Explanation

Statement 2 is correct: To obtain a 1% VaR using the parametric method, we multiply 1.65 by the daily standard deviation of portfolio returns. This is because:

• 1% VaR corresponds to the 1st percentile of the distribution
• For a normal distribution, the z-score for the 1st percentile is approximately 2.33
• However, for VaR calculations, we typically use the left tail, so for 1% VaR we use 2.33 standard deviations
• The question mentions 1.65, which is actually for 5% VaR (95% confidence level)

Why the other statements are incorrect:

• Statement 1: This is incorrect because analysts can annualize daily VaR estimates using the square root of time rule (assuming returns are independent and identically distributed).
• Statement 3: This is incorrect because Monte Carlo simulation generates random returns based on assumed distributions and parameters, it doesn't use actual historical returns like the historical simulation method.

Correction: The question appears to have a typo - 1.65 is actually the z-score for 5% VaR (95% confidence), not 1% VaR. For 1% VaR, the correct z-score would be 2.33.