
Explanation:
For a portfolio with normally distributed geometric (log) returns, the worst-case geometric return at a 95% confidence level is calculated using the Z-score for 95% (1.645):
The worst-case portfolio value is:
W^{*} = W_0 \times e^{R_{G}^{*}} = \`85 \text{ million} \times e^{-0.4064} = \85` \text{ million} \times 0.6660 = \`56.61` \text{ million}$
The lognormal VaR is the difference between the initial portfolio value and the worst-case portfolio value:
VaR = W_0 - W^{*} = \`85 \text{ million} - \56.61` \text{ million} = \`28.39` \text{ million}$
Thus, Option D is the correct answer.
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Q.2 An analyst has gathered the following information about a portfolio which has normally distributed geometric returns:
| Mean | 12% |
| Standard deviation | 32% |
| Portfolio value | 85 million |
What is the 95% lognormal VaR for this portfolio?
A
$33.40 million
B
$27.20 million
C
$56.61 million
D
$28.39 million