Explanation:
The portfolio VaR reduces to the following expression in case the correlation ρ is zero:
\text{VaR in 2017} = \sqrt{(6.3^2 + 4.1^2)} = \`$7.52` \text{ million}and are both positive if the correlation is exactly 1, and thus the equation becomes:
\text{VaR in 2018} = 6.3 + 4.1 = \`$10.4` \text{ million}The portfolio VaR increased by $10.4 - 7.52 = ` million
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Q.3166 MaYong Li is a portfolio manager at Xing Nan Investment, a large asset management company in mainland China. He has a mandate to manage $100 million to be invested in only those shares whose business are related to the Chinese shipping industry. Due to this limited scope, he has selected only two stocks worth investing in. He has $60 million invested in BeiXin Shipping and $40 million invested in TongChi Logistics with a 95% 1-day VaR of $6.3 million and $4.1 million, respectively. Assuming that returns are normally distributed and that individual VaRs also remains unchanged, what effect will this have on the 95% 1-day portfolio VaR if the correlation between the returns of both shares change from zero in 2017 to perfectly correlated in 2018?
A
The portfolio VaR will remain unchanged
B
The portfolio VaR will increase by $2.88 million
C
The portfolio VaR will decrease by $2.88 million
D
The portfolio VaR will decrease by 3.4 million