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Extreme values and backtesting

Extreme values are those which exceed a threshold and are used to determine if risk measures such as VaR are accurately reflecting the risk of loss.

You'll explore extreme values by computing the 95% VaR of the equally-weighted investment bank portfolio for 2009-2010 (recall that this is equivalent to historical simulation from 2010 onwards), and then backtesting on data from 2007-2008.

2009-2010 portfolio losses are available in estimate_data, from which you'll compute the 95% VaR estimate. Then find extreme values exceeding the VaR estimate, from the 2007-2008 portfolio losses in the available backtest_data.

Compare the relative frequency of extreme values to the 95% VaR, and finally visualize the extreme values with a stem plot.

Cet exercice fait partie du cours

Quantitative Risk Management in Python

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Instructions

  • Compute the 95% VaR on estimate_data using np.quantile().
  • Find the extreme_values from backtest_data using VaR_95 as the loss threshold.
  • Compare the relative frequency of extreme_values to the VaR_95 estimate. Are they the same?
  • Display a stem plot of extreme_values, showing how large deviations clustered during the crisis.

Exercice interactif pratique

Essayez cet exercice en complétant cet exemple de code.

# Compute the 95% VaR on 2009-2010 losses
VaR_95 = ____.____(estimate_data, 0.95)

# Find backtest_data exceeding the 95% VaR
extreme_values = backtest_data[____ > VaR_95]

# Compare the fraction of extreme values for 2007-2008 to the Var_95 estimate
print("VaR_95: ", VaR_95, "; Backtest: ", len(____) / len(backtest_data) )

# Plot the extreme values and look for clustering
plt.stem(extreme_values.index, ____)
plt.ylabel("Extreme values > VaR_95"); plt.xlabel("Date")
plt.show()
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