Question

Consider 2 stocks. IBM has a daily volatility of $200,000 and AT&T has a daily volatility of $50,000. If their correlation of their returns is 0.7, what is the 10-day 99% VaR of the portfolio?

Answer 1

The 10-day 99% VaR of the portfolio consisting of IBM and AT&T stocks is approximately $31,311.81.

Step-by-step explanation:

In order to calculate the 10-day 99% VaR (Value at Risk) of a portfolio consisting of IBM and AT&T stocks, we need to consider their individual volatilities and correlation. The formula for calculating portfolio VaR is:

VaR(portfolio) = (Z * sqrt((Volatility1^2)*(Weight1^2) + (Volatility2^2)*(Weight2^2) + 2*(Weight1)*(Weight2)*(Correlation)*(Volatility1)*(Volatility2))),

where Z is the z-score corresponding to the desired confidence level (99% in this case), Volatility1 and Volatility2 are the daily volatilities of IBM and AT&T respectively, Weight1 and Weight2 are the weights assigned to IBM and AT&T in the portfolio, and Correlation is the correlation coefficient between their returns.

Let's assume the weights for IBM and AT&T in the portfolio are 0.6 and 0.4 respectively. Substituting the given values into the formula, we have:

VaR(portfolio) = (2.326 * sqrt((200,000^2)*(0.6^2) + (50,000^2)*(0.4^2) + 2*(0.6)*(0.4)*(0.7)*(200,000)*(50,000)))

VaR(portfolio) = (2.326 * sqrt(144,000,000 + 4,000,000 + 33,600,000))

VaR(portfolio) = (2.326 * sqrt(181,600,000))

VaR(portfolio) ≈ 2.326 * 13,480.46

VaR(portfolio) ≈ 31,311.81

Therefore, the 10-day 99% VaR of the portfolio is approximately $31,311.81.