migrated min_vol to cvxpy (with l2 reg)

pypfopt/__init__.py

@@ -0,0 +1,20 @@
+from .black_litterman import (
+    market_implied_prior_returns,
+    market_implied_risk_aversion,
+    BlackLittermanModel,
+)
+from .cla import CLA
+from .discrete_allocation import get_latest_prices, DiscreteAllocation
+from .efficient_frontier import EfficientFrontier
+from .hierarchical_risk_parity import HRPOpt
+
+__all__ = [
+    "market_implied_prior_returns",
+    "market_implied_risk_aversion",
+    "BlackLittermanModel",
+    "CLA",
+    "get_latest_prices",
+    "DiscreteAllocation",
+    "EfficientFrontier",
+    "HRPOpt",
+]

pypfopt/base_optimizer.py

@@ -1,6 +1,6 @@
 """
 The ``base_optimizer`` module houses the parent classes ``BaseOptimizer`` and
-``BaseScipyOptimizer``, from which all optimisers will inherit. The later is for
+``BaseConvexOptimizer``, from which all optimisers will inherit. The later is for
 optimisers that use the scipy solver.
 
 Additionally, we define a general utility function ``portfolio_performance`` to
@@ -10,6 +10,7 @@ evaluate return and risk for a given set of portfolio weights.
 import json
 import numpy as np
 import pandas as pd
+import cvxpy as cp
 from . import objective_functions
 
 
@@ -96,7 +97,7 @@ class BaseOptimizer:
                 f.write(str(clean_weights))
 
 
-class BaseScipyOptimizer(BaseOptimizer):
+class BaseConvexOptimizer(BaseOptimizer):
 
     """
     Instance variables:
@@ -105,9 +106,13 @@ class BaseScipyOptimizer(BaseOptimizer):
     - ``tickers`` - str list
     - ``weights`` - np.ndarray
     - ``bounds`` - float tuple OR (float tuple) list
-    - ``initial_guess`` - np.ndarray
     - ``constraints`` - dict list
-    - ``opt_method`` - the optimisation algorithm to use. Defaults to SLSQP.
+
+    Public methods:
+
+    - ``set_weights()`` creates self.weights (np.ndarray) from a weights dict
+    - ``clean_weights()`` rounds the weights and clips near-zeros.
+    - ``save_weights_to_file()`` saves the weights to csv, json, or txt.
     """
 
     def __init__(self, n_assets, tickers=None, weight_bounds=(0, 1)):
@@ -118,46 +123,58 @@ class BaseScipyOptimizer(BaseOptimizer):
         :type weight_bounds: tuple OR tuple list, optional
         """
         super().__init__(n_assets, tickers)
-        self.bounds = self._make_valid_bounds(weight_bounds)
-        # Optimisation parameters
-        self.initial_guess = np.array([1 / self.n_assets] * self.n_assets)
-        self.constraints = [{"type": "eq", "fun": lambda x: np.sum(x) - 1}]
-        self.opt_method = "SLSQP"
 
-    def _make_valid_bounds(self, test_bounds):
+        # Optimisation variables
+        self._w = cp.Variable(n_assets)
+        self._objective = None
+        self._additional_objectives = []
+        self._constraints = []
+        self._map_bounds_to_constraints(weight_bounds)
+
+    def _map_bounds_to_constraints(self, test_bounds):
         """
-        Private method: process input bounds into a form acceptable by scipy.optimize,
-        and check the validity of said bounds.
+        Process input bounds into a form acceptable by cvxpy and add to the constraints list.
 
         :param test_bounds: minimum and maximum weight of each asset OR single min/max pair
-                              if all identical, defaults to (0, 1).
-        :type test_bounds: tuple OR list/tuple of tuples.
-        :raises ValueError: if ``test_bounds`` is not a tuple of length two OR a collection
-                            of pairs.
-        :raises ValueError: if the lower bound is too high
-        :return: a tuple of bounds, e.g ((0, 1), (0, 1), (0, 1) ...)
-        :rtype: tuple of tuples
+                            if all identical OR pair of arrays corresponding to lower/upper bounds. defaults to (0, 1).
+        :type test_bounds: tuple OR list/tuple of tuples OR pair of np arrays
+        :raises TypeError: if ``test_bounds`` is not of the right type
+        :return: bounds suitable for cvxpy
+        :rtype: tuple pair of np.ndarray
         """
         # If it is a collection with the right length, assume they are all bounds.
         if len(test_bounds) == self.n_assets and not isinstance(
             test_bounds[0], (float, int)
         ):
-            bounds = test_bounds
+            bounds = np.array(test_bounds, dtype=np.float)
+            lower = np.nan_to_num(bounds[:, 0], nan=-np.inf)
+            upper = np.nan_to_num(bounds[:, 1], nan=np.inf)
         else:
-            if len(test_bounds) != 2 or not isinstance(test_bounds, tuple):
-                raise ValueError(
-                    "test_bounds must be a tuple of (lower bound, upper bound) "
-                    "OR collection of bounds for each asset"
+            # Otherwise this must be a pair.
+            if len(test_bounds) != 2 or not isinstance(test_bounds, (tuple, list)):
+                raise TypeError(
+                    "test_bounds must be a pair (lower bound, upper bound) "
+                    "OR a collection of bounds for each asset"
                 )
-            bounds = (test_bounds,) * self.n_assets
+            lower, upper = test_bounds
 
-        # Ensure lower bound is not too high
-        if sum((0 if b[0] is None else b[0]) for b in bounds) > 1:
-            raise ValueError(
-                "Lower bound is too high. Impossible to construct valid portfolio"
-            )
+            # Replace None values with the appropriate infinity.
+            if np.isscalar(lower) or lower is None:
+                lower = -np.inf if lower is None else lower
+                upper = np.inf if upper is None else upper
+            else:
+                lower = np.nan_to_num(lower, nan=-np.inf)
+                upper = np.nan_to_num(upper, nan=np.inf)
 
-        return bounds
+        self._constraints.append(self._w >= lower)
+        self._constraints.append(self._w <= upper)
+
+    @staticmethod
+    def _make_scipy_bounds():
+        """
+        Convert the current cvxpy bounds to scipy bounds
+        """
+        raise NotImplementedError
 
 
 def portfolio_performance(
@@ -199,7 +216,8 @@ def portfolio_performance(
         new_weights = np.asarray(weights)
     else:
         raise ValueError("Weights is None")
-    sigma = np.sqrt(objective_functions.volatility(new_weights, cov_matrix))
+
+    sigma = np.sqrt(objective_functions.portfolio_variance(new_weights, cov_matrix))
     mu = new_weights.dot(expected_returns)
 
     sharpe = -objective_functions.negative_sharpe(

pypfopt/efficient_frontier.py

@@ -6,14 +6,16 @@ generates optimal portfolios for various possible objective functions and parame
 import warnings
 import numpy as np
 import pandas as pd
+import cvxpy as cp
 import scipy.optimize as sco
+from . import exceptions
 from . import objective_functions, base_optimizer
 
 
-class EfficientFrontier(base_optimizer.BaseScipyOptimizer):
+class EfficientFrontier(base_optimizer.BaseConvexOptimizer):
 
     """
-    An EfficientFrontier object (inheriting from BaseScipyOptimizer) contains multiple
+    An EfficientFrontier object (inheriting from BaseConvexOptimizer) contains multiple
     optimisation methods that can be called (corresponding to different objective
     functions) with various parameters.
 
@@ -24,8 +26,8 @@ class EfficientFrontier(base_optimizer.BaseScipyOptimizer):
         - ``n_assets`` - int
         - ``tickers`` - str list
         - ``bounds`` - float tuple OR (float tuple) list
-        - ``cov_matrix`` - pd.DataFrame
-        - ``expected_returns`` - pd.Series
+        - ``cov_matrix`` - np.ndarray
+        - ``expected_returns`` - np.ndarray
 
     - Optimisation parameters:
 
@@ -67,33 +69,104 @@ class EfficientFrontier(base_optimizer.BaseScipyOptimizer):
         :raises TypeError: if ``cov_matrix`` is not a dataframe or array
         """
         # Inputs
-        self.cov_matrix = cov_matrix
-        if expected_returns is not None:
-            if not isinstance(expected_returns, (pd.Series, list, np.ndarray)):
-                raise TypeError("expected_returns is not a series, list or array")
-            if not isinstance(cov_matrix, (pd.DataFrame, np.ndarray)):
-                raise TypeError("cov_matrix is not a dataframe or array")
-            self.expected_returns = expected_returns
+        self.cov_matrix = EfficientFrontier._validate_cov_matrix(cov_matrix)
+        self.expected_returns = EfficientFrontier._validate_expected_returns(
+            expected_returns
+        )
+
+        # Labels
         if isinstance(expected_returns, pd.Series):
             tickers = list(expected_returns.index)
         elif isinstance(cov_matrix, pd.DataFrame):
             tickers = list(cov_matrix.columns)
-        else:
+        else:  # use integer labels
             tickers = list(range(len(expected_returns)))
 
+        if cov_matrix.shape != (len(expected_returns), len(expected_returns)):
+            raise ValueError("Covariance matrix does not match expected returns")
+
         super().__init__(len(tickers), tickers, weight_bounds)
 
-        if not isinstance(gamma, (int, float)):
-            raise ValueError("gamma should be numeric")
-        if gamma < 0:
-            warnings.warn("in most cases, gamma should be positive", UserWarning)
-        self.gamma = gamma
+    @staticmethod
+    def _validate_expected_returns(expected_returns):
+        if expected_returns is None:
+            raise ValueError("expected_returns must be provided")
+        elif isinstance(expected_returns, pd.Series):
+            return expected_returns.values
+        elif isinstance(expected_returns, list):
+            return np.array(expected_returns)
+        elif isinstance(expected_returns, np.ndarray):
+            return expected_returns.ravel()
+        else:
+            raise TypeError("expected_returns is not a series, list or array")
+
+    @staticmethod
+    def _validate_cov_matrix(cov_matrix):
+        if cov_matrix is None:
+            raise ValueError("cov_matrix must be provided")
+        elif isinstance(cov_matrix, pd.DataFrame):
+            return cov_matrix.values
+        elif isinstance(cov_matrix, np.ndarray):
+            return cov_matrix
+        else:
+            raise TypeError("cov_matrix is not a series, list or array")
+
+    def add_objective(self, new_objective, **kwargs):
+        """
+        Add a new term into the objective function. This term must be convex,
+        and built from cvxpy atomic functions.
+
+        Example:
+
+        def L1_norm(w, k=1):
+            return k * cp.norm(w, 1)
+
+        ef.add_objective(L1_norm, k=2)
+
+        :param new_objective: the objective to be added
+        :type new_objective: cp.Expression (i.e function of cp.Variable)
+        """
+        self._additional_objectives.append(new_objective(self._w, **kwargs))
+
+    def add_constraint(self, new_constraint):
+        """
+        Add a new constraint to the optimisation problem. This constraint must be linear and
+        must be either an equality or simple inequality.
+
+        Examples:
+
+        ef.add_constraint(lambda x : x[0] == 0.02)
+        ef.add_constraint(lambda x : x >= 0.01)
+        ef.add_constraint(lambda x: x <= np.array([0.01, 0.08, ..., 0.5]))
+
+        :param new_constraint: the constraint to be added
+        :type constraintfunc: lambda function
+        """
+        if not callable(new_constraint):
+            raise TypeError("New constraint must be provided as a lambda function")
+        self._constraints.append(new_constraint(self._w))
+
+    def convex_optimize(custom_objective, constraints):
+        pass
+
+    def nonconvex_optimize(custom_objective, constraints):
+        # opt using scip
+        # args = (self.cov_matrix, self.gamma)
+        # result = sco.minimize(
+        #     objective_functions.volatility,
+        #     x0=self.initial_guess,
+        #     args=args,
+        #     method=self.opt_method,
+        #     bounds=self.bounds,
+        #     constraints=self.constraints,
+        # )
+        # self.weights = result["x"]
+        pass
 
     def max_sharpe(self, risk_free_rate=0.02):
         """
         Maximise the Sharpe Ratio. The result is also referred to as the tangency portfolio,
-        as it is the tangent to the efficient frontier curve that intercepts the risk-free
-        rate.
+        as it is the portfolio for which the capital market line is tangent to the efficient frontier.
 
         :param risk_free_rate: risk-free rate of borrowing/lending, defaults to 0.02.
                                The period of the risk-free rate should correspond to the
@@ -125,16 +198,23 @@ class EfficientFrontier(base_optimizer.BaseScipyOptimizer):
         :return: asset weights for the volatility-minimising portfolio
         :rtype: dict
         """
-        args = (self.cov_matrix, self.gamma)
-        result = sco.minimize(
-            objective_functions.volatility,
-            x0=self.initial_guess,
-            args=args,
-            method=self.opt_method,
-            bounds=self.bounds,
-            constraints=self.constraints,
+        self._objective = objective_functions.portfolio_variance(
+            self._w, self.cov_matrix
         )
-        self.weights = result["x"]
+        for obj in self._additional_objectives:
+            self._objective += obj
+
+        self._constraints.append(cp.sum(self._w) == 1)
+
+        try:
+            opt = cp.Problem(cp.Minimize(self._objective), self._constraints)
+        except TypeError:
+            raise exceptions.OptimizationError
+
+        opt.solve()
+        if opt.status != "optimal":
+            raise exceptions.OptimizationError
+        self.weights = self._w.value.round(20)
         return dict(zip(self.tickers, self.weights))
 
     def max_unconstrained_utility(self, risk_aversion=1):
@@ -224,7 +304,7 @@ class EfficientFrontier(base_optimizer.BaseScipyOptimizer):
                     "Market neutrality requires shorting - bounds have been amended",
                     RuntimeWarning,
                 )
-                self.bounds = self._make_valid_bounds((-1, 1))
+                self.bounds = self._map_bounds_to_constraints((-1, 1))
             constraints = [
                 {"type": "eq", "fun": lambda x: np.sum(x)},
                 target_constraint,
@@ -283,7 +363,7 @@ class EfficientFrontier(base_optimizer.BaseScipyOptimizer):
                     "Market neutrality requires shorting - bounds have been amended",
                     RuntimeWarning,
                 )
-                self.bounds = self._make_valid_bounds((-1, 1))
+                self.bounds = self._map_bounds_to_constraints((-1, 1))
             constraints = [
                 {"type": "eq", "fun": lambda x: np.sum(x)},
                 target_constraint,

pypfopt/exceptions.py

@@ -12,7 +12,9 @@ class OptimizationError(Exception):
     """
 
     def __init__(self, *args, **kwargs):
-        default_message = "Please check your constraints or use a different solver."
+        default_message = (
+            "Please check your objectives/constraints or use a different solver."
+        )
 
         if not (args or kwargs):
             args = (default_message,)

pypfopt/objective_functions.py

@@ -19,7 +19,45 @@ Currently implemented:
 """
 
 import numpy as np
-import scipy.stats
+import cvxpy as cp
+import pandas as pd
+
+
+def _objective_value(w, obj):
+    """
+    Helper method to return either the value of the objective function
+    or the objective function as a cvxpy object depending on whether
+    w is a cvxpy variable or np array.
+
+    :param w: weights
+    :type w: np.ndarray OR cp.Variable
+    :param obj: objective function expression
+    :type obj: cp.Expression
+    :return: value of the objective function OR objective function expression
+    :rtype: float OR cp.Expression
+    """
+    if isinstance(w, np.ndarray):
+        if np.isscalar(obj.value):
+            return obj.value
+        else:
+            return obj.value.item()
+    else:
+        return obj
+
+
+def portfolio_variance(w, cov_matrix):
+    if isinstance(w, pd.Series):
+        w = w.values
+
+    variance = cp.quad_form(w, cov_matrix)
+    return _objective_value(w, variance)
+
+
+def L2_reg(w, gamma=1):
+    if isinstance(w, pd.Series):
+        w = w.values
+    L2_reg = gamma * cp.sum_squares(w)
+    return _objective_value(w, L2_reg)
 
 
 def negative_mean_return(weights, expected_returns):
@@ -107,32 +145,33 @@ def negative_quadratic_utility(
     return -(mu - 0.5 * risk_aversion * portfolio_volatility) + L2_reg
 
 
-def negative_cvar(weights, returns, s=10000, beta=0.95, random_state=None):
-    """
-    Calculate the negative CVaR. Though we want the "min CVaR portfolio", we
-    actually need to maximise the expected return of the worst q% cases, thus
-    we need this value to be negative.
+# def negative_cvar(weights, returns, s=10000, beta=0.95, random_state=None):
+#     """
+#     Calculate the negative CVaR. Though we want the "min CVaR portfolio", we
+#     actually need to maximise the expected return of the worst q% cases, thus
+#     we need this value to be negative.
 
-    :param weights: asset weights of the portfolio
-    :type weights: np.ndarray
-    :param returns: asset returns
-    :type returns: pd.DataFrame or np.ndarray
-    :param s: number of bootstrap draws, defaults to 10000
-    :type s: int, optional
-    :param beta: "significance level" (i. 1 - q), defaults to 0.95
-    :type beta: float, optional
-    :param random_state: seed for random sampling, defaults to None
-    :type random_state: int, optional
-    :return: negative CVaR
-    :rtype: float
-    """
-    np.random.seed(seed=random_state)
-    # Calcualte the returns given the weights
-    portfolio_returns = (weights * returns).sum(axis=1)
-    # Sample from the historical distribution
-    dist = scipy.stats.gaussian_kde(portfolio_returns)
-    sample = dist.resample(s)
-    # Calculate the value at risk
-    var = portfolio_returns.quantile(1 - beta)
-    # Mean of all losses worse than the value at risk
-    return -sample[sample < var].mean()
+#     :param weights: asset weights of the portfolio
+#     :type weights: np.ndarray
+#     :param returns: asset returns
+#     :type returns: pd.DataFrame or np.ndarray
+#     :param s: number of bootstrap draws, defaults to 10000
+#     :type s: int, optional
+#     :param beta: "significance level" (i. 1 - q), defaults to 0.95
+#     :type beta: float, optional
+#     :param random_state: seed for random sampling, defaults to None
+#     :type random_state: int, optional
+#     :return: negative CVaR
+#     :rtype: float
+#     """
+#     import scipy.stats
+#     np.random.seed(seed=random_state)
+#     # Calcualte the returns given the weights
+#     portfolio_returns = (weights * returns).sum(axis=1)
+#     # Sample from the historical distribution
+#     dist = scipy.stats.gaussian_kde(portfolio_returns)
+#     sample = dist.resample(s)
+#     # Calculate the value at risk
+#     var = portfolio_returns.quantile(1 - beta)
+#     # Mean of all losses worse than the value at risk
+#     return -sample[sample < var].mean()

tests/test_base_optimizer.py

@@ -2,7 +2,8 @@ import json
 import os
 import numpy as np
 import pytest
-from pypfopt.efficient_frontier import EfficientFrontier
+from pypfopt import EfficientFrontier
+from pypfopt import exceptions
 from tests.utilities_for_tests import get_data, setup_efficient_frontier
 
 
@@ -10,7 +11,7 @@ def test_custom_upper_bound():
     ef = EfficientFrontier(
         *setup_efficient_frontier(data_only=True), weight_bounds=(0, 0.10)
     )
-    ef.max_sharpe()
+    ef.min_volatility()
     ef.portfolio_performance()
     assert ef.weights.max() <= 0.1
     np.testing.assert_almost_equal(ef.weights.sum(), 1)
@@ -20,7 +21,7 @@ def test_custom_lower_bound():
     ef = EfficientFrontier(
         *setup_efficient_frontier(data_only=True), weight_bounds=(0.02, 1)
     )
-    ef.max_sharpe()
+    ef.min_volatility()
     assert ef.weights.min() >= 0.02
     np.testing.assert_almost_equal(ef.weights.sum(), 1)
 
@@ -29,18 +30,18 @@ def test_custom_bounds_same():
     ef = EfficientFrontier(
         *setup_efficient_frontier(data_only=True), weight_bounds=(0.03, 0.13)
     )
-    ef.max_sharpe()
+    ef.min_volatility()
     assert ef.weights.min() >= 0.03
     assert ef.weights.max() <= 0.13
     np.testing.assert_almost_equal(ef.weights.sum(), 1)
 
 
-def test_custom_bounds_different():
+def test_custom_bounds_different_values():
     bounds = [(0.01, 0.13), (0.02, 0.11)] * 10
     ef = EfficientFrontier(
         *setup_efficient_frontier(data_only=True), weight_bounds=bounds
     )
-    ef.max_sharpe()
+    ef.min_volatility()
     assert (0.01 <= ef.weights[::2]).all() and (ef.weights[::2] <= 0.13).all()
     assert (0.02 <= ef.weights[1::2]).all() and (ef.weights[1::2] <= 0.11).all()
     np.testing.assert_almost_equal(ef.weights.sum(), 1)
@@ -51,22 +52,49 @@ def test_custom_bounds_different():
     )
 
 
-def test_bounds_errors():
-    with pytest.raises(ValueError):
-        EfficientFrontier(
-            *setup_efficient_frontier(data_only=True), weight_bounds=(0.06, 1)
-        )
+def test_bound_input_types():
+    bounds = [0.01, 0.13]
+    ef = EfficientFrontier(
+        *setup_efficient_frontier(data_only=True), weight_bounds=bounds
+    )
+    lb = np.array([0.01, 0.02] * 10)
+    ub = np.array([0.07, 0.2] * 10)
+    assert EfficientFrontier(
+        *setup_efficient_frontier(data_only=True), weight_bounds=(lb, ub)
+    )
+    bounds = ((0.01, 0.13), (0.02, 0.11)) * 10
+    assert EfficientFrontier(
+        *setup_efficient_frontier(data_only=True), weight_bounds=bounds
+    )
 
+
+def test_bound_failure():
+    # Ensure optimisation fails when lower bound is too high or upper bound is too low
+    ef = EfficientFrontier(
+        *setup_efficient_frontier(data_only=True), weight_bounds=(0.06, 0.13)
+    )
+    with pytest.raises(exceptions.OptimizationError):
+        ef.min_volatility()
+
+    ef = EfficientFrontier(
+        *setup_efficient_frontier(data_only=True), weight_bounds=(0, 0.04)
+    )
+    with pytest.raises(exceptions.OptimizationError):
+        ef.min_volatility()
+
+
+def test_bounds_errors():
     assert EfficientFrontier(
         *setup_efficient_frontier(data_only=True), weight_bounds=(0, 1)
     )
 
-    with pytest.raises(ValueError):
+    with pytest.raises(TypeError):
         EfficientFrontier(
             *setup_efficient_frontier(data_only=True), weight_bounds=(0.06, 1, 3)
         )
 
-    with pytest.raises(ValueError):
+    with pytest.raises(TypeError):
+        # Not enough bounds
         bounds = [(0.01, 0.13), (0.02, 0.11)] * 5
         EfficientFrontier(
             *setup_efficient_frontier(data_only=True), weight_bounds=bounds
@@ -75,7 +103,7 @@ def test_bounds_errors():
 
 def test_clean_weights():
     ef = setup_efficient_frontier()
-    ef.max_sharpe()
+    ef.min_volatility()
     number_tiny_weights = sum(ef.weights < 1e-4)
     cleaned = ef.clean_weights(cutoff=1e-4, rounding=5)
     cleaned_weights = cleaned.values()
@@ -91,7 +119,7 @@ def test_clean_weights_short():
     ef = EfficientFrontier(
         *setup_efficient_frontier(data_only=True), weight_bounds=(-1, 1)
     )
-    ef.max_sharpe()
+    ef.min_volatility()
     # In practice we would never use such a high cutoff
     number_tiny_weights = sum(np.abs(ef.weights) < 0.05)
     cleaned = ef.clean_weights(cutoff=0.05)
@@ -104,7 +132,7 @@ def test_clean_weights_error():
     ef = setup_efficient_frontier()
     with pytest.raises(AttributeError):
         ef.clean_weights()
-    ef.max_sharpe()
+    ef.min_volatility()
     with pytest.raises(ValueError):
         ef.clean_weights(rounding=1.3)
     with pytest.raises(ValueError):
@@ -114,7 +142,7 @@ def test_clean_weights_error():
 
 def test_clean_weights_no_rounding():
     ef = setup_efficient_frontier()
-    ef.max_sharpe()
+    ef.min_volatility()
     # ensure the call does not fail
     # in previous commits, this call would raise a ValueError
     cleaned = ef.clean_weights(rounding=None, cutoff=0)
@@ -136,7 +164,7 @@ def test_efficient_frontier_init_errors():
 
 def test_set_weights():
     ef = setup_efficient_frontier()
-    w1 = ef.max_sharpe()
+    w1 = ef.min_volatility()
     test_weights = ef.weights
     ef.min_volatility()
     ef.set_weights(w1)
@@ -145,7 +173,7 @@ def test_set_weights():
 
 def test_save_weights_to_file():
     ef = setup_efficient_frontier()
-    ef.max_sharpe()
+    ef.min_volatility()
     ef.save_weights_to_file("tests/test.txt")
     with open("tests/test.txt", "r") as f:
         file = f.read()