Exercise

# Extreme values and backtesting

Extreme values are those which exceed a threshold and are used to determine if risk measures such as VaR are accurately reflecting the risk of loss.

You'll explore extreme values by computing the 95% VaR of the equally-weighted investment bank portfolio for 2009-2010 (recall that this is equivalent to historical simulation from 2010 onwards), and then ** backtesting** on data from 2007-2008.

2009-2010 portfolio losses are available in `estimate_data`

, from which you'll compute the 95% VaR estimate. Then find extreme values exceeding the VaR estimate, from the 2007-2008 portfolio losses in the available `backtest_data`

.

Compare the relative frequency of extreme values to the 95% VaR, and finally visualize the extreme values with a stem plot.

Instructions

**100 XP**

- Compute the 95% VaR on
`estimate_data`

using`np.quantile()`

. - Find the
`extreme_values`

from`backtest_data`

using`VaR_95`

as the loss threshold. - Compare the relative frequency of
`extreme_values`

to the`VaR_95`

estimate. Are they the same? - Display a stem plot of
`extreme_values`

, showing how large deviations clustered during the crisis.