# Efficient Frontier
This tutorial uses the [`MeanRisk`](https://skfolio.org/generated/skfolio.optimization.MeanRisk.html.md#skfolio.optimization.MeanRisk) optimization to find an
ensemble of portfolios belonging to the Mean-Variance efficient frontier (Pareto front).
## Data
We load the S&P 500 [dataset](https://skfolio.org/user_guide/datasets.html.md#datasets) composed of the daily prices of 20
assets from the S&P 500 Index composition starting from 1990-01-02 up to 2022-12-28:
```Python
import numpy as np
from plotly.io import show
from sklearn.model_selection import train_test_split
from skfolio import PerfMeasure, RatioMeasure, RiskMeasure
from skfolio.datasets import load_sp500_dataset
from skfolio.optimization import MeanRisk
from skfolio.preprocessing import prices_to_returns
prices = load_sp500_dataset()
X = prices_to_returns(prices)
X_train, X_test = train_test_split(X, test_size=0.33, shuffle=False)
```
## Model
We create the Mean-Variance model and then fit it on the training set.
The parameter `efficient_frontier_size=30` is used to find 30 portfolios on the entire
efficient frontier:
```Python
model = MeanRisk(
risk_measure=RiskMeasure.VARIANCE,
efficient_frontier_size=30,
portfolio_params=dict(name="Variance"),
)
model.fit(X_train)
print(model.weights_.shape)
```
```none
(30, 20)
```
## Prediction
We predict this model on both the training set and the test set.
The `predict` method returns the [`Population`](https://skfolio.org/generated/skfolio.population.Population.html.md#skfolio.population.Population) of
30 [`Portfolio`](https://skfolio.org/generated/skfolio.portfolio.Portfolio.html.md#skfolio.portfolio.Portfolio):
```Python
population_train = model.predict(X_train)
population_test = model.predict(X_test)
```
## Analysis
For improved analysis, we add a “Train” and “Test” tag to the portfolios and
concatenate the training and the test populations:
```Python
population_train.set_portfolio_params(tag="Train")
population_test.set_portfolio_params(tag="Test")
population = population_train + population_test
fig = population.plot_measures(
x=RiskMeasure.ANNUALIZED_STANDARD_DEVIATION,
y=PerfMeasure.ANNUALIZED_MEAN,
color_scale=RatioMeasure.ANNUALIZED_SHARPE_RATIO,
hover_measures=[RiskMeasure.MAX_DRAWDOWN, RatioMeasure.ANNUALIZED_SORTINO_RATIO],
)
show(fig)
```
[plotly figure stripped from llms output]
Let’s plot the composition of the 30 portfolios:
```Python
population_train.plot_composition()
```
[plotly figure stripped from llms output]
Let’s print the Sharpe Ratio of the 30 portfolios on the test set:
```Python
population_test.measures(measure=RatioMeasure.ANNUALIZED_SHARPE_RATIO)
```
```none
array([0.91785162, 0.93000375, 0.9401232 , 0.95027284, 0.96861483,
0.98463685, 0.9983657 , 1.00992555, 1.01943433, 1.02702131,
1.032813 , 1.03704654, 1.03993049, 1.04204356, 1.0430764 ,
1.04289017, 1.04158213, 1.03774863, 1.02943678, 1.02092595,
1.01241175, 1.00356473, 0.97964062, 0.93749217, 0.87986871,
0.78090544, 0.68550154, 0.59858003, 0.53398775, 0.55455742])
```
Finally, we can show a full summary of the 30 portfolios evaluated on the test set:
```Python
population.summary()
```
[plotly figure stripped from llms output]
**Total running time of the script:** (0 minutes 1.858 seconds)