Exercise

# CVaR and loss cover selection

In previous exercises you saw that both the **T** and the **Gaussian KDE** distributions fit portfolio losses for the crisis period fairly well. Given this, which of these is best for *risk management*? One way to choose is to select the distribution that provides the largest *loss cover*, to cover the "worst worst-case scenario" of losses.

The `t`

and `kde`

distributions are available and have been fit to 2007-2008 portfolio `losses`

(`t`

fitted parameters are in `p`

). You'll derive the one day 99% CVaR estimate for each distribution; the largest CVaR estimate is then the 'safest' **reserve amount** to hold, covering expected losses that exceed the 99% VaR.

The `kde`

instance has been given a special `.expect()`

method, *just for this exercise*, to compute the expected value needed for the CVaR.

Instructions

**100 XP**

- Find the 99% VaR using
`np.quantile()`

applied to random samples from the`t`

and`kde`

distributions. - Compute the integral required for the CVaR estimates using the
`.expect()`

method for each distribution. - Find and display the 99% CVaR estimates for both distributions.