Explanation:
The percentage contribution of each asset's component VaR to the total portfolio VaR is equal to the asset's weight multiplied by its beta, divided by the sum of (weight × beta) across all assets in the portfolio. In this case, we can use the dollar amounts instead of weights, which yields the same proportional results.
Amount of A () = $2.5 million
Amount of B () = $1 million
Total Portfolio Value = $3.5 million
Contribution factor for A =
Contribution factor for B =
Total factor = $2.425 + 1.075 = 3.500$
Percentage contribution of A = $2.425 / 3.500 = 69.285...% \approx 69.3%1.07`5 / 3.500 = 30.714...% \approx 30.7%$
Therefore, the contributions are 69.3% and 30.7% respectively.
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Q.30 James Wit is a portfolio manager at ABC Investment Ltd. His goal is to create a new pool of investments comprising of different assets. Wit begins the investment process by adding two assets A and B into a new portfolio. Assume that the idiosyncratic components of the assets are uncorrelated and that the assets have a volatility of 6% and 10%, respectively. The amount invested in asset A is $2.5 million, while that invested in B is $1 million. Additionally, the asset betas are 0.97 and 1.075 respectively. Calculate the percentage contribution of the component VaRs of both assets to the portfolio VaR at the 95% confidence level.
A
[28.7%
71.3%]
B
[86.2%
13.8%]
C
[81.6%
18.6%]
D
[69.3%
30.7%]
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