The current market portfolio of an investment bank has a current value of $150 million and a daily standard deviation of 1%. In the last year (250 trading days), the ten worst losses have been $3,500,000, $3,200,000, $3,000,000, $2,700,000, $2,500,000, $2,300,000, $2,000,000, $1,800,000, $1,700,000, $1,500,000.

1. Calculate the 99% daily Value-at-Risk using the delta-normal approach.

(6 marks)

2. Calculate the 99% daily Value-at-Risk using the historical simulation approach.

(6 marks)

3. Suppose that the Value-at-Risk estimate obtained in question 3a is exactly the same number that was obtained one year ago, when the same calculation was performed (and the daily standard deviation was still 1%). You can look back at the last year to see how the risk model has performed. What can you say about the quality of the risk model?