VaR and CVaR analysis, why are they needed in the world of professional trading? – Analysis and Forecast – January 21, 2024

Value at risk (VaR) and conditional value at risk (CVaR), also known as expected shortfall, are risk management metrics used to estimate and quantify potential losses in financial transactions. Below is a brief overview of how VaR and CVaR are used to calculate risk in forex trading.

Value at Risk (VaR):

VaR represents the maximum potential loss within a certain confidence level over a given period of time. This provides a single summary statistic for your risk exposure.

official: VaR = Portfolio Value × (Z-Score × Portfolio Standard Deviation) was=portfolio value×(Z-score×Portfolio standard deviation)

• Z-score: Corresponds to the number of standard deviations from the mean. Based on the confidence level you choose.

yes: If you have a $100,000 trading portfolio, 95% confidence level, and 1% standard deviation, VaR is calculated as follows: VaR = $100,000 × (1,645 × 0.01) was=$100,000×(1.645×0.01) In this example, a Z-Score of 1.645 corresponds to a 95% confidence level.

Conditional Value at Risk (CVaR):

Expected Shortfall (CVaR) goes beyond VaR by providing an expected loss if the loss exceeds the VaR threshold. Measures the average loss under extreme scenarios.

official: CVaR = 1 1 − � ∫ − infinite VaR � ⋅ � ( � ) � � CVaR=One–allOne​∫–∨was​X⋅F(X)dX

• � all Indicates the confidence level (e.g. 0.05 for 95% confidence).
• � ( � ) F(X) Probability density function of portfolio returns.

yes: If your VaR is $1,000 at a 95% confidence level and you know the loss distribution, you can use the formula above to calculate CVaR.

Calculation steps:

1. Portfolio return calculation:

   • Calculate the profits of your forex trading portfolio based on historical data or other methods.

2. VaR determination:

   • Choose a confidence level (e.g. 95%) and calculate the Z-score.
   • Calculate the standard deviation of portfolio returns.
   • Apply the VaR formula.

3. CVaR decision:

   • Use the calculated VaR as the threshold.
   • Beyond VaR, we calculate the expected shortfall by integrating the tails of the distribution.

4. Translate:

   • VaR provides a single point estimate of potential loss at a specific confidence level.
   • CVaR provides additional insight by providing the expected loss in the tail of the distribution.