07. Calculation of the Expected Shortfall

PRDTM2-787 AI Trading C4 L4 Vid7 Calculation Of The Expected Shortfall

Understanding Expected Shortfall and Its Calculation

Expected shortfall, a financial risk measure, indicates potential losses exceeding a certain confidence level, complementing Value at Risk (VaR). Key elements include:

  • Conditional Expectation: This expectation considers losses that surpass VaR at a given confidence level, using a straightforward formula where:

    • Denominator: Probability of exceeding VaR, denoted as 1 minus confidence level (1 - Alpha).
    • Numerator: Expected loss beyond VaR, evaluated through integration.

  • Loss Distribution: Assumed to follow a normal distribution with:

    • Mean = -Mu (negative due to losses)
    • Standard Deviation = Sigma

  • Integration: Utilizes a standard normal variable (z) to rewrite expected loss integral, simplifying to an expression involving the inverse of the normal distribution function.

  • Calculation with Python:

    • Implemented as expected_shortfall function within the GBM class.
    • Uses mean and standard deviation approximations for computational efficiency.

  • Parameters:

    • Mu, Sigma (GBM class variables)
    • T (Time horizon)
    • Confidence (Confidence level)

This streamlined process enables effective calculation of expected shortfall, aiding in risk management strategies.

Your colleagues have determined that the loss distribution in a year of your portfolio is normal with the mean equal to -20% and the standard deviation equal to 15%. What is the 99% expected shortfall of your portfolio?
SOLUTION: 0.2

Next Concept