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Explanation:
To find the difference between the Normal VaR and Lognormal VaR, we need to calculate the 1-day 99% VaR under both distributions. For a 99% confidence level, the z-score is approximately $2.326$.
Normal VaR calculation at the 1-day holding period: VaR_{\text{normal}} = \`$1`,000,000 \times (2.326 \times 0.025198 - 0.00079365) VaR_{\text{normal}} = \`$1`,000,000 \times (0.0586105 - 0.00079365) = \`$57`,816.90
Lognormal VaR calculation at the 1-day holding period: VaR_{\text{lognormal}} = \`$1`,000,000 \times (1 - e^{0.00079365 - 2.326 \times 0.025198}) VaR_{\text{lognormal}} = \`$1`,000,000 \times (1 - e^{-0.05781685}) VaR_{\text{lognormal}} = \`$1`,000,000 \times (1 - 0.943823) = \`$56`,177.10
The difference is: VaR_{\text{normal}} - VaR_{\text{lognormal}} = \`$57`,816.90 - \`$56`,177.10 = \`$1`,639.80 \approx \`$1`,640
Thus, Normal 99% VaR is greater than Lognormal 99% VaR at the 1-day holding period by $1640.
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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