From 4b5d5d428faed82b21392d7eec93bb9bd38f5767 Mon Sep 17 00:00:00 2001
From: Gavin Chan <gavincyi@gmail.com>
Date: Wed, 21 Jun 2023 22:53:02 +0100
Subject: [PATCH] feat: add covariance estimator

---
 .../crypto_statistical_risk_model.ipynb       | 263 +++++++++---------
 src/fpm_risk_model/cov_estimator.py           |  99 +++++++
 src/fpm_risk_model/risk_model.py              |  19 +-
 tests/test_cov_estimator.py                   | 137 +++++++++
 4 files changed, 377 insertions(+), 141 deletions(-)
 create mode 100644 src/fpm_risk_model/cov_estimator.py
 create mode 100644 tests/test_cov_estimator.py

diff --git a/examples/notebook/crypto_statistical_risk_model.ipynb b/examples/notebook/crypto_statistical_risk_model.ipynb
index 8ced840..4f686d0 100644
--- a/examples/notebook/crypto_statistical_risk_model.ipynb
+++ b/examples/notebook/crypto_statistical_risk_model.ipynb
@@ -54,28 +54,30 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
-            "Requirement already satisfied: matplotlib in /usr/local/lib/python3.10/dist-packages (3.7.1)\n",
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-            "Requirement already satisfied: contourpy>=1.0.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (1.0.7)\n",
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-            "Requirement already satisfied: fonttools>=4.22.0 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (4.39.3)\n",
-            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (1.4.4)\n",
-            "Requirement already satisfied: numpy>=1.20 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (1.22.4)\n",
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-            "Requirement already satisfied: pillow>=6.2.0 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (8.4.0)\n",
-            "Requirement already satisfied: pyparsing>=2.3.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (3.0.9)\n",
-            "Requirement already satisfied: python-dateutil>=2.7 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (2.8.2)\n",
-            "Requirement already satisfied: pandas<1.4.0,>=1.3.5 in /usr/local/lib/python3.10/dist-packages (from factor-pricing-model-risk-model) (1.3.5)\n",
-            "Requirement already satisfied: pydantic<2.0.0,>=1.10.4 in /usr/local/lib/python3.10/dist-packages (from factor-pricing-model-risk-model) (1.10.7)\n",
-            "Requirement already satisfied: scikit-learn<2.0.0,>=1.1.3 in /usr/local/lib/python3.10/dist-packages (from factor-pricing-model-risk-model) (1.2.2)\n",
-            "Requirement already satisfied: tqdm<5.0.0,>=4.64.1 in /usr/local/lib/python3.10/dist-packages (from factor-pricing-model-risk-model) (4.65.0)\n",
-            "Requirement already satisfied: pytz>=2017.3 in /usr/local/lib/python3.10/dist-packages (from pandas<1.4.0,>=1.3.5->factor-pricing-model-risk-model) (2022.7.1)\n",
-            "Requirement already satisfied: typing-extensions>=4.2.0 in /usr/local/lib/python3.10/dist-packages (from pydantic<2.0.0,>=1.10.4->factor-pricing-model-risk-model) (4.5.0)\n",
-            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.10/dist-packages (from python-dateutil>=2.7->matplotlib) (1.16.0)\n",
-            "Requirement already satisfied: scipy>=1.3.2 in /usr/local/lib/python3.10/dist-packages (from scikit-learn<2.0.0,>=1.1.3->factor-pricing-model-risk-model) (1.10.1)\n",
-            "Requirement already satisfied: joblib>=1.1.1 in /usr/local/lib/python3.10/dist-packages (from scikit-learn<2.0.0,>=1.1.3->factor-pricing-model-risk-model) (1.2.0)\n",
-            "Requirement already satisfied: threadpoolctl>=2.0.0 in /usr/local/lib/python3.10/dist-packages (from scikit-learn<2.0.0,>=1.1.3->factor-pricing-model-risk-model) (3.1.0)\n"
+            "Requirement already satisfied: matplotlib in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (3.7.1)\n",
+            "Requirement already satisfied: factor-pricing-model-risk-model in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (2023.3.0)\n",
+            "Requirement already satisfied: pyparsing>=2.3.1 in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (from matplotlib) (3.0.9)\n",
+            "Requirement already satisfied: kiwisolver>=1.0.1 in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (from matplotlib) (1.4.4)\n",
+            "Requirement already satisfied: numpy>=1.20 in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (from matplotlib) (1.23.5)\n",
+            "Requirement already satisfied: packaging>=20.0 in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (from matplotlib) (22.0)\n",
+            "Requirement already satisfied: contourpy>=1.0.1 in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (from matplotlib) (1.0.7)\n",
+            "Requirement already satisfied: fonttools>=4.22.0 in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (from matplotlib) (4.39.3)\n",
+            "Requirement already satisfied: python-dateutil>=2.7 in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (from matplotlib) (2.8.2)\n",
+            "Requirement already satisfied: pillow>=6.2.0 in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (from matplotlib) (9.5.0)\n",
+            "Requirement already satisfied: cycler>=0.10 in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (from matplotlib) (0.11.0)\n",
+            "Requirement already satisfied: scikit-learn<2.0.0,>=1.1.3 in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (from factor-pricing-model-risk-model) (1.2.0)\n",
+            "Requirement already satisfied: pandas<1.4.0,>=1.3.5 in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (from factor-pricing-model-risk-model) (1.3.5)\n",
+            "Requirement already satisfied: pydantic<2.0.0,>=1.10.4 in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (from factor-pricing-model-risk-model) (1.10.4)\n",
+            "Requirement already satisfied: tqdm<5.0.0,>=4.64.1 in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (from factor-pricing-model-risk-model) (4.64.1)\n",
+            "Requirement already satisfied: pytz>=2017.3 in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (from pandas<1.4.0,>=1.3.5->factor-pricing-model-risk-model) (2022.6)\n",
+            "Requirement already satisfied: typing-extensions>=4.2.0 in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (from pydantic<2.0.0,>=1.10.4->factor-pricing-model-risk-model) (4.4.0)\n",
+            "Requirement already satisfied: six>=1.5 in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (from python-dateutil>=2.7->matplotlib) (1.16.0)\n",
+            "Requirement already satisfied: joblib>=1.1.1 in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (from scikit-learn<2.0.0,>=1.1.3->factor-pricing-model-risk-model) (1.2.0)\n",
+            "Requirement already satisfied: threadpoolctl>=2.0.0 in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (from scikit-learn<2.0.0,>=1.1.3->factor-pricing-model-risk-model) (3.1.0)\n",
+            "Requirement already satisfied: scipy>=1.3.2 in /Users/gavinchan/workspace/factor-pricing-model-risk-model/.env/lib/python3.10/site-packages (from scikit-learn<2.0.0,>=1.1.3->factor-pricing-model-risk-model) (1.9.3)\n",
+            "\n",
+            "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m A new release of pip is available: \u001b[0m\u001b[31;49m23.0.1\u001b[0m\u001b[39;49m -> \u001b[0m\u001b[32;49m23.1.2\u001b[0m\n",
+            "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m To update, run: \u001b[0m\u001b[32;49mpip install --upgrade pip\u001b[0m\n"
           ]
         }
       ],
@@ -83,6 +85,16 @@
         "!pip install matplotlib factor-pricing-model-risk-model"
       ]
     },
+    {
+      "cell_type": "code",
+      "execution_count": 1,
+      "metadata": {},
+      "outputs": [],
+      "source": [
+        "%load_ext autoreload\n",
+        "%autoreload 2"
+      ]
+    },
     {
       "cell_type": "code",
       "execution_count": 2,
@@ -99,6 +111,7 @@
       },
       "outputs": [],
       "source": [
+        "from functools import partial\n",
         "import pandas as pd\n",
         "\n",
         "from fpm_risk_model.dataset.crypto import (\n",
@@ -307,12 +320,14 @@
         {
           "name": "stderr",
           "output_type": "stream",
-          "text": []
+          "text": [
+            "                                                     \r"
+          ]
         },
         {
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             "text/plain": [
-              "<fpm_risk_model.rolling_factor_risk_model.RollingFactorRiskModel at 0x7fc3a11efb80>"
+              "<fpm_risk_model.rolling_factor_risk_model.RollingFactorRiskModel at 0x133151ae0>"
             ]
           },
           "execution_count": 6,
@@ -358,10 +373,7 @@
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+              "<div>\n",
               "<style scoped>\n",
               "    .dataframe tbody tr th:only-of-type {\n",
               "        vertical-align: middle;\n",
@@ -396,83 +408,7 @@
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               "  </tbody>\n",
               "</table>\n",
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-              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
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-              "          const element = document.querySelector('#df-bc658b9e-3f3e-456f-bc0f-6ffc7759f983');\n",
-              "          const dataTable =\n",
-              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
-              "                                                     [key], {});\n",
-              "          if (!dataTable) return;\n",
-              "\n",
-              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
-              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
-              "            + ' to learn more about interactive tables.';\n",
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-              "  </div>\n",
-              "  "
+              "</div>"
             ],
             "text/plain": [
               "           bitcoin  ethereum\n",
@@ -642,12 +578,14 @@
         {
           "name": "stderr",
           "output_type": "stream",
-          "text": []
+          "text": [
+            "                                                     \r"
+          ]
         },
         {
           "data": {
             "text/plain": [
-              "<fpm_risk_model.rolling_factor_risk_model.RollingFactorRiskModel at 0x7fc3a11efb80>"
+              "<fpm_risk_model.rolling_factor_risk_model.RollingFactorRiskModel at 0x133151ae0>"
             ]
           },
           "execution_count": 10,
@@ -706,6 +644,20 @@
         "tags": []
       },
       "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "> \u001b[0;32m/Users/gavinchan/workspace/factor-pricing-model-risk-model/src/fpm_risk_model/accuracy/bias.py\u001b[0m(55)\u001b[0;36mcompute_standardized_returns\u001b[0;34m()\u001b[0m\n",
+            "\u001b[0;32m     53 \u001b[0;31m            \u001b[0;32mif\u001b[0m \u001b[0mindex\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrolling_risk_model\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkeys\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0m\u001b[0;32m     54 \u001b[0;31m                \u001b[0;32mimport\u001b[0m \u001b[0mpdb\u001b[0m\u001b[0;34m;\u001b[0m \u001b[0mpdb\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_trace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0m\u001b[0;32m---> 55 \u001b[0;31m                \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0m\u001b[0;32m     56 \u001b[0;31m            \u001b[0;32mif\u001b[0m \u001b[0mrisk_model\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0m\u001b[0;32m     57 \u001b[0;31m                \u001b[0;32mcontinue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0m\n",
+            "1\n"
+          ]
+        },
         {
           "data": {
             "text/plain": [
@@ -802,6 +754,44 @@
         "var_breach_statistics.plot()"
       ]
     },
+    {
+      "attachments": {},
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "## Covariance Estimator\n",
+        "\n",
+        "Covariance estimator is another way to retrieve covariances from the factor models\n",
+        "with advanced techniques.\n",
+        "\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 36,
+      "metadata": {},
+      "outputs": [],
+      "source": [
+        "from fpm_risk_model.cov_estimator import RollingCovarianceEstimator\n",
+        "ewma_vol = model_universe_returns.ewm(halflife=63, min_periods=30).std()\n",
+        "pca_ewma_adj_vol_covs = (\n",
+        "    RollingCovarianceEstimator(rolling_risk_model)\n",
+        "    .cov(volatility=ewma_vol)\n",
+        ")\n",
+        "pca_ewma_adj_vol_covs_bias_statistics = compute_bias_statistics(\n",
+        "    X=model_universe_returns.where(model_universe_returns.abs() < 0.2),\n",
+        "    weights=weights,\n",
+        "    window=63,\n",
+        "    rolling_risk_model=pca_ewma_adj_vol_covs,\n",
+        ")\n",
+        "pca_ewma_adj_vol_covs_var_breach_statistics = compute_value_at_risk_rolling_breach_statistics(\n",
+        "    X=model_universe_returns.where(model_universe_returns.abs() < 0.2),\n",
+        "    weights=weights,\n",
+        "    window=63,\n",
+        "    rolling_risk_model=pca_ewma_adj_vol_covs,\n",
+        ")"
+      ]
+    },
     {
       "attachments": {},
       "cell_type": "markdown",
@@ -819,7 +809,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 13,
+      "execution_count": 14,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
@@ -832,7 +822,19 @@
         {
           "name": "stderr",
           "output_type": "stream",
-          "text": []
+          "text": [
+            "                                                     \r"
+          ]
+        },
+        {
+          "data": {
+            "text/plain": [
+              "<Axes: title={'center': 'VaR Breach comparison'}>"
+            ]
+          },
+          "execution_count": 14,
+          "metadata": {},
+          "output_type": "execute_result"
         },
         {
           "data": {
@@ -883,36 +885,21 @@
         "    weights=weights,\n",
         "    window=63,\n",
         "    rolling_risk_model=rolling_apca_risk_model,\n",
-        ")\n",
-        "apca_bias_statistics = compute_bias_statistics(\n",
-        "    X=model_universe_returns.where(model_universe_returns.abs() < 0.2),\n",
-        "    weights=weights,\n",
-        "    window=63,\n",
-        "    rolling_risk_model=rolling_apca_risk_model,\n",
-        ")\n",
-        "apca_var_breach_statistics = compute_value_at_risk_rolling_breach_statistics(\n",
-        "    X=model_universe_returns.where(model_universe_returns.abs() < 0.2),\n",
-        "    weights=weights,\n",
-        "    window=63,\n",
-        "    rolling_risk_model=rolling_apca_risk_model,\n",
-        ")\n",
-        "\n",
-        "bias_statistics_comparison = pd.concat({\n",
-        "    '1. PCA': bias_statistics,\n",
-        "    '2. APCA': apca_bias_statistics\n",
-        "}, axis=1)\n",
-        "\n",
-        "var_breach_comparison = pd.concat({\n",
-        "    '1. PCA': var_breach_statistics,\n",
-        "    '2. APCA': apca_var_breach_statistics\n",
-        "}, axis=1)\n",
-        "\n",
-        "bias_statistics_comparison = pd.concat({\n",
+        ")"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {},
+      "outputs": [],
+      "source": [
+        "pd.concat({\n",
         "    '1. PCA': bias_statistics,\n",
         "    '2. APCA': apca_bias_statistics\n",
         "}, axis=1).plot(title=\"Bias statistics comparison\")\n",
         "\n",
-        "var_breach_comparison = pd.concat({\n",
+        "pd.concat({\n",
         "    '1. PCA': var_breach_statistics,\n",
         "    '2. APCA': apca_var_breach_statistics\n",
         "}, axis=1).plot(title=\"VaR Breach comparison\")"
@@ -930,10 +917,8 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 13,
-      "metadata": {
-        "id": "PH5mzfcKjvwN"
-      },
+      "execution_count": null,
+      "metadata": {},
       "outputs": [],
       "source": []
     }
diff --git a/src/fpm_risk_model/cov_estimator.py b/src/fpm_risk_model/cov_estimator.py
new file mode 100644
index 0000000..db2b670
--- /dev/null
+++ b/src/fpm_risk_model/cov_estimator.py
@@ -0,0 +1,99 @@
+from typing import Optional
+
+from pandas import DataFrame, Series
+
+from .risk_model import RiskModel
+from .rolling_factor_risk_model import RollingFactorRiskModel
+
+
+class CovarianceEstimator:
+    """
+    Covariance estimator.
+    """
+
+    def __init__(self, risk_model: RiskModel):
+        """
+        Constructor.
+
+        Parameters
+        ----------
+        risk_model : RiskModel
+          Risk model object.
+        """
+        self._risk_model = risk_model
+
+    def corr(self) -> DataFrame:
+        """
+        Correlation
+        """
+        return self._risk_model.corr()
+
+    def cov(
+        self, volatility: Optional[Series] = None, strict: bool = True
+    ) -> DataFrame:
+        """
+        Correlation
+
+        Parameters
+        ----------
+        volatility : pd.Series
+          Volaility series to convert from correlation to covariance. Optional.
+        strict : bool
+          Indicates to throw exception if volatility series does not align with
+          correlation matrix.
+        """
+        if volatility is None:
+            return self._risk_model.cov()
+
+        corr = self._risk_model.corr()
+        if strict and set(volatility.index) != set(corr.index):
+            raise ValueError(
+                "Incorrect volatility series passed. Length of volatility "
+                f"is {len(volatility.index)} while that of correlation is "
+                f"{len(corr.index)}"
+            )
+        elif len(volatility.index) < len(corr.index):
+            instruments = volatility.index
+        else:
+            instruments = corr.index
+
+        volatility = volatility.loc[instruments]
+        cov = (
+            corr.loc[instruments, instruments]
+            .mul(volatility, axis=0)
+            .mul(volatility, axis=1)
+        )
+        return cov
+
+
+class RollingCovarianceEstimator:
+    """
+    Rolling covariance estimator.
+    """
+
+    def __init__(self, rolling_risk_model: RollingFactorRiskModel):
+        """
+        Constructor.
+
+        Parameters
+        ----------
+        rolling_risk_model : RollingFactorRiskModel
+          Rolling risk model object.
+        """
+        self._rolling_risk_model = rolling_risk_model
+
+    def cov(self, volatility: Optional[DataFrame] = None):
+        """
+        Correlation
+
+        Parameters
+        ----------
+        volatility : DataFrame
+          Volaility series to convert from correlation to covariance. Optional.
+        """
+        return {
+            date: CovarianceEstimator(risk_model).cov(
+                volatility.loc[date], strict=False
+            )
+            for date, risk_model in self._rolling_risk_model.items()
+        }
diff --git a/src/fpm_risk_model/risk_model.py b/src/fpm_risk_model/risk_model.py
index 2beabcd..2bad22a 100644
--- a/src/fpm_risk_model/risk_model.py
+++ b/src/fpm_risk_model/risk_model.py
@@ -1,7 +1,7 @@
 from abc import ABC, abstractmethod
 from typing import Any, Union
 
-from numpy import ndarray
+from numpy import diagonal, ndarray, sqrt
 from pandas import DataFrame, Series
 
 from .config import Config
@@ -73,7 +73,22 @@ def cov(self, **kwargs) -> ndarray:
             diagonal entries are the variances.
         """
 
-    def corr(self, **kwargs):
+    def vol(self, **kwargs) -> ndarray:
+        """
+        Get the volatility series.
+
+        Returns
+        -------
+        numpy.ndarray
+            Volatility series derived from covariance matrix.
+        """
+        cov = self.cov(**kwargs)
+        vol = sqrt(diagonal(cov))
+        if isinstance(cov, DataFrame):
+            vol = Series(vol, index=cov.index)
+        return vol
+
+    def corr(self, **kwargs) -> ndarray:
         """
         Get the correlation matrix.
 
diff --git a/tests/test_cov_estimator.py b/tests/test_cov_estimator.py
new file mode 100644
index 0000000..ba30ef5
--- /dev/null
+++ b/tests/test_cov_estimator.py
@@ -0,0 +1,137 @@
+import pytest
+from numpy import array
+from pandas import DataFrame, Series, bdate_range
+from pandas.testing import assert_frame_equal
+
+from fpm_risk_model.cov_estimator import CovarianceEstimator
+from fpm_risk_model.factor_risk_model import FactorRiskModel
+
+
+@pytest.fixture(scope="module")
+def instruments():
+    return ["A", "AAL", "AAP", "AAPL"]
+
+
+@pytest.fixture(scope="module")
+def valid_instruments():
+    return ["A", "AAL", "AAPL"]
+
+
+@pytest.fixture(scope="module")
+def dates():
+    return bdate_range("2016-01-04", "2016-01-15")
+
+
+@pytest.fixture(scope="module")
+def factors():
+    return ["factor_1", "factor_2"]
+
+
+@pytest.fixture(scope="module")
+def factor_exposures():
+    return array(
+        [
+            [-0.15454215, -0.22795166, 0.0, -0.17179763],
+            [0.00706732, 0.08354979, 0.0, -0.11721647],
+        ]
+    )
+
+
+@pytest.fixture(scope="module")
+def factor_returns():
+    return array(
+        [
+            [0.06323026, -0.15644581],
+            [0.01829957, 0.09617634],
+            [-0.06074615, 0.17670851],
+            [0.1238173, 0.14189995],
+            [-0.03715707, -0.04710242],
+            [-0.08798148, -0.03209175],
+            [-0.1300186, 0.00469255],
+            [0.14264733, -0.05445549],
+            [-0.13802269, -0.07709159],
+            [0.10593153, -0.05229029],
+        ]
+    )
+
+
+@pytest.fixture(scope="module")
+def residual_returns():
+    return array(
+        [
+            [-0.00422976, 0.00199051, 0.0, 0.00116378],
+            [0.01038799, -0.00488857, 0.0, -0.00285816],
+            [0.00548287, -0.00258023, 0.0, -0.00150856],
+            [-0.01266259, 0.00595899, 0.0, 0.003484],
+            [-0.00424175, 0.00199616, 0.0, 0.00116708],
+            [-0.01853336, 0.00872176, 0.0, 0.00509929],
+            [-0.00185692, 0.00087386, 0.0, 0.00051091],
+            [-0.00071556, 0.00033674, 0.0, 0.00019688],
+            [0.01124235, -0.00529063, 0.0, -0.00309323],
+            [0.01512673, -0.00711861, 0.0, -0.00416198],
+        ]
+    )
+
+
+@pytest.fixture(scope="module")
+def factor_risk_model_np(factor_exposures, factor_returns, residual_returns):
+    return FactorRiskModel(
+        factor_exposures=factor_exposures,
+        factor_returns=factor_returns,
+        residual_returns=residual_returns,
+    )
+
+
+@pytest.fixture(scope="module")
+def factor_risk_model(
+    factor_exposures,
+    factor_returns,
+    residual_returns,
+    dates,
+    instruments,
+    factors,
+):
+    return FactorRiskModel(
+        factor_exposures=DataFrame(
+            factor_exposures, index=factors, columns=instruments
+        ),
+        factor_returns=DataFrame(factor_returns, index=dates, columns=factors),
+        residual_returns=DataFrame(residual_returns, index=dates, columns=instruments),
+    )
+
+
+def test_cov_estimator_no_adj(factor_risk_model):
+    cov_estimator = CovarianceEstimator(factor_risk_model)
+    cov = cov_estimator.cov()
+    target_cov = DataFrame(
+        [
+            [0.00038113, 0.00039798, 0.0002858],
+            [0.00039798, 0.00068043, 0.00032631],
+            [0.0002858, 0.00032631, 0.00048932],
+        ],
+        index=cov.index,
+        columns=cov.columns,
+    )
+    assert_frame_equal(
+        cov,
+        target_cov,
+    )
+
+
+def test_cov_estimator_vol_adj(factor_risk_model, instruments):
+    cov_estimator = CovarianceEstimator(factor_risk_model)
+    vol = Series(0.2, index=instruments)
+    cov = cov_estimator.cov(volatility=vol, strict=False)
+    target_cov = DataFrame(
+        [
+            [0.04, 0.03126062, 0.02647162],
+            [0.03126062, 0.04, 0.02262061],
+            [0.02647162, 0.02262061, 0.04],
+        ],
+        index=cov.index,
+        columns=cov.columns,
+    )
+    assert_frame_equal(
+        cov,
+        target_cov,
+    )