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CVaR and risk exposure

Recall that CVaR is the expected value of loss given a minimum loss threshold. So CVaR is already in the form of a risk exposure--it is the sum (or integral) of the probability of loss in the distribution tail multiplied, by the loss amount.

To derive the 99% CVaR you'll first fit a T distribution to available crisis_losses portfolio data from 2008 - 2009, using the t.fit() method. This returns the T distribution parameters p used to find the VaR with the .ppf() method.

Next you'll compute the 99% VaR, since it's used to find the CVaR.

Finally you'll compute the 99% CVaR measure using the t.expect() method, which is the same method you used to compute CVaR for the Normal distribution in an earlier exercise.

The t distribution from scipy.stats is also available.

This exercise is part of the course

Quantitative Risk Management in Python

View Course

Exercise instructions

  • Find the distribution parameters p using the .fit() method applied to crisis_losses.
  • Compute VaR_99 using the fitted parameters p and the percent point function of t.
  • Compute CVaR_99 using the t.expect() method and the fitted parameters p, and display the result.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Fit the Student's t distribution to crisis losses
p = t.____(crisis_losses)

# Compute the VaR_99 for the fitted distribution
VaR_99 = t.____(____, *p)

# Use the fitted parameters and VaR_99 to compute CVaR_99
tail_loss = t.expect(____ y: y, args = (p[0],), loc = p[1], scale = p[2], lb = VaR_99 )
CVaR_99 = (1 / (1 - ____)) * tail_loss
print(CVaR_99)
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