skfolio.optimization
.MaximumDiversification#
- class skfolio.optimization.MaximumDiversification(prior_estimator=None, min_weights=0.0, max_weights=1.0, budget=1.0, min_budget=None, max_budget=None, max_short=None, max_long=None, transaction_costs=0.0, management_fees=0.0, previous_weights=None, groups=None, linear_constraints=None, left_inequality=None, right_inequality=None, l1_coef=0.0, l2_coef=0.0, risk_free_rate=0.0, min_return=None, max_tracking_error=None, max_turnover=None, solver='CLARABEL', solver_params=None, scale_objective=None, scale_constraints=None, save_problem=False, raise_on_failure=True, add_objective=None, add_constraints=None, portfolio_params=None)[source]#
Maximum Diversification Optimization estimator.
Maximizes the diversification ratio which is the ratio of the weighted volatilities over the total volatility.
It is a special case of the
MeanRisk
estimator where the expected return from the objective function is replaced by the weighted volatilities.- Parameters:
- prior_estimatorBasePrior, optional
Prior estimator. The prior estimator is used to estimate the
PriorModel
containing the estimation of assets expected returns, covariance matrix, returns and Cholesky decomposition of the covariance. The default (None
) is to useEmpiricalPrior
.- min_weightsfloat | dict[str, float] | array-like of shape (n_assets, ) | None, default=0.0
Minimum assets weights (weights lower bounds). If a float is provided, it is applied to each asset.
None
is equivalent to-np.Inf
(no lower bound). If a dictionary is provided, its (key/value) pair must be the (asset name/asset minium weight) and the inputX
of thefit
method must be a DataFrame with the assets names in columns. When using a dictionary, assets values that are not provided are assigned a minimum weight of0.0
. The default value is0.0
(no short selling).Example:
min_weights = 0
–> long only portfolio (no short selling).min_weights = None
–> no lower bound (same as-np.Inf
).min_weights = -2
–> each weight must be above -200%.min_weights = {"SX5E": 0, "SPX": -2}
min_weights = [0, -2]
- max_weightsfloat | dict[str, float] | array-like of shape (n_assets, ) | None, default=1.0
Maximum assets weights (weights upper bounds). If a float is provided, it is applied to each asset.
None
is equivalent to+np.Inf
(no upper bound). If a dictionary is provided, its (key/value) pair must be the (asset name/asset maximum weight) and the inputX
of thefit
method must be a DataFrame with the assets names in columns. When using a dictionary, assets values that are not provided are assigned a minimum weight of1.0
. The default value is1.0
(each asset is below 100%).Example:
max_weights = 0
–> no long position (short only portfolio).max_weights = None
–> no upper bound.max_weights = 2
–> each weight must be below 200%.max_weights = {"SX5E": 1, "SPX": 2}
max_weights = [1, 2]
- budgetfloat | None, default=1.0
Investment budget. It is the sum of long positions and short positions (sum of all weights).
None
means no budget constraints. The default value is1.0
(fully invested portfolio).Examples:
budget = 1
–> fully invested portfolio.budget = 0
–> market neutral portfolio.budget = None
–> no constraints on the sum of weights.
- min_budgetfloat, optional
Minimum budget. It is the lower bound of the sum of long and short positions (sum of all weights). If provided, you must set
budget=None
. The default (None
) means no minimum budget constraint.- max_budgetfloat, optional
Maximum budget. It is the upper bound of the sum of long and short positions (sum of all weights). If provided, you must set
budget=None
. The default (None
) means no maximum budget constraint.- max_shortfloat, optional
Maximum short position. The short position is defined as the sum of negative weights (in absolute term). The default (
None
) means no maximum short position.- max_longfloat, optional
Maximum long position. The long position is defined as the sum of positive weights. The default (
None
) means no maximum long position.- transaction_costsfloat | dict[str, float] | array-like of shape (n_assets, ), default=0.0
Transaction costs of the assets. It is used to add linear transaction costs to the optimization problem:
\[total\_cost = \sum_{i=1}^{N} c_{i} \times |w_{i} - w\_prev_{i}|\]with \(c_{i}\) the transaction cost of asset i, \(w_{i}\) its weight and \(w\_prev_{i}\) its previous weight (defined in
previous_weights
). The float \(total\_cost\) is impacting the portfolio expected return in the optimization:\[expected\_return = \mu^{T} \cdot w - total\_cost\]with \(\mu\) the vector af assets’ expected returns and \(w\) the vector of assets weights.
If a float is provided, it is applied to each asset. If a dictionary is provided, its (key/value) pair must be the (asset name/asset cost) and the input
X
of thefit
method must be a DataFrame with the assets names in columns. The default value is0.0
.Warning
Based on the above formula, the periodicity of the transaction costs needs to be homogenous to the periodicity of \(\mu\). For example, if the input
X
is composed of daily returns, thetransaction_costs
need to be expressed as daily costs. (See Transaction Costs)- management_feesfloat | dict[str, float] | array-like of shape (n_assets, ), default=0.0
Management fees of the assets. It is used to add linear management fees to the optimization problem:
\[total\_fee = \sum_{i=1}^{N} f_{i} \times w_{i}\]with \(f_{i}\) the management fee of asset i and \(w_{i}\) its weight. The float \(total\_fee\) is impacting the portfolio expected return in the optimization:
\[expected\_return = \mu^{T} \cdot w - total\_fee\]with \(\mu\) the vector af assets expected returns and \(w\) the vector of assets weights.
If a float is provided, it is applied to each asset. If a dictionary is provided, its (key/value) pair must be the (asset name/asset fee) and the input
X
of thefit
method must be a DataFrame with the assets names in columns. The default value is0.0
.Warning
Based on the above formula, the periodicity of the management fees needs to be homogenous to the periodicity of \(\mu\). For example, if the input
X
is composed of daily returns, themanagement_fees
need to be expressed in daily fees.Note
Another approach is to directly impact the management fees to the input
X
in order to express the returns net of fees. However, when estimating the \(\mu\) parameter using for example Shrinkage estimators, this approach would mix a deterministic value with an uncertain one leading to unwanted bias in the management fees.- previous_weightsfloat | dict[str, float] | array-like of shape (n_assets, ), optional
Previous weights of the assets. Previous weights are used to compute the portfolio cost and the portfolio turnover. If a float is provided, it is applied to each asset. If a dictionary is provided, its (key/value) pair must be the (asset name/asset previous weight) and the input
X
of thefit
method must be a DataFrame with the assets names in columns. The default (None
) means no previous weights.- l1_coeffloat, default=0.0
L1 regularization coefficient. It is used to penalize the objective function by the L1 norm:
\[l1\_coef \times \Vert w \Vert_{1} = l1\_coef \times \sum_{i=1}^{N} |w_{i}|\]Increasing this coefficient will reduce the number of non-zero weights (cardinality). It tends to increase robustness (out-of-sample stability) but reduces diversification. The default value is
0.0
.- l2_coeffloat, default=0.0
L2 regularization coefficient. It is used to penalize the objective function by the L2 norm:
\[l2\_coef \times \Vert w \Vert_{2}^{2} = l2\_coef \times \sum_{i=1}^{N} w_{i}^2\]It tends to increase robustness (out-of-sample stability). The default value is
0.0
.- linear_constraintsarray-like of shape (n_constraints,), optional
Linear constraints. The linear constraints must match any of following patterns:
“2.5 * ref1 + 0.10 * ref2 + 0.0013 <= 2.5 * ref3”
“ref1 >= 2.9 * ref2”
“ref1 <= ref2”
“ref1 >= ref1”
With “ref1”, “ref2” … the assets names or the groups names provided in the parameter
groups
. Assets names can be referenced without the need ofgroups
if the inputX
of thefit
method is a DataFrame with these assets names in columns.Examples:
“SPX >= 0.10” –> SPX weight must be greater than 10% (note that you can also use
min_weights
)“SX5E + TLT >= 0.2” –> the sum of SX5E and TLT weights must be greater than 20%
“US >= 0.7” –> the sum of all US weights must be greater than 70%
“Equity <= 3 * Bond” –> the sum of all Equity weights must be less or equal to 3 times the sum of all Bond weights.
“2*SPX + 3*Europe <= Bond + 0.05” –> mixing assets and group constraints
- groupsdict[str, list[str]] or array-like of shape (n_groups, n_assets), optional
The assets groups referenced in
linear_constraints
. If a dictionary is provided, its (key/value) pair must be the (asset name/asset groups) and the inputX
of thefit
method must be a DataFrame with the assets names in columns.Examples:
groups = {“SX5E”: [“Equity”, “Europe”], “SPX”: [“Equity”, “US”], “TLT”: [“Bond”, “US”]}
groups = [[“Equity”, “Equity”, “Bond”], [“Europe”, “US”, “US”]]
- left_inequalityarray-like of shape (n_constraints, n_assets), optional
Left inequality matrix \(A\) of the linear constraint \(A \cdot w \leq b\).
- right_inequalityarray-like of shape (n_constraints, ), optional
Right inequality vector \(b\) of the linear constraint \(A \cdot w \leq b\).
- risk_free_ratefloat, default=0.0
Risk-free interest rate. The default value is
0.0
.- max_tracking_errorfloat, optional
Upper bound constraint on the tracking error. The tracking error is defined as the RMSE (root-mean-square error) of the portfolio returns compared to a target returns. If
max_tracking_error
is provided, the target returnsy
must be provided in thefit
method.- max_turnoverfloat, optional
Upper bound constraint of the turnover. The turnover is defined as the absolute difference between the portfolio weights and the
previous_weights
. Note that another way to control for turnover is by using thetransaction_costs
parameter.- min_returnfloat | array-like of shape (n_optimization), optional
Lower bound constraint on the expected return.
- min_returnfloat | array-like of shape (n_optimization), optional
Lower bound constraint on the expected return.
- add_objectiveCallable[[cp.Variable], cp.Expression], optional
Add a custom objective to the existing objective expression. It is a function that must take as argument the weights
w
and returns a CVXPY expression.- add_constraintsCallable[[cp.Variable], cp.Expression|list[cp.Expression]], optional
Add a custom constraint or a list of constraints to the existing constraints. It is a function that must take as argument the weights
w
and returns a CVPXY expression or a list of CVPXY expressions.- solverstr, default=”CLARABEL”
The solver to use. The default is “CLARABEL” which is written in Rust and has better numerical stability and performance than ECOS and SCS. Cvxpy will replace its default solver “ECOS” by “CLARABEL” in future releases. For more details about available solvers, check the CVXPY documentation: https://www.cvxpy.org/tutorial/advanced/index.html#choosing-a-solver
- solver_paramsdict, optional
Solver parameters. For example,
solver_params=dict(verbose=True)
. The default (None
) is use{"tol_gap_abs": 1e-9, "tol_gap_rel": 1e-9}
for the solver “CLARABEL” and the CVXPY default otherwise. For more details about solver arguments, check the CVXPY documentation: https://www.cvxpy.org/tutorial/advanced/index.html#setting-solver-options- scale_objectivefloat, optional
Scale each objective element by this value. It can be used to increase the optimization accuracies in specific cases. The default (
None
) is set depending on the problem.- scale_constraintsfloat, optional
Scale each constraint element by this value. It can be used to increase the optimization accuracies in specific cases. The default (
None
) is set depending on the problem.- save_problembool, default=False
If this is set to True, the CVXPY Problem is saved in
problem_
. The default isFalse
.- raise_on_failurebool, default=True
If this is set to True, an error is raised when the optimization fail otherwise it passes with a warning.
- portfolio_paramsdict, optional
Portfolio parameters passed to the portfolio evaluated by the
predict
andscore
methods. If not provided, thename
,transaction_costs
,management_fees
,previous_weights
andrisk_free_rate
are copied from the optimization model and passed to the portfolio.
- Attributes:
- weights_ndarray of shape (n_assets,) or (n_optimizations, n_assets)
Weights of the assets.
- problem_values_dict[str, float] | list[dict[str, float]] of size n_optimizations
Expression values retrieved from the CVXPY problem.
- prior_estimator_BasePrior
Fitted
prior_estimator
.- problem_: cvxpy.Problem
CVXPY problem used for the optimization. Only when
save_problem
is set toTrue
.- n_features_in_int
Number of assets seen during
fit
.- feature_names_in_ndarray of shape (
n_features_in_
,) Names of assets seen during
fit
. Defined only whenX
has assets names that are all strings.
Methods
fit
(X[, y])Fit the Maximum Diversification Optimization estimator.
fit_predict
(X)Perform
fit
onX
and returns the predictedPortfolio
orPopulation
ofPortfolio
onX
based on the fittedweights
.Get metadata routing of this object.
get_params
([deep])Get parameters for this estimator.
predict
(X)Predict the
Portfolio
orPopulation
ofPortfolio
onX
based on the fitted weights.score
(X[, y])Prediction score.
set_params
(**params)Set the parameters of this estimator.
- fit(X, y=None, **fit_params)[source]#
Fit the Maximum Diversification Optimization estimator.
- Parameters:
- Xarray-like of shape (n_observations, n_assets)
Price returns of the assets.
- yarray-like of shape (n_observations, n_targets), optional
Price returns of factors or a target benchmark. The default is
None
.- **fit_paramsdict
Parameters to pass to the underlying estimators. Only available if
enable_metadata_routing=True
, which can be set by usingsklearn.set_config(enable_metadata_routing=True)
. See Metadata Routing User Guide for more details.
- Returns:
- selfMaximumDiversification
Fitted estimator.
- fit_predict(X)#
Perform
fit
onX
and returns the predictedPortfolio
orPopulation
ofPortfolio
onX
based on the fittedweights
. For factor models, usefit(X, y)
thenpredict(X)
separately.- Parameters:
- Xarray-like of shape (n_observations, n_assets)
Price returns of the assets.
- Returns:
- predictionPortfolio | Population
Portfolio
orPopulation
ofPortfolio
estimated onX
based on the fittedweights
.
- get_metadata_routing()#
Get metadata routing of this object.
Please check User Guide on how the routing mechanism works.
- Returns:
- routingMetadataRequest
A
MetadataRequest
encapsulating routing information.
- get_params(deep=True)#
Get parameters for this estimator.
- Parameters:
- deepbool, default=True
If True, will return the parameters for this estimator and contained subobjects that are estimators.
- Returns:
- paramsdict
Parameter names mapped to their values.
- predict(X)#
Predict the
Portfolio
orPopulation
ofPortfolio
onX
based on the fitted weights.Optimization estimators can return a 1D or a 2D array of
weights
. For a 1D array, the prediction returns aPortfolio
. For a 2D array, the prediction returns aPopulation
ofPortfolio
.If
name
is not provided in the portfolio arguments, we use the first 500 characters of the estimator name.- Parameters:
- Xarray-like of shape (n_observations, n_assets)
Price returns of the assets.
- Returns:
- predictionPortfolio | Population
Portfolio
orPopulation
ofPortfolio
estimated onX
based on the fittedweights
.
- score(X, y=None)#
Prediction score. If the prediction is a single
Portfolio
, the score is the Sharpe Ratio. If the prediction is aPopulation
ofPortfolio
, the score is the mean of all the portfolios Sharpe Ratios in the population.- Parameters:
- Xarray-like of shape (n_observations, n_assets)
Price returns of the assets.
- yIgnored
Not used, present here for API consistency by convention.
- Returns:
- scorefloat
The Sharpe Ratio of the portfolio if the prediction is a single
Portfolio
or the mean of all the portfolios Sharpe Ratios if the prediction is aPopulation
ofPortfolio
.
- set_params(**params)#
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as
Pipeline
). The latter have parameters of the form<component>__<parameter>
so that it’s possible to update each component of a nested object.- Parameters:
- **paramsdict
Estimator parameters.
- Returns:
- selfestimator instance
Estimator instance.