Explanation:
The diversified VaR benefit is the difference between the sum of the individual (undiversified) VaRs and the diversified Portfolio VaR.
At a 95% confidence level, the z-score is approximately 1.645 (or 1.65).
$450m × 16% × 1.645 = $118.44 million$250m × 11% × 1.645 = $45.2375 million$118.44 + $45.2375 = $163.6775 million$700m × 14% × 1.645 = $161.21 million$163.6775 - $161.21 = $2.4675 million.This is closest to $2.5 million. (Using z = 1.65 results in a similar difference: Undiversified = $164.175m, Diversified = $161.7m, Benefit = $2.475m ≈ $2.5 million).
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Q.18 Richard Burns is a risk analyst at Platinum Investment Trust, a large asset management company managing portfolios of multiple high-net-worth clients, most of whom are in the search of long-term superior returns above market returns. Currently, he is assisting his portfolio manager in evaluating a two-asset portfolio that consists of stock in the aviation industry, namely Venus Airline and Mars Airline. The risk and return data on the stocks and the portfolio are shown below:
| Asset Position Value (million) | Return Standard Deviation (%) | Beta | |
|---|---|---|---|
| Venus | 450 | 16 | 1.5 |
| Mars | 250 | 11 | 0.9 |
| Portfolio | 700 | 14 | 1.3 |
Based on this information, the portfolio's estimated diversified VaR benefit at the 95% confidence level is closest to:
A
$166.7 million
B
$164.2 million
C
$2.5 million
D
$161.7 million
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