Portfolio standard deviation
In order to calculate portfolio volatility, you will need the covariance matrix, the portfolio weights, and knowledge of the transpose operation. The transpose of a numpy array can be calculated using the .T attribute. The np.dot() function is the dot-product of two arrays.
The formula for portfolio volatility is:
$$ \sigma_{Portfolio} = \sqrt{ w_T \cdot \Sigma \cdot w } $$
- \( \sigma_{Portfolio} \): Portfolio volatility
- \( \Sigma \): Covariance matrix of returns
- w: Portfolio weights (\( w_T \) is transposed portfolio weights)
- \( \cdot \) The dot-multiplication operator
portfolio_weights and cov_mat_annual are available in your workspace.
Este ejercicio forma parte del curso
Introduction to Portfolio Risk Management in Python
Instrucciones de ejercicio
Calculate the portfolio volatility assuming you use the portfolio_weights by following the formula above.
Ejercicio interactivo práctico
Pruebe este ejercicio completando este código de muestra.
# Import numpy as np
import numpy as np
# Calculate the portfolio standard deviation
portfolio_volatility = ____(np.dot(portfolio_weights.T, np.dot(cov_mat_annual, portfolio_weights)))
print(portfolio_volatility)