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Financial Risk Manager Part 2

Financial Risk Manager Part 2


Explanation:

First, we find the initial portfolio VaR: VaRp=VaRA2+VaRB2+2×ρ×VaRA×VaRB\text{VaR}_p = \sqrt{\text{VaR}_A^2 + \text{VaR}_B^2 + 2 \times \rho \times \text{VaR}_A \times \text{VaR}_B}VaRp​=VaRA2​+VaRB2​+2×ρ×VaRA​×VaRB​​ VaRinitial=0.582+1.862+2×0.7×0.58×1.86\text{VaR}_{\text{initial}} = \sqrt{0.58^2 + 1.86^2 + 2 \times 0.7 \times 0.58 \times 1.86}VaRinitial​=0.582+1.862+2×0.7×0.58×1.86​ VaRinitial=0.3364+3.4596+1.5103=5.3063≈2.3035 million\text{VaR}_{\text{initial}} = \sqrt{0.3364 + 3.4596 + 1.5103} = \sqrt{5.3063} \approx 2.3035 \text{ million}VaRinitial​=0.3364+3.4596+1.5103​=5.3063​≈2.3035 million

The portfolio manager rebalances the portfolio to equal weights. The total portfolio value is $5 + 10 = 15 \text{ million}.Equalweightmeans. Equal weight means .Equalweightmeans`7.5‘ million7.5` \text{ million}7.5‘ million in each asset.

The new individual VaRs scale linearly with the position sizes: New VaRA=0.58×(7.55)=0.87 million\text{New VaR}_A = 0.58 \times \left(\frac{7.5}{5}\right) = 0.87 \text{ million}New VaRA​=0.58×(57.5​)=0.87 million New VaRB=1.86×(7.510)=1.395 million\text{New VaR}_B = 1.86 \times \left(\frac{7.5}{10}\right) = 1.395 \text{ million}New VaRB​=1.86×(107.5​)=1.395 million

Calculating the new portfolio VaR: VaRnew=0.872+1.3952+2×0.7×0.87×1.395\text{VaR}_{\text{new}} = \sqrt{0.87^2 + 1.395^2 + 2 \times 0.7 \times 0.87 \times 1.395}VaRnew​=0.872+1.3952+2×0.7×0.87×1.395​ VaRnew=0.7569+1.9460+1.6991=4.4020≈2.0981 million\text{VaR}_{\text{new}} = \sqrt{0.7569 + 1.9460 + 1.6991} = \sqrt{4.4020} \approx 2.0981 \text{ million}VaRnew​=0.7569+1.9460+1.6991​=4.4020​≈2.0981 million

The effect on the portfolio VaR is the difference: Change in VaR=2.3035−2.0981=0.2054 million\text{Change in VaR} = 2.3035 - 2.0981 = 0.2054 \text{ million}Change in VaR=2.3035−2.0981=0.2054 million

The VaR decreases by approximately $0.20 \text{ million}$. Option D is correct.

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Q.5 A portfolio consists of two assets – A and B.

ValueReturn99% 1 day VaRCorrelation
A5 million5%0.58 million
B10 million6%1.86 million0.7

The portfolio manager decides to rebalance the portfolio so that both the assets are equally weighted. If there is no change in the volatility of the two assets, what will be the effect of this rebalancing on the portfolio VaR?

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UAnonymous
Last updated: July 5, 2026 at 07:20
0

    A

    0.40 million


    B

    0.17 million


    C

    0.87 million


    D

    0.20 million

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