Explanation:
Normal VaR calculation: Normal VaR assumes returns are normally distributed. Using a 99% confidence level, the z-score is approximately 2.326. Normal VaR = Portfolio Value * (z * σ - μ) Normal VaR = £10,000,000 * (2.326 * 0.30 - 0.15) Normal VaR = £10,000,000 * (0.6978 - 0.15) = £10,000,000 * 0.5478 = £5,478,000
Lognormal VaR calculation: Lognormal VaR ensures that the worst-case portfolio value cannot drop below zero. Lognormal VaR = Portfolio Value * (1 - e^(μ - z * σ)) Lognormal VaR = £10,000,000 * (1 - e^(0.15 - 2.326 * 0.30)) Lognormal VaR = £10,000,000 * (1 - e^(-0.5478)) Lognormal VaR = £10,000,000 * (1 - 0.5782) = £4,218,000
Comparison: Difference = Normal VaR - Lognormal VaR = £5,478,000 - £4,218,000 = £1,260,000
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Q.22 A risk analyst wishes to establish the VaR of a portfolio under his management. At present, the portfolio has a value of £10 million. The annual mean and volatility of the portfolio are 15% and 30%, respectively. Evaluate how the 1-year 99% VaR, calculated using the normal distribution assumption (normal VaR), compares with the 1-year 99% VaR, calculated on the basis of the lognormal distribution (lognormal VaR).
A
£1,000,000
B
£500,000
C
£527,834
D
£1,260,000
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