Question

7. Suppose the VARs calculated for two segments of a business are $50 million and $92 million. The correlation between the losses is estimated as 0.7. An estimate of the total VAR is?

give me the formula

Answer 1

VAR(Value at Risk) is the measure of maximum possible loss for a period of time say one day, one year etc. It is used as an effective tool for shaping the strategies on the trading floor.

Now, getting to the question:

VAR for first segment(VAR₁) = $50 million

VAR for second segment(VAR₂) = $92 million

Correlation(r) between the losses is 0.7

Calculation of portfolio VAR using the below formula:

$\sqrt{(VAR_{1})^{2}+(VAR_{2})^{2}+2*VAR_{1}*VAR_{2}*Correlation}$

=$\sqrt{50^{2}+92^{2}+2*50*92*0.7} million$

=$\sqrt{2500+8464+100*64.4} million$

=$\sqrt{2500+8464+6440} million$

=$\sqrt{17404} million$

=

Total estimated VAR is $131.924 million.

Note: The million written after the formula can also be used in the formula. Answer will be the same. It has been taken for calculation convenience.