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Exercise

VaR and risk exposure

Previously you computed the VaR and CVaR when losses were Normally distributed. Here you'll find the VaR using another common loss distribution, the Student's t-distribution (or T) contained in scipy.stats.

You'll compute an array of 99% VaR measures from the T distribution (with 30 - 1 = 29 degrees of freedom), using 30-day rolling windows from investment bank portfolio losses.

First you'll find the mean and standard deviation of each window, creating a list of rolling_parameters. You'll use these to compute the 99% VaR array of measures.

Then you'll use this array to plot the risk exposure for a portfolio initially worth $100,000. Recall that risk exposure is the probability of loss (this is 1%) multiplied by the loss amount (this is the loss given by the 99% VaR).

Instructions

100 XP
  • Import the Student's t-distribution from scipy.stats.
  • Compute the 30-day window mean mu and standard deviation sigma vectors from losses, and place into rolling_parameters.
  • Compute a Numpy array of 99% VaR measures VaR_99 using t.ppf(), from a list of T distributions using the elements of rolling_parameters.
  • Compute and visualize the risk exposure associated with the VaR_99 array.