What is the portfolio VaR?

James Johnson has a $1 million long position in ThetaGroup with a VaR of 0.3 million, and $1 million long position in VolgaCorp with a VaR of 0.4 million. The returns of the two companies have zero correlation.

What is the portfolio VaR?
A . $1 million
B . $0.7 million
C . $0.5 million
D . $0.4 million

View Answer

Answer: C

Explanation:

The portfolio VaR when the returns of two assets are uncorrelated can be calculated using the formula:

Portfolio VaR=(VaR of ThetaGroup)2+(VaR of VolgaCorp)2Portfolio VaR=(VaR of ThetaGroup)2+(VaR of VolgaCorp)2?

Plugging in the values:

Portfolio VaR=(0.3)2+(0.4)2=0.09+0.16=0.25=0.5Portfolio VaR=(0.3)2+(0.4)2?=0.09+0.16?=0.25?=0.5

So, the portfolio VaR is $0.5 million.