
Explanation:
Initial Portfolio 1-day 95% VaR: Using the portfolio VaR formula: million.
Rebalanced Positions:
New Canadian position = $72 - 20 = 5258` + 20 = 78VaR_C = 2.5 \times \frac{52}{72} = 1.8056VaR_E = 2.5 \times \frac{78}{58} = 3.3621$ million.
New Portfolio 1-day 95% VaR: million.
Adjusting to 10-day 99% VaR:
Conversion factor = .
New 10-day 99% VaR = $4.5024 \times 4.4715 = 20.132$ million.
Change in VaR: Change = New 10-day 99% VaR - Old 1-day 95% VaR million.
Option D matches this calculation perfectly. (Note: Option C represents the new absolute portfolio VaR, but the question asks for the change).
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Q.35 A renowned investment bank has a portfolio consisting of CAD 72 million invested in Canadian equities and a further CAD 58 million invested in emerging market equities. Each of these positions has a 1-day VaR of CAD 2.5 million. For optimal performance, the bank decides to rebalance the portfolio by simultaneously selling CAD 20 million of the Canadian equities and buying CAD 20 million of the emerging market equities. The bank’s chief risk officer also recommends a wider VaR measure – from the current 1-day 95% VaR to a 10-day 99% VaR. The correlation between Canadian equities and emerging market equities stands at 0.47. Determine the change in portfolio VaR that will be brought about by the combined effect of portfolio rebalancing and change in risk measure. (Assume that returns are normally distributed, and that rebalancing has no effect on the volatility of the individual equity positions)
A
VaR increases by 0.215 million
B
VaR increases by 0.881 million
C
VaR increases by 20.131 million
D
VaR increases by 15.844 million
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