Exercise

# VaR for the Normal distribution

To get accustomed to the **Value at Risk** (VaR) measure, it helps to apply it to a known distribution. The **Normal** (or *Gaussian*) distribution is especially appealing as it 1) has an analytically simple form, and 2) represents a wide variety of empirical phenomena. For this exercise you'll assume that the **loss** of a portfolio is normally distributed, i.e., the higher the value drawn from the distribution, the higher the loss.

You'll learn how to apply both `scipy.stats.norm`

's `ppf()`

(percent point function) and `numpy`

's `quantile()`

function to find the VaR at the 95% and 99% confidence levels, respectively, for a standard Normal distribution. You'll also visualize the VaR as a threshold on a Normal distribution plot.

Instructions

**100 XP**

- Use
`norm`

's`.ppf()`

percent point function to find the VaR measure at the 95% confidence level. - Now find the 99% VaR measure using Numpy's
`quantile()`

function applied to 100,000 random Normal`draws`

. - Compare the 95% and 99% VaR measures using a
`print`

statement. - Plot the Normal distribution, and add a line indicating the 95% VaR.