VaR Calculations

Compass uses a variant of the Variance-Covariance (parametric) method for calculating VaR. We look at a 95% 1-day vaR value, i.e. the maximum we can expect to lose over a day, with a 95% confidence metric.

The parametric method, also known as the variance-covariance method, is a risk management technique for calculating the VaR of a portfolio of assets that first identifies the mean, or expected value, and standard deviation of an investment portfolio. The parametric method looks at the price movements of investments over a look-back period and uses probability theory to compute a portfolio's maximum loss. The variance-covariance method for the value at risk calculates the standard deviation of price movements of an investment or security. Assuming stock price returns and volatility follow a normal distribution, the maximum loss within the specified confidence level is calculated.

The Compass VaR calculation is based on currency-bucketed positions. Each instrument in Compass has a calculated VaR contribution per 1 unit traded which dynamically changes as market volatility and variance-covariance relationships change. The covariance matrix is typically calibrated on 3 months of data and looks at hourly changes in relationships.

In short, this involves calculating the mean and standard deviation of the positions in a book.
VaR_1681202183.pdf

Example with Two Securities

Let's consider a forex portfolio consisting of two currency pairs, EURUSD and GBPJPY. For simplicity, we'll use arbitrary values for weights, standard deviations, and the correlation coefficient.

Suppose:

• The weight of EURUSD is 30% (w1)
• The weight of GBPJPY is 70% (w2)
• The standard deviation of EURUSD returns is 0.02 (sd1)
• The standard deviation of GBPJPY returns is 0.03 (sd2)
• The correlation coefficient between EURUSD and GBPJPY is 0.15 (c)
• The z-score for a 95% confidence level is -1.645 (z)
• The portfolio value is $100,000 (v)

The value at risk of a portfolio with two securities can be determined by first calculating the portfolio's volatility.

Portfolio Volatility

Multiply the square of the first asset's weight by the square of the first asset's standard deviation and add it to the square of the second asset's weight multiplied by the square of the second asset's standard deviation.

Add that value to two multiplied by the weights of the first and second assets, the correlation coefficient between the two assets, and the standard deviation of the first and second assets.

Portfolio Volatility = (w1^2×sd1^2)+(w2^2×sd2^2)+2(w1×w2×c×sd1×sd2)

Portfolio VaR

For the Portfolio VaR, multiply the square root of that portfolio volatility (vol) by the z-score and the portfolio value:

Portfolio VaR = √(vol) * z * v

So, the parametric VaR for this forex portfolio, with a 95% confidence level, is approximately $3,732. This means that there is a 5% chance of the portfolio losing more than $3,732 over the specified time horizon under normal market conditions.

Further, for this total VaR value, each asset in the book is assigned a portion of that risk, which in total represent the Equivalent Positions - i.e. the optimal hedge to clear risk in that asset. Floating PnL is not included in the VaR calculation.