06. Introduction to quantitative risk management

PRDTM2-787 AI Trading C4 L4 Vid6 Introduction To Quantitative Risk Management

Understanding Investment Risk Metrics: VAR and Expected Shortfall

Key Risk Measures

  • Value at Risk (VAR):

    • Indicates potential loss in investments at a given confidence level.
    • Example: 95% VAR implies a high likelihood (95%) that losses will not exceed a specific percentage (e.g., 1%) over a specified time (e.g., one month).

  • Expected Shortfall:

    • Provides average loss if losses exceed the VAR threshold.
    • Example: If VAR is breached, the expected shortfall predicts an average loss.

Probability Distribution Impact:

  • Losses framed as negative profits and vice-versa.
  • VAR and expected shortfall calculated using the potential loss distribution.
  • A normal distribution is often assumed (characterized by mean and standard deviation).

Mathematical Concepts:

  • VAR utilizes a cumulative distribution function (CDF) of normal distributions.
  • Calculation of expected shortfall requires more complex, conditional probabilities.

This breakdown clarifies the concepts of VAR and expected shortfall and sets the foundation for more detailed discussions in subsequent lessons.

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% value at risk of your portfolio?
SOLUTION: 0.15

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