Question

Consider a $5 million in AT&T stock. X = 99% confidence level. Assume daily volatility is 1%. What is its Var after 10 days?

Answer 1

To calculate the 10-day VaR for a $5 million investment in AT&T stock at a 99% confidence level with 1% daily volatility, we use the investment value, z-value for the confidence level, daily volatility, and the square root of the time horizon to determine that the VaR is approximately $368,000.

Step-by-step explanation:

To calculate the Value at Risk (VaR) after 10 days for a $5 million investment in AT&T stock at a 99% confidence level with a daily volatility of 1%, we use the VaR formula that incorporates the z-value for the confidence level, the standard deviation (volatility), and the square root of the time horizon.

The z-value for a 99% confidence level is approximately 2.33. VaR is then calculated as:

VaR = Investment Value * z-value * Volatility * sqrt(Time)

For 10 days, this is:

VaR = $5,000,000 * 2.33 * 0.01 * sqrt(10)

Now calculating the actual VaR:

VaR = $5,000,000 * 2.33 * 0.01 * 3.16227766016838 (approx for sqrt(10))

VaR = $5,000,000 * 0.0736 (approx value for 2.33 * 0.01 * sqrt(10))

VaR = $368,000 (rounded to nearest thousand)

The VaR after 10 days for AT&T stock at a 99% confidence level is approximately $368,000.