
Explanation:
Let's calculate the 1-day 99% VaR under both normal and lognormal assumptions.
The critical value for 99% confidence is approximately $2.326$.
Given:
$1,000,0001. Normal 99% VaR at 1-day: \text{VaR}_{\text{Normal}} = 1,000,000 \times (0.05861 - 0.00079365) = 1,000,000 \times 0.057816 = \`57`,816$
2. Lognormal 99% VaR at 1-day: \text{VaR}_{\text{Lognormal}} = 1,000,000 \times (1 - 0.943823) = \`56`,177$
Difference:
\text{Difference} = \text{VaR}_{\text{Normal}} - \text{VaR}_{\text{Lognormal}} = 57,816 - 56,177 = \`1,639 \approx \
Thus, the Normal 99% VaR is greater than the Lognormal 99% VaR by approximately $1640 at the 1-day holding period, making Statement C true.
Ultimate access to all questions.
No comments yet.
Q.33 A risk manager at a mid-sized bank wishes to estimate the market risk of a portfolio by employing both the normal and the lognormal distribution assumptions. The manager has gathered the following data on the portfolio:
$1,000,000Which of the following statements is true?
A
Normal 95% VaR is greater than Lognormal 95% VaR at the 1-day holding period by $36,745
B
Normal 95% VaR is greater than Lognormal 95% VaR at the 1-year holding period by $800
C
Normal 99% VaR is greater than Lognormal 99% VaR at the 1-day holding period by $1640
D
Normal 99% VaR is greater than Lognormal 99% VaR at the 1-year holding period by $421,255