Question

Consider $10 million in IBM stock, N=10 days (2 trading weeks), and X=99% confidence level. Assume daily volatility of 2%. Assume successive days' returns are independent. What will be the VaR after 10 days?

Answer 1

The answer involves using the provided daily volatility and the 99% Z-score from a standard normal distribution to calculate the 10-day Value at Risk (VaR) for the investment in IBM stock.

Step-by-step explanation:

The student has asked about calculating the Value at Risk (VaR) after 10 days for a $10 million investment in IBM stock at a 99% confidence level and with daily volatility of 2%. VaR is a statistical measure used in finance to assess the risk of investment losses. To calculate the 10-day VaR at 99% confidence level, one typically uses the formula VaR = Z * σ * √(N), where Z is the Z-score corresponding to the desired confidence level, σ is daily volatility, and N is the number of days.

To find the 99% Z-score, we would look at a standard normal distribution table which is often rounded to 2.33. Using the given daily volatility of 2% and the square root of time horizon √(10), we can calculate: VaR = 2.33 * 2% * √(10) * $10 million. Substituting the appropriate values and performing the arithmetic gives us a 10-day VaR.