Exercise

# 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.

Instructions

**100 XP**

Calculate the portfolio volatility assuming you use the `portfolio_weights`

by following the formula above.