CVaR: Conditional Value at Risk

Conditional Value at Risk (CVaR), also known as Expected Shortfall (ES), is a risk assessment measure that quantifies the amount of tail risk an investment portfolio has. Unlike Value at Risk (VaR), which tells you the potential loss for a given confidence interval, CVaR gives you the expected loss beyond the VaR threshold.

Here’s a basic explanation of how to calculate CVaR:

1. Choose a Confidence Level: Typically, this is 95% or 99%. This means you’re looking at the worst 5% or 1% of cases.
2. Calculate VaR: Value at Risk is the threshold such that the losses on the portfolio over the given time horizon exceed this value only with a specified probability (the confidence level). This can be done through various methods like historical simulation, parametric VaR (based on distribution assumptions), or Monte Carlo simulations.
3. Calculate CVaR: Once VaR is determined, CVaR is calculated as the average of the losses that exceed the VaR level. Mathematically, if L represents the loss, and α is the confidence level (say, 95% or 0.95), then CVaR is calculated as:

In simpler terms, you take all the instances where the loss is worse than the VaR, and then compute their average. This provides a measure of the expected loss in the worst-case scenarios beyond the VaR threshold.

Keep in mind that the calculation of CVaR depends heavily on the accuracy of the loss distribution model. In practice, especially in asset management, it’s crucial to have robust models and historical data to accurately estimate these risk metrics.

For a practical computation, often a data set of historical returns or simulated returns is used. You would sort these returns, find the return at your VaR threshold, and then calculate the average of returns worse than this. This average is your CVaR.

REFERENCES

OpenAI. (2024). ChatGPT [Large language model]. https://chat.openai.com