# Risk Parity - Variance
This tutorial uses the [`RiskBudgeting`](https://skfolio.org/generated/skfolio.optimization.RiskBudgeting.html.md#skfolio.optimization.RiskBudgeting) optimization to
find the risk parity portfolio with variance as the risk measure.
## 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
from plotly.io import show
from sklearn.model_selection import train_test_split
from skfolio import Population, RiskMeasure
from skfolio.datasets import load_sp500_dataset
from skfolio.optimization import InverseVolatility, RiskBudgeting
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 risk parity model and then fit it on the training set:
```Python
model = RiskBudgeting(
risk_measure=RiskMeasure.VARIANCE,
portfolio_params=dict(name="Risk Parity - Variance"),
)
model.fit(X_train)
model.weights_
```
```none
array([0.04135318, 0.03210824, 0.0337272 , 0.03785076, 0.06105329,
0.04432756, 0.04252214, 0.06593567, 0.03451845, 0.06469326,
0.05418886, 0.05209518, 0.04535298, 0.0656811 , 0.0510388 ,
0.06894497, 0.04046537, 0.04667777, 0.05626949, 0.06119573])
```
To compare this model, we use an inverse volatility benchmark using
the [`InverseVolatility`](https://skfolio.org/generated/skfolio.optimization.InverseVolatility.html.md#skfolio.optimization.InverseVolatility) estimator.
```Python
bench = InverseVolatility(portfolio_params=dict(name="Inverse Vol"))
bench.fit(X_train)
bench.weights_
```
```none
array([0.03306735, 0.02548697, 0.03551377, 0.0296872 , 0.06358463,
0.05434705, 0.04742354, 0.07049715, 0.03882539, 0.06697905,
0.05570808, 0.05576851, 0.04723274, 0.06351213, 0.05581397,
0.0676481 , 0.02564642, 0.03970752, 0.05744543, 0.06610498])
```
## Risk Contribution Analysis
Let’s analyze the risk contribution of both models on the training set.
As expected, the risk parity model has the same variance contribution for each asset:
```Python
ptf_model_train = model.predict(X_train)
ptf_model_train.plot_contribution(measure=RiskMeasure.ANNUALIZED_VARIANCE)
```
[plotly figure stripped from llms output]
And the inverse volatility model has non-equal variance contribution. This is because
the correlation is not taken into account in an inverse volatility model:
```Python
ptf_bench_train = bench.predict(X_train)
ptf_bench_train.plot_contribution(measure=RiskMeasure.ANNUALIZED_VARIANCE)
```
[plotly figure stripped from llms output]
## Prediction
We predict the model and the benchmark on the test set:
```Python
ptf_model_test = model.predict(X_test)
ptf_bench_test = bench.predict(X_test)
```
The `predict` method returns a [`Portfolio`](https://skfolio.org/generated/skfolio.portfolio.Portfolio.html.md#skfolio.portfolio.Portfolio) object.
## Analysis
For improved analysis, we load both predicted portfolios into a
[`Population`](https://skfolio.org/generated/skfolio.population.Population.html.md#skfolio.population.Population):
```Python
population = Population([ptf_model_test, ptf_bench_test])
```
Let’s plot each portfolio composition:
```Python
population.plot_composition()
```
[plotly figure stripped from llms output]
Let’s plot each portfolio cumulative returns:
```Python
fig = population.plot_cumulative_returns()
show(fig)
```
[plotly figure stripped from llms output]
Finally, we print a full summary of both strategies evaluated on the test set:
```Python
population.summary()
```
|
Risk Parity - Variance |
Inverse Vol |
| Mean |
0.065% |
0.064% |
| Annualized Mean |
16.40% |
16.06% |
| Variance |
0.00010 |
0.00010 |
| Annualized Variance |
2.63% |
2.56% |
| Semi-Variance |
0.000054 |
0.000053 |
| Annualized Semi-Variance |
1.36% |
1.33% |
| Standard Deviation |
1.02% |
1.01% |
| Annualized Standard Deviation |
16.22% |
16.00% |
| Semi-Deviation |
0.73% |
0.73% |
| Annualized Semi-Deviation |
11.66% |
11.54% |
| Mean Absolute Deviation |
0.66% |
0.65% |
| CVaR at 95% |
2.37% |
2.35% |
| EVaR at 95% |
5.23% |
5.29% |
| Worst Realization |
10.34% |
10.49% |
| CDaR at 95% |
12.39% |
12.22% |
| MAX Drawdown |
34.30% |
34.83% |
| Average Drawdown |
2.40% |
2.34% |
| EDaR at 95% |
19.86% |
20.05% |
| First Lower Partial Moment |
0.33% |
0.32% |
| Ulcer Index |
0.041 |
0.040 |
| Gini Mean Difference |
1.00% |
0.98% |
| Value at Risk at 95% |
1.46% |
1.45% |
| Drawdown at Risk at 95% |
8.97% |
8.79% |
| Entropic Risk Measure at 95% |
3.00 |
3.00 |
| Fourth Central Moment |
0.000023% |
0.000022% |
| Fourth Lower Partial Moment |
0.000011% |
0.000011% |
| Skew |
-5.68% |
-14.95% |
| Kurtosis |
2067.02% |
2118.56% |
| Sharpe Ratio |
0.064 |
0.063 |
| Annualized Sharpe Ratio |
1.01 |
1.00 |
| Sortino Ratio |
0.089 |
0.088 |
| Annualized Sortino Ratio |
1.41 |
1.39 |
| Mean Absolute Deviation Ratio |
0.098 |
0.098 |
| First Lower Partial Moment Ratio |
0.20 |
0.20 |
| Value at Risk Ratio at 95% |
0.045 |
0.044 |
| CVaR Ratio at 95% |
0.027 |
0.027 |
| Entropic Risk Measure Ratio at 95% |
0.00022 |
0.00021 |
| EVaR Ratio at 95% |
0.012 |
0.012 |
| Worst Realization Ratio |
0.0063 |
0.0061 |
| Drawdown at Risk Ratio at 95% |
0.0073 |
0.0073 |
| CDaR Ratio at 95% |
0.0053 |
0.0052 |
| Calmar Ratio |
0.0019 |
0.0018 |
| Average Drawdown Ratio |
0.027 |
0.027 |
| EDaR Ratio at 95% |
0.0033 |
0.0032 |
| Ulcer Index Ratio |
0.016 |
0.016 |
| Gini Mean Difference Ratio |
0.065 |
0.065 |
| Effective Number of Assets |
18.9958444521665 |
18.460872007821077 |
| Assets Number |
20 |
20 |
**Total running time of the script:** (0 minutes 1.628 seconds)