Historical expected shortfall

Expected Shortfall, otherwise known as CVaR, or conditional value at risk, is simply the expected loss of the worst case scenarios of returns.

For example, if your portfolio has a VaR(95) of -3%, then the CVaR(95) would be the average value of all losses exceeding -3%.

Returns data is available (in percent) in the variable StockReturns_perc. var_95 from the previous exercise is also available in your workspace.

This exercise is part of the course

Introduction to Portfolio Risk Management in Python

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Exercise instructions

Calculate the average of returns in StockReturns_perc where StockReturns_perc is less than or equal to var_95 and assign it to cvar_95.
Plot the histogram of sorted returns (sorted_rets) using the plt.hist() function.

Hands-on interactive exercise

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

# Historical CVaR 95
cvar_95 = ____
print(cvar_95)

# Sort the returns for plotting
sorted_rets = sorted(StockReturns_perc)

# Plot the probability of each return quantile
____(____, density=True, stacked=True)

# Denote the VaR 95 and CVaR 95 quantiles
plt.axvline(x=var_95, color="r", linestyle="-", label='VaR 95: {0:.2f}%'.format(var_95))
plt.axvline(x=cvar_95, color='b', linestyle='-', label='CVaR 95: {0:.2f}%'.format(cvar_95))
plt.show()

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