Q.5 A portfolio consists of two assets – A and B.
| | Value | Return | 99% 1 day VaR | Correlation |
|-------|-----------|--------|---------------|-------------|
| A | 5 million | 5% | 0.58 million | |
| B | 10 million| 6% | 1.86 million | 0.7 |
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? | Financial Risk Manager Part 2 Quiz - LeetQuiz
Financial Risk Manager Part 2
Explanation:
First, we find the initial portfolio VaR:
VaRp=VaRA2+VaRB2+2×ρ×VaRA×VaRBVaRinitial=0.582+1.862+2×0.7×0.58×1.86VaRinitial=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`7.5‘ million in each asset.
The new individual VaRs scale linearly with the position sizes:
New VaRA=0.58×(57.5)=0.87 millionNew VaRB=1.86×(107.5)=1.395 million
Calculating the new portfolio VaR:
VaRnew=0.872+1.3952+2×0.7×0.87×1.395VaRnew=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
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.
Value
Return
99% 1 day VaR
Correlation
A
5 million
5%
0.58 million
B
10 million
6%
1.86 million
0.7
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?