Merge branch 'v1.2.5' into master

2022-11-27 18:02:41 +03:00 · 2020-08-31 19:59:21 +08:00
parent 53b048ae77 188616a418
commit 2afc244c7f
26 changed files with 545 additions and 612 deletions
--- a/README.md
+++ b/README.md
@@ -203,7 +203,6 @@ As of v1.2.0:
  - Introduced a new API, in which the function `expected_returns.return_model(method="...")` allows
    all the different return models to be called. This should make testing easier.
  - Added option to 'properly' compound returns.
-  - James-Stein shrinkage estimator
  - CAPM return model.
 - `from pypfopt import plotting`: moved all plotting functionality into a new class and added
  new plots. All other plotting functions (scattered in different classes) have been retained,
@@ -244,9 +243,6 @@ A far more comprehensive version of this can be found on [ReadTheDocs](https://p
 - Exponentially weighted mean historical returns:
    - similar to mean historical returns, except it gives exponentially more weight to recent prices
    - it is likely the case that an asset's most recent returns hold more weight than returns from 10 years ago when it comes to estimating future returns.
- James-Stein shrinkage:
-    - a slightly more robust estimate of future returns
-    - by shrinking mean returns to the grand average, we can reduce loss.
 - Capital Asset Pricing Model (CAPM):
    - a simple model to predict returns based on the beta to the market
    - this is used all over finance!
--- a/cookbook/1-RiskReturnModels.ipynb
+++ b/cookbook/1-RiskReturnModels.ipynb
--- a/cookbook/HierarchicalRiskParity.ipynb
+++ b/cookbook/HierarchicalRiskParity.ipynb
@@ -1,88 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Hierarchical Risk Parity Portfolio\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import pandas as pd\n",
-    "from pypfopt import HRPOpt, risk_models, plotting, DiscreteAllocation\n",
-    "\n",
-    "\n",
-    "df = pd.read_csv(\"tests/stock_prices.csv\", parse_dates=True, index_col=\"date\")\n",
-    "print(df.shape)\n",
-    "df.tail()\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "returns = risk_models.returns_from_prices(df)\n",
-    "hrp = HRPOpt(returns)\n",
-    "weights = hrp.optimize()\n",
-    "hrp.portfolio_performance(verbose=True);"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "plotting.plot_dendrogram(hrp);"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "da = DiscreteAllocation(weights, df.iloc[-1], total_portfolio_value=10000)\n",
-    "w, leftover = da.lp_portfolio()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "plotting.plot_weights(weights);"
-   ]
-  }
- ],
- "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": "3.7.5"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
--- a/docs/ExpectedReturns.rst
+++ b/docs/ExpectedReturns.rst
@@ -46,20 +46,6 @@ superior models and feed them into the optimiser.
        the mean historical return. However, if you plan on rebalancing much more frequently,
        there is a case to be made for lowering the span in order to capture recent trends.

-    .. autofunction:: james_stein_shrinkage
-
-        A surprising result in statistics is that the MLE estimator for a 3+ dimensional
-        Normal distribution is an *inadmissible* estimator. That is, there exists an estimator
-        :math:`\hat{\mu}^{JS}` such that:
-
-        .. math::
-
-            E\{ \lVert \hat{\mu}^{JS} - \mu \rVert^2 \} < E \{ \lVert \bar{\mu} - \mu \rVert^2 \}
-
-        In essence, to reduce account for the fact that our sample may not be representative and
-        thus reduce loss, we shrink the sample means to the "grand average" (mean of means). For
-        a more detailed explanation, refer to Efron and Hastie (2010) [1]_
-
    .. autofunction:: capm_return

    .. autofunction:: returns_from_prices
@@ -69,7 +55,5 @@ superior models and feed them into the optimiser.
    .. autofunction:: prices_from_returns


-References
-==========
-
-.. [1] Efron and Hastie (2010) `Empirical Bayes and the James–Stein Estimator <http://statweb.stanford.edu/~ckirby/brad/LSI/chapter1.pdf>`_.
+.. References
+.. ==========
--- a/examples.py
+++ b/examples.py
@@ -38,7 +38,7 @@ Sharpe Ratio: 1.09

 # Black-Litterman
 spy_prices = pd.read_csv(
-    "tests/spy_prices.csv", parse_dates=True, index_col=0, squeeze=True
+    "tests/resources/spy_prices.csv", parse_dates=True, index_col=0, squeeze=True
 )
 delta = black_litterman.market_implied_risk_aversion(spy_prices)

--- a/poetry.lock
+++ b/poetry.lock
@@ -16,6 +16,23 @@ optional = false
 python-versions = "*"
 version = "0.1.0"

+[[package]]
+category = "dev"
+description = "The secure Argon2 password hashing algorithm."
+name = "argon2-cffi"
+optional = false
+python-versions = "*"
+version = "20.1.0"
+
+[package.dependencies]
+cffi = ">=1.0.0"
+six = "*"
+
+[package.extras]
+dev = ["coverage (>=5.0.2)", "hypothesis", "pytest", "sphinx", "wheel", "pre-commit"]
+docs = ["sphinx"]
+tests = ["coverage (>=5.0.2)", "hypothesis", "pytest"]
+
 [[package]]
 category = "dev"
 description = "Atomic file writes."
@@ -30,13 +47,12 @@ description = "Classes Without Boilerplate"
 name = "attrs"
 optional = false
 python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
-version = "19.3.0"
+version = "20.1.0"

 [package.extras]
-azure-pipelines = ["coverage", "hypothesis", "pympler", "pytest (>=4.3.0)", "six", "zope.interface", "pytest-azurepipelines"]
-dev = ["coverage", "hypothesis", "pympler", "pytest (>=4.3.0)", "six", "zope.interface", "sphinx", "pre-commit"]
-docs = ["sphinx", "zope.interface"]
-tests = ["coverage", "hypothesis", "pympler", "pytest (>=4.3.0)", "six", "zope.interface"]
+dev = ["coverage (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "six", "zope.interface", "sphinx", "sphinx-rtd-theme", "pre-commit"]
+docs = ["sphinx", "sphinx-rtd-theme", "zope.interface"]
+tests = ["coverage (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "six", "zope.interface"]

 [[package]]
 category = "dev"
@@ -44,7 +60,7 @@ description = "Specifications for callback functions passed in to an API"
 name = "backcall"
 optional = false
 python-versions = "*"
-version = "0.1.0"
+version = "0.2.0"

 [[package]]
 category = "dev"
@@ -77,6 +93,17 @@ packaging = "*"
 six = ">=1.9.0"
 webencodings = "*"

+[[package]]
+category = "dev"
+description = "Foreign Function Interface for Python calling C code."
+name = "cffi"
+optional = false
+python-versions = "*"
+version = "1.14.2"
+
+[package.dependencies]
+pycparser = "*"
+
 [[package]]
 category = "dev"
 description = "Composable command line interface toolkit"
@@ -95,21 +122,28 @@ optional = false
 python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
 version = "0.4.3"

+[[package]]
+category = "main"
+description = "Convex optimization package"
+name = "cvxopt"
+optional = false
+python-versions = "*"
+version = "1.2.5"
+
 [[package]]
 category = "main"
 description = "A domain-specific language for modeling convex optimization problems in Python."
 name = "cvxpy"
 optional = false
-python-versions = "*"
-version = "1.0.31"
+python-versions = ">=3.5"
+version = "1.1.5"

 [package.dependencies]
 ecos = ">=2"
-multiprocess = "*"
 numpy = ">=1.15"
 osqp = ">=0.4.1"
 scipy = ">=1.1.0"
-scs = ">=1.1.3"
+scs = ">=1.1.5"

 [[package]]
 category = "dev"
@@ -127,17 +161,6 @@ optional = false
 python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
 version = "0.6.0"

-[[package]]
-category = "main"
-description = "serialize all of python"
-name = "dill"
-optional = false
-python-versions = ">=2.6, !=3.0.*"
-version = "0.3.1.1"
-
-[package.extras]
-graph = ["objgraph (>=1.7.2)"]
-
 [[package]]
 category = "main"
 description = "This is the Python package for ECOS: Embedded Cone Solver. See Github page for more information."
@@ -164,7 +187,7 @@ description = "the modular source code checker: pep8 pyflakes and co"
 name = "flake8"
 optional = false
 python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,>=2.7"
-version = "3.8.2"
+version = "3.8.3"

 [package.dependencies]
 mccabe = ">=0.6.0,<0.7.0"
@@ -190,7 +213,7 @@ marker = "python_version < \"3.8\""
 name = "importlib-metadata"
 optional = false
 python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,!=3.4.*,>=2.7"
-version = "1.6.1"
+version = "1.7.0"

 [package.dependencies]
 zipp = ">=0.5"
@@ -205,7 +228,7 @@ description = "IPython Kernel for Jupyter"
 name = "ipykernel"
 optional = false
 python-versions = ">=3.5"
-version = "5.3.0"
+version = "5.3.4"

 [package.dependencies]
 appnope = "*"
@@ -288,14 +311,14 @@ description = "An autocompletion tool for Python that can be used for text edito
 name = "jedi"
 optional = false
 python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
-version = "0.17.0"
+version = "0.17.2"

 [package.dependencies]
-parso = ">=0.7.0"
+parso = ">=0.7.0,<0.8.0"

 [package.extras]
 qa = ["flake8 (3.7.9)"]
-testing = ["colorama", "docopt", "pytest (>=3.9.0,<5.0.0)"]
+testing = ["Django (<3.1)", "colorama", "docopt", "pytest (>=3.9.0,<5.0.0)"]

 [[package]]
 category = "dev"
@@ -355,7 +378,7 @@ description = "Jupyter protocol implementation and client libraries"
 name = "jupyter-client"
 optional = false
 python-versions = ">=3.5"
-version = "6.1.3"
+version = "6.1.7"

 [package.dependencies]
 jupyter-core = ">=4.6.0"
@@ -365,7 +388,7 @@ tornado = ">=4.1"
 traitlets = "*"

 [package.extras]
-test = ["ipykernel", "ipython", "mock", "pytest"]
+test = ["ipykernel", "ipython", "mock", "pytest", "pytest-asyncio", "async-generator", "pytest-timeout"]

 [[package]]
 category = "dev"
@@ -428,18 +451,7 @@ marker = "python_version > \"2.7\""
 name = "more-itertools"
 optional = false
 python-versions = ">=3.5"
-version = "8.3.0"
-
-[[package]]
-category = "main"
-description = "better multiprocessing and multithreading in python"
-name = "multiprocess"
-optional = false
-python-versions = "*"
-version = "0.70.9"
-
-[package.dependencies]
-dill = ">=0.3.1"
+version = "8.5.0"

 [[package]]
 category = "dev"
@@ -475,7 +487,7 @@ description = "The Jupyter Notebook format"
 name = "nbformat"
 optional = false
 python-versions = ">=3.5"
-version = "5.0.6"
+version = "5.0.7"

 [package.dependencies]
 ipython-genutils = "*"
@@ -484,7 +496,7 @@ jupyter-core = "*"
 traitlets = ">=4.1"

 [package.extras]
-test = ["testpath", "pytest", "pytest-cov"]
+test = ["pytest", "pytest-cov", "testpath"]

 [[package]]
 category = "dev"
@@ -492,10 +504,11 @@ description = "A web-based notebook environment for interactive computing"
 name = "notebook"
 optional = false
 python-versions = ">=3.5"
-version = "6.0.3"
+version = "6.1.3"

 [package.dependencies]
 Send2Trash = "*"
+argon2-cffi = "*"
 ipykernel = "*"
 ipython-genutils = "*"
 jinja2 = "*"
@@ -505,12 +518,13 @@ nbconvert = "*"
 nbformat = "*"
 prometheus-client = "*"
 pyzmq = ">=17"
-terminado = ">=0.8.1"
+terminado = ">=0.8.3"
 tornado = ">=5.0"
 traitlets = ">=4.2.1"

 [package.extras]
-test = ["nose", "coverage", "requests", "nose-warnings-filters", "nbval", "nose-exclude", "selenium", "pytest", "pytest-cov", "nose-exclude"]
+docs = ["sphinx", "nbsphinx", "sphinxcontrib-github-alt"]
+test = ["nose", "coverage", "requests", "nose-warnings-filters", "nbval", "nose-exclude", "selenium", "pytest", "pytest-cov", "requests-unixsocket"]

 [[package]]
 category = "main"
@@ -572,7 +586,7 @@ description = "A Python Parser"
 name = "parso"
 optional = false
 python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
-version = "0.7.0"
+version = "0.7.1"

 [package.extras]
 testing = ["docopt", "pytest (>=3.0.7)"]
@@ -663,7 +677,7 @@ description = "library with cross-python path, ini-parsing, io, code, log facili
 name = "py"
 optional = false
 python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
-version = "1.8.1"
+version = "1.9.0"

 [[package]]
 category = "dev"
@@ -673,6 +687,14 @@ optional = false
 python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
 version = "2.6.0"

+[[package]]
+category = "dev"
+description = "C parser in Python"
+name = "pycparser"
+optional = false
+python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
+version = "2.20"
+
 [[package]]
 category = "dev"
 description = "passive checker of Python programs"
@@ -770,7 +792,7 @@ marker = "sys_platform == \"win32\""
 name = "pywin32"
 optional = false
 python-versions = "*"
-version = "227"
+version = "228"

 [[package]]
 category = "dev"
@@ -787,7 +809,7 @@ description = "Python bindings for 0MQ"
 name = "pyzmq"
 optional = false
 python-versions = ">=2.7,!=3.0.*,!=3.1.*,!=3.2.*"
-version = "19.0.1"
+version = "19.0.2"

 [[package]]
 category = "dev"
@@ -795,7 +817,7 @@ description = "Jupyter Qt console"
 name = "qtconsole"
 optional = false
 python-versions = "*"
-version = "4.7.4"
+version = "4.7.6"

 [package.dependencies]
 ipykernel = ">=4.1"
@@ -929,7 +951,7 @@ description = "Measures the displayed width of unicode strings in a terminal"
 name = "wcwidth"
 optional = false
 python-versions = "*"
-version = "0.2.3"
+version = "0.2.5"

 [[package]]
 category = "dev"
@@ -977,7 +999,7 @@ matplotlib = []
 scikit-learn = []

 [metadata]
-content-hash = "d25a25d8c927137e2fb52a061ae18663175879217a6a4a632b4c3e0b166acc55"
+content-hash = "0ec98fc57e383a229e29979c086e8fc1417f6654529c9441afa00209c19f012d"
 python-versions = "^3.5"

 [metadata.files]
@@ -989,17 +1011,35 @@ appnope = [
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+argon2-cffi = [
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 atomicwrites = [
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+    {file = "pyzmq-19.0.2-cp37-cp37m-manylinux1_i686.whl", hash = "sha256:c40fbb2b9933369e994b837ee72193d6a4c35dfb9a7c573257ef7ff28961272c"},
+    {file = "pyzmq-19.0.2-cp37-cp37m-manylinux1_x86_64.whl", hash = "sha256:5d9fc809aa8d636e757e4ced2302569d6e60e9b9c26114a83f0d9d6519c40493"},
+    {file = "pyzmq-19.0.2-cp37-cp37m-win32.whl", hash = "sha256:3fa6debf4bf9412e59353defad1f8035a1e68b66095a94ead8f7a61ae90b2675"},
+    {file = "pyzmq-19.0.2-cp37-cp37m-win_amd64.whl", hash = "sha256:73483a2caaa0264ac717af33d6fb3f143d8379e60a422730ee8d010526ce1913"},
+    {file = "pyzmq-19.0.2-cp38-cp38-macosx_10_9_x86_64.whl", hash = "sha256:36ab114021c0cab1a423fe6689355e8f813979f2c750968833b318c1fa10a0fd"},
+    {file = "pyzmq-19.0.2-cp38-cp38-manylinux1_i686.whl", hash = "sha256:8b66b94fe6243d2d1d89bca336b2424399aac57932858b9a30309803ffc28112"},
+    {file = "pyzmq-19.0.2-cp38-cp38-manylinux1_x86_64.whl", hash = "sha256:654d3e06a4edc566b416c10293064732516cf8871a4522e0a2ba00cc2a2e600c"},
+    {file = "pyzmq-19.0.2-cp38-cp38-win32.whl", hash = "sha256:276ad604bffd70992a386a84bea34883e696a6b22e7378053e5d3227321d9702"},
+    {file = "pyzmq-19.0.2-cp38-cp38-win_amd64.whl", hash = "sha256:09d24a80ccb8cbda1af6ed8eb26b005b6743e58e9290566d2a6841f4e31fa8e0"},
+    {file = "pyzmq-19.0.2-pp27-pypy_73-macosx_10_9_x86_64.whl", hash = "sha256:c1a31cd42905b405530e92bdb70a8a56f048c8a371728b8acf9d746ecd4482c0"},
+    {file = "pyzmq-19.0.2-pp36-pypy36_pp73-macosx_10_9_x86_64.whl", hash = "sha256:a7e7f930039ee0c4c26e4dfee015f20bd6919cd8b97c9cd7afbde2923a5167b6"},
+    {file = "pyzmq-19.0.2.tar.gz", hash = "sha256:296540a065c8c21b26d63e3cea2d1d57902373b16e4256afe46422691903a438"},
 ]
 qtconsole = [
-    {file = "qtconsole-4.7.4-py2.py3-none-any.whl", hash = "sha256:89442727940126c65c2f94a058f1b4693a0f5d4c4b192fd6518ba3b11f4791aa"},
-    {file = "qtconsole-4.7.4.tar.gz", hash = "sha256:fd48bf1051d6e69cec1f9e2596cfaa94e3c726c70c5d848681ebce10c029f5fd"},
+    {file = "qtconsole-4.7.6-py2.py3-none-any.whl", hash = "sha256:570b9e1dd4f9b727699b0ed04c6943d9d32d5a2085aa69d82d814e039bbcf74b"},
+    {file = "qtconsole-4.7.6.tar.gz", hash = "sha256:6c24397c19a49a5cf69582c931db4b0f6b00a78530a2bfd122936f2ebfae2fef"},
 ]
 qtpy = [
    {file = "QtPy-1.9.0-py2.py3-none-any.whl", hash = "sha256:fa0b8363b363e89b2a6f49eddc162a04c0699ae95e109a6be3bb145a913190ea"},
@@ -1466,8 +1559,8 @@ traitlets = [
    {file = "traitlets-4.3.3.tar.gz", hash = "sha256:d023ee369ddd2763310e4c3eae1ff649689440d4ae59d7485eb4cfbbe3e359f7"},
 ]
 wcwidth = [
-    {file = "wcwidth-0.2.3-py2.py3-none-any.whl", hash = "sha256:980fbf4f3c196c0f329cdcd1e84c554d6a211f18e252e525a0cf4223154a41d6"},
-    {file = "wcwidth-0.2.3.tar.gz", hash = "sha256:edbc2b718b4db6cdf393eefe3a420183947d6aa312505ce6754516f458ff8830"},
+    {file = "wcwidth-0.2.5-py2.py3-none-any.whl", hash = "sha256:beb4802a9cebb9144e99086eff703a642a13d6a0052920003a230f3294bbe784"},
+    {file = "wcwidth-0.2.5.tar.gz", hash = "sha256:c4d647b99872929fdb7bdcaa4fbe7f01413ed3d98077df798530e5b04f116c83"},
 ]
 webencodings = [
    {file = "webencodings-0.5.1-py2.py3-none-any.whl", hash = "sha256:a0af1213f3c2226497a97e2b3aa01a7e4bee4f403f95be16fc9acd2947514a78"},
--- a/pypfopt/base_optimizer.py
+++ b/pypfopt/base_optimizer.py
@@ -220,8 +220,8 @@ class BaseConvexOptimizer(BaseOptimizer):
                opt.solve(solver=self._solver, verbose=self._verbose)
            else:
                opt.solve(verbose=self._verbose)
-        except (TypeError, cp.DCPError):
-            raise exceptions.OptimizationError
+        except (TypeError, cp.DCPError) as e:
+            raise exceptions.OptimizationError from e

        if opt.status != "optimal":
            raise exceptions.OptimizationError
@@ -341,6 +341,7 @@ class BaseConvexOptimizer(BaseOptimizer):
        weights_sum_to_one=True,
        constraints=None,
        solver="SLSQP",
+        initial_guess=None,
    ):
        """
        Optimise some objective function using the scipy backend. This can
@@ -374,6 +375,8 @@ class BaseConvexOptimizer(BaseOptimizer):
        :param solver: which SCIPY solver to use, e.g "SLSQP", "COBYLA", "BFGS".
                       User beware: different optimisers require different inputs.
        :type solver: string
+        :param initial_guess: the initial guess for the weights, shape (n,) or (n, 1)
+        :type initial_guess: np.ndarray
        :return: asset weights that optimise the custom objective
        :rtype: OrderedDict
        """
@@ -385,7 +388,8 @@ class BaseConvexOptimizer(BaseOptimizer):
        bound_array = np.vstack((self._lower_bounds, self._upper_bounds)).T
        bounds = list(map(tuple, bound_array))

-        initial_guess = np.array([1 / self.n_assets] * self.n_assets)
+        if initial_guess is None:
+            initial_guess = np.array([1 / self.n_assets] * self.n_assets)

        # Construct constraints
        final_constraints = []
--- a/pypfopt/cla.py
+++ b/pypfopt/cla.py
@@ -375,7 +375,7 @@ class CLA(base_optimizer.BaseOptimizer):
        """
        Maximise the Sharpe ratio.

-        :return: asset weights for the volatility-minimising portfolio
+        :return: asset weights for the max-sharpe portfolio
        :rtype: OrderedDict
        """
        if not self.w:
--- a/pypfopt/discrete_allocation.py
+++ b/pypfopt/discrete_allocation.py
@@ -297,19 +297,21 @@ class DiscreteAllocation:
        # Integer allocation
        x = cp.Variable(n, integer=True)
        # Remaining dollars
-        r = self.total_portfolio_value - p.T * x
+        r = self.total_portfolio_value - p.T @ x

-        # Objective function is remaining dollars + sum of absolute deviations from ideality.
-        objective = r + cp.norm(w * self.total_portfolio_value - cp.multiply(x, p), 1)
-        constraints = [r + p.T * x == self.total_portfolio_value, x >= 0, r >= 0]
+        # Set up linear program
+        eta = w * self.total_portfolio_value - cp.multiply(x, p)
+        u = cp.Variable(n)
+        constraints = [eta <= u, eta >= -u, x >= 0, r >= 0]
+        objective = cp.sum(u) + r

        opt = cp.Problem(cp.Minimize(objective), constraints)
-        opt.solve()
+        opt.solve(solver="GLPK_MI")

        if opt.status not in {"optimal", "optimal_inaccurate"}:
            raise exceptions.OptimizationError("Please try greedy_portfolio")

-        vals = np.rint(x.value)
+        vals = np.rint(x.value).astype(int)
        self.allocation = self._remove_zero_positions(
            collections.OrderedDict(zip([i[0] for i in self.weights], vals))
        )
--- a/pypfopt/efficient_frontier.py
+++ b/pypfopt/efficient_frontier.py
@@ -271,6 +271,15 @@ class EfficientFrontier(base_optimizer.BaseConvexOptimizer):
        if not isinstance(target_volatility, (float, int)) or target_volatility < 0:
            raise ValueError("target_volatility should be a positive float")

+        global_min_volatility = np.sqrt(1 / np.sum(np.linalg.inv(self.cov_matrix)))
+
+        if target_volatility < global_min_volatility:
+            raise ValueError(
+                "The minimum volatility is {:.3f}. Please use a higher target_volatility".format(
+                    global_min_volatility
+                )
+            )
+
        self._objective = objective_functions.portfolio_return(
            self._w, self.expected_returns
        )
--- a/pypfopt/exceptions.py
+++ b/pypfopt/exceptions.py
@@ -3,7 +3,6 @@ The ``exceptions`` module houses custom exceptions. Currently implemented:

 - OptimizationError
 """
-import traceback


 class OptimizationError(Exception):
@@ -16,9 +15,4 @@ class OptimizationError(Exception):
        default_message = (
            "Please check your objectives/constraints or use a different solver."
        )
-
-        if not (args or kwargs):
-            args = (default_message,)
-        super().__init__(*args, **kwargs)
-
-        traceback.print_exc()
+        super().__init__(default_message, *args, **kwargs)
--- a/pypfopt/expected_returns.py
+++ b/pypfopt/expected_returns.py
@@ -15,7 +15,6 @@ Currently implemented:
    - general return model function, allowing you to run any return model from one function.
    - mean historical return
    - exponentially weighted mean historical return
-    - James-Stein shrinkage
    - CAPM estimate of returns

 Additionally, we provide utility functions to convert from returns to prices and vice-versa.
@@ -26,17 +25,22 @@ import pandas as pd
 import numpy as np


-def returns_from_prices(prices):
+def returns_from_prices(prices, log_returns=False):
    """
    Calculate the returns given prices.

    :param prices: adjusted (daily) closing prices of the asset, each row is a
                   date and each column is a ticker/id.
    :type prices: pd.DataFrame
+    :param log_returns: whether to compute using log returns
+    :type log_returns: bool, defaults to False
    :return: (daily) returns
    :rtype: pd.DataFrame
    """
-    return prices.pct_change().dropna(how="all")
+    if log_returns:
+        return np.log(1 + prices.pct_change()).dropna(how="all")
+    else:
+        return prices.pct_change().dropna(how="all")


 def log_returns_from_prices(prices):
@@ -49,10 +53,13 @@ def log_returns_from_prices(prices):
    :return: (daily) returns
    :rtype: pd.DataFrame
    """
+    warnings.warn(
+        "log_returns_from_prices is deprecated. Please use returns_from_prices(prices, log_returns=True)"
+    )
    return np.log(1 + prices.pct_change()).dropna(how="all")


-def prices_from_returns(returns):
+def prices_from_returns(returns, log_returns=False):
    """
    Calculate the pseudo-prices given returns. These are not true prices because
    the initial prices are all set to 1, but it behaves as intended when passed
@@ -60,9 +67,13 @@ def prices_from_returns(returns):

    :param returns: (daily) percentage returns of the assets
    :type returns: pd.DataFrame
+    :param log_returns: whether to compute using log returns
+    :type log_returns: bool, defaults to False
    :return: (daily) pseudo-prices.
    :rtype: pd.DataFrame
    """
+    if log_returns:
+        returns = np.exp(returns)
    ret = 1 + returns
    ret.iloc[0] = 1  # set first day pseudo-price
    return ret.cumprod()
@@ -81,7 +92,6 @@ def return_model(prices, method="mean_historical_return", **kwargs):

        - ``mean_historical_return``
        - ``ema_historical_return``
-        - ``james_stein_shrinkage``
        - ``capm_return``

    :type method: str, optional
@@ -93,19 +103,16 @@ def return_model(prices, method="mean_historical_return", **kwargs):
        return mean_historical_return(prices, **kwargs)
    elif method == "ema_historical_return":
        return ema_historical_return(prices, **kwargs)
-    elif method == "james_stein_shrinkage":
-        return james_stein_shrinkage(prices, **kwargs)
    elif method == "capm_return":
        return capm_return(prices, **kwargs)
    else:
        raise NotImplementedError("Return model {} not implemented".format(method))


-def mean_historical_return(
-    prices, returns_data=False, compounding=False, frequency=252
-):
+def mean_historical_return(prices, returns_data=False, compounding=True, frequency=252):
    """
    Calculate annualised mean (daily) historical return from input (daily) asset prices.
+    By default, this uses the arithmetic mean (correct if log_returns are used).

    :param prices: adjusted closing prices of the asset, each row is a date
                   and each column is a ticker/id.
@@ -113,7 +120,7 @@ def mean_historical_return(
    :param returns_data: if true, the first argument is returns instead of prices.
    :type returns_data: bool, defaults to False.
    :param compounding: whether to properly compound the returns, optional.
-    :type compounding: bool, defaults to False
+    :type compounding: bool, defaults to True
    :param frequency: number of time periods in a year, defaults to 252 (the number
                      of trading days in a year)
    :type frequency: int, optional
@@ -128,13 +135,13 @@ def mean_historical_return(
    else:
        returns = returns_from_prices(prices)
    if compounding:
-        return (1 + returns.mean()) ** frequency - 1
+        return (1 + returns).prod() ** (frequency / returns.count()) - 1
    else:
        return returns.mean() * frequency


 def ema_historical_return(
-    prices, returns_data=False, compounding=False, span=500, frequency=252
+    prices, returns_data=False, compounding=True, span=500, frequency=252
 ):
    """
    Calculate the exponentially-weighted mean of (daily) historical returns, giving
@@ -146,7 +153,7 @@ def ema_historical_return(
    :param returns_data: if true, the first argument is returns instead of prices.
    :type returns_data: bool, defaults to False.
    :param compounding: whether to properly compound the returns, optional.
-    :type compounding: bool, defaults to False
+    :type compounding: bool, defaults to True
    :param frequency: number of time periods in a year, defaults to 252 (the number
                      of trading days in a year)
    :type frequency: int, optional
@@ -169,49 +176,10 @@ def ema_historical_return(
        return returns.ewm(span=span).mean().iloc[-1] * frequency


-def james_stein_shrinkage(prices, returns_data=False, compounding=False, frequency=252):
-    r"""
-    Compute the James-Stein shrinkage estimator, i.e
-
-    .. math::
-
-        \hat{\mu}_i^{JS} = \hat{\kappa} \bar{\mu} + (1-\hat{\kappa}) \mu_i,
-
-    where :math:`\kappa` is the shrinkage parameter, :math:`\bar{\mu}` is the shrinkage
-    target (grand average), and :math:`\mu` is the vector of mean returns.
-
-    :param prices: adjusted closing prices of the asset, each row is a date
-                   and each column is a ticker/id.
-    :type prices: pd.DataFrame
-    :param returns_data: if true, the first argument is returns instead of prices.
-    :type returns_data: bool, defaults to False.
-    :param compounded: whether to properly compound the returns, optional.
-    :type compounding: bool, defaults to False
-    :param frequency: number of time periods in a year, defaults to 252 (the number
-                      of trading days in a year)
-    :type frequency: int, optional
-    :return: James-Stein estimate of annualised return
-    :rtype: pd.Series
-    """
-    if not isinstance(prices, pd.DataFrame):
-        warnings.warn("prices are not in a dataframe", RuntimeWarning)
-        prices = pd.DataFrame(prices)
-    if returns_data:
-        returns = prices
-    else:
-        returns = returns_from_prices(prices)
-
-    T, n = returns.shape
-    mu = returns.mean(axis=0)
-    mu_bar = mu.mean()
-    sigma_squared = 1 / T * mu_bar * (1 - mu_bar)  # binomial estimate
-    kappa = 1 - (n - 3) * sigma_squared / np.sum((mu - mu_bar) ** 2)
-    theta_js = (1 - kappa) * mu + kappa * mu_bar
-
-    if compounding:
-        return (1 + theta_js) ** frequency - 1
-    else:
-        return theta_js * frequency
+def james_stein_shrinkage(prices, returns_data=False, compounding=True, frequency=252):
+    raise NotImplementedError(
+        "Deprecated because its implementation here was misguided."
+    )


 def capm_return(
@@ -219,7 +187,7 @@ def capm_return(
    market_prices=None,
    returns_data=False,
    risk_free_rate=0.02,
-    compounding=False,
+    compounding=True,
    frequency=252,
 ):
    """
@@ -244,7 +212,7 @@ def capm_return(
                           to the frequency parameter.
    :type risk_free_rate: float, optional
    :param compounding: whether to properly compound the returns, optional.
-    :type compounding: bool, defaults to False
+    :type compounding: bool, defaults to True
    :param frequency: number of time periods in a year, defaults to 252 (the number
                        of trading days in a year)
    :type frequency: int, optional
@@ -267,7 +235,6 @@ def capm_return(
    if market_returns is None:
        # Append market return to right and compute sample covariance matrix
        returns["mkt"] = returns.mean(axis=1)
-
    else:
        market_returns.columns = ["mkt"]
        returns = returns.join(market_returns, how="left")
@@ -279,7 +246,9 @@ def capm_return(
    betas = betas.drop("mkt")
    # Find mean market return on a given time period
    if compounding:
-        mkt_mean_ret = (1 + returns["mkt"].mean()) ** frequency - 1
+        mkt_mean_ret = (1 + returns["mkt"]).prod() ** (
+            frequency / returns["mkt"].count()
+        ) - 1
    else:
        mkt_mean_ret = returns["mkt"].mean() * frequency

--- a/pypfopt/hierarchical_portfolio.py
+++ b/pypfopt/hierarchical_portfolio.py
@@ -13,7 +13,6 @@ Currently implemented:
 """

 import collections
-import warnings
 import numpy as np
 import pandas as pd
 import scipy.cluster.hierarchy as sch
@@ -139,13 +138,19 @@ class HRPOpt(base_optimizer.BaseOptimizer):
                w[second_cluster] *= 1 - alpha  # weight 2
        return w

-    def optimize(self):
+    def optimize(self, linkage_method="single"):
        """
-        Construct a hierarchical risk parity portfolio
+        Construct a hierarchical risk parity portfolio, using Scipy hierarchical clustering
+        (see `here <https://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.hierarchy.linkage.html>`_)

+        :param linkage_method: which scipy linkage method to use
+        :type linkage_method: str
        :return: weights for the HRP portfolio
        :rtype: OrderedDict
        """
+        if linkage_method not in sch._LINKAGE_METHODS:
+            raise ValueError("linkage_method must be one recognised by scipy")
+
        if self.returns is None:
            cov = self.cov_matrix
            corr = risk_models.cov_to_corr(self.cov_matrix).round(6)
@@ -159,7 +164,7 @@ class HRPOpt(base_optimizer.BaseOptimizer):
        matrix = np.sqrt(np.clip((1.0 - corr) / 2.0, a_min=0.0, a_max=1.0))
        dist = ssd.squareform(matrix, checks=False)

-        self.clusters = sch.linkage(dist, "single")
+        self.clusters = sch.linkage(dist, linkage_method)
        sort_ix = HRPOpt._get_quasi_diag(self.clusters)
        ordered_tickers = corr.index[sort_ix].tolist()
        hrp = HRPOpt._raw_hrp_allocation(cov, ordered_tickers)
--- a/pypfopt/objective_functions.py
+++ b/pypfopt/objective_functions.py
@@ -117,6 +117,12 @@ def L2_reg(w, gamma=1):
    r"""
    L2 regularisation, i.e :math:`\gamma ||w||^2`, to increase the number of nonzero weights.

+    Example::
+
+        ef = EfficientFrontier(mu, S)
+        ef.add_objective(objective_functions.L2_reg, gamma=2)
+        ef.min_volatility()
+
    :param w: asset weights in the portfolio
    :type w: np.ndarray OR cp.Variable
    :param gamma: L2 regularisation parameter, defaults to 1. Increase if you want more
--- a/pypfopt/risk_models.py
+++ b/pypfopt/risk_models.py
@@ -39,7 +39,8 @@ def _is_positive_semidefinite(matrix):
    :rtype: bool
    """
    try:
-        np.linalg.cholesky(matrix)
+        # Significantly more efficient than checking eigenvalues (stackoverflow.com/questions/16266720)
+        np.linalg.cholesky(matrix + 1e-16 * np.eye(len(matrix)))
        return True
    except np.linalg.LinAlgError:
        return False
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -35,7 +35,8 @@ python = "^3.5"
 numpy = "^1.12"
 scipy = "^1.3"
 pandas = ">=0.19"
-cvxpy = "~1.0"
+cvxpy = "^1.0"
+cvxopt = "^1.2"

 [tool.poetry.dev-dependencies]
 pytest = "^4.6"
--- a/requirements.txt
+++ b/requirements.txt
@@ -3,4 +3,5 @@ numpy>=1.17
 pandas>=0.19
 scikit-learn>=0.19
 scipy>=1.3
-cvxpy==1.0.28
+cvxpy>=1.0
+cvxopt>=1.0
--- a/tests/test_black_litterman.py
+++ b/tests/test_black_litterman.py
@@ -143,26 +143,26 @@ def test_bl_returns_all_views():
        posterior_rets,
        np.array(
            [
-                0.11774473,
-                0.1709139,
-                0.12180833,
-                0.21202423,
-                0.28120945,
-                -0.2787358,
-                0.17274774,
-                0.12714698,
-                0.25492005,
-                0.11229777,
-                0.07182723,
-                -0.01521839,
-                -0.21235465,
-                0.06399515,
-                -0.11738365,
-                0.28865661,
-                0.23828607,
-                0.12038049,
-                0.2331218,
-                0.10485376,
+                0.11168648,
+                0.16782938,
+                0.12516799,
+                0.24067997,
+                0.32848296,
+                -0.22789895,
+                0.16311297,
+                0.11928542,
+                0.25414308,
+                0.11007738,
+                0.06282615,
+                -0.03140218,
+                -0.16977172,
+                0.05254821,
+                -0.10463884,
+                0.32173375,
+                0.26399864,
+                0.1118594,
+                0.22999558,
+                0.08977448,
            ]
        ),
    )
--- a/tests/test_cla.py
+++ b/tests/test_cla.py
@@ -28,7 +28,7 @@ def test_cla_max_sharpe_long_only():

    np.testing.assert_allclose(
        cla.portfolio_performance(),
-        (0.3253436663900292, 0.21333530089904357, 1.4312852355106793),
+        (0.2994470912768992, 0.21764331657015668, 1.283968171780824),
    )


@@ -40,7 +40,7 @@ def test_cla_max_sharpe_short():
    np.testing.assert_almost_equal(cla.weights.sum(), 1)
    np.testing.assert_allclose(
        cla.portfolio_performance(),
-        (0.3799273115521356, 0.23115368271125736, 1.5570909679242886),
+        (0.44859872371106785, 0.26762066559448255, 1.601515797589826),
    )
    sharpe = cla.portfolio_performance()[2]

@@ -72,7 +72,7 @@ def test_cla_min_volatility():
    np.testing.assert_almost_equal(cla.weights.sum(), 1)
    np.testing.assert_allclose(
        cla.portfolio_performance(),
-        (0.1793123248125915, 0.15915084514118688, 1.00101463282373),
+        (0.1505682139948257, 0.15915084514118688, 0.8204054077060994),
    )


@@ -99,7 +99,7 @@ def test_cla_max_sharpe_semicovariance():
    np.testing.assert_almost_equal(cla.weights.sum(), 1)
    np.testing.assert_allclose(
        cla.portfolio_performance(),
-        (0.2936179968144084, 0.06362345488289835, 4.300583759841616),
+        (0.2686858719299194, 0.06489248187610204, 3.8322755539652578),
    )


@@ -113,7 +113,7 @@ def test_cla_max_sharpe_exp_cov():
    np.testing.assert_almost_equal(cla.weights.sum(), 1)
    np.testing.assert_allclose(
        cla.portfolio_performance(),
-        (0.3619453128519127, 0.1724297730592084, 1.9830990135009723),
+        (0.32971891062187103, 0.17670121760851704, 1.7527831149871063),
    )


@@ -127,7 +127,7 @@ def test_cla_min_volatility_exp_cov_short():
    np.testing.assert_almost_equal(cla.weights.sum(), 1)
    np.testing.assert_allclose(
        cla.portfolio_performance(),
-        (0.2634735528776959, 0.13259590618253303, 1.8362071642131053),
+        (0.23215576461823062, 0.1325959061825329, 1.6000174569958052),
    )


--- a/tests/test_custom_objectives.py
+++ b/tests/test_custom_objectives.py
@@ -91,7 +91,7 @@ def test_custom_convex_logarithmic_barrier():

    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.23978400459553223, 0.21100848889958182, 1.041588448605623),
+        (0.17261881638711316, 0.21100848889958182, 0.7232828270702603),
    )


@@ -101,7 +101,7 @@ def test_custom_convex_deviation_risk_parity_error():

    def deviation_risk_parity(w, cov_matrix):
        n = cov_matrix.shape[0]
-        rp = (w * (cov_matrix @ w)) / cp.quad_form(w, cov_matrix)
+        rp = (w @ (cov_matrix @ w)) / cp.quad_form(w, cov_matrix)
        return cp.sum_squares(rp - 1 / n)

    with pytest.raises(exceptions.OptimizationError):
@@ -287,6 +287,6 @@ def test_custom_nonconvex_objective_market_neutral_efficient_risk():
    )
    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.2309497754562942, target_risk, 1.1102600451243954),
+        (0.2591296227818582, target_risk, 1.258574109251818),
        atol=1e-6,
    )
--- a/tests/test_discrete_allocation.py
+++ b/tests/test_discrete_allocation.py
@@ -67,7 +67,9 @@ def test_greedy_allocation_rmse_error():
    latest_prices = get_latest_prices(df)
    da = DiscreteAllocation(w, latest_prices)
    da.greedy_portfolio()
-    np.testing.assert_almost_equal(da._allocation_rmse_error(), 0.025762032436733803)
+    np.testing.assert_almost_equal(
+        da._allocation_rmse_error(verbose=False), 0.017086185150415774
+    )


 def test_greedy_portfolio_allocation_short():
@@ -81,25 +83,25 @@ def test_greedy_portfolio_allocation_short():
    da = DiscreteAllocation(w, latest_prices)
    allocation, leftover = da.greedy_portfolio()

-    assert da.allocation == {
-        "MA": 15,
-        "PFE": 45,
-        "FB": 8,
+    assert allocation == {
+        "MA": 19,
+        "PFE": 42,
+        "FB": 7,
+        "GOOG": 1,
        "BABA": 5,
        "AAPL": 4,
-        "BBY": 8,
-        "AMZN": 1,
-        "SBUX": 9,
-        "WMT": 2,
-        "XOM": 2,
+        "SBUX": 8,
+        "BBY": 6,
+        "XOM": 4,
+        "WMT": 3,
        "BAC": -32,
-        "GM": -16,
-        "GE": -43,
-        "SHLD": -110,
-        "AMD": -34,
-        "JPM": -1,
-        "T": -1,
-        "UAA": -1,
+        "AMD": -48,
+        "SHLD": -132,
+        "GM": -9,
+        "RRC": -19,
+        "GE": -14,
+        "T": -5,
+        "UAA": -8,
    }
    long_total = 0
    short_total = 0
@@ -123,7 +125,9 @@ def test_greedy_allocation_rmse_error_short():
    latest_prices = get_latest_prices(df)
    da = DiscreteAllocation(w, latest_prices)
    da.greedy_portfolio()
-    np.testing.assert_almost_equal(da._allocation_rmse_error(), 0.033070015016740284)
+    np.testing.assert_almost_equal(
+        da._allocation_rmse_error(verbose=False), 0.06063511265243106
+    )


 def test_greedy_portfolio_allocation_short_different_params():
@@ -139,27 +143,26 @@ def test_greedy_portfolio_allocation_short_different_params():
    )
    allocation, leftover = da.greedy_portfolio()

-    assert da.allocation == {
-        "MA": 77,
-        "PFE": 225,
-        "FB": 41,
-        "BABA": 25,
-        "AAPL": 23,
-        "BBY": 44,
+    assert allocation == {
+        "MA": 96,
+        "PFE": 211,
+        "FB": 34,
+        "GOOG": 4,
+        "BABA": 22,
+        "AAPL": 17,
+        "SBUX": 38,
        "AMZN": 2,
-        "SBUX": 45,
-        "GOOG": 3,
-        "WMT": 11,
-        "XOM": 11,
-        "BAC": -271,
-        "GM": -133,
-        "GE": -356,
-        "SHLD": -922,
-        "AMD": -285,
-        "JPM": -5,
-        "T": -14,
-        "UAA": -8,
-        "RRC": -3,
+        "BBY": 27,
+        "XOM": 19,
+        "WMT": 10,
+        "BAC": -269,
+        "AMD": -399,
+        "SHLD": -1099,
+        "GM": -78,
+        "RRC": -154,
+        "GE": -119,
+        "T": -41,
+        "UAA": -64,
    }
    long_total = 0
    short_total = 0
@@ -182,15 +185,15 @@ def test_lp_portfolio_allocation():
    da = DiscreteAllocation(w, latest_prices)
    allocation, leftover = da.lp_portfolio()

-    assert da.allocation == {
-        "AAPL": 5,
-        "FB": 11,
-        "BABA": 5,
-        "AMZN": 1,
-        "BBY": 7,
-        "MA": 14,
-        "PFE": 50,
-        "SBUX": 5,
+    assert allocation == {
+        "GOOG": 1,
+        "AAPL": 4,
+        "FB": 12,
+        "BABA": 4,
+        "BBY": 2,
+        "MA": 20,
+        "PFE": 54,
+        "SBUX": 1,
    }
    total = 0
    for ticker, num in allocation.items():
@@ -208,7 +211,9 @@ def test_lp_allocation_rmse_error():
    latest_prices = get_latest_prices(df)
    da = DiscreteAllocation(w, latest_prices)
    da.lp_portfolio()
-    np.testing.assert_almost_equal(da._allocation_rmse_error(verbose=False), 0.017070218149194846)
+    np.testing.assert_almost_equal(
+        da._allocation_rmse_error(verbose=False), 0.017082871441954087, decimal=5
+    )


 def test_lp_portfolio_allocation_short():
@@ -222,25 +227,25 @@ def test_lp_portfolio_allocation_short():
    da = DiscreteAllocation(w, latest_prices)
    allocation, leftover = da.lp_portfolio()

-    assert da.allocation == {
+    assert allocation == {
        "GOOG": 1,
-        "AAPL": 5,
-        "FB": 8,
+        "AAPL": 4,
+        "FB": 7,
        "BABA": 5,
-        "WMT": 2,
-        "XOM": 2,
-        "BBY": 9,
-        "MA": 16,
-        "PFE": 46,
-        "SBUX": 9,
-        "GE": -43,
-        "AMD": -34,
+        "WMT": 3,
+        "XOM": 4,
+        "BBY": 6,
+        "MA": 19,
+        "PFE": 42,
+        "SBUX": 8,
+        "GE": -14,
+        "AMD": -48,
        "BAC": -32,
-        "GM": -16,
-        "T": -1,
-        "UAA": -1,
-        "SHLD": -110,
-        "JPM": -1,
+        "GM": -9,
+        "T": -5,
+        "UAA": -8,
+        "SHLD": -132,
+        "RRC": -19,
    }
    long_total = 0
    short_total = 0
@@ -264,7 +269,9 @@ def test_lp_allocation_rmse_error_short():
    latest_prices = get_latest_prices(df)
    da = DiscreteAllocation(w, latest_prices)
    da.lp_portfolio()
-    np.testing.assert_almost_equal(da._allocation_rmse_error(), 0.027018566693989568)
+    np.testing.assert_almost_equal(
+        da._allocation_rmse_error(verbose=False), 0.06063511265243109
+    )


 def test_lp_portfolio_allocation_different_params():
@@ -280,19 +287,18 @@ def test_lp_portfolio_allocation_different_params():
    )
    allocation, leftover = da.lp_portfolio()

-    assert da.allocation == {
-        "GOOG": 1,
-        "AAPL": 43,
-        "FB": 95,
-        "BABA": 44,
-        "AMZN": 4,
-        "AMD": 1,
-        "SHLD": 3,
-        "BBY": 69,
-        "MA": 114,
-        "PFE": 412,
-        "SBUX": 51,
+    assert allocation == {
+        "GOOG": 3,
+        "AAPL": 32,
+        "FB": 100,
+        "BABA": 34,
+        "AMZN": 2,
+        "BBY": 15,
+        "MA": 164,
+        "PFE": 438,
+        "SBUX": 15,
    }
+
    total = 0
    for ticker, num in allocation.items():
        total += num * latest_prices[ticker]
--- a/tests/test_efficient_frontier.py
+++ b/tests/test_efficient_frontier.py
@@ -61,7 +61,7 @@ def test_min_volatility():

    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.17931232481259154, 0.15915084514118694, 1.00101463282373),
+        (0.15056821399482578, 0.15915084514118694, 0.8204054077060996),
    )


@@ -72,7 +72,7 @@ def test_min_volatility_different_solver():
    assert set(w.keys()) == set(ef.tickers)
    np.testing.assert_almost_equal(ef.weights.sum(), 1)
    assert all([i >= 0 for i in w.values()])
-    test_performance = (0.179312, 0.159151, 1.001015)
+    test_performance = (0.150567, 0.159150, 0.820403)
    np.testing.assert_allclose(ef.portfolio_performance(), test_performance, atol=1e-5)

    ef = setup_efficient_frontier(solver="OSQP")
@@ -124,7 +124,7 @@ def test_min_volatility_short():
    np.testing.assert_almost_equal(ef.weights.sum(), 1)
    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.1721356467349655, 0.1555915367269669, 0.9777887019776287),
+        (0.1516319319875544, 0.1555915367269669, 0.8460095886741129),
    )

    # Shorting should reduce volatility
@@ -156,7 +156,7 @@ def test_min_volatility_L2_reg():

    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.23129890623344232, 0.1955254118258614, 1.080672349748733),
+        (0.17356099329164965, 0.1955254118258614, 0.785376140408869),
    )


@@ -205,7 +205,7 @@ def test_min_volatility_tx_costs_L2_reg():

    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.2316565265271545, 0.1959773703677164, 1.0800049318450338),
+        (0.17363446634404042, 0.1959773703677164, 0.7839398296638683),
    )


@@ -335,7 +335,7 @@ def test_max_sharpe_long_only():

    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.33035037367760506, 0.21671276571944567, 1.4320816434015786),
+        (0.3047768672819914, 0.22165566922402932, 1.2847714127003216),
    )


@@ -380,7 +380,7 @@ def test_max_sharpe_short():
    np.testing.assert_almost_equal(ef.weights.sum(), 1)
    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.4072439477276246, 0.24823487545231313, 1.5599900981762558),
+        (0.4937195216716211, 0.29516576454651955, 1.6049270564945908),
    )
    sharpe = ef.portfolio_performance()[2]

@@ -395,7 +395,7 @@ def test_max_sharpe_L2_reg():
    ef = setup_efficient_frontier()
    ef.add_objective(objective_functions.L2_reg, gamma=5)

-    with warnings.catch_warnings(record=True) as w:
+    with pytest.warns(UserWarning) as w:
        weights = ef.max_sharpe()
        assert len(w) == 1

@@ -405,7 +405,7 @@ def test_max_sharpe_L2_reg():
    assert all([i >= 0 for i in weights.values()])
    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.2936875354933478, 0.22783545277575057, 1.2012508683744123),
+        (0.2516854357026833, 0.22043282695478603, 1.051047790401043),
    )

    ef2 = setup_efficient_frontier()
@@ -481,7 +481,7 @@ def test_max_sharpe_L2_reg_with_shorts():
    np.testing.assert_almost_equal(ef.weights.sum(), 1)
    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.3076093180094401, 0.22415982749409985, 1.2830546901496447),
+        (0.2995338981166366, 0.2234696161770517, 1.2508810052063901),
    )
    new_number = sum(ef.weights > 0.01)
    assert new_number >= initial_number
@@ -733,7 +733,7 @@ def test_max_quadratic_utility():

    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.40064324249527605, 0.2917825266124642, 1.3045443362029479),
+        (0.3677732711751504, 0.2921342197778279, 1.1904571516463793),
    )

    ret1, var1, _ = ef.portfolio_performance()
@@ -752,7 +752,7 @@ def test_max_quadratic_utility_with_shorts():

    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (1.3318330413711252, 1.0198436183533854, 1.2863080356272452),
+        (1.4170505733098597, 1.0438577623242156, 1.3383533884915872),
    )


@@ -764,7 +764,7 @@ def test_max_quadratic_utility_market_neutral():
    np.testing.assert_almost_equal(ef.weights.sum(), 0)
    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (1.13434841843883, 0.9896404148973286, 1.1260134506071473),
+        (1.248936321062371, 1.0219175004907117, 1.2025787996313317),
    )


@@ -789,7 +789,7 @@ def test_max_quadratic_utility_L2_reg():
    assert all([i >= 0 for i in weights.values()])
    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.2602803268728476, 0.21603540587515674, 1.112226608872166),
+        (0.19774277217586125, 0.2104822672707046, 0.8444548535162986),
    )

    ef2 = setup_efficient_frontier()
@@ -820,7 +820,7 @@ def test_efficient_risk():
    assert all([i >= 0 for i in w.values()])
    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.28577452556155075, 0.19, 1.3988132892376837),
+        (0.2552422849133517, 0.1900000002876062, 1.2381172871434818),
        atol=1e-6,
    )

@@ -834,7 +834,7 @@ def test_efficient_risk_error():
    assert ef.efficient_risk(min_possible_vol + 0.01)

    ef = setup_efficient_frontier()
-    with pytest.raises(exceptions.OptimizationError):
+    with pytest.raises(ValueError):
        # This volatility is too low
        ef.efficient_risk(min_possible_vol - 0.01)

@@ -859,7 +859,7 @@ def test_efficient_risk_short():
    np.testing.assert_almost_equal(ef.weights.sum(), 1)
    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.30468522897430295, 0.19, 1.4983424153337392),
+        (0.30035471606347336, 0.1900000003049494, 1.4755511348079207),
        atol=1e-6,
    )
    sharpe = ef.portfolio_performance()[2]
@@ -882,7 +882,7 @@ def test_efficient_risk_L2_reg():
    assert all([i >= 0 for i in weights.values()])
    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.24087463760460398, 0.19, 1.162498090632486),
+        (0.1931352562313653, 0.18999999989010993, 0.9112381912184281),
        atol=1e-6,
    )

@@ -908,7 +908,7 @@ def test_efficient_risk_market_neutral():
    assert (ef.weights < 1).all() and (ef.weights > -1).all()
    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.2552600197428133, 0.21, 1.1202858085349783),
+        (0.28640632960825885, 0.20999999995100788, 1.2686015698590967),
        atol=1e-6,
    )
    sharpe = ef.portfolio_performance()[2]
@@ -933,17 +933,16 @@ def test_efficient_risk_market_neutral_L2_reg():

    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.10755645826336145, 0.11079556786108302, 0.7902523535340413),
+        (0.12790320789339854, 0.1175336636355454, 0.9180621496492316),
        atol=1e-6,
    )


 def test_efficient_risk_market_neutral_warning():
    ef = setup_efficient_frontier()
-    with warnings.catch_warnings(record=True) as w:
+    with pytest.warns(RuntimeWarning) as w:
        ef.efficient_risk(0.19, market_neutral=True)
        assert len(w) == 1
-        assert issubclass(w[0].category, RuntimeWarning)
        assert (
            str(w[0].message)
            == "Market neutrality requires shorting - bounds have been amended"
@@ -959,7 +958,7 @@ def test_efficient_return():
    assert all([i >= 0 for i in w.values()])
    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.25, 0.1738852429895079, 1.3227114391408021),
+        (0.25, 0.18723269942026335, 1.2284179030274036),
        atol=1e-6,
    )

@@ -994,7 +993,7 @@ def test_efficient_return_short():
    assert set(w.keys()) == set(ef.tickers)
    np.testing.assert_almost_equal(ef.weights.sum(), 1)
    np.testing.assert_allclose(
-        ef.portfolio_performance(), (0.25, 0.16826225873038014, 1.3669137793315087)
+        ef.portfolio_performance(), (0.25, 0.17149595234895817, 1.3411395245760582)
    )
    sharpe = ef.portfolio_performance()[2]

@@ -1014,7 +1013,7 @@ def test_efficient_return_L2_reg():
    np.testing.assert_almost_equal(ef.weights.sum(), 1)
    assert all([i >= 0 for i in w.values()])
    np.testing.assert_allclose(
-        ef.portfolio_performance(), (0.25, 0.20033592447690426, 1.1480716731187948)
+        ef.portfolio_performance(), (0.25, 0.20961660883459776, 1.0972412981906703)
    )


@@ -1028,22 +1027,21 @@ def test_efficient_return_market_neutral():
    np.testing.assert_almost_equal(ef.weights.sum(), 0)
    assert (ef.weights < 1).all() and (ef.weights > -1).all()
    np.testing.assert_almost_equal(
-        ef.portfolio_performance(), (0.25, 0.20567263154580923, 1.1182819914898223)
+        ef.portfolio_performance(), (0.25, 0.1833060046337015, 1.2547324920403273)
    )
    sharpe = ef.portfolio_performance()[2]
    ef_long_only = setup_efficient_frontier()
    ef_long_only.efficient_return(0.25)
    long_only_sharpe = ef_long_only.portfolio_performance()[2]
-    assert long_only_sharpe > sharpe
+    assert long_only_sharpe < sharpe


 def test_efficient_return_market_neutral_warning():
    # This fails
    ef = setup_efficient_frontier()
-    with warnings.catch_warnings(record=True) as w:
+    with pytest.warns(RuntimeWarning) as w:
        ef.efficient_return(0.25, market_neutral=True)
        assert len(w) == 1
-        assert issubclass(w[0].category, RuntimeWarning)
        assert (
            str(w[0].message)
            == "Market neutrality requires shorting - bounds have been amended"
@@ -1061,7 +1059,7 @@ def test_max_sharpe_semicovariance():
    assert all([i >= 0 for i in w.values()])
    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.2972184894480104, 0.06443145011260347, 4.302533762060766),
+        (0.2732301946250426, 0.06603231922971581, 3.834943215368455),
    )


@@ -1077,7 +1075,7 @@ def test_max_sharpe_short_semicovariance():
    np.testing.assert_almost_equal(ef.weights.sum(), 1)
    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.3564305116656491, 0.07201282488003401, 4.671813836300796),
+        (0.3907992623559733, 0.0809285460933456, 4.581810501430255),
    )


@@ -1097,7 +1095,7 @@ def test_min_volatilty_shrunk_L2_reg():
    assert all([i >= 0 for i in w.values()])
    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.23127396601517256, 0.19563960638632416, 1.0799140824173181),
+        (0.17358178582309983, 0.19563960638632416, 0.7850239972361532),
    )


@@ -1113,7 +1111,7 @@ def test_efficient_return_shrunk():
    np.testing.assert_almost_equal(ef.weights.sum(), 1)
    assert all([i >= 0 for i in w.values()])
    np.testing.assert_allclose(
-        ef.portfolio_performance(), (0.22, 0.0849639369932322, 2.353939884117318)
+        ef.portfolio_performance(), (0.22, 0.08892192396903059, 2.2491641101878916)
    )


@@ -1128,7 +1126,7 @@ def test_max_sharpe_exp_cov():
    assert all([i >= 0 for i in w.values()])
    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.3678817256187322, 0.1753405505478982, 1.9840346373481956),
+        (0.33700887443850647, 0.1807332515488447, 1.7540152225548384),
    )


@@ -1144,7 +1142,7 @@ def test_min_volatility_exp_cov_L2_reg():
    assert all([i >= 0 for i in w.values()])
    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.2434082300792007, 0.17835412793427002, 1.2526103694192867),
+        (0.1829496087575576, 0.17835412793427002, 0.9136295898775636),
    )


@@ -1161,6 +1159,6 @@ def test_efficient_risk_exp_cov_market_neutral():
    assert (ef.weights < 1).all() and (ef.weights > -1).all()
    np.testing.assert_allclose(
        ef.portfolio_performance(),
-        (0.3908928033782067, 0.18999999995323363, 1.9520673866815672),
+        (0.3934093962620499, 0.18999999989011893, 1.9653126130421081),
        atol=1e-6,
    )
--- a/tests/test_expected_returns.py
+++ b/tests/test_expected_returns.py
@@ -38,7 +38,7 @@ def test_returns_from_prices():
 def test_log_returns_from_prices():
    df = get_data()
    old_nan = df.isnull().sum(axis=1).sum()
-    log_rets = expected_returns.log_returns_from_prices(df)
+    log_rets = expected_returns.returns_from_prices(df, log_returns=True)
    new_nan = log_rets.isnull().sum(axis=1).sum()
    assert new_nan == old_nan
    np.testing.assert_almost_equal(log_rets.iloc[-1, -1], 0.0001682740081102576)
@@ -55,17 +55,12 @@ def test_mean_historical_returns_dummy():
        ]
    )
    mean = expected_returns.mean_historical_return(data, frequency=1)
-    test_answer = pd.Series([0.00865598, 0.025, 0.01286968, -0.03632333])
-    pd.testing.assert_series_equal(mean, test_answer)
-    mean = expected_returns.mean_historical_return(data, compounding=True, frequency=1)
-    pd.testing.assert_series_equal(mean, test_answer)
+    test_answer = pd.Series([0.0061922, 0.0241137, 0.0122722, -0.0421775])
+    pd.testing.assert_series_equal(mean, test_answer, check_less_precise=4)

-
-def test_mean_historical_returns_compounding():
-    df = get_data()
-    mean = expected_returns.mean_historical_return(df)
-    mean2 = expected_returns.mean_historical_return(df, compounding=True)
-    assert (mean2 >= mean).all()
+    mean = expected_returns.mean_historical_return(data, compounding=False, frequency=1)
+    test_answer = pd.Series([0.0086560, 0.0250000, 0.0128697, -0.03632333])
+    pd.testing.assert_series_equal(mean, test_answer, check_less_precise=4)


 def test_mean_historical_returns():
@@ -77,26 +72,26 @@ def test_mean_historical_returns():
    assert mean.dtype == "float64"
    correct_mean = np.array(
        [
-            0.26770284,
-            0.3637864,
-            0.31709032,
-            0.22616723,
-            0.49982007,
-            0.16888704,
-            0.22754479,
-            0.14783539,
-            0.19001915,
-            0.08150653,
-            0.12826351,
-            0.25797816,
-            0.07580128,
-            0.16087243,
-            0.20510267,
-            0.3511536,
-            0.38808003,
-            0.24635612,
-            0.21798433,
-            0.28474973,
+            0.247967,
+            0.294304,
+            0.284037,
+            0.1923164,
+            0.371327,
+            0.1360093,
+            0.0328503,
+            0.1200115,
+            0.105540,
+            0.0423457,
+            0.1002559,
+            0.1442237,
+            -0.0792602,
+            0.1430506,
+            0.0736356,
+            0.238835,
+            0.388665,
+            0.226717,
+            0.1561701,
+            0.2318153,
        ]
    )
    np.testing.assert_array_almost_equal(mean.values, correct_mean)
@@ -106,10 +101,9 @@ def test_mean_historical_returns_type_warning():
    df = get_data()
    mean = expected_returns.mean_historical_return(df)

-    with warnings.catch_warnings(record=True) as w:
+    with pytest.warns(RuntimeWarning) as w:
        mean_from_array = expected_returns.mean_historical_return(np.array(df))
        assert len(w) == 1
-        assert issubclass(w[0].category, RuntimeWarning)
        assert str(w[0].message) == "prices are not in a dataframe"

    np.testing.assert_array_almost_equal(mean.values, mean_from_array.values, decimal=6)
@@ -117,8 +111,8 @@ def test_mean_historical_returns_type_warning():

 def test_mean_historical_returns_frequency():
    df = get_data()
-    mean = expected_returns.mean_historical_return(df)
-    mean2 = expected_returns.mean_historical_return(df, frequency=52)
+    mean = expected_returns.mean_historical_return(df, compounding=False)
+    mean2 = expected_returns.mean_historical_return(df, compounding=False, frequency=52)
    np.testing.assert_array_almost_equal(mean / 252, mean2 / 52)


@@ -133,56 +127,18 @@ def test_ema_historical_return():

 def test_ema_historical_return_frequency():
    df = get_data()
-    mean = expected_returns.ema_historical_return(df)
-    mean2 = expected_returns.ema_historical_return(df, frequency=52)
+    mean = expected_returns.ema_historical_return(df, compounding=False)
+    mean2 = expected_returns.ema_historical_return(df, compounding=False, frequency=52)
    np.testing.assert_array_almost_equal(mean / 252, mean2 / 52)

-    mean3 = expected_returns.ema_historical_return(df, compounding=True)
-    assert (abs(mean3) > mean).all()
-

 def test_ema_historical_return_limit():
    df = get_data()
-    sma = expected_returns.mean_historical_return(df)
-    ema = expected_returns.ema_historical_return(df, span=1e10)
+    sma = expected_returns.mean_historical_return(df, compounding=False)
+    ema = expected_returns.ema_historical_return(df, compounding=False, span=1e10)
    np.testing.assert_array_almost_equal(ema.values, sma.values)


-def test_james_stein():
-    df = get_data()
-    js = expected_returns.james_stein_shrinkage(df)
-    correct_mean = np.array(
-        [
-            0.25870218,
-            0.32318595,
-            0.29184719,
-            0.23082673,
-            0.41448111,
-            0.19238474,
-            0.23175124,
-            0.17825652,
-            0.20656697,
-            0.13374178,
-            0.16512141,
-            0.25217574,
-            0.12991287,
-            0.18700597,
-            0.21668984,
-            0.3147078,
-            0.33948993,
-            0.24437593,
-            0.225335,
-            0.27014272,
-        ]
-    )
-    np.testing.assert_array_almost_equal(js.values, correct_mean)
-
-    # Test shrinkage
-    y = expected_returns.returns_from_prices(df).mean(axis=0) * 252
-    nu = y.mean()
-    assert (((js <= nu) & (js >= y)) | ((js >= nu) & (js <= y))).all()
-
-
 def test_capm_no_benchmark():
    df = get_data()
    mu = expected_returns.capm_return(df)
@@ -192,26 +148,26 @@ def test_capm_no_benchmark():
    assert mu.dtype == "float64"
    correct_mu = np.array(
        [
-            0.21803135,
-            0.27902605,
-            0.14475533,
-            0.14668971,
-            0.40944875,
-            0.22361704,
-            0.39057166,
-            0.164807,
-            0.31280876,
-            0.17018046,
-            0.15044284,
-            0.34609161,
-            0.3233097,
-            0.1479624,
-            0.26403991,
-            0.31124465,
-            0.27312086,
-            0.16703193,
-            0.30396023,
-            0.25182927,
+            0.22148462799238577,
+            0.2835429647498704,
+            0.14693081977908462,
+            0.1488989354304723,
+            0.4162399750335195,
+            0.22716772604184535,
+            0.3970337136813829,
+            0.16733214988182069,
+            0.31791477659742146,
+            0.17279931642386534,
+            0.15271750464365566,
+            0.351778014382922,
+            0.32859883451716376,
+            0.1501938182844417,
+            0.268295486802897,
+            0.31632339201710874,
+            0.27753479916328516,
+            0.16959588523287855,
+            0.3089119447773357,
+            0.2558719211959501,
        ]
    )
    np.testing.assert_array_almost_equal(mu.values, correct_mu)
@@ -228,26 +184,26 @@ def test_capm_with_benchmark():
    assert mu.dtype == "float64"
    correct_mu = np.array(
        [
-            0.10903299,
-            0.11891232,
-            0.0659977,
-            0.07369941,
-            0.15948144,
-            0.12308759,
-            0.15907944,
-            0.08680978,
-            0.15778843,
-            0.0903294,
-            0.09043133,
-            0.14716681,
-            0.12510181,
-            0.0927869,
-            0.10990104,
-            0.12317033,
-            0.13596521,
-            0.09344662,
-            0.15457909,
-            0.11430041,
+            0.09115799375654746,
+            0.09905386632033128,
+            0.05676282405265752,
+            0.06291827346436336,
+            0.13147799781014877,
+            0.10239088012000815,
+            0.1311567086884512,
+            0.07339649698626659,
+            0.1301248935078549,
+            0.07620949056643983,
+            0.07629095442513395,
+            0.12163575425541985,
+            0.10400070536161658,
+            0.0781736030988492,
+            0.09185177050469516,
+            0.10245700691271296,
+            0.11268307946677197,
+            0.07870087187919145,
+            0.1275598841214107,
+            0.09536788741392595,
        ]
    )
    np.testing.assert_array_almost_equal(mu.values, correct_mu)
@@ -257,12 +213,7 @@ def test_risk_matrix_and_returns_data():
    # Test the switcher method for simple calls
    df = get_data()

-    for method in {
-        "mean_historical_return",
-        "ema_historical_return",
-        "james_stein_shrinkage",
-        "capm_return",
-    }:
+    for method in {"mean_historical_return", "ema_historical_return", "capm_return"}:
        mu = expected_returns.return_model(df, method=method)

        assert isinstance(mu, pd.Series)
--- a/tests/test_hrp.py
+++ b/tests/test_hrp.py
@@ -10,7 +10,7 @@ def test_hrp_portfolio():
    df = get_data()
    returns = df.pct_change().dropna(how="all")
    hrp = HRPOpt(returns)
-    w = hrp.optimize()
+    w = hrp.optimize(linkage_method="single")

    # uncomment this line if you want generating a new file
    # pd.Series(w).to_csv(resource("weights_hrp.csv"))
@@ -32,7 +32,7 @@ def test_portfolio_performance():
    hrp = HRPOpt(returns)
    with pytest.raises(ValueError):
        hrp.portfolio_performance()
-    hrp.optimize()
+    hrp.optimize(linkage_method="single")
    np.testing.assert_allclose(
        hrp.portfolio_performance(),
        (0.21353402380950973, 0.17844159743748936, 1.084579081272277),
@@ -43,7 +43,7 @@ def test_pass_cov_matrix():
    df = get_data()
    S = CovarianceShrinkage(df).ledoit_wolf()
    hrp = HRPOpt(cov_matrix=S)
-    hrp.optimize()
+    hrp.optimize(linkage_method="single")
    perf = hrp.portfolio_performance()
    assert perf[0] is None and perf[2] is None
    np.testing.assert_almost_equal(perf[1], 0.10002783894982334)
@@ -62,6 +62,6 @@ def test_quasi_dag():
    df = get_data()
    returns = df.pct_change().dropna(how="all")
    hrp = HRPOpt(returns)
-    hrp.optimize()
+    hrp.optimize(linkage_method="single")
    clusters = hrp.clusters
    assert HRPOpt._get_quasi_diag(clusters)[:5] == [12, 6, 15, 14, 2]
--- a/tests/test_plotting.py
+++ b/tests/test_plotting.py
@@ -36,9 +36,9 @@ def test_ef_plot():
    cla = CLA(rets, S)

    ax = plotting.plot_efficient_frontier(cla, showfig=False)
-    assert len(ax.findobj()) == 137
+    assert len(ax.findobj()) == 143
    ax = plotting.plot_efficient_frontier(cla, show_assets=False, showfig=False)
-    assert len(ax.findobj()) == 149
+    assert len(ax.findobj()) == 161


 def test_weight_plot():
--- a/tests/test_risk_models.py
+++ b/tests/test_risk_models.py
@@ -27,6 +27,11 @@ def test_sample_cov_dummy():
    pd.testing.assert_frame_equal(S, test_answer)


+def test_is_positive_semidefinite():
+    a = np.zeros((100, 100))
+    assert risk_models._is_positive_semidefinite(a)
+
+
 def test_sample_cov_real_data():
    df = get_data()
    S = risk_models.sample_cov(df)
@@ -42,11 +47,9 @@ def test_sample_cov_type_warning():
    cov_from_df = risk_models.sample_cov(df)

    returns_as_array = np.array(df)
-    with warnings.catch_warnings(record=True) as w:
+    with pytest.warns(RuntimeWarning) as w:
        cov_from_array = risk_models.sample_cov(returns_as_array)
-
        assert len(w) == 1
-        assert issubclass(w[0].category, RuntimeWarning)
        assert str(w[0].message) == "data is not in a dataframe"

    np.testing.assert_array_almost_equal(
@@ -59,11 +62,10 @@ def test_sample_cov_npd():
    assert not risk_models._is_positive_semidefinite(S)

    for method in {"spectral", "diag"}:
-        with warnings.catch_warnings(record=True) as w:
+        with pytest.warns(UserWarning) as w:
            S2 = risk_models.fix_nonpositive_semidefinite(S, fix_method=method)
            assert risk_models._is_positive_semidefinite(S2)
            assert len(w) == 1
-            assert issubclass(w[0].category, UserWarning)
            assert (
                str(w[0].message)
                == "The covariance matrix is non positive semidefinite. Amending eigenvalues."
@@ -148,10 +150,9 @@ def test_cov_to_corr():
    test_corr = risk_models.cov_to_corr(rets.cov())
    pd.testing.assert_frame_equal(test_corr, rets.corr())

-    with warnings.catch_warnings(record=True) as w:
+    with pytest.warns(RuntimeWarning) as w:
        test_corr_numpy = risk_models.cov_to_corr(rets.cov().values)
        assert len(w) == 1
-        assert issubclass(w[0].category, RuntimeWarning)
        assert str(w[0].message) == "cov_matrix is not a dataframe"
        np.testing.assert_array_almost_equal(test_corr_numpy, rets.corr().values)