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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.