Exercise

# Comparing CVaR and VaR

The **conditional value at risk** (CVaR), or expected shortfall (ES), asks what the average loss will be, *conditional* upon losses exceeding some threshold at a certain confidence level. It uses VaR as a point of departure, but contains more information because it takes into consideration the **tail** of the loss distribution.

You'll first compute the 95% VaR for a Normal distribution of portfolio losses, with the same mean and standard deviation as the 2005-2010 investment bank `portfolio_losses`

. You'll then use the VaR to compute the 95% CVaR, and plot both against the Normal distribution.

The `portfolio_losses`

are available in your workspace, as well as the `norm`

Normal distribution from `scipy.stats`

.

Instructions

**100 XP**

- Compute the mean and standard deviation of
`portfolio_returns`

and assign them to`pm`

and`ps`

, respectively. - Find the 95% VaR using
`norm`

's`.ppf() method`

--this takes arguments`loc`

for the mean and`scale`

for the standard deviation. - Use the 95% VaR and
`norm`

's`.expect()`

method to find the`tail_loss`

, and use it to compute the CVaR at the same level of confidence. - Add vertical lines showing the VaR (in red) and the CVaR (in green) to a histogram plot of the Normal distribution.