# Risk Budgeting - CVaR
This tutorial uses the [`RiskBudgeting`](https://skfolio.org/generated/skfolio.optimization.RiskBudgeting.html.md#skfolio.optimization.RiskBudgeting) optimization to
build a risk budgeting portfolio by specifying a risk budget on each asset with CVaR 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)
```
## Risk Budget
We chose the following risk budget: 1.5 on Apple, 0.2 on General Electric and
JPMorgan and 1.0 on the remaining assets:
```Python
risk_budget = {asset_name: 1 for asset_name in X.columns}
risk_budget["AAPL"] = 1.5
risk_budget["GE"] = 0.2
risk_budget["JPM"] = 0.2
```
## Model
We create the risk budgeting model and then fit it on the training set:
```Python
model = RiskBudgeting(
risk_measure=RiskMeasure.CVAR,
risk_budget=risk_budget,
portfolio_params=dict(name="Risk Budgeting - CVaR"),
)
model.fit(X_train)
model.weights_
```
```none
array([0.06173048, 0.03257426, 0.03336027, 0.03994757, 0.06349066,
0.00930166, 0.04579232, 0.06880897, 0.00765321, 0.06700255,
0.05537176, 0.05430752, 0.0482822 , 0.07033578, 0.05371225,
0.0689283 , 0.04230919, 0.04897363, 0.06251636, 0.06560108])
```
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 budgeting model has 50% more CVaR contribution to Apple and 80%
less to General Electric and JPMorgan compared to the other assets:
```Python
ptf_model_train = model.predict(X_train)
fig = ptf_model_train.plot_contribution(measure=RiskMeasure.CVAR)
show(fig)
```
[plotly figure stripped from llms output]
And the inverse volatility model has different CVaR contribution for each asset:
```Python
ptf_bench_train = bench.predict(X_train)
ptf_bench_train.plot_contribution(measure=RiskMeasure.CVAR)
```
[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)
```
## Analysis
For improved analysis, it’s possible to 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 Budgeting - CVaR |
Inverse Vol |
| Mean |
0.067% |
0.064% |
| Annualized Mean |
17.00% |
16.06% |
| Variance |
0.00010 |
0.00010 |
| Annualized Variance |
2.57% |
2.56% |
| Semi-Variance |
0.000052 |
0.000053 |
| Annualized Semi-Variance |
1.32% |
1.33% |
| Standard Deviation |
1.01% |
1.01% |
| Annualized Standard Deviation |
16.02% |
16.00% |
| Semi-Deviation |
0.72% |
0.73% |
| Annualized Semi-Deviation |
11.50% |
11.54% |
| Mean Absolute Deviation |
0.65% |
0.65% |
| CVaR at 95% |
2.33% |
2.35% |
| EVaR at 95% |
5.12% |
5.29% |
| Worst Realization |
10.08% |
10.49% |
| CDaR at 95% |
12.03% |
12.22% |
| MAX Drawdown |
32.78% |
34.83% |
| Average Drawdown |
2.34% |
2.34% |
| EDaR at 95% |
18.98% |
20.05% |
| First Lower Partial Moment |
0.33% |
0.32% |
| Ulcer Index |
0.040 |
0.040 |
| Gini Mean Difference |
0.99% |
0.98% |
| Value at Risk at 95% |
1.43% |
1.45% |
| Drawdown at Risk at 95% |
8.81% |
8.79% |
| Entropic Risk Measure at 95% |
3.00 |
3.00 |
| Fourth Central Moment |
0.000021% |
0.000022% |
| Fourth Lower Partial Moment |
0.000010% |
0.000011% |
| Skew |
-2.47% |
-14.95% |
| Kurtosis |
2033.11% |
2118.56% |
| Sharpe Ratio |
0.067 |
0.063 |
| Annualized Sharpe Ratio |
1.06 |
1.00 |
| Sortino Ratio |
0.093 |
0.088 |
| Annualized Sortino Ratio |
1.48 |
1.39 |
| Mean Absolute Deviation Ratio |
0.10 |
0.098 |
| First Lower Partial Moment Ratio |
0.21 |
0.20 |
| Value at Risk Ratio at 95% |
0.047 |
0.044 |
| CVaR Ratio at 95% |
0.029 |
0.027 |
| Entropic Risk Measure Ratio at 95% |
0.00023 |
0.00021 |
| EVaR Ratio at 95% |
0.013 |
0.012 |
| Worst Realization Ratio |
0.0067 |
0.0061 |
| Drawdown at Risk Ratio at 95% |
0.0077 |
0.0073 |
| CDaR Ratio at 95% |
0.0056 |
0.0052 |
| Calmar Ratio |
0.0021 |
0.0018 |
| Average Drawdown Ratio |
0.029 |
0.027 |
| EDaR Ratio at 95% |
0.0036 |
0.0032 |
| Ulcer Index Ratio |
0.017 |
0.016 |
| Gini Mean Difference Ratio |
0.068 |
0.065 |
| Effective Number of Assets |
17.7281118539998 |
18.460872007821077 |
| Assets Number |
20 |
20 |
**Total running time of the script:** (0 minutes 1.901 seconds)