AFML 16.1.ipynb

{
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    "### Machine-Learning Asset Allocation\n",
    "\n",
    "Most of the functions below can be found under:\n",
    "\n",
    "* Portfolio_opt/**\n",
    "\n",
    "This exercise is more about portfolio optimization and asset-allocation using ML.\n",
    "\n",
    "There are quite a number of monte-carlos simulation.\n",
    "\n",
    "If this chapter doesn't blow up your mind.. it's probably going to blow up your com.\n",
    "\n",
    "The focused portfolio management style will be Hierarchical Risk Parity (HRP), but comparison will be made to Critical Line Agorithm (CLA) approach as well as Inverse-Variance approach (IVP).\n",
    "\n",
    "3 different quantitative portfolio management style to which how systematic and idiosyncratic risk are managed. (Bottom up/ Top down approach)\n",
    "\n",
    "**Warning**\n",
    "\n",
    "Save your notebook often for this chapter. Infinite loops is highly likely if you are not careful.\n",
    "\n",
    "If you are keen on generating synthetic data for your research, copy the code snippets [Generate synthetic raw data](https://gist.github.com/boyboi86/5e00faf48f60abfdbe838fbdee269471) in my gist.\n",
    "\n",
    "**Note**\n",
    "\n",
    "A seperate jupyter notebook was created to demostrate MV portfolio using convexity-optimization, nested clustered algorithm and monte-carlos simulation selection was created. However, this is not part of the syllabus.\n",
    "\n",
    "[AFML 16.1.1](https://github.com/boyboi86/AFML/blob/master/AFML%2016.1.1.ipynb)\n",
    "\n",
    "Additional resource: \n",
    "* [Critical Line Aglorithm](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2197616)\n",
    "* [EF Robust Estimator](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3469961)\n",
    "* [Research Paper](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2708678)\n",
    "* [Blog post](https://gmarti.gitlab.io/qfin/2018/10/02/hierarchical-risk-parity-part-1.html)\n",
    "* [Detection of False Investment Strategies Using Unsupervised Learning Methods](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3167017)\n",
    "\n",
    "Contact: boyboi86@gmail.com"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Num of CPU core:  4\n",
      "Machine info:  Windows-10-10.0.18362-SP0\n",
      "Python 3.7.4 (default, Aug  9 2019, 18:34:13) [MSC v.1915 64 bit (AMD64)]\n",
      "Numpy 1.18.5\n",
      "Pandas 1.0.4\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import research as rs\n",
    "from scipy.cluster.hierarchy import dendrogram, linkage, fclusterdata\n",
    "import random\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def quasi_diag(link):\n",
    "    link = link.astype(int)\n",
    "    sort_idx = pd.Series([link[-1,0], link[-1,1]])\n",
    "    n_items = link[-1,3]\n",
    "    while sort_idx.max() >= n_items:\n",
    "        sort_idx.index = np.arange(0, sort_idx.shape[0] * 2, 2)\n",
    "        df0 = sort_idx[sort_idx>=n_items]\n",
    "        i = df0.index\n",
    "        j = df0.values - n_items\n",
    "        sort_idx[i] = link[j,0]\n",
    "        df0 = pd.Series(link[j,1], index = i+1)\n",
    "        sort_idx = sort_idx.append(df0)\n",
    "        sort_idx = sort_idx.sort_index()\n",
    "        sort_idx.index = np.arange(sort_idx.shape[0])\n",
    "    return sort_idx.tolist()\n",
    "\n",
    "def IVP(cov, **kwarg):\n",
    "    ivp = 1./np.diag(cov)\n",
    "    ivp /= ivp.sum()\n",
    "    return ivp\n",
    "\n",
    "def corr_dist(corr):\n",
    "    #dist = ((1-corr)/2.) ** .5\n",
    "    dist = np.sqrt((1 - corr) / 2.)\n",
    "    return dist\n",
    "\n",
    "def corr_mtx_plot(corr: float, path: str = None, labels = None, title = None):\n",
    "    plt.figure(figsize=(8,6))\n",
    "    if labels is None: \n",
    "        labels = []\n",
    "    plt.pcolor(corr)\n",
    "    plt.colorbar()\n",
    "    plt.yticks(np.arange(.5, corr.shape[0] + .5), labels)\n",
    "    plt.xticks(np.arange(.5, corr.shape[0] + .5), labels)\n",
    "    if path is not None:\n",
    "        plt.savefig(path)\n",
    "        plt.clf()\n",
    "        plt.close()\n",
    "    if title is not None:\n",
    "        plt.title(title)\n",
    "    plt.show()\n",
    "\n",
    "def ddg_plot(link, labels = None):\n",
    "    plt.figure(figsize=(8,6))\n",
    "    dn = dendrogram(link,\n",
    "                        labels = labels, #change label num count if you are increasing size\n",
    "                        above_threshold_color='y',\n",
    "                        orientation='top')\n",
    "    \n",
    "    plt.title(\"Dendogram of Cluster Formation\")\n",
    "    plt.show()   \n",
    "    \n",
    "def hrp(x: pd.DataFrame):\n",
    "    \n",
    "    cov, corr = x.cov(), x.corr()\n",
    "    labels = np.arange(1,len(corr)+1)\n",
    "    corr_mtx_plot(corr = corr, path = None, labels = None, title = \"Original Covariance Matrix Heat-Map\")\n",
    "    dist = corr_dist(corr = corr)\n",
    "    link = linkage(dist, 'single')\n",
    "    ddg_plot(link = link, labels = labels)\n",
    "    sort_idx = quasi_diag(link = link)\n",
    "    sort_idx = corr.index[sort_idx].tolist()\n",
    "    df0 = corr.loc[sort_idx, sort_idx]\n",
    "    corr_mtx_plot(corr = df0, path = None, labels = df0.columns, title = \"After Quasi-Diagonization\")    \n",
    "\n",
    "def cla(cov):\n",
    "    if isinstance(cov, pd.DataFrame):\n",
    "        cov = cov.to_numpy()\n",
    "    mean = np.arange(1,cov.shape[0] +1).reshape(-1,1)\n",
    "    lb = np.zeros(mean.shape)\n",
    "    ub = np.ones(mean.shape)\n",
    "    _cla = rs.CLA(mean, cov, lb, ub)\n",
    "    _cla.solve()\n",
    "    return _cla.w[-1].flatten()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**\n",
    "\n",
    "Before you go any further down, spend some time on these information I gathered.\n",
    "\n",
    "They are casual and easy way to understand what we will be doing next. Unless you already know we are dealing with KNN Algorithm, otherwise please go to these links and watch the videos.\n",
    "\n",
    "[Youtube Link: Flat and Hierarchical Clustering | The Dendrogram Explained](https://www.youtube.com/watch?v=ijUMKMC4f9I)\n",
    "\n",
    "[Youtube LinkL K-Nearest Neighbour](https://www.youtube.com/watch?v=HVXime0nQeI)\n",
    "\n",
    "**Note**\n",
    "\n",
    "One of the video is really cheesy..\n",
    "\n",
    "**Note**\n",
    "\n",
    "It's important for any quant to understand what they are using to profit.."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dendogram based on the below grouping\n",
      "[(4, 6), (1, 7), (3, 8), (3, 9), (2, 10), (3, 11), (5, 12), (4, 13), (2, 14), (3, 15)]\n"
     ]
    }
   ],
   "source": [
    "n_obs = 10000\n",
    "size0 = 5\n",
    "size1 = 10\n",
    "sig1 = .25\n",
    "seed = 12345\n",
    "\n",
    "mtx = rs.generate_HRP_data(n_obs = n_obs,\n",
    "                        size0 = size0,\n",
    "                        size1 = size1,\n",
    "                        sig1 = sig1,\n",
    "                        seed = seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Wei_X\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:59: ClusterWarning: scipy.cluster: The symmetric non-negative hollow observation matrix looks suspiciously like an uncondensed distance matrix\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hrp = hrp(x = mtx)\n",
    "\n",
    "# Either very strong corr or very weak (Yellow or dark purple)\n",
    "# Sparse Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**\n",
    "\n",
    "The below heatmaps and dendrograms are plotted based on daily return (original) against weekly returns.\n",
    "\n",
    "**Note**\n",
    "\n",
    "In order to use Hierarchical Risk Parity (HRP) portfolio management method.\n",
    "\n",
    "Your portfolio needs to spread across entire investment universe (Equities, Bonds and alternatives). If assets are are too similar i.e. commodities ETF against commodities trading equities.\n",
    "\n",
    "You might want to use CLA instead, since the amount that would be used in rebalance is insignificant. (It will still overweight some and give non-zero weight to the remaining)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sub_corr_mtx_plot(corr1: float, corr2:float):\n",
    "    fig, axes = plt.subplots(1,2, figsize=(12,8), sharey = 'row',sharex='col')\n",
    "    axes[0].pcolor(corr1)\n",
    "    axes[1].pcolor(corr2)\n",
    "    for ax in axes.flat:\n",
    "        im = ax.imshow(np.random.random((len(corr1),len(corr1))), vmin=0, vmax=1)\n",
    "    fig.colorbar(im, ax=axes.ravel().tolist())\n",
    "    \n",
    "    axes[0].title.set_text('Daily Return Corr Matrix')\n",
    "    axes[1].title.set_text('Weekly Return Corr Matrix')\n",
    "    plt.show()\n",
    "    \n",
    "def sub_ddg_plot(corr1, corr2):\n",
    "    dist1 = corr_dist(corr = corr1)\n",
    "    link1 = linkage(dist1, 'single')\n",
    "    dist2 = corr_dist(corr = corr2)\n",
    "    link2 = linkage(dist2, 'single')\n",
    "    fig, axes = plt.subplots(1, 2, figsize=(12, 6), sharey = 'row',sharex='col')\n",
    "    dn1 = dendrogram(link1, ax=axes[0], \n",
    "                     above_threshold_color='y',\n",
    "                     labels = np.arange(1,len(corr1)+1),\n",
    "                     orientation='top')\n",
    "    dn2 = dendrogram(link2, ax=axes[1],\n",
    "                        above_threshold_color='y',\n",
    "                     labels = np.arange(1,len(corr2)+1),\n",
    "                       orientation='top')\n",
    "    \n",
    "    axes[0].title.set_text('Daily Return Dendrogram')\n",
    "    axes[1].title.set_text('Weekly Return Dendrogram')\n",
    "    plt.show()\n",
    "\n",
    "w_df = mtx.resample('W', axis = 0).mean() # resampled\n",
    "\n",
    "sub_corr_mtx_plot(corr1 = mtx.corr(method='pearson'), corr2 = w_df.corr(method='pearson'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**\n",
    "\n",
    "Notice the overall correlation matrix has changed.\n",
    "\n",
    "Initially, we would have believed it was sparse. (Mostly dark purple shade)\n",
    "\n",
    "After we resampled our data into weekly returns, now it became more \"dense\". (Most purple became lighter)\n",
    "\n",
    "[Sparse Matrix Wiki Explanation](https://en.wikipedia.org/wiki/Sparse_matrix)\n",
    "\n",
    "**Note**\n",
    "\n",
    "Heatmaps portion that were originally yellow are still yellow.\n",
    "\n",
    "**Note**\n",
    "\n",
    "Perhapes it was due to the fact pnl was in small decimal places (1e-3).\n",
    "\n",
    "Hence, when we try to \"downsample\", it became obvious which are the assets that does have valid correlations.\n",
    "\n",
    "If they were really correlated, their mean result would be somewhat similar (Even when downsampled)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sub_ddg_plot(corr1 = np.corrcoef(mtx, rowvar = 0), corr2 = np.corrcoef(w_df, rowvar = 0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**\n",
    "\n",
    "After we resampled into weekly average return the weekly return dendrogram displayed an obvious \"classification\" of these hierarchical clusters order.\n",
    "\n",
    "There was a change in their distance; as a result 2 groups have changed their Hierarchy order:\n",
    "\n",
    "* (14, 2, 10)\n",
    "* (13, 4, 6)\n",
    "\n",
    "The rest apart from changing their distance remained. (Increased from zero)\n",
    "\n",
    "**Note**\n",
    "\n",
    "We are using \"single\" method; minimal distance from each point.\n",
    "\n",
    "Distance measure from right to left, bottom to top.\n",
    "\n",
    "**Note**\n",
    "\n",
    "The below bar chart represents asset weightage (Based on daily and weekly returns).\n",
    "\n",
    "It would seem that because of the change, a drastic change in weight has occured between (13, 4, 6).\n",
    "\n",
    "With Asset 13 being further, with Asset 6 becoming closer.\n",
    "\n",
    "**Note**\n",
    "\n",
    "Most of the asset allocation weights that were below the dotted line will \"moderate\" with heavier weights when using resampled weekly returns.\n",
    "\n",
    "**Note**\n",
    "\n",
    "Scipy Cluster Warning is related to the fact we are passing in a redundant matrix (Pandas cov() ). \n",
    "\n",
    "If you use numpy squareform to obtain a condense matrix, the Hierachy will no longer make sense.\n",
    "\n",
    "Use the below numpy method instead to get correlation and set rowvar = 0.\n",
    "\n",
    "    np.corrcoef()\n",
    "    \n",
    "[Numpy corrcoef()](https://numpy.org/doc/stable/reference/generated/numpy.corrcoef.html#:~:text=Return%20Pearson%20product%2Dmoment%20correlation%20coefficients.&text=The%20values%20of%20R%20are%20between%20%2D1%20and%201%2C%20inclusive.&text=A%201%2DD%20or%202,containing%20multiple%20variables%20and%20observations.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "w_hrp = rs.HRP(data = w_df).solve(method = 'single')\n",
    "d_hrp = rs.HRP(data = mtx).solve(method = 'single')\n",
    "\n",
    "df_plot = pd.DataFrame({'Weekly Returns': w_hrp, 'Daily Returns': d_hrp})\n",
    "\n",
    "df_plot.plot.bar(figsize=(12,8))\n",
    "plt.ylabel(\"Weights\", fontsize=12)\n",
    "plt.xlabel(\"Assets\", fontsize=12)\n",
    "plt.axhline(y = 0.05, ls='--', c='g')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "w_ivp = IVP(cov = w_df.cov())\n",
    "w_clas = cla(cov = w_df.cov())\n",
    "\n",
    "df1 = pd.DataFrame({'IVP':w_ivp, 'CLA': w_clas, 'HRP': w_hrp})\n",
    "\n",
    "df1.plot.bar(figsize=(12,8))\n",
    "plt.ylabel(\"Weights\", fontsize=12)\n",
    "plt.xlabel(\"Assets\", fontsize=12)\n",
    "plt.title(\"Asset Allocation Comparison\")\n",
    "plt.axhline(y=0.074, ls='--', c= 'r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Asset allocation comparison outcome\n",
    "\n",
    "**Above red line:**\n",
    "    \n",
    "* Only Critical Line Algorithm (CLA) and Hierarchical Risk Parity (HRP) methods are present.\n",
    "* Inverse Variance Parity (IVP) is totally absent.\n",
    "* HRP and CLA has the close number of weightage above the red line (Estimated 5 - 6 in total).\n",
    "* CLA usually provide the highest possible weight to a single asset among the 3 methods.\n",
    "* However, HRP has rarely provides an asset allocation weightage more than CLA in any assets.\n",
    "* CLA clearly provides a heavier weight than HRP method.\n",
    "\n",
    "**Below the red line:**\n",
    "\n",
    "* CLA weightage is absent from some of the assets allocation weightage.\n",
    "* HRP and IVP are the only 2 methods that will provide a asset allocation weightage.\n",
    "* IVP will always provide heavier weightage than HRP.\n",
    "\n",
    "**Note**\n",
    "\n",
    "Further analysis, HRP method will usually provide the second heaviest weight in all instances among the 3 methods or in some cases binary methods.\n",
    "\n",
    "\n",
    "### Conclusion\n",
    "\n",
    "IVP is distributing weight almost equally among all asset classes; this makes it susceptible to systematic risk.\n",
    "\n",
    "CLA is distributing weight almost unequally among all asset classes; this makes it susceptible to idiosyncratic risk.\n",
    "\n",
    "Only HRP will provide moderation which makes it the recommened method when it comes to portfolio rebalance and optimization.\n",
    "\n",
    "**Personal Opinion**\n",
    "\n",
    "If your 50% of your portfolio consist of ETFs or assets that were \"already\" diversified (No direct investment). CLA maybe a better choice. Possible Strategy includes ETF Rotational Portfolio.\n",
    "\n",
    "If your portfolio is sector or asset-class focused. IVP maybe a better solution. (Possible Strategy includes Macro-Global FoF) \n",
    "\n",
    "HRP requires a wide variety of direct investments to maximise it's potential. (Possible combination: Equities, Bonds, FX, Real-estate, Commodities)\n",
    "\n",
    "As a result, HRP is only suitable for Macro-global/ Multi-assets Hedge Funds. (AUM should be a sizable amount (Preferably x > USD 350 millions at least). \n",
    "\n",
    "In order to fully utilize this algorithm, a large number of assets will be required."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "num = w_df.shape[1]\n",
    "labels = np.arange(1, num + 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "e_val, e_vec = np.linalg.eig(w_df.cov()) #to decompose"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**\n",
    "\n",
    "[Eigen-decomposition](https://en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "e_matrix = np.identity(n=num) * e_val\n",
    "e_df = pd.DataFrame(e_matrix, index = labels, columns = labels)\n",
    "np.random.seed(0) # seed used!\n",
    "eps = np.random.uniform(0, 1, size = num)\n",
    "e_df = (num * eps * e_df * (sum(eps) **-1)) #based on formula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "e_df1 = e_vec @ e_df @ np.linalg.inv(e_vec) #this is matrix do not use * to multiply\n",
    "e_df1 = pd.DataFrame(e_df1)\n",
    "e_df1.index = labels\n",
    "e_df1.columns = labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compare between 3 methods after decomposition\n",
    "\n",
    "w_hrp1 = rs.HRP(data = e_df1).solve(method = 'single')\n",
    "w_ivp1 = IVP(cov = e_df1)\n",
    "w_clas1 = cla(cov = e_df1)\n",
    "\n",
    "df2 = pd.DataFrame({'IVP': w_ivp1, 'CLA': w_clas1, 'HRP': w_hrp1})\n",
    "df2.plot.bar(figsize=(12,8))\n",
    "plt.ylabel(\"Weights\", fontsize=12)\n",
    "plt.xlabel(\"Assets\", fontsize=12)\n",
    "plt.title(\"Asset Allocation Comparison\")\n",
    "plt.axhline(y=0.074, ls='--', c= 'r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x1440 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Comparing before and after decomposition\n",
    "\n",
    "fig, axes = plt.subplots(nrows=3, ncols=1, figsize=(12,20))\n",
    "df_hrp = pd.DataFrame({'HRP Before Decompose': w_hrp, 'HRP After Decompose': w_hrp1})\n",
    "df_cla = pd.DataFrame({'CLA Before Decompose': w_clas, 'CLA After Decompose': w_clas1})\n",
    "df_cla.index = labels\n",
    "df_ivp = pd.DataFrame({'IVP Before Decompose': w_ivp, 'IVP After Decompose': w_ivp1})\n",
    "df_ivp.index = labels\n",
    "df_hrp.plot.bar(ax = axes[0])\n",
    "df_cla.plot.bar(ax = axes[1])\n",
    "df_ivp.plot.bar(ax = axes[2])\n",
    "\n",
    "axes[0].axhline(y=0.074, ls='--', c= 'r')\n",
    "axes[0].set_title('Hierarchical Risk Parity')\n",
    "axes[1].axhline(y=0.074, ls='--', c= 'r')\n",
    "axes[1].set_title('Critical Line Algorithm')\n",
    "axes[2].axhline(y=0.074, ls='--', c= 'r')\n",
    "axes[2].set_title('Inverse Variance Portfolio')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Asset allocation based on new covariance matrix\n",
    "\n",
    "**Using the red line as benchmark:**\n",
    "\n",
    "CLA: Some change in allocation was notice, however most of the assets that were above the red line before are still present. Some reduction and improvement in allocation is noticed.\n",
    "\n",
    "IVP: Outcome is similar to CLA, but there are some changes that was also reflected in HRP. (Assets that have higher allocation in HRP also seen an increase in IVP)\n",
    "\n",
    "HRP: Drastic shift in asset allocation, some assets that were previously above red line are currently below. Those that were below are now above. (Reflect in a big shift in asset allocation)\n",
    "\n",
    "**Note**\n",
    "\n",
    "Most change observed in HRP followed by IVP. The change in allocation seems unanimous across all 3 methods, just difference in magnitude.\n",
    "\n",
    "**Note**\n",
    "\n",
    "Notice Asset 5 and 12 which in accordance to the hierachy cluster seems to be the above threshold (Yellow color in dendrogram), reflects a change in their allocation. The other asset classes for HRP reflect the \"distance\" correctly after the eigen-decomposition.\n",
    "\n",
    "The first group which consist of asset 3, 8, 9, 11, 15. Experience an overall lower allocation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Wei_X\\Desktop\\Python\\research\\Portfolio_opt\\hrp.py:31: ClusterWarning: scipy.cluster: The symmetric non-negative hollow observation matrix looks suspiciously like an uncondensed distance matrix\n",
      "  link = sch.linkage(y = dist, method = method, metric='euclidean')\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hrp_df = rs.HRP(data = w_df).rescale_solve(method = 'single',\n",
    "                                           n_run = 100,\n",
    "                                           long_only = True) #Monte-Carlos based on my algo\n",
    "\n",
    "hrp_mc = pd.DataFrame(index=hrp_df.index).assign(Original = w_hrp, \n",
    "                                                 Single_Random = w_hrp1, \n",
    "                                                 Monte_Carlos = hrp_df)\n",
    "hrp_mc.plot.bar(figsize=(12,8))\n",
    "plt.ylabel(\"Weights\", fontsize=12)\n",
    "plt.xlabel(\"Assets\", fontsize=12)\n",
    "plt.axhline(y = 0.074, ls='--', c='r')\n",
    "plt.title(\"Hierarchical Risk Parity Methods Comparison\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**\n",
    "\n",
    "The above method was based on Monte-Carlos Simulation plotted against the original weekly returns and single random decomposed covariance matrix.\n",
    "\n",
    "Based on monte-carlos method, the weightage seems more moderated and the \"correct\" Hierarchical cluster weightage is also intact.\n",
    "\n",
    "The original number of assets above the red dotted line should be the same as the number of assets above dotted red line above threshold (Othewise try increasing your Monte-Carlos runs).\n",
    "\n",
    "Monte-Carlos simulation will always provide the \"correct\" mean in terms of weightage. However, to ensure the allocation is correct, it would be preferred to run about 10,000 times.\n",
    "\n",
    "**Note**\n",
    "\n",
    "The rescaling is to ensure that co-relation is minimized as much as possible. To ensure accuracy, HRP rescale should employ monte-carlo simulation.\n",
    "\n",
    "**Note**\n",
    "\n",
    "Do not perform convexity optimization for HRP, linkage method already \"optimized\" by minimizing the distance.\n",
    "\n",
    "Convexity optimization is for IVP, which require more than just a normal \"CAPM optimization\".\n",
    "\n",
    "It probably requires trinomial expansion as well. \n",
    "\n",
    "**Note**\n",
    "\n",
    "In case if you have not notice, it will take some time to run this process. Do not worry.\n",
    "\n",
    "In view of exchange regulations, once the recommended allocation is produced, it will still take time to unload or accumulate your positions.\n",
    "\n",
    "To ensure your portfolio's profitability, do not perform direct investment more than certain threshold so that it would be easier to unload or accumulate any positions.\n",
    "\n",
    "**Note**\n",
    "\n",
    "The next section covers zero-sum hedge method (Allocation equals to zero), throughout the whole exercise we are only dealing with long-only portfolio.\n",
    "\n",
    "Before that, you will need to go through this [presentation slide](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3512994)\n",
    "\n",
    "Zero-sum hedge would require long-short portfolio method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t_cluster = e_df1.mean(axis=0).quantile(q = 0.9) #as an estimate set quartile 0.9\n",
    "\n",
    "c_grp = fclusterdata(X = e_df1, #based on eign-matrix\n",
    "                     t = t_cluster, #based on eign-matrix\n",
    "                     criterion='distance', \n",
    "                     metric='euclidean', \n",
    "                     depth=2, \n",
    "                     method='single', \n",
    "                     R=None)\n",
    "\n",
    "hrp_df1 = rs.HRP(data = w_df).rescale_solve(method = 'single',\n",
    "                                            n_run = 100,\n",
    "                                            long_only = False)\n",
    "hrp_df1['Long Only'] = hrp_df\n",
    "hrp_df1['Average Returns'] = w_df.mean(axis = 0)\n",
    "\n",
    "hrp_df1['grp'] = c_grp\n",
    "grp_df= hrp_df1.sort_values(by='grp')\n",
    "grp_df.rename(columns={\"weights\": \"Bi-Directional\"}).drop(columns = [\"grp\"]).plot.bar(figsize=(12,8))\n",
    "plt.title(\"Investment Style Weightage\")\n",
    "plt.ylabel(\"Weights\", fontsize=12)\n",
    "plt.xlabel(\"Assets\", fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "grp_df.rename(columns={\"weights\": \"Bi-Directional\"}).groupby(\"grp\").mean().plot.bar(figsize=(12,8))\n",
    "plt.title(\"Investment Style Grouping Average Weightage\")\n",
    "plt.ylabel(\"Weights/ Returns\", fontsize=12)\n",
    "plt.yticks(np.arange(-0.01, 0.1, step = 0.01))\n",
    "plt.xlabel(\"Assets Groups\", fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Long vs bi-directional portfolio\n",
    "\n",
    "**Based on grouped individual asset bar chart**\n",
    "\n",
    "There is an obvious descending asset weightage trend (right to left), for both bi-directionl and long only portfolio.\n",
    "\n",
    "As long as returns were positive in the observed order (Long-portfolio), HRP tends to give heavier weightage.\n",
    "\n",
    "For bi-directional portfolio (Long/ short), it ignores the direction but rather focus on height of return bars. (Longer bar equals to higher allocation).\n",
    "\n",
    "**Based on the asset group average weight bar chart**\n",
    "\n",
    "Last group which is group 5 (Consist of [1, 7]), tends to enjoy higher weights while first group (Consist of [3, 8, 9, 11, 15]) then to have lower \"averaged out\" weights.\n",
    "\n",
    "If it wasn't the fact that last group has negative returns, the long method would probably assign greater weight to it.\n",
    "\n",
    "For long method, eventually most remaining weights were given to the first group.\n",
    "\n",
    "While for long/ short method (blue bars), it is obvious weights were assigned based on magnitude/ height of return bars (Until exhausted). Rather than directions.\n",
    "\n",
    "The deviation for both methods are minimal based on the above asset group graph.\n",
    "\n",
    "**Note**\n",
    "\n",
    "Each group is assumed to be different asset type or class. This is based on pearson's correlation recommendation.\n",
    "\n",
    "Hence to avoid clash between theories, we will use bi-directional portfolio to complete zero-sum hedge.\n",
    "\n",
    "The key idea is to ensure full-diversification across asset classes, which is a central idea to portfolio risk management.\n",
    "\n",
    "For simplicity, we will short those assets that gave negative returns and long those with positive returns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Total Allocation Sum for the Bi-Directional Portfolio: -0.000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "\n",
    "grp_df[\"weights\"] = grp_df[\"weights\"].mul(np.sign(grp_df[\"Average Returns\"]))\n",
    "positive_sum = grp_df[grp_df[\"weights\"] > 0].weights.sum()\n",
    "negative_sum = grp_df[grp_df[\"weights\"] <= 0].weights.sum() * -1\n",
    "grp_df[\"weights\"] = grp_df[\"weights\"].apply(lambda x: x / positive_sum if x > 0 else x/negative_sum )\n",
    "grp_df[\"weights\"] = grp_df[\"weights\"].mul(0.5) # To ensure we have 50/50 balance in both directions\n",
    "\n",
    "grp_df[\"weights\"].plot.bar(figsize=(12,8))\n",
    "plt.title(\"Zero-Sum Diversified Bi-Directional Portfolio\")\n",
    "plt.ylabel(\"Weights/ Returns\", fontsize=12)\n",
    "plt.yticks(np.arange(-0.1, 0.15, step = 0.01))\n",
    "plt.xlabel(\"Assets\", fontsize=12)\n",
    "plt.show()\n",
    "\n",
    "print(\"\\nTotal Allocation Sum for the Bi-Directional Portfolio: {0:.3f}\\n\".format((grp_df[\"weights\"].sum())))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**\n",
    "\n",
    "Assuming weightage represents our confidence in each asset (Total Probability)\n",
    "\n",
    "    Expected Return = Probability of Earning Returns * Returns till date\n",
    "    \n",
    "**Note**\n",
    "\n",
    "The expected returns may seem unusual because last group that was given the most weight contains the least expected returns.\n",
    "\n",
    "HRP is based on correlation as an estimate, to produce diversified porfolio.\n",
    "\n",
    "**Update**\n",
    "\n",
    "This expected return formula may not be author's original intention."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Er = grp_df[\"weights\"].mul(grp_df[\"Average Returns\"])\n",
    "Er.plot.bar(figsize=(12,8))\n",
    "plt.title(\"Expected Returns for Zero-Sum Diversified Bi-Directional Portfolio\")\n",
    "plt.xlabel(\"Assets\", fontsize=12)\n",
    "plt.ylabel(\"Expected Returns\", fontsize=12)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}