Note
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Online Evaluation of Portfolio Optimization#
This tutorial shows how to tune a MeanRisk estimator with
online search and evaluate it out-of-sample with an online walk-forward procedure.
Unlike the previous tutorial, which tuned the covariance estimator in isolation, here we optimize the portfolio model end-to-end using a portfolio-level metric.
The online approach is equivalent to combining scikit-learn’s
GridSearchCV with
WalkForward using expand_train=True, but instead of
refitting every candidate from scratch at each split, it calls partial_fit to
incrementally update each estimator. This is significantly faster for estimators that
support this method.
Data#
We load the S&P 500 dataset composed of the daily prices of 20 assets from the S&P 500 Index composition starting from 2010-01-04 up to 2022-12-28.
import numpy as np
from plotly.io import show
from skfolio import Population
from skfolio.datasets import load_sp500_dataset
from skfolio.model_selection import OnlineGridSearch, online_predict
from skfolio.moments import EWMu, RegimeAdjustedEWCovariance
from skfolio.optimization import MeanRisk, ObjectiveFunction
from skfolio.preprocessing import prices_to_returns
from skfolio.prior import EmpiricalPrior
prices = load_sp500_dataset()
X = prices_to_returns(prices)
X = X["2010":]
Baseline Portfolio Model#
We start with a simple Minimum Variance optimization via
MeanRisk. All sub-estimators support partial_fit, so
the entire pipeline can be updated incrementally during walk-forward evaluation.
baseline_model = MeanRisk(
prior_estimator=EmpiricalPrior(
mu_estimator=EWMu(half_life=40),
covariance_estimator=RegimeAdjustedEWCovariance(
half_life=40,
corr_half_life=80,
regime_half_life=20,
),
),
)
Online Portfolio Search#
We search directly over the portfolio estimator using a portfolio-level metric. For
portfolio optimization estimators, OnlineGridSearch
defaults to the Sharpe ratio when scoring=None.
We tune both the optimization objective and a few covariance hyperparameters. The double-underscore syntax reaches into nested sub-estimators, just like in scikit-learn model selection.
Here, warmup_size=252 reserves the first year of observations for initialization and
test_size=5 evaluates windows of 5 consecutive daily observations (one trading week).
portfolio_search = OnlineGridSearch(
estimator=baseline_model,
param_grid={
"objective_function": [
ObjectiveFunction.MINIMIZE_RISK,
ObjectiveFunction.MAXIMIZE_RATIO,
],
"prior_estimator__covariance_estimator__half_life": [20, 40, 60],
"prior_estimator__covariance_estimator__corr_half_life": [40, 80],
},
warmup_size=252,
test_size=5,
n_jobs=-1,
return_predictions=True,
)
portfolio_search.fit(X)
print(f"Best params: {portfolio_search.best_params_}")
print(
f"Best score (Annualized Sharpe): {np.sqrt(252) * portfolio_search.best_score_:.6f}"
)
Best params: {'objective_function': MINIMIZE_RISK, 'prior_estimator__covariance_estimator__corr_half_life': 40, 'prior_estimator__covariance_estimator__half_life': 60}
Best score (Annualized Sharpe): 0.966177
Online Evaluation#
online_predict walks forward through the data,
updates the estimator via partial_fit at each step, and predicts on the next test
window. The result is a MultiPeriodPortfolio.
baseline_prediction = online_predict(
baseline_model,
X,
warmup_size=252,
test_size=5,
portfolio_params=dict(name="Baseline"),
)
The tuned model’s walk-forward prediction can be obtained in two ways.
The first calls the same function on the tuned estimator:
tuned_prediction = online_predict(
portfolio_search.best_estimator_,
X,
warmup_size=252,
test_size=5,
portfolio_params=dict(name="Tuned"),
)
The second, used below, reads the prediction that the search already retained through
return_predictions=True. Both return the same portfolio here, because the search
evaluated its candidates on the same data with the same warmup_size and test_size,
so reading it back avoids a second walk-forward pass. Call online_predict to
evaluate on different data or with different window sizes.
tuned_prediction = portfolio_search.cv_results_["predictions"][
portfolio_search.best_index_
]
tuned_prediction.name = "Tuned"
Portfolio Comparison#
We collect both portfolio evaluations into a Population
for side-by-side comparison.
population = Population([baseline_prediction, tuned_prediction])
population.summary()
fig = population.plot_cumulative_returns()
show(fig)
Online Score#
online_score runs the same walk-forward evaluation
and returns a scalar score. This is useful when the prediction path is not needed:
from skfolio.measures import RatioMeasure
from skfolio.model_selection import online_score
baseline_score = online_score(
baseline_model,
X,
warmup_size=252,
test_size=5,
scoring=RatioMeasure.ANNUALIZED_SHARPE_RATIO,
)
tuned_score = online_score(
portfolio_search.best_estimator_,
X,
warmup_size=252,
test_size=5,
scoring=RatioMeasure.ANNUALIZED_SHARPE_RATIO,
)
Both prediction paths are already available here, so the scores are read from them below rather than running two additional walk-forward passes:
baseline_score = baseline_prediction.annualized_sharpe_ratio
tuned_score = tuned_prediction.annualized_sharpe_ratio
print(f"Baseline Sharpe: {baseline_score:.4f}")
print(f"Tuned Sharpe: {tuned_score:.4f}")
Baseline Sharpe: 0.9365
Tuned Sharpe: 0.9662
Conclusion#
This tutorial demonstrated the portfolio-level online workflow:
Define an incremental
MeanRiskestimator whose sub-estimators all supportpartial_fit.Tune it with
OnlineGridSearchusing a portfolio-level metric.Evaluate the tuned estimator out-of-sample with
online_predictand visualize the results withPopulation.Summarize the walk-forward performance as a scalar with
online_score.
This complements the previous tutorial: covariance tuning improves the statistical forecast, while direct portfolio search optimizes the full allocation problem end-to-end.
Total running time of the script: (1 minutes 10.591 seconds)
