A portfolio has an average daily return of 0.1% and a daily standard deviation of 1.2%. What is the 1-day 95% Historical VaR if the worst 5% of returns over the past 200 days observed historically were -1.8%, -2.1%, -2.5%, -2.8%, -3.0%, -3.2%, -3.5%, -3.8%, -4.0%, -4.2%?

Question: A portfolio has an average daily return of 0.1% and a daily standard deviation of 1.2%. What is the 1-day 95% Historical VaR if the worst 5% of returns over the past 200 days observed historically were -1.8%, -2.1%, -2.5%, -2.8%, -3.0%, -3.2%, -3.5%, -3.8%, -4.0%, -4.2%?

Answer options:

• $2.8% ✅ $3.0%
• $3.2%
• $3.5%

Correct answer: $3.0%

Explanation: Historical VaR relies on ordering past returns. For 200 observations, the 95% VaR (or worst 5%) means looking at the 10th worst observation (200 * 0.05 = 10). In the given list of the worst 5% returns, -3.0% is the 10th worst return, meaning the 1-day 95% VaR is 3.0%.