VaR from a fitted distribution
Minimizing CVaR requires calculating the VaR at a confidence level, say 95%. Previously you derived the VaR as a quantile from a Normal (or Gaussian) distribution, but minimizing the CVaR more generally requires computing the quantile from a distribution that best fits the data.
In this exercise a fitted
loss distribution is provided, which fits losses from an equal-weighted investment bank portfolio from 2005-2010. You'll first plot this distribution using its .evaluate()
method (fitted distributions will be covered in more detail in Chapter 4).
Next you'll use the .resample()
method of the fitted
object to draw a random sample
of 100,000 observations from the fitted distribution.
Finally, using np.quantile()
on the random sample
will then compute the 95% VaR.
This exercise is part of the course
Quantitative Risk Management in Python
Exercise instructions
- Plot the
fitted
loss distribution. Notice how thefitted
distribution is different from a Normal distribution. - Create a 100,000 point
sample
of random draws from the fitted distribution usingfitted
's.resample()
method. - Use
np.quantile()
to find the 95% VaR from the randomsample
, and display the result.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Visualize the fitted distribution with a plot
x = np.linspace(-0.25,0.25,1000)
plt.____(x,fitted.evaluate(x))
plt.show()
# Create a random sample of 100,000 observations from the fitted distribution
sample = fitted.____(____)
# Compute and display the 95% VaR from the random sample
VaR_95 = np.____(sample, ____)
print(VaR_95)