_SUMMARY CHARTS FOR OSEM RUN.ipynb

{
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  {
   "cell_type": "markdown",
   "id": "3f175eb6",
   "metadata": {},
   "source": [
    "# SUMMARY CHARTS FOR OSEM RUN\n",
    "\n",
    "OSEM model projects and actively trades a portfolio of corporate bonds and equities in light of commitments. The basic unit in OSEM is a cash flow. The purpose of this script is to show a how different types of cash flows are treated in the latest run.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "585652cf",
   "metadata": {},
   "source": [
    "# Table of Contents  \n",
    " 1. Loading the summary csv\n",
    " \n",
    "       Equity\n",
    "        \n",
    "       Corporate bonds\n",
    "       \n",
    "       Cash\n",
    "\n",
    "       Liability profile\n",
    " \n",
    " 2. The initial portfolio\n",
    "      \n",
    "      Periodic cash flows\n",
    "\n",
    "      Terminal cash flows\n",
    "      \n",
    "      Cash movement\n",
    "\n",
    "      End of period market value\n",
    "\n",
    "      \n",
    " 3. Test 1 Return of portfolio\n",
    " 4. Test 2 no vanishing cash flows"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c495112",
   "metadata": {},
   "source": [
    "<a id=\"1\"></a> <br>\n",
    "## Loading the summary csv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "de5f2301",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import datetime as dt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2910d990",
   "metadata": {},
   "outputs": [],
   "source": [
    "out = pd.read_csv(\"Output/Results.csv\",index_col=0, parse_dates=[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3398648b",
   "metadata": {},
   "source": [
    "<a id=\"2\"></a> <br>\n",
    "## The initial portfolio\n",
    "\n",
    "This section shows what the initial inputs of the run were. Currently OSEM can handle three types of financial instruments and one type of liability profile."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91cbe6fa",
   "metadata": {},
   "source": [
    "### Equity\n",
    "\n",
    "Shares in companies:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f4e40d86",
   "metadata": {},
   "outputs": [],
   "source": [
    "equity = pd.read_csv(\"Input/Equity_Portfolio_test.csv\",index_col=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7aac3185",
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Asset_Type</th>\n",
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       "      <th>Growth_Rate</th>\n",
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       "    <tr>\n",
       "      <th>Asset_ID</th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1125</th>\n",
       "      <td>Equity_Share</td>\n",
       "      <td>A1.4.5</td>\n",
       "      <td>3/12/2021</td>\n",
       "      <td>0.03</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>94</td>\n",
       "      <td>1</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2123</th>\n",
       "      <td>Equity_Share</td>\n",
       "      <td>B5.2.0</td>\n",
       "      <td>3/12/2021</td>\n",
       "      <td>0.05</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>92</td>\n",
       "      <td>1</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3232</th>\n",
       "      <td>Equity_Share</td>\n",
       "      <td>B8.9.3</td>\n",
       "      <td>3/12/2019</td>\n",
       "      <td>0.04</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>96</td>\n",
       "      <td>1</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3237</th>\n",
       "      <td>Equity_Share</td>\n",
       "      <td>B8.9.3</td>\n",
       "      <td>3/12/2019</td>\n",
       "      <td>0.04</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>96</td>\n",
       "      <td>1</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "            Asset_Type    NACE Issue_Date  Dividend_Yield  Frequency  Units  \\\n",
       "Asset_ID                                                                      \n",
       "1125      Equity_Share  A1.4.5  3/12/2021            0.03          1      1   \n",
       "2123      Equity_Share  B5.2.0  3/12/2021            0.05          1      1   \n",
       "3232      Equity_Share  B8.9.3  3/12/2019            0.04          1      1   \n",
       "3237      Equity_Share  B8.9.3  3/12/2019            0.04          1      1   \n",
       "\n",
       "          Market_Price  Terminal  Default_Probability  Growth_Rate  \n",
       "Asset_ID                                                            \n",
       "1125                94         1                 0.03         0.01  \n",
       "2123                92         1                 0.03         0.02  \n",
       "3232                96         1                 0.03         0.04  \n",
       "3237                96         1                 0.03         0.00  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(equity)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e14d8dd",
   "metadata": {},
   "source": [
    "### Corporate bonds\n",
    "\n",
    "Corporate bonds:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "efe3f757",
   "metadata": {},
   "outputs": [],
   "source": [
    "bonds = pd.read_csv(\"Input/Bond_Portfolio_test.csv\",index_col=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "441012de",
   "metadata": {},
   "outputs": [
    {
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1234</th>\n",
       "      <td>Corporate_Bond</td>\n",
       "      <td>A1.4.5</td>\n",
       "      <td>3/12/2021</td>\n",
       "      <td>12/12/2026</td>\n",
       "      <td>100</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.01</td>\n",
       "      <td>1</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.03</td>\n",
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       "      <td>94</td>\n",
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       "    <tr>\n",
       "      <th>2889</th>\n",
       "      <td>Corporate_Bond</td>\n",
       "      <td>B5.2.0</td>\n",
       "      <td>3/12/2021</td>\n",
       "      <td>12/12/2028</td>\n",
       "      <td>100</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.01</td>\n",
       "      <td>2</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.03</td>\n",
       "      <td>2</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>Corporate_Bond</td>\n",
       "      <td>B8.9.3</td>\n",
       "      <td>3/12/2019</td>\n",
       "      <td>3/12/2025</td>\n",
       "      <td>100</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.01</td>\n",
       "      <td>12</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.03</td>\n",
       "      <td>3</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
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      "text/plain": [
       "              Asset_Type    NACE Issue_Date Maturity_Date  Notional_Amount  \\\n",
       "Asset_ID                                                                     \n",
       "1234      Corporate_Bond  A1.4.5  3/12/2021    12/12/2026              100   \n",
       "2889      Corporate_Bond  B5.2.0  3/12/2021    12/12/2028              100   \n",
       "31        Corporate_Bond  B8.9.3  3/12/2019     3/12/2025              100   \n",
       "\n",
       "          Coupon_Rate  Z_Spread  Frequency  Recovery_Rate  \\\n",
       "Asset_ID                                                    \n",
       "1234             0.03      0.01          1            0.4   \n",
       "2889             0.05      0.01          2            0.4   \n",
       "31               0.04      0.01         12            0.4   \n",
       "\n",
       "          Default_Probability  Units  Market_Price  \n",
       "Asset_ID                                            \n",
       "1234                     0.03      1            94  \n",
       "2889                     0.03      2            92  \n",
       "31                       0.03      3            96  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(bonds)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ff24892",
   "metadata": {},
   "source": [
    "### Cash\n",
    "\n",
    "Initial cash position:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1a47498e",
   "metadata": {},
   "outputs": [],
   "source": [
    "cash = pd.read_csv(\"Input/Cash_Portfolio_test.csv\",index_col=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6a392a2e",
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>Bank_Account</th>\n",
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       "      <th>1</th>\n",
       "      <td>10000</td>\n",
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       "          Bank_Account\n",
       "Asset_ID              \n",
       "1                10000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(cash)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3d4d432",
   "metadata": {},
   "source": [
    "### Liability profile\n",
    "\n",
    "An aggregated view of liabilities displayed as aggregated outflows at future dates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9445d8a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "liability = pd.read_csv(\"Input/Liability_Cashflow.csv\",index_col=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7b952e34",
   "metadata": {},
   "outputs": [
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       "      <th>Liability_Size</th>\n",
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       "      <th></th>\n",
       "    </tr>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1/9/2023</th>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2/10/2023</th>\n",
       "      <td>92</td>\n",
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       "      <th>2/11/2023</th>\n",
       "      <td>93</td>\n",
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       "      <th>3/12/2023</th>\n",
       "      <td>2</td>\n",
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       "      <th>3/1/2024</th>\n",
       "      <td>7</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
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       "      <th>19/3/2049</th>\n",
       "      <td>14</td>\n",
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       "    <tr>\n",
       "      <th>19/4/2049</th>\n",
       "      <td>28</td>\n",
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       "    <tr>\n",
       "      <th>20/5/2049</th>\n",
       "      <td>53</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20/6/2049</th>\n",
       "      <td>92</td>\n",
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       "    <tr>\n",
       "      <th>21/7/2049</th>\n",
       "      <td>41</td>\n",
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       "<p>306 rows × 1 columns</p>\n",
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      "text/plain": [
       "                Liability_Size\n",
       "Liability_Date                \n",
       "1/9/2023                     6\n",
       "2/10/2023                   92\n",
       "2/11/2023                   93\n",
       "3/12/2023                    2\n",
       "3/1/2024                     7\n",
       "...                        ...\n",
       "19/3/2049                   14\n",
       "19/4/2049                   28\n",
       "20/5/2049                   53\n",
       "20/6/2049                   92\n",
       "21/7/2049                   41\n",
       "\n",
       "[306 rows x 1 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(liability)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da3280f5",
   "metadata": {},
   "source": [
    "<a id=\"3\"></a> <br>\n",
    "## What is in the summary csv\n",
    "\n",
    "During the OSEM run, pieces of information area saved into the \"Summary\" dataframe. The object captures the performance of the portfolio and size of cash flows in each step."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da091298",
   "metadata": {},
   "source": [
    "***\n",
    "<span style=color:black>\n",
    "    <b>SUMMARY OBJECT</b>\n",
    "</span>\n",
    "<br>\n",
    "<span style=color:black>   \n",
    "    All collumns\n",
    "</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "fd4ee55c",
   "metadata": {},
   "outputs": [
    {
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       "      <th>Start cash</th>\n",
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       "      <th>2023-04-29</th>\n",
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       "      <th>2024-04-28</th>\n",
       "      <td>1.000000e+04</td>\n",
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       "      <td>944.000000</td>\n",
       "      <td>1131.647758</td>\n",
       "      <td>11094.910085</td>\n",
       "      <td>0.198779</td>\n",
       "      <td>15.262327</td>\n",
       "      <td>167.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-219.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-04-28</th>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>-6.821210e-13</td>\n",
       "      <td>11094.910085</td>\n",
       "      <td>11257.140153</td>\n",
       "      <td>12979.814124</td>\n",
       "      <td>0.014622</td>\n",
       "      <td>152.371222</td>\n",
       "      <td>1637.302749</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-67.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2026-04-28</th>\n",
       "      <td>-6.821210e-13</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>12979.814124</td>\n",
       "      <td>13090.969540</td>\n",
       "      <td>17276.502093</td>\n",
       "      <td>0.008564</td>\n",
       "      <td>178.930021</td>\n",
       "      <td>1345.240337</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3391.362195</td>\n",
       "      <td>-730.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2027-04-28</th>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>-5.911716e-12</td>\n",
       "      <td>17276.502093</td>\n",
       "      <td>17395.189415</td>\n",
       "      <td>18978.761104</td>\n",
       "      <td>0.006870</td>\n",
       "      <td>240.546475</td>\n",
       "      <td>343.134796</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1491.890418</td>\n",
       "      <td>-492.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2028-04-27</th>\n",
       "      <td>-5.911716e-12</td>\n",
       "      <td>-1.136868e-12</td>\n",
       "      <td>18978.761104</td>\n",
       "      <td>19090.621750</td>\n",
       "      <td>18958.562891</td>\n",
       "      <td>0.005894</td>\n",
       "      <td>267.400197</td>\n",
       "      <td>325.540943</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-725.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2029-04-27</th>\n",
       "      <td>-1.136868e-12</td>\n",
       "      <td>-9.094947e-13</td>\n",
       "      <td>18958.562891</td>\n",
       "      <td>19072.185893</td>\n",
       "      <td>22132.001591</td>\n",
       "      <td>0.005993</td>\n",
       "      <td>270.636452</td>\n",
       "      <td>323.289022</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3232.890224</td>\n",
       "      <td>-767.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2030-04-27</th>\n",
       "      <td>-9.094947e-13</td>\n",
       "      <td>-1.136868e-13</td>\n",
       "      <td>22132.001591</td>\n",
       "      <td>22263.127554</td>\n",
       "      <td>21957.250051</td>\n",
       "      <td>0.005925</td>\n",
       "      <td>320.122497</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-626.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2031-04-27</th>\n",
       "      <td>-1.136868e-13</td>\n",
       "      <td>-1.023182e-12</td>\n",
       "      <td>21957.250051</td>\n",
       "      <td>22088.246116</td>\n",
       "      <td>21861.138535</td>\n",
       "      <td>0.005966</td>\n",
       "      <td>321.892419</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-549.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2032-04-26</th>\n",
       "      <td>-1.023182e-12</td>\n",
       "      <td>-6.821210e-13</td>\n",
       "      <td>21861.138535</td>\n",
       "      <td>22003.641584</td>\n",
       "      <td>21805.518160</td>\n",
       "      <td>0.006519</td>\n",
       "      <td>324.876576</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-523.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Start cash      End cash  Start market value  \\\n",
       "2023-04-29           NaN  1.000000e+04                 NaN   \n",
       "2024-04-28  1.000000e+04  0.000000e+00          944.000000   \n",
       "2025-04-28  0.000000e+00 -6.821210e-13        11094.910085   \n",
       "2026-04-28 -6.821210e-13  0.000000e+00        12979.814124   \n",
       "2027-04-28  0.000000e+00 -5.911716e-12        17276.502093   \n",
       "2028-04-27 -5.911716e-12 -1.136868e-12        18978.761104   \n",
       "2029-04-27 -1.136868e-12 -9.094947e-13        18958.562891   \n",
       "2030-04-27 -9.094947e-13 -1.136868e-13        22132.001591   \n",
       "2031-04-27 -1.136868e-13 -1.023182e-12        21957.250051   \n",
       "2032-04-26 -1.023182e-12 -6.821210e-13        21861.138535   \n",
       "\n",
       "            After growth market value  End market value  Portfolio return  \\\n",
       "2023-04-29                        NaN        944.000000               NaN   \n",
       "2024-04-28                1131.647758      11094.910085          0.198779   \n",
       "2025-04-28               11257.140153      12979.814124          0.014622   \n",
       "2026-04-28               13090.969540      17276.502093          0.008564   \n",
       "2027-04-28               17395.189415      18978.761104          0.006870   \n",
       "2028-04-27               19090.621750      18958.562891          0.005894   \n",
       "2029-04-27               19072.185893      22132.001591          0.005993   \n",
       "2030-04-27               22263.127554      21957.250051          0.005925   \n",
       "2031-04-27               22088.246116      21861.138535          0.005966   \n",
       "2032-04-26               22003.641584      21805.518160          0.006519   \n",
       "\n",
       "            Dividend cash flow  Coupon cash flow  Terminal cash flow  \\\n",
       "2023-04-29                 NaN               NaN                 NaN   \n",
       "2024-04-28           15.262327        167.000000                 0.0   \n",
       "2025-04-28          152.371222       1637.302749                 0.0   \n",
       "2026-04-28          178.930021       1345.240337                 0.0   \n",
       "2027-04-28          240.546475        343.134796                 0.0   \n",
       "2028-04-27          267.400197        325.540943                 0.0   \n",
       "2029-04-27          270.636452        323.289022                 0.0   \n",
       "2030-04-27          320.122497          0.000000                 0.0   \n",
       "2031-04-27          321.892419          0.000000                 0.0   \n",
       "2032-04-26          324.876576          0.000000                 0.0   \n",
       "\n",
       "            Notional cash flow  Liability cash flow  \n",
       "2023-04-29                 NaN                  NaN  \n",
       "2024-04-28            0.000000               -219.0  \n",
       "2025-04-28            0.000000                -67.0  \n",
       "2026-04-28         3391.362195               -730.0  \n",
       "2027-04-28         1491.890418               -492.0  \n",
       "2028-04-27            0.000000               -725.0  \n",
       "2029-04-27         3232.890224               -767.0  \n",
       "2030-04-27            0.000000               -626.0  \n",
       "2031-04-27            0.000000               -549.0  \n",
       "2032-04-26            0.000000               -523.0  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b977832c",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59fd3008",
   "metadata": {},
   "source": [
    "<a id=\"4\"></a> <br>\n",
    "### Periodic cash flows\n",
    "\n",
    "The portfolio generates periodic cash flows from its investment portfolio and outflows from liabilities that the company commited to. Example of recurent inflows are dividends and coupons.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "fc0220d6",
   "metadata": {},
   "outputs": [],
   "source": [
    "time_axis = out.index[:-1]\n",
    "\n",
    "div_axis = out[\"Dividend cash flow\"][:-1]\n",
    "coup_axis = out[\"Coupon cash flow\"][:-1]\n",
    "liab_axis = out[\"Liability cash flow\"][:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "87870927",
   "metadata": {},
   "outputs": [
    {
     "data": {
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DPO99e0vY/pYrFWma/H3g75hsb10prRLiPF4IK5DkGKwEHGjXRLQkYE3OKlZp8vdBIPcd9eRodQ1P35AVtOQYrAQcSNeEJmClnE2Tvxtv/ff+HphsrislmMkxHIlZKRWd4iIdgF3Ude1UVFVj+K5rZ3lJRX3fe2MpyYkkJ8Y3KEtOjOfGwRd6LK/rxlFKqUiLyT1/f+9HGsiY7LN14yilVCTFXPL3dvC2uUvgBjImW7tSlFJ2FnPJ39se/tmGW2oyV0pFk5jr82/uRCvtp1dKxYqYS/7eDt6mpSTzxLhMzkuoBUz9a+2nV0pFo5jr9vF28FbvR6qUiiUxl/zPdvBWKaViQcSSv4j8CHgGiAdeNMbMDvY6vJ20pXv4SqlYF5HkLyLxwB+Bq3Hd0L1IRN42xmwN1jq8DekEdC9fKRXzxHi5Dk1IVyoyFJhljBllvZ4JYIx5wts8OTk5pri42Od1DJu9ioqqav7Ppr/S/WhFfXmrhHiyL0rhwIEDAFxwwQUN5vNW3ty0UJdH+7rDsQ5dt36uTl33N507MfLVV5usw1cissEYk9OkPELJfzzwI2PMndbrScBgY8y0RvWmAFMALrroogFffPGFz+voNuNdDDRJ/gBDundoWQOUUipMWvXqyQUPPRTw/N6Sf6T6/MVDWZOtkDFmPjAfXHv+/qyg7kYkz/cb3aA8LSWZG2aM9GdRSikVdSI1zr8cuNDtdTqwL5grmD6qh560pZRSXkSq2ycB+BS4CqgAioCbjDFbmpnnMOB7vw8Ql9yufXyb9mkSn3COqT39be3xIxVnqr8+0pLYgyAV+CrCMURCrLYbYrft2u7I+wrAGPOjxhMi0u1jjDktItOAFbiGev65ucRvzdMxLMGFmIgUe+p/i3ax2m6I3bZru+0tYuP8jTHvAe9Fav1KKRXLYu7aPkoppTT5R8L8SAcQIbHabojdtmu7bSwiB3yVUkpFlu75K6VUDNLkr5RSMUiTfwuJyIUislpEtonIFhH5pVXeXkQ+EJHPrMfzrfJBIlJq/W0UkbFuyxogImUislNE5oqIpzOhbcHfdrvNd5GIHBeRX7mVOabdENBnniEi1W6f+zy3ZTmm7YF85iLST0QKrfplIpJklUdtu0VkottnXSoiZ0Qky5pmn3YbY/SvBX9AF+Ay63lbXCev9QaeBGZY5TOA/7aetwYS3OY95Pb6Y2Aorstf/B34caTbF6x2u833F+BN4FduZY5pd4CfeQaw2cuyHNP2ANqdAGwC+luvOwDx0d7uRvNmAp/b8fPWPf8WMsbsN8Z8Yj0/BmwD0oDRwAKr2gJgjFXnhDHmtFWehHVNIxHpArQzxhQa13/Jwrp57MjfdgOIyBjgc2CLW5mj2g2Btd0Tp7U9gHb/ENhkjNlozVNpjKmNgXa7uxFYDPb7vDX5B5GIZADZwL+AzsaY/eD65wE6udUbLCJbgDJgqrUxSMN1zaM65VaZ7fnSbhE5F3gQeLTR7I5tN/j+mQPdRKRERP4pIrlWmWPb7mO7vw8YEVkhIp+IyP9vlUd7u93dgJX8sVm7Y+42jqEiIm1wdWncZ4z5urmuPGPMv4A+ItILWCAif8fHK53ajR/tfhR42hhzvFEdR7Yb/Gr7fuAiY0yliAwAlotIHxzadj/anQAMBwYCJ4APRWQD8LWHutHU7rr6g4ETxpjNdUUeqkWs3Y4Z55+ammoyMjIiHYbtVZ2o4cDXJ6mpPUNifBwXtEsipXVipMNSSkXIhg0bvjIero3mmD3/jIwM/LmTVyyqu3VlqnXrSoDExHh+My5Tb12pVIwSEY9XQ9Y+/yiSv2JH/T2L61TX1JK/YkeEIlJK2ZUm/yiyr6rar3KlVOzS5B9FuqYk+1WulIpdjunzV2c3fVQPZi4ra9D1o7eujG01NTWUl5dz8uTJSIeiQiwpKYn09HQSE30b4KHJP4rUHdT9j4U7qD2nmrTzk5k+qoce7I1h5eXltG3bloyMDGx8BQXVQsYYKisrKS8vp1u3bj7No8k/yozJTmPO/a5kv2ZNZGNRkXfy5ElN/DFAROjQoQOHDx/2eR7t81cqymnijw3+fs6656+Uqre8pIL8FTvYV1VN1xTtNoxmuuevHG95SQXDZq+i24x3GTZ7FctLKiIdkiPVnSRYUVWNASqqqpm5rKzF7+eBAweYMGECl1xyCb179+aaa67h008/DU7QNrFmzRquvfbas9bbvn07WVlZZGdns2vXLtq0aROG6DzT5K8cLVQJKxaF4iRBYwxjx45lxIgR7Nq1i61bt/L4449z8ODBlobrSMuXL2f06NGUlJRwySWXRDQWTf7K0fSs5uAJxUmCq1evJjExkalTp9aXZWVlkZubizGG6dOn07dvXzIzM1myZAnQdC962rRpvPLKK4DrMi8PPvgggwYNYtCgQezcuROAL774gquuuop+/fpx1VVX8eWXXwJw2223ce+993L55ZfTvXt3li5d6jHOhQsX0q9fP/r378+kSZMA+Nvf/sbgwYPJzs7mBz/4Qf0G65///CdZWVn1e/DHjh0D4Pjx44wfP56ePXsyceJEGl837b333mPOnDm8+OKLXHnllQ2meXsv7r77bt5++20Axo4dyx133AHASy+9xG9+8xt/PoomNPkrR9OzmoMnFCcJbt68mQEDBnictmzZMkpLS9m4cSMrV65k+vTp7N+//6zLbNeuHR9//DHTpk3jvvvuA1wbiFtuuYVNmzYxceJE7r333vr6+/fvZ926dbzzzjvMmDGjyfK2bNnCY489xqpVq9i4cSPPPPMMAMOHD+ejjz6ipKSECRMm8OSTTwLw1FNP8cc//pHS0lIKCgpITna9PyUlJcyZM4etW7fy+eefs379+gbrueaaa5g6dSr3338/q1ev9um9yMvLo6CgAICKigq2bt0KwLp168jNzaUlNPkrR9OzmoNn+qgeJCfGNygL5UmC69at48YbbyQ+Pp7OnTtzxRVXUFRUdNb5brzxxvrHwsJCAAoLC7npppsAmDRpEuvWrauvP2bMGOLi4ujdu7fH7qZVq1Yxfvx4UlNTAWjfvj3gOkdi1KhRZGZmkp+fz5YtrnsQDRs2jAceeIC5c+dSVVVFQoJr3MygQYNIT08nLi6OrKws9uzZ0+L3Ijc3l4KCArZu3Urv3r3p3Lkz+/fvp7CwkMsvv9zn5XuiyV85WrgTVjQbk53GE+MyiT+VDAbSUpJ5ooVXhO3Tpw8bNmzwOM3b5eQTEhI4c+ZM/evGZye7D2n0NrzRvbxVq1bNrtMY43E599xzD9OmTaOsrIznn3++Po4ZM2bw4osvUl1dzZAhQ9i+fXuT9cTHx3P69Okmy/TG23uRlpbGv//9b95//33y8vLIzc3ljTfeoE2bNrRt29bn5XuiQz2Vo+lZzb478PjjnNq2vdk62cDvS13Ps7KALeDxesCWVr16csFDD3mdPnLkSB566CFeeOEFJk+eDEBRUREnTpwgLy+P559/nltvvZUjR46wdu1a8vPzqampYevWrZw6dYqTJ0/y4YcfMnz48PplLlmyhBkzZrBkyRKGDh0KwOWXX87rr7/OpEmTWLRoUYP6Z3PVVVcxduxY7r//fjp06MCRI0do3749R48eJS3N9X+0YMGC+vq7du0iMzOTzMxMCgsL2b59OykpKT6vzxNv7wXA0KFDmTNnDqtWraKyspLx48czfvz4Fq0PNPmrKKBnNQdXVlbwliUivPXWW9x3333Mnj2bpKQkMjIymDNnDnl5eRQWFtK/f39EhCeffJILLrgAgJ/97Gf069ePSy+9lOzs7AbLPHXqFIMHD+bMmTMsXuy6Q+LcuXO54447yM/Pp2PHjrz88ss+x9inTx9+/etfc8UVVxAfH092djavvPIKs2bN4vrrryctLY0hQ4awe/duAObMmcPq1auJj4+nd+/e/PjHP67vfgrU2LFjvb4Xubm5/OMf/+B73/seF198MUeOHGlxfz846E5eOTk5Rm/m4psRI1yPsZQIY7HNvti2bRu9evWKdBhBU3dTp7r+edWQp89bRDYYY3Ia19U+f6WUikHa7aOUcgx/RtCo5umev1JRzildu6pl/P2cfU7+IvJnETkkIpvdytqLyAci8pn1eL7btJkislNEdojIKLfyASJSZk2bK3rJQaVCJikpicrKSt0ARLm66/knJSX5PI8/3T6vAM8CC93KZgAfGmNmi8gM6/WDItIbmAD0AboCK0Xk+8aYWuA5YArwEfAe8CPg737EoZTyUXp6OuXl5X5d5105U92dvHzlc/I3xqwVkYxGxaOBEdbzBcAa4EGr/HVjzClgt4jsBAaJyB6gnTGmEEBEFgJj0OSvVEgkJib6fGcnFVta2uff2RizH8B67GSVpwF73eqVW2Vp1vPG5UoppcIoVAd8PfXjm2bKPS9EZIqIFItIsf5sVUqp4Glp8j8oIl0ArMdDVnk5cKFbvXRgn1We7qHcI2PMfGNMjjEmp2PHji0MVSmlVJ2WJv+3gVut57cCf3UrnyAirUSkG3Ap8LHVNXRMRIZYo3xucZtHKaVUmPh8wFdEFuM6uJsqIuXAI8Bs4A0R+TnwJXA9gDFmi4i8AWwFTgO/sEb6ANyFa+RQMq4DvXqwVymlwsyf0T43epl0lZf6jwGPeSgvBvr6ul6llFLBp2f4KqVUDNLkr5RSMUiTv1JKxSBN/kopFYM0+SulVAzS5K+UUjFIk79SSsUgTf5KKRWDNPkrpVQM0uSvlFIxSJO/UkrFIE3+SikVgzT5K6VUDNLkr5RSMUiTv1JKxSCfr+evlLKP5SUV5K/Ywb6qarqmJDN9VA/GZKdFOizlIJr8lXKY5SUVzFxWRnWN6+Z4FVXVzFxWBhC1G4BY3NiFus3a7aOUw+Sv2FGf+OtU19SSv2JHhCIKrbqNXUVVNYbvNnbLSyoiHVrIhKPNmvyVcph9VdV+lTtdrG3sIDxt1uSvlMN0TUn2q9zpYm1jB+FpsyZ/pRxm+qgeJCfGNyhLToxn+qgeEYootGJtYwfhaXNUJ//lJRUMm72KbjPeZdjsVVHdR6hix5jsNJ4Yl0n8qWQwkJaSzBPjMqP2AGisbewgPG2O2tE+sTgiQsWOMdlpzLnf9X+8Zk1kYwm1uu/rfyzcQe051aSdH/2jfcLR5qhN/s0dMInmfxqlolEsbezqhLrNUdvtE4sHiZRSyldRm/xj8SCRUkr5KmqTfyweJFJKKV9FLPmLyI9EZIeI7BSRGcFefqyNiFBKKX9E5ICviMQDfwSuBsqBIhF52xizNZjricWDREop5YtIjfYZBOw0xnwOICKvA6OBoCZ/gOu/fpz0mu18MSnYS7av+ytdj9rm6BZrbY619oKrzeWJPYGHgr7sSCX/NGCv2+tyYHDjSiIyBZgCcNFFFwW0ouvGw6ltAc3qWFlZkY4g/LTN0S/W2guuNg/uFZplRyr5i4cy06TAmPnAfICcnJwm031xwUPB32IqpZTTReqAbzlwodvrdGBfhGJRSqmYI8YEtEPdspWKJACfAlcBFUARcJMxZksz8xwGvghPhBGRCnwV6SDCTNscG7TNkXWxMaZj48KIdPsYY06LyDRgBRAP/Lm5xG/N0yT4aCIixcaYnEjHEU7a5tigbbaniF3bxxjzHvBepNavlFKxLGrP8FVKKeWdJn/7mB/pACJA2xwbtM02FJEDvkoppSJL9/yVUioGafJXSqkYpMk/RETkQhFZLSLbRGSLiPzSKm8vIh+IyGfW4/lW+dUiskFEyqzHkW7LWmNdAbXU+usUqXY1J8htPkdE5ovIpyKyXUSui1S7mhOsNotIW7fPt1REvhKRORFsmldB/pxvtMo3icj7IpIaqXY1J8htvsFq7xYReTJSbcIYo38h+AO6AJdZz9viOqmtN/AkMMMqnwH8t/U8G+hqPe8LVLgtaw2QE+k2hbnNjwK/s57HAamRbl+o29xouRuAvEi3L5RtxjXU/FDdZ2vNPyvS7QtxmzsAXwIdrdcLgKsi0qZIv6mx8gf8FdclrHcAXdz+oXZ4qCtAJdDKeu2I5B/kNu8Fzo10G8LZZrfyS632S6TbE8o2A4nAYeBiq3weMCXS7QlxmwcCK92mTQL+FIk2aLdPGIhIBq49gX8BnY0x+wGsR09dONcBJcaYU25lL1vdAf8pIp4ujGcrLWmziKRYZf8lIp+IyJsi0jkMYbdIkD5ngBuBJcbKDnbWkjYbY2qAu4AyXNf26g28FI64W6KFn/NOoKeIZFiXuRlDw+uchU+kt6DR/ge0wfUTfpz1uqrR9H83et0H2AVc4laWZj22Bf4B3BLpdoWyzbiui2KA66zXDwD/E+l2hfpzdpu2FRgQ6TaF4XNOBD4ELsG1d/ws8JtItyvUnzPwU1wbjkLg/wJvRaItERvnLyI/Ap7BdW2fF40xs5urn5qaajIyMsIRmlJKRY0NGzZ8ZexyYbdAbuOYkZFBcXFxuEJUSqmoICIer4Yc9bdxPPD445zatj3Yi1VKqbBo1atnSG5KFakDvp5u45jWuJKITBGRYhEpPnz4cGBrWvoXKC31vX5pqe/1/akb6vp2isXf+hpLcOprLPaPxd/6paWuHBYCkbqZy/XAKGPMndbrScAgY8w93ubJyckxAXX7jBjhelyzJvj1Q7lsJ8fib32NJTj1NRb7x+JvfX+X7YGIbDAe7i0QqW4fW97GcXlJBfnZU9h3Tju6zl7F9FE9GJPd5AeJ8qCmpoby8nJOnjzpKnjkEdfjtm1nn9mfuqGub6dY/K0f5liSkpJIT08nMTHRt/mVrUQq+RcBl4pIN1y3cZwA3BShWABX4p+5rIzqVucBUFFVzcxlZQC6AfBBeXk5bdu2JSMjAxGBOKtHsUePs8/sT91Q17dTLP7WD2MsxhgqKyspLy+nW7duvs2vbCUiff7GmNNA3W0ctwFvmLPcxjHU8lfsoLqmtkFZdU0t+St2RCgiZzl58iQdOnTAAeefqSAQETp06PDdLz3lOHobR8u+qmq/ylVTmvhji37ezhax5G83XVOSqfCQ6LumJEcgmui3vKSC/BU72FdVTddzE5g+oD1jfOx9UEq1nF7bxzJ9VA+SE+MblCUnxjN9lGakYKs7vlJRVY0BKr45zcz1h1leUtGi5bZp06ZJ2bx581i4fHmz8912220sXbq0SXlxcTH33nsvAK+88grTpk37bpkLF7rKly1j38GDLYo7EJ7a2tipU6f4wQ9+QFZWFkuWLGHEiBF6oqSqp3v+lrqDuvV7oynJOtonRDweX6k15K/YEfT3e+rUqbAjsOM2OTk55OQ0GSHnWqbllbfeou+ll9I14AhDp6SkhJqaGkqtMeXPPfdcZANStqJ7/m7GZKexfsZIds/+CetnjNTEHyLhPL4ya9YsnnrJdaHIF154gYEDB9K/f3+uu+46Tpw4UV9v5cqV5Obm8v1Ro3hn9WoA1qxZw7XXXut5mU89xdKlSynesoWJ06eTlZXFu+++y9ixY+vrffDBB4wbN67J/EVlZVx++eX079+fQYMGcezYMfbs2UNubi6XXXYZl112Gf/7v/8LwP5Dh8i7+WaysrLo27cvBQUF9cv59a9/Tf/+/RkyZAgHG/36OHToEDfffDOlpaVkZWWxa9euBtMXL15M5k9/St+f/pQHH3wQgDfeeIMHHngAgGeeeYbu3bsDsGvXLoYPH+7jO66cQpO/Cjtvx1FCfXxl3LhxFBUVsXHjRnr16sVLL3139eA9e/bwz3/+k3eff56ps2b5NIpl/Pjx5PTpw6L8fEpLS7nmmmvYtm0bdWejv/zyy9x+++0N5vn222+54f77eeaZZ9i4cSMrV64kOTmZTp068cEHH/DJJ5+wZMmS+u6m1955h1HDh1NaWsrGjRvJysoC4JtvvmHIkCFs3LiRvLw8XnjhhQbr6dSpEy+++CK5ubmUlpZyySWX1E/bt28fDz74IKsWLKD0rbcoKipi+fLl5OXl1W9cCgoK6NChAxUVFaxbt47c3Fz/33Bla5r8Vdh5PL4SLyE/vrJ582Zyc3PJzMxk0aJFbNny3ejin/3sZ8TFxXFpRgbdL7yQ7dv9vx6UiDBp0iReffVVqqqqKCws5Mc//nGDOjt276ZLx44MHDgQgHbt2pGQkEBNTQ2TJ08mMzOT66+/nq1bXZe5GpiZycvLljFr1izKyspo27YtAOecc079r5IBAwawZ88en+MsKipixIgRdGzfnoSEBCZOnMjatWu54IILOH78OMeOHWPv3r3cdNNNrF27loKCAk3+EbC8pIJh2VPoNvhXDJu9qsXHxBrT5K/Cbkx2Gk+MyyTt1FHEGNLOTeCJYR1D3s1222238eyzz1JWVsYjjzzSYO++8bDFQIcx3n777bz66qssXryY66+/noSEhofVjJdlP/3003Tu3JmNGzdSXFzMt99+C0DewIGs/Z//IS0tjUmTJtUfaE5MTKxfTnx8PKdPn/Y5xuYu6TJ06FBefvllevToQW5uLgUFBRQWFjJs2DCfl69arn5QRKvzMCL1J50GcwMQ1Qd89XINkXHg8cc59cknrhfJrT3WyQZeq7u4VY/vw0b4YrHnuhCcKxseO3aMLl26UFNTw6JFi0hL++5/4c033+TWW29l95df8vnevfTo0YOPPvrorMtse+65HPvmm/rXXbt2pWvXrvzud7/jgw8+aFK/Z7du7Dt0iKKiIgYOHMixY8dITk7m6NGjpKenExcXx4IFC6itdR0Q/6KigrTOnZk8eTLffPMNn3zyCbfcckuL3ofBgwfzy1/+kq/uvpvz27Vj8eLF3HOP67JaeXl5PPzwwzz88MNkZ2ezevVqkpOTOe+88+DAgRatV/muuZNOg5XDojb56+UaHMDqv6b6RLPVfHXixAnS09PrX9cdvKzzX//1XwwePJiLL76YzMxMjh07Vj+tR48eXHHFFRzcu5d5s2aRlJTk0zpvGzuWqbNmkfz00xQWFpKcnMzEiRM5fPgwvXv3blL/nHPOYcnTT3PPPfdQXV1NcnIyK1eu5O677+a6667jzTff5Morr+Tcc88FYM3HH5P/5z+TeO65tGnTpn7PvyW6dOnCE088wZW33IIBrhkzhtGjRwOQm5vL3r17ycvLIz4+ngsvvJCePXu2eJ3KP+EYFBGxO3n5y9+reg6bvcrjSVtpKcmsnzEyOEE5+ep/Qa6/bds2evXq9V1B3fBKX64b40/dUNcPwrKnTZtGdnY2P//5z0Oy/KDUDVL9Jp97Hf1utKh+MPOXt6t6Rm2fv16uQUXCgAED2LRpEzfffHOkQ1EOFo6TTqO220cv16AiYcOGDZEOQUWBcJx0GrXJf/qoHq4+f7eDJnq5htAyxujFvmKIU7qMnWpMdlpIj09GbbdP/XDClGQEV1/ZE+My9WBviCQlJVFZWakJIUbUXc/f1wPjyn6ids8fQr/lVN9JT0+nvLy8/uzW+mGBZ86cfWZ/6oa6vp1i8bd+mGOpu5OXcqaoTv4qfBITExve0emuu1yPvoyA8KduqOvbKRZ/69spFmV7Udvto5RSyjtN/kopFYM0+SulVAzS5K+UUjFIk79SSsUgTf5KhUmor8+ulD80+StlCWVyDsf12ZXyhyZ/pQh9cm7u+uyRoL9ClCZ/pQh9crbTVWb1V4gCTf5KAaFPzpG6ab0ndvsVoiJDk79ShD45h+P67L6y06+QWGOn7jZN/koR+uRsp6vM2ulXSCyxW3dbi5K/iMwSkQoRKbX+rnGbNlNEdorIDhEZ5VY+QETKrGlzJUYuAG+nLb5qKhzJeUx2GutnjGT37J+wfsbIiF1x1k6/QmKJ3brbgnFVz6eNMU+5F4hIb2AC0AfoCqwUke8bY2qB54ApwEfAe8CPgL8HIQ7b0pvJO0OsXAI8HHeJUk3ZrbstVJd0Hg28bow5BewWkZ3AIBHZA7QzxhQCiMhCYAxRnvyb2+JH4xdueUkF+dlT2HdOO7rOXhXUxBLKZceSUG7o9DPyzG63lg1Gn/80EdkkIn8WkfOtsjRgr1udcqsszXreuNwjEZkiIsUiUlx/kxAHstsWP5RC2a9ptz5T7cprKhyfkVPfd7t1t501+YvIShHZ7OFvNK4unEuALGA/8H/rZvOwKNNMuUfGmPnGmBxjTE7Hjh3PFqptOf0Amz9ftlD2a9qpz9RuGyK7CPVn5OT33U4H/cGHbh9jzA98WZCIvAC8Y70sBy50m5wO7LPK0z2URzUn30ze3+MVofyVY6dfULHWleerUH9GTn/f7XRcqaWjfbq4vRwLbLaevw1MEJFWItINuBT42BizHzgmIkOsUT63AH9tSQxOYLctvj/83ZML5a8cO/2CstOGyE5C/Rnp+x48Le3zf9IatrkJuBK4H8AYswV4A9gKvA/8whrpA3AX8CKwE9hFlB/srWOXYX7+8vfLFsp+TTv1mdppQ2Qnof6MQv2+O/V4QiBaNNrHGDOpmWmPAY95KC8G+rZkvSp8/B2hEMphhHYaoujkrrxQCvVnFMr3PdaGZIdqqKeKEoF82ULZr2mXPlM7bYjCwZ/hm6H+/MH3992fuJ1+PMFfmvxjkL9fZHBukgvlmPNQb4jsMl7ebnvEvr7vdhqsYEea/GNMIF9ku+xt+8tuScsfdordqXvE/sZtt5OwQk0v7BZj7DRWPtSc3FY7xe7UPWI7DVawI03+McapX+RAOLmtdordqSOb/I3byUOyA6HdPjEmln7aOrmtdordqSOb7DZYwW50zz/GxNJPWye31U6xO3WP2Klxh4vu+ccYp4/e8YeT22q32J26R+zUuMNBjPF6XTVbycnJMcXFxZEOo97ykgryF/7TNQzv/NZB/2L6vfwRI1yPa9YELYZwCPX7GCsc/z469P8XsH3sIrLBGJPTuFz3/AMQ6mF4dhrmF0qx0s5Q0/dRBUL7/AMQ6mF4dhrmF0qx0s5Q0/dRBUKTfwBCPQzP3+U79WJUdhrO6GT6PqpAaPIPQKjHPfuzfCff3MKp48ftxunvo1N3XsDZsWvyD0Coh+H5s3wn/+S303BGJ3Py++jknRcnxw6a/AMS6vHD/izfyT/5dRx2cDj5fXTyzouTYwcd7ROwUI8f9nX5djoTNBA6Djs4nPo+Onnnxcmxg+75O56Tf/Ir5eTjFU6OHTT5O56Tf/Ir5eSdFyfHDg46w1dEDgNf+Fg9FfgqhOGEksYeGRp7+KUCX8Ult2sf36Z9msQnnGNqT39be/xIxZnqr49EOrizcFLsFxtjOjYudEzy94eIFHs6ndkJNPbI0NjDz6lxg7Njr6PdPkopFYM0+SulVAyK1uQ/P9IBtIDGHhkae/g5NW5wduxAlPb5K6WUal607vkrpZRqhiZ/pZSKQY5I/iJyoYisFpFtIrJFRH5plbcXkQ9E5DPr8Xyr/GoR2SAiZdbjSA/LfFtENjspdhG50SrfJCLvi0iqzWIfJCKl1t9GERlrlbcWkXdFZLu1nNmhjDuYsVvTzhGR+SLyqdWG6+wUu9t8F4nIcRH5lVvZAOt/ZqeIzBURcULcbtNs+T1tLvZwf08DZoyx/R/QBbjMet4W+BToDTwJzLDKZwD/bT3PBrpaz/sCFY2WNw54DdjslNhxXYfpEJBqvX4SmGWz2FsDCW7zHrLibg1caZWfAxQAP3ZC7NbrR4HfWc/j6j4Du8TuNt9fgDeBX7mVfQwMBQT4eyjf92DGbZXb9nvqLfZIfE8DbnOkAwjwg/orcDWwA+ji9uHt8FBXgEqglfW6DbDO+mBD/k8VrNiBROAwcLFVPg+YYuPYuwEH6xJoo2nPAJOdEjuwFzg33P8r/sQOjAHygVluiagLsN2tzo3A83aP2yq3/ffUy3se8e+pz22MdAABfCgZwJdAO6Cq0bR/e6g/Hljp9vppYKy1nLD+UwUh9vHA18B+YC0Qb7fYgcHAFuA4MNbDclKAz4HuTojdincv8HvgE1x7eZ3tFDtwLlBoJUz3RJTT6P8nF3jH7nFb02z9PT1L7BH7nvrz54g+/zoi0gbXz6z7jDFf+1C/D/DfwP+xXmcB3zPGvBXKOL3E0tLYE4G7sLqFgE3AzJAF3DAWn2M3xvzLGNMHGAjMFJEkt+UkAIuBucaYz0MZs9s6Wxp7ApAOrDfGXIbrC/9UiMMG/Ir9UeBpY8zxxovwUDfkY7tbGrdDvqfeYo/Y99Rvkd76+LE1TgRWAA+4lTX3kywdV7/dMLeyu4B9wB6gHPgWWOOQ2AcCH7q9zgPes1vsjeZdDeS4vf4zrsRvy/8ZT7HjSqDfAHFW+YXAFjvFjusYyh7rrwo4AkwjAt0+QYrb9t/TZmKPyPc0kD9H7PlbIxReArYZY37vNult4Fbr+a24+ukQkRTgXWCmMWZ9XWVjzHPGmK7GmAxgOPCpMWaEE2IHKoDeIlJ3db6rgW0hDD2Q2LtZe/eIyMVAD1xfDkTkd8B5wH2hjDnYsRvXN/hvwAhrnquArXaK3RiTa4zJsP6v5wCPG2OeNcbsB46JyBBrmbfUzWPzuG3/PfUWOxH4ngYs0lsfH7fIw3H9XN0ElFp/1wAdgA+Bz6zH9lb93+DaWyt1++vUaJkZhGcUQdBiB6bi+kfahCshdbBZ7JNw9ZmX4uofH2OVp1vL2ea2nDudELs17WJcfbebrHkuslPsjeadRcP+5xxgM7ALeBbrrH67x+1WnoENv6dnec/D+j0N9E8v76CUUjHIEd0+SimlgkuTv1JKxSBN/kopFYM0+SulVAzS5K+UUjFIk79SSsUgTf5KKRWD/h/X79c6Dz1j4gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1,ax2,ax3) = plt.subplots(3)\n",
    "ax1.stem(time_axis[div_axis>0], div_axis[div_axis>0], linefmt='grey',label='Dividend cash flow')\n",
    "ax2.stem(time_axis[coup_axis>0], coup_axis[coup_axis>0], linefmt='blue', label=\"Coupon cash flow\")\n",
    "ax3.stem(time_axis[liab_axis<0], liab_axis[liab_axis<0], linefmt='red', label= \"Liability cash flow\")\n",
    "\n",
    "ax1.legend()\n",
    "ax2.legend()\n",
    "ax3.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c140763",
   "metadata": {},
   "source": [
    "### Terminal cash flows\n",
    "\n",
    "Each asset in OSEM has a terminal value. For fixed income instruments, these are the notional payments at the maturity date, for equitiess, OSEM assumes that the all equity positions are sold at the end of the modelling window at market rates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "9d102200",
   "metadata": {},
   "outputs": [],
   "source": [
    "not_axis = out[\"Notional cash flow\"]\n",
    "term_axis = out[\"Terminal cash flow\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5aff5aae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1,ax2) = plt.subplots(2)\n",
    "ax1.stem(out.index[not_axis>0], not_axis[not_axis>0], linefmt='grey',label='Return of notional amount')\n",
    "ax2.stem(out.index[term_axis>0], term_axis[term_axis>0], linefmt='blue', label=\"Sale of equity portfolio\")\n",
    "\n",
    "ax1.legend()\n",
    "ax2.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "753de981",
   "metadata": {},
   "source": [
    "#### Cash movement"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d4dfd2a",
   "metadata": {},
   "source": [
    "The manangement of cash between periods is fundamental to OSEM. If the initial cash is high, then in the first period, the large cash position is sold in line with the asset allocation rule. This is why the initial cash is represented separately. After the first period, cash swings as the ballance of inflows/outflows changes through time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "28862566",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_axis = out.index\n",
    "end_cash_axis = out[\"End cash\"]\n",
    "start_cash_axis = out[\"Start cash\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e62a8775",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UlrzjYzUwH2gmGVRwyfnEPpZmlRuADc65wyl5rATeBQ6SvEcLwCPAzd7z1On4XyH56z11rugbvG6VZ80sdYLLXOvyG+Bsrw5+1CVVe7cWaM3j40AlsCrXunj5VBBsfV738gT4HNDTzPqGuC5550M9/hfwL8BH7WzmtJ+xzgpDPczsdjN7k2Sr4s7cahKOupDlMSyWAcXMykh2H9ztnPs5p05338Xru643s1+Z2TUk7xB5a+pCLjkvWX+gG8muEZxzvyD5xYeUqfWdcxtItlBa/QdQ4ZwbAbzMiZuHdaYu73dg+U93tC5tV02T1vZ9mwI865w7lmbZDglJfe4FLjOzDcBlwC68HxzZKGBd8qqz9TCzKuCTzrkXTrdqmjTfrlsISz2cc99zzn0CmAXc17HSn1K2MNQl+2NYZ5pjYXyQ7DpYCfz3lLQ3ObnL60PgU97/15CM4Je2k+ctwEKgBGggeQfK35O+uXgQKG+zfglwwKe6ZGz6kpza//dZ1qUB+EaGurTtjtgAXOLzvgmsPl56GdAY5rq0WcbXLi8/6gF8heQtJXaQ/IX7X8CaHD9jsaiHl96FgL73eahLh45hOR0YwvogGW2fAua3Sf8+8I73fC5wxHtDN5Hsomr0Xrse2Az8DtjqPd8MvA3ckZLf5cAy7/lvSQ6Ytg5o/YXkGEr/lOU/B/zap7o8wsmDcw97z3vjdeW0Wb4s5YPYFViaWpc2y7aty9Uprw31Ppzm874peH28/dPFe/5N2hy0w1iXlHV8Cyh+1aPNuhW0PwCc8TMWh3rg/VD1nv89UBfhumR9DMv6wBDmBzCGZHNtIyei8NVAFfAB8AeSUbo1uNxHsrXSkPL4GHC29yZvJDmA+29A15TtXM6JgFJDMui8SfLX5Q6SB6xveeu+DqwGzvWpLn2BX3h1+QXQpzN1abPNtnWxlNfmAQ/lYd8UvD4k77fzB5K/6n5AmwHykNblYZK/NFu8v/O89JHe/x+SHJB9o9D1aJNnBe0fvDLtk7jU41+9fdlA8nv/6SA+Wz7VJetjWFFMveINbi1zzg3z/n8V+K5z7ifeOdcjnHOvZ5Hf5cC9zrlr0ry2A6hxzsXlXgoiIh0Sy0H5VGa2BFgHDDWzRjP7MvAF4Mtm9jrJCHxdFvn9iuR1DH/r5dd6Q7E7zaz1FscbzewHftdFRCTMiqKFIiIi+Rf7FoqIiBRG16AL0FFm9gTJU3zfbR0LaU95ebmrqKjIe7lEROKkvr5+r8vxnvKRCSgkTydcSPKUutOqqKigrq4urwUSEems2g27eGTlNna/18yA3glmThjK5GpfJxDIipn9Odd1IxNQnHO/9M7WEhGJhdoNu5jz/CaajyQnn9j1XjNznt8EEGhQyVWsxlDMbIaZ1ZlZ3Z49e4IujohIux5Zue14MGnVfOQYj6zcFlCJOidWAcU5t8g5V+Ocq+nXL6cuQBGRgtn9XnNW6WEXmS4vPxw5coTGxkYOHToUdFGkQLp3786gQYMoLS0NuigipxjQO8GuNMFjQO9EAKXpvKIKKI2NjfTs2ZOKigq8m5JJjDnnaGpqorGxkcrKyqCLIzkK26C1n2ZOGHrSGApAorSEmROGBliq3EWmyyvDFe9ZOXToEH379lUwKRJmRt++fdUijbDWQetd7zXjODFoXbthV9BF88Xk6oF86/rhlBxOgIOBvRN86/rhkQ2YkWmhOOem+pGPgklx0f6OtvYGraN60G1rcvVA5t+TrMuaNcGWpbMiE1CCEOemtkgUxG3QOu4i0+VVaPlsar/wwguYGVu3bj2etmPHDoYNS04AsGbNGq655pSJjFm8eDF33HFHVttavHgxu3fvTvva1q1bqaqqorq6mjfffJNLLrkkq7znz5/PRx+1d3fR3NXV1XHnndndPbWiooK9ezXJc5xkGpyO6qB13CmgZJDP88OXLFnCmDFjeOaZZzqd1+m0F1Bqa2u57rrr2LBhA5/4xCd49dVXT1nm2LHMd/vNV0A5evQoNTU1LFiwwPe8JVpmThhKorTkpLQoD1rHnQJKBvlqan/wwQe88sor/PCHP8wpoOzcuZOJEycydOhQHnjgAeDk1g3Ad77zHebNm8ezzz5LXV0dX/jCF6iqqqK5+UTZX3zxRebPn88PfvADxo0bB0BZWRmQbCGNGzeOm266ieHDh/Phhx8yadIkLrjgAoYNG8bSpUtZsGABu3fvZty4ccfXT1VRUcGsWbMYNWoUo0aNYvv27QDs2bOHG264gZEjRzJy5EheeeUVAObNm8eMGTMYP34806dPP6mVtm/fPiZPnsyIESO46KKL2LhxIwBNTU2MHz+e6upqbr31VjRzdvzEbdA67jSGkkG+zg+vra1l4sSJnHPOOfTp04fXXnuNCy+8sMPrr1+/ns2bN9OjRw9GjhzJpEmTKC8vT7vsjTfeyMKFC/nOd75DTU3NSa9dffXV3HbbbZSVlXHvvfdm3E5lZSXPPfccAwYMYPny5QAcOHCAM888k0cffZTVq1dn3H6vXr1Yv349Tz31FHfffTfLli3jrrvu4p577mHMmDG89dZbTJgwgS1btgBQX1/P2rVrSSQSrEkZnbz//vuprq6mtraWVatWMX36dBoaGnjggQcYM2YMc+fOZfny5SxatKjD76NER5wGrfMt6HFftVAyyFdTe8mSJUyZMgWAKVOmsGTJkqzWv/LKK+nbty+JRILrr7+etWvXdqo8mYwaNer4tRvDhw/n5ZdfZtasWfzqV7/izDPP7FAeU6dOPf533bp1ALz88svccccdVFVVce211/L+++9z8OBBAK699loSiVMD9tq1a7n55psBuOKKK2hqauLAgQP88pe/ZNq0aQBMmjSJs846q3OVFomwMJxirRZKBq1R/Z+f2saxv2pm4Fmdj/ZNTU2sWrWKzZs3Y2YcO3YMM+Phhx/ucB5tT4M1M7p27UpLS8vxND+uuzjjjDOOPz/nnHOor6/nxRdfZM6cOYwfP565c+dmVdbW5y0tLaxbty5t4EjdZqp0XVmt+em0YJGkMJxiXbQB5Z0HH+Twlq3tLlMNPNqQfF5VBbwB7c3r3O28c/nrr30t4+vPPvss06dP5/vf//7xtMsuu4y1a9cyePDgDpX7pZdeYt++fSQSCWpra3niiSc4++yzeffdd2lqaqKsrIxly5YxceJEAHr27Hm8BZCr3bt306dPH6ZNm0ZZWRmLFy8+Ke9MXV5Lly5l9uzZLF26lIsvvhiA8ePHs3DhQmbOnAlAQ0MDVVVV7W5/7NixPP3003z9619nzZo1lJeX06tXr+Pp9913HytWrGD//v2dqqdIlIXhFOuiDSgddZpjXVaWLFnC7NmzT0q74YYb+PGPf8ysWbM6lMeYMWO4+eab2b59OzfddNPxsZG5c+cyevRoKisrOffcc48v/8UvfpHbbruNRCKRsWVwOps2bWLmzJl06dKF0tJSHnvsMQBmzJjBVVddRf/+/Vm9evUp6x0+fJjRo0fT0tJyvGtvwYIF3H777YwYMYKjR48yduxYHn/88Xa3P2/ePL70pS8xYsQIevTowZNPPgkkx1amTp3KhRdeyGWXXcaQIUOyrptIXIRhXrDY3lO+pqbGtb3B1pYtWzjvvPMCKlFxab3BWabWSyFpv0ff5Zcn/8Z1UN6P+rW9twokx32zPSvOzOqdczWnX/JUaqGIiMRAPsZ9s6WAInmxY8eOoIsgUnSCPsW66AKKc05nBhWRuHbpRlnQ10pI/hTVdSjdu3enqalJB5ki0Xo/lO7duwddFPGE4VoJyZ+iaqEMGjSIxsZGdL/54tF6x0YJhzBcKyH5U1QBpbS0VHfuEwlQGK6VkPwpqoBSSOonFjlVoa6V0PcvGEU1hlIo6icWSa8Q09Hr+xccBZQ8yOe9VESirBDT0RfD9692wy4ufWgVlbOXc+lDq0ITLNXllQfqJ44+dZnkT76vlYj796/tFfGtLTAg8M+oWih5oNuWRpu6TKIt7t+/MLfAFFDyQLctjbYwf2Hl9OL+/QtzC0xdXnkQhjl1JHdh/sLmWxy6+uL+/QvDrMKZKKDkSdBz6oRRVA5WYf7C5lOY++azFefv38wJQ9POKhyGFpi6vKQgojQuEfcuk0zU1Zdffp2ZVYgz5XKlFooURJSm3Ih7l0kmxdzVl29+t/7C2gJTQJGCiNrBKqxf2Hwq1q6+QojSD6rOUECJoTCOVehglV9+7PMw981HXdR+UOVKASVmwjqwGvTBKsggm+9t+7XPi7WrrxCK5QeVBuVjJqwDq0EOJAZ5QkAhtu3nPp9cPZDBG66g4jeTeGX2FQomPimWEz3UQomZMDetgxqXCLL/2s9tZ2rphHmfS1KxtP4UUGKmWJrW2QjygOvXttvr1tI+j4ZiONFDXV4xE3TTOoyzoAY5t5Nf226vpRP0PhdppYASM36PVWQTIMJ68WKQB1y/tt1eSyfMF7pJcVGXVwz51bTO9uyhQo1VZHvWVJD9135t+3TdWsXQnRI2YTw9P2gKKCEStg9otgGiEGMVuZ4iG+QB149tB33atZwsrKfnB01dXh2U77GBMHYXZRsgCjFWEdbTovNN3VrhUqyfw9NRC6UDCvFrJIxTM2R79pDfv6LTtdiK+RRZdWuFRzF/DtujgNIBfh/s/TpQ5ruLLNsA4edYRaYg3rtHKfs/OnLK8gN6J0LXZXg6USuvnKBTtdOLVEAxs4nAvwIlwA+ccw8VYrt+/hrJ5UCZTT7gX6splwDh16/oTEG8W9cuJEpLTgly487tF6k+7aj1wSv4nUxjWulFZgzFzEqA7wFXAecDU83s/EJs28+xgUwHSufI6vTSQvXhBjUVR6ZgfaD5SNqxhNVb90SqT7tQ+8+Psb8wju8FTWNa6ZlzLugydIiZXQzMc85N8P6fA+Cc+1a65WtqalxdXV1O23rnwQc5vGXr8f/3fnCYP+79kJaWE+9Vly7G35SfQXlZt4z5NDQk/1ZVnUj79R+bMi7/yY+V8eZfmnF2jG5dSxjcJ5Ex//byuehv+qbddq6yzau95Tua14a33uPw0WOnpHfrWkL1kN6n5HO69yObbWdb1lzy6kh5sy1T29f8+tyebl/kohD7ws/959c2Mi3vZ/0aGqCx9Fxuf+1rHc8shZnVO+dqclk3Sl1eA4GdKf83AqNTFzCzGcAMgCFDhuS8oeeehUFHTuyo1i/fzn3NHD566sE+045N9+Ho1rUk45ezvKxbxi962220l0+mbWfK63TpmfLKdvls8hrcJ5H2YDi4TyJtPqd7P7LZdq7LZ5PX6crrx3u7c1/zSe8fQEuLY+e+ZOsv04+XtvmkK2fb9CA/U35tI1P63g8Od/i9yrVMftavqgpGn5c5v3yKUgvl88AE59w/ef/fDIxyzn013fK5tlBqN+zKelD58suTfzsyZtC27xySXVunay633Uau+bRX3mzr4eeFgum2nU2/fT7ej1yW72hepytvtmVKp3L2cjJ9u9ONQ2V6ry59aFXaAeiBvRO8MvsKwJ/PVC7L+7mNTJ9BP76vneFnXh1RLC2URmBwyv+DgN1+bqD1w3OsW/4HurMZ4KzdsIud1cmD96UPnbx8EAOlhXifWvPqaH5Bvh+5KER5M52JVGKW1VmLxTwAHcbT+cMsSgHlt8CnzKwS2AVMAW7ycwOF+vBkc6A83cE7lynQMwWnjgrrlyyX9yNI+S5vpkDQdt+1ynQiRNSCtZ90vUl2IhNQnHNHzewOYCXJ04afcM694ec2wvjh8ft+Gn60LML4PoWBH8HaT5kCwSMrt2V9DUXUgrVfdL1JdiITUACccy8CL+Yr/zB+ePw8ePsVnML4PgWtUN2A2coUCIq1CyvboF/M3X25iMx1KIUQxvtK+HkNjF/BKYzvU9CiNLdT6zUUA3snMIrnGooTQb8ZrGPX0xTre5WrSLVQ8i2MfcV+/kJqr2WRzS+3ML5PQYtaN2AxdmHl2kIvxvcqVwoobYTtw+PnwTtTcGqdtiSb7pqwvU9BUzdg+EUt6EeRAkoE+HXwbm+QNoxnbUWJ+trDT0E//xRQiky64HTP0oa0y+qXW8epGzD8FPTzTwFF9MvNJ+oGDDcF/fxTQJGi/uUWtmtHoijI9zDbbSvo55cCihTtL7ewXjsSJUG+h9p/4aOAIkBx/nLTyQidF+R76PcsEmqpdp4CihStXG+7rAPPCUGeiuvXttXS8Y+ulJeile0sBLlcaZ2LZNBaxY7Rud9lsVD8nMkhqG1HaZaDsFNAkaKV7RQyhTjwFCpo+SXIaXj82rYuePSPAooUrWznaSrEgSdqv5aDnOvKr20H2cqKG42hSFHL5mSEQlyvE8Vfy0Ge0OHHtov5tHm/qYUi0kGF6N7Rr+XC04zC/lELRaSDCnG9jn4tB6MYT5vPBwUUkSzk+8BTrBeZgk7JjgMFFJGQKcZfy7oWJB40hiIigYva2W2SngKKiAQuime3yakUUDopSlc1i4RVnM5uK+ZjggJKJ0TtqmaRQsrmwBrkFfd+KvZjggJKJ6jfVyS9bA+scbkWpNiPCTrLqxPU7yuSXi5Ty8fh7LZiPyaohdIJcer3DVIx9znHVbEeWIv9mKCA0glx6fcNUrH3OcdVsR5Yi/2YoIDSCXHp9w1Ssfc5x1WxHliL/ZigMZROikO/b5CKtWsk7op5CpliPiYooEigCjElvASjmA+sxUpdXhKoYu0aEYkjtVAkUMXcNSISNwooEjh1jYjEg7q8RETEFwooIiLiC3V5iYiEVNTuYqmAIiISQlG8i6W6vEREQiiKs0gooIiIhFAUZ5FQQBERCaEoTrCpgCIiEkJRnEVCg/IiIiEUxVkkFFBEREIqarNImHMu6DLkhZntAf4cdDmyVA7sDboQAVC9i4vqHW4fd871y2XF2AaUKDKzOudcTdDlKDTVu7io3vGlQXkREfGFAoqIiPhCASVcFgVdgICo3sVF9Y4pjaGIiIgv1EIRERFfKKCIiIgvFFDyyMwGm9lqM9tiZm+Y2V1eeh8ze8nM/uD9PctLH2VmDd7jdTP7XEpenzGzTWa23cwWmJkFVa/TybbeKesNMbMPzOzelLTY1tvMKsysOWWfP56SV2zr7b02wszWectvMrPuXnps621mX0jZ1w1m1mJmVd5rkal3u5xzeuTpAfQHLvSe9wR+D5wPPAzM9tJnA9/2nvcAuqas+27K/+uBiwEDVgBXBV0/v+qdst5zwE+Ae1PSYltvoALYnCGvONe7K7ARuMD7vy9QEvd6t1l3OPDHKO7v9h5qoeSRc+5t59xr3vODwBZgIHAd8KS32JPAZG+Zj5xzR7307oADMLP+QC/n3DqX/PQ91bpOGGVbbwAzmwz8EXgjJS329U6nCOo9HtjonHvdW6fJOXesCOqdaiqwBKK3v9ujgFIgZlYBVAO/Ac52zr0NyQ8l8LGU5Uab2RvAJuA2L8AMBBpTsmv00kKvI/U2szOAWcADbVaPdb09lWa2wcz+08w+66XFvd7nAM7MVprZa2b2P7z0uNc71T/gBRQiXO+2NDlkAZhZGcnunLudc++31z3qnPsN8GkzOw940sxWkGwGn7JoXgrroyzq/QDwXefcB22WiXu93waGOOeazOwzQK2ZfZr417srMAYYCXwE/MLM6oH30ywbp3q3Lj8a+Mg5t7k1Kc1ioa93OgooeWZmpSQ/bE875573kv9iZv2dc297zd13267nnNtiZh8Cw0j+YhmU8vIgYHeei94pWdZ7NHCjmT0M9AZazOyQt35s6+2cOwwc9p7Xm9mbJH+9x31/NwL/6Zzb6637InAh8H+Jd71bTeFE6wQiuL8zUZdXHnlnavwQ2OKcezTlpZ8Bt3jPbwF+6i1faWZdvecfB4YCO7xm80Ezu8jLc3rrOmGUbb2dc591zlU45yqA+cCDzrmFca+3mfUzsxLv+d8AnyI5UBvregMrgRFm1sP7vF8G/K4I6o2ZdQE+DzzTmha1ercr6LMC4vwg2ax3JM9oafAeV5M8q+UXwB+8v3285W8mOSjdALwGTE7JqwbYDLwJLMSb5SCMj2zr3WbdeZx8llds6w3c4O3v1739/ffFUG9vnWle3TcDDxdRvS8Hfp0mr8jUu72Hpl4RERFfqMtLRER8oYAiIiK+UEARERFfKKCIiIgvFFBERMQXCigiIuILBRQREfHF/wePnbd95CIzfQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(2)\n",
    "ax1.stem(x_axis[0:2], end_cash_axis[0:2]-start_cash_axis[0:2], linefmt='b', label='First period')\n",
    "ax2.stem(x_axis[2:], end_cash_axis[2:]-start_cash_axis[2:], linefmt='b', label='All but first period')\n",
    "\n",
    "ax1.legend()\n",
    "ax2.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4945f847",
   "metadata": {},
   "source": [
    "#### End of period market value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "0fcdf74d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "start_mv_axis = out[\"After growth market value\"]\n",
    "end_mv_axis = out[\"End market value\"]\n",
    "\n",
    "fig, ax = plt.subplots(1)\n",
    "ax.stem(out.index, end_mv_axis, linefmt='b' , label='End market value')\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f037d623",
   "metadata": {},
   "source": [
    "## Test 1 Return of portfolio\n",
    "\n",
    "The purpose of this test is to verify if the reported return of the porfolio is equal to the increase/decrease of the total market value of the porfolio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "20505dcc",
   "metadata": {},
   "outputs": [],
   "source": [
    "return_calculated = (out[\"After growth market value\"]/out['Start market value']-1)[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "9503744d",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_1 = out[\"Portfolio return\"][1:]-return_calculated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "61a518fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "ax.stem(out.index[1:], test_1,linefmt='b' , label='Test return difference')\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "afcdc12e",
   "metadata": {},
   "source": [
    "## Test 2 no vanishing cash flows\n",
    "\n",
    "The purpose of this test is to verify if the inflows and outflows balance at every period. This test shows that all types of cash flows are accounted correctly and there is no \"leakage\".\n",
    "\n",
    "\n",
    "Starting values are\n",
    "\n",
    " * Start cash\n",
    " * After growth market value\n",
    "\n",
    "Cash flows occuring during the period and accumulating inside the bank account are\n",
    " * Coupon payments\n",
    " * Dividend payments\n",
    " * Notional payments of fixed income assets\n",
    " * Terminal value sales\n",
    "\n",
    "\n",
    "The end values are:\n",
    " * End cash value\n",
    " * End market value\n",
    "\n",
    "The test performs the following check\n",
    "\n",
    "$$\n",
    "C^{start}_i + MV^{ag}_i + CF^a_i - CF^l_i = C^{end}_i + MV^{end}_i \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cda1775f",
   "metadata": {},
   "source": [
    "Where:\n",
    "$$\n",
    "CF^a_i := div_i + coup_i + not_i + term_i\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ba7e782",
   "metadata": {},
   "source": [
    "And:\n",
    " * $i$ is the calculation period\n",
    " * $C^{start}_i$ is the initial cash position\n",
    " * $MV^{ag}_i$ is the market value after portfolio growth but before any trading\n",
    " * $CF^l_i$ are the accumulated outflows from company's commitments\n",
    " * $C^{end}_i$ is the final cash position\n",
    " * $MV^{end}_i$ is the final market value of the portfolio\n",
    " * $div_i$ is the accumulated dividend inflows\n",
    " * $coup_i$ is the accumulated coupon inflows\n",
    " * $not_i$ is the accumulated inflows from matured fixed income instruments (bonds)\n",
    " * $term_i$ is the accumulated inflows from equity positions sold at the end of the modelling window\n",
    " \n",
    "Note that the asset growth occurs before trading therefore, \"Cash after growth\" is used as the starting value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "283c2700",
   "metadata": {},
   "outputs": [],
   "source": [
    "cf_assets = coup_axis+div_axis+not_axis[:-1]+term_axis[:-1]\n",
    "\n",
    "test_2 = start_cash_axis + start_mv_axis + cf_assets + liab_axis - end_mv_axis - end_cash_axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "184c8502",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "ax.stem(x_axis, test_2,linefmt='b' , label='Test return difference')\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}