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.
This is a part of the course
“Introduction to Portfolio Risk Management in Python”
Exercise instructions
Calculate the portfolio volatility assuming you use the portfolio_weights by following the formula above.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# 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)