Total VaR by unit

Total VaR by unit will be more than the firm-wide VaR when the correlation between units is less than 1.0, the firm-wide VaR will be less than their simple summation. what’s the formula for VaR of a portfolio? How did they reach this conclusion?

Look at the formula for VAR by the Analytic Mean-Variance method.

Mean - Confidence Level * Standard Deviation = VAR.

Mean of Portfolio => you know the formula - and there is NO impact of correlation between various components of the Portfolio.

Standard Deviation of Portfolio - is affected by the correlation between parts of the portfolio - and if Correlation is < 1 - there is a diversification effect - lower Variance - hence Lower Standard Deviation.

Now if you calculate a new VAR - this will be a SMALLER number…