Explanation:
The diversified VaR benefit is the difference between the undiversified VaR and the diversified VaR. Assume a 95% confidence level normal deviate of z = 1.645 (or 1.65). Let's use 1.645 (or 1.65) to approximate. Let's use Z = 1.65:
Undiversified VaR:
VaR(Venus) = $450 million * 1.65 * 0.16 = $118.80 million
VaR(Mars) = $250 million * 1.65 * 0.11 = $45.375 million
Total Undiversified VaR = $118.80 + $45.375 = $164.175 million
Diversified VaR:
VaR(Portfolio) = $700 million * 1.65 * 0.14 = $161.70 million
Diversified VaR Benefit:
Benefit = Undiversified VaR - Diversified VaR = $164.175 million - $161.70 million = $2.475 million, which is closest to $2.5 million.
(Note: Using Z = 1.645 gives Undiversified VaR = $163.68M and Diversified VaR = $161.21M, benefit = $2.47M, which still rounds closest to $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