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IntermediateOptions, Derivatives & FinancePython

Run this module

cd "Finance - Expected Shortfall"
python "expected_shortfall.py"

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Expected Shortfall (CVaR)

Expected Shortfall (ES), also called Conditional Value at Risk (CVaR), measures the expected loss given that losses exceed the VaR threshold. It is a coherent risk measure — unlike VaR, it captures tail severity, not just frequency.

Functions

Function Description
historical_es(returns, confidence_level) Non-parametric ES from actual distribution
parametric_es(returns, confidence_level) Normal-assumption ES
cornish_fisher_es(returns, confidence_level) Skewness/kurtosis-adjusted ES
es_summary(returns, confidence_level) All three estimates in one dict

Key Concepts

  • VaR vs ES: VaR says "you won't lose more than X with 95% probability." ES says "given you exceed VaR, your average loss is Y."
  • Coherence: ES satisfies subadditivity — diversification always reduces risk. VaR does not.
  • Cornish-Fisher: Adjusts the normal quantile using higher moments. Better for fat-tailed (leptokurtic) returns.

Example

from expected_shortfall import es_summary
import numpy as np

returns = np.random.normal(0.001, 0.02, 252)
summary = es_summary(returns, confidence_level=0.95)
print(summary)
# {'historical_es': 0.0412, 'parametric_es': 0.0398, 'cornish_fisher_es': 0.0405, ...}

When to Use

  • Portfolio risk reporting (ES is required under Basel III / FRTB)
  • Comparing risk across strategies with different tail behaviors
  • Stress testing alongside VaR

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