <td>0.017300</td>\n",
       "      <td>0.022600</td>\n",
       "      <td>0.039500</td>\n",
       "      <td>0.074300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>0.023400</td>\n",
       "      <td>0.040400</td>\n",
       "      <td>0.079400</td>\n",
       "      <td>0.134300</td>\n",
       "      <td>0.339900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sharpe</th>\n",
       "      <td>2.029252</td>\n",
       "      <td>1.031875</td>\n",
       "      <td>0.513276</td>\n",
       "      <td>0.197086</td>\n",
       "      <td>0.074137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sharpe_annual</th>\n",
       "      <td>7.029536</td>\n",
       "      <td>3.574519</td>\n",
       "      <td>1.778041</td>\n",
       "      <td>0.682726</td>\n",
       "      <td>0.256819</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                        a           b           c           d           e\n",
       "count          240.000000  240.000000  240.000000  240.000000  240.000000\n",
       "mean             0.010000    0.010500    0.010000    0.008800    0.007300\n",
       "std              0.004900    0.010200    0.019400    0.044800    0.098500\n",
       "min             -0.003200   -0.014600   -0.042700   -0.106500   -0.264700\n",
       "25%              0.006600    0.003400   -0.002800   -0.022400   -0.063300\n",
       "50%              0.010400    0.010100    0.009500    0.009100    0.002000\n",
       "75%              0.013100    0.017300    0.022600    0.039500    0.074300\n",
       "max              0.023400    0.040400    0.079400    0.134300    0.339900\n",
       "sharpe           2.029252    1.031875    0.513276    0.197086    0.074137\n",
       "sharpe_annual    7.029536    3.574519    1.778041    0.682726    0.256819"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x576 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu = 0.01 #monthly returns\n",
    "# Express sigma in relation to mean\n",
    "multipliers = (0.5,1,2,5,10)\n",
    "collect = {}\n",
    "for s,m in zip(list('abcde'), multipliers):\n",
    "    collect[s] = np.random.normal(loc=mu, scale=m*mu, size=240)\n",
    "df = pd.DataFrame(collect)\n",
    "axes = df.plot(kind='kde', title='Distribution of returns', subplots=True, figsize=(8,8))\n",
    "for ax in axes:\n",
    "    ax.axvline(0.01, color='red')\n",
    "ep.cum_returns(df).plot(title='Cumulative returns')\n",
    "s = df.describe().round(4)\n",
    "s = s.append(pd.Series(df.mean()/df.std(), name='sharpe'))\n",
    "s = s.append(pd.Series((df.mean()/df.std())*np.sqrt(12), name='sharpe_annual'))\n",
    "s\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although all values are generated from the normal distribution with a fixed mean of 0.01, we could see a stark difference.\n",
    "\n",
    "\n",
    "The first plot shows the distribution or the spread of returns where **a and b** are close to the mean of 0.01 (the red line) while e is just nowhere. You can also look at the table where the minimum and maximum returns for a are much closer while for e they are much wider. This implies this is very difficult to infer the mean returns of e as they wildly swing from one extreme to other while on the other hand we could be fairly confident with our estimates for a. From a risk perspective, it is very difficult to differentiate the actual mean value of stock e due to its high volatility. A look at the sharpe ratio for the instruments also follow this pattern.\n",
    "\n",
    "A look at the cumulative returns suggests that stock e has left everybody behind and despite wild swings, it is way above; it seems that volatility helps in the long run. But this is only a single simulation of how prices would behave for a given risk/return profile.\n",
    "\n",
    "<!-- TEASER_END -->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multiple stocks\n",
    "\n",
    "Let us now create a simulation of 1000 samples of 240 days for each of the stocks and see how they behave.\n",
    "\n",
    "We assume 5 risk profiles in the market and draw 1000 samples from each of them, so 5000 instruments. We would like to see how well one would have fared had he invested in these instruments. Theroetically, we only have 5 different profiles but let us do the simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_samples(mu=0.01,sigma=0.01,size=1000,n=240):\n",
    "    samples = np.random.normal(loc=mu,scale=sigma,size=(size,n))\n",
    "    return samples\n",
    "\n",
    "mu = 0.01\n",
    "multipliers = (0.5,1,2,5,10)\n",
    "sharpe_ratios_dict = {}\n",
    "returns_dict = {}\n",
    "for s,m in zip(list('abcde'), multipliers):\n",
    "    samples = draw_samples(mu=mu, sigma=m*mu)\n",
    "    sharpe_ratios_dict[s] = (samples.mean(axis=1)/samples.std(axis=1))*np.sqrt(12)\n",
    "    returns_dict[s] = (samples+1).prod(axis=1)\n",
    "sharpe_ratios = pd.DataFrame(sharpe_ratios_dict)\n",
    "returns = pd.DataFrame(returns_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>a</th>\n",
       "      <th>b</th>\n",
       "      <th>c</th>\n",
       "      <th>d</th>\n",
       "      <th>e</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>6.967714</td>\n",
       "      <td>3.486953</td>\n",
       "      <td>1.720395</td>\n",
       "      <td>0.701139</td>\n",
       "      <td>0.347342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.388638</td>\n",
       "      <td>0.269404</td>\n",
       "      <td>0.241078</td>\n",
       "      <td>0.224136</td>\n",
       "      <td>0.229707</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>5.895596</td>\n",
       "      <td>2.539873</td>\n",
       "      <td>1.085622</td>\n",
       "      <td>0.013065</td>\n",
       "      <td>-0.357694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>6.703311</td>\n",
       "      <td>3.296277</td>\n",
       "      <td>1.555953</td>\n",
       "      <td>0.546643</td>\n",
       "      <td>0.189775</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>6.962238</td>\n",
       "      <td>3.472023</td>\n",
       "      <td>1.713981</td>\n",
       "      <td>0.696831</td>\n",
       "      <td>0.342244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>7.207982</td>\n",
       "      <td>3.669762</td>\n",
       "      <td>1.883917</td>\n",
       "      <td>0.846708</td>\n",
       "      <td>0.492320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>8.344530</td>\n",
       "      <td>4.487707</td>\n",
       "      <td>2.659887</td>\n",
       "      <td>1.467446</td>\n",
       "      <td>1.111180</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 a            b            c            d            e\n",
       "count  1000.000000  1000.000000  1000.000000  1000.000000  1000.000000\n",
       "mean      6.967714     3.486953     1.720395     0.701139     0.347342\n",
       "std       0.388638     0.269404     0.241078     0.224136     0.229707\n",
       "min       5.895596     2.539873     1.085622     0.013065    -0.357694\n",
       "25%       6.703311     3.296277     1.555953     0.546643     0.189775\n",
       "50%       6.962238     3.472023     1.713981     0.696831     0.342244\n",
       "75%       7.207982     3.669762     1.883917     0.846708     0.492320\n",
       "max       8.344530     4.487707     2.659887     1.467446     1.111180"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "axes = sns.boxplot(data=sharpe_ratios)\n",
    "axes.set_ylabel('sharpe ratio annualized')\n",
    "sharpe_ratios.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Returns table\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>a</th>\n",
       "      <th>b</th>\n",
       "      <th>c</th>\n",
       "      <th>d</th>\n",
       "      <th>e</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>10.896863</td>\n",
       "      <td>10.933012</td>\n",
       "      <td>10.653770</td>\n",
       "      <td>10.903785</td>\n",
       "      <td>10.821143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.857940</td>\n",
       "      <td>1.624779</td>\n",
       "      <td>3.449507</td>\n",
       "      <td>9.316623</td>\n",
       "      <td>25.780611</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>8.590849</td>\n",
       "      <td>6.487331</td>\n",
       "      <td>4.177566</td>\n",
       "      <td>0.769188</td>\n",
       "      <td>0.018077</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>10.305349</td>\n",
       "      <td>9.731464</td>\n",
       "      <td>8.260418</td>\n",
       "      <td>4.854084</td>\n",
       "      <td>1.118406</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>10.883962</td>\n",
       "      <td>10.760017</td>\n",
       "      <td>10.176355</td>\n",
       "      <td>8.129088</td>\n",
       "      <td>3.199901</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>11.471836</td>\n",
       "      <td>12.031740</td>\n",
       "      <td>12.411460</td>\n",
       "      <td>13.602479</td>\n",
       "      <td>9.056051</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>13.911014</td>\n",
       "      <td>16.577768</td>\n",
       "      <td>29.737484</td>\n",
       "      <td>79.659031</td>\n",
       "      <td>397.597440</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 a            b            c            d            e\n",
       "count  1000.000000  1000.000000  1000.000000  1000.000000  1000.000000\n",
       "mean     10.896863    10.933012    10.653770    10.903785    10.821143\n",
       "std       0.857940     1.624779     3.449507     9.316623    25.780611\n",
       "min       8.590849     6.487331     4.177566     0.769188     0.018077\n",
       "25%      10.305349     9.731464     8.260418     4.854084     1.118406\n",
       "50%      10.883962    10.760017    10.176355     8.129088     3.199901\n",
       "75%      11.471836    12.031740    12.411460    13.602479     9.056051\n",
       "max      13.911014    16.577768    29.737484    79.659031   397.597440"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "axes = sns.boxplot(data=returns.loc[:,'a':'d'])\n",
    "axes.set_title('Distribution of returns')\n",
    "axes.set_ylabel('Cumulative returns')\n",
    "plt.figure()\n",
    "axes2 = sns.boxplot(data=returns.e)\n",
    "axes.set_ylabel('Cumulative returns')\n",
    "print('Returns table')\n",
    "returns.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Though we only have 5 risk profiles and a fixed mean, there is a massive difference in the results.\n",
    "\n",
    "The sharpe ratios for stock a and b are closely clustered. So if you have invested in any of the stocks falling into the risk profile a, you would end up more or less the same way the others have ended. The difference between the minimum and maximum returns would just be 2 times, volatility would not have played a big role and this risk profile have performed better in all times. The box plot shows the sharpe ratio decreasing with an increase in volatility.\n",
    "\n",
    "On the other end of the spectrum, the maximum and minimum returns in profile e is just crazy. You could have even ended up in a loss or could have become a millionare. \n",
    "\n",
    "Despite the same returns, risk does some crazy things."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probability of returns\n",
    "\n",
    "The monthly return in our example is 1%. So, if you have invested for 20 years, your return should be \n",
    "\n",
    "`1.01**240 = ~10.9`\n",
    "\n",
    "From the returns table, you could straight away infer that for profiles a,b,c the mean and median or more or less close to this value. Let us calculate the number of portfolios that beat this benchmark in all of the risk profiles.\n",
    "\n",
    "Also, half of the returns is `1.005**240 = ~3.3`\n",
    "\n",
    "Let us also calculate the number of portfolios that beat this benchmark too"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>full_returns</th>\n",
       "      <th>half_returns</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>491</td>\n",
       "      <td>1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>472</td>\n",
       "      <td>1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c</th>\n",
       "      <td>404</td>\n",
       "      <td>1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>d</th>\n",
       "      <td>347</td>\n",
       "      <td>885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>e</th>\n",
       "      <td>217</td>\n",
       "      <td>496</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   full_returns  half_returns\n",
       "a           491          1000\n",
       "b           472          1000\n",
       "c           404          1000\n",
       "d           347           885\n",
       "e           217           496"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def calculate_probability(returns, v):\n",
    "    \"\"\"\n",
    "    Given an array of returns and a value v, return the number of\n",
    "    times returns exceed v \n",
    "    \"\"\"\n",
    "    length = len(returns)\n",
    "    positive = (returns>v).sum()\n",
    "    return positive\n",
    "\n",
    "full_returns = [calculate_probability(returns[col],1.01**240) for col in returns]\n",
    "half_returns = [calculate_probability(returns[col],1.005**240) for col in returns]\n",
    "prob = pd.DataFrame({'full_returns': full_returns, 'half_returns': half_returns},\n",
    "                   index=list('abcde'))\n",
    "prob"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Profiles a,b,c got 1000 out of 1000 in gaining half the monthly returns while profile e can't even fulfil 50% returns. Thus, if 1000 people has got their investments in profile c, even half of them would not have got 3 times the money; they would have even fared worse.\n",
    "\n",
    "Thus, an increase in volatility becomes more of luck and less of skill. Looking at only the returns in deciding on a portfolio is fraught with too much risk and may just turn out to be a lucky affair which may not work out for all the people."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sharpe multipliers\n",
    "\n",
    "When I generated the samples, I used a fixed monthly mean of 1% but for deviation, multipliers are used. The mean is multiplied by the deviation to get the numbers.\n",
    "\n",
    "```python\n",
    "multipliers = (0.5,1,2,5,10)\n",
    "```\n",
    "\n",
    "These multipliers are just inverse for the original formula `standard_deviation/mean`, something similar to the P/E ratio. The higher this number, then the portfolio is risky, the lower this number the better. These are not annualized and hence they could not be compared on a similar scale. Below are the tables for the multipliers and their annualized sharpe ratios.\n",
    "\n",
    "Thus if you portfolio has a mean of 0.2% and a deviation of 0.6% on a weekly basis, then your sharpe multiple is **0.6/0.2 = 3** and since it is on a weekly basis, the annualized sharpe ratio is **(0.2/0.6) x sqrt(52) = ~2.4**"
   ]
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     "name": "stdout",
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     "text": [
      "Annualized sharpe ratios for sharpe multiples\n"
     ]
    },
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>daily</th>\n",
       "      <th>weekly</th>\n",
       "      <th>monthly</th>\n",
       "      <th>yearly</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>15.8745</td>\n",
       "      <td>7.2111</td>\n",
       "      <td>2.2361</td>\n",
       "      <td>1.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7.9373</td>\n",
       "      <td>3.6056</td>\n",
       "      <td>1.1180</td>\n",
       "      <td>0.5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.2915</td>\n",
       "      <td>2.4037</td>\n",
       "      <td>0.7454</td>\n",
       "      <td>0.3333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.9686</td>\n",
       "      <td>1.8028</td>\n",
       "      <td>0.5590</td>\n",
       "      <td>0.2500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3.1749</td>\n",
       "      <td>1.4422</td>\n",
       "      <td>0.4472</td>\n",
       "      <td>0.2000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2.6458</td>\n",
       "      <td>1.2019</td>\n",
       "      <td>0.3727</td>\n",
       "      <td>0.1667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2.2678</td>\n",
       "      <td>1.0302</td>\n",
       "      <td>0.3194</td>\n",
       "      <td>0.1429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.9843</td>\n",
       "      <td>0.9014</td>\n",
       "      <td>0.2795</td>\n",
       "      <td>0.1250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.7638</td>\n",
       "      <td>0.8012</td>\n",
       "      <td>0.2485</td>\n",
       "      <td>0.1111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1.5875</td>\n",
       "      <td>0.7211</td>\n",
       "      <td>0.2236</td>\n",
       "      <td>0.1000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      daily  weekly  monthly  yearly\n",
       "1   15.8745  7.2111   2.2361  1.0000\n",
       "2    7.9373  3.6056   1.1180  0.5000\n",
       "3    5.2915  2.4037   0.7454  0.3333\n",
       "4    3.9686  1.8028   0.5590  0.2500\n",
       "5    3.1749  1.4422   0.4472  0.2000\n",
       "6    2.6458  1.2019   0.3727  0.1667\n",
       "7    2.2678  1.0302   0.3194  0.1429\n",
       "8    1.9843  0.9014   0.2795  0.1250\n",
       "9    1.7638  0.8012   0.2485  0.1111\n",
       "10   1.5875  0.7211   0.2236  0.1000"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "multipliers = np.arange(1,11)\n",
    "periods = np.array([252,52,5,1]).reshape(4,1)\n",
    "base = 1\n",
    "index = ['daily', 'weekly', 'monthly', 'yearly']\n",
    "print('Annualized sharpe ratios for sharpe multiples')\n",
    "pd.DataFrame((1/multipliers)*np.sqrt(periods),\n",
    "            index=index, columns=multipliers).T.round(4)"
   ]
  }
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  "nikola": {
   "category": "risk management",
   "date": "2021-11-06 06:52:05 UTC",
   "slug": "sharpe-ratio-deep-dive",
   "tags": "sharpe,risk",
   "title": "Sharpe ratio - A deep dive"
  }
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