Question

Calculate the 5-day 90% Value at Risk (VaR) for the stock whose historical price information is given below by using historical simulation approach.

Week Stock Price 0 49.00 1 48.12 2 47.37 3 50.25 4 51.75 5 53.12 6 53.00 7 51.87 8 51.38 9 53.00 10 49.88

Answer 1

VaR finds the value at risk based on percentiles, taking 90% VaR we find the 10% that is at risk. To do this, and find the VaR we can use excel.

Lets first find the daily returns for each day, this can be done by:

Return of day1 = (Price on day1 - Price on day 0)/ Price on day 0

Once we find the returns, we can apply the following formula, which basically gives us the 10% at risk, considering a window of 5 days. So we can find the VaR for every day from the 6th day. The formula in excel is:

=percentile(Select previous 5 returns, 10%)* the previous day price

This gives us the follwing table:

Thus, if we are at day 10, the value at risk if we own 1 share, is 0.8783 for the next day.