Small fix for Volatility Harvesting

Paper_Volatility_Harvesting.ipynb

@@ -22,6 +22,21 @@
     "See the [GitHub repository](https://github.com/Hvass-Labs/FinanceOps) for instructions on how to install and run this Python Notebook. The Python source-code is well-documented so you can hopefully understand and modify it yourself, but there is otherwise a minimum of explanations in this Notebook because it is all explained in the paper."
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Errata\n",
+    "\n",
+    "### Forward-Filled Share-Prices\n",
+    "\n",
+    "The original version had forward-filled the share-prices before calculating the daily returns. Some stocks such as YHOO were delisted and did not have share-prices until the end. Due to the forward-filled share-prices, the delisted stocks were therefore padded with daily returns of zero percent.\n",
+    "\n",
+    "This does not make any difference for the Buy&Hold portfolios, but for the Rebalanced portfolios it corresponds to having that small part of the portfolio invested in cash instead, and therefore rebalancing a small part of the portfolio into cash at each time-step, which could distort the results of the rebalancing.\n",
+    "\n",
+    "The relevant code has been marked with the word \"Correction\" so you can switch between the original version and the corrected version. I have tested it and there is no material difference in the plots, statistics and conclusions of this paper."
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -665,17 +680,28 @@
     }
    ],
    "source": [
+    "# Fill-method for the daily share-prices.\n",
+    "# Correction: See the Errata-section above for a detailed explanation.\n",
+    "# You can experiment with the two options. But there does not appear\n",
+    "# to be any material difference in the resulting plots and statistics.\n",
+    "if True:\n",
+    "    # Forward-filling of missing share-prices, as used in the paper.\n",
+    "    fill_method = 'ffill'\n",
+    "else:\n",
+    "    # Missing share-prices are not filled.\n",
+    "    fill_method = None\n",
+    "\n",
     "# Daily stock-returns calculated from the \"Total Return\".\n",
     "# We add 1.0 so we don't have to repeatedly add it later.\n",
-    "# We forward-fill missing prices, which should not be necessary,\n",
-    "# but we do it in case there is missing data-points.\n",
     "# We could have used SimFin's function hub.returns() but\n",
     "# this code makes it easier for you to use another data-source.\n",
     "# This is a Pandas DataFrame in matrix-form where the rows are\n",
     "# time-steps and the columns are for the individual tickers.\n",
-    "daily_returns_all = daily_prices.ffill().pct_change(periods=1) + 1.0\n",
+    "daily_returns_all = \\\n",
+    "    daily_prices.pct_change(periods=1,\n",
+    "                            fill_method=fill_method) + 1.0\n",
     "\n",
-    "# Remove empty rows (this should only be the first row).\n",
+    "# Remove empty rows where all elements are NaN (Not-a-Number).\n",
     "daily_returns_all = daily_returns_all.dropna(how='all')\n",
     "\n",
     "# Show it.\n",